Subgroups — C₃₁×#61778 #21518537

Order 7936.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#560	—	2	2	no	—
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	C₂²	1	2	yes	complemented
23	C₃₁×#555	—	2	1	no	—
24	C₃₁×#555	C₂²	1	2	yes	complemented
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#553	C₂²	1	2	yes	complemented
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#552	C₂²	1	2	yes	complemented
31	D₄²×C₃₁	—	2	2	no	—
32	D₄²×C₃₁	C₂²	1	2	yes	—
33	D₄²×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#540	C₂²	1	2	yes	—
36	C₃₁×#538	—	2	1	no	—
37	C₃₁×#538	—	2	1	no	—
38	C₃₁×#538	—	2	2	no	—
39	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#535	C₂²	1	2	yes	—
41	C₃₁×#534	—	2	1	no	—
42	C₃₁×#534	—	2	1	no	—
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#525	C₂²	1	1	yes	characteristic
45	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#499	C₂²	1	2	yes	complemented
53	C₃₁×#490	C₂²	1	2	yes	complemented
54	C₃₁×#486	C₂²	1	2	yes	complemented
55	C₃₁×#485	C₂²	1	2	yes	complemented
56	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#482	C₂²	1	2	yes	complemented
59	C₃₁×#482	C₂²	1	2	yes	complemented
60	C₃₁×#482	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#482	C₂²	1	2	yes	complemented
67	C₃₁×#481	C₂²	1	2	yes	complemented
68	C₃₁×#481	C₂²	1	2	yes	complemented
69	C₃₁×#481	C₂²	1	2	yes	complemented
70	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	1	yes	characteristic, 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×#469	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#466	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	2	yes	complemented
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#450	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#436	C₂²	1	2	yes	complemented
104	C₃₁×#436	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#428	C₂²	1	2	yes	complemented
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₃₁×#428	C₂²	1	2	yes	complemented
111	C₃₁×#427	C₂²	1	2	yes	complemented
112	C₃₁×#418	C₂²	1	2	yes	complemented
113	C₃₁×#418	C₂²	1	2	yes	complemented
114	C₃₁×#418	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₃₁	—	2	1	no	—
122	C₂²×D₄×C₃₁	—	2	1	no	—
123	C₂²×D₄×C₃₁	—	2	2	no	—
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	—	2	1	no	—
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×#127	—	2	2	no	—
140	C₃₁×#127	C₂³	1	2	yes	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	C₂³	1	2	yes	—
150	C₃₁×#125	C₂³	1	2	yes	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	1	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	D₄	1	2	yes	—
163	C₃₁×C₂²⋊Q₈	—	2	1	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
166	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
167	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×#121	—	2	2	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	—	2	2	no	—
173	C₃₁×#121	—	2	1	no	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	1	no	—
177	C₃₁×#121	—	2	1	no	—
178	C₃₁×#121	—	2	1	no	—
179	C₃₁×#121	—	2	1	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	—	2	2	no	—
184	C₃₁×#121	D₄	1	1	yes	characteristic
185	C₃₁×#121	D₄	1	1	yes	characteristic
