Subgroups — C₃₁×#62617 #21519376

Order 7936.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3369	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×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3173	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	complemented
34	C₃₁×#550	C₂²	1	2	yes	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#547	—	2	1	no	—
37	C₃₁×#547	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	2	yes	complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	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	—
46	C₃₁×#542	C₂²	1	2	yes	complemented
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#537	—	2	1	no	—
49	C₃₁×#536	—	2	2	no	—
50	C₃₁×#535	—	2	1	no	—
51	C₃₁×#535	C₂²	1	2	yes	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#498	C₂²	1	2	yes	complemented
59	C₃₁×#496	C₂²	1	1	yes	characteristic
60	C₃₁×#495	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	1	yes	characteristic
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#489	C₂²	1	2	yes	complemented
66	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#488	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	complemented
69	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#486	C₂²	1	2	yes	—
74	C₃₁×#486	C₂²	1	2	yes	complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#483	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#481	C₂²	1	2	yes	—
79	C₃₁×#481	C₂²	1	2	yes	—
80	C₃₁×#481	C₂²	1	2	yes	complemented
81	C₃₁×#479	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#476	C₂²	1	2	yes	complemented
88	C₃₁×#475	C₂²	1	2	yes	complemented
89	C₃₁×#470	C₂²	1	2	yes	complemented
90	C₃₁×#469	C₂²	1	2	yes	—
91	C₃₁×#469	C₂²	1	1	yes	characteristic
92	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#468	C₂²	1	1	yes	characteristic
94	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#465	C₂²	1	2	yes	—
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#464	C₂²	1	2	yes	—
98	C₃₁×#463	C₂²	1	2	yes	—
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	2	yes	complemented
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#459	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	2	yes	—
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×#441	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#418	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	complemented
129	C₃₁×#417	C₂²	1	2	yes	complemented
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×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	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×#127	—	2	2	no	—
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	D₄	1	2	yes	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	D₄	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#125	C₂³	1	1	yes	characteristic
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	D₄	1	1	yes	characteristic
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	1	yes	characteristic
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	D₄	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	1	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	2	yes	—
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₃₁×#121	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	2	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	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	yes	characteristic
268	C₃₁×#106	C₂³	1	1	yes	characteristic
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
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	2	yes	—
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	2	yes	—
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
