Subgroups — C₂×C₃₁×#3533 #21519485

Order 7936.

7430 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3533	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#547	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#540	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#525	C₂	1	2	yes	maximal, complemented
20	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	2	yes	—
22	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#563	C₂²	1	16	yes	complemented
27	C₃₁×#562	C₂²	1	32	yes	complemented
28	C₃₁×#560	C₂²	1	16	yes	complemented
29	C₃₁×#559	C₂²	1	16	yes	complemented
30	C₃₁×#553	C₂²	1	32	yes	complemented
31	C₃₁×#552	C₂²	1	32	yes	complemented
32	C₃₁×#551	C₂²	1	32	yes	complemented
33	C₃₁×#551	C₂²	1	16	yes	complemented
34	C₃₁×#547	C₂²	1	32	yes	complemented
35	C₃₁×#546	C₂²	1	32	yes	complemented
36	C₃₁×#542	C₂²	1	32	yes	complemented
37	C₃₁×#540	C₂²	1	32	yes	complemented
38	C₃₁×#539	C₂²	1	32	yes	complemented
39	C₃₁×#538	C₂²	1	32	yes	complemented
40	C₃₁×#538	C₂²	1	32	yes	complemented
41	C₃₁×#535	C₂²	1	16	yes	complemented
42	C₃₁×#534	C₂²	1	16	yes	complemented
43	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, 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×#125	C₂²	1	2	yes	complemented
53	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
54	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
55	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
59	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
60	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
61	C₃₁×#525	C₂²	1	32	yes	complemented
62	C₂×C₃₁×#123	C₂²	1	2	yes	—
63	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#123	C₂²	1	2	yes	—
66	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#123	C₂²	1	2	yes	—
68	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
70	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic, 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×#123	C₂²	1	2	yes	complemented
76	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
77	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
78	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
79	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
80	C₂×C₃₁×#123	C₂²	1	16	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×C₂²⋊Q₈	C₂²	1	2	yes	complemented
84	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
85	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
86	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
88	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
89	C₂×C₃₁×#121	C₂²	1	2	yes	—
90	C₂×C₃₁×#121	C₂²	1	2	yes	—
91	C₂×C₃₁×#121	C₂²	1	2	yes	—
92	C₂×C₃₁×#121	C₂²	1	2	yes	—
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	2	yes	complemented
100	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
101	C₂×C₃₁×#120	C₂²	1	2	yes	—
102	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
103	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
104	C₂×C₃₁×#120	C₂²	1	2	yes	—
105	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
106	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
107	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
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×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
117	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
118	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
120	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
121	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
122	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
123	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
124	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
126	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
127	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
128	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
129	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×#41×C₃₁	—	4	8	no	—
131	C₂×#41×C₃₁	—	4	4	no	—
132	C₂×#41×C₃₁	C₂³	1	16	yes	—
133	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
134	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₃₁	—	4	4	no	—
138	C₂²×D₄×C₃₁	—	4	4	no	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
149	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
156	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
157	C₂³×C₄×C₃₁	—	4	4	no	—
158	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
159	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
169	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂³×C₄×C₃₁	C₂³	1	8	yes	complemented
172	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
173	C₃₁×#127	C₂³	1	8	yes	—
174	C₃₁×#127	C₂³	1	8	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×#126	C₂³	1	16	yes	complemented
180	C₃₁×#126	C₂³	1	16	yes	complemented
181	C₃₁×#125	C₂³	1	16	yes	complemented
182	C₃₁×#125	C₂³	1	16	yes	complemented
183	C₃₁×#125	C₂³	1	16	yes	complemented
184	C₃₁×#124	C₂³	1	8	yes	—
185	C₃₁×#124	C₂³	1	8	yes	complemented
186	C₃₁×#124	C₂³	1	16	yes	complemented
187	C₃₁×#124	C₂³	1	16	yes	complemented
188	C₃₁×#124	C₂³	1	16	yes	complemented
189	C₃₁×#124	C₂³	1	16	yes	complemented
190	C₃₁×#123	C₂³	1	16	yes	—
191	C₃₁×#123	C₂³	1	8	yes	—
192	C₃₁×#123	C₂³	1	8	yes	—
193	C₃₁×#123	C₂³	1	16	yes	—
194	C₃₁×#123	C₂³	1	8	yes	—
195	C₃₁×#123	C₂³	1	16	yes	—
196	C₃₁×#123	C₂³	1	8	yes	—
197	C₃₁×#123	C₂³	1	16	yes	complemented
198	C₃₁×#123	C₂³	1	8	yes	complemented
199	C₃₁×#123	C₂³	1	8	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×C₂²⋊Q₈	C₂³	1	16	yes	complemented
209	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
210	C₃₁×C₂²⋊Q₈	C₂³	1	16	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	16	yes	—
217	C₃₁×#121	C₂³	1	16	yes	—
218	C₃₁×#121	C₂³	1	16	yes	—
219	C₃₁×#121	C₂³	1	16	yes	—
220	C₃₁×#121	C₂³	1	16	yes	complemented
221	C₃₁×#121	C₂³	1	16	yes	complemented
222	C₃₁×#121	C₂³	1	16	yes	complemented
