Subgroups — C₃₁×#62598 #21519357

Order 7936.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3180	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#560	—	2	2	no	—
23	C₃₁×#559	C₂²	1	1	yes	characteristic
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	C₂²	1	2	yes	complemented
26	C₃₁×#553	C₂²	1	2	yes	complemented
27	C₃₁×#550	C₂²	1	1	yes	characteristic
28	C₃₁×#550	C₂²	1	1	yes	characteristic
29	C₃₁×#547	—	2	2	no	—
30	C₃₁×#547	C₂²	1	2	yes	complemented
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#546	C₂²	1	2	yes	—
33	D₄²×C₃₁	—	2	1	no	—
34	D₄²×C₃₁	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#540	—	2	1	no	—
38	C₃₁×#540	C₂²	1	2	yes	—
39	C₃₁×#540	C₂²	1	2	yes	complemented
40	C₃₁×#539	—	2	2	no	—
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#535	—	2	1	no	—
44	C₃₁×#535	C₂²	1	2	yes	—
45	C₃₁×#534	—	2	2	no	—
46	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#499	C₂²	1	2	yes	complemented
53	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#493	C₂²	1	2	yes	complemented
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	complemented
57	C₃₁×#490	C₂²	1	2	yes	complemented
58	C₃₁×#490	C₂²	1	2	yes	complemented
59	C₃₁×#490	C₂²	1	2	yes	complemented
60	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#486	C₂²	1	2	yes	complemented
66	C₃₁×#486	C₂²	1	2	yes	complemented
67	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	1	yes	characteristic
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	1	yes	characteristic
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#476	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#469	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	—
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#459	C₂²	1	2	yes	—
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	2	yes	complemented
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#447	C₂²	1	2	yes	complemented
96	C₃₁×#447	C₂²	1	2	yes	complemented
97	C₃₁×#447	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	complemented
101	C₃₁×#442	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
105	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#418	C₂²	1	2	yes	complemented
112	C₃₁×#417	C₂²	1	2	yes	complemented
113	C₃₁×#416	C₂²	1	2	yes	complemented
114	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₃₁	—	2	2	no	—
124	C₂²×D₄×C₃₁	—	2	1	no	—
125	C₂²×D₄×C₃₁	—	2	1	no	—
126	C₂²×D₄×C₃₁	—	2	1	no	—
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	2	yes	—
133	C₂×D₈×C₃₁	C₂³	1	2	yes	—
134	C₂×D₈×C₃₁	C₂³	1	2	yes	—
135	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
137	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	—	2	2	no	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×#127	—	2	1	no	—
142	C₃₁×#127	—	2	1	no	—
143	C₃₁×#127	—	2	1	no	—
144	C₃₁×#127	C₂³	1	1	yes	characteristic
145	C₃₁×#127	C₂³	1	2	yes	—
146	C₃₁×#127	C₂³	1	1	yes	characteristic
147	C₃₁×#127	C₂³	1	2	yes	—
148	C₃₁×#127	C₂³	1	1	yes	characteristic
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	1	no	—
152	C₃₁×#126	D₄	1	2	yes	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	1	no	—
155	C₃₁×#125	—	2	1	no	—
