Subgroups — C₃₁×#61277 #21518036

Order 7936.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3493	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3342	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#556	—	2	1	no	—
28	C₃₁×#556	C₂²	1	2	yes	—
29	C₃₁×#556	C₂²	1	2	yes	—
30	C₃₁×#555	—	2	1	no	—
31	C₃₁×#555	C₂²	1	2	yes	—
32	C₃₁×#554	C₂²	1	2	yes	—
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#552	—	2	2	no	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	C₃₁×#552	C₂²	1	2	yes	—
39	C₃₁×#552	C₂²	1	2	yes	—
40	C₃₁×#551	—	2	2	no	—
41	C₃₁×#544	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#538	—	2	2	no	—
46	C₃₁×#537	C₂²	1	1	yes	characteristic
47	C₃₁×#536	C₂²	1	1	yes	characteristic
48	C₃₁×#533	—	2	1	no	—
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#525	C₂²	1	1	yes	characteristic
52	C₃₁×#525	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃₁×#520	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	1	yes	characteristic
56	C₃₁×#520	C₂²	1	1	yes	characteristic
57	C₃₁×#519	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
60	C₃₁×#501	C₂²	1	2	yes	complemented
61	C₃₁×#501	C₂²	1	2	yes	complemented
62	C₃₁×#500	C₂²	1	2	yes	complemented
63	C₃₁×#499	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	—
65	C₃₁×#485	C₂²	1	1	yes	characteristic
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	1	yes	characteristic
70	C₃₁×#485	C₂²	1	2	yes	complemented
71	C₃₁×#485	C₂²	1	2	yes	complemented
72	C₃₁×#485	C₂²	1	2	yes	complemented
73	C₃₁×#484	C₂²	1	1	yes	characteristic
74	C₃₁×#484	C₂²	1	2	yes	complemented
75	C₃₁×#484	C₂²	1	2	yes	complemented
76	C₃₁×#483	C₂²	1	1	yes	characteristic
77	C₃₁×#483	C₂²	1	2	yes	complemented
78	C₃₁×#482	C₂²	1	1	yes	characteristic
79	C₃₁×#482	C₂²	1	1	yes	characteristic
80	C₃₁×#482	C₂²	1	2	yes	complemented
81	C₃₁×#481	C₂²	1	1	yes	characteristic
82	C₃₁×#480	C₂²	1	1	yes	characteristic
83	C₃₁×#480	C₂²	1	2	yes	complemented
84	C₃₁×#479	C₂²	1	2	yes	complemented
85	C₃₁×#479	C₂²	1	2	yes	complemented
86	C₃₁×#479	C₂²	1	2	yes	complemented
87	C₃₁×#478	C₂²	1	2	yes	complemented
88	C₃₁×#477	C₂²	1	2	yes	complemented
89	C₃₁×#476	C₂²	1	2	yes	complemented
90	C₃₁×#475	C₂²	1	2	yes	complemented
91	C₃₁×#475	C₂²	1	2	yes	complemented
92	C₃₁×#470	C₂²	1	2	yes	—
93	C₃₁×#470	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#467	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₃₁×#436	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₃₁	C₂²	1	2	yes	—
108	C₃₁×#428	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	1	yes	characteristic
110	C₃₁×#428	C₂²	1	2	yes	—
111	C₃₁×#428	C₂²	1	2	yes	—
112	C₃₁×#428	C₂²	1	1	yes	characteristic
113	C₃₁×#428	C₂²	1	1	yes	characteristic
114	C₃₁×#428	C₂²	1	1	yes	characteristic
115	C₃₁×#428	C₂²	1	2	yes	complemented
116	C₃₁×#428	C₂²	1	2	yes	complemented
117	C₃₁×#427	C₂²	1	2	yes	—
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₃₁×#427	C₂²	1	2	yes	—
120	C₃₁×#427	C₂²	1	1	yes	characteristic
121	C₃₁×#427	C₂²	1	2	yes	complemented
122	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
123	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
124	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
