Subgroups — C₂×C₃₁×#3534 #21519480

Order 7936.

8166 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3534	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#562	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²×C₃₁	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#538	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#534	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
23	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
26	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
27	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
28	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#562	C₂²	1	32	yes	complemented
30	C₃₁×#560	C₂²	1	32	yes	complemented
31	C₃₁×#553	C₂²	1	32	yes	complemented
32	C₃₁×#551	C₂²	1	32	yes	complemented
33	C₃₁×#546	C₂²	1	32	yes	complemented
34	C₃₁×#546	C₂²	1	32	yes	complemented
35	C₃₁×#546	C₂²	1	32	yes	complemented
36	D₄²×C₃₁	C₂²	1	32	yes	complemented
37	C₃₁×#540	C₂²	1	32	yes	complemented
38	C₃₁×#539	C₂²	1	32	yes	complemented
39	C₃₁×#539	C₂²	1	16	yes	complemented
40	C₃₁×#538	C₂²	1	16	yes	complemented
41	C₃₁×#538	C₂²	1	32	yes	complemented
42	C₃₁×#537	C₂²	1	16	yes	complemented
43	C₃₁×#534	C₂²	1	32	yes	complemented
44	C₃₁×#534	C₂²	1	16	yes	complemented
45	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
46	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
47	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
48	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
49	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
50	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
51	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
52	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
53	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
54	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
55	C₃₁×#525	C₂²	1	16	yes	complemented
56	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
59	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
60	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
61	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
62	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
63	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
64	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
65	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
66	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
67	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
68	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
69	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
70	C₂×C₃₁×#123	C₂²	1	16	yes	complemented
71	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
79	C₂×C₃₁×#121	C₂²	1	2	yes	—
80	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
85	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
88	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
89	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
90	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
91	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
92	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
93	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
94	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
95	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
96	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
97	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
98	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
99	C₂×C₃₁×#121	C₂²	1	16	yes	complemented
100	C₂×C₃₁×#120	C₂²	1	2	yes	—
101	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
102	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
103	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
104	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
105	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
106	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
107	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
110	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
112	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
113	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
118	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
127	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
128	C₂⁵×C₃₁	C₂³	1	2	yes	—
129	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
130	C₂⁵×C₃₁	C₂³	1	2	yes	—
131	C₂×#41×C₃₁	—	4	4	no	—
132	C₂×#41×C₃₁	—	4	8	no	—
133	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
134	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
135	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₃₁	—	4	4	no	—
138	C₂²×D₄×C₃₁	—	4	4	no	—
139	C₂²×D₄×C₃₁	—	4	8	no	—
140	C₂²×D₄×C₃₁	—	4	8	no	—
141	C₂²×D₄×C₃₁	—	4	8	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
148	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
151	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
153	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
155	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
156	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
157	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
158	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
159	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
161	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
162	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
163	C₂²×D₄×C₃₁	C₂³	1	8	yes	complemented
164	C₂²×D₄×C₃₁	C₂³	1	16	yes	complemented
165	C₂²×D₄×C₃₁	C₂³	1	16	yes	complemented
166	C₂²×D₄×C₃₁	C₂³	1	16	yes	complemented
167	C₂³×C₄×C₃₁	—	4	4	no	—
168	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
173	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
176	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
177	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
178	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
179	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
182	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
183	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₃₁	C₂³	1	8	yes	complemented
185	C₃₁×#127	C₂³	1	16	yes	complemented
186	C₃₁×#126	C₂³	1	16	yes	complemented
187	C₃₁×#126	C₂³	1	16	yes	complemented
188	C₃₁×#126	C₂³	1	16	yes	complemented
189	C₃₁×#126	C₂³	1	16	yes	complemented
190	C₃₁×#125	C₂³	1	16	yes	complemented
191	C₃₁×#125	C₂³	1	16	yes	complemented
192	C₃₁×#124	C₂³	1	16	yes	complemented
193	C₃₁×#124	C₂³	1	16	yes	complemented
194	C₃₁×#124	C₂³	1	16	yes	complemented
195	C₃₁×#123	C₂³	1	16	yes	complemented
196	C₃₁×#123	C₂³	1	16	yes	complemented
197	C₃₁×#123	C₂³	1	16	yes	complemented
198	C₃₁×#123	C₂³	1	16	yes	complemented
199	C₃₁×#123	C₂³	1	16	yes	complemented
200	C₃₁×#123	C₂³	1	16	yes	complemented
201	C₃₁×#123	C₂³	1	16	yes	complemented
202	C₃₁×#123	C₂³	1	16	yes	complemented
203	C₃₁×#123	C₂³	1	16	yes	complemented
204	C₃₁×#123	C₂³	1	16	yes	complemented
205	C₃₁×#123	C₂³	1	16	yes	complemented
206	C₃₁×#123	C₂³	1	16	yes	complemented
207	C₃₁×#123	C₂³	1	16	yes	complemented
208	C₃₁×#123	C₂³	1	16	yes	complemented
209	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
210	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
211	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
212	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
213	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
214	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
215	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
216	C₃₁×#121	C₂³	1	8	yes	—
217	C₃₁×#121	C₂³	1	16	yes	—
218	C₃₁×#121	C₂³	1	8	yes	complemented
219	C₃₁×#121	C₂³	1	8	yes	complemented