156	C₃₁×#125	D₄	1	1	yes	characteristic
157	C₃₁×#125	C₂³	1	2	yes	—
158	C₃₁×#125	C₂³	1	2	yes	—
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	1	yes	characteristic
161	C₃₁×#124	—	2	1	no	—
162	C₃₁×#124	—	2	1	no	—
163	C₃₁×#124	D₄	1	1	yes	characteristic
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	1	yes	characteristic
166	C₃₁×#123	—	2	1	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	D₄	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
186	C₃₁×#121	—	2	2	no	—
187	C₃₁×#121	—	2	2	no	—
188	C₃₁×#121	—	2	1	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	2	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	D₄	1	1	yes	characteristic
202	C₃₁×#121	C₂³	1	2	yes	—
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₃₁×#120	—	2	2	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₃₁×#120	—	2	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₃₁×#117	—	2	1	no	—
231	C₃₁×#117	C₂³	1	2	yes	—
232	C₃₁×#117	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	1	yes	characteristic
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	2	no	—
281	C₂⁴×C₃₁	—	2	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	8	2	no	—
285	#41×C₃₁	—	8	4	no	—
286	#41×C₃₁	—	8	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂×D₄×C₃₁	—	2	1	no	—
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	1	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	1	no	—
309	C₂×D₄×C₃₁	—	2	1	no	—
310	C₂×D₄×C₃₁	—	4	2	no	—
311	C₂×D₄×C₃₁	—	4	2	no	—
312	C₂×D₄×C₃₁	—	4	2	no	—
313	C₂×D₄×C₃₁	—	4	2	no	—
314	C₂×D₄×C₃₁	—	8	2	no	—
315	C₂×D₄×C₃₁	—	8	2	no	—
316	C₂×D₄×C₃₁	—	8	2	no	—
317	C₂×D₄×C₃₁	—	8	4	no	—
318	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
321	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	2	no	—
332	C₂²×C₄×C₃₁	—	2	2	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
338	SD₁₆×C₃₁	—	4	2	no	—
339	D₈×C₃₁	—	4	2	no	—
340	D₈×C₃₁	—	4	2	no	—
341	D₈×C₃₁	—	4	2	no	—
342	D₈×C₃₁	—	4	2	no	—
343	D₈×C₃₁	—	4	2	no	—
344	M₁₆×C₃₁	—	4	2	no	—
345	C₂×C₈×C₃₁	—	4	2	no	—
346	C₂×C₈×C₃₁	—	4	2	no	—
347	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
348	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
349	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
350	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	1	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	1	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	1	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	1	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	1	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	1	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄²×C₃₁	—	2	1	no	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄²×C₃₁	C₂⁴	1	2	yes	—
406	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
407	#62598	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	2	no	—
411	C₂³×C₃₁	—	2	2	no	—
412	C₂³×C₃₁	—	4	4	no	—
413	C₂³×C₃₁	—	8	2	no	—
414	C₂³×C₃₁	—	8	2	no	—
415	C₂³×C₃₁	—	8	2	no	—
416	C₂³×C₃₁	—	8	2	no	—
417	C₂³×C₃₁	—	8	2	no	—
418	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
419	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₃₁	—	2	2	no	—
421	Q₈×C₃₁	—	4	1	no	—