186	C₃₁×#121	C₂³	1	2	yes	—
187	C₃₁×#121	C₂³	1	1	yes	characteristic
188	C₃₁×#121	C₂³	1	1	yes	characteristic
189	C₃₁×#121	C₂³	1	2	yes	—
190	C₃₁×#121	C₂³	1	2	yes	—
191	C₃₁×#121	C₂³	1	2	yes	—
192	C₃₁×#121	C₂³	1	2	yes	—
193	C₃₁×#121	C₂³	1	2	yes	—
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₃₁×#120	—	2	1	no	—
196	C₃₁×#120	—	2	2	no	—
197	C₃₁×#120	—	2	2	no	—
198	C₃₁×#120	—	2	2	no	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	—	2	2	no	—
201	C₃₁×#120	—	2	2	no	—
202	C₃₁×#120	D₄	1	2	yes	—
203	C₄×Q₈×C₃₁	—	2	1	no	—
204	C₄×Q₈×C₃₁	—	2	2	no	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	1	no	—
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	2	no	—
211	C₄×D₄×C₃₁	—	2	2	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	2	no	—
223	C₃₁×#117	—	2	2	no	—
224	C₃₁×#117	C₂³	1	2	yes	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₃₁×#117	C₂³	1	2	yes	—
228	C₃₁×#117	C₂³	1	1	yes	characteristic
229	C₃₁×#117	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₄²×C₃₁	—	2	1	no	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	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	2	yes	—
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂⁴×C₃₁	—	2	1	no	—
282	C₂⁴×C₃₁	—	2	2	no	—
283	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	4	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂×D₄×C₃₁	—	2	1	no	—
290	C₂×D₄×C₃₁	—	2	2	no	—
291	C₂×D₄×C₃₁	—	2	2	no	—
292	C₂×D₄×C₃₁	—	2	1	no	—
293	C₂×D₄×C₃₁	—	2	1	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	2	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	2	no	—
304	C₂×D₄×C₃₁	—	4	2	no	—
305	C₂×D₄×C₃₁	—	4	2	no	—
306	C₂×D₄×C₃₁	—	4	2	no	—
307	C₂×D₄×C₃₁	—	4	2	no	—
308	C₂×D₄×C₃₁	—	8	4	no	—
309	C₂×D₄×C₃₁	—	8	4	no	—
310	C₂×D₄×C₃₁	—	8	2	no	—
311	C₂×D₄×C₃₁	—	8	2	no	—
312	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	—	2	1	no	—
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	4	2	no	—
329	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	SD₁₆×C₃₁	—	4	2	no	—
337	SD₁₆×C₃₁	—	4	2	no	—
338	D₈×C₃₁	—	4	2	no	—
339	D₈×C₃₁	—	4	2	no	—
340	M₁₆×C₃₁	—	4	2	no	—
341	M₁₆×C₃₁	—	4	2	no	—
342	M₁₆×C₃₁	—	4	2	no	—
343	C₂×C₈×C₃₁	—	4	2	no	—
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
346	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
347	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	1	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	1	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	1	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	—	2	2	no	—
401	C₄²×C₃₁	—	2	1	no	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	C₂⁴	1	2	yes	—
404	#61778	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	4	1	no	—
409	C₂³×C₃₁	—	4	1	no	—
410	C₂³×C₃₁	—	4	1	no	—
411	C₂³×C₃₁	—	4	2	no	—
412	C₂³×C₃₁	—	4	2	no	—
413	C₂³×C₃₁	—	8	1	no	—
414	C₂³×C₃₁	—	8	1	no	—
415	C₂³×C₃₁	—	8	2	no	—
416	C₂³×C₃₁	—	8	2	no	—
417	C₂³×C₃₁	—	8	1	no	—
418	C₂³×C₃₁	—	8	1	no	—
419	C₂³×C₃₁	—	8	2	no	—
420	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
421	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
422	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