306	C₃₁×#97	C₂³	1	1	yes	characteristic
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	4	no	—
319	#41×C₃₁	—	8	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	8	2	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
365	Q₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	4	1	no	—
369	SD₁₆×C₃₁	—	4	1	no	—
370	D₈×C₃₁	—	4	1	no	—
371	D₈×C₃₁	—	4	1	no	—
372	D₈×C₃₁	—	4	2	no	—
373	M₁₆×C₃₁	—	4	1	no	—
374	M₁₆×C₃₁	—	4	1	no	—
375	M₁₆×C₃₁	—	4	2	no	—
376	C₂×C₈×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	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	2	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	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	#62617	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	1	no	—
451	C₂³×C₃₁	—	2	2	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	8	2	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	8	1	no	—
464	Q₈×C₃₁	—	8	2	no	—
465	Q₈×C₃₁	—	8	1	no	—
466	Q₈×C₃₁	—	8	2	no	—
467	Q₈×C₃₁	—	8	1	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	8	1	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	1	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	2	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	4	1	no	—
506	C₂×C₄×C₃₁	—	4	4	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	2	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	1	no	—
529	C₈×C₃₁	—	2	2	no	—
530	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3332	C₂×C₃₁	1	2	yes	complemented
537	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3323	C₂×C₃₁	1	2	yes	complemented
540	#3317	C₂×C₃₁	1	2	yes	complemented
541	#3306	C₂×C₃₁	1	2	yes	complemented
542	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3244	C₂×C₃₁	1	2	yes	complemented
545	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3224	C₂×C₃₁	1	2	yes	complemented
547	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3173	C₂×C₃₁	1	2	yes	complemented
549	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3136	C₂×C₃₁	1	2	yes	complemented
552	#2969	C₂×C₃₁	1	1	yes	characteristic, complemented
553	C₂²×C₃₁	—	2	1	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	1	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	2	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	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	1	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	16	4	no	—
572	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₃₁	—	2	1	no	—
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	#577	1	2	yes	—
589	C₄×C₃₁	#585	1	1	yes	characteristic
590	C₄×C₃₁	#585	1	1	yes	characteristic
591	#563	—	2	2	no	—
592	#560	—	2	2	no	—
593	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#556	C₂²×C₃₁	1	1	yes	characteristic
595	#555	C₂²×C₃₁	1	1	yes	characteristic
596	#554	C₂²×C₃₁	1	1	yes	characteristic
597	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#553	—	2	1	no	—
599	#552	—	2	1	no	—
600	#552	C₂²×C₃₁	1	2	yes	complemented
601	#550	C₂²×C₃₁	1	2	yes	—
602	#550	C₂²×C₃₁	1	1	yes	characteristic
603	#547	—	2	1	no	—
604	#547	C₂²×C₃₁	1	1	yes	characteristic
605	#547	C₂²×C₃₁	1	2	yes	complemented
606	#546	—	2	1	no	—
607	#546	C₂²×C₃₁	1	2	yes	—
608	D₄²	C₂²×C₃₁	1	1	yes	characteristic
609	#544	—	2	1	no	—
610	#544	C₂²×C₃₁	1	2	yes	complemented
611	#542	—	2	1	no	—
612	#542	C₂²×C₃₁	1	2	yes	—
613	#542	C₂²×C₃₁	1	2	yes	complemented
614	#538	—	2	2	no	—
615	#537	—	2	1	no	—
616	#536	—	2	2	no	—
617	#535	—	2	1	no	—
618	#535	C₂²×C₃₁	1	2	yes	—
619	#532	C₂²×C₃₁	1	1	yes	characteristic
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#529	C₂²×C₃₁	1	1	yes	characteristic