422	Q₈×C₃₁	—	8	1	no	—
423	Q₈×C₃₁	—	8	2	no	—
424	D₄×C₃₁	—	2	4	no	—
425	D₄×C₃₁	—	2	2	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	2	2	no	—
432	D₄×C₃₁	—	4	1	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	2	no	—
435	D₄×C₃₁	—	4	2	no	—
436	D₄×C₃₁	—	4	4	no	—
437	D₄×C₃₁	—	8	1	no	—
438	D₄×C₃₁	—	8	2	no	—
439	D₄×C₃₁	—	8	2	no	—
440	D₄×C₃₁	—	8	2	no	—
441	D₄×C₃₁	—	8	1	no	—
442	D₄×C₃₁	—	8	1	no	—
443	D₄×C₃₁	—	8	2	no	—
444	D₄×C₃₁	—	8	2	no	—
445	D₄×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	8	1	no	—
447	D₄×C₃₁	—	8	2	no	—
448	D₄×C₃₁	—	8	2	no	—
449	D₄×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	8	2	no	—
451	D₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	1	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	4	1	no	—
463	C₂×C₄×C₃₁	—	4	2	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	—	8	2	no	—
466	C₂×C₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	2	no	—
469	C₂×C₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	1	no	—
472	C₂×C₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	—	2	2	no	—
484	C₈×C₃₁	—	2	2	no	—
485	C₈×C₃₁	—	2	2	no	—
486	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3543	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3370	C₂×C₃₁	1	2	yes	complemented
489	#3366	C₂×C₃₁	1	2	yes	complemented
490	#3318	C₂×C₃₁	1	2	yes	complemented
491	#3318	C₂×C₃₁	1	2	yes	complemented
492	#3309	C₂×C₃₁	1	2	yes	complemented
493	#3306	C₂×C₃₁	1	2	yes	complemented
494	#3297	C₂×C₃₁	1	2	yes	complemented
495	#3294	C₂×C₃₁	1	2	yes	complemented
496	#3241	C₂×C₃₁	1	2	yes	complemented
497	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3220	C₂×C₃₁	1	2	yes	complemented
499	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3180	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#3176	C₂×C₃₁	1	2	yes	complemented
502	#3136	C₂×C₃₁	1	2	yes	complemented
503	C₂×#490	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#2968	C₂×C₃₁	1	1	yes	characteristic, complemented
505	C₂²×C₃₁	—	2	1	no	—
506	C₂²×C₃₁	—	2	1	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	2	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	1	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	4	1	no	—
521	C₂²×C₃₁	—	4	2	no	—
522	C₂²×C₃₁	—	16	4	no	—
523	C₂²×C₃₁	—	16	4	no	—
524	C₂²×C₃₁	#576	1	2	yes	—
525	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
526	C₄×C₃₁	—	2	1	no	—
527	C₄×C₃₁	—	2	1	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	2	2	no	—
530	C₄×C₃₁	—	2	1	no	—
531	C₄×C₃₁	—	2	1	no	—
532	C₄×C₃₁	—	2	1	no	—
533	C₄×C₃₁	—	2	2	no	—
534	C₄×C₃₁	—	4	1	no	—
535	C₄×C₃₁	—	4	2	no	—
536	C₄×C₃₁	—	4	1	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	#585	1	2	yes	—
541	#563	—	2	1	no	—
542	#562	—	2	1	no	—
543	#560	—	2	2	no	—
544	#559	C₂²×C₃₁	1	1	yes	characteristic
545	#554	C₂²×C₃₁	1	2	yes	complemented
546	#553	C₂²×C₃₁	1	2	yes	complemented
547	#553	C₂²×C₃₁	1	2	yes	complemented
548	#550	C₂²×C₃₁	1	1	yes	characteristic
549	#550	C₂²×C₃₁	1	1	yes	characteristic
550	#547	—	2	2	no	—
551	#547	C₂²×C₃₁	1	2	yes	complemented
552	#546	—	2	1	no	—
553	#546	C₂²×C₃₁	1	2	yes	—
554	D₄²	—	2	1	no	—
555	D₄²	C₂²×C₃₁	1	2	yes	—