220	C₃₁×#121	C₂³	1	8	yes	complemented
221	C₃₁×#121	C₂³	1	16	yes	complemented
222	C₃₁×#121	C₂³	1	16	yes	complemented
223	C₃₁×#121	C₂³	1	8	yes	complemented
224	C₃₁×#121	C₂³	1	8	yes	complemented
225	C₃₁×#121	C₂³	1	16	yes	complemented
226	C₃₁×#121	C₂³	1	16	yes	complemented
227	C₃₁×#121	C₂³	1	16	yes	complemented
228	C₃₁×#121	C₂³	1	16	yes	complemented
229	C₃₁×#121	C₂³	1	16	yes	complemented
230	C₃₁×#121	C₂³	1	16	yes	complemented
231	C₃₁×#121	C₂³	1	16	yes	complemented
232	C₃₁×#121	C₂³	1	16	yes	complemented
233	C₃₁×#121	C₂³	1	16	yes	complemented
234	C₃₁×#121	C₂³	1	16	yes	complemented
235	C₃₁×#121	C₂³	1	16	yes	complemented
236	C₃₁×#121	C₂³	1	16	yes	complemented
237	C₃₁×#120	C₂³	1	16	yes	—
238	C₃₁×#120	C₂³	1	16	yes	complemented
239	C₃₁×#120	C₂³	1	16	yes	complemented
240	C₃₁×#120	C₂³	1	16	yes	complemented
241	C₃₁×#120	C₂³	1	16	yes	complemented
242	C₃₁×#120	C₂³	1	16	yes	complemented
243	C₃₁×#120	C₂³	1	16	yes	complemented
244	C₃₁×#120	C₂³	1	16	yes	complemented
245	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
246	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
247	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
248	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
249	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
250	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
251	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
252	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
253	C₃₁×#117	C₂³	1	8	yes	complemented
254	C₃₁×#117	C₂³	1	16	yes	complemented
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
278	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
289	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
291	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
292	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
296	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
297	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
301	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
302	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
303	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
304	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
305	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
306	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
307	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
308	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
309	C₂⁴×C₃₁	—	2	4	no	—
310	C₂⁴×C₃₁	—	2	4	no	—
311	C₂⁴×C₃₁	—	2	4	no	—
312	C₂⁴×C₃₁	—	2	8	no	—
313	C₂⁴×C₃₁	—	4	2	no	—
314	C₂⁴×C₃₁	—	4	2	no	—
315	C₂⁴×C₃₁	—	4	4	no	—
316	C₂⁴×C₃₁	—	4	4	no	—
317	C₂⁴×C₃₁	—	4	4	no	—
318	C₂⁴×C₃₁	—	4	2	no	—
319	C₂⁴×C₃₁	—	4	4	no	—
320	C₂⁴×C₃₁	—	4	4	no	—
321	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
322	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
323	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
325	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
326	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
327	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
330	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
331	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
332	#41×C₃₁	—	4	16	no	—
333	#41×C₃₁	—	4	32	no	—
334	C₂×Q₈×C₃₁	—	4	2	no	—
335	C₂×Q₈×C₃₁	—	4	4	no	—
336	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
337	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
338	C₂×D₄×C₃₁	—	2	8	no	—
339	C₂×D₄×C₃₁	—	2	8	no	—
340	C₂×D₄×C₃₁	—	2	8	no	—
341	C₂×D₄×C₃₁	—	2	8	no	—
342	C₂×D₄×C₃₁	—	2	8	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	4	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	4	4	no	—
347	C₂×D₄×C₃₁	—	4	4	no	—
348	C₂×D₄×C₃₁	—	4	4	no	—
349	C₂×D₄×C₃₁	—	4	4	no	—
350	C₂×D₄×C₃₁	—	4	4	no	—
351	C₂×D₄×C₃₁	—	4	4	no	—
352	C₂×D₄×C₃₁	—	4	4	no	—
353	C₂×D₄×C₃₁	—	4	16	no	—
354	C₂×D₄×C₃₁	—	4	4	no	—
355	C₂×D₄×C₃₁	—	4	4	no	—
356	C₂×D₄×C₃₁	—	4	4	no	—
357	C₂×D₄×C₃₁	—	4	2	no	—
358	C₂×D₄×C₃₁	—	4	4	no	—
359	C₂×D₄×C₃₁	—	4	16	no	—
360	C₂×D₄×C₃₁	—	4	32	no	—
361	C₂×D₄×C₃₁	—	4	32	no	—
362	C₂×D₄×C₃₁	—	4	32	no	—
363	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
364	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
365	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
366	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
367	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
368	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
369	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
370	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
371	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
372	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
373	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
374	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
375	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
376	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
377	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
378	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
379	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
380	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
381	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
382	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₃₁	—	2	4	no	—
384	C₂²×C₄×C₃₁	—	2	4	no	—
385	C₂²×C₄×C₃₁	—	2	4	no	—
386	C₂²×C₄×C₃₁	—	4	2	no	—
387	C₂²×C₄×C₃₁	—	4	2	no	—
388	C₂²×C₄×C₃₁	—	4	2	no	—
389	C₂²×C₄×C₃₁	—	4	2	no	—
390	C₂²×C₄×C₃₁	—	4	16	no	—
391	C₂²×C₄×C₃₁	—	4	2	no	—
392	C₂²×C₄×C₃₁	—	4	4	no	—
393	C₂²×C₄×C₃₁	—	4	2	no	—
394	C₂²×C₄×C₃₁	—	4	4	no	—
395	C₂²×C₄×C₃₁	—	4	4	no	—
396	C₂²×C₄×C₃₁	—	4	4	no	—
397	C₂²×C₄×C₃₁	—	4	4	no	—
398	C₂²×C₄×C₃₁	—	4	4	no	—
399	C₂²×C₄×C₃₁	—	4	4	no	—
400	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
401	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
402	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
403	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
417	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
418	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
419	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
421	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
422	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
423	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
424	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
426	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
427	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
428	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
430	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
431	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
432	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
433	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
435	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
438	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
439	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
442	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
443	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
444	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
454	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
455	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
456	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
458	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
460	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
461	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
463	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
464	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
