Subgroups — C₂×C₃₁×#3560 #21519494

Order 7936.

7398 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3560	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	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×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#542	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×#538	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
23	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#563	C₂²	1	32	yes	complemented
25	C₃₁×#560	C₂²	1	32	yes	complemented
26	C₃₁×#553	C₂²	1	32	yes	complemented
27	C₃₁×#553	C₂²	1	32	yes	complemented
28	C₃₁×#551	C₂²	1	32	yes	complemented
29	C₃₁×#547	C₂²	1	32	yes	complemented
30	C₃₁×#546	C₂²	1	32	yes	complemented
31	C₃₁×#546	C₂²	1	32	yes	complemented
32	C₃₁×#542	C₂²	1	32	yes	complemented
33	C₃₁×#539	C₂²	1	32	yes	complemented
34	C₃₁×#539	C₂²	1	16	yes	complemented
35	C₃₁×#538	C₂²	1	16	yes	complemented
36	C₃₁×#538	C₂²	1	32	yes	complemented
37	C₃₁×#538	C₂²	1	32	yes	complemented
38	C₃₁×#537	C₂²	1	16	yes	complemented
39	C₃₁×#534	C₂²	1	16	yes	complemented
40	C₃₁×#532	C₂²	1	16	yes	complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#529	C₂²	1	16	yes	complemented
45	C₂×C₃₁×#126	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×#126	C₂²	1	2	yes	complemented
51	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
52	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
53	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
54	C₂×C₃₁×#126	C₂²	1	16	yes	complemented
55	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#124	C₂²	1	2	yes	—
59	C₂×C₃₁×#124	C₂²	1	2	yes	—
60	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
62	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
63	C₂×C₃₁×#123	C₂²	1	2	yes	—
64	C₂×C₃₁×#123	C₂²	1	2	yes	—
65	C₂×C₃₁×#123	C₂²	1	2	yes	—
66	C₂×C₃₁×#123	C₂²	1	2	yes	—
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	2	yes	complemented
71	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
72	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
73	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
74	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
75	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
79	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
80	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
81	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
82	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
83	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
84	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
85	C₂×C₃₁×#121	C₂²	1	2	yes	—
86	C₂×C₃₁×#121	C₂²	1	2	yes	—
87	C₂×C₃₁×#121	C₂²	1	2	yes	—
88	C₂×C₃₁×#121	C₂²	1	2	yes	—
89	C₂×C₃₁×#121	C₂²	1	2	yes	—
90	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, 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×#120	C₂²	1	2	yes	—
99	C₂×C₃₁×#120	C₂²	1	2	yes	—
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×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, 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×C₃₁×#117	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
117	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
121	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
125	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
126	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
127	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
128	C₂⁵×C₃₁	C₂³	1	2	yes	—
129	C₂×#41×C₃₁	—	4	8	no	—
130	C₂×#41×C₃₁	—	4	8	no	—
131	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
132	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
133	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₃₁	—	4	8	no	—
137	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
152	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
153	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
160	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
161	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
162	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
163	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
164	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
165	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
166	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
168	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
169	C₃₁×#127	C₂³	1	8	yes	complemented
170	C₃₁×#126	C₂³	1	16	yes	complemented
171	C₃₁×#126	C₂³	1	16	yes	complemented
172	C₃₁×#126	C₂³	1	16	yes	complemented
173	C₃₁×#126	C₂³	1	16	yes	complemented
174	C₃₁×#126	C₂³	1	16	yes	complemented
175	C₃₁×#126	C₂³	1	16	yes	complemented
176	C₃₁×#126	C₂³	1	16	yes	complemented
177	C₃₁×#126	C₂³	1	16	yes	complemented
178	C₃₁×#126	C₂³	1	16	yes	complemented
179	C₃₁×#125	C₂³	1	8	yes	complemented
180	C₃₁×#125	C₂³	1	16	yes	complemented
181	C₃₁×#125	C₂³	1	16	yes	complemented
182	C₃₁×#124	C₂³	1	16	yes	—
183	C₃₁×#124	C₂³	1	16	yes	—
184	C₃₁×#124	C₂³	1	8	yes	complemented
185	C₃₁×#124	C₂³	1	16	yes	complemented
186	C₃₁×#124	C₂³	1	16	yes	complemented
187	C₃₁×#123	C₂³	1	16	yes	—
188	C₃₁×#123	C₂³	1	16	yes	—
189	C₃₁×#123	C₂³	1	16	yes	—
190	C₃₁×#123	C₂³	1	16	yes	—
191	C₃₁×#123	C₂³	1	16	yes	complemented
192	C₃₁×#123	C₂³	1	16	yes	complemented
193	C₃₁×#123	C₂³	1	16	yes	complemented
194	C₃₁×#123	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×C₂²⋊Q₈	C₂³	1	8	yes	complemented
200	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
201	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
207	C₃₁×#121	C₂³	1	8	yes	—
208	C₃₁×#121	C₂³	1	8	yes	—
209	C₃₁×#121	C₂³	1	16	yes	—
210	C₃₁×#121	C₂³	1	16	yes	—
211	C₃₁×#121	C₂³	1	16	yes	—
212	C₃₁×#121	C₂³	1	16	yes	—
213	C₃₁×#121	C₂³	1	16	yes	—
214	C₃₁×#121	C₂³	1	8	yes	complemented
215	C₃₁×#121	C₂³	1	16	yes	complemented
216	C₃₁×#121	C₂³	1	16	yes	complemented
217	C₃₁×#121	C₂³	1	16	yes	complemented
218	C₃₁×#121	C₂³	1	16	yes	complemented
219	C₃₁×#121	C₂³	1	16	yes	complemented
220	C₃₁×#121	C₂³	1	16	yes	complemented
221	C₃₁×#121	C₂³	1	16	yes	complemented
222	C₃₁×#120	C₂³	1	16	yes	—
223	C₃₁×#120	C₂³	1	16	yes	—
224	C₃₁×#120	C₂³	1	16	yes	—
225	C₃₁×#120	C₂³	1	16	yes	complemented