556	D₄²	C₂²×C₃₁	1	1	yes	characteristic
557	#544	C₂²×C₃₁	1	2	yes	complemented
558	#540	—	2	1	no	—
559	#540	C₂²×C₃₁	1	2	yes	—
560	#540	C₂²×C₃₁	1	2	yes	complemented
561	#539	—	2	2	no	—
562	#539	—	2	1	no	—
563	#537	—	2	1	no	—
564	#535	—	2	1	no	—
565	#535	C₂²×C₃₁	1	2	yes	—
566	#534	—	2	2	no	—
567	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
569	#529	C₂²×C₃₁	1	1	yes	characteristic
570	#529	C₂²×C₃₁	1	1	yes	characteristic
571	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	#499	C₂²×C₃₁	1	2	yes	complemented
574	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
575	#493	C₂²×C₃₁	1	2	yes	complemented
576	#490	C₂²×C₃₁	1	2	yes	—
577	#490	C₂²×C₃₁	1	2	yes	complemented
578	#490	C₂²×C₃₁	1	2	yes	complemented
579	#490	C₂²×C₃₁	1	2	yes	complemented
580	#490	C₂²×C₃₁	1	2	yes	complemented
581	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#489	C₂²×C₃₁	1	2	yes	complemented
583	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#488	C₂²×C₃₁	1	2	yes	complemented
585	#488	C₂²×C₃₁	1	2	yes	complemented
586	#486	C₂²×C₃₁	1	2	yes	complemented
587	#486	C₂²×C₃₁	1	2	yes	complemented
588	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
589	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#482	C₂²×C₃₁	1	2	yes	complemented
591	#482	C₂²×C₃₁	1	2	yes	complemented
592	#481	C₂²×C₃₁	1	1	yes	characteristic
593	#481	C₂²×C₃₁	1	2	yes	complemented
594	#480	C₂²×C₃₁	1	1	yes	characteristic
595	#480	C₂²×C₃₁	1	2	yes	complemented
596	#479	C₂²×C₃₁	1	2	yes	complemented
597	#478	C₂²×C₃₁	1	2	yes	complemented
598	#478	C₂²×C₃₁	1	2	yes	complemented
599	#478	C₂²×C₃₁	1	2	yes	complemented
600	#476	C₂²×C₃₁	1	2	yes	complemented
601	#474	C₂²×C₃₁	1	2	yes	complemented
602	#469	C₂²×C₃₁	1	2	yes	complemented
603	#469	C₂²×C₃₁	1	2	yes	complemented
604	#466	C₂²×C₃₁	1	2	yes	—
605	#466	C₂²×C₃₁	1	2	yes	complemented
606	#466	C₂²×C₃₁	1	2	yes	complemented
607	#465	C₂²×C₃₁	1	2	yes	complemented
608	#463	C₂²×C₃₁	1	2	yes	complemented
609	#463	C₂²×C₃₁	1	2	yes	complemented
610	#459	C₂²×C₃₁	1	2	yes	—
611	#459	C₂²×C₃₁	1	2	yes	complemented
612	#459	C₂²×C₃₁	1	2	yes	complemented
613	#459	C₂²×C₃₁	1	2	yes	complemented
614	#449	C₂²×C₃₁	1	2	yes	complemented
615	#449	C₂²×C₃₁	1	2	yes	complemented
616	#447	C₂²×C₃₁	1	2	yes	complemented
617	#447	C₂²×C₃₁	1	2	yes	complemented
618	#447	C₂²×C₃₁	1	2	yes	complemented
619	#447	C₂²×C₃₁	1	2	yes	complemented
620	#446	C₂²×C₃₁	1	2	yes	complemented
621	#442	C₂²×C₃₁	1	2	yes	complemented
622	#442	C₂²×C₃₁	1	2	yes	complemented
623	#442	C₂²×C₃₁	1	2	yes	complemented
624	#440	C₂²×C₃₁	1	2	yes	complemented
625	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
626	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
627	#435	C₂²×C₃₁	1	2	yes	complemented
628	#435	C₂²×C₃₁	1	2	yes	complemented
629	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
630	#433	C₂²×C₃₁	1	2	yes	complemented
631	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#418	C₂²×C₃₁	1	2	yes	complemented
633	#417	C₂²×C₃₁	1	2	yes	complemented
634	#416	C₂²×C₃₁	1	2	yes	complemented
635	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
636	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