223	C₃₁×#121	C₂³	1	16	yes	complemented
224	C₃₁×#121	C₂³	1	16	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×#120	C₂³	1	16	yes	—
229	C₃₁×#120	C₂³	1	8	yes	—
230	C₃₁×#120	C₂³	1	8	yes	—
231	C₃₁×#120	C₂³	1	16	yes	—
232	C₃₁×#120	C₂³	1	16	yes	complemented
233	C₃₁×#120	C₂³	1	16	yes	complemented
234	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
235	C₄×D₄×C₃₁	C₂³	1	16	yes	—
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	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
240	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
241	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
242	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
243	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
244	C₃₁×#117	C₂³	1	16	yes	complemented
245	C₃₁×#117	C₂³	1	8	yes	complemented
246	C₃₁×#117	C₂³	1	16	yes	complemented
247	C₃₁×#117	C₂³	1	16	yes	complemented
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	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	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	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	16	yes	complemented
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
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	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	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	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	8	yes	complemented
299	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
302	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
303	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
304	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
306	C₂⁴×C₃₁	—	2	4	no	—
307	C₂⁴×C₃₁	—	2	4	no	—
308	C₂⁴×C₃₁	—	4	4	no	—
309	C₂⁴×C₃₁	—	4	2	no	—
310	C₂⁴×C₃₁	—	4	4	no	—
311	C₂⁴×C₃₁	—	4	4	no	—
312	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
316	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
318	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
320	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
321	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
322	#41×C₃₁	—	4	32	no	—
323	#41×C₃₁	—	4	16	no	—
324	C₂×Q₈×C₃₁	—	4	4	no	—
325	C₂×Q₈×C₃₁	—	4	4	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
330	C₂×D₄×C₃₁	—	2	8	no	—
331	C₂×D₄×C₃₁	—	2	8	no	—
332	C₂×D₄×C₃₁	—	4	2	no	—
333	C₂×D₄×C₃₁	—	4	2	no	—
334	C₂×D₄×C₃₁	—	4	2	no	—
335	C₂×D₄×C₃₁	—	4	2	no	—
336	C₂×D₄×C₃₁	—	4	16	no	—
337	C₂×D₄×C₃₁	—	4	4	no	—
338	C₂×D₄×C₃₁	—	4	4	no	—
339	C₂×D₄×C₃₁	—	4	4	no	—
340	C₂×D₄×C₃₁	—	4	4	no	—
341	C₂×D₄×C₃₁	—	4	4	no	—
342	C₂×D₄×C₃₁	—	4	4	no	—
343	C₂×D₄×C₃₁	—	4	4	no	—
344	C₂×D₄×C₃₁	—	4	4	no	—
345	C₂×D₄×C₃₁	—	4	4	no	—
346	C₂×D₄×C₃₁	—	4	2	no	—
347	C₂×D₄×C₃₁	—	4	16	no	—
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	8	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	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
357	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
358	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
359	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
360	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
361	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
362	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
363	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₃₁	—	2	8	no	—
365	C₂²×C₄×C₃₁	—	2	4	no	—
366	C₂²×C₄×C₃₁	—	4	2	no	—
367	C₂²×C₄×C₃₁	—	4	4	no	—
368	C₂²×C₄×C₃₁	—	4	2	no	—
369	C₂²×C₄×C₃₁	—	4	16	no	—
370	C₂²×C₄×C₃₁	—	4	4	no	—
371	C₂²×C₄×C₃₁	—	4	4	no	—
372	C₂²×C₄×C₃₁	—	4	4	no	—
373	C₂²×C₄×C₃₁	—	4	4	no	—
374	C₂²×C₄×C₃₁	—	4	2	no	—
375	C₂²×C₄×C₃₁	—	4	4	no	—
376	C₂²×C₄×C₃₁	—	4	4	no	—
377	C₂²×C₄×C₃₁	—	4	4	no	—
378	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
379	C₂²×C₄×C₃₁	C₂⁴	1	4	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	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
399	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
400	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
401	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
402	C₂²×C₄×C₃₁	C₂⁴	1	4	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	8	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	8	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	8	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
419	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
421	C₄⋊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	4	yes	—
426	C₂²⋊C₄×C₃₁	C₂⁴	1	4	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	4	yes	—
433	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
434	C₂²⋊C₄×C₃₁	C₂⁴	1	4	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	C₂²⋊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	C₄²×C₃₁	C₂⁴	1	4	yes	—
450	C₄²×C₃₁	C₂⁴	1	8	yes	—
451	C₄²×C₃₁	C₂⁴	1	8	yes	—
452	C₄²×C₃₁	C₂⁴	1	8	yes	—
453	C₄²×C₃₁	C₂⁴	1	4	yes	—
454	C₄²×C₃₁	C₂⁴	1	8	yes	—
455	C₂×#3533	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂³×C₃₁	—	2	4	no	—
457	C₂³×C₃₁	—	2	4	no	—
458	C₂³×C₃₁	—	2	8	no	—
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	2	2	no	—
461	C₂³×C₃₁	—	2	4	no	—
462	C₂³×C₃₁	—	2	2	no	—
463	C₂³×C₃₁	—	2	2	no	—
464	C₂³×C₃₁	—	2	4	no	—
465	C₂³×C₃₁	—	2	4	no	—
466	C₂³×C₃₁	—	2	4	no	—
467	C₂³×C₃₁	—	2	4	no	—
468	C₂³×C₃₁	—	2	4	no	—
469	C₂³×C₃₁	—	2	4	no	—
470	C₂³×C₃₁	—	2	4	no	—
471	C₂³×C₃₁	—	2	4	no	—
472	C₂³×C₃₁	—	2	8	no	—
473	C₂³×C₃₁	—	4	8	no	—
474	C₂³×C₃₁	—	4	4	no	—
475	C₂³×C₃₁	—	4	8	no	—
476	C₂³×C₃₁	—	4	8	no	—
477	C₂³×C₃₁	—	4	16	no	—
478	C₂³×C₃₁	—	8	8	no	—
479	C₂³×C₃₁	—	8	8	no	—
480	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
481	C₂³×C₃₁	C₂⁵	1	2	yes	—
482	C₂³×C₃₁	C₂⁵	1	2	yes	—
483	C₂³×C₃₁	C₂⁵	1	2	yes	—
484	C₂³×C₃₁	C₂⁵	1	4	yes	—
485	C₂³×C₃₁	C₂⁵	1	2	yes	—
486	C₂³×C₃₁	C₂⁵	1	4	yes	—
487	C₂³×C₃₁	C₂⁵	1	2	yes	—
488	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
489	Q₈×C₃₁	—	4	8	no	—
490	Q₈×C₃₁	—	4	8	no	—
491	Q₈×C₃₁	—	4	4	no	—