423	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₃₁	—	2	2	no	—
425	Q₈×C₃₁	—	4	1	no	—
426	Q₈×C₃₁	—	8	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	2	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	1	no	—
435	D₄×C₃₁	—	4	2	no	—
436	D₄×C₃₁	—	4	4	no	—
437	D₄×C₃₁	—	4	4	no	—
438	D₄×C₃₁	—	4	2	no	—
439	D₄×C₃₁	—	8	1	no	—
440	D₄×C₃₁	—	8	1	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	2	no	—
443	D₄×C₃₁	—	8	2	no	—
444	D₄×C₃₁	—	8	1	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	C₂×C₄×C₃₁	—	2	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	2	no	—
457	C₂×C₄×C₃₁	—	2	1	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	4	1	no	—
464	C₂×C₄×C₃₁	—	4	1	no	—
465	C₂×C₄×C₃₁	—	4	1	no	—
466	C₂×C₄×C₃₁	—	4	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	1	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	1	no	—
473	C₂×C₄×C₃₁	—	8	1	no	—
474	C₂×C₄×C₃₁	—	8	1	no	—
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	2	yes	—
478	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	#3537	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3493	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3355	C₂×C₃₁	1	2	yes	complemented
489	#3351	C₂×C₃₁	1	2	yes	complemented
490	#3350	C₂×C₃₁	1	2	yes	complemented
491	#3347	C₂×C₃₁	1	2	yes	complemented
492	#3325	C₂×C₃₁	1	2	yes	complemented
493	#3324	C₂×C₃₁	1	2	yes	complemented
494	#3318	C₂×C₃₁	1	2	yes	complemented
495	#3310	C₂×C₃₁	1	2	yes	complemented
496	#3241	C₂×C₃₁	1	2	yes	complemented
497	#3198	C₂×C₃₁	1	2	yes	complemented
498	#3194	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3194	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3119	C₂×C₃₁	1	2	yes	complemented
501	#3096	C₂×C₃₁	1	2	yes	complemented
502	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	1	no	—
507	C₂²×C₃₁	—	2	1	no	—
508	C₂²×C₃₁	—	2	1	no	—
509	C₂²×C₃₁	—	2	1	no	—
510	C₂²×C₃₁	—	2	1	no	—
511	C₂²×C₃₁	—	2	1	no	—
512	C₂²×C₃₁	—	2	2	no	—
513	C₂²×C₃₁	—	2	1	no	—
514	C₂²×C₃₁	—	2	1	no	—
515	C₂²×C₃₁	—	2	1	no	—
516	C₂²×C₃₁	—	2	2	no	—
517	C₂²×C₃₁	—	4	1	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	4	2	no	—
521	C₂²×C₃₁	—	4	2	no	—
522	C₂²×C₃₁	—	4	1	no	—
523	C₂²×C₃₁	—	4	1	no	—
524	C₂²×C₃₁	—	4	2	no	—
525	C₂²×C₃₁	—	4	2	no	—
526	C₂²×C₃₁	—	8	2	no	—
527	C₂²×C₃₁	—	16	2	no	—
528	C₂²×C₃₁	—	16	2	no	—
529	C₂²×C₃₁	—	16	4	no	—
530	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	2	2	no	—
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	1	no	—
535	C₄×C₃₁	—	2	1	no	—
536	C₄×C₃₁	—	2	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	—	4	2	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	2	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	#585	1	2	yes	—
545	#560	—	2	2	no	—
546	#556	—	2	1	no	—
547	#556	C₂²×C₃₁	1	2	yes	complemented
548	#555	—	2	1	no	—
549	#555	C₂²×C₃₁	1	2	yes	complemented
550	#553	—	2	1	no	—
551	#553	C₂²×C₃₁	1	2	yes	—
552	#553	C₂²×C₃₁	1	2	yes	—
553	#553	C₂²×C₃₁	1	2	yes	complemented
554	#552	—	2	1	no	—
555	#552	C₂²×C₃₁	1	2	yes	complemented
556	D₄²	—	2	2	no	—
557	D₄²	C₂²×C₃₁	1	2	yes	—
558	D₄²	C₂²×C₃₁	1	2	yes	—
559	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#540	C₂²×C₃₁	1	2	yes	—
561	#538	—	2	1	no	—
