Subgroups — C₃₁×#62552 #21519311

Order 7936.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	C₂²	1	2	yes	complemented
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	C₃₁×#547	—	2	1	no	—
36	C₃₁×#547	C₂²	1	2	yes	complemented
37	C₃₁×#546	—	2	1	no	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	D₄²×C₃₁	—	2	1	no	—
40	D₄²×C₃₁	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	complemented
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	complemented
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#540	C₂²	1	2	yes	—
48	C₃₁×#536	—	2	2	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	2	yes	—
51	C₃₁×#534	—	2	2	no	—
52	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#496	C₂²	1	2	yes	complemented
60	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#488	C₂²	1	2	yes	complemented
66	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#486	C₂²	1	1	yes	characteristic
69	C₃₁×#486	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#486	C₂²	1	2	yes	complemented
73	C₃₁×#486	C₂²	1	2	yes	complemented
74	C₃₁×#486	C₂²	1	2	yes	complemented
75	C₃₁×#483	C₂²	1	2	yes	complemented
76	C₃₁×#482	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#481	C₂²	1	2	yes	complemented
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#474	C₂²	1	2	yes	complemented
89	C₃₁×#469	C₂²	1	2	yes	complemented
90	C₃₁×#468	C₂²	1	2	yes	complemented
91	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#466	C₂²	1	1	yes	characteristic
93	C₃₁×#466	C₂²	1	2	yes	complemented
94	C₃₁×#465	C₂²	1	1	yes	characteristic
95	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#464	C₂²	1	2	yes	complemented
98	C₃₁×#463	C₂²	1	2	yes	complemented
99	C₃₁×#460	C₂²	1	1	yes	characteristic
100	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	2	yes	complemented
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#459	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#447	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	2	yes	complemented
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#418	C₂²	1	2	yes	complemented
128	C₃₁×#417	C₂²	1	2	yes	complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
131	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	2	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×D₄×C₃₁	—	2	2	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	—	2	2	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×#127	—	2	1	no	—
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#127	C₂³	1	2	yes	—
172	C₃₁×#127	C₂³	1	2	yes	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	D₄	1	2	yes	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	D₄	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#125	C₂³	1	1	yes	characteristic
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	D₄	1	1	yes	characteristic
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#124	C₂³	1	1	yes	characteristic
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	1	no	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	D₄	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	1	no	—
219	C₃₁×#121	—	2	1	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	D₄	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	2	yes	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₃₁×#120	—	2	2	no	—
235	C₃₁×#120	—	2	2	no	—
236	C₃₁×#120	—	2	2	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#103	C₂³	1	1	yes	characteristic
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	1	yes	characteristic
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	1	yes	characteristic
284	C₃₁×#102	C₂³	1	2	yes	—
285	C₃₁×#102	C₂³	1	1	yes	characteristic
286	C₃₁×#102	C₂³	1	2	yes	—
287	C₃₁×#102	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	8	4	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₃₁	—	2	1	no	—
327	C₂×D₄×C₃₁	—	2	1	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	4	2	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	8	2	no	—
347	C₂×D₄×C₃₁	—	8	2	no	—
348	C₂×D₄×C₃₁	—	8	2	no	—
349	C₂×D₄×C₃₁	—	8	4	no	—