623	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#498	C₂²×C₃₁	1	2	yes	complemented
626	#496	C₂²×C₃₁	1	1	yes	characteristic
627	#495	C₂²×C₃₁	1	2	yes	complemented
628	#490	C₂²×C₃₁	1	1	yes	characteristic
629	#490	C₂²×C₃₁	1	2	yes	complemented
630	#489	C₂²×C₃₁	1	2	yes	—
631	#489	C₂²×C₃₁	1	2	yes	complemented
632	#489	C₂²×C₃₁	1	2	yes	complemented
633	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#488	C₂²×C₃₁	1	2	yes	—
635	#488	C₂²×C₃₁	1	2	yes	complemented
636	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#486	C₂²×C₃₁	1	1	yes	characteristic
639	#486	C₂²×C₃₁	1	1	yes	characteristic
640	#486	C₂²×C₃₁	1	2	yes	—
641	#486	C₂²×C₃₁	1	2	yes	complemented
642	#485	C₂²×C₃₁	1	2	yes	complemented
643	#483	C₂²×C₃₁	1	2	yes	complemented
644	#482	C₂²×C₃₁	1	2	yes	—
645	#481	C₂²×C₃₁	1	2	yes	—
646	#481	C₂²×C₃₁	1	2	yes	—
647	#481	C₂²×C₃₁	1	2	yes	complemented
648	#479	C₂²×C₃₁	1	2	yes	complemented
649	#478	C₂²×C₃₁	1	2	yes	complemented
650	#476	C₂²×C₃₁	1	1	yes	characteristic
651	#476	C₂²×C₃₁	1	1	yes	characteristic
652	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#476	C₂²×C₃₁	1	2	yes	complemented
655	#475	C₂²×C₃₁	1	2	yes	complemented
656	#470	C₂²×C₃₁	1	2	yes	complemented
657	#469	C₂²×C₃₁	1	2	yes	—
658	#469	C₂²×C₃₁	1	1	yes	characteristic
659	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#468	C₂²×C₃₁	1	1	yes	characteristic
661	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#465	C₂²×C₃₁	1	2	yes	—
663	#465	C₂²×C₃₁	1	2	yes	complemented
664	#464	C₂²×C₃₁	1	2	yes	—
665	#463	C₂²×C₃₁	1	2	yes	—
666	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#460	C₂²×C₃₁	1	1	yes	characteristic
669	#460	C₂²×C₃₁	1	2	yes	complemented
670	#459	C₂²×C₃₁	1	1	yes	characteristic
671	#459	C₂²×C₃₁	1	2	yes	complemented
672	#452	C₂²×C₃₁	1	2	yes	complemented
673	#452	C₂²×C₃₁	1	2	yes	complemented
674	#450	C₂²×C₃₁	1	2	yes	—
675	#449	C₂²×C₃₁	1	2	yes	complemented
676	#449	C₂²×C₃₁	1	2	yes	complemented
677	#447	C₂²×C₃₁	1	2	yes	—
678	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#442	C₂²×C₃₁	1	2	yes	complemented
681	#441	C₂²×C₃₁	1	2	yes	complemented
682	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
686	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#436	C₂²×C₃₁	1	1	yes	characteristic
689	#436	C₂²×C₃₁	1	2	yes	complemented
690	#435	C₂²×C₃₁	1	2	yes	complemented
691	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
692	#433	C₂²×C₃₁	1	2	yes	complemented
693	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#418	C₂²×C₃₁	1	2	yes	—
695	#417	C₂²×C₃₁	1	2	yes	complemented
696	#417	C₂²×C₃₁	1	2	yes	complemented
697	#417	C₂²×C₃₁	1	2	yes	complemented
698	#416	C₂²×C₃₁	1	2	yes	complemented
699	C₂×#102	C₂²×C₃₁	1	2	yes	—
700	#405	C₂²×C₃₁	1	2	yes	complemented
701	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	C₂×C₃₁	—	4	1	no	—
703	C₂×C₃₁	—	4	2	no	—
704	C₂×C₃₁	—	8	1	no	—
705	C₂×C₃₁	—	8	1	no	—
706	C₂×C₃₁	—	8	2	no	—
707	C₂×C₃₁	—	8	1	no	—
708	C₂×C₃₁	#3500	1	1	yes	characteristic
709	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
710	C₂×C₃₁	#3585	1	1	yes	characteristic
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	2	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	C₂³×C₃₁	1	2	yes	—
715	C₂×#41	C₂³×C₃₁	1	2	yes	—
716	C₂²×Q₈	—	2	1	no	—
717	C₂²×D₄	—	2	1	no	—
718	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₃₁	1	2	yes	—
727	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
742	#127	—	2	2	no	—
743	#127	C₂³×C₃₁	1	1	yes	characteristic
744	#127	C₂³×C₃₁	1	1	yes	characteristic
745	#127	C₂³×C₃₁	1	2	yes	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	1	no	—
751	#126	D₄×C₃₁	1	2	yes	—
752	#125	—	2	1	no	—