226	C₃₁×#120	C₂³	1	16	yes	complemented
227	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
228	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
229	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
230	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
231	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
232	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
233	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
234	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
235	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
236	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
237	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
238	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
239	C₃₁×#117	C₂³	1	16	yes	complemented
240	C₃₁×#117	C₂³	1	16	yes	complemented
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
266	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
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	16	yes	complemented
295	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
296	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
301	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
302	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
303	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
304	C₂⁴×C₃₁	—	2	4	no	—
305	C₂⁴×C₃₁	—	4	4	no	—
306	C₂⁴×C₃₁	—	4	2	no	—
307	C₂⁴×C₃₁	—	4	2	no	—
308	C₂⁴×C₃₁	—	4	4	no	—
309	C₂⁴×C₃₁	—	4	4	no	—
310	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
311	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
312	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
313	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
314	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
316	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
317	#41×C₃₁	—	4	32	no	—
318	#41×C₃₁	—	4	32	no	—
319	C₂×Q₈×C₃₁	—	4	2	no	—
320	C₂×Q₈×C₃₁	—	4	4	no	—
321	C₂×Q₈×C₃₁	—	4	4	no	—
322	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
323	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
324	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
325	C₂×D₄×C₃₁	—	2	8	no	—
326	C₂×D₄×C₃₁	—	2	8	no	—
327	C₂×D₄×C₃₁	—	2	8	no	—
328	C₂×D₄×C₃₁	—	4	4	no	—
329	C₂×D₄×C₃₁	—	4	4	no	—
330	C₂×D₄×C₃₁	—	4	4	no	—
331	C₂×D₄×C₃₁	—	4	4	no	—
332	C₂×D₄×C₃₁	—	4	4	no	—
333	C₂×D₄×C₃₁	—	4	4	no	—
334	C₂×D₄×C₃₁	—	4	2	no	—
335	C₂×D₄×C₃₁	—	4	2	no	—
336	C₂×D₄×C₃₁	—	4	4	no	—
337	C₂×D₄×C₃₁	—	4	2	no	—
338	C₂×D₄×C₃₁	—	4	4	no	—
339	C₂×D₄×C₃₁	—	4	4	no	—
340	C₂×D₄×C₃₁	—	4	32	no	—
341	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
346	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₃₁	—	2	4	no	—
357	C₂²×C₄×C₃₁	—	2	4	no	—
358	C₂²×C₄×C₃₁	—	4	4	no	—
359	C₂²×C₄×C₃₁	—	4	2	no	—
360	C₂²×C₄×C₃₁	—	4	2	no	—
361	C₂²×C₄×C₃₁	—	4	2	no	—
362	C₂²×C₄×C₃₁	—	4	4	no	—
363	C₂²×C₄×C₃₁	—	4	4	no	—
364	C₂²×C₄×C₃₁	—	4	2	no	—
365	C₂²×C₄×C₃₁	—	4	4	no	—
366	C₂²×C₄×C₃₁	—	4	4	no	—
367	C₂²×C₄×C₃₁	—	4	4	no	—
368	C₂²×C₄×C₃₁	—	4	4	no	—
369	C₂²×C₄×C₃₁	—	4	4	no	—
370	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
371	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
372	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
390	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
391	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
392	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
393	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
394	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
395	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
396	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
397	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
414	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	8	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	8	yes	—
424	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
425	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
426	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
427	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
428	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
429	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
430	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
431	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
432	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
433	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
434	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
435	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
436	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
437	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
438	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
439	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
440	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
441	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
444	C₄²×C₃₁	C₂⁴	1	4	yes	—
445	C₄²×C₃₁	C₂⁴	1	4	yes	—
446	C₄²×C₃₁	C₂⁴	1	4	yes	—
447	C₄²×C₃₁	C₂⁴	1	4	yes	—
448	C₄²×C₃₁	C₂⁴	1	8	yes	—
449	C₄²×C₃₁	C₂⁴	1	8	yes	—
450	C₄²×C₃₁	C₂⁴	1	8	yes	—
451	C₂×#3560	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	2	2	no	—
454	C₂³×C₃₁	—	2	4	no	—
455	C₂³×C₃₁	—	2	4	no	—
456	C₂³×C₃₁	—	2	4	no	—
457	C₂³×C₃₁	—	2	4	no	—
458	C₂³×C₃₁	—	2	4	no	—
459	C₂³×C₃₁	—	2	4	no	—
460	C₂³×C₃₁	—	2	4	no	—
461	C₂³×C₃₁	—	2	4	no	—
462	C₂³×C₃₁	—	2	4	no	—
463	C₂³×C₃₁	—	2	4	no	—
464	C₂³×C₃₁	—	2	4	no	—
465	C₂³×C₃₁	—	2	4	no	—
466	C₂³×C₃₁	—	2	8	no	—
467	C₂³×C₃₁	—	4	8	no	—
468	C₂³×C₃₁	—	4	4	no	—
469	C₂³×C₃₁	—	4	4	no	—
470	C₂³×C₃₁	—	4	8	no	—
471	C₂³×C₃₁	—	4	8	no	—
472	C₂³×C₃₁	—	8	8	no	—
473	C₂³×C₃₁	—	8	16	no	—
474	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
475	C₂³×C₃₁	C₂⁵	1	4	yes	—
476	C₂³×C₃₁	C₂⁵	1	4	yes	—
477	C₂³×C₃₁	C₂⁵	1	4	yes	—
478	C₂³×C₃₁	C₂⁵	1	4	yes	—
479	C₂³×C₃₁	C₂⁵	1	2	yes	—
480	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
481	Q₈×C₃₁	—	4	4	no	—
482	Q₈×C₃₁	—	4	8	no	—
483	Q₈×C₃₁	—	4	8	no	—
484	D₄×C₃₁	—	2	16	no	—
485	D₄×C₃₁	—	2	16	no	—
486	D₄×C₃₁	—	2	16	no	—
487	D₄×C₃₁	—	4	8	no	—
488	D₄×C₃₁	—	4	8	no	—
489	D₄×C₃₁	—	4	8	no	—
490	D₄×C₃₁	—	4	8	no	—
491	D₄×C₃₁	—	4	8	no	—
492	D₄×C₃₁	—	4	8	no	—
493	D₄×C₃₁	—	4	4	no	—