350	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
368	Q₁₆×C₃₁	—	4	1	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	4	1	no	—
371	SD₁₆×C₃₁	—	4	1	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	D₈×C₃₁	—	4	2	no	—
374	D₈×C₃₁	—	4	1	no	—
375	D₈×C₃₁	—	4	2	no	—
376	M₁₆×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	—	4	2	no	—
378	C₂×C₈×C₃₁	—	4	1	no	—
379	C₂×C₈×C₃₁	—	4	1	no	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	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	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	2	yes	—
450	#62552	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	4	4	no	—
456	C₂³×C₃₁	—	8	2	no	—
457	C₂³×C₃₁	—	8	2	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	—	8	2	no	—
460	C₂³×C₃₁	—	8	2	no	—
461	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	Q₈×C₃₁	—	8	1	no	—
471	Q₈×C₃₁	—	8	2	no	—
472	D₄×C₃₁	—	2	4	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	4	4	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	2	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3543	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3310	C₂×C₃₁	1	2	yes	complemented
544	#3306	C₂×C₃₁	1	2	yes	complemented
545	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3296	C₂×C₃₁	1	2	yes	complemented
547	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3294	C₂×C₃₁	1	2	yes	complemented
549	#3241	C₂×C₃₁	1	2	yes	complemented
550	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3224	C₂×C₃₁	1	2	yes	complemented
552	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3179	C₂×C₃₁	1	2	yes	complemented
554	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3136	C₂×C₃₁	1	2	yes	complemented
556	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	4	2	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	16	4	no	—
576	C₂²×C₃₁	—	16	4	no	—
577	C₂²×C₃₁	#576	1	2	yes	—
578	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	2	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	#577	1	2	yes	—
595	C₄×C₃₁	#585	1	1	yes	characteristic
596	C₄×C₃₁	#585	1	1	yes	characteristic
597	#563	—	2	2	no	—
598	#560	—	2	2	no	—
599	#559	C₂²×C₃₁	1	1	yes	characteristic
600	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#552	—	2	1	no	—
605	#552	C₂²×C₃₁	1	2	yes	complemented
606	#550	C₂²×C₃₁	1	1	yes	characteristic
607	#550	C₂²×C₃₁	1	1	yes	characteristic
608	#547	—	2	1	no	—
609	#547	C₂²×C₃₁	1	2	yes	complemented
610	#546	—	2	1	no	—
611	#546	C₂²×C₃₁	1	2	yes	—
612	D₄²	—	2	1	no	—
613	D₄²	C₂²×C₃₁	1	2	yes	—
614	D₄²	C₂²×C₃₁	1	1	yes	characteristic
615	#544	—	2	1	no	—
616	#544	C₂²×C₃₁	1	2	yes	complemented
617	#542	—	2	1	no	—
618	#542	C₂²×C₃₁	1	2	yes	complemented
619	#540	—	2	1	no	—
620	#540	C₂²×C₃₁	1	2	yes	—
621	#536	—	2	2	no	—
622	#535	—	2	1	no	—
623	#535	C₂²×C₃₁	1	2	yes	—
624	#534	—	2	2	no	—
625	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
627	#529	C₂²×C₃₁	1	1	yes	characteristic
628	#529	C₂²×C₃₁	1	1	yes	characteristic
629	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#501	C₂²×C₃₁	1	2	yes	complemented
631	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#496	C₂²×C₃₁	1	2	yes	complemented
633	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#490	C₂²×C₃₁	1	2	yes	complemented
635	#490	C₂²×C₃₁	1	2	yes	complemented
636	#489	C₂²×C₃₁	1	2	yes	complemented
637	#489	C₂²×C₃₁	1	2	yes	complemented
638	#488	C₂²×C₃₁	1	2	yes	complemented
639	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#486	C₂²×C₃₁	1	1	yes	characteristic
642	#486	C₂²×C₃₁	1	1	yes	characteristic
643	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#486	C₂²×C₃₁	1	2	yes	complemented
646	#486	C₂²×C₃₁	1	2	yes	complemented
647	#486	C₂²×C₃₁	1	2	yes	complemented
648	#483	C₂²×C₃₁	1	2	yes	complemented
649	#482	C₂²×C₃₁	1	2	yes	complemented
650	#482	C₂²×C₃₁	1	2	yes	complemented
651	#481	C₂²×C₃₁	1	2	yes	complemented
652	#480	C₂²×C₃₁	1	2	yes	—
653	#480	C₂²×C₃₁	1	2	yes	complemented
654	#478	C₂²×C₃₁	1	2	yes	complemented
655	#478	C₂²×C₃₁	1	2	yes	complemented