125	C₃₁×#424	C₂²	1	1	yes	characteristic
126	C₃₁×#419	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₃₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₃₁×#137	—	2	4	no	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
142	C₃₁×#131	—	2	4	no	—
143	C₂×M₁₆×C₃₁	—	2	4	no	—
144	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	1	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	D₄	1	2	yes	—
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	2	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	D₄	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	D₄	1	1	yes	characteristic
207	C₃₁×#121	C₂³	1	1	yes	characteristic
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	1	yes	characteristic
210	C₃₁×#120	—	2	1	no	—
211	C₃₁×#120	D₄	1	2	yes	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	2	no	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	1	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	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₃₁×#117	—	2	1	no	—
234	C₃₁×#117	—	2	1	no	—
235	C₃₁×#117	—	2	1	no	—
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	2	no	—
239	C₃₁×#117	—	2	2	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	1	yes	characteristic
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₃₁×#117	C₂³	1	1	yes	characteristic
248	C₃₁×#117	C₂³	1	2	yes	—
249	C₃₁×#117	C₂³	1	2	yes	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₄²×C₃₁	—	2	1	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×#106	C₂³	1	2	yes	—
285	C₃₁×#106	C₂³	1	2	yes	—
286	C₃₁×#106	C₂³	1	2	yes	—
287	C₃₁×#106	C₂³	1	1	yes	characteristic
288	C₃₁×#106	C₂³	1	1	yes	characteristic
289	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
290	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₃₁	—	2	4	no	—
357	SD₁₆×C₃₁	—	2	4	no	—
358	M₁₆×C₃₁	—	2	2	no	—
359	M₁₆×C₃₁	—	2	4	no	—
360	M₁₆×C₃₁	—	2	4	no	—
361	M₁₆×C₃₁	#41	1	4	yes	—
362	C₂×C₈×C₃₁	—	2	2	no	—
363	C₂×C₈×C₃₁	—	2	2	no	—
364	C₂×C₈×C₃₁	—	2	4	no	—
365	C₂×C₈×C₃₁	—	2	4	no	—
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#61277	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	2	no	—
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	—	4	1	no	—
450	C₂³×C₃₁	—	4	1	no	—
451	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	4	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	D₄×C₃₁	—	2	4	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	8	2	no	—
471	D₄×C₃₁	—	8	1	no	—
472	D₄×C₃₁	—	8	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	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	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	1	no	—
499	C₂×C₄×C₃₁	—	8	1	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	1	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
510	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
511	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
512	C₈×C₃₁	—	2	1	no	—
513	C₈×C₃₁	—	2	1	no	—
514	C₈×C₃₁	—	2	2	no	—
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	C₂×#41	1	4	yes	—
518	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3493	C₂×C₃₁	1	1	yes	characteristic
520	#3357	C₂×C₃₁	1	2	yes	complemented