494	D₄×C₃₁	—	4	4	no	—
495	D₄×C₃₁	—	4	8	no	—
496	D₄×C₃₁	—	4	4	no	—
497	D₄×C₃₁	—	4	8	no	—
498	D₄×C₃₁	—	4	8	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	4	no	—
501	C₂×C₄×C₃₁	—	2	2	no	—
502	C₂×C₄×C₃₁	—	2	8	no	—
503	C₂×C₄×C₃₁	—	2	8	no	—
504	C₂×C₄×C₃₁	—	2	4	no	—
505	C₂×C₄×C₃₁	—	2	4	no	—
506	C₂×C₄×C₃₁	—	2	4	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	4	no	—
509	C₂×C₄×C₃₁	—	2	4	no	—
510	C₂×C₄×C₃₁	—	2	4	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	2	2	no	—
513	C₂×C₄×C₃₁	—	2	4	no	—
514	C₂×C₄×C₃₁	—	2	2	no	—
515	C₂×C₄×C₃₁	—	4	8	no	—
516	C₂×C₄×C₃₁	—	4	4	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	4	no	—
519	C₂×C₄×C₃₁	—	4	8	no	—
520	C₂×C₄×C₃₁	—	4	8	no	—
521	C₂×C₄×C₃₁	—	4	4	no	—
522	C₂×C₄×C₃₁	—	4	8	no	—
523	C₂×C₄×C₃₁	—	4	8	no	—
524	C₂×C₄×C₃₁	—	4	8	no	—
525	C₂×C₄×C₃₁	—	4	8	no	—
526	C₂×C₄×C₃₁	—	4	8	no	—
527	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
528	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
529	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
530	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
531	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
532	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
533	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
534	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
535	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
536	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
537	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
538	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
539	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
540	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
541	#3560	C₂×C₃₁	1	32	yes	direct product factor
542	C₂×#563	C₂×C₃₁	1	2	yes	complemented
543	C₂×#560	C₂×C₃₁	1	2	yes	complemented
544	C₂×#553	C₂×C₃₁	1	2	yes	complemented
545	C₂×#553	C₂×C₃₁	1	2	yes	complemented
546	C₂×#551	C₂×C₃₁	1	2	yes	complemented
547	C₂×#547	C₂×C₃₁	1	2	yes	complemented
548	C₂×#546	C₂×C₃₁	1	2	yes	complemented
549	C₂×#546	C₂×C₃₁	1	2	yes	complemented
550	C₂×#542	C₂×C₃₁	1	2	yes	complemented
551	C₂×#539	C₂×C₃₁	1	2	yes	complemented
552	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
553	C₂×#538	C₂×C₃₁	1	1	yes	characteristic, complemented
554	C₂×#538	C₂×C₃₁	1	2	yes	complemented
555	C₂×#538	C₂×C₃₁	1	2	yes	complemented
556	C₂×#537	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₂×#534	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
560	C₂²×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	8	no	—
564	C₂²×C₃₁	—	2	4	no	—
565	C₂²×C₃₁	—	2	4	no	—
566	C₂²×C₃₁	—	2	4	no	—
567	C₂²×C₃₁	—	2	4	no	—
568	C₂²×C₃₁	—	2	4	no	—
569	C₂²×C₃₁	—	2	4	no	—
570	C₂²×C₃₁	—	2	4	no	—
571	C₂²×C₃₁	—	2	4	no	—
572	C₂²×C₃₁	—	2	4	no	—
573	C₂²×C₃₁	—	2	4	no	—
574	C₂²×C₃₁	—	2	4	no	—
575	C₂²×C₃₁	—	2	4	no	—
576	C₂²×C₃₁	—	4	8	no	—
577	C₂²×C₃₁	—	4	8	no	—
578	C₂²×C₃₁	—	4	8	no	—
579	C₂²×C₃₁	—	4	8	no	—
580	C₂²×C₃₁	—	8	8	no	—
581	C₂²×C₃₁	—	8	16	no	—
582	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
583	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
584	C₂²×C₃₁	#585	1	2	yes	—
585	C₂²×C₃₁	#585	1	2	yes	—
586	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	2	4	no	—
589	C₄×C₃₁	—	2	2	no	—
590	C₄×C₃₁	—	2	4	no	—
591	C₄×C₃₁	—	2	4	no	—
592	C₄×C₃₁	—	2	4	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	4	no	—
595	C₄×C₃₁	—	2	4	no	—
596	C₄×C₃₁	—	2	4	no	—
597	C₄×C₃₁	—	2	2	no	—
598	C₄×C₃₁	—	2	2	no	—
599	C₄×C₃₁	—	2	4	no	—
600	C₄×C₃₁	—	2	2	no	—
601	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
602	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
603	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
604	#563	C₂²×C₃₁	1	32	yes	complemented
605	#560	C₂²×C₃₁	1	32	yes	complemented
606	#553	C₂²×C₃₁	1	32	yes	complemented
607	#553	C₂²×C₃₁	1	32	yes	complemented
608	#551	C₂²×C₃₁	1	32	yes	complemented
609	#547	C₂²×C₃₁	1	32	yes	complemented
610	#546	C₂²×C₃₁	1	32	yes	complemented
611	#546	C₂²×C₃₁	1	32	yes	complemented
612	#542	C₂²×C₃₁	1	32	yes	complemented
613	#539	C₂²×C₃₁	1	32	yes	complemented
614	#539	C₂²×C₃₁	1	16	yes	complemented
615	#538	C₂²×C₃₁	1	16	yes	complemented
616	#538	C₂²×C₃₁	1	32	yes	complemented
617	#538	C₂²×C₃₁	1	32	yes	complemented
618	#537	C₂²×C₃₁	1	16	yes	complemented
619	#534	C₂²×C₃₁	1	16	yes	complemented
620	#532	C₂²×C₃₁	1	16	yes	complemented
621	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
623	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#529	C₂²×C₃₁	1	16	yes	complemented
625	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
626	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
627	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
628	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
629	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
630	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
631	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
632	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
633	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
634	C₂×#126	C₂²×C₃₁	1	16	yes	complemented
635	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
637	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
638	C₂×#124	C₂²×C₃₁	1	2	yes	—
639	C₂×#124	C₂²×C₃₁	1	2	yes	—
640	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
642	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
643	C₂×#123	C₂²×C₃₁	1	2	yes	—
644	C₂×#123	C₂²×C₃₁	1	2	yes	—
645	C₂×#123	C₂²×C₃₁	1	2	yes	—
646	C₂×#123	C₂²×C₃₁	1	2	yes	—
647	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
648	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
649	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
650	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
651	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
652	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
653	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
654	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
655	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
657	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
658	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