637	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
638	#405	C₂²×C₃₁	1	2	yes	complemented
639	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	C₂×C₃₁	—	2	2	no	—
641	C₂×C₃₁	—	4	2	no	—
642	C₂×C₃₁	—	8	2	no	—
643	C₂×C₃₁	—	8	2	no	—
644	C₂×C₃₁	—	8	1	no	—
645	C₂×C₃₁	—	8	2	no	—
646	C₂×C₃₁	#3500	1	1	yes	characteristic
647	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
648	C₂×C₃₁	#3585	1	1	yes	characteristic
649	C₂×#41	—	2	1	no	—
650	C₂×#41	—	2	2	no	—
651	C₂×#41	—	2	1	no	—
652	C₂×#41	C₂³×C₃₁	1	2	yes	—
653	C₂²×D₄	—	2	2	no	—
654	C₂²×D₄	—	2	1	no	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	—	2	1	no	—
657	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
660	C₂×D₈	C₂³×C₃₁	1	2	yes	—
661	C₂×D₈	C₂³×C₃₁	1	2	yes	—
662	C₂×D₈	C₂³×C₃₁	1	2	yes	—
663	C₂×D₈	C₂³×C₃₁	1	2	yes	—
664	C₂×D₈	C₂³×C₃₁	1	2	yes	—
665	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
667	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
668	C₄⋊Q₈	—	2	2	no	—
669	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
670	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
671	#127	—	2	1	no	—
672	#127	—	2	1	no	—
673	#127	—	2	1	no	—
674	#127	C₂³×C₃₁	1	2	yes	—
675	#127	C₂³×C₃₁	1	1	yes	characteristic
676	#127	C₂³×C₃₁	1	1	yes	characteristic
677	#127	C₂³×C₃₁	1	1	yes	characteristic
678	#127	C₂³×C₃₁	1	2	yes	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	1	no	—
682	#126	D₄×C₃₁	1	2	yes	—
683	#125	—	2	2	no	—
684	#125	—	2	1	no	—
685	#125	—	2	1	no	—
686	#125	D₄×C₃₁	1	1	yes	characteristic
687	#125	C₂³×C₃₁	1	2	yes	—
688	#125	C₂³×C₃₁	1	2	yes	—
689	#125	C₂³×C₃₁	1	1	yes	characteristic
690	#125	C₂³×C₃₁	1	2	yes	—
691	#124	—	2	1	no	—
692	#124	—	2	1	no	—
693	#124	D₄×C₃₁	1	1	yes	characteristic
694	#124	C₂³×C₃₁	1	1	yes	characteristic
695	#124	C₂³×C₃₁	1	2	yes	—
696	#123	—	2	1	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	D₄×C₃₁	1	2	yes	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
715	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	1	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	1	no	—
723	#121	—	2	1	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	D₄×C₃₁	1	1	yes	characteristic
732	#121	C₂³×C₃₁	1	1	yes	characteristic
733	#121	C₂³×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#121	C₂³×C₃₁	1	2	yes	—
736	#121	C₂³×C₃₁	1	2	yes	—
737	#121	C₂³×C₃₁	1	2	yes	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	—	2	2	no	—
741	#120	—	2	2	no	—
742	#120	—	2	2	no	—
743	#120	—	2	2	no	—
744	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄×D₄	—	2	1	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
753	C₄×D₄	C₂³×C₃₁	1	2	yes	—
754	C₄×D₄	C₂³×C₃₁	1	2	yes	—
755	C₄×D₄	C₂³×C₃₁	1	2	yes	—
756	C₄×D₄	C₂³×C₃₁	1	2	yes	—
757	C₄×D₄	C₂³×C₃₁	1	2	yes	—
758	C₄×D₄	C₂³×C₃₁	1	2	yes	—
759	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
760	#117	—	2	1	no	—
761	#117	C₂³×C₃₁	1	2	yes	—
762	#117	C₂³×C₃₁	1	2	yes	—
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	—	2	1	no	—
765	C₂×C₄⋊C₄	—	2	2	no	—
766	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
769	C₂×C₂²⋊C₄	—	2	2	no	—
770	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
771	#107	C₂³×C₃₁	1	2	yes	—
