Subgroups — C₃₁×#60866 #21517625

Order 7936.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3240	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3239	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3238	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3233	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3232	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3166	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3140	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3095	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3094	C₂	1	2	yes	maximal
12	C₃₁×#3078	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3077	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#533	—	2	1	no	—
16	C₃₁×#533	—	2	1	no	—
17	C₃₁×#533	—	2	1	no	—
18	C₃₁×#533	—	2	1	no	—
19	C₃₁×#533	C₂²	1	2	yes	—
20	C₃₁×#533	C₂²	1	2	yes	—
21	C₃₁×#533	C₂²	1	2	yes	complemented
22	C₃₁×#533	C₂²	1	2	yes	complemented
23	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#529	—	2	1	no	—
26	C₃₁×#529	—	2	1	no	—
27	C₃₁×#529	—	2	1	no	—
28	C₃₁×#529	—	2	1	no	—
29	C₃₁×#529	C₂²	1	2	yes	—
30	C₃₁×#529	C₂²	1	2	yes	—
31	C₃₁×#529	C₂²	1	2	yes	—
32	C₃₁×#529	C₂²	1	2	yes	—
33	C₂×C₃₁×#126	—	2	1	no	—
34	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#123	—	2	1	no	—
38	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
43	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	—	2	1	no	—
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	—	2	1	no	—
48	C₂×C₃₁×#117	C₂²	1	2	yes	—
49	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#501	C₂²	1	4	yes	complemented
51	C₃₁×#501	C₂²	1	4	yes	complemented
52	C₃₁×#499	C₂²	1	8	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	complemented
54	C₃₁×#489	C₂²	1	4	yes	complemented
55	C₃₁×#488	C₂²	1	8	yes	complemented
56	C₃₁×#485	C₂²	1	8	yes	complemented
57	C₃₁×#484	C₂²	1	4	yes	complemented
58	C₃₁×#483	C₂²	1	4	yes	complemented
59	C₃₁×#482	C₂²	1	8	yes	—
60	C₃₁×#481	C₂²	1	4	yes	—
61	C₃₁×#480	C₂²	1	4	yes	—
62	C₃₁×#479	C₂²	1	8	yes	complemented
63	C₃₁×#478	C₂²	1	8	yes	complemented
64	C₃₁×#477	C₂²	1	4	yes	complemented
65	C₃₁×#476	C₂²	1	4	yes	complemented
66	C₃₁×#475	C₂²	1	4	yes	complemented
67	C₃₁×#474	C₂²	1	4	yes	complemented
68	C₃₁×#432	C₂²	1	2	yes	complemented
69	C₃₁×#432	C₂²	1	2	yes	complemented
70	C₃₁×#431	C₂²	1	2	yes	complemented
71	C₃₁×#431	C₂²	1	2	yes	complemented
72	C₃₁×#428	C₂²	1	4	yes	—
73	C₃₁×#428	C₂²	1	4	yes	—
74	C₃₁×#423	C₂²	1	2	yes	—
75	C₃₁×#419	C₂²	1	4	yes	—
76	C₃₁×#418	C₂²	1	4	yes	—
77	C₃₁×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
79	C₂²×Q₈×C₃₁	—	2	1	no	—
80	C₂²×Q₈×C₃₁	—	2	1	no	—
81	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	—	2	1	no	—
85	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
89	C₃₁×C₄⋊Q₈	—	2	1	no	—
90	C₃₁×C₄⋊Q₈	—	2	1	no	—
91	C₃₁×C₄⋊Q₈	—	2	1	no	—
92	C₃₁×C₄⋊Q₈	—	2	1	no	—
93	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃₁×#126	—	2	2	no	—
98	C₃₁×#126	—	2	2	no	—
99	C₃₁×#126	—	2	2	no	—
100	C₃₁×#126	—	2	2	no	—
101	C₃₁×#125	—	2	1	no	—
102	C₃₁×#125	—	2	1	no	—
103	C₃₁×#125	—	2	2	no	—
104	C₃₁×#125	—	2	2	no	—
105	C₃₁×#125	C₂³	1	4	yes	—
106	C₃₁×#125	C₂³	1	4	yes	—
107	C₃₁×#125	C₂³	1	2	yes	—
108	C₃₁×#125	C₂³	1	2	yes	—
109	C₃₁×#124	—	2	1	no	—
110	C₃₁×#124	—	2	1	no	—
111	C₃₁×#124	C₂³	1	2	yes	—
112	C₃₁×#124	C₂³	1	2	yes	—
113	C₃₁×#123	—	2	2	no	—
114	C₃₁×#123	—	2	2	no	—