753	#125	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	D₄×C₃₁	1	1	yes	characteristic
756	#125	C₂³×C₃₁	1	1	yes	characteristic
757	#125	C₂³×C₃₁	1	2	yes	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	D₄×C₃₁	1	1	yes	characteristic
763	#124	C₂³×C₃₁	1	1	yes	characteristic
764	#124	C₂³×C₃₁	1	2	yes	—
765	#124	C₂³×C₃₁	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	D₄×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	D₄×C₃₁	1	1	yes	characteristic
802	#121	C₂³×C₃₁	1	1	yes	characteristic
803	#121	C₂³×C₃₁	1	1	yes	characteristic
804	#121	C₂³×C₃₁	1	1	yes	characteristic
805	#121	C₂³×C₃₁	1	2	yes	—
806	#121	C₂³×C₃₁	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₃₁	1	2	yes	—
826	C₄×D₄	C₂³×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	2	yes	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	—	2	1	no	—
833	#117	C₂³×C₃₁	1	2	yes	—
834	#117	C₂³×C₃₁	1	2	yes	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	#97	C₂³×C₃₁	1	1	yes	characteristic
882	#97	C₂³×C₃₁	1	1	yes	characteristic
883	#97	C₂³×C₃₁	1	2	yes	—
884	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₃₁	1	2	yes	—
887	C₄×C₈	C₂³×C₃₁	1	2	yes	—
888	C₃₁	#62617	1	1	yes	characteristic, direct product factor, Sylow
889	C₂⁴	—	2	2	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	8	2	no	—
895	#41	—	8	4	no	—
896	#41	—	8	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	8	2	no	—
903	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	8	2	no	—
923	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
924	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
927	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
942	Q₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	1	no	—
947	D₈	—	4	1	no	—
948	D₈	—	4	1	no	—
949	D₈	—	4	2	no	—
950	M₁₆	—	4	1	no	—
951	M₁₆	—	4	1	no	—
952	M₁₆	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
956	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
958	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	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	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1033	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	8	1	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	1	no	—
1043	Q₈	—	8	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	1	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1099	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1100	C₈	—	2	1	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	16	4	no	—
1125	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	C₃₁×#577	1	2	yes	—
1142	C₄	C₃₁×#585	1	1	yes	characteristic
1143	C₄	C₃₁×#585	1	1	yes	characteristic
1144	C₂	—	4	2	no	—
1145	C₂	—	4	1	no	—
1146	C₂	—	8	1	no	—
1147	C₂	—	8	2	no	—
1148	C₂	—	8	1	no	—
1149	C₂	—	8	1	no	—
1150	C₂	C₃₁×#3500	1	1	yes	characteristic
1151	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1152	C₂	C₃₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3546	C₂	semidirect
2. C₃₁×#3544	C₂	semidirect
3. C₃₁×#3369	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3362	C₂	semidirect
6. C₃₁×#3360	C₂	semidirect
7. C₃₁×#3332	C₂	semidirect
8. C₃₁×#3331	C₂	semidirect
9. C₃₁×#3325	C₂	semidirect
10. C₃₁×#3323	C₂	semidirect
11. C₃₁×#3317	C₂	semidirect
12. C₃₁×#3306	C₂	semidirect
13. C₃₁×#3303	C₂	semidirect
14. C₃₁×#3295	C₂	semidirect
15. C₃₁×#3244	C₂	semidirect
16. C₃₁×#3227	C₂	semidirect
17. C₃₁×#3224	C₂	semidirect
18. C₃₁×#3212	C₂	semidirect
19. C₃₁×#3173	C₂	semidirect
20. C₃₁×#3171	C₂	semidirect
21. C₃₁×#3141	C₂	semidirect
22. C₃₁×#3136	C₂	semidirect
23. C₃₁×#2969	C₂	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