467	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
468	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
469	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
470	C₄²×C₃₁	C₂⁴	1	8	yes	—
471	C₄²×C₃₁	C₂⁴	1	8	yes	—
472	C₄²×C₃₁	C₂⁴	1	8	yes	—
473	C₂×#3534	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂³×C₃₁	—	2	2	no	—
475	C₂³×C₃₁	—	2	2	no	—
476	C₂³×C₃₁	—	2	2	no	—
477	C₂³×C₃₁	—	2	2	no	—
478	C₂³×C₃₁	—	2	8	no	—
479	C₂³×C₃₁	—	2	2	no	—
480	C₂³×C₃₁	—	2	4	no	—
481	C₂³×C₃₁	—	2	4	no	—
482	C₂³×C₃₁	—	2	4	no	—
483	C₂³×C₃₁	—	2	4	no	—
484	C₂³×C₃₁	—	2	4	no	—
485	C₂³×C₃₁	—	2	4	no	—
486	C₂³×C₃₁	—	2	4	no	—
487	C₂³×C₃₁	—	2	8	no	—
488	C₂³×C₃₁	—	2	2	no	—
489	C₂³×C₃₁	—	2	4	no	—
490	C₂³×C₃₁	—	2	4	no	—
491	C₂³×C₃₁	—	2	2	no	—
492	C₂³×C₃₁	—	2	4	no	—
493	C₂³×C₃₁	—	2	4	no	—
494	C₂³×C₃₁	—	2	4	no	—
495	C₂³×C₃₁	—	2	8	no	—
496	C₂³×C₃₁	—	2	16	no	—
497	C₂³×C₃₁	—	4	4	no	—
498	C₂³×C₃₁	—	4	4	no	—
499	C₂³×C₃₁	—	4	8	no	—
500	C₂³×C₃₁	—	4	8	no	—
501	C₂³×C₃₁	—	4	8	no	—
502	C₂³×C₃₁	—	4	4	no	—
503	C₂³×C₃₁	—	4	8	no	—
504	C₂³×C₃₁	—	4	8	no	—
505	C₂³×C₃₁	—	4	16	no	—
506	C₂³×C₃₁	—	8	16	no	—
507	C₂³×C₃₁	—	8	8	no	—
508	C₂³×C₃₁	—	8	16	no	—
509	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
510	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
511	C₂³×C₃₁	C₂⁵	1	4	yes	—
512	C₂³×C₃₁	C₂⁵	1	4	yes	—
513	C₂³×C₃₁	C₂⁵	1	2	yes	—
514	C₂³×C₃₁	C₂⁵	1	4	yes	—
515	C₂³×C₃₁	C₂⁵	1	4	yes	—
516	C₂³×C₃₁	C₂⁵	1	2	yes	—
517	C₂³×C₃₁	C₂⁵	1	2	yes	—
518	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
519	Q₈×C₃₁	—	4	4	no	—
520	Q₈×C₃₁	—	4	8	no	—
521	D₄×C₃₁	—	2	16	no	—
522	D₄×C₃₁	—	2	16	no	—
523	D₄×C₃₁	—	2	16	no	—
524	D₄×C₃₁	—	2	16	no	—
525	D₄×C₃₁	—	2	16	no	—
526	D₄×C₃₁	—	4	4	no	—
527	D₄×C₃₁	—	4	8	no	—
528	D₄×C₃₁	—	4	4	no	—
529	D₄×C₃₁	—	4	8	no	—
530	D₄×C₃₁	—	4	8	no	—
531	D₄×C₃₁	—	4	8	no	—
532	D₄×C₃₁	—	4	8	no	—
533	D₄×C₃₁	—	4	8	no	—
534	D₄×C₃₁	—	4	8	no	—
535	D₄×C₃₁	—	4	8	no	—
536	D₄×C₃₁	—	4	8	no	—
537	D₄×C₃₁	—	4	8	no	—
538	D₄×C₃₁	—	4	8	no	—
539	D₄×C₃₁	—	4	4	no	—
540	D₄×C₃₁	—	4	8	no	—
541	C₂×C₄×C₃₁	—	2	2	no	—
542	C₂×C₄×C₃₁	—	2	8	no	—
543	C₂×C₄×C₃₁	—	2	2	no	—
544	C₂×C₄×C₃₁	—	2	2	no	—
545	C₂×C₄×C₃₁	—	2	2	no	—
546	C₂×C₄×C₃₁	—	2	4	no	—
547	C₂×C₄×C₃₁	—	2	8	no	—
548	C₂×C₄×C₃₁	—	2	8	no	—
549	C₂×C₄×C₃₁	—	2	4	no	—
550	C₂×C₄×C₃₁	—	2	4	no	—
551	C₂×C₄×C₃₁	—	2	4	no	—
552	C₂×C₄×C₃₁	—	2	4	no	—
553	C₂×C₄×C₃₁	—	2	4	no	—
554	C₂×C₄×C₃₁	—	2	4	no	—
555	C₂×C₄×C₃₁	—	2	4	no	—
556	C₂×C₄×C₃₁	—	4	4	no	—
557	C₂×C₄×C₃₁	—	4	4	no	—
558	C₂×C₄×C₃₁	—	4	4	no	—
559	C₂×C₄×C₃₁	—	4	4	no	—
560	C₂×C₄×C₃₁	—	4	4	no	—
561	C₂×C₄×C₃₁	—	4	8	no	—
562	C₂×C₄×C₃₁	—	4	4	no	—
563	C₂×C₄×C₃₁	—	4	8	no	—
564	C₂×C₄×C₃₁	—	4	8	no	—
565	C₂×C₄×C₃₁	—	4	8	no	—
566	C₂×C₄×C₃₁	—	4	8	no	—
567	C₂×C₄×C₃₁	—	4	8	no	—
568	C₂×C₄×C₃₁	—	4	8	no	—
569	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
570	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
571	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
572	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
573	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
574	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
575	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
576	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
577	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
578	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
579	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
580	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
581	#3534	C₂×C₃₁	1	32	yes	direct product factor
582	C₂×#562	C₂×C₃₁	1	2	yes	complemented
583	C₂×#560	C₂×C₃₁	1	2	yes	complemented
584	C₂×#553	C₂×C₃₁	1	2	yes	complemented
585	C₂×#551	C₂×C₃₁	1	2	yes	complemented
586	C₂×#546	C₂×C₃₁	1	2	yes	complemented
587	C₂×#546	C₂×C₃₁	1	2	yes	complemented
588	C₂×#546	C₂×C₃₁	1	2	yes	complemented
589	C₂×D₄²	C₂×C₃₁	1	2	yes	complemented
590	C₂×#540	C₂×C₃₁	1	2	yes	complemented
591	C₂×#539	C₂×C₃₁	1	2	yes	complemented
592	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
593	C₂×#538	C₂×C₃₁	1	1	yes	characteristic, complemented
594	C₂×#538	C₂×C₃₁	1	2	yes	complemented
595	C₂×#537	C₂×C₃₁	1	1	yes	characteristic, complemented
596	C₂×#534	C₂×C₃₁	1	2	yes	complemented
597	C₂×#534	C₂×C₃₁	1	1	yes	characteristic, complemented
598	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
599	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
600	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
601	C₂²×C₃₁	—	2	2	no	—
602	C₂²×C₃₁	—	2	2	no	—
603	C₂²×C₃₁	—	2	2	no	—
604	C₂²×C₃₁	—	2	2	no	—
605	C₂²×C₃₁	—	2	8	no	—
606	C₂²×C₃₁	—	2	8	no	—
607	C₂²×C₃₁	—	2	2	no	—
608	C₂²×C₃₁	—	2	4	no	—
609	C₂²×C₃₁	—	2	4	no	—
610	C₂²×C₃₁	—	2	4	no	—
611	C₂²×C₃₁	—	2	4	no	—
612	C₂²×C₃₁	—	2	4	no	—
613	C₂²×C₃₁	—	2	4	no	—
614	C₂²×C₃₁	—	2	4	no	—
615	C₂²×C₃₁	—	2	2	no	—
616	C₂²×C₃₁	—	2	4	no	—
617	C₂²×C₃₁	—	2	4	no	—
618	C₂²×C₃₁	—	2	2	no	—
619	C₂²×C₃₁	—	2	4	no	—
620	C₂²×C₃₁	—	2	4	no	—
621	C₂²×C₃₁	—	2	4	no	—
622	C₂²×C₃₁	—	4	16	no	—
623	C₂²×C₃₁	—	4	4	no	—
624	C₂²×C₃₁	—	4	8	no	—
625	C₂²×C₃₁	—	4	8	no	—
626	C₂²×C₃₁	—	4	8	no	—
627	C₂²×C₃₁	—	4	8	no	—
628	C₂²×C₃₁	—	8	16	no	—
629	C₂²×C₃₁	—	8	8	no	—
630	C₂²×C₃₁	—	8	16	no	—
631	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
632	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
633	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
634	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
635	C₂²×C₃₁	#585	1	2	yes	—
636	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
637	C₄×C₃₁	—	2	2	no	—
638	C₄×C₃₁	—	2	2	no	—
639	C₄×C₃₁	—	2	2	no	—
640	C₄×C₃₁	—	2	2	no	—
641	C₄×C₃₁	—	2	4	no	—
642	C₄×C₃₁	—	2	4	no	—
643	C₄×C₃₁	—	2	4	no	—
644	C₄×C₃₁	—	2	4	no	—
645	C₄×C₃₁	—	2	4	no	—
646	C₄×C₃₁	—	2	4	no	—
647	C₄×C₃₁	—	2	4	no	—
648	C₄×C₃₁	—	2	4	no	—
649	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
651	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
652	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
654	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
655	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
656	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#562	C₂²×C₃₁	1	32	yes	complemented
658	#560	C₂²×C₃₁	1	32	yes	complemented
659	#553	C₂²×C₃₁	1	32	yes	complemented
660	#551	C₂²×C₃₁	1	32	yes	complemented
661	#546	C₂²×C₃₁	1	32	yes	complemented
662	#546	C₂²×C₃₁	1	32	yes	complemented
663	#546	C₂²×C₃₁	1	32	yes	complemented
664	D₄²	C₂²×C₃₁	1	32	yes	complemented
665	#540	C₂²×C₃₁	1	32	yes	complemented
666	#539	C₂²×C₃₁	1	32	yes	complemented
667	#539	C₂²×C₃₁	1	16	yes	complemented
668	#538	C₂²×C₃₁	1	16	yes	complemented
669	#538	C₂²×C₃₁	1	32	yes	complemented
670	#537	C₂²×C₃₁	1	16	yes	complemented
671	#534	C₂²×C₃₁	1	32	yes	complemented
672	#534	C₂²×C₃₁	1	16	yes	complemented
673	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
674	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
675	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
676	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
677	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
678	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
679	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
680	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
681	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
682	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
683	#525	C₂²×C₃₁	1	16	yes	complemented
684	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
685	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
686	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
687	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
