Subgroups — C₃₁×#62141 #21518900

Order 7936.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#556	—	2	2	no	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	2	yes	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#555	C₂²	1	1	yes	characteristic
31	C₃₁×#555	C₂²	1	2	yes	—
32	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#551	—	2	2	no	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#548	—	2	1	no	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	2	yes	complemented
47	C₃₁×#529	—	2	2	no	—
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₃₁×#529	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	1	no	—
52	C₃₁×#519	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#117	—	2	1	no	—
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	2	yes	—
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#484	C₂²	1	1	yes	characteristic
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#482	C₂²	1	2	yes	—
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#481	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#479	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	1	yes	characteristic
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	1	yes	characteristic
83	C₃₁×#478	C₂²	1	2	yes	complemented
84	C₃₁×#477	C₂²	1	2	yes	complemented
85	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	2	yes	—
87	C₃₁×#476	C₂²	1	1	yes	characteristic
88	C₃₁×#476	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	1	yes	characteristic
93	C₃₁×#474	C₂²	1	1	yes	characteristic
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#463	C₂²	1	1	yes	characteristic
104	C₃₁×#463	C₂²	1	2	yes	—
105	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	complemented
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#435	C₂²	1	2	yes	—
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#427	C₂²	1	2	yes	complemented
129	C₃₁×#427	C₂²	1	2	yes	complemented
130	C₃₁×#423	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	—	2	1	no	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	1	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	C₂³	1	1	yes	characteristic
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	C₂³	1	1	yes	characteristic
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	1	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	C₂³	1	1	yes	characteristic
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#120	—	2	2	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	2	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	D₄	1	2	yes	—
229	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
230	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	2	yes	—
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	1	no	—
241	C₃₁×#117	—	2	1	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	—	2	1	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	D₄	1	1	yes	characteristic
250	C₃₁×#117	D₄	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄²×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	C₂×Q₈×C₃₁	—	2	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	4	4	no	—
322	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	4	1	no	—
332	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	4	4	no	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	Q₁₆×C₃₁	—	4	2	no	—
354	SD₁₆×C₃₁	—	2	2	no	—
355	SD₁₆×C₃₁	—	4	1	no	—
356	SD₁₆×C₃₁	—	4	2	no	—
357	D₈×C₃₁	—	2	2	no	—
358	D₈×C₃₁	—	4	1	no	—
359	M₁₆×C₃₁	—	4	2	no	—
360	C₂×C₈×C₃₁	—	4	2	no	—
361	C₂×C₈×C₃₁	—	4	2	no	—
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
367	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	2	yes	—
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	#62141	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	—	2	1	no	—
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	4	2	no	—
446	C₂³×C₃₁	—	4	2	no	—
447	C₂³×C₃₁	—	8	1	no	—
448	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
450	Q₈×C₃₁	—	2	2	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	4	4	no	—
456	Q₈×C₃₁	—	4	2	no	—
457	Q₈×C₃₁	—	8	2	no	—
458	Q₈×C₃₁	—	8	1	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	D₄×C₃₁	—	2	2	no	—
461	D₄×C₃₁	—	2	1	no	—
462	D₄×C₃₁	—	2	1	no	—
463	D₄×C₃₁	—	2	1	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	4	no	—
469	D₄×C₃₁	—	8	2	no	—
470	D₄×C₃₁	—	8	2	no	—