492	D₄×C₃₁	—	2	16	no	—
493	D₄×C₃₁	—	2	16	no	—
494	D₄×C₃₁	—	4	4	no	—
495	D₄×C₃₁	—	4	4	no	—
496	D₄×C₃₁	—	4	4	no	—
497	D₄×C₃₁	—	4	4	no	—
498	D₄×C₃₁	—	4	8	no	—
499	D₄×C₃₁	—	4	8	no	—
500	D₄×C₃₁	—	4	8	no	—
501	D₄×C₃₁	—	4	8	no	—
502	D₄×C₃₁	—	4	8	no	—
503	D₄×C₃₁	—	4	8	no	—
504	D₄×C₃₁	—	4	8	no	—
505	D₄×C₃₁	—	4	8	no	—
506	D₄×C₃₁	—	4	8	no	—
507	D₄×C₃₁	—	4	4	no	—
508	C₂×C₄×C₃₁	—	2	4	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	4	no	—
511	C₂×C₄×C₃₁	—	2	16	no	—
512	C₂×C₄×C₃₁	—	2	2	no	—
513	C₂×C₄×C₃₁	—	2	8	no	—
514	C₂×C₄×C₃₁	—	2	4	no	—
515	C₂×C₄×C₃₁	—	2	4	no	—
516	C₂×C₄×C₃₁	—	2	4	no	—
517	C₂×C₄×C₃₁	—	2	4	no	—
518	C₂×C₄×C₃₁	—	2	4	no	—
519	C₂×C₄×C₃₁	—	2	4	no	—
520	C₂×C₄×C₃₁	—	2	4	no	—
521	C₂×C₄×C₃₁	—	2	4	no	—
522	C₂×C₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	4	8	no	—
524	C₂×C₄×C₃₁	—	4	4	no	—
525	C₂×C₄×C₃₁	—	4	8	no	—
526	C₂×C₄×C₃₁	—	4	8	no	—
527	C₂×C₄×C₃₁	—	4	8	no	—
528	C₂×C₄×C₃₁	—	4	8	no	—
529	C₂×C₄×C₃₁	—	4	4	no	—
530	C₂×C₄×C₃₁	—	4	8	no	—
531	C₂×C₄×C₃₁	—	4	8	no	—
532	C₂×C₄×C₃₁	—	4	8	no	—
533	C₂×C₄×C₃₁	C₂⁵	1	4	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	2	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	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
542	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
543	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
544	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
545	#3533	C₂×C₃₁	1	32	yes	direct product factor
546	C₂×#563	C₂×C₃₁	1	1	yes	characteristic, complemented
547	C₂×#562	C₂×C₃₁	1	2	yes	complemented
548	C₂×#560	C₂×C₃₁	1	1	yes	characteristic, complemented
549	C₂×#559	C₂×C₃₁	1	1	yes	characteristic, complemented
550	C₂×#553	C₂×C₃₁	1	2	yes	complemented
551	C₂×#552	C₂×C₃₁	1	2	yes	complemented
552	C₂×#551	C₂×C₃₁	1	2	yes	complemented
553	C₂×#551	C₂×C₃₁	1	1	yes	characteristic, complemented
554	C₂×#547	C₂×C₃₁	1	2	yes	complemented
555	C₂×#546	C₂×C₃₁	1	2	yes	complemented
556	C₂×#542	C₂×C₃₁	1	2	yes	complemented
557	C₂×#540	C₂×C₃₁	1	2	yes	complemented
558	C₂×#539	C₂×C₃₁	1	2	yes	complemented
559	C₂×#538	C₂×C₃₁	1	2	yes	complemented
560	C₂×#538	C₂×C₃₁	1	2	yes	complemented
561	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
562	C₂×#534	C₂×C₃₁	1	1	yes	characteristic, complemented
563	C₂×#525	C₂×C₃₁	1	2	yes	complemented
564	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
565	C₂²×C₃₁	—	2	4	no	—
566	C₂²×C₃₁	—	2	8	no	—
567	C₂²×C₃₁	—	2	4	no	—
568	C₂²×C₃₁	—	2	2	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	2	4	no	—
571	C₂²×C₃₁	—	2	2	no	—
572	C₂²×C₃₁	—	2	2	no	—
573	C₂²×C₃₁	—	2	4	no	—
574	C₂²×C₃₁	—	2	4	no	—
575	C₂²×C₃₁	—	2	4	no	—
576	C₂²×C₃₁	—	2	4	no	—
577	C₂²×C₃₁	—	2	4	no	—
578	C₂²×C₃₁	—	2	4	no	—
579	C₂²×C₃₁	—	2	4	no	—
580	C₂²×C₃₁	—	2	4	no	—
581	C₂²×C₃₁	—	4	16	no	—
582	C₂²×C₃₁	—	4	8	no	—
583	C₂²×C₃₁	—	4	4	no	—
584	C₂²×C₃₁	—	4	4	no	—
585	C₂²×C₃₁	—	4	8	no	—
586	C₂²×C₃₁	—	4	4	no	—
587	C₂²×C₃₁	—	4	4	no	—
588	C₂²×C₃₁	—	8	8	no	—
589	C₂²×C₃₁	—	8	8	no	—
590	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
591	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
592	C₂²×C₃₁	#585	1	4	yes	—
593	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
594	C₄×C₃₁	—	2	4	no	—
595	C₄×C₃₁	—	2	2	no	—
596	C₄×C₃₁	—	2	4	no	—
597	C₄×C₃₁	—	2	2	no	—
598	C₄×C₃₁	—	2	4	no	—
599	C₄×C₃₁	—	2	4	no	—
600	C₄×C₃₁	—	2	4	no	—
601	C₄×C₃₁	—	2	4	no	—
602	C₄×C₃₁	—	2	4	no	—
603	C₄×C₃₁	—	2	4	no	—
604	C₄×C₃₁	—	2	4	no	—
605	C₄×C₃₁	—	2	4	no	—
606	C₂²×#41	C₂²×C₃₁	1	2	yes	—
607	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
609	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
610	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#563	C₂²×C₃₁	1	16	yes	complemented
612	#562	C₂²×C₃₁	1	32	yes	complemented
613	#560	C₂²×C₃₁	1	16	yes	complemented
614	#559	C₂²×C₃₁	1	16	yes	complemented
615	#553	C₂²×C₃₁	1	32	yes	complemented
616	#552	C₂²×C₃₁	1	32	yes	complemented
617	#551	C₂²×C₃₁	1	32	yes	complemented
618	#551	C₂²×C₃₁	1	16	yes	complemented
619	#547	C₂²×C₃₁	1	32	yes	complemented
620	#546	C₂²×C₃₁	1	32	yes	complemented
621	#542	C₂²×C₃₁	1	32	yes	complemented
622	#540	C₂²×C₃₁	1	32	yes	complemented
623	#539	C₂²×C₃₁	1	32	yes	complemented
624	#538	C₂²×C₃₁	1	32	yes	complemented
625	#538	C₂²×C₃₁	1	32	yes	complemented
626	#535	C₂²×C₃₁	1	16	yes	complemented
627	#534	C₂²×C₃₁	1	16	yes	complemented
628	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
629	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
630	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, 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	2	yes	complemented
635	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
636	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
637	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
638	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
639	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
640	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
641	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
643	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
644	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
645	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
646	#525	C₂²×C₃₁	1	32	yes	complemented
647	C₂×#123	C₂²×C₃₁	1	2	yes	—
648	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
650	C₂×#123	C₂²×C₃₁	1	2	yes	—
651	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
652	C₂×#123	C₂²×C₃₁	1	2	yes	—
653	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
655	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
658	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
659	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
660	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
661	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
662	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
663	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