656	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#476	C₂²×C₃₁	1	2	yes	complemented
660	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#474	C₂²×C₃₁	1	2	yes	complemented
662	#469	C₂²×C₃₁	1	2	yes	complemented
663	#468	C₂²×C₃₁	1	2	yes	complemented
664	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#466	C₂²×C₃₁	1	1	yes	characteristic
666	#466	C₂²×C₃₁	1	2	yes	complemented
667	#465	C₂²×C₃₁	1	1	yes	characteristic
668	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#465	C₂²×C₃₁	1	2	yes	complemented
670	#464	C₂²×C₃₁	1	2	yes	complemented
671	#463	C₂²×C₃₁	1	2	yes	complemented
672	#460	C₂²×C₃₁	1	1	yes	characteristic
673	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#460	C₂²×C₃₁	1	2	yes	complemented
675	#459	C₂²×C₃₁	1	1	yes	characteristic
676	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#459	C₂²×C₃₁	1	2	yes	complemented
678	#452	C₂²×C₃₁	1	2	yes	complemented
679	#450	C₂²×C₃₁	1	2	yes	complemented
680	#450	C₂²×C₃₁	1	2	yes	complemented
681	#449	C₂²×C₃₁	1	2	yes	complemented
682	#447	C₂²×C₃₁	1	2	yes	complemented
683	#447	C₂²×C₃₁	1	2	yes	complemented
684	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#442	C₂²×C₃₁	1	2	yes	complemented
687	#440	C₂²×C₃₁	1	2	yes	complemented
688	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
692	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
693	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#435	C₂²×C₃₁	1	2	yes	complemented
696	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
697	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#433	C₂²×C₃₁	1	2	yes	complemented
699	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#418	C₂²×C₃₁	1	2	yes	complemented
701	#417	C₂²×C₃₁	1	2	yes	complemented
702	#416	C₂²×C₃₁	1	2	yes	complemented
703	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
704	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
705	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
706	#405	C₂²×C₃₁	1	2	yes	complemented
707	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	C₂×C₃₁	—	2	2	no	—
709	C₂×C₃₁	—	4	2	no	—
710	C₂×C₃₁	—	8	1	no	—
711	C₂×C₃₁	—	8	2	no	—
712	C₂×C₃₁	—	8	2	no	—
713	C₂×C₃₁	—	8	1	no	—
714	C₂×C₃₁	#3500	1	1	yes	characteristic
715	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
716	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	2	no	—
719	C₂×#41	C₂³×C₃₁	1	2	yes	—
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×D₄	—	2	2	no	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
726	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×D₈	C₂³×C₃₁	1	2	yes	—
733	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×D₈	C₂³×C₃₁	1	2	yes	—
735	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
739	C₄⋊Q₈	—	2	2	no	—
740	C₄⋊Q₈	—	2	2	no	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
748	#127	—	2	1	no	—
749	#127	—	2	1	no	—
750	#127	—	2	1	no	—
751	#127	C₂³×C₃₁	1	2	yes	—
752	#127	C₂³×C₃₁	1	1	yes	characteristic
753	#127	C₂³×C₃₁	1	1	yes	characteristic
754	#127	C₂³×C₃₁	1	2	yes	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#126	—	2	1	no	—
759	#126	D₄×C₃₁	1	2	yes	—
760	#125	—	2	1	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	D₄×C₃₁	1	1	yes	characteristic
764	#125	C₂³×C₃₁	1	1	yes	characteristic
765	#125	C₂³×C₃₁	1	1	yes	characteristic
766	#125	C₂³×C₃₁	1	2	yes	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	D₄×C₃₁	1	1	yes	characteristic
771	#124	C₂³×C₃₁	1	1	yes	characteristic
772	#124	C₂³×C₃₁	1	1	yes	characteristic
773	#124	C₂³×C₃₁	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	1	no	—
776	#123	—	2	1	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	D₄×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₃₁	1	1	yes	characteristic
808	#121	C₂³×C₃₁	1	1	yes	characteristic
809	#121	C₂³×C₃₁	1	1	yes	characteristic
810	#121	C₂³×C₃₁	1	2	yes	—
811	#121	C₂³×C₃₁	1	2	yes	—
812	#121	C₂³×C₃₁	1	2	yes	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
823	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	2	yes	—
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	C₂³×C₃₁	1	2	yes	—