562	#538	—	2	1	no	—
563	#538	—	2	2	no	—
564	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	#535	C₂²×C₃₁	1	2	yes	—
566	#534	—	2	1	no	—
567	#534	—	2	1	no	—
568	#529	—	2	2	no	—
569	#525	C₂²×C₃₁	1	1	yes	characteristic
570	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
572	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
573	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
575	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
576	#501	C₂²×C₃₁	1	2	yes	complemented
577	#499	C₂²×C₃₁	1	2	yes	complemented
578	#490	C₂²×C₃₁	1	2	yes	complemented
579	#486	C₂²×C₃₁	1	2	yes	complemented
580	#485	C₂²×C₃₁	1	2	yes	complemented
581	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#482	C₂²×C₃₁	1	2	yes	complemented
584	#482	C₂²×C₃₁	1	2	yes	complemented
585	#482	C₂²×C₃₁	1	2	yes	complemented
586	#482	C₂²×C₃₁	1	2	yes	complemented
587	#482	C₂²×C₃₁	1	2	yes	complemented
588	#482	C₂²×C₃₁	1	2	yes	complemented
589	#482	C₂²×C₃₁	1	2	yes	complemented
590	#482	C₂²×C₃₁	1	2	yes	complemented
591	#482	C₂²×C₃₁	1	2	yes	complemented
592	#481	C₂²×C₃₁	1	2	yes	complemented
593	#481	C₂²×C₃₁	1	2	yes	complemented
594	#481	C₂²×C₃₁	1	2	yes	complemented
595	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#480	C₂²×C₃₁	1	2	yes	complemented
597	#480	C₂²×C₃₁	1	2	yes	complemented
598	#480	C₂²×C₃₁	1	2	yes	complemented
599	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#479	C₂²×C₃₁	1	2	yes	complemented
601	#478	C₂²×C₃₁	1	2	yes	complemented
602	#478	C₂²×C₃₁	1	2	yes	complemented
603	#478	C₂²×C₃₁	1	2	yes	complemented
604	#476	C₂²×C₃₁	1	2	yes	complemented
605	#474	C₂²×C₃₁	1	2	yes	complemented
606	#469	C₂²×C₃₁	1	2	yes	complemented
607	#469	C₂²×C₃₁	1	2	yes	complemented
608	#469	C₂²×C₃₁	1	2	yes	complemented
609	#468	C₂²×C₃₁	1	2	yes	complemented
610	#468	C₂²×C₃₁	1	2	yes	complemented
611	#468	C₂²×C₃₁	1	2	yes	complemented
612	#466	C₂²×C₃₁	1	2	yes	complemented
613	#465	C₂²×C₃₁	1	2	yes	complemented
614	#460	C₂²×C₃₁	1	2	yes	complemented
615	#459	C₂²×C₃₁	1	2	yes	complemented
616	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#450	C₂²×C₃₁	1	2	yes	complemented
619	#449	C₂²×C₃₁	1	2	yes	complemented
620	#449	C₂²×C₃₁	1	2	yes	complemented
621	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#447	C₂²×C₃₁	1	2	yes	complemented
624	#442	C₂²×C₃₁	1	2	yes	complemented
625	#440	C₂²×C₃₁	1	2	yes	complemented
626	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
627	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
628	#436	C₂²×C₃₁	1	2	yes	complemented
629	#436	C₂²×C₃₁	1	2	yes	complemented
630	#435	C₂²×C₃₁	1	2	yes	complemented
631	#435	C₂²×C₃₁	1	2	yes	complemented
632	#433	C₂²×C₃₁	1	2	yes	complemented
633	#428	C₂²×C₃₁	1	2	yes	complemented
634	#428	C₂²×C₃₁	1	2	yes	complemented
635	#428	C₂²×C₃₁	1	2	yes	complemented
636	#427	C₂²×C₃₁	1	2	yes	complemented
637	#418	C₂²×C₃₁	1	2	yes	complemented
638	#418	C₂²×C₃₁	1	2	yes	complemented
639	#418	C₂²×C₃₁	1	2	yes	complemented
640	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
641	#408	C₂²×C₃₁	1	2	yes	complemented
642	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	C₂×C₃₁	—	4	1	no	—
645	C₂×C₃₁	—	4	1	no	—
646	C₂×C₃₁	—	4	1	no	—