688	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
689	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
690	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
691	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
692	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
693	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
694	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
695	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
697	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
698	C₂×#123	C₂²×C₃₁	1	16	yes	complemented
699	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
702	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
703	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
704	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
705	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
706	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
707	C₂×#121	C₂²×C₃₁	1	2	yes	—
708	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
712	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
713	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
716	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
717	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
718	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
719	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
720	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
721	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
722	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
723	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
724	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
725	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
726	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
727	C₂×#121	C₂²×C₃₁	1	16	yes	complemented
728	C₂×#120	C₂²×C₃₁	1	2	yes	—
729	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
730	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
731	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
732	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
733	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
734	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
735	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
736	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
737	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
738	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
739	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
740	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
741	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
742	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
743	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
744	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
745	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
746	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
747	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
748	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
750	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
751	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
752	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
753	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
754	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
755	C₂×C₃₁	—	2	4	no	—
756	C₂×C₃₁	—	2	4	no	—
757	C₂×C₃₁	—	4	2	no	—
758	C₂×C₃₁	—	4	4	no	—
759	C₂×C₃₁	—	4	4	no	—
760	C₂×C₃₁	—	4	4	no	—
761	C₂×C₃₁	—	4	4	no	—
762	C₂×C₃₁	#3534	1	4	yes	direct product factor
763	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
766	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
767	C₂⁵	C₂³×C₃₁	1	2	yes	—
768	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
769	C₂⁵	C₂³×C₃₁	1	2	yes	—
770	C₂×#41	—	4	4	no	—
771	C₂×#41	—	4	8	no	—
772	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
773	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
774	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²×D₄	—	4	4	no	—
777	C₂²×D₄	—	4	4	no	—
778	C₂²×D₄	—	4	8	no	—
779	C₂²×D₄	—	4	8	no	—
780	C₂²×D₄	—	4	8	no	—
781	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
782	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
783	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
784	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
785	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
786	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
787	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
788	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
789	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
790	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
792	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
793	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
794	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
795	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
796	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
797	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
798	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
800	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
801	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
802	C₂²×D₄	C₂³×C₃₁	1	8	yes	complemented
803	C₂²×D₄	C₂³×C₃₁	1	16	yes	complemented
804	C₂²×D₄	C₂³×C₃₁	1	16	yes	complemented
805	C₂²×D₄	C₂³×C₃₁	1	16	yes	complemented
806	C₂³×C₄	—	4	4	no	—
807	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
812	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
814	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
815	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
816	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
817	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
818	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
821	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
822	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₂³×C₄	C₂³×C₃₁	1	8	yes	complemented
824	#127	C₂³×C₃₁	1	16	yes	complemented
825	#126	C₂³×C₃₁	1	16	yes	complemented
826	#126	C₂³×C₃₁	1	16	yes	complemented
827	#126	C₂³×C₃₁	1	16	yes	complemented
828	#126	C₂³×C₃₁	1	16	yes	complemented
829	#125	C₂³×C₃₁	1	16	yes	complemented
830	#125	C₂³×C₃₁	1	16	yes	complemented
831	#124	C₂³×C₃₁	1	16	yes	complemented
832	#124	C₂³×C₃₁	1	16	yes	complemented
833	#124	C₂³×C₃₁	1	16	yes	complemented
834	#123	C₂³×C₃₁	1	16	yes	complemented
835	#123	C₂³×C₃₁	1	16	yes	complemented
836	#123	C₂³×C₃₁	1	16	yes	complemented
837	#123	C₂³×C₃₁	1	16	yes	complemented
838	#123	C₂³×C₃₁	1	16	yes	complemented
839	#123	C₂³×C₃₁	1	16	yes	complemented
840	#123	C₂³×C₃₁	1	16	yes	complemented
841	#123	C₂³×C₃₁	1	16	yes	complemented
842	#123	C₂³×C₃₁	1	16	yes	complemented
843	#123	C₂³×C₃₁	1	16	yes	complemented
844	#123	C₂³×C₃₁	1	16	yes	complemented
845	#123	C₂³×C₃₁	1	16	yes	complemented
846	#123	C₂³×C₃₁	1	16	yes	complemented
847	#123	C₂³×C₃₁	1	16	yes	complemented
848	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
849	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
850	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
851	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
852	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
853	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
854	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
855	#121	C₂³×C₃₁	1	8	yes	—
856	#121	C₂³×C₃₁	1	16	yes	—
857	#121	C₂³×C₃₁	1	8	yes	complemented
858	#121	C₂³×C₃₁	1	8	yes	complemented
859	#121	C₂³×C₃₁	1	8	yes	complemented