521	#3352	C₂×C₃₁	1	2	yes	complemented
522	#3350	C₂×C₃₁	1	2	yes	complemented
523	#3349	C₂×C₃₁	1	2	yes	complemented
524	#3348	C₂×C₃₁	1	2	yes	complemented
525	#3344	C₂×C₃₁	1	2	yes	complemented
526	#3342	C₂×C₃₁	1	2	yes	complemented
527	#3337	C₂×C₃₁	1	2	yes	complemented
528	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
532	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3056	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#2933	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#2912	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#2911	C₂×C₃₁	1	1	yes	characteristic, complemented
541	C₂²×C₃₁	—	2	1	no	—
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	8	2	no	—
556	C₂²×C₃₁	#547	1	2	yes	—
557	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	#547	1	2	yes	—
575	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
576	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
577	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
578	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
579	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
580	#556	—	2	1	no	—
581	#556	C₂²×C₃₁	1	2	yes	—
582	#556	C₂²×C₃₁	1	2	yes	—
583	#555	—	2	1	no	—
584	#555	C₂²×C₃₁	1	2	yes	—
585	#554	C₂²×C₃₁	1	2	yes	—
586	#553	—	2	1	no	—
587	#553	C₂²×C₃₁	1	2	yes	—
588	#552	—	2	2	no	—
589	#552	—	2	1	no	—
590	#552	C₂²×C₃₁	1	2	yes	—
591	#552	C₂²×C₃₁	1	2	yes	—
592	#552	C₂²×C₃₁	1	2	yes	—
593	#551	—	2	2	no	—
594	#544	C₂²×C₃₁	1	1	yes	characteristic
595	#544	C₂²×C₃₁	1	1	yes	characteristic
596	#542	—	2	1	no	—
597	#541	—	2	1	no	—
598	#538	—	2	2	no	—
599	#537	C₂²×C₃₁	1	1	yes	characteristic
600	#536	C₂²×C₃₁	1	1	yes	characteristic
601	#533	—	2	1	no	—
602	#529	—	2	2	no	—
603	#529	—	2	1	no	—
604	#525	C₂²×C₃₁	1	1	yes	characteristic
605	#525	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
607	#520	C₂²×C₃₁	1	1	yes	characteristic
608	#520	C₂²×C₃₁	1	1	yes	characteristic
609	#520	C₂²×C₃₁	1	1	yes	characteristic
610	#519	C₂²×C₃₁	1	1	yes	characteristic
611	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
612	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
613	#501	C₂²×C₃₁	1	2	yes	complemented
614	#501	C₂²×C₃₁	1	2	yes	complemented
615	#500	C₂²×C₃₁	1	2	yes	complemented
616	#499	C₂²×C₃₁	1	2	yes	complemented
617	#485	C₂²×C₃₁	1	2	yes	—
618	#485	C₂²×C₃₁	1	1	yes	characteristic
619	#485	C₂²×C₃₁	1	2	yes	—
620	#485	C₂²×C₃₁	1	2	yes	—
621	#485	C₂²×C₃₁	1	2	yes	—
622	#485	C₂²×C₃₁	1	1	yes	characteristic
623	#485	C₂²×C₃₁	1	2	yes	complemented
624	#485	C₂²×C₃₁	1	2	yes	complemented
625	#485	C₂²×C₃₁	1	2	yes	complemented
626	#484	C₂²×C₃₁	1	1	yes	characteristic
627	#484	C₂²×C₃₁	1	2	yes	complemented
628	#484	C₂²×C₃₁	1	2	yes	complemented
629	#483	C₂²×C₃₁	1	1	yes	characteristic
630	#483	C₂²×C₃₁	1	2	yes	complemented
631	#482	C₂²×C₃₁	1	1	yes	characteristic
632	#482	C₂²×C₃₁	1	1	yes	characteristic
633	#482	C₂²×C₃₁	1	2	yes	complemented
634	#481	C₂²×C₃₁	1	1	yes	characteristic
635	#480	C₂²×C₃₁	1	1	yes	characteristic
636	#480	C₂²×C₃₁	1	2	yes	complemented
637	#479	C₂²×C₃₁	1	2	yes	complemented
638	#479	C₂²×C₃₁	1	2	yes	complemented
639	#479	C₂²×C₃₁	1	2	yes	complemented
640	#478	C₂²×C₃₁	1	2	yes	complemented