659	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
660	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
661	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
662	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
663	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
665	C₂×#121	C₂²×C₃₁	1	2	yes	—
666	C₂×#121	C₂²×C₃₁	1	2	yes	—
667	C₂×#121	C₂²×C₃₁	1	2	yes	—
668	C₂×#121	C₂²×C₃₁	1	2	yes	—
669	C₂×#121	C₂²×C₃₁	1	2	yes	—
670	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
672	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
673	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
674	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
675	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
676	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
677	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
678	C₂×#120	C₂²×C₃₁	1	2	yes	—
679	C₂×#120	C₂²×C₃₁	1	2	yes	—
680	C₂×#120	C₂²×C₃₁	1	2	yes	—
681	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
682	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
683	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
686	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
687	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
690	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
691	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
692	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
693	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
694	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
695	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
697	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
701	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
702	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
703	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
704	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
705	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
706	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₂×C₃₁	—	2	4	no	—
708	C₂×C₃₁	—	4	4	no	—
709	C₂×C₃₁	—	4	4	no	—
710	C₂×C₃₁	—	4	4	no	—
711	C₂×C₃₁	—	4	4	no	—
712	C₂×C₃₁	#3560	1	4	yes	direct product factor
713	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
715	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
716	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
717	C₂⁵	C₂³×C₃₁	1	2	yes	—
718	C₂×#41	—	4	8	no	—
719	C₂×#41	—	4	8	no	—
720	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
721	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
722	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
724	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
725	C₂²×D₄	—	4	8	no	—
726	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
727	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
728	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
729	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
730	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
733	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
734	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
735	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
736	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
737	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
738	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
739	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
740	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
741	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
742	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
744	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
746	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
748	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
749	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
750	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
751	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
752	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
753	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
754	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
755	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
756	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
757	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
758	#127	C₂³×C₃₁	1	8	yes	complemented
759	#126	C₂³×C₃₁	1	16	yes	complemented
760	#126	C₂³×C₃₁	1	16	yes	complemented
761	#126	C₂³×C₃₁	1	16	yes	complemented
762	#126	C₂³×C₃₁	1	16	yes	complemented
763	#126	C₂³×C₃₁	1	16	yes	complemented
764	#126	C₂³×C₃₁	1	16	yes	complemented
765	#126	C₂³×C₃₁	1	16	yes	complemented
766	#126	C₂³×C₃₁	1	16	yes	complemented
767	#126	C₂³×C₃₁	1	16	yes	complemented
768	#125	C₂³×C₃₁	1	8	yes	complemented
769	#125	C₂³×C₃₁	1	16	yes	complemented
770	#125	C₂³×C₃₁	1	16	yes	complemented
771	#124	C₂³×C₃₁	1	16	yes	—
772	#124	C₂³×C₃₁	1	16	yes	—
773	#124	C₂³×C₃₁	1	8	yes	complemented
774	#124	C₂³×C₃₁	1	16	yes	complemented
775	#124	C₂³×C₃₁	1	16	yes	complemented
776	#123	C₂³×C₃₁	1	16	yes	—
777	#123	C₂³×C₃₁	1	16	yes	—
778	#123	C₂³×C₃₁	1	16	yes	—
779	#123	C₂³×C₃₁	1	16	yes	—
780	#123	C₂³×C₃₁	1	16	yes	complemented
781	#123	C₂³×C₃₁	1	16	yes	complemented
782	#123	C₂³×C₃₁	1	16	yes	complemented
783	#123	C₂³×C₃₁	1	16	yes	complemented
784	#123	C₂³×C₃₁	1	16	yes	complemented
785	#123	C₂³×C₃₁	1	16	yes	complemented
786	#123	C₂³×C₃₁	1	16	yes	complemented
787	#123	C₂³×C₃₁	1	16	yes	complemented
788	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
789	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
790	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
791	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
792	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
793	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
794	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
795	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
796	#121	C₂³×C₃₁	1	8	yes	—
797	#121	C₂³×C₃₁	1	8	yes	—
798	#121	C₂³×C₃₁	1	16	yes	—
799	#121	C₂³×C₃₁	1	16	yes	—
800	#121	C₂³×C₃₁	1	16	yes	—
801	#121	C₂³×C₃₁	1	16	yes	—
802	#121	C₂³×C₃₁	1	16	yes	—
803	#121	C₂³×C₃₁	1	8	yes	complemented