471	D₄×C₃₁	—	8	1	no	—
472	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	4	1	no	—
489	C₂×C₄×C₃₁	—	4	2	no	—
490	C₂×C₄×C₃₁	—	4	4	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	4	4	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
508	C₈×C₃₁	—	2	1	no	—
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	1	no	—
511	C₈×C₃₁	—	2	1	no	—
512	C₈×C₃₁	—	2	2	no	—
513	C₈×C₃₁	—	2	2	no	—
514	#3518	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3349	C₂×C₃₁	1	2	yes	complemented
521	#3348	C₂×C₃₁	1	2	yes	complemented
522	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3319	C₂×C₃₁	1	2	yes	complemented
525	#3311	C₂×C₃₁	1	2	yes	complemented
526	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3250	C₂×C₃₁	1	2	yes	complemented
530	#3240	C₂×C₃₁	1	2	yes	complemented
531	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3111	C₂×C₃₁	1	2	yes	complemented
533	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3076	C₂×C₃₁	1	2	yes	complemented
536	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
537	C₂²×C₃₁	—	2	2	no	—
538	C₂²×C₃₁	—	2	1	no	—
539	C₂²×C₃₁	—	2	2	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	8	4	no	—
553	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	4	2	no	—
562	C₄×C₃₁	—	4	2	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	#575	1	2	yes	—
571	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
572	C₄×C₃₁	#585	1	1	yes	characteristic
573	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#556	—	2	2	no	—
575	#556	—	2	1	no	—
576	#556	C₂²×C₃₁	1	1	yes	characteristic
577	#556	C₂²×C₃₁	1	2	yes	—
578	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	#555	C₂²×C₃₁	1	1	yes	characteristic
580	#555	C₂²×C₃₁	1	2	yes	—
581	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#554	C₂²×C₃₁	1	1	yes	characteristic
583	#553	—	2	1	no	—
584	#552	—	2	1	no	—
585	#552	C₂²×C₃₁	1	2	yes	—
586	#551	—	2	2	no	—
587	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
588	#548	—	2	1	no	—
589	#547	C₂²×C₃₁	1	1	yes	characteristic
590	#546	C₂²×C₃₁	1	2	yes	—
591	#542	—	2	1	no	—
592	#542	—	2	2	no	—
593	#533	C₂²×C₃₁	1	1	yes	characteristic
594	#533	C₂²×C₃₁	1	1	yes	characteristic
595	#533	C₂²×C₃₁	1	2	yes	complemented
596	#529	—	2	2	no	—
597	#529	C₂²×C₃₁	1	1	yes	characteristic
598	#529	C₂²×C₃₁	1	2	yes	—
599	#529	C₂²×C₃₁	1	2	yes	complemented
600	#525	—	2	1	no	—
601	#519	—	2	1	no	—
602	C₄×#41	C₂²×C₃₁	1	2	yes	—
603	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
605	C₂×#117	—	2	1	no	—
606	#501	C₂²×C₃₁	1	2	yes	complemented
607	#501	C₂²×C₃₁	1	2	yes	complemented
608	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#489	C₂²×C₃₁	1	2	yes	—
611	#489	C₂²×C₃₁	1	2	yes	—
612	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#485	C₂²×C₃₁	1	2	yes	—
615	#485	C₂²×C₃₁	1	2	yes	—
616	#485	C₂²×C₃₁	1	2	yes	complemented
617	#485	C₂²×C₃₁	1	2	yes	complemented
618	#485	C₂²×C₃₁	1	2	yes	complemented
619	#484	C₂²×C₃₁	1	1	yes	characteristic
620	#482	C₂²×C₃₁	1	2	yes	—
621	#482	C₂²×C₃₁	1	2	yes	—
622	#482	C₂²×C₃₁	1	2	yes	complemented
623	#481	C₂²×C₃₁	1	1	yes	characteristic
624	#479	C₂²×C₃₁	1	2	yes	complemented
625	#479	C₂²×C₃₁	1	2	yes	complemented
626	#479	C₂²×C₃₁	1	2	yes	complemented
627	#479	C₂²×C₃₁	1	2	yes	complemented
628	#478	C₂²×C₃₁	1	1	yes	characteristic
629	#478	C₂²×C₃₁	1	2	yes	—
630	#478	C₂²×C₃₁	1	2	yes	—
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#478	C₂²×C₃₁	1	2	yes	complemented
633	#477	C₂²×C₃₁	1	2	yes	complemented
634	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#476	C₂²×C₃₁	1	2	yes	—
636	#476	C₂²×C₃₁	1	1	yes	characteristic
637	#476	C₂²×C₃₁	1	1	yes	characteristic
638	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#475	C₂²×C₃₁	1	2	yes	complemented
640	#474	C₂²×C₃₁	1	2	yes	—
641	#474	C₂²×C₃₁	1	1	yes	characteristic
642	#474	C₂²×C₃₁	1	1	yes	characteristic
643	#470	C₂²×C₃₁	1	2	yes	—
644	#468	C₂²×C₃₁	1	2	yes	—
645	#467	C₂²×C₃₁	1	2	yes	complemented
646	#466	C₂²×C₃₁	1	2	yes	—
647	#465	C₂²×C₃₁	1	2	yes	—
648	#465	C₂²×C₃₁	1	2	yes	complemented
649	#464	C₂²×C₃₁	1	2	yes	—
650	#464	C₂²×C₃₁	1	2	yes	complemented
651	#463	C₂²×C₃₁	1	1	yes	characteristic
652	#463	C₂²×C₃₁	1	1	yes	characteristic
653	#463	C₂²×C₃₁	1	2	yes	—
654	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#452	C₂²×C₃₁	1	2	yes	—
657	#450	C₂²×C₃₁	1	1	yes	characteristic
658	#449	C₂²×C₃₁	1	2	yes	—