860	#121	C₂³×C₃₁	1	16	yes	complemented
861	#121	C₂³×C₃₁	1	16	yes	complemented
862	#121	C₂³×C₃₁	1	8	yes	complemented
863	#121	C₂³×C₃₁	1	8	yes	complemented
864	#121	C₂³×C₃₁	1	16	yes	complemented
865	#121	C₂³×C₃₁	1	16	yes	complemented
866	#121	C₂³×C₃₁	1	16	yes	complemented
867	#121	C₂³×C₃₁	1	16	yes	complemented
868	#121	C₂³×C₃₁	1	16	yes	complemented
869	#121	C₂³×C₃₁	1	16	yes	complemented
870	#121	C₂³×C₃₁	1	16	yes	complemented
871	#121	C₂³×C₃₁	1	16	yes	complemented
872	#121	C₂³×C₃₁	1	16	yes	complemented
873	#121	C₂³×C₃₁	1	16	yes	complemented
874	#121	C₂³×C₃₁	1	16	yes	complemented
875	#121	C₂³×C₃₁	1	16	yes	complemented
876	#120	C₂³×C₃₁	1	16	yes	—
877	#120	C₂³×C₃₁	1	16	yes	complemented
878	#120	C₂³×C₃₁	1	16	yes	complemented
879	#120	C₂³×C₃₁	1	16	yes	complemented
880	#120	C₂³×C₃₁	1	16	yes	complemented
881	#120	C₂³×C₃₁	1	16	yes	complemented
882	#120	C₂³×C₃₁	1	16	yes	complemented
883	#120	C₂³×C₃₁	1	16	yes	complemented
884	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
885	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
886	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
887	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
888	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
889	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
890	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
891	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
892	#117	C₂³×C₃₁	1	8	yes	complemented
893	#117	C₂³×C₃₁	1	16	yes	complemented
894	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
895	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
898	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
899	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
900	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
901	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
903	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
905	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
906	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
907	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
908	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
911	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
912	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
913	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
914	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
915	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
916	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
917	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
918	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
919	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
920	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
921	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
922	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
923	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
925	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
926	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
928	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
929	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
930	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
932	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
933	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
934	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
935	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
936	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
937	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
938	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
939	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
940	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
941	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
942	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
943	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
944	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
945	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
946	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
947	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
948	C₃₁	C₂×#3534	1	1	yes	characteristic, direct product factor, Sylow
949	C₂⁴	—	2	4	no	—
950	C₂⁴	—	2	4	no	—
951	C₂⁴	—	2	4	no	—
952	C₂⁴	—	2	8	no	—
953	C₂⁴	—	4	2	no	—
954	C₂⁴	—	4	2	no	—
955	C₂⁴	—	4	4	no	—
956	C₂⁴	—	4	4	no	—
957	C₂⁴	—	4	4	no	—
958	C₂⁴	—	4	2	no	—
959	C₂⁴	—	4	4	no	—
960	C₂⁴	—	4	4	no	—
961	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
962	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
963	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
965	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
966	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
967	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
970	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
971	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
972	#41	—	4	16	no	—
973	#41	—	4	32	no	—
974	C₂×Q₈	—	4	2	no	—
975	C₂×Q₈	—	4	4	no	—
976	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
977	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
978	C₂×D₄	—	2	8	no	—
979	C₂×D₄	—	2	8	no	—
980	C₂×D₄	—	2	8	no	—
981	C₂×D₄	—	2	8	no	—
982	C₂×D₄	—	2	8	no	—
983	C₂×D₄	—	4	2	no	—
984	C₂×D₄	—	4	4	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	4	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	—	4	4	no	—
989	C₂×D₄	—	4	4	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	4	16	no	—
994	C₂×D₄	—	4	4	no	—
995	C₂×D₄	—	4	4	no	—
996	C₂×D₄	—	4	4	no	—
997	C₂×D₄	—	4	2	no	—
998	C₂×D₄	—	4	4	no	—
999	C₂×D₄	—	4	16	no	—
1000	C₂×D₄	—	4	32	no	—
1001	C₂×D₄	—	4	32	no	—
1002	C₂×D₄	—	4	32	no	—
1003	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1004	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1005	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1006	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1007	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1008	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1009	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1010	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1011	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1012	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1013	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1014	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1015	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1016	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1017	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1018	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1019	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1020	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
1021	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1022	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
1023	C₂²×C₄	—	2	4	no	—
1024	C₂²×C₄	—	2	4	no	—
1025	C₂²×C₄	—	2	4	no	—
1026	C₂²×C₄	—	4	2	no	—
1027	C₂²×C₄	—	4	2	no	—
1028	C₂²×C₄	—	4	2	no	—
1029	C₂²×C₄	—	4	2	no	—
1030	C₂²×C₄	—	4	16	no	—
1031	C₂²×C₄	—	4	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	—	4	2	no	—
1034	C₂²×C₄	—	4	4	no	—
1035	C₂²×C₄	—	4	4	no	—
1036	C₂²×C₄	—	4	4	no	—
1037	C₂²×C₄	—	4	4	no	—
1038	C₂²×C₄	—	4	4	no	—
1039	C₂²×C₄	—	4	4	no	—