641	#477	C₂²×C₃₁	1	2	yes	complemented
642	#476	C₂²×C₃₁	1	2	yes	complemented
643	#475	C₂²×C₃₁	1	2	yes	complemented
644	#475	C₂²×C₃₁	1	2	yes	complemented
645	#470	C₂²×C₃₁	1	2	yes	—
646	#470	C₂²×C₃₁	1	2	yes	complemented
647	#468	C₂²×C₃₁	1	2	yes	—
648	#468	C₂²×C₃₁	1	2	yes	complemented
649	#467	C₂²×C₃₁	1	2	yes	—
650	#467	C₂²×C₃₁	1	2	yes	complemented
651	#465	C₂²×C₃₁	1	2	yes	—
652	#465	C₂²×C₃₁	1	2	yes	complemented
653	#441	C₂²×C₃₁	1	2	yes	complemented
654	#440	C₂²×C₃₁	1	2	yes	complemented
655	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
656	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
657	#436	C₂²×C₃₁	1	2	yes	—
658	#435	C₂²×C₃₁	1	2	yes	—
659	#435	C₂²×C₃₁	1	2	yes	—
660	C₈×D₄	C₂²×C₃₁	1	2	yes	—
661	#428	C₂²×C₃₁	1	1	yes	characteristic
662	#428	C₂²×C₃₁	1	1	yes	characteristic
663	#428	C₂²×C₃₁	1	2	yes	—
664	#428	C₂²×C₃₁	1	2	yes	—
665	#428	C₂²×C₃₁	1	1	yes	characteristic
666	#428	C₂²×C₃₁	1	1	yes	characteristic
667	#428	C₂²×C₃₁	1	1	yes	characteristic
668	#428	C₂²×C₃₁	1	2	yes	complemented
669	#428	C₂²×C₃₁	1	2	yes	complemented
670	#427	C₂²×C₃₁	1	2	yes	—
671	#427	C₂²×C₃₁	1	1	yes	characteristic
672	#427	C₂²×C₃₁	1	2	yes	—
673	#427	C₂²×C₃₁	1	1	yes	characteristic
674	#427	C₂²×C₃₁	1	2	yes	complemented
675	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
676	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
677	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
678	#424	C₂²×C₃₁	1	1	yes	characteristic
679	#419	C₂²×C₃₁	1	1	yes	characteristic
680	#417	C₂²×C₃₁	1	1	yes	characteristic
681	#416	C₂²×C₃₁	1	1	yes	characteristic
682	#416	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
684	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
685	#408	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
687	#405	C₂²×C₃₁	1	1	yes	characteristic
688	C₂×C₃₁	—	2	2	no	—
689	C₂×C₃₁	—	4	2	no	—
690	C₂×C₃₁	—	4	1	no	—
691	C₂×C₃₁	—	4	1	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
694	C₂×C₃₁	#3584	1	1	yes	characteristic
695	C₂×C₃₁	#3586	1	1	yes	characteristic
696	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
700	#137	—	2	4	no	—
701	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
703	#131	—	2	4	no	—
704	C₂×M₁₆	—	2	4	no	—
705	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
710	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	C₂³×C₃₁	1	2	yes	—
733	#125	C₂³×C₃₁	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	D₄×C₃₁	1	2	yes	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
754	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	D₄×C₃₁	1	1	yes	characteristic
767	#121	D₄×C₃₁	1	1	yes	characteristic
768	#121	C₂³×C₃₁	1	1	yes	characteristic
769	#121	C₂³×C₃₁	1	1	yes	characteristic
770	#121	C₂³×C₃₁	1	2	yes	—
771	#120	—	2	1	no	—
772	#120	D₄×C₃₁	1	2	yes	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	C₂³×C₃₁	1	2	yes	—
792	C₄×D₄	C₂³×C₃₁	1	2	yes	—
793	C₄×D₄	C₂³×C₃₁	1	2	yes	—
794	#117	—	2	1	no	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	C₂³×C₃₁	1	1	yes	characteristic
805	#117	C₂³×C₃₁	1	1	yes	characteristic
806	#117	C₂³×C₃₁	1	1	yes	characteristic
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	#117	C₂³×C₃₁	1	1	yes	characteristic