664	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
665	C₂×#123	C₂²×C₃₁	1	16	yes	complemented
666	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
667	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
668	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
669	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
670	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
671	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
672	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
673	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
674	C₂×#121	C₂²×C₃₁	1	2	yes	—
675	C₂×#121	C₂²×C₃₁	1	2	yes	—
676	C₂×#121	C₂²×C₃₁	1	2	yes	—
677	C₂×#121	C₂²×C₃₁	1	2	yes	—
678	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
679	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
680	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
681	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
682	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
683	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
684	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
685	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
686	C₂×#120	C₂²×C₃₁	1	2	yes	—
687	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
688	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
689	C₂×#120	C₂²×C₃₁	1	2	yes	—
690	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
691	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
692	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
693	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
694	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
695	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
696	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
697	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
698	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
699	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
700	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
701	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
702	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
703	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
705	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
706	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
707	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
708	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
709	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
710	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
712	C₂×C₃₁	—	2	4	no	—
713	C₂×C₃₁	—	4	4	no	—
714	C₂×C₃₁	—	4	2	no	—
715	C₂×C₃₁	—	4	2	no	—
716	C₂×C₃₁	—	4	4	no	—
717	C₂×C₃₁	—	4	2	no	—
718	C₂×C₃₁	—	4	2	no	—
719	C₂×C₃₁	#3533	1	4	yes	direct product factor
720	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×C₃₁	C₂×#585	1	2	yes	—
722	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
723	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
724	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×#41	—	4	8	no	—
726	C₂×#41	—	4	4	no	—
727	C₂×#41	C₂³×C₃₁	1	16	yes	—
728	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
729	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
730	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
731	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₂²×D₄	—	4	4	no	—
733	C₂²×D₄	—	4	4	no	—
734	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
735	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
736	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
742	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
743	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
746	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
748	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
750	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
751	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
752	C₂³×C₄	—	4	4	no	—
753	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
754	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
755	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
756	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
757	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
758	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
759	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
760	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
761	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
762	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
764	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
765	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
766	C₂³×C₄	C₂³×C₃₁	1	8	yes	complemented
767	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
768	#127	C₂³×C₃₁	1	8	yes	—
769	#127	C₂³×C₃₁	1	8	yes	complemented
770	#126	C₂³×C₃₁	1	16	yes	complemented
771	#126	C₂³×C₃₁	1	16	yes	complemented
772	#126	C₂³×C₃₁	1	16	yes	complemented
773	#126	C₂³×C₃₁	1	16	yes	complemented
774	#126	C₂³×C₃₁	1	16	yes	complemented
775	#126	C₂³×C₃₁	1	16	yes	complemented
776	#125	C₂³×C₃₁	1	16	yes	complemented
777	#125	C₂³×C₃₁	1	16	yes	complemented
778	#125	C₂³×C₃₁	1	16	yes	complemented
779	#124	C₂³×C₃₁	1	8	yes	—
780	#124	C₂³×C₃₁	1	8	yes	complemented
781	#124	C₂³×C₃₁	1	16	yes	complemented
782	#124	C₂³×C₃₁	1	16	yes	complemented
783	#124	C₂³×C₃₁	1	16	yes	complemented
784	#124	C₂³×C₃₁	1	16	yes	complemented
785	#123	C₂³×C₃₁	1	16	yes	—
786	#123	C₂³×C₃₁	1	8	yes	—
787	#123	C₂³×C₃₁	1	8	yes	—
788	#123	C₂³×C₃₁	1	16	yes	—
789	#123	C₂³×C₃₁	1	8	yes	—
790	#123	C₂³×C₃₁	1	16	yes	—
791	#123	C₂³×C₃₁	1	8	yes	—
792	#123	C₂³×C₃₁	1	16	yes	complemented
793	#123	C₂³×C₃₁	1	8	yes	complemented
794	#123	C₂³×C₃₁	1	8	yes	complemented
795	#123	C₂³×C₃₁	1	16	yes	complemented
796	#123	C₂³×C₃₁	1	16	yes	complemented
797	#123	C₂³×C₃₁	1	16	yes	complemented
798	#123	C₂³×C₃₁	1	16	yes	complemented
799	#123	C₂³×C₃₁	1	16	yes	complemented
800	#123	C₂³×C₃₁	1	16	yes	complemented