772	#107	C₂³×C₃₁	1	2	yes	—
773	#107	C₂³×C₃₁	1	2	yes	—
774	#106	C₂³×C₃₁	1	2	yes	—
775	#106	C₂³×C₃₁	1	2	yes	—
776	#106	C₂³×C₃₁	1	2	yes	—
777	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
778	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
779	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
780	#103	C₂³×C₃₁	1	2	yes	—
781	#103	C₂³×C₃₁	1	2	yes	—
782	#103	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	#102	C₂³×C₃₁	1	2	yes	—
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	#102	C₂³×C₃₁	1	2	yes	—
790	#102	C₂³×C₃₁	1	2	yes	—
791	#102	C₂³×C₃₁	1	2	yes	—
792	#102	C₂³×C₃₁	1	2	yes	—
793	#102	C₂³×C₃₁	1	2	yes	—
794	#102	C₂³×C₃₁	1	2	yes	—
795	#102	C₂³×C₃₁	1	2	yes	—
796	#102	C₂³×C₃₁	1	2	yes	—
797	#102	C₂³×C₃₁	1	2	yes	—
798	#102	C₂³×C₃₁	1	2	yes	—
799	#102	C₂³×C₃₁	1	2	yes	—
800	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
804	#97	C₂³×C₃₁	1	1	yes	characteristic
805	#97	C₂³×C₃₁	1	1	yes	characteristic
806	#97	C₂³×C₃₁	1	2	yes	—
807	#97	C₂³×C₃₁	1	2	yes	—
808	C₄×C₈	C₂³×C₃₁	1	2	yes	—
809	C₄×C₈	C₂³×C₃₁	1	2	yes	—
810	C₃₁	#62598	1	1	yes	characteristic, direct product factor, Sylow
811	C₂⁴	—	2	2	no	—
812	C₂⁴	—	2	2	no	—
813	#41	—	4	2	no	—
814	#41	—	4	2	no	—
815	#41	—	8	2	no	—
816	#41	—	8	4	no	—
817	#41	—	8	2	no	—
818	C₂×Q₈	—	2	2	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	8	2	no	—
846	C₂×D₄	—	8	2	no	—
847	C₂×D₄	—	8	2	no	—
848	C₂×D₄	—	8	4	no	—
849	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
850	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
851	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
852	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
854	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
869	SD₁₆	—	4	2	no	—
870	D₈	—	4	2	no	—
871	D₈	—	4	2	no	—
872	D₈	—	4	2	no	—
873	D₈	—	4	2	no	—
874	D₈	—	4	2	no	—
875	M₁₆	—	4	2	no	—
876	C₂×C₈	—	4	2	no	—
877	C₂×C₈	—	4	2	no	—
878	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
879	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
880	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
881	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
900	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
905	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
906	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	1	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
930	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₄²	—	2	1	no	—
932	C₄²	—	2	2	no	—
933	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
935	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₄²	C₂⁴×C₃₁	1	2	yes	—
937	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	4	4	no	—
943	C₂³	—	8	2	no	—
944	C₂³	—	8	2	no	—
945	C₂³	—	8	2	no	—
946	C₂³	—	8	2	no	—
947	C₂³	—	8	2	no	—
948	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
949	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
950	Q₈	—	2	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	8	1	no	—
953	Q₈	—	8	2	no	—
954	D₄	—	2	4	no	—
955	D₄	—	2	2	no	—
956	D₄	—	2	2	no	—
957	D₄	—	2	2	no	—
958	D₄	—	2	2	no	—
959	D₄	—	2	2	no	—
960	D₄	—	2	2	no	—