841	#117	C₂³×C₃₁	1	2	yes	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
848	#107	C₂³×C₃₁	1	1	yes	characteristic
849	#107	C₂³×C₃₁	1	2	yes	—
850	#107	C₂³×C₃₁	1	1	yes	characteristic
851	#107	C₂³×C₃₁	1	2	yes	—
852	#106	C₂³×C₃₁	1	1	yes	characteristic
853	#106	C₂³×C₃₁	1	1	yes	characteristic
854	#106	C₂³×C₃₁	1	2	yes	—
855	#106	C₂³×C₃₁	1	2	yes	—
856	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	1	yes	characteristic
865	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	1	yes	characteristic
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	1	yes	characteristic
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
887	#97	C₂³×C₃₁	1	2	yes	—
888	#97	C₂³×C₃₁	1	2	yes	—
889	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₃₁	1	2	yes	—
894	C₃₁	#62552	1	1	yes	characteristic, direct product factor, Sylow
895	C₂⁴	—	2	2	no	—
896	C₂⁴	—	2	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	4	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	8	2	no	—
906	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	—	8	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	—	8	4	no	—
933	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
938	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
951	Q₁₆	—	4	1	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	1	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	D₈	—	4	2	no	—
957	D₈	—	4	1	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	—	4	1	no	—
962	C₂×C₈	—	4	1	no	—
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
968	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₃₁	1	2	yes	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	8	2	no	—
1039	C₂³	—	8	2	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	2	no	—
1054	D₄	—	2	4	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	16	4	no	—
1135	C₂²	—	16	4	no	—
1136	C₂²	C₃₁×#576	1	2	yes	—
1137	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	C₃₁×#577	1	2	yes	—
1154	C₄	C₃₁×#585	1	1	yes	characteristic
1155	C₄	C₃₁×#585	1	1	yes	characteristic
1156	C₂	—	2	2	no	—
1157	C₂	—	4	2	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	1	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	C₃₁×#3500	1	1	yes	characteristic
1163	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1164	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3544	C₂	semidirect
2. C₃₁×#3543	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3362	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3325	C₂	semidirect
9. C₃₁×#3310	C₂	semidirect
10. C₃₁×#3306	C₂	semidirect
11. C₃₁×#3305	C₂	semidirect
12. C₃₁×#3296	C₂	semidirect
13. C₃₁×#3295	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3241	C₂	semidirect
16. C₃₁×#3238	C₂	semidirect
17. C₃₁×#3224	C₂	semidirect
18. C₃₁×#3217	C₂	semidirect
19. C₃₁×#3179	C₂	semidirect
20. C₃₁×#3168	C₂	semidirect
21. C₃₁×#3136	C₂	semidirect
22. C₂×C₃₁×#486	C₂	semidirect
23. C₃₁×#2966	C₂	semidirect
27. Q₈²×C₃₁	C₂²	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
32. C₃₁×#552	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
43. C₃₁×#544	C₂²	semidirect
45. C₃₁×#542	C₂²	semidirect
52. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#499	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
63. C₃₁×#489	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
66. C₃₁×#488	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
70. C₃₁×#486	C₂²	semidirect
71. C₃₁×#486	C₂²	semidirect
72. C₃₁×#486	C₂²	semidirect
73. C₃₁×#486	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#483	C₂²	semidirect
76. C₃₁×#482	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
78. C₃₁×#481	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#477	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
89. C₃₁×#469	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
91. C₃₁×#467	C₂²	semidirect
93. C₃₁×#466	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#464	C₂²	semidirect
98. C₃₁×#463	C₂²	semidirect
100. C₃₁×#460	C₂²	semidirect