1040	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1041	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1043	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1044	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1045	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1046	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1047	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1048	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1049	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1053	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1054	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1055	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1056	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1057	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1058	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1059	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1060	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1061	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1062	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1063	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1064	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1065	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1066	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
1067	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
1068	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1069	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1070	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1071	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1072	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1073	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1074	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1075	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1076	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1077	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1078	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1079	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1080	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1081	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1082	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1083	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1084	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1085	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1086	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1087	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1088	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1089	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1090	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1091	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1092	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1093	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1094	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1095	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1096	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1097	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1098	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1099	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1100	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1101	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1102	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1103	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1104	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1105	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1106	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1107	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1108	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1109	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1110	C₄²	C₂⁴×C₃₁	1	8	yes	—
1111	C₄²	C₂⁴×C₃₁	1	8	yes	—
1112	C₄²	C₂⁴×C₃₁	1	8	yes	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	2	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	8	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	4	no	—
1120	C₂³	—	2	4	no	—
1121	C₂³	—	2	4	no	—
1122	C₂³	—	2	4	no	—
1123	C₂³	—	2	4	no	—
1124	C₂³	—	2	4	no	—
1125	C₂³	—	2	4	no	—
1126	C₂³	—	2	8	no	—
1127	C₂³	—	2	2	no	—
1128	C₂³	—	2	4	no	—
1129	C₂³	—	2	4	no	—
1130	C₂³	—	2	2	no	—
1131	C₂³	—	2	4	no	—
1132	C₂³	—	2	4	no	—
1133	C₂³	—	2	4	no	—
1134	C₂³	—	2	8	no	—
1135	C₂³	—	2	16	no	—
1136	C₂³	—	4	4	no	—
1137	C₂³	—	4	4	no	—
1138	C₂³	—	4	8	no	—
1139	C₂³	—	4	8	no	—
1140	C₂³	—	4	8	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	8	no	—
1143	C₂³	—	4	8	no	—
1144	C₂³	—	4	16	no	—
1145	C₂³	—	8	16	no	—
1146	C₂³	—	8	8	no	—
1147	C₂³	—	8	16	no	—
1148	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
1149	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
1150	C₂³	C₂⁵×C₃₁	1	4	yes	—
1151	C₂³	C₂⁵×C₃₁	1	4	yes	—
1152	C₂³	C₂⁵×C₃₁	1	2	yes	—
1153	C₂³	C₂⁵×C₃₁	1	4	yes	—
1154	C₂³	C₂⁵×C₃₁	1	4	yes	—
1155	C₂³	C₂⁵×C₃₁	1	2	yes	—
1156	C₂³	C₂⁵×C₃₁	1	2	yes	—
1157	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1158	Q₈	—	4	4	no	—
1159	Q₈	—	4	8	no	—
1160	D₄	—	2	16	no	—
1161	D₄	—	2	16	no	—
1162	D₄	—	2	16	no	—
1163	D₄	—	2	16	no	—
1164	D₄	—	2	16	no	—
1165	D₄	—	4	4	no	—
1166	D₄	—	4	8	no	—
1167	D₄	—	4	4	no	—
1168	D₄	—	4	8	no	—
1169	D₄	—	4	8	no	—
1170	D₄	—	4	8	no	—
1171	D₄	—	4	8	no	—
1172	D₄	—	4	8	no	—
1173	D₄	—	4	8	no	—
1174	D₄	—	4	8	no	—
1175	D₄	—	4	8	no	—
1176	D₄	—	4	8	no	—
1177	D₄	—	4	8	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	8	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	8	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	4	no	—
1186	C₂×C₄	—	2	8	no	—
1187	C₂×C₄	—	2	8	no	—
1188	C₂×C₄	—	2	4	no	—
1189	C₂×C₄	—	2	4	no	—
1190	C₂×C₄	—	2	4	no	—
1191	C₂×C₄	—	2	4	no	—
1192	C₂×C₄	—	2	4	no	—
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	4	no	—
1195	C₂×C₄	—	4	4	no	—
1196	C₂×C₄	—	4	4	no	—
1197	C₂×C₄	—	4	4	no	—
1198	C₂×C₄	—	4	4	no	—
1199	C₂×C₄	—	4	4	no	—
1200	C₂×C₄	—	4	8	no	—
1201	C₂×C₄	—	4	4	no	—
1202	C₂×C₄	—	4	8	no	—
1203	C₂×C₄	—	4	8	no	—
1204	C₂×C₄	—	4	8	no	—
1205	C₂×C₄	—	4	8	no	—
1206	C₂×C₄	—	4	8	no	—
1207	C₂×C₄	—	4	8	no	—
1208	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1209	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1210	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1211	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1212	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1213	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1214	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1215	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1216	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1217	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1218	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1219	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	8	no	—
1225	C₂²	—	2	8	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	2	4	no	—
1229	C₂²	—	2	4	no	—
1230	C₂²	—	2	4	no	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	4	no	—
1234	C₂²	—	2	2	no	—
1235	C₂²	—	2	4	no	—
1236	C₂²	—	2	4	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	4	no	—
1239	C₂²	—	2	4	no	—
1240	C₂²	—	2	4	no	—
1241	C₂²	—	4	16	no	—
1242	C₂²	—	4	4	no	—
1243	C₂²	—	4	8	no	—
1244	C₂²	—	4	8	no	—
1245	C₂²	—	4	8	no	—
1246	C₂²	—	4	8	no	—
1247	C₂²	—	8	16	no	—
1248	C₂²	—	8	8	no	—
1249	C₂²	—	8	16	no	—
1250	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
1251	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
1252	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1253	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1254	C₂²	C₃₁×#585	1	2	yes	—
1255	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1256	C₄	—	2	2	no	—