115	C₃₁×#123	—	2	2	no	—
116	C₃₁×#123	—	2	2	no	—
117	C₃₁×C₂²⋊Q₈	—	2	2	no	—
118	C₃₁×C₂²⋊Q₈	—	2	2	no	—
119	C₃₁×C₂²⋊Q₈	—	2	2	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	2	no	—
122	C₃₁×C₂²⋊Q₈	—	2	2	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	1	no	—
126	C₃₁×C₂²⋊Q₈	—	2	1	no	—
127	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×#121	—	2	1	no	—
130	C₃₁×#121	—	2	1	no	—
131	C₃₁×#121	C₂³	1	2	yes	—
132	C₃₁×#121	C₂³	1	2	yes	—
133	C₄×Q₈×C₃₁	—	2	2	no	—
134	C₄×Q₈×C₃₁	—	2	2	no	—
135	C₄×Q₈×C₃₁	—	2	2	no	—
136	C₄×Q₈×C₃₁	—	2	2	no	—
137	C₄×Q₈×C₃₁	—	2	2	no	—
138	C₄×Q₈×C₃₁	—	2	2	no	—
139	C₄×Q₈×C₃₁	—	2	2	no	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	1	no	—
150	C₄×D₄×C₃₁	—	2	1	no	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	2	yes	—
153	C₃₁×#117	—	2	2	no	—
154	C₃₁×#117	—	2	2	no	—
155	C₃₁×#117	—	2	2	no	—
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	—	2	2	no	—
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	C₂³	1	4	yes	—
160	C₃₁×#117	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
162	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
163	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
166	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄²×C₃₁	—	2	1	no	—
180	C₂×C₄²×C₃₁	—	2	2	no	—
181	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
182	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₃₁×#107	C₂³	1	8	yes	—
194	C₃₁×#107	C₂³	1	8	yes	—
195	C₃₁×#106	C₂³	1	8	yes	—
196	C₃₁×#106	C₂³	1	8	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
198	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	8	yes	—
200	C₃₁×#103	C₂³	1	8	yes	—
201	C₃₁×#102	C₂³	1	8	yes	—
202	C₃₁×#102	C₂³	1	8	yes	—
203	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₃₁×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₃₁	C₂³	1	4	yes	—
207	C₂⁴×C₃₁	—	2	1	no	—
208	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₃₁	—	2	1	no	—
210	C₂×Q₈×C₃₁	—	2	2	no	—
211	C₂×Q₈×C₃₁	—	2	2	no	—
212	C₂×Q₈×C₃₁	—	2	2	no	—
213	C₂×Q₈×C₃₁	—	2	2	no	—
214	C₂×Q₈×C₃₁	—	2	4	no	—
215	C₂×Q₈×C₃₁	—	4	4	no	—
216	C₂×Q₈×C₃₁	—	4	4	no	—
217	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
218	C₂×D₄×C₃₁	—	2	2	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	1	no	—
221	C₂×D₄×C₃₁	—	2	4	no	—
222	C₂×D₄×C₃₁	—	4	4	no	—
223	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	1	no	—
226	C₂²×C₄×C₃₁	—	2	1	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	1	no	—
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	—	4	2	no	—
234	C₂²×C₄×C₃₁	—	4	4	no	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	M₁₆×C₃₁	—	2	8	no	—
254	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	4	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	2	no	—
283	C₂²⋊C₄×C₃₁	—	2	2	no	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₄²×C₃₁	—	2	2	no	—
292	C₄²×C₃₁	—	2	2	no	—
293	C₄²×C₃₁	—	2	4	no	—
294	C₄²×C₃₁	—	2	4	no	—
295	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
311	#60866	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂³×C₃₁	—	2	2	no	—
313	C₂³×C₃₁	—	2	2	no	—
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	4	1	no	—
316	C₂³×C₃₁	—	4	2	no	—
317	C₂³×C₃₁	—	4	2	no	—
318	C₂³×C₃₁	—	4	2	no	—
319	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
322	Q₈×C₃₁	—	2	4	no	—
323	Q₈×C₃₁	—	4	4	no	—
324	Q₈×C₃₁	—	4	4	no	—
325	Q₈×C₃₁	—	4	4	no	—