801	#123	C₂³×C₃₁	1	16	yes	complemented
802	#123	C₂³×C₃₁	1	16	yes	complemented
803	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
804	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
805	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
806	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
807	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
808	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
809	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
810	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
811	#121	C₂³×C₃₁	1	16	yes	—
812	#121	C₂³×C₃₁	1	16	yes	—
813	#121	C₂³×C₃₁	1	16	yes	—
814	#121	C₂³×C₃₁	1	16	yes	—
815	#121	C₂³×C₃₁	1	16	yes	complemented
816	#121	C₂³×C₃₁	1	16	yes	complemented
817	#121	C₂³×C₃₁	1	16	yes	complemented
818	#121	C₂³×C₃₁	1	16	yes	complemented
819	#121	C₂³×C₃₁	1	16	yes	complemented
820	#121	C₂³×C₃₁	1	16	yes	complemented
821	#121	C₂³×C₃₁	1	16	yes	complemented
822	#121	C₂³×C₃₁	1	16	yes	complemented
823	#120	C₂³×C₃₁	1	16	yes	—
824	#120	C₂³×C₃₁	1	8	yes	—
825	#120	C₂³×C₃₁	1	8	yes	—
826	#120	C₂³×C₃₁	1	16	yes	—
827	#120	C₂³×C₃₁	1	16	yes	complemented
828	#120	C₂³×C₃₁	1	16	yes	complemented
829	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
830	C₄×D₄	C₂³×C₃₁	1	16	yes	—
831	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
832	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
833	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
834	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
835	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
836	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
837	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
838	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
839	#117	C₂³×C₃₁	1	16	yes	complemented
840	#117	C₂³×C₃₁	1	8	yes	complemented
841	#117	C₂³×C₃₁	1	16	yes	complemented
842	#117	C₂³×C₃₁	1	16	yes	complemented
843	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
844	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
849	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
850	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
852	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
853	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
855	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
856	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
857	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
858	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
859	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
861	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
862	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
863	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
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	1	yes	characteristic
868	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	16	yes	—
872	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	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	1	yes	characteristic
877	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
878	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
884	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
885	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
886	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
887	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
888	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
889	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
890	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
891	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
892	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
893	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
894	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
895	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
896	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
897	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
898	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
899	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
900	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
901	C₃₁	C₂×#3533	1	1	yes	characteristic, direct product factor, Sylow
902	C₂⁴	—	2	4	no	—
903	C₂⁴	—	2	4	no	—
904	C₂⁴	—	4	4	no	—
905	C₂⁴	—	4	2	no	—
906	C₂⁴	—	4	4	no	—
907	C₂⁴	—	4	4	no	—
908	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
912	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
914	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
916	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
917	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
918	#41	—	4	32	no	—
919	#41	—	4	16	no	—
920	C₂×Q₈	—	4	4	no	—
921	C₂×Q₈	—	4	4	no	—
922	C₂×Q₈	—	4	2	no	—
923	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
924	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
925	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
926	C₂×D₄	—	2	8	no	—
927	C₂×D₄	—	2	8	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	4	16	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	4	4	no	—
935	C₂×D₄	—	4	4	no	—
936	C₂×D₄	—	4	4	no	—
937	C₂×D₄	—	4	4	no	—
938	C₂×D₄	—	4	4	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	—	4	4	no	—
941	C₂×D₄	—	4	4	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	4	16	no	—
944	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
945	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
946	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
947	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
948	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
949	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
950	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
951	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
952	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
953	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