647	C₂×C₃₁	—	4	2	no	—
648	C₂×C₃₁	—	8	1	no	—
649	C₂×C₃₁	—	8	2	no	—
650	C₂×C₃₁	—	8	2	no	—
651	C₂×C₃₁	#3485	1	1	yes	characteristic
652	C₂×C₃₁	#3585	1	1	yes	characteristic
653	C₂×C₃₁	#3585	1	1	yes	characteristic
654	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
656	C₂²×D₄	—	2	1	no	—
657	C₂²×D₄	—	2	1	no	—
658	C₂²×D₄	—	2	2	no	—
659	C₂²×D₄	—	2	2	no	—
660	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
663	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×D₈	C₂³×C₃₁	1	2	yes	—
667	C₂×D₈	C₂³×C₃₁	1	2	yes	—
668	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
674	#127	—	2	2	no	—
675	#127	C₂³×C₃₁	1	2	yes	—
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#125	—	2	2	no	—
683	#125	—	2	1	no	—
684	#125	C₂³×C₃₁	1	2	yes	—
685	#125	C₂³×C₃₁	1	2	yes	—
686	#124	—	2	2	no	—
687	#124	—	2	2	no	—
688	#124	—	2	2	no	—
689	#124	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	1	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	D₄×C₃₁	1	2	yes	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
701	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
702	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	1	no	—
712	#121	—	2	1	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	D₄×C₃₁	1	1	yes	characteristic
720	#121	D₄×C₃₁	1	1	yes	characteristic
721	#121	C₂³×C₃₁	1	2	yes	—
722	#121	C₂³×C₃₁	1	2	yes	—
723	#121	C₂³×C₃₁	1	2	yes	—
724	#121	C₂³×C₃₁	1	2	yes	—
725	#121	C₂³×C₃₁	1	1	yes	characteristic
726	#121	C₂³×C₃₁	1	1	yes	characteristic
727	#121	C₂³×C₃₁	1	2	yes	—
728	#121	C₂³×C₃₁	1	2	yes	—
729	#121	C₂³×C₃₁	1	2	yes	—
730	#120	—	2	1	no	—
731	#120	—	2	2	no	—
732	#120	—	2	2	no	—
733	#120	—	2	2	no	—
734	#120	—	2	2	no	—
735	#120	—	2	2	no	—
736	#120	—	2	2	no	—
737	#120	D₄×C₃₁	1	2	yes	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	1	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	C₂³×C₃₁	1	2	yes	—
750	C₄×D₄	C₂³×C₃₁	1	2	yes	—
751	C₄×D₄	C₂³×C₃₁	1	2	yes	—
752	C₄×D₄	C₂³×C₃₁	1	2	yes	—
753	C₄×D₄	C₂³×C₃₁	1	2	yes	—
754	#117	—	2	1	no	—
755	#117	—	2	1	no	—
756	#117	—	2	1	no	—
757	#117	—	2	2	no	—
758	#117	—	2	2	no	—
759	#117	C₂³×C₃₁	1	2	yes	—
760	#117	C₂³×C₃₁	1	2	yes	—
761	#117	C₂³×C₃₁	1	1	yes	characteristic
762	#117	C₂³×C₃₁	1	2	yes	—
763	#117	C₂³×C₃₁	1	2	yes	—
764	#117	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×C₄⋊C₄	—	2	1	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×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	—	2	1	no	—
772	C₂×C₂²⋊C₄	—	2	1	no	—
773	C₂×C₂²⋊C₄	—	2	1	no	—
774	C₂×C₄²	—	2	1	no	—
775	#107	C₂³×C₃₁	1	2	yes	—
776	#107	C₂³×C₃₁	1	2	yes	—
777	#107	C₂³×C₃₁	1	2	yes	—
778	#107	C₂³×C₃₁	1	2	yes	—
779	#107	C₂³×C₃₁	1	2	yes	—
780	#107	C₂³×C₃₁	1	2	yes	—
781	#106	C₂³×C₃₁	1	2	yes	—
782	#106	C₂³×C₃₁	1	2	yes	—
783	#106	C₂³×C₃₁	1	2	yes	—
784	#106	C₂³×C₃₁	1	2	yes	—
785	#106	C₂³×C₃₁	1	2	yes	—
786	#106	C₂³×C₃₁	1	2	yes	—
787	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
788	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
789	#103	C₂³×C₃₁	1	2	yes	—
790	#103	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	#102	C₂³×C₃₁	1	2	yes	—
801	#102	C₂³×C₃₁	1	2	yes	—
802	#102	C₂³×C₃₁	1	2	yes	—
803	#102	C₂³×C₃₁	1	2	yes	—
804	#102	C₂³×C₃₁	1	2	yes	—