659	#447	C₂²×C₃₁	1	1	yes	characteristic
660	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#442	C₂²×C₃₁	1	2	yes	—
663	#441	C₂²×C₃₁	1	2	yes	complemented
664	#440	C₂²×C₃₁	1	2	yes	—
665	#440	C₂²×C₃₁	1	2	yes	complemented
666	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
668	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
670	#435	C₂²×C₃₁	1	2	yes	—
671	#435	C₂²×C₃₁	1	2	yes	—
672	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#432	C₂²×C₃₁	1	2	yes	complemented
675	#431	C₂²×C₃₁	1	1	yes	characteristic
676	#428	C₂²×C₃₁	1	2	yes	—
677	#427	C₂²×C₃₁	1	2	yes	complemented
678	#427	C₂²×C₃₁	1	2	yes	complemented
679	#423	C₂²×C₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
681	#418	C₂²×C₃₁	1	2	yes	—
682	#416	C₂²×C₃₁	1	2	yes	—
683	#416	C₂²×C₃₁	1	2	yes	—
684	C₂×C₃₁	—	4	2	no	—
685	C₂×C₃₁	—	4	1	no	—
686	C₂×C₃₁	—	4	2	no	—
687	C₂×C₃₁	—	8	1	no	—
688	C₂×C₃₁	—	8	1	no	—
689	C₂×C₃₁	#3489	1	1	yes	characteristic
690	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
691	C₂×C₃₁	#3584	1	1	yes	characteristic
692	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
693	C₂×#41	C₂³×C₃₁	1	2	yes	—
694	C₂²×Q₈	—	2	1	no	—
695	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂³×C₄	—	2	1	no	—
697	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
701	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
705	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
706	C₄⋊Q₈	—	2	1	no	—
707	C₄⋊Q₈	—	2	2	no	—
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	1	no	—
721	#126	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	1	no	—
724	#125	C₂³×C₃₁	1	1	yes	characteristic
725	#125	C₂³×C₃₁	1	2	yes	—
726	#125	C₂³×C₃₁	1	2	yes	—
727	#124	—	2	2	no	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	C₂³×C₃₁	1	1	yes	characteristic
734	#124	C₂³×C₃₁	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	C₂³×C₃₁	1	2	yes	—
761	#121	C₂³×C₃₁	1	1	yes	characteristic
762	#121	C₂³×C₃₁	1	2	yes	—
763	#120	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
774	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
775	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
777	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	D₄×C₃₁	1	2	yes	—
786	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₃₁	1	2	yes	—
792	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₃₁	1	2	yes	—
794	C₄×D₄	C₂³×C₃₁	1	2	yes	—
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	—	2	2	no	—
806	#117	D₄×C₃₁	1	1	yes	characteristic
807	#117	D₄×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	#117	C₂³×C₃₁	1	2	yes	—
810	#117	C₂³×C₃₁	1	2	yes	—
811	#117	C₂³×C₃₁	1	2	yes	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	—	2	1	no	—
816	C₂×C₂²⋊C₄	—	2	2	no	—
817	C₂×C₄²	—	2	2	no	—
818	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
820	#107	C₂³×C₃₁	1	1	yes	characteristic
821	#107	C₂³×C₃₁	1	2	yes	—
822	#107	C₂³×C₃₁	1	2	yes	—
823	#107	C₂³×C₃₁	1	2	yes	—
824	#107	C₂³×C₃₁	1	2	yes	—
825	#107	C₂³×C₃₁	1	1	yes	characteristic
826	#107	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	1	yes	characteristic
828	#106	C₂³×C₃₁	1	2	yes	—
829	#106	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	2	yes	—
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	1	yes	characteristic
833	#106	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	1	yes	characteristic
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	1	yes	characteristic
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
865	#97	C₂³×C₃₁	1	2	yes	—
866	#97	C₂³×C₃₁	1	2	yes	—
867	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₃₁	#62141	1	1	yes	characteristic, direct product factor, Sylow
870	C₂⁴	—	2	1	no	—
871	#41	—	2	4	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	4	4	no	—
880	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	4	1	no	—
890	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	2	2	no	—
913	SD₁₆	—	4	1	no	—
914	SD₁₆	—	4	2	no	—
915	D₈	—	2	2	no	—
916	D₈	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	C₂×C₈	—	4	2	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
925	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	C₂×D₄×C₃₁	1	2	yes	—
993	C₄²	C₂×D₄×C₃₁	1	2	yes	—
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄²	C₂⁴×C₃₁	1	2	yes	—
998	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	4	2	no	—