954	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
955	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
956	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
957	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
958	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
959	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
960	C₂²×C₄	—	2	8	no	—
961	C₂²×C₄	—	2	4	no	—
962	C₂²×C₄	—	4	2	no	—
963	C₂²×C₄	—	4	4	no	—
964	C₂²×C₄	—	4	2	no	—
965	C₂²×C₄	—	4	16	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	—	4	4	no	—
968	C₂²×C₄	—	4	4	no	—
969	C₂²×C₄	—	4	4	no	—
970	C₂²×C₄	—	4	2	no	—
971	C₂²×C₄	—	4	4	no	—
972	C₂²×C₄	—	4	4	no	—
973	C₂²×C₄	—	4	4	no	—
974	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
976	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
978	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
981	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
982	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
984	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
985	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
987	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
988	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
989	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
990	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
991	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
992	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
993	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
994	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
995	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
996	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
997	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
998	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1000	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1001	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1002	C₄⋊C₄	C₂⁴×C₃₁	1	8	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	8	yes	—
1007	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1008	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1009	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1010	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1011	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1012	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1013	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1014	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1015	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1016	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1017	C₄⋊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	4	yes	—
1022	C₂²⋊C₄	C₂⁴×C₃₁	1	4	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	4	yes	—
1029	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₃₁	1	4	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	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1035	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1036	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1037	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1038	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1039	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1040	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1041	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1042	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1043	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1044	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
1045	C₄²	C₂⁴×C₃₁	1	4	yes	—
1046	C₄²	C₂⁴×C₃₁	1	8	yes	—
1047	C₄²	C₂⁴×C₃₁	1	8	yes	—
1048	C₄²	C₂⁴×C₃₁	1	8	yes	—
1049	C₄²	C₂⁴×C₃₁	1	4	yes	—
1050	C₄²	C₂⁴×C₃₁	1	8	yes	—
1051	C₂³	—	2	4	no	—
1052	C₂³	—	2	4	no	—
1053	C₂³	—	2	8	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	4	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	4	no	—
1061	C₂³	—	2	4	no	—
1062	C₂³	—	2	4	no	—
1063	C₂³	—	2	4	no	—
1064	C₂³	—	2	4	no	—
1065	C₂³	—	2	4	no	—
1066	C₂³	—	2	4	no	—
1067	C₂³	—	2	8	no	—
1068	C₂³	—	4	8	no	—
1069	C₂³	—	4	4	no	—
1070	C₂³	—	4	8	no	—
1071	C₂³	—	4	8	no	—
1072	C₂³	—	4	16	no	—
1073	C₂³	—	8	8	no	—
1074	C₂³	—	8	8	no	—
1075	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
1076	C₂³	C₂⁵×C₃₁	1	2	yes	—
1077	C₂³	C₂⁵×C₃₁	1	2	yes	—
1078	C₂³	C₂⁵×C₃₁	1	2	yes	—
1079	C₂³	C₂⁵×C₃₁	1	4	yes	—
1080	C₂³	C₂⁵×C₃₁	1	2	yes	—
1081	C₂³	C₂⁵×C₃₁	1	4	yes	—
1082	C₂³	C₂⁵×C₃₁	1	2	yes	—
1083	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1084	Q₈	—	4	8	no	—
1085	Q₈	—	4	8	no	—
1086	Q₈	—	4	4	no	—
1087	D₄	—	2	16	no	—
1088	D₄	—	2	16	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	8	no	—
1094	D₄	—	4	8	no	—
1095	D₄	—	4	8	no	—
1096	D₄	—	4	8	no	—
1097	D₄	—	4	8	no	—
1098	D₄	—	4	8	no	—
1099	D₄	—	4	8	no	—
1100	D₄	—	4	8	no	—
1101	D₄	—	4	8	no	—
1102	D₄	—	4	4	no	—
1103	C₂×C₄	—	2	4	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	4	no	—
1106	C₂×C₄	—	2	16	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	8	no	—
1109	C₂×C₄	—	2	4	no	—
1110	C₂×C₄	—	2	4	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	4	no	—
1113	C₂×C₄	—	2	4	no	—
1114	C₂×C₄	—	2	4	no	—
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	4	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	8	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	8	no	—
1121	C₂×C₄	—	4	8	no	—
1122	C₂×C₄	—	4	8	no	—
1123	C₂×C₄	—	4	8	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	8	no	—
1126	C₂×C₄	—	4	8	no	—
1127	C₂×C₄	—	4	8	no	—
1128	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1129	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1130	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1131	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1132	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1133	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1134	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1135	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1136	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1137	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1138	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