805	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
806	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
807	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
813	#97	C₂³×C₃₁	1	2	yes	—
814	C₄×C₈	C₂³×C₃₁	1	2	yes	—
815	C₃₁	#61778	1	1	yes	characteristic, direct product factor, Sylow
816	C₂⁴	—	2	1	no	—
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	2	no	—
819	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
820	#41	—	4	2	no	—
821	#41	—	4	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	8	4	no	—
845	C₂×D₄	—	8	4	no	—
846	C₂×D₄	—	8	2	no	—
847	C₂×D₄	—	8	2	no	—
848	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
850	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
851	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
852	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
853	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
854	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	4	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	C₂×D₄×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	D₈	—	4	2	no	—
875	D₈	—	4	2	no	—
876	M₁₆	—	4	2	no	—
877	M₁₆	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
881	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
882	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
905	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
907	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	1	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	1	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	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
932	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₄²	—	2	2	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	1	no	—
938	C₄²	—	2	2	no	—
939	C₄²	C₂⁴×C₃₁	1	2	yes	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	4	1	no	—
944	C₂³	—	4	1	no	—
945	C₂³	—	4	1	no	—
946	C₂³	—	4	2	no	—
947	C₂³	—	4	2	no	—
948	C₂³	—	8	1	no	—
949	C₂³	—	8	1	no	—
950	C₂³	—	8	2	no	—
951	C₂³	—	8	2	no	—
952	C₂³	—	8	1	no	—
953	C₂³	—	8	1	no	—
954	C₂³	—	8	2	no	—
955	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
956	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
957	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
958	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	Q₈	—	2	2	no	—
960	Q₈	—	4	1	no	—
961	Q₈	—	8	2	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	2	no	—
964	D₄	—	2	2	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	2	no	—
967	D₄	—	4	2	no	—
968	D₄	—	4	2	no	—
969	D₄	—	4	1	no	—
970	D₄	—	4	2	no	—
971	D₄	—	4	4	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	2	no	—
974	D₄	—	8	1	no	—
975	D₄	—	8	1	no	—
976	D₄	—	8	2	no	—
977	D₄	—	8	2	no	—
978	D₄	—	8	2	no	—
979	D₄	—	8	1	no	—
980	D₄	—	8	2	no	—
981	D₄	—	8	1	no	—
982	D₄	—	8	2	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	4	1	no	—
1001	C₂×C₄	—	4	2	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	—	8	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	—	8	1	no	—
1006	C₂×C₄	—	8	2	no	—
1007	C₂×C₄	—	8	1	no	—
1008	C₂×C₄	—	8	1	no	—
1009	C₂×C₄	—	8	1	no	—