810	#117	C₂³×C₃₁	1	1	yes	characteristic
811	#117	C₂³×C₃₁	1	2	yes	—
812	#117	C₂³×C₃₁	1	2	yes	—
813	#117	C₂³×C₃₁	1	1	yes	characteristic
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	—	2	1	no	—
828	#107	C₂³×C₃₁	1	2	yes	—
829	#107	C₂³×C₃₁	1	2	yes	—
830	#107	C₂³×C₃₁	1	2	yes	—
831	#107	C₂³×C₃₁	1	2	yes	—
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	2	yes	—
834	#107	C₂³×C₃₁	1	1	yes	characteristic
835	#107	C₂³×C₃₁	1	1	yes	characteristic
836	#107	C₂³×C₃₁	1	1	yes	characteristic
837	#107	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	2	yes	—
839	#106	C₂³×C₃₁	1	2	yes	—
840	#106	C₂³×C₃₁	1	2	yes	—
841	#106	C₂³×C₃₁	1	1	yes	characteristic
842	#106	C₂³×C₃₁	1	2	yes	—
843	#106	C₂³×C₃₁	1	2	yes	—
844	#106	C₂³×C₃₁	1	1	yes	characteristic
845	#106	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	2	yes	—
847	#106	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	1	yes	characteristic
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	1	yes	characteristic
858	#103	C₂³×C₃₁	1	1	yes	characteristic
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	1	yes	characteristic
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	C₄×C₈	C₂³×C₃₁	1	2	yes	—
876	C₃₁	#61277	1	1	yes	characteristic, direct product factor, Sylow
877	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	—	2	2	no	—
881	#41	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
918	Q₁₆	—	2	4	no	—
919	SD₁₆	—	2	4	no	—
920	M₁₆	—	2	2	no	—
921	M₁₆	—	2	4	no	—
922	M₁₆	—	2	4	no	—
923	M₁₆	#41×C₃₁	1	4	yes	—
924	C₂×C₈	—	2	2	no	—
925	C₂×C₈	—	2	2	no	—
926	C₂×C₈	—	2	4	no	—
927	C₂×C₈	—	2	4	no	—
928	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
933	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	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	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	C₂⁴×C₃₁	1	2	yes	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1013	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1015	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	8	2	no	—
1032	D₄	—	8	1	no	—
1033	D₄	—	8	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1071	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1072	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	C₂×#41×C₃₁	1	4	yes	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	2	no	—
1094	C₂²	C₃₁×#547	1	2	yes	—
1095	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	C₃₁×#547	1	2	yes	—
1113	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1114	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
1121	C₂	C₃₁×#3584	1	1	yes	characteristic
1122	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3493	C₂
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×#3495	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3352	C₂	semidirect
5. C₃₁×#3350	C₂	semidirect
6. C₃₁×#3349	C₂	semidirect
7. C₃₁×#3348	C₂	semidirect
8. C₃₁×#3344	C₂	semidirect
9. C₃₁×#3342	C₂	semidirect
10. C₃₁×#3337	C₂	semidirect
11. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3098	C₂	semidirect
13. C₃₁×#3097	C₂	semidirect
14. C₃₁×#3091	C₂	semidirect
15. C₂×C₃₁×#485	C₂	semidirect