1139	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	8	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	4	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	2	4	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	4	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	4	no	—
1155	C₂²	—	2	4	no	—
1156	C₂²	—	4	16	no	—
1157	C₂²	—	4	4	no	—
1158	C₂²	—	4	4	no	—
1159	C₂²	—	4	4	no	—
1160	C₂²	—	4	8	no	—
1161	C₂²	—	4	4	no	—
1162	C₂²	—	4	8	no	—
1163	C₂²	—	8	8	no	—
1164	C₂²	—	8	8	no	—
1165	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
1166	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1167	C₂²	C₃₁×#585	1	4	yes	—
1168	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
1169	C₄	—	2	4	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	4	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	2	4	no	—
1174	C₄	—	2	4	no	—
1175	C₄	—	2	4	no	—
1176	C₄	—	2	4	no	—
1177	C₄	—	2	4	no	—
1178	C₄	—	2	4	no	—
1179	C₄	—	2	4	no	—
1180	C₄	—	2	4	no	—
1181	C₂	—	2	4	no	—
1182	C₂	—	4	2	no	—
1183	C₂	—	4	2	no	—
1184	C₂	—	4	2	no	—
1185	C₂	—	4	4	no	—
1186	C₂	—	4	2	no	—
1187	C₂	—	4	4	no	—
1188	C₂	C₃₁×#3533	1	4	yes	direct product factor
1189	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂	C₂×C₃₁×#585	1	2	yes	—

	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×#3533	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#562	C₂	semidirect
4. C₂×C₃₁×#560	C₂	semidirect
5. C₂×C₃₁×#559	C₂	semidirect
6. C₂×C₃₁×#553	C₂	semidirect
7. C₂×C₃₁×#552	C₂	semidirect
8. C₂×C₃₁×#551	C₂	semidirect
9. C₂×C₃₁×#551	C₂	semidirect
10. C₂×C₃₁×#547	C₂	semidirect
11. C₂×C₃₁×#546	C₂	semidirect
12. C₂×C₃₁×#542	C₂	semidirect
13. C₂×C₃₁×#540	C₂	semidirect
14. C₂×C₃₁×#539	C₂	semidirect
15. C₂×C₃₁×#538	C₂	semidirect
16. C₂×C₃₁×#538	C₂	semidirect
17. C₂×C₃₁×#535	C₂	semidirect
18. C₂×C₃₁×#534	C₂	semidirect
19. C₂×C₃₁×#525	C₂	semidirect
20. C₂²×C₃₁×#123	C₂	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
25. C₂⁴×C₄×C₃₁	C₂²	semidirect
26. C₃₁×#563	C₂²	semidirect
27. C₃₁×#562	C₂²	semidirect
28. C₃₁×#560	C₂²	semidirect
29. C₃₁×#559	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
32. C₃₁×#551	C₂²	semidirect
33. C₃₁×#551	C₂²	semidirect
34. C₃₁×#547	C₂²	semidirect
35. C₃₁×#546	C₂²	semidirect
36. C₃₁×#542	C₂²	semidirect
37. C₃₁×#540	C₂²	semidirect
38. C₃₁×#539	C₂²	semidirect
39. C₃₁×#538	C₂²	semidirect
40. C₃₁×#538	C₂²	semidirect
41. C₃₁×#535	C₂²	semidirect
42. C₃₁×#534	C₂²	semidirect
43. C₂×C₃₁×C₄⋊Q₈	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×#126	C₂²	semidirect
51. C₂×C₃₁×#126	C₂²	semidirect
52. C₂×C₃₁×#125	C₂²	semidirect
53. C₂×C₃₁×#125	C₂²	semidirect
54. C₂×C₃₁×#125	C₂²	semidirect
56. C₂×C₃₁×#124	C₂²	semidirect
57. C₂×C₃₁×#124	C₂²	semidirect
58. C₂×C₃₁×#124	C₂²	semidirect
59. C₂×C₃₁×#124	C₂²	semidirect
60. C₂×C₃₁×#124	C₂²	semidirect
61. C₃₁×#525	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×#123	C₂²	semidirect
76. C₂×C₃₁×#123	C₂²	semidirect
77. C₂×C₃₁×#123	C₂²	semidirect
78. C₂×C₃₁×#123	C₂²	semidirect
79. C₂×C₃₁×#123	C₂²	semidirect
80. C₂×C₃₁×#123	C₂²	semidirect
81. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
82. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
83. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
84. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
85. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₃₁×C₂²⋊Q₈	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
100. C₂×C₃₁×#121	C₂²	semidirect
105. C₂×C₃₁×#120	C₂²	semidirect
106. C₂×C₃₁×#120	C₂²	semidirect
107. C₂×C₄×Q₈×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×C₄×D₄×C₃₁	C₂²	semidirect
117. C₂×C₃₁×#117	C₂²	semidirect
118. C₂×C₃₁×#117	C₂²	semidirect
119. C₂×C₃₁×#117	C₂²	semidirect
120. C₂×C₃₁×#117	C₂²	semidirect
121. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
122. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
125. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
133. C₂×#41×C₃₁	C₂³	semidirect
171. C₂³×C₄×C₃₁	C₂³	semidirect
172. C₃₁×C₄⋊Q₈	C₂³	semidirect
174. C₃₁×#127	C₂³	semidirect
175. C₃₁×#126	C₂³	semidirect
176. C₃₁×#126	C₂³	semidirect
177. C₃₁×#126	C₂³	semidirect
178. C₃₁×#126	C₂³	semidirect
179. C₃₁×#126	C₂³	semidirect
180. C₃₁×#126	C₂³	semidirect
181. C₃₁×#125	C₂³	semidirect
182. C₃₁×#125	C₂³	semidirect
183. C₃₁×#125	C₂³	semidirect
185. C₃₁×#124	C₂³	semidirect
186. C₃₁×#124	C₂³	semidirect
187. C₃₁×#124	C₂³	semidirect
188. C₃₁×#124	C₂³	semidirect
189. C₃₁×#124	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×C₂²⋊Q₈	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
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
232. C₃₁×#120	C₂³	semidirect
233. C₃₁×#120	C₂³	semidirect
234. C₄×Q₈×C₃₁	C₂³	semidirect
236. C₄×D₄×C₃₁	C₂³	semidirect
237. C₄×D₄×C₃₁	C₂³	semidirect
238. C₄×D₄×C₃₁	C₂³	semidirect
239. C₄×D₄×C₃₁	C₂³	semidirect
240. C₄×D₄×C₃₁	C₂³	semidirect
241. C₄×D₄×C₃₁	C₂³	semidirect
242. C₄×D₄×C₃₁	C₂³	semidirect
243. C₄×D₄×C₃₁	C₂³	semidirect
244. C₃₁×#117	C₂³	semidirect
245. C₃₁×#117	C₂³	semidirect
246. C₃₁×#117	C₂³	semidirect
247. C₃₁×#117	C₂³	semidirect
267. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
268. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
298. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
299. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
455. C₂×#3533	C₃₁	direct (N × H)
545. #3533	C₂×C₃₁	direct (N × H)
546. C₂×#563	C₂×C₃₁	semidirect
547. C₂×#562	C₂×C₃₁	semidirect
548. C₂×#560	C₂×C₃₁	semidirect
549. C₂×#559	C₂×C₃₁	semidirect
550. C₂×#553	C₂×C₃₁	semidirect
551. C₂×#552	C₂×C₃₁	semidirect
552. C₂×#551	C₂×C₃₁	semidirect