961	D₄	—	2	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	2	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	2	no	—
966	D₄	—	4	4	no	—
967	D₄	—	8	1	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	1	no	—
971	D₄	—	8	1	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	D₄	—	8	1	no	—
976	D₄	—	8	2	no	—
977	D₄	—	8	2	no	—
978	D₄	—	8	2	no	—
979	D₄	—	8	2	no	—
980	D₄	—	8	2	no	—
981	D₄	—	8	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	—	4	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	—	8	1	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1008	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1009	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1010	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1011	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1012	C₈	—	2	2	no	—
1013	C₈	—	2	2	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	2	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	16	4	no	—
1034	C₂²	—	16	4	no	—
1035	C₂²	C₃₁×#576	1	2	yes	—
1036	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	2	no	—
1051	C₄	C₃₁×#585	1	2	yes	—
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	—	8	2	no	—
1055	C₂	—	8	1	no	—
1056	C₂	—	8	2	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₃₁×#3500	1	1	yes	characteristic
1059	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1060	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3559	C₂	semidirect
2. C₃₁×#3543	C₂	semidirect
3. C₃₁×#3370	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3318	C₂	semidirect
6. C₃₁×#3318	C₂	semidirect
7. C₃₁×#3309	C₂	semidirect
8. C₃₁×#3306	C₂	semidirect
9. C₃₁×#3297	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. C₃₁×#3241	C₂	semidirect
12. C₃₁×#3232	C₂	semidirect
13. C₃₁×#3220	C₂	semidirect
14. C₃₁×#3205	C₂	semidirect
15. C₃₁×#3180	C₂	semidirect
16. C₃₁×#3176	C₂	semidirect
17. C₃₁×#3136	C₂	semidirect
18. C₂×C₃₁×#490	C₂	semidirect
19. C₃₁×#2968	C₂	semidirect
24. C₃₁×#554	C₂²	semidirect
25. C₃₁×#553	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
39. C₃₁×#540	C₂²	semidirect
46. C₃₁×#532	C₂²	semidirect
50. C₂×C₃₁×#125	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#496	C₂²	semidirect
54. C₃₁×#493	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#490	C₂²	semidirect
58. C₃₁×#490	C₂²	semidirect
59. C₃₁×#490	C₂²	semidirect
60. C₃₁×#490	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#466	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
92. C₃₁×#459	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#447	C₂²	semidirect
96. C₃₁×#447	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#442	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
102. C₃₁×#442	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×D₈×C₃₁	C₂²	semidirect
105. C₄×D₈×C₃₁	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₈×D₄×C₃₁	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#431	C₂²	semidirect
111. C₃₁×#418	C₂²	semidirect
112. C₃₁×#417	C₂²	semidirect
113. C₃₁×#416	C₂²	semidirect
114. C₂×C₃₁×#102	C₂²	semidirect
115. C₂×C₃₁×#102	C₂²	semidirect
116. C₂×C₃₁×#102	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
118. C₂×C₃₁×#97	C₂²	semidirect