1010	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1011	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1013	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1014	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1016	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1017	C₈	—	2	2	no	—
1018	C₈	—	2	2	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	8	2	no	—
1043	C₂²	—	16	2	no	—
1044	C₂²	—	16	2	no	—
1045	C₂²	—	16	4	no	—
1046	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	C₃₁×#585	1	2	yes	—
1061	C₂	—	4	1	no	—
1062	C₂	—	4	1	no	—
1063	C₂	—	4	1	no	—
1064	C₂	—	4	2	no	—
1065	C₂	—	8	2	no	—
1066	C₂	—	8	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₃₁×#3485	1	1	yes	characteristic
1069	C₂	C₃₁×#3585	1	1	yes	characteristic
1070	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3537	C₂	semidirect
2. C₃₁×#3493	C₂	semidirect
3. C₃₁×#3355	C₂	semidirect
4. C₃₁×#3351	C₂	semidirect
5. C₃₁×#3350	C₂	semidirect
6. C₃₁×#3347	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3324	C₂	semidirect
9. C₃₁×#3318	C₂	semidirect
10. C₃₁×#3310	C₂	semidirect
11. C₃₁×#3241	C₂	semidirect
12. C₃₁×#3198	C₂	semidirect
13. C₃₁×#3194	C₂	semidirect
14. C₃₁×#3194	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3096	C₂	semidirect
17. C₃₁×#3094	C₂	semidirect
18. C₃₁×#3094	C₂	semidirect
19. C₃₁×#2978	C₂	semidirect
22. C₃₁×#556	C₂²	semidirect
24. C₃₁×#555	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
30. C₃₁×#552	C₂²	semidirect
34. C₃₁×#544	C₂²	semidirect
39. C₃₁×#537	C₂²	semidirect
45. C₃₁×#525	C₂²	semidirect
48. C₃₁×#520	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₂×C₃₁×#117	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#490	C₂²	semidirect
54. C₃₁×#486	C₂²	semidirect
55. C₃₁×#485	C₂²	semidirect
56. C₃₁×#483	C₂²	semidirect
57. C₃₁×#483	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#482	C₂²	semidirect
60. C₃₁×#482	C₂²	semidirect
61. C₃₁×#482	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#482	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#482	C₂²	semidirect
67. C₃₁×#481	C₂²	semidirect
68. C₃₁×#481	C₂²	semidirect
69. C₃₁×#481	C₂²	semidirect
70. C₃₁×#480	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	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
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#466	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#450	C₂²	semidirect
92. C₃₁×#450	C₂²	semidirect
93. C₃₁×#450	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#447	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#442	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
102. C₄×D₈×C₃₁	C₂²	semidirect
103. C₃₁×#436	C₂²	semidirect
104. C₃₁×#436	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#428	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
110. C₃₁×#428	C₂²	semidirect
111. C₃₁×#427	C₂²	semidirect
112. C₃₁×#418	C₂²	semidirect
113. C₃₁×#418	C₂²	semidirect
114. C₃₁×#418	C₂²	semidirect
115. C₂×C₃₁×#102	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
117. C₃₁×#407	C₂²	semidirect
118. C₃₁×#407	C₂²	semidirect
404. #61778	C₃₁	direct (N × H)
486. #3537	C₂×C₃₁	semidirect
487. #3493	C₂×C₃₁	semidirect
488. #3355	C₂×C₃₁	semidirect
489. #3351	C₂×C₃₁	semidirect