804	#121	C₂³×C₃₁	1	16	yes	complemented
805	#121	C₂³×C₃₁	1	16	yes	complemented
806	#121	C₂³×C₃₁	1	16	yes	complemented
807	#121	C₂³×C₃₁	1	16	yes	complemented
808	#121	C₂³×C₃₁	1	16	yes	complemented
809	#121	C₂³×C₃₁	1	16	yes	complemented
810	#121	C₂³×C₃₁	1	16	yes	complemented
811	#120	C₂³×C₃₁	1	16	yes	—
812	#120	C₂³×C₃₁	1	16	yes	—
813	#120	C₂³×C₃₁	1	16	yes	—
814	#120	C₂³×C₃₁	1	16	yes	complemented
815	#120	C₂³×C₃₁	1	16	yes	complemented
816	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
817	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
818	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
819	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
820	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
821	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
822	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
823	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
824	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
825	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
826	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
827	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
828	#117	C₂³×C₃₁	1	16	yes	complemented
829	#117	C₂³×C₃₁	1	16	yes	complemented
830	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
847	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
852	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
853	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
854	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
855	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
859	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
861	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
862	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
863	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
865	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
868	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
869	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
870	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
871	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
872	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
873	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
874	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
875	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
876	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
877	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
878	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
879	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
880	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
881	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
882	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
883	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
884	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
885	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
886	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
887	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
888	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
889	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
890	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
891	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
892	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
893	C₃₁	C₂×#3560	1	1	yes	characteristic, direct product factor, Sylow
894	C₂⁴	—	2	4	no	—
895	C₂⁴	—	4	4	no	—
896	C₂⁴	—	4	2	no	—
897	C₂⁴	—	4	2	no	—
898	C₂⁴	—	4	4	no	—
899	C₂⁴	—	4	4	no	—
900	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
901	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
902	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
903	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
904	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
906	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
907	#41	—	4	32	no	—
908	#41	—	4	32	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	4	no	—
911	C₂×Q₈	—	4	4	no	—
912	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
913	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
914	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
915	C₂×D₄	—	2	8	no	—
916	C₂×D₄	—	2	8	no	—
917	C₂×D₄	—	2	8	no	—
918	C₂×D₄	—	4	4	no	—
919	C₂×D₄	—	4	4	no	—
920	C₂×D₄	—	4	4	no	—
921	C₂×D₄	—	4	4	no	—
922	C₂×D₄	—	4	4	no	—
923	C₂×D₄	—	4	4	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	4	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	4	no	—
929	C₂×D₄	—	4	4	no	—
930	C₂×D₄	—	4	32	no	—
931	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
932	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
933	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
934	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
936	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
937	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
938	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
939	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
940	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
941	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
942	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
943	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
944	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
945	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
946	C₂²×C₄	—	2	4	no	—
947	C₂²×C₄	—	2	4	no	—
948	C₂²×C₄	—	4	4	no	—
949	C₂²×C₄	—	4	2	no	—
950	C₂²×C₄	—	4	2	no	—
951	C₂²×C₄	—	4	2	no	—
952	C₂²×C₄	—	4	4	no	—
953	C₂²×C₄	—	4	4	no	—
954	C₂²×C₄	—	4	2	no	—
955	C₂²×C₄	—	4	4	no	—
956	C₂²×C₄	—	4	4	no	—
957	C₂²×C₄	—	4	4	no	—
958	C₂²×C₄	—	4	4	no	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
972	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
973	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
974	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
976	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
977	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
978	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