407. #62598	C₃₁	direct (N × H)
486. #3559	C₂×C₃₁	semidirect
487. #3543	C₂×C₃₁	semidirect
488. #3370	C₂×C₃₁	semidirect
489. #3366	C₂×C₃₁	semidirect
490. #3318	C₂×C₃₁	semidirect
491. #3318	C₂×C₃₁	semidirect
492. #3309	C₂×C₃₁	semidirect
493. #3306	C₂×C₃₁	semidirect
494. #3297	C₂×C₃₁	semidirect
495. #3294	C₂×C₃₁	semidirect
496. #3241	C₂×C₃₁	semidirect
497. #3232	C₂×C₃₁	semidirect
498. #3220	C₂×C₃₁	semidirect
499. #3205	C₂×C₃₁	semidirect
500. #3180	C₂×C₃₁	semidirect
501. #3176	C₂×C₃₁	semidirect
502. #3136	C₂×C₃₁	semidirect
503. C₂×#490	C₂×C₃₁	semidirect
504. #2968	C₂×C₃₁	semidirect
545. #554	C₂²×C₃₁	semidirect
546. #553	C₂²×C₃₁	semidirect
547. #553	C₂²×C₃₁	semidirect
551. #547	C₂²×C₃₁	semidirect
557. #544	C₂²×C₃₁	semidirect
560. #540	C₂²×C₃₁	semidirect
567. #532	C₂²×C₃₁	semidirect
571. C₂×#125	C₂²×C₃₁	semidirect
572. #501	C₂²×C₃₁	semidirect
573. #499	C₂²×C₃₁	semidirect
574. #496	C₂²×C₃₁	semidirect
575. #493	C₂²×C₃₁	semidirect
577. #490	C₂²×C₃₁	semidirect
578. #490	C₂²×C₃₁	semidirect
579. #490	C₂²×C₃₁	semidirect
580. #490	C₂²×C₃₁	semidirect
581. #490	C₂²×C₃₁	semidirect
582. #489	C₂²×C₃₁	semidirect
583. #489	C₂²×C₃₁	semidirect
584. #488	C₂²×C₃₁	semidirect
585. #488	C₂²×C₃₁	semidirect
586. #486	C₂²×C₃₁	semidirect
587. #486	C₂²×C₃₁	semidirect
588. #484	C₂²×C₃₁	semidirect
589. #483	C₂²×C₃₁	semidirect
590. #482	C₂²×C₃₁	semidirect
591. #482	C₂²×C₃₁	semidirect
593. #481	C₂²×C₃₁	semidirect
595. #480	C₂²×C₃₁	semidirect
596. #479	C₂²×C₃₁	semidirect
597. #478	C₂²×C₃₁	semidirect
598. #478	C₂²×C₃₁	semidirect
599. #478	C₂²×C₃₁	semidirect
600. #476	C₂²×C₃₁	semidirect
601. #474	C₂²×C₃₁	semidirect
602. #469	C₂²×C₃₁	semidirect
603. #469	C₂²×C₃₁	semidirect
605. #466	C₂²×C₃₁	semidirect
606. #466	C₂²×C₃₁	semidirect
607. #465	C₂²×C₃₁	semidirect
608. #463	C₂²×C₃₁	semidirect
609. #463	C₂²×C₃₁	semidirect
611. #459	C₂²×C₃₁	semidirect
612. #459	C₂²×C₃₁	semidirect
613. #459	C₂²×C₃₁	semidirect
614. #449	C₂²×C₃₁	semidirect
615. #449	C₂²×C₃₁	semidirect
616. #447	C₂²×C₃₁	semidirect
617. #447	C₂²×C₃₁	semidirect
618. #447	C₂²×C₃₁	semidirect
619. #447	C₂²×C₃₁	semidirect
620. #446	C₂²×C₃₁	semidirect
621. #442	C₂²×C₃₁	semidirect
622. #442	C₂²×C₃₁	semidirect
623. #442	C₂²×C₃₁	semidirect
624. #440	C₂²×C₃₁	semidirect
625. C₄×D₈	C₂²×C₃₁	semidirect
626. C₄×D₈	C₂²×C₃₁	semidirect
627. #435	C₂²×C₃₁	semidirect
628. #435	C₂²×C₃₁	semidirect
629. C₈×D₄	C₂²×C₃₁	semidirect
630. #433	C₂²×C₃₁	semidirect
631. #431	C₂²×C₃₁	semidirect
632. #418	C₂²×C₃₁	semidirect
633. #417	C₂²×C₃₁	semidirect
634. #416	C₂²×C₃₁	semidirect
635. C₂×#102	C₂²×C₃₁	semidirect
636. C₂×#102	C₂²×C₃₁	semidirect
637. C₂×#102	C₂²×C₃₁	semidirect
638. #405	C₂²×C₃₁	semidirect
639. C₂×#97	C₂²×C₃₁	semidirect
810. C₃₁	#62598	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×#3559	2
C₃₁×#3543	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3318	2
C₃₁×#3309	2
C₃₁×#3306	2
C₃₁×#3297	2
C₃₁×#3294	2
C₃₁×#3241	2
C₃₁×#3232	2
C₃₁×#3220	2
C₃₁×#3205	2
C₃₁×#3180	2
C₃₁×#3176	2
C₃₁×#3136	2
C₂×C₃₁×#490	2
C₃₁×#2968	2
#62598	31

Subgroups — C31×#62598 #21519357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62598 #21519357