1257	C₄	—	2	2	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	4	no	—
1261	C₄	—	2	4	no	—
1262	C₄	—	2	4	no	—
1263	C₄	—	2	4	no	—
1264	C₄	—	2	4	no	—
1265	C₄	—	2	4	no	—
1266	C₄	—	2	4	no	—
1267	C₄	—	2	4	no	—
1268	C₂	—	2	4	no	—
1269	C₂	—	2	4	no	—
1270	C₂	—	4	2	no	—
1271	C₂	—	4	4	no	—
1272	C₂	—	4	4	no	—
1273	C₂	—	4	4	no	—
1274	C₂	—	4	4	no	—
1275	C₂	C₃₁×#3534	1	4	yes	direct product factor
1276	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1277	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1278	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#3534	C₂	direct (N × H)
2. C₂×C₃₁×#562	C₂	semidirect
3. C₂×C₃₁×#560	C₂	semidirect
4. C₂×C₃₁×#553	C₂	semidirect
5. C₂×C₃₁×#551	C₂	semidirect
6. C₂×C₃₁×#546	C₂	semidirect
7. C₂×C₃₁×#546	C₂	semidirect
8. C₂×C₃₁×#546	C₂	semidirect
9. C₂×D₄²×C₃₁	C₂	semidirect
10. C₂×C₃₁×#540	C₂	semidirect
11. C₂×C₃₁×#539	C₂	semidirect
12. C₂×C₃₁×#539	C₂	semidirect
13. C₂×C₃₁×#538	C₂	semidirect
14. C₂×C₃₁×#538	C₂	semidirect
15. C₂×C₃₁×#537	C₂	semidirect
16. C₂×C₃₁×#534	C₂	semidirect
17. C₂×C₃₁×#534	C₂	semidirect
18. C₂×C₃₁×#525	C₂	semidirect
19. C₂²×C₃₁×#123	C₂	semidirect
20. C₂²×C₃₁×#121	C₂	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
24. C₂³×D₄×C₃₁	C₂²	semidirect
25. C₂³×D₄×C₃₁	C₂²	semidirect
26. C₂³×D₄×C₃₁	C₂²	semidirect
27. C₂³×D₄×C₃₁	C₂²	semidirect
28. C₂⁴×C₄×C₃₁	C₂²	semidirect
29. C₃₁×#562	C₂²	semidirect
30. C₃₁×#560	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
32. C₃₁×#551	C₂²	semidirect
33. C₃₁×#546	C₂²	semidirect
34. C₃₁×#546	C₂²	semidirect
35. C₃₁×#546	C₂²	semidirect
36. D₄²×C₃₁	C₂²	semidirect
37. C₃₁×#540	C₂²	semidirect
38. C₃₁×#539	C₂²	semidirect
39. C₃₁×#539	C₂²	semidirect
40. C₃₁×#538	C₂²	semidirect
41. C₃₁×#538	C₂²	semidirect
42. C₃₁×#537	C₂²	semidirect
43. C₃₁×#534	C₂²	semidirect
44. C₃₁×#534	C₂²	semidirect
45. C₂×C₃₁×#127	C₂²	semidirect
46. C₂×C₃₁×#126	C₂²	semidirect
47. C₂×C₃₁×#126	C₂²	semidirect
48. C₂×C₃₁×#126	C₂²	semidirect
49. C₂×C₃₁×#126	C₂²	semidirect
50. C₂×C₃₁×#125	C₂²	semidirect
51. C₂×C₃₁×#125	C₂²	semidirect
52. C₂×C₃₁×#124	C₂²	semidirect
53. C₂×C₃₁×#124	C₂²	semidirect
54. C₂×C₃₁×#124	C₂²	semidirect
55. C₃₁×#525	C₂²	semidirect
56. C₂×C₃₁×#123	C₂²	semidirect
57. C₂×C₃₁×#123	C₂²	semidirect
58. C₂×C₃₁×#123	C₂²	semidirect
59. C₂×C₃₁×#123	C₂²	semidirect
60. C₂×C₃₁×#123	C₂²	semidirect
61. C₂×C₃₁×#123	C₂²	semidirect
62. C₂×C₃₁×#123	C₂²	semidirect
63. C₂×C₃₁×#123	C₂²	semidirect
64. C₂×C₃₁×#123	C₂²	semidirect
65. C₂×C₃₁×#123	C₂²	semidirect
66. C₂×C₃₁×#123	C₂²	semidirect
67. C₂×C₃₁×#123	C₂²	semidirect
68. C₂×C₃₁×#123	C₂²	semidirect
69. C₂×C₃₁×#123	C₂²	semidirect
70. C₂×C₃₁×#123	C₂²	semidirect
71. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
72. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
73. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
74. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
75. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
76. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
77. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
80. C₂×C₃₁×#121	C₂²	semidirect
81. C₂×C₃₁×#121	C₂²	semidirect
82. C₂×C₃₁×#121	C₂²	semidirect
83. C₂×C₃₁×#121	C₂²	semidirect
84. C₂×C₃₁×#121	C₂²	semidirect
85. C₂×C₃₁×#121	C₂²	semidirect
86. C₂×C₃₁×#121	C₂²	semidirect
87. C₂×C₃₁×#121	C₂²	semidirect
88. C₂×C₃₁×#121	C₂²	semidirect
89. C₂×C₃₁×#121	C₂²	semidirect
90. C₂×C₃₁×#121	C₂²	semidirect
91. C₂×C₃₁×#121	C₂²	semidirect
92. C₂×C₃₁×#121	C₂²	semidirect
93. C₂×C₃₁×#121	C₂²	semidirect
94. C₂×C₃₁×#121	C₂²	semidirect
95. C₂×C₃₁×#121	C₂²	semidirect
96. C₂×C₃₁×#121	C₂²	semidirect
97. C₂×C₃₁×#121	C₂²	semidirect
98. C₂×C₃₁×#121	C₂²	semidirect
99. C₂×C₃₁×#121	C₂²	semidirect
101. C₂×C₃₁×#120	C₂²	semidirect
102. C₂×C₃₁×#120	C₂²	semidirect
103. C₂×C₃₁×#120	C₂²	semidirect
104. C₂×C₃₁×#120	C₂²	semidirect
105. C₂×C₃₁×#120	C₂²	semidirect
106. C₂×C₃₁×#120	C₂²	semidirect
107. C₂×C₃₁×#120	C₂²	semidirect
108. C₂×C₄×D₄×C₃₁	C₂²	semidirect
109. C₂×C₄×D₄×C₃₁	C₂²	semidirect
110. C₂×C₄×D₄×C₃₁	C₂²	semidirect
111. C₂×C₄×D₄×C₃₁	C₂²	semidirect
112. C₂×C₄×D₄×C₃₁	C₂²	semidirect
113. C₂×C₄×D₄×C₃₁	C₂²	semidirect
114. C₂×C₄×D₄×C₃₁	C₂²	semidirect
115. C₂×C₄×D₄×C₃₁	C₂²	semidirect
116. C₂×C₃₁×#117	C₂²	semidirect
117. C₂×C₃₁×#117	C₂²	semidirect
118. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
119. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
120. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
121. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
123. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
124. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
125. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
133. C₂×#41×C₃₁	C₂³	semidirect
134. C₂×#41×C₃₁	C₂³	semidirect
163. C₂²×D₄×C₃₁	C₂³	semidirect
164. C₂²×D₄×C₃₁	C₂³	semidirect
165. C₂²×D₄×C₃₁	C₂³	semidirect
166. C₂²×D₄×C₃₁	C₂³	semidirect
184. C₂³×C₄×C₃₁	C₂³	semidirect
185. C₃₁×#127	C₂³	semidirect
186. C₃₁×#126	C₂³	semidirect
187. C₃₁×#126	C₂³	semidirect
188. C₃₁×#126	C₂³	semidirect
189. C₃₁×#126	C₂³	semidirect
190. C₃₁×#125	C₂³	semidirect
191. C₃₁×#125	C₂³	semidirect
192. C₃₁×#124	C₂³	semidirect
193. C₃₁×#124	C₂³	semidirect
194. C₃₁×#124	C₂³	semidirect
195. C₃₁×#123	C₂³	semidirect
196. C₃₁×#123	C₂³	semidirect
197. C₃₁×#123	C₂³	semidirect
198. C₃₁×#123	C₂³	semidirect
199. C₃₁×#123	C₂³	semidirect
200. C₃₁×#123	C₂³	semidirect
201. C₃₁×#123	C₂³	semidirect
202. C₃₁×#123	C₂³	semidirect
203. C₃₁×#123	C₂³	semidirect
204. C₃₁×#123	C₂³	semidirect
205. C₃₁×#123	C₂³	semidirect
206. C₃₁×#123	C₂³	semidirect
207. C₃₁×#123	C₂³	semidirect
208. C₃₁×#123	C₂³	semidirect
209. C₃₁×C₂²⋊Q₈	C₂³	semidirect
210. C₃₁×C₂²⋊Q₈	C₂³	semidirect
211. C₃₁×C₂²⋊Q₈	C₂³	semidirect
212. C₃₁×C₂²⋊Q₈	C₂³	semidirect
213. C₃₁×C₂²⋊Q₈	C₂³	semidirect
214. C₃₁×C₂²⋊Q₈	C₂³	semidirect
215. C₃₁×C₂²⋊Q₈	C₂³	semidirect
218. C₃₁×#121	C₂³	semidirect
219. C₃₁×#121	C₂³	semidirect
220. C₃₁×#121	C₂³	semidirect
221. C₃₁×#121	C₂³	semidirect
222. C₃₁×#121	C₂³	semidirect
223. C₃₁×#121	C₂³	semidirect
224. C₃₁×#121	C₂³	semidirect
225. C₃₁×#121	C₂³	semidirect
226. C₃₁×#121	C₂³	semidirect
227. C₃₁×#121	C₂³	semidirect
228. C₃₁×#121	C₂³	semidirect
229. C₃₁×#121	C₂³	semidirect
230. C₃₁×#121	C₂³	semidirect
231. C₃₁×#121	C₂³	semidirect
232. C₃₁×#121	C₂³	semidirect
233. C₃₁×#121	C₂³	semidirect
234. C₃₁×#121	C₂³	semidirect
235. C₃₁×#121	C₂³	semidirect
236. C₃₁×#121	C₂³	semidirect
238. C₃₁×#120	C₂³	semidirect
239. C₃₁×#120	C₂³	semidirect
240. C₃₁×#120	C₂³	semidirect
241. C₃₁×#120	C₂³	semidirect
242. C₃₁×#120	C₂³	semidirect
243. C₃₁×#120	C₂³	semidirect
244. C₃₁×#120	C₂³	semidirect
245. C₄×D₄×C₃₁	C₂³	semidirect
246. C₄×D₄×C₃₁	C₂³	semidirect
247. C₄×D₄×C₃₁	C₂³	semidirect
248. C₄×D₄×C₃₁	C₂³	semidirect
249. C₄×D₄×C₃₁	C₂³	semidirect
250. C₄×D₄×C₃₁	C₂³	semidirect
251. C₄×D₄×C₃₁	C₂³	semidirect
252. C₄×D₄×C₃₁	C₂³	semidirect
253. C₃₁×#117	C₂³	semidirect
254. C₃₁×#117	C₂³	semidirect
272. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
273. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
274. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
300. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
301. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
302. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
303. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
304. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
305. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
473. C₂×#3534	C₃₁	direct (N × H)
581. #3534	C₂×C₃₁	direct (N × H)