101. C₃₁×#460	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#450	C₂²	semidirect
107. C₃₁×#450	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#447	C₂²	semidirect
110. C₃₁×#447	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#418	C₂²	semidirect
128. C₃₁×#417	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₂×C₃₁×#102	C₂²	semidirect
131. C₂×C₃₁×#102	C₂²	semidirect
132. C₂×C₃₁×#102	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
450. #62552	C₃₁	direct (N × H)
535. #3544	C₂×C₃₁	semidirect
536. #3543	C₂×C₃₁	semidirect
537. #3375	C₂×C₃₁	semidirect
538. #3366	C₂×C₃₁	semidirect
539. #3362	C₂×C₃₁	semidirect
540. #3361	C₂×C₃₁	semidirect
541. #3333	C₂×C₃₁	semidirect
542. #3325	C₂×C₃₁	semidirect
543. #3310	C₂×C₃₁	semidirect
544. #3306	C₂×C₃₁	semidirect
545. #3305	C₂×C₃₁	semidirect
546. #3296	C₂×C₃₁	semidirect
547. #3295	C₂×C₃₁	semidirect
548. #3294	C₂×C₃₁	semidirect
549. #3241	C₂×C₃₁	semidirect
550. #3238	C₂×C₃₁	semidirect
551. #3224	C₂×C₃₁	semidirect
552. #3217	C₂×C₃₁	semidirect
553. #3179	C₂×C₃₁	semidirect
554. #3168	C₂×C₃₁	semidirect
555. #3136	C₂×C₃₁	semidirect
556. C₂×#486	C₂×C₃₁	semidirect
557. #2966	C₂×C₃₁	semidirect
600. Q₈²	C₂²×C₃₁	semidirect
601. #555	C₂²×C₃₁	semidirect
602. #554	C₂²×C₃₁	semidirect
603. #554	C₂²×C₃₁	semidirect
605. #552	C₂²×C₃₁	semidirect
609. #547	C₂²×C₃₁	semidirect
616. #544	C₂²×C₃₁	semidirect
618. #542	C₂²×C₃₁	semidirect
625. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
629. #529	C₂²×C₃₁	semidirect
630. #501	C₂²×C₃₁	semidirect
631. #499	C₂²×C₃₁	semidirect
632. #496	C₂²×C₃₁	semidirect
633. #495	C₂²×C₃₁	semidirect
634. #490	C₂²×C₃₁	semidirect
635. #490	C₂²×C₃₁	semidirect
636. #489	C₂²×C₃₁	semidirect
637. #489	C₂²×C₃₁	semidirect
638. #488	C₂²×C₃₁	semidirect
639. #488	C₂²×C₃₁	semidirect
640. #488	C₂²×C₃₁	semidirect
643. #486	C₂²×C₃₁	semidirect
644. #486	C₂²×C₃₁	semidirect
645. #486	C₂²×C₃₁	semidirect
646. #486	C₂²×C₃₁	semidirect
647. #486	C₂²×C₃₁	semidirect
648. #483	C₂²×C₃₁	semidirect
649. #482	C₂²×C₃₁	semidirect
650. #482	C₂²×C₃₁	semidirect
651. #481	C₂²×C₃₁	semidirect
653. #480	C₂²×C₃₁	semidirect
654. #478	C₂²×C₃₁	semidirect
655. #478	C₂²×C₃₁	semidirect
656. #477	C₂²×C₃₁	semidirect
657. #477	C₂²×C₃₁	semidirect
658. #476	C₂²×C₃₁	semidirect
659. #476	C₂²×C₃₁	semidirect
660. #476	C₂²×C₃₁	semidirect
661. #474	C₂²×C₃₁	semidirect
662. #469	C₂²×C₃₁	semidirect
663. #468	C₂²×C₃₁	semidirect
664. #467	C₂²×C₃₁	semidirect
666. #466	C₂²×C₃₁	semidirect
668. #465	C₂²×C₃₁	semidirect
669. #465	C₂²×C₃₁	semidirect
670. #464	C₂²×C₃₁	semidirect
671. #463	C₂²×C₃₁	semidirect
673. #460	C₂²×C₃₁	semidirect
674. #460	C₂²×C₃₁	semidirect
676. #459	C₂²×C₃₁	semidirect
677. #459	C₂²×C₃₁	semidirect
678. #452	C₂²×C₃₁	semidirect
679. #450	C₂²×C₃₁	semidirect
680. #450	C₂²×C₃₁	semidirect
681. #449	C₂²×C₃₁	semidirect
682. #447	C₂²×C₃₁	semidirect
683. #447	C₂²×C₃₁	semidirect
684. #446	C₂²×C₃₁	semidirect
685. C₈×Q₈	C₂²×C₃₁	semidirect
686. #442	C₂²×C₃₁	semidirect
687. #440	C₂²×C₃₁	semidirect
688. C₄×Q₁₆	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
691. C₄×SD₁₆	C₂²×C₃₁	semidirect
692. C₄×D₈	C₂²×C₃₁	semidirect
693. C₄×D₈	C₂²×C₃₁	semidirect
694. #436	C₂²×C₃₁	semidirect
695. #435	C₂²×C₃₁	semidirect
696. C₈×D₄	C₂²×C₃₁	semidirect
697. C₈×D₄	C₂²×C₃₁	semidirect
698. #433	C₂²×C₃₁	semidirect
699. #432	C₂²×C₃₁	semidirect
700. #418	C₂²×C₃₁	semidirect
701. #417	C₂²×C₃₁	semidirect
702. #416	C₂²×C₃₁	semidirect
703. C₂×#102	C₂²×C₃₁	semidirect
704. C₂×#102	C₂²×C₃₁	semidirect
705. C₂×#102	C₂²×C₃₁	semidirect
706. #405	C₂²×C₃₁	semidirect
707. C₂×C₄×C₈	C₂²×C₃₁	semidirect
894. C₃₁	#62552	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×#3544	2
C₃₁×#3543	2
C₃₁×#3375	2
C₃₁×#3366	2
C₃₁×#3362	2
C₃₁×#3361	2
C₃₁×#3333	2
C₃₁×#3325	2
C₃₁×#3310	2
C₃₁×#3306	2
C₃₁×#3305	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3241	2
C₃₁×#3238	2
C₃₁×#3224	2
C₃₁×#3217	2
C₃₁×#3179	2
C₃₁×#3168	2
C₃₁×#3136	2
C₂×C₃₁×#486	2
C₃₁×#2966	2
#62552	31

Subgroups — C31×#62552 #21519311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62552 #21519311