553. C₂×#551	C₂×C₃₁	semidirect
554. C₂×#547	C₂×C₃₁	semidirect
555. C₂×#546	C₂×C₃₁	semidirect
556. C₂×#542	C₂×C₃₁	semidirect
557. C₂×#540	C₂×C₃₁	semidirect
558. C₂×#539	C₂×C₃₁	semidirect
559. C₂×#538	C₂×C₃₁	semidirect
560. C₂×#538	C₂×C₃₁	semidirect
561. C₂×#535	C₂×C₃₁	semidirect
562. C₂×#534	C₂×C₃₁	semidirect
563. C₂×#525	C₂×C₃₁	semidirect
564. C₂²×#123	C₂×C₃₁	semidirect
607. C₂²×#41	C₂²×C₃₁	semidirect
610. C₂⁴×C₄	C₂²×C₃₁	semidirect
611. #563	C₂²×C₃₁	semidirect
612. #562	C₂²×C₃₁	semidirect
613. #560	C₂²×C₃₁	semidirect
614. #559	C₂²×C₃₁	semidirect
615. #553	C₂²×C₃₁	semidirect
616. #552	C₂²×C₃₁	semidirect
617. #551	C₂²×C₃₁	semidirect
618. #551	C₂²×C₃₁	semidirect
619. #547	C₂²×C₃₁	semidirect
620. #546	C₂²×C₃₁	semidirect
621. #542	C₂²×C₃₁	semidirect
622. #540	C₂²×C₃₁	semidirect
623. #539	C₂²×C₃₁	semidirect
624. #538	C₂²×C₃₁	semidirect
625. #538	C₂²×C₃₁	semidirect
626. #535	C₂²×C₃₁	semidirect
627. #534	C₂²×C₃₁	semidirect
628. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
630. C₂×#127	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×#126	C₂²×C₃₁	semidirect
636. C₂×#126	C₂²×C₃₁	semidirect
637. C₂×#125	C₂²×C₃₁	semidirect
638. C₂×#125	C₂²×C₃₁	semidirect
639. C₂×#125	C₂²×C₃₁	semidirect
641. C₂×#124	C₂²×C₃₁	semidirect
642. C₂×#124	C₂²×C₃₁	semidirect
643. C₂×#124	C₂²×C₃₁	semidirect
644. C₂×#124	C₂²×C₃₁	semidirect
645. C₂×#124	C₂²×C₃₁	semidirect
646. #525	C₂²×C₃₁	semidirect
654. C₂×#123	C₂²×C₃₁	semidirect
655. C₂×#123	C₂²×C₃₁	semidirect
656. C₂×#123	C₂²×C₃₁	semidirect
657. C₂×#123	C₂²×C₃₁	semidirect
658. C₂×#123	C₂²×C₃₁	semidirect
659. C₂×#123	C₂²×C₃₁	semidirect
660. C₂×#123	C₂²×C₃₁	semidirect
661. C₂×#123	C₂²×C₃₁	semidirect
662. C₂×#123	C₂²×C₃₁	semidirect
663. C₂×#123	C₂²×C₃₁	semidirect
664. C₂×#123	C₂²×C₃₁	semidirect
665. C₂×#123	C₂²×C₃₁	semidirect
666. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
667. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
668. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
669. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
670. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
671. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
672. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
673. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
678. C₂×#121	C₂²×C₃₁	semidirect
679. C₂×#121	C₂²×C₃₁	semidirect
680. C₂×#121	C₂²×C₃₁	semidirect
681. C₂×#121	C₂²×C₃₁	semidirect
682. C₂×#121	C₂²×C₃₁	semidirect
683. C₂×#121	C₂²×C₃₁	semidirect
684. C₂×#121	C₂²×C₃₁	semidirect
685. C₂×#121	C₂²×C₃₁	semidirect
690. C₂×#120	C₂²×C₃₁	semidirect
691. C₂×#120	C₂²×C₃₁	semidirect
692. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
694. C₂×C₄×D₄	C₂²×C₃₁	semidirect
695. C₂×C₄×D₄	C₂²×C₃₁	semidirect
696. C₂×C₄×D₄	C₂²×C₃₁	semidirect
697. C₂×C₄×D₄	C₂²×C₃₁	semidirect
698. C₂×C₄×D₄	C₂²×C₃₁	semidirect
699. C₂×C₄×D₄	C₂²×C₃₁	semidirect
700. C₂×C₄×D₄	C₂²×C₃₁	semidirect
701. C₂×C₄×D₄	C₂²×C₃₁	semidirect
702. C₂×#117	C₂²×C₃₁	semidirect
703. C₂×#117	C₂²×C₃₁	semidirect
704. C₂×#117	C₂²×C₃₁	semidirect
705. C₂×#117	C₂²×C₃₁	semidirect
706. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
707. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
710. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
711. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
719. C₂×C₃₁	#3533	direct (N × H)
728. C₂×#41	C₂³×C₃₁	semidirect
766. C₂³×C₄	C₂³×C₃₁	semidirect
767. C₄⋊Q₈	C₂³×C₃₁	semidirect
769. #127	C₂³×C₃₁	semidirect
770. #126	C₂³×C₃₁	semidirect
771. #126	C₂³×C₃₁	semidirect
772. #126	C₂³×C₃₁	semidirect
773. #126	C₂³×C₃₁	semidirect
774. #126	C₂³×C₃₁	semidirect
775. #126	C₂³×C₃₁	semidirect
776. #125	C₂³×C₃₁	semidirect
777. #125	C₂³×C₃₁	semidirect
778. #125	C₂³×C₃₁	semidirect
780. #124	C₂³×C₃₁	semidirect
781. #124	C₂³×C₃₁	semidirect
782. #124	C₂³×C₃₁	semidirect
783. #124	C₂³×C₃₁	semidirect
784. #124	C₂³×C₃₁	semidirect
792. #123	C₂³×C₃₁	semidirect
793. #123	C₂³×C₃₁	semidirect
794. #123	C₂³×C₃₁	semidirect
795. #123	C₂³×C₃₁	semidirect
796. #123	C₂³×C₃₁	semidirect
797. #123	C₂³×C₃₁	semidirect
798. #123	C₂³×C₃₁	semidirect
799. #123	C₂³×C₃₁	semidirect
800. #123	C₂³×C₃₁	semidirect
801. #123	C₂³×C₃₁	semidirect
802. #123	C₂³×C₃₁	semidirect
803. C₂²⋊Q₈	C₂³×C₃₁	semidirect
804. C₂²⋊Q₈	C₂³×C₃₁	semidirect
805. C₂²⋊Q₈	C₂³×C₃₁	semidirect
806. C₂²⋊Q₈	C₂³×C₃₁	semidirect
807. C₂²⋊Q₈	C₂³×C₃₁	semidirect
808. C₂²⋊Q₈	C₂³×C₃₁	semidirect
809. C₂²⋊Q₈	C₂³×C₃₁	semidirect
810. C₂²⋊Q₈	C₂³×C₃₁	semidirect
815. #121	C₂³×C₃₁	semidirect
816. #121	C₂³×C₃₁	semidirect
817. #121	C₂³×C₃₁	semidirect
818. #121	C₂³×C₃₁	semidirect
819. #121	C₂³×C₃₁	semidirect
820. #121	C₂³×C₃₁	semidirect
821. #121	C₂³×C₃₁	semidirect
822. #121	C₂³×C₃₁	semidirect
827. #120	C₂³×C₃₁	semidirect
828. #120	C₂³×C₃₁	semidirect
829. C₄×Q₈	C₂³×C₃₁	semidirect
831. C₄×D₄	C₂³×C₃₁	semidirect
832. C₄×D₄	C₂³×C₃₁	semidirect
833. C₄×D₄	C₂³×C₃₁	semidirect
834. C₄×D₄	C₂³×C₃₁	semidirect
835. C₄×D₄	C₂³×C₃₁	semidirect
836. C₄×D₄	C₂³×C₃₁	semidirect
837. C₄×D₄	C₂³×C₃₁	semidirect
838. C₄×D₄	C₂³×C₃₁	semidirect
839. #117	C₂³×C₃₁	semidirect
840. #117	C₂³×C₃₁	semidirect
841. #117	C₂³×C₃₁	semidirect
842. #117	C₂³×C₃₁	semidirect
862. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
863. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
893. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
894. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
901. C₃₁	C₂×#3533	direct (N × H)
1188. C₂	C₃₁×#3533	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×#3533	2
C₂×C₃₁×#563	2
C₂×C₃₁×#562	2
C₂×C₃₁×#560	2
C₂×C₃₁×#559	2
C₂×C₃₁×#553	2
C₂×C₃₁×#552	2
C₂×C₃₁×#551	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×C₃₁×#542	2
C₂×C₃₁×#540	2
C₂×C₃₁×#539	2
C₂×C₃₁×#538	2
C₂×C₃₁×#535	2
C₂×C₃₁×#534	2
C₂×C₃₁×#525	2
C₂²×C₃₁×#123	2
C₂×#3533	31

Subgroups — C2×C31×#3533 #21519485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3533 #21519485