582. C₂×#562	C₂×C₃₁	semidirect
583. C₂×#560	C₂×C₃₁	semidirect
584. C₂×#553	C₂×C₃₁	semidirect
585. C₂×#551	C₂×C₃₁	semidirect
586. C₂×#546	C₂×C₃₁	semidirect
587. C₂×#546	C₂×C₃₁	semidirect
588. C₂×#546	C₂×C₃₁	semidirect
589. C₂×D₄²	C₂×C₃₁	semidirect
590. C₂×#540	C₂×C₃₁	semidirect
591. C₂×#539	C₂×C₃₁	semidirect
592. C₂×#539	C₂×C₃₁	semidirect
593. C₂×#538	C₂×C₃₁	semidirect
594. C₂×#538	C₂×C₃₁	semidirect
595. C₂×#537	C₂×C₃₁	semidirect
596. C₂×#534	C₂×C₃₁	semidirect
597. C₂×#534	C₂×C₃₁	semidirect
598. C₂×#525	C₂×C₃₁	semidirect
599. C₂²×#123	C₂×C₃₁	semidirect
600. C₂²×#121	C₂×C₃₁	semidirect
649. C₂²×#41	C₂²×C₃₁	semidirect
650. C₂²×#41	C₂²×C₃₁	semidirect
652. C₂³×D₄	C₂²×C₃₁	semidirect
653. C₂³×D₄	C₂²×C₃₁	semidirect
654. C₂³×D₄	C₂²×C₃₁	semidirect
655. C₂³×D₄	C₂²×C₃₁	semidirect
656. C₂⁴×C₄	C₂²×C₃₁	semidirect
657. #562	C₂²×C₃₁	semidirect
658. #560	C₂²×C₃₁	semidirect
659. #553	C₂²×C₃₁	semidirect
660. #551	C₂²×C₃₁	semidirect
661. #546	C₂²×C₃₁	semidirect
662. #546	C₂²×C₃₁	semidirect
663. #546	C₂²×C₃₁	semidirect
664. D₄²	C₂²×C₃₁	semidirect
665. #540	C₂²×C₃₁	semidirect
666. #539	C₂²×C₃₁	semidirect
667. #539	C₂²×C₃₁	semidirect
668. #538	C₂²×C₃₁	semidirect
669. #538	C₂²×C₃₁	semidirect
670. #537	C₂²×C₃₁	semidirect
671. #534	C₂²×C₃₁	semidirect
672. #534	C₂²×C₃₁	semidirect
673. C₂×#127	C₂²×C₃₁	semidirect
674. C₂×#126	C₂²×C₃₁	semidirect
675. C₂×#126	C₂²×C₃₁	semidirect
676. C₂×#126	C₂²×C₃₁	semidirect
677. C₂×#126	C₂²×C₃₁	semidirect
678. C₂×#125	C₂²×C₃₁	semidirect
679. C₂×#125	C₂²×C₃₁	semidirect
680. C₂×#124	C₂²×C₃₁	semidirect
681. C₂×#124	C₂²×C₃₁	semidirect
682. C₂×#124	C₂²×C₃₁	semidirect
683. #525	C₂²×C₃₁	semidirect
684. C₂×#123	C₂²×C₃₁	semidirect
685. C₂×#123	C₂²×C₃₁	semidirect
686. C₂×#123	C₂²×C₃₁	semidirect
687. C₂×#123	C₂²×C₃₁	semidirect
688. C₂×#123	C₂²×C₃₁	semidirect
689. C₂×#123	C₂²×C₃₁	semidirect
690. C₂×#123	C₂²×C₃₁	semidirect
691. C₂×#123	C₂²×C₃₁	semidirect
692. C₂×#123	C₂²×C₃₁	semidirect
693. C₂×#123	C₂²×C₃₁	semidirect
694. C₂×#123	C₂²×C₃₁	semidirect
695. C₂×#123	C₂²×C₃₁	semidirect
696. C₂×#123	C₂²×C₃₁	semidirect
697. C₂×#123	C₂²×C₃₁	semidirect
698. C₂×#123	C₂²×C₃₁	semidirect
699. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
700. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
701. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
702. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
703. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
704. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
705. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
708. C₂×#121	C₂²×C₃₁	semidirect
709. C₂×#121	C₂²×C₃₁	semidirect
710. C₂×#121	C₂²×C₃₁	semidirect
711. C₂×#121	C₂²×C₃₁	semidirect
712. C₂×#121	C₂²×C₃₁	semidirect
713. C₂×#121	C₂²×C₃₁	semidirect
714. C₂×#121	C₂²×C₃₁	semidirect
715. C₂×#121	C₂²×C₃₁	semidirect
716. C₂×#121	C₂²×C₃₁	semidirect
717. C₂×#121	C₂²×C₃₁	semidirect
718. C₂×#121	C₂²×C₃₁	semidirect
719. C₂×#121	C₂²×C₃₁	semidirect
720. C₂×#121	C₂²×C₃₁	semidirect
721. C₂×#121	C₂²×C₃₁	semidirect
722. C₂×#121	C₂²×C₃₁	semidirect
723. C₂×#121	C₂²×C₃₁	semidirect
724. C₂×#121	C₂²×C₃₁	semidirect
725. C₂×#121	C₂²×C₃₁	semidirect
726. C₂×#121	C₂²×C₃₁	semidirect
727. C₂×#121	C₂²×C₃₁	semidirect
729. C₂×#120	C₂²×C₃₁	semidirect
730. C₂×#120	C₂²×C₃₁	semidirect
731. C₂×#120	C₂²×C₃₁	semidirect
732. C₂×#120	C₂²×C₃₁	semidirect
733. C₂×#120	C₂²×C₃₁	semidirect
734. C₂×#120	C₂²×C₃₁	semidirect
735. C₂×#120	C₂²×C₃₁	semidirect
736. C₂×C₄×D₄	C₂²×C₃₁	semidirect
737. C₂×C₄×D₄	C₂²×C₃₁	semidirect
738. C₂×C₄×D₄	C₂²×C₃₁	semidirect
739. C₂×C₄×D₄	C₂²×C₃₁	semidirect
740. C₂×C₄×D₄	C₂²×C₃₁	semidirect
741. C₂×C₄×D₄	C₂²×C₃₁	semidirect
742. C₂×C₄×D₄	C₂²×C₃₁	semidirect
743. C₂×C₄×D₄	C₂²×C₃₁	semidirect
744. C₂×#117	C₂²×C₃₁	semidirect
745. C₂×#117	C₂²×C₃₁	semidirect
746. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
747. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
748. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
749. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
750. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
751. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
752. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
753. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
754. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
762. C₂×C₃₁	#3534	direct (N × H)
772. C₂×#41	C₂³×C₃₁	semidirect
773. C₂×#41	C₂³×C₃₁	semidirect
802. C₂²×D₄	C₂³×C₃₁	semidirect
803. C₂²×D₄	C₂³×C₃₁	semidirect
804. C₂²×D₄	C₂³×C₃₁	semidirect
805. C₂²×D₄	C₂³×C₃₁	semidirect
823. C₂³×C₄	C₂³×C₃₁	semidirect
824. #127	C₂³×C₃₁	semidirect
825. #126	C₂³×C₃₁	semidirect
826. #126	C₂³×C₃₁	semidirect
827. #126	C₂³×C₃₁	semidirect
828. #126	C₂³×C₃₁	semidirect
829. #125	C₂³×C₃₁	semidirect
830. #125	C₂³×C₃₁	semidirect
831. #124	C₂³×C₃₁	semidirect
832. #124	C₂³×C₃₁	semidirect
833. #124	C₂³×C₃₁	semidirect
834. #123	C₂³×C₃₁	semidirect
835. #123	C₂³×C₃₁	semidirect
836. #123	C₂³×C₃₁	semidirect
837. #123	C₂³×C₃₁	semidirect
838. #123	C₂³×C₃₁	semidirect
839. #123	C₂³×C₃₁	semidirect
840. #123	C₂³×C₃₁	semidirect
841. #123	C₂³×C₃₁	semidirect
842. #123	C₂³×C₃₁	semidirect
843. #123	C₂³×C₃₁	semidirect
844. #123	C₂³×C₃₁	semidirect
845. #123	C₂³×C₃₁	semidirect
846. #123	C₂³×C₃₁	semidirect
847. #123	C₂³×C₃₁	semidirect
848. C₂²⋊Q₈	C₂³×C₃₁	semidirect
849. C₂²⋊Q₈	C₂³×C₃₁	semidirect
850. C₂²⋊Q₈	C₂³×C₃₁	semidirect
851. C₂²⋊Q₈	C₂³×C₃₁	semidirect
852. C₂²⋊Q₈	C₂³×C₃₁	semidirect
853. C₂²⋊Q₈	C₂³×C₃₁	semidirect
854. C₂²⋊Q₈	C₂³×C₃₁	semidirect
857. #121	C₂³×C₃₁	semidirect
858. #121	C₂³×C₃₁	semidirect
859. #121	C₂³×C₃₁	semidirect
860. #121	C₂³×C₃₁	semidirect
861. #121	C₂³×C₃₁	semidirect
862. #121	C₂³×C₃₁	semidirect
863. #121	C₂³×C₃₁	semidirect
864. #121	C₂³×C₃₁	semidirect
865. #121	C₂³×C₃₁	semidirect
866. #121	C₂³×C₃₁	semidirect
867. #121	C₂³×C₃₁	semidirect
868. #121	C₂³×C₃₁	semidirect
869. #121	C₂³×C₃₁	semidirect
870. #121	C₂³×C₃₁	semidirect
871. #121	C₂³×C₃₁	semidirect
872. #121	C₂³×C₃₁	semidirect
873. #121	C₂³×C₃₁	semidirect
874. #121	C₂³×C₃₁	semidirect
875. #121	C₂³×C₃₁	semidirect
877. #120	C₂³×C₃₁	semidirect
878. #120	C₂³×C₃₁	semidirect
879. #120	C₂³×C₃₁	semidirect
880. #120	C₂³×C₃₁	semidirect
881. #120	C₂³×C₃₁	semidirect
882. #120	C₂³×C₃₁	semidirect
883. #120	C₂³×C₃₁	semidirect
884. C₄×D₄	C₂³×C₃₁	semidirect
885. C₄×D₄	C₂³×C₃₁	semidirect
886. C₄×D₄	C₂³×C₃₁	semidirect
887. C₄×D₄	C₂³×C₃₁	semidirect
888. C₄×D₄	C₂³×C₃₁	semidirect
889. C₄×D₄	C₂³×C₃₁	semidirect
890. C₄×D₄	C₂³×C₃₁	semidirect
891. C₄×D₄	C₂³×C₃₁	semidirect
892. #117	C₂³×C₃₁	semidirect
893. #117	C₂³×C₃₁	semidirect
911. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
912. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
913. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
939. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
940. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
941. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
942. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
943. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
944. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
948. C₃₁	C₂×#3534	direct (N × H)
1275. C₂	C₃₁×#3534	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3534	2
C₂×C₃₁×#562	2
C₂×C₃₁×#560	2
C₂×C₃₁×#553	2
C₂×C₃₁×#551	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#540	2
C₂×C₃₁×#539	2
C₂×C₃₁×#538	2
C₂×C₃₁×#537	2
C₂×C₃₁×#534	2
C₂×C₃₁×#525	2
C₂²×C₃₁×#123	2
C₂²×C₃₁×#121	2
C₂×#3534	31

Subgroups — C2×C31×#3534 #21519480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3534 #21519480