16. C₃₁×#3084	C₂	semidirect
17. C₃₁×#3082	C₂	semidirect
18. C₃₁×#3063	C₂	semidirect
19. C₃₁×#3056	C₂	semidirect
20. C₃₁×#2947	C₂	semidirect
21. C₃₁×#2933	C₂	semidirect
22. C₃₁×#2912	C₂	semidirect
23. C₃₁×#2911	C₂	semidirect
60. C₃₁×#501	C₂²	semidirect
61. C₃₁×#501	C₂²	semidirect
62. C₃₁×#500	C₂²	semidirect
63. C₃₁×#499	C₂²	semidirect
70. C₃₁×#485	C₂²	semidirect
71. C₃₁×#485	C₂²	semidirect
72. C₃₁×#485	C₂²	semidirect
74. C₃₁×#484	C₂²	semidirect
75. C₃₁×#484	C₂²	semidirect
77. C₃₁×#483	C₂²	semidirect
80. C₃₁×#482	C₂²	semidirect
83. C₃₁×#480	C₂²	semidirect
84. C₃₁×#479	C₂²	semidirect
85. C₃₁×#479	C₂²	semidirect
86. C₃₁×#479	C₂²	semidirect
87. C₃₁×#478	C₂²	semidirect
88. C₃₁×#477	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#475	C₂²	semidirect
93. C₃₁×#470	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
97. C₃₁×#467	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₃₁×#428	C₂²	semidirect
116. C₃₁×#428	C₂²	semidirect
121. C₃₁×#427	C₂²	semidirect
124. C₂×C₃₁×#106	C₂²	semidirect
446. #61277	C₃₁	direct (N × H)
518. #3495	C₂×C₃₁	semidirect
520. #3357	C₂×C₃₁	semidirect
521. #3352	C₂×C₃₁	semidirect
522. #3350	C₂×C₃₁	semidirect
523. #3349	C₂×C₃₁	semidirect
524. #3348	C₂×C₃₁	semidirect
525. #3344	C₂×C₃₁	semidirect
526. #3342	C₂×C₃₁	semidirect
527. #3337	C₂×C₃₁	semidirect
528. #3164	C₂×C₃₁	semidirect
529. #3098	C₂×C₃₁	semidirect
530. #3097	C₂×C₃₁	semidirect
531. #3091	C₂×C₃₁	semidirect
532. C₂×#485	C₂×C₃₁	semidirect
533. #3084	C₂×C₃₁	semidirect
534. #3082	C₂×C₃₁	semidirect
535. #3063	C₂×C₃₁	semidirect
536. #3056	C₂×C₃₁	semidirect
537. #2947	C₂×C₃₁	semidirect
538. #2933	C₂×C₃₁	semidirect
539. #2912	C₂×C₃₁	semidirect
540. #2911	C₂×C₃₁	semidirect
613. #501	C₂²×C₃₁	semidirect
614. #501	C₂²×C₃₁	semidirect
615. #500	C₂²×C₃₁	semidirect
616. #499	C₂²×C₃₁	semidirect
623. #485	C₂²×C₃₁	semidirect
624. #485	C₂²×C₃₁	semidirect
625. #485	C₂²×C₃₁	semidirect
627. #484	C₂²×C₃₁	semidirect
628. #484	C₂²×C₃₁	semidirect
630. #483	C₂²×C₃₁	semidirect
633. #482	C₂²×C₃₁	semidirect
636. #480	C₂²×C₃₁	semidirect
637. #479	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
639. #479	C₂²×C₃₁	semidirect
640. #478	C₂²×C₃₁	semidirect
641. #477	C₂²×C₃₁	semidirect
642. #476	C₂²×C₃₁	semidirect
643. #475	C₂²×C₃₁	semidirect
644. #475	C₂²×C₃₁	semidirect
646. #470	C₂²×C₃₁	semidirect
648. #468	C₂²×C₃₁	semidirect
650. #467	C₂²×C₃₁	semidirect
652. #465	C₂²×C₃₁	semidirect
653. #441	C₂²×C₃₁	semidirect
654. #440	C₂²×C₃₁	semidirect
655. C₄×Q₁₆	C₂²×C₃₁	semidirect
656. C₄×SD₁₆	C₂²×C₃₁	semidirect
668. #428	C₂²×C₃₁	semidirect
669. #428	C₂²×C₃₁	semidirect
674. #427	C₂²×C₃₁	semidirect
677. C₂×#106	C₂²×C₃₁	semidirect
876. C₃₁	#61277	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×#3495	2
C₃₁×#3493	2
C₃₁×#3357	2
C₃₁×#3352	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3344	2
C₃₁×#3342	2
C₃₁×#3337	2
C₃₁×#3164	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3091	2
C₂×C₃₁×#485	2
C₃₁×#3084	2
C₃₁×#3082	2
C₃₁×#3063	2
C₃₁×#3056	2
C₃₁×#2947	2
C₃₁×#2933	2
C₃₁×#2912	2
C₃₁×#2911	2
#61277	31

Subgroups — C31×#61277 #21518036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61277 #21518036