979	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
980	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
981	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
982	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
983	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
984	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
985	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
986	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
987	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
988	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
989	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
991	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
992	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
994	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
997	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1000	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1001	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1002	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1003	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1004	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1005	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1006	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1007	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
1008	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1009	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1010	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1011	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1012	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1013	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1014	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1015	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1016	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1017	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1018	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1019	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1020	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1021	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1022	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1023	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1024	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1025	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1026	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1027	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1028	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1029	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1031	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1032	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1033	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1034	C₄²	C₂⁴×C₃₁	1	4	yes	—
1035	C₄²	C₂⁴×C₃₁	1	4	yes	—
1036	C₄²	C₂⁴×C₃₁	1	4	yes	—
1037	C₄²	C₂⁴×C₃₁	1	4	yes	—
1038	C₄²	C₂⁴×C₃₁	1	8	yes	—
1039	C₄²	C₂⁴×C₃₁	1	8	yes	—
1040	C₄²	C₂⁴×C₃₁	1	8	yes	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	4	no	—
1044	C₂³	—	2	4	no	—
1045	C₂³	—	2	4	no	—
1046	C₂³	—	2	4	no	—
1047	C₂³	—	2	4	no	—
1048	C₂³	—	2	4	no	—
1049	C₂³	—	2	4	no	—
1050	C₂³	—	2	4	no	—
1051	C₂³	—	2	4	no	—
1052	C₂³	—	2	4	no	—
1053	C₂³	—	2	4	no	—
1054	C₂³	—	2	4	no	—
1055	C₂³	—	2	8	no	—
1056	C₂³	—	4	8	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	4	8	no	—
1060	C₂³	—	4	8	no	—
1061	C₂³	—	8	8	no	—
1062	C₂³	—	8	16	no	—
1063	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
1064	C₂³	C₂⁵×C₃₁	1	4	yes	—
1065	C₂³	C₂⁵×C₃₁	1	4	yes	—
1066	C₂³	C₂⁵×C₃₁	1	4	yes	—
1067	C₂³	C₂⁵×C₃₁	1	4	yes	—
1068	C₂³	C₂⁵×C₃₁	1	2	yes	—
1069	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1070	Q₈	—	4	4	no	—
1071	Q₈	—	4	8	no	—
1072	Q₈	—	4	8	no	—
1073	D₄	—	2	16	no	—
1074	D₄	—	2	16	no	—
1075	D₄	—	2	16	no	—
1076	D₄	—	4	8	no	—
1077	D₄	—	4	8	no	—
1078	D₄	—	4	8	no	—
1079	D₄	—	4	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	8	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	8	no	—
1087	D₄	—	4	8	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	8	no	—
1093	C₂×C₄	—	2	4	no	—
1094	C₂×C₄	—	2	4	no	—
1095	C₂×C₄	—	2	4	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	4	no	—
1098	C₂×C₄	—	2	4	no	—
1099	C₂×C₄	—	2	4	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	4	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	4	8	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	8	no	—
1112	C₂×C₄	—	4	8	no	—
1113	C₂×C₄	—	4	8	no	—
1114	C₂×C₄	—	4	8	no	—
1115	C₂×C₄	—	4	8	no	—
1116	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1117	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1118	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1119	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1120	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1121	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1122	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1123	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1124	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1125	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1126	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1127	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1128	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1129	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	8	no	—
1133	C₂²	—	2	4	no	—
1134	C₂²	—	2	4	no	—
1135	C₂²	—	2	4	no	—
1136	C₂²	—	2	4	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	2	4	no	—
1139	C₂²	—	2	4	no	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	4	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	4	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	4	8	no	—
1146	C₂²	—	4	8	no	—
1147	C₂²	—	4	8	no	—
1148	C₂²	—	4	8	no	—
1149	C₂²	—	8	8	no	—
1150	C₂²	—	8	16	no	—
1151	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
1152	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1153	C₂²	C₃₁×#585	1	2	yes	—
1154	C₂²	C₃₁×#585	1	2	yes	—
1155	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	4	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	4	no	—