1003	C₂³	—	4	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	4	no	—
1013	Q₈	—	4	2	no	—
1014	Q₈	—	8	2	no	—
1015	Q₈	—	8	1	no	—
1016	Q₈	—	8	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	1	no	—
1029	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	8	4	no	—
1087	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1088	C₄	—	2	2	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	C₃₁×#575	1	2	yes	—
1105	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1106	C₄	C₃₁×#585	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	4	2	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	8	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₃₁×#3489	1	1	yes	characteristic
1113	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1114	C₂	C₃₁×#3584	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3518	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3349	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3341	C₂	semidirect
10. C₃₁×#3340	C₂	semidirect
11. C₃₁×#3319	C₂	semidirect
12. C₃₁×#3311	C₂	semidirect
13. C₃₁×#3303	C₂	semidirect
14. C₃₁×#3302	C₂	semidirect
15. C₃₁×#3252	C₂	semidirect
16. C₃₁×#3250	C₂	semidirect
17. C₃₁×#3240	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3077	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
24. Q₈²×C₃₁	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
32. C₃₁×#555	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
50. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
78. C₃₁×#479	C₂²	semidirect
83. C₃₁×#478	C₂²	semidirect
84. C₃₁×#477	C₂²	semidirect
85. C₃₁×#477	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
96. C₃₁×#467	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
105. C₃₁×#462	C₂²	semidirect
106. C₃₁×#461	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
114. C₃₁×#441	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
129. C₃₁×#427	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
441. #62141	C₃₁	direct (N × H)
514. #3518	C₂×C₃₁	semidirect
515. #3475	C₂×C₃₁	semidirect
516. #3385	C₂×C₃₁	semidirect
517. #3384	C₂×C₃₁	semidirect
518. #3369	C₂×C₃₁	semidirect
519. #3367	C₂×C₃₁	semidirect
520. #3349	C₂×C₃₁	semidirect
521. #3348	C₂×C₃₁	semidirect
522. #3341	C₂×C₃₁	semidirect
523. #3340	C₂×C₃₁	semidirect
524. #3319	C₂×C₃₁	semidirect
525. #3311	C₂×C₃₁	semidirect
526. #3303	C₂×C₃₁	semidirect
527. #3302	C₂×C₃₁	semidirect
528. #3252	C₂×C₃₁	semidirect
529. #3250	C₂×C₃₁	semidirect
530. #3240	C₂×C₃₁	semidirect
531. #3231	C₂×C₃₁	semidirect
532. #3111	C₂×C₃₁	semidirect
533. #3105	C₂×C₃₁	semidirect
534. #3077	C₂×C₃₁	semidirect
535. #3076	C₂×C₃₁	semidirect
536. #2990	C₂×C₃₁	semidirect
573. Q₈²	C₂²×C₃₁	semidirect
578. #556	C₂²×C₃₁	semidirect
581. #555	C₂²×C₃₁	semidirect
587. D₄×Q₈	C₂²×C₃₁	semidirect
595. #533	C₂²×C₃₁	semidirect
599. #529	C₂²×C₃₁	semidirect
606. #501	C₂²×C₃₁	semidirect
607. #501	C₂²×C₃₁	semidirect
608. #500	C₂²×C₃₁	semidirect
609. #498	C₂²×C₃₁	semidirect
612. #487	C₂²×C₃₁	semidirect
613. #487	C₂²×C₃₁	semidirect
616. #485	C₂²×C₃₁	semidirect
617. #485	C₂²×C₃₁	semidirect
618. #485	C₂²×C₃₁	semidirect
622. #482	C₂²×C₃₁	semidirect
624. #479	C₂²×C₃₁	semidirect
625. #479	C₂²×C₃₁	semidirect
626. #479	C₂²×C₃₁	semidirect
627. #479	C₂²×C₃₁	semidirect
632. #478	C₂²×C₃₁	semidirect
633. #477	C₂²×C₃₁	semidirect
634. #477	C₂²×C₃₁	semidirect
638. #476	C₂²×C₃₁	semidirect
639. #475	C₂²×C₃₁	semidirect
645. #467	C₂²×C₃₁	semidirect
648. #465	C₂²×C₃₁	semidirect
650. #464	C₂²×C₃₁	semidirect
654. #462	C₂²×C₃₁	semidirect
655. #461	C₂²×C₃₁	semidirect
660. #446	C₂²×C₃₁	semidirect
661. #446	C₂²×C₃₁	semidirect
663. #441	C₂²×C₃₁	semidirect
665. #440	C₂²×C₃₁	semidirect
672. C₈×D₄	C₂²×C₃₁	semidirect
673. C₈×D₄	C₂²×C₃₁	semidirect
674. #432	C₂²×C₃₁	semidirect
677. #427	C₂²×C₃₁	semidirect
678. #427	C₂²×C₃₁	semidirect
680. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
869. C₃₁	#62141	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×#3518	2
C₃₁×#3475	2
C₃₁×#3385	2
C₃₁×#3384	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#3319	2
C₃₁×#3311	2
C₃₁×#3303	2
C₃₁×#3302	2
C₃₁×#3252	2
C₃₁×#3250	2
C₃₁×#3240	2
C₃₁×#3231	2
C₃₁×#3111	2
C₃₁×#3105	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#2990	2
#62141	31

Subgroups — C31×#62141 #21518900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62141 #21518900