490. #3350	C₂×C₃₁	semidirect
491. #3347	C₂×C₃₁	semidirect
492. #3325	C₂×C₃₁	semidirect
493. #3324	C₂×C₃₁	semidirect
494. #3318	C₂×C₃₁	semidirect
495. #3310	C₂×C₃₁	semidirect
496. #3241	C₂×C₃₁	semidirect
497. #3198	C₂×C₃₁	semidirect
498. #3194	C₂×C₃₁	semidirect
499. #3194	C₂×C₃₁	semidirect
500. #3119	C₂×C₃₁	semidirect
501. #3096	C₂×C₃₁	semidirect
502. #3094	C₂×C₃₁	semidirect
503. #3094	C₂×C₃₁	semidirect
504. #2978	C₂×C₃₁	semidirect
547. #556	C₂²×C₃₁	semidirect
549. #555	C₂²×C₃₁	semidirect
553. #553	C₂²×C₃₁	semidirect
555. #552	C₂²×C₃₁	semidirect
559. #544	C₂²×C₃₁	semidirect
564. #537	C₂²×C₃₁	semidirect
570. #525	C₂²×C₃₁	semidirect
573. #520	C₂²×C₃₁	semidirect
574. #520	C₂²×C₃₁	semidirect
575. C₂×#117	C₂²×C₃₁	semidirect
576. #501	C₂²×C₃₁	semidirect
577. #499	C₂²×C₃₁	semidirect
578. #490	C₂²×C₃₁	semidirect
579. #486	C₂²×C₃₁	semidirect
580. #485	C₂²×C₃₁	semidirect
581. #483	C₂²×C₃₁	semidirect
582. #483	C₂²×C₃₁	semidirect
583. #482	C₂²×C₃₁	semidirect
584. #482	C₂²×C₃₁	semidirect
585. #482	C₂²×C₃₁	semidirect
586. #482	C₂²×C₃₁	semidirect
587. #482	C₂²×C₃₁	semidirect
588. #482	C₂²×C₃₁	semidirect
589. #482	C₂²×C₃₁	semidirect
590. #482	C₂²×C₃₁	semidirect
591. #482	C₂²×C₃₁	semidirect
592. #481	C₂²×C₃₁	semidirect
593. #481	C₂²×C₃₁	semidirect
594. #481	C₂²×C₃₁	semidirect
595. #480	C₂²×C₃₁	semidirect
596. #480	C₂²×C₃₁	semidirect
597. #480	C₂²×C₃₁	semidirect
598. #480	C₂²×C₃₁	semidirect
599. #480	C₂²×C₃₁	semidirect
600. #479	C₂²×C₃₁	semidirect
601. #478	C₂²×C₃₁	semidirect
602. #478	C₂²×C₃₁	semidirect
603. #478	C₂²×C₃₁	semidirect
604. #476	C₂²×C₃₁	semidirect
605. #474	C₂²×C₃₁	semidirect
606. #469	C₂²×C₃₁	semidirect
607. #469	C₂²×C₃₁	semidirect
608. #469	C₂²×C₃₁	semidirect
609. #468	C₂²×C₃₁	semidirect
610. #468	C₂²×C₃₁	semidirect
611. #468	C₂²×C₃₁	semidirect
612. #466	C₂²×C₃₁	semidirect
613. #465	C₂²×C₃₁	semidirect
614. #460	C₂²×C₃₁	semidirect
615. #459	C₂²×C₃₁	semidirect
616. #450	C₂²×C₃₁	semidirect
617. #450	C₂²×C₃₁	semidirect
618. #450	C₂²×C₃₁	semidirect
619. #449	C₂²×C₃₁	semidirect
620. #449	C₂²×C₃₁	semidirect
621. #447	C₂²×C₃₁	semidirect
622. #447	C₂²×C₃₁	semidirect
623. #447	C₂²×C₃₁	semidirect
624. #442	C₂²×C₃₁	semidirect
625. #440	C₂²×C₃₁	semidirect
626. C₄×SD₁₆	C₂²×C₃₁	semidirect
627. C₄×D₈	C₂²×C₃₁	semidirect
628. #436	C₂²×C₃₁	semidirect
629. #436	C₂²×C₃₁	semidirect
630. #435	C₂²×C₃₁	semidirect
631. #435	C₂²×C₃₁	semidirect
632. #433	C₂²×C₃₁	semidirect
633. #428	C₂²×C₃₁	semidirect
634. #428	C₂²×C₃₁	semidirect
635. #428	C₂²×C₃₁	semidirect
636. #427	C₂²×C₃₁	semidirect
637. #418	C₂²×C₃₁	semidirect
638. #418	C₂²×C₃₁	semidirect
639. #418	C₂²×C₃₁	semidirect
640. C₂×#102	C₂²×C₃₁	semidirect
641. #408	C₂²×C₃₁	semidirect
642. #407	C₂²×C₃₁	semidirect
643. #407	C₂²×C₃₁	semidirect
815. C₃₁	#61778	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×#3537	2
C₃₁×#3493	2
C₃₁×#3355	2
C₃₁×#3351	2
C₃₁×#3350	2
C₃₁×#3347	2
C₃₁×#3325	2
C₃₁×#3324	2
C₃₁×#3318	2
C₃₁×#3310	2
C₃₁×#3241	2
C₃₁×#3198	2
C₃₁×#3194	2
C₃₁×#3119	2
C₃₁×#3096	2
C₃₁×#3094	2
C₃₁×#2978	2
#61778	31

Subgroups — C31×#61778 #21518537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61778 #21518537