1160	C₄	—	2	4	no	—
1161	C₄	—	2	4	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	4	no	—
1164	C₄	—	2	4	no	—
1165	C₄	—	2	4	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	4	no	—
1169	C₄	—	2	2	no	—
1170	C₂	—	2	4	no	—
1171	C₂	—	4	4	no	—
1172	C₂	—	4	4	no	—
1173	C₂	—	4	4	no	—
1174	C₂	—	4	4	no	—
1175	C₂	C₃₁×#3560	1	4	yes	direct product factor
1176	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂	C₂×C₃₁×#585	1	1	yes	characteristic
1178	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×#3560	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#560	C₂	semidirect
4. C₂×C₃₁×#553	C₂	semidirect
5. C₂×C₃₁×#553	C₂	semidirect
6. C₂×C₃₁×#551	C₂	semidirect
7. C₂×C₃₁×#547	C₂	semidirect
8. C₂×C₃₁×#546	C₂	semidirect
9. C₂×C₃₁×#546	C₂	semidirect
10. C₂×C₃₁×#542	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×#538	C₂	semidirect
16. C₂×C₃₁×#537	C₂	semidirect
17. C₂×C₃₁×#534	C₂	semidirect
18. C₂×C₃₁×#532	C₂	semidirect
19. C₂×C₃₁×#529	C₂	semidirect
20. C₂²×C₃₁×#126	C₂	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
24. C₃₁×#563	C₂²	semidirect
25. C₃₁×#560	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
27. C₃₁×#553	C₂²	semidirect
28. C₃₁×#551	C₂²	semidirect
29. C₃₁×#547	C₂²	semidirect
30. C₃₁×#546	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
32. C₃₁×#542	C₂²	semidirect
33. C₃₁×#539	C₂²	semidirect
34. C₃₁×#539	C₂²	semidirect
35. C₃₁×#538	C₂²	semidirect
36. C₃₁×#538	C₂²	semidirect
37. C₃₁×#538	C₂²	semidirect
38. C₃₁×#537	C₂²	semidirect
39. C₃₁×#534	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₃₁×#127	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
45. C₂×C₃₁×#126	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×#126	C₂²	semidirect
51. C₂×C₃₁×#126	C₂²	semidirect
52. C₂×C₃₁×#126	C₂²	semidirect
53. C₂×C₃₁×#126	C₂²	semidirect
54. C₂×C₃₁×#126	C₂²	semidirect
55. C₂×C₃₁×#125	C₂²	semidirect
56. C₂×C₃₁×#125	C₂²	semidirect
57. C₂×C₃₁×#125	C₂²	semidirect
60. C₂×C₃₁×#124	C₂²	semidirect
61. C₂×C₃₁×#124	C₂²	semidirect
62. C₂×C₃₁×#124	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×#123	C₂²	semidirect
72. C₂×C₃₁×#123	C₂²	semidirect
73. C₂×C₃₁×#123	C₂²	semidirect
74. C₂×C₃₁×#123	C₂²	semidirect
75. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
76. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
77. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
78. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
79. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
80. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
81. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
82. C₂×C₃₁×C₂²⋊Q₈	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
101. C₂×C₃₁×#120	C₂²	semidirect
102. C₂×C₃₁×#120	C₂²	semidirect
103. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
104. C₂×C₄×D₄×C₃₁	C₂²	semidirect
105. C₂×C₄×D₄×C₃₁	C₂²	semidirect
106. C₂×C₄×D₄×C₃₁	C₂²	semidirect
107. C₂×C₄×D₄×C₃₁	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×C₃₁×#117	C₂²	semidirect
116. C₂×C₃₁×#117	C₂²	semidirect
117. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
118. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
119. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
120. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
124. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
125. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
126. C₂²×C₄²×C₃₁	C₂²	semidirect
131. C₂×#41×C₃₁	C₂³	semidirect
132. C₂×#41×C₃₁	C₂³	semidirect
167. C₃₁×C₄⋊Q₈	C₂³	semidirect
168. C₃₁×C₄⋊Q₈	C₂³	semidirect
169. C₃₁×#127	C₂³	semidirect
170. C₃₁×#126	C₂³	semidirect
171. C₃₁×#126	C₂³	semidirect
172. C₃₁×#126	C₂³	semidirect
173. C₃₁×#126	C₂³	semidirect
174. C₃₁×#126	C₂³	semidirect
175. C₃₁×#126	C₂³	semidirect
176. C₃₁×#126	C₂³	semidirect
177. C₃₁×#126	C₂³	semidirect
178. C₃₁×#126	C₂³	semidirect
179. C₃₁×#125	C₂³	semidirect
180. C₃₁×#125	C₂³	semidirect
181. C₃₁×#125	C₂³	semidirect
184. C₃₁×#124	C₂³	semidirect
185. C₃₁×#124	C₂³	semidirect
186. C₃₁×#124	C₂³	semidirect
191. C₃₁×#123	C₂³	semidirect
192. C₃₁×#123	C₂³	semidirect
193. C₃₁×#123	C₂³	semidirect
194. C₃₁×#123	C₂³	semidirect
195. C₃₁×#123	C₂³	semidirect
196. C₃₁×#123	C₂³	semidirect
197. C₃₁×#123	C₂³	semidirect
198. C₃₁×#123	C₂³	semidirect
199. C₃₁×C₂²⋊Q₈	C₂³	semidirect
200. C₃₁×C₂²⋊Q₈	C₂³	semidirect
201. C₃₁×C₂²⋊Q₈	C₂³	semidirect
202. C₃₁×C₂²⋊Q₈	C₂³	semidirect
203. C₃₁×C₂²⋊Q₈	C₂³	semidirect
204. C₃₁×C₂²⋊Q₈	C₂³	semidirect
205. C₃₁×C₂²⋊Q₈	C₂³	semidirect
206. C₃₁×C₂²⋊Q₈	C₂³	semidirect
214. C₃₁×#121	C₂³	semidirect
215. C₃₁×#121	C₂³	semidirect
216. C₃₁×#121	C₂³	semidirect
217. C₃₁×#121	C₂³	semidirect
218. C₃₁×#121	C₂³	semidirect
219. C₃₁×#121	C₂³	semidirect
220. C₃₁×#121	C₂³	semidirect
221. C₃₁×#121	C₂³	semidirect
225. C₃₁×#120	C₂³	semidirect
226. C₃₁×#120	C₂³	semidirect
227. C₄×Q₈×C₃₁	C₂³	semidirect
228. C₄×D₄×C₃₁	C₂³	semidirect
229. C₄×D₄×C₃₁	C₂³	semidirect
230. C₄×D₄×C₃₁	C₂³	semidirect
231. C₄×D₄×C₃₁	C₂³	semidirect
232. C₄×D₄×C₃₁	C₂³	semidirect
233. C₄×D₄×C₃₁	C₂³	semidirect
234. C₄×D₄×C₃₁	C₂³	semidirect
235. C₄×D₄×C₃₁	C₂³	semidirect
236. C₄×D₄×C₃₁	C₂³	semidirect
237. C₄×D₄×C₃₁	C₂³	semidirect
238. C₄×D₄×C₃₁	C₂³	semidirect
239. C₃₁×#117	C₂³	semidirect
240. C₃₁×#117	C₂³	semidirect
262. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
263. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
264. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
265. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
294. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
295. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
303. C₂×C₄²×C₃₁	C₂³	semidirect
451. C₂×#3560	C₃₁	direct (N × H)
541. #3560	C₂×C₃₁	direct (N × H)
542. C₂×#563	C₂×C₃₁	semidirect
543. C₂×#560	C₂×C₃₁	semidirect
544. C₂×#553	C₂×C₃₁	semidirect
545. C₂×#553	C₂×C₃₁	semidirect
546. C₂×#551	C₂×C₃₁	semidirect
547. C₂×#547	C₂×C₃₁	semidirect
548. C₂×#546	C₂×C₃₁	semidirect
549. C₂×#546	C₂×C₃₁	semidirect
550. C₂×#542	C₂×C₃₁	semidirect
551. C₂×#539	C₂×C₃₁	semidirect
552. C₂×#539	C₂×C₃₁	semidirect
553. C₂×#538	C₂×C₃₁	semidirect
554. C₂×#538	C₂×C₃₁	semidirect