33. C₃₁×#552	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
43. C₃₁×#544	C₂²	semidirect
46. C₃₁×#542	C₂²	semidirect
54. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#498	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
69. C₃₁×#487	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
76. C₃₁×#483	C₂²	semidirect
80. C₃₁×#481	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#470	C₂²	semidirect
92. C₃₁×#469	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
102. C₃₁×#460	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
114. C₃₁×#441	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
128. C₃₁×#417	C₂²	semidirect
129. C₃₁×#417	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
448. #62617	C₃₁	direct (N × H)
530. #3546	C₂×C₃₁	semidirect
531. #3544	C₂×C₃₁	semidirect
532. #3369	C₂×C₃₁	semidirect
533. #3366	C₂×C₃₁	semidirect
534. #3362	C₂×C₃₁	semidirect
535. #3360	C₂×C₃₁	semidirect
536. #3332	C₂×C₃₁	semidirect
537. #3331	C₂×C₃₁	semidirect
538. #3325	C₂×C₃₁	semidirect
539. #3323	C₂×C₃₁	semidirect
540. #3317	C₂×C₃₁	semidirect
541. #3306	C₂×C₃₁	semidirect
542. #3303	C₂×C₃₁	semidirect
543. #3295	C₂×C₃₁	semidirect
544. #3244	C₂×C₃₁	semidirect
545. #3227	C₂×C₃₁	semidirect
546. #3224	C₂×C₃₁	semidirect
547. #3212	C₂×C₃₁	semidirect
548. #3173	C₂×C₃₁	semidirect
549. #3171	C₂×C₃₁	semidirect
550. #3141	C₂×C₃₁	semidirect
551. #3136	C₂×C₃₁	semidirect
552. #2969	C₂×C₃₁	semidirect
593. Q₈²	C₂²×C₃₁	semidirect
597. #554	C₂²×C₃₁	semidirect
600. #552	C₂²×C₃₁	semidirect
605. #547	C₂²×C₃₁	semidirect
610. #544	C₂²×C₃₁	semidirect
613. #542	C₂²×C₃₁	semidirect
621. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
623. #529	C₂²×C₃₁	semidirect
624. #501	C₂²×C₃₁	semidirect
625. #498	C₂²×C₃₁	semidirect
627. #495	C₂²×C₃₁	semidirect
629. #490	C₂²×C₃₁	semidirect
631. #489	C₂²×C₃₁	semidirect
632. #489	C₂²×C₃₁	semidirect
633. #489	C₂²×C₃₁	semidirect
635. #488	C₂²×C₃₁	semidirect
636. #487	C₂²×C₃₁	semidirect
637. #487	C₂²×C₃₁	semidirect
641. #486	C₂²×C₃₁	semidirect
642. #485	C₂²×C₃₁	semidirect
643. #483	C₂²×C₃₁	semidirect
647. #481	C₂²×C₃₁	semidirect
648. #479	C₂²×C₃₁	semidirect
649. #478	C₂²×C₃₁	semidirect
652. #476	C₂²×C₃₁	semidirect
653. #476	C₂²×C₃₁	semidirect
654. #476	C₂²×C₃₁	semidirect
655. #475	C₂²×C₃₁	semidirect
656. #470	C₂²×C₃₁	semidirect
659. #469	C₂²×C₃₁	semidirect
661. #468	C₂²×C₃₁	semidirect
663. #465	C₂²×C₃₁	semidirect
666. #462	C₂²×C₃₁	semidirect
667. #461	C₂²×C₃₁	semidirect
669. #460	C₂²×C₃₁	semidirect
671. #459	C₂²×C₃₁	semidirect
672. #452	C₂²×C₃₁	semidirect
673. #452	C₂²×C₃₁	semidirect
675. #449	C₂²×C₃₁	semidirect
676. #449	C₂²×C₃₁	semidirect
678. #446	C₂²×C₃₁	semidirect
679. C₈×Q₈	C₂²×C₃₁	semidirect
680. #442	C₂²×C₃₁	semidirect
681. #441	C₂²×C₃₁	semidirect
683. C₄×SD₁₆	C₂²×C₃₁	semidirect
684. C₄×SD₁₆	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
687. C₄×D₈	C₂²×C₃₁	semidirect
689. #436	C₂²×C₃₁	semidirect
690. #435	C₂²×C₃₁	semidirect
692. #433	C₂²×C₃₁	semidirect
693. #431	C₂²×C₃₁	semidirect
695. #417	C₂²×C₃₁	semidirect
696. #417	C₂²×C₃₁	semidirect
697. #417	C₂²×C₃₁	semidirect
698. #416	C₂²×C₃₁	semidirect
700. #405	C₂²×C₃₁	semidirect
701. C₄×M₁₆	C₂²×C₃₁	semidirect
888. C₃₁	#62617	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×#3546	2
C₃₁×#3544	2
C₃₁×#3369	2
C₃₁×#3366	2
C₃₁×#3362	2
C₃₁×#3360	2
C₃₁×#3332	2
C₃₁×#3331	2
C₃₁×#3325	2
C₃₁×#3323	2
C₃₁×#3317	2
C₃₁×#3306	2
C₃₁×#3303	2
C₃₁×#3295	2
C₃₁×#3244	2
C₃₁×#3227	2
C₃₁×#3224	2
C₃₁×#3212	2
C₃₁×#3173	2
C₃₁×#3171	2
C₃₁×#3141	2
C₃₁×#3136	2
C₃₁×#2969	2
#62617	31

Subgroups — C31×#62617 #21519376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62617 #21519376