555. C₂×#538	C₂×C₃₁	semidirect
556. C₂×#537	C₂×C₃₁	semidirect
557. C₂×#534	C₂×C₃₁	semidirect
558. C₂×#532	C₂×C₃₁	semidirect
559. C₂×#529	C₂×C₃₁	semidirect
560. C₂²×#126	C₂×C₃₁	semidirect
601. C₂²×#41	C₂²×C₃₁	semidirect
602. C₂²×#41	C₂²×C₃₁	semidirect
604. #563	C₂²×C₃₁	semidirect
605. #560	C₂²×C₃₁	semidirect
606. #553	C₂²×C₃₁	semidirect
607. #553	C₂²×C₃₁	semidirect
608. #551	C₂²×C₃₁	semidirect
609. #547	C₂²×C₃₁	semidirect
610. #546	C₂²×C₃₁	semidirect
611. #546	C₂²×C₃₁	semidirect
612. #542	C₂²×C₃₁	semidirect
613. #539	C₂²×C₃₁	semidirect
614. #539	C₂²×C₃₁	semidirect
615. #538	C₂²×C₃₁	semidirect
616. #538	C₂²×C₃₁	semidirect
617. #538	C₂²×C₃₁	semidirect
618. #537	C₂²×C₃₁	semidirect
619. #534	C₂²×C₃₁	semidirect
620. #532	C₂²×C₃₁	semidirect
621. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
622. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
623. C₂×#127	C₂²×C₃₁	semidirect
624. #529	C₂²×C₃₁	semidirect
625. C₂×#126	C₂²×C₃₁	semidirect
626. C₂×#126	C₂²×C₃₁	semidirect
627. C₂×#126	C₂²×C₃₁	semidirect
628. C₂×#126	C₂²×C₃₁	semidirect
629. C₂×#126	C₂²×C₃₁	semidirect
630. C₂×#126	C₂²×C₃₁	semidirect
631. C₂×#126	C₂²×C₃₁	semidirect
632. C₂×#126	C₂²×C₃₁	semidirect
633. C₂×#126	C₂²×C₃₁	semidirect
634. C₂×#126	C₂²×C₃₁	semidirect
635. C₂×#125	C₂²×C₃₁	semidirect
636. C₂×#125	C₂²×C₃₁	semidirect
637. C₂×#125	C₂²×C₃₁	semidirect
640. C₂×#124	C₂²×C₃₁	semidirect
641. C₂×#124	C₂²×C₃₁	semidirect
642. C₂×#124	C₂²×C₃₁	semidirect
647. C₂×#123	C₂²×C₃₁	semidirect
648. C₂×#123	C₂²×C₃₁	semidirect
649. C₂×#123	C₂²×C₃₁	semidirect
650. C₂×#123	C₂²×C₃₁	semidirect
651. C₂×#123	C₂²×C₃₁	semidirect
652. C₂×#123	C₂²×C₃₁	semidirect
653. C₂×#123	C₂²×C₃₁	semidirect
654. C₂×#123	C₂²×C₃₁	semidirect
655. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
656. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
657. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
658. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
659. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
660. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
661. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
662. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
670. C₂×#121	C₂²×C₃₁	semidirect
671. C₂×#121	C₂²×C₃₁	semidirect
672. C₂×#121	C₂²×C₃₁	semidirect
673. C₂×#121	C₂²×C₃₁	semidirect
674. C₂×#121	C₂²×C₃₁	semidirect
675. C₂×#121	C₂²×C₃₁	semidirect
676. C₂×#121	C₂²×C₃₁	semidirect
677. C₂×#121	C₂²×C₃₁	semidirect
681. C₂×#120	C₂²×C₃₁	semidirect
682. C₂×#120	C₂²×C₃₁	semidirect
683. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
684. C₂×C₄×D₄	C₂²×C₃₁	semidirect
685. C₂×C₄×D₄	C₂²×C₃₁	semidirect
686. C₂×C₄×D₄	C₂²×C₃₁	semidirect
687. C₂×C₄×D₄	C₂²×C₃₁	semidirect
688. C₂×C₄×D₄	C₂²×C₃₁	semidirect
689. C₂×C₄×D₄	C₂²×C₃₁	semidirect
690. C₂×C₄×D₄	C₂²×C₃₁	semidirect
691. C₂×C₄×D₄	C₂²×C₃₁	semidirect
692. C₂×C₄×D₄	C₂²×C₃₁	semidirect
693. C₂×C₄×D₄	C₂²×C₃₁	semidirect
694. C₂×C₄×D₄	C₂²×C₃₁	semidirect
695. C₂×#117	C₂²×C₃₁	semidirect
696. C₂×#117	C₂²×C₃₁	semidirect
697. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
698. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
699. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
700. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
704. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
705. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
706. C₂²×C₄²	C₂²×C₃₁	semidirect
712. C₂×C₃₁	#3560	direct (N × H)
720. C₂×#41	C₂³×C₃₁	semidirect
721. C₂×#41	C₂³×C₃₁	semidirect
756. C₄⋊Q₈	C₂³×C₃₁	semidirect
757. C₄⋊Q₈	C₂³×C₃₁	semidirect
758. #127	C₂³×C₃₁	semidirect
759. #126	C₂³×C₃₁	semidirect
760. #126	C₂³×C₃₁	semidirect
761. #126	C₂³×C₃₁	semidirect
762. #126	C₂³×C₃₁	semidirect
763. #126	C₂³×C₃₁	semidirect
764. #126	C₂³×C₃₁	semidirect
765. #126	C₂³×C₃₁	semidirect
766. #126	C₂³×C₃₁	semidirect
767. #126	C₂³×C₃₁	semidirect
768. #125	C₂³×C₃₁	semidirect
769. #125	C₂³×C₃₁	semidirect
770. #125	C₂³×C₃₁	semidirect
773. #124	C₂³×C₃₁	semidirect
774. #124	C₂³×C₃₁	semidirect
775. #124	C₂³×C₃₁	semidirect
780. #123	C₂³×C₃₁	semidirect
781. #123	C₂³×C₃₁	semidirect
782. #123	C₂³×C₃₁	semidirect
783. #123	C₂³×C₃₁	semidirect
784. #123	C₂³×C₃₁	semidirect
785. #123	C₂³×C₃₁	semidirect
786. #123	C₂³×C₃₁	semidirect
787. #123	C₂³×C₃₁	semidirect
788. C₂²⋊Q₈	C₂³×C₃₁	semidirect
789. C₂²⋊Q₈	C₂³×C₃₁	semidirect
790. C₂²⋊Q₈	C₂³×C₃₁	semidirect
791. C₂²⋊Q₈	C₂³×C₃₁	semidirect
792. C₂²⋊Q₈	C₂³×C₃₁	semidirect
793. C₂²⋊Q₈	C₂³×C₃₁	semidirect
794. C₂²⋊Q₈	C₂³×C₃₁	semidirect
795. C₂²⋊Q₈	C₂³×C₃₁	semidirect
803. #121	C₂³×C₃₁	semidirect
804. #121	C₂³×C₃₁	semidirect
805. #121	C₂³×C₃₁	semidirect
806. #121	C₂³×C₃₁	semidirect
807. #121	C₂³×C₃₁	semidirect
808. #121	C₂³×C₃₁	semidirect
809. #121	C₂³×C₃₁	semidirect
810. #121	C₂³×C₃₁	semidirect
814. #120	C₂³×C₃₁	semidirect
815. #120	C₂³×C₃₁	semidirect
816. C₄×Q₈	C₂³×C₃₁	semidirect
817. C₄×D₄	C₂³×C₃₁	semidirect
818. C₄×D₄	C₂³×C₃₁	semidirect
819. C₄×D₄	C₂³×C₃₁	semidirect
820. C₄×D₄	C₂³×C₃₁	semidirect
821. C₄×D₄	C₂³×C₃₁	semidirect
822. C₄×D₄	C₂³×C₃₁	semidirect
823. C₄×D₄	C₂³×C₃₁	semidirect
824. C₄×D₄	C₂³×C₃₁	semidirect
825. C₄×D₄	C₂³×C₃₁	semidirect
826. C₄×D₄	C₂³×C₃₁	semidirect
827. C₄×D₄	C₂³×C₃₁	semidirect
828. #117	C₂³×C₃₁	semidirect
829. #117	C₂³×C₃₁	semidirect
851. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
852. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
853. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
854. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
883. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
884. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
892. C₂×C₄²	C₂³×C₃₁	semidirect
893. C₃₁	C₂×#3560	direct (N × H)
1175. C₂	C₃₁×#3560	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×#3560	2
C₂×C₃₁×#563	2
C₂×C₃₁×#560	2
C₂×C₃₁×#553	2
C₂×C₃₁×#551	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×C₃₁×#542	2
C₂×C₃₁×#539	2
C₂×C₃₁×#538	2
C₂×C₃₁×#537	2
C₂×C₃₁×#534	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂²×C₃₁×#126	2
C₂×#3560	31

Subgroups — C2×C31×#3560 #21519494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3560 #21519494