326	Q₈×C₃₁	—	4	2	no	—
327	Q₈×C₃₁	—	4	4	no	—
328	D₄×C₃₁	—	2	4	no	—
329	D₄×C₃₁	—	4	4	no	—
330	D₄×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	4	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	4	no	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	4	1	no	—
348	C₂×C₄×C₃₁	—	4	1	no	—
349	C₂×C₄×C₃₁	—	4	1	no	—
350	C₂×C₄×C₃₁	—	4	1	no	—
351	C₂×C₄×C₃₁	—	4	1	no	—
352	C₂×C₄×C₃₁	—	4	1	no	—
353	C₂×C₄×C₃₁	—	4	1	no	—
354	C₂×C₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	4	2	no	—
356	C₂×C₄×C₃₁	—	4	2	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	4	2	no	—
359	C₂×C₄×C₃₁	—	4	4	no	—
360	C₂×C₄×C₃₁	—	4	4	no	—
361	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
373	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
374	C₈×C₃₁	—	2	8	no	—
375	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
376	C₂×#529	C₂×C₃₁	1	1	yes	characteristic
377	#3240	C₂×C₃₁	1	4	yes	complemented
378	#3239	C₂×C₃₁	1	2	yes	complemented
379	#3238	C₂×C₃₁	1	2	yes	complemented
380	#3233	C₂×C₃₁	1	4	yes	complemented
381	#3232	C₂×C₃₁	1	4	yes	complemented
382	#3166	C₂×C₃₁	1	2	yes	complemented
383	#3140	C₂×C₃₁	1	2	yes	complemented
384	#3095	C₂×C₃₁	1	2	yes	complemented
385	#3094	C₂×C₃₁	1	2	yes	—
386	#3078	C₂×C₃₁	1	2	yes	complemented
387	#3077	C₂×C₃₁	1	2	yes	complemented
388	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
389	C₂²×C₃₁	—	2	1	no	—
390	C₂²×C₃₁	—	2	1	no	—
391	C₂²×C₃₁	—	2	1	no	—
392	C₂²×C₃₁	—	2	1	no	—
393	C₂²×C₃₁	—	2	1	no	—
394	C₂²×C₃₁	—	2	1	no	—
395	C₂²×C₃₁	—	2	1	no	—
396	C₂²×C₃₁	—	4	4	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	2	no	—
400	C₂²×C₃₁	—	8	4	no	—
401	C₂²×C₃₁	#536	1	2	yes	—
402	C₂²×C₃₁	#575	1	2	yes	—
403	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₃₁	—	2	1	no	—
405	C₄×C₃₁	—	2	1	no	—
406	C₄×C₃₁	—	2	1	no	—
407	C₄×C₃₁	—	2	1	no	—
408	C₄×C₃₁	—	2	1	no	—
409	C₄×C₃₁	—	2	1	no	—
410	C₄×C₃₁	—	2	1	no	—
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	2	1	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	4	no	—
417	C₄×C₃₁	—	4	4	no	—
418	C₄×C₃₁	#536	1	2	yes	—
419	C₄×C₃₁	#575	1	2	yes	—
420	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
421	#533	—	2	1	no	—
422	#533	—	2	1	no	—
423	#533	—	2	1	no	—
424	#533	—	2	1	no	—
425	#533	C₂²×C₃₁	1	2	yes	—
426	#533	C₂²×C₃₁	1	2	yes	—
427	#533	C₂²×C₃₁	1	2	yes	complemented
428	#533	C₂²×C₃₁	1	2	yes	complemented
429	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
431	#529	—	2	1	no	—
432	#529	—	2	1	no	—
433	#529	—	2	1	no	—
434	#529	—	2	1	no	—
435	#529	C₂²×C₃₁	1	2	yes	—
436	#529	C₂²×C₃₁	1	2	yes	—
437	#529	C₂²×C₃₁	1	2	yes	—
438	#529	C₂²×C₃₁	1	2	yes	—
439	C₂×#126	—	2	1	no	—
440	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
442	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#123	—	2	1	no	—
444	C₂×C₂²⋊Q₈	—	2	1	no	—
445	C₂×C₂²⋊Q₈	—	2	1	no	—
446	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×C₄×Q₈	—	2	1	no	—
449	C₂×C₄×Q₈	—	2	1	no	—
450	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×C₄×D₄	—	2	1	no	—
452	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#117	—	2	1	no	—
454	C₂×#117	C₂²×C₃₁	1	2	yes	—
455	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
456	#501	C₂²×C₃₁	1	4	yes	complemented
457	#501	C₂²×C₃₁	1	4	yes	complemented
458	#499	C₂²×C₃₁	1	8	yes	complemented
459	#489	C₂²×C₃₁	1	4	yes	complemented
460	#489	C₂²×C₃₁	1	4	yes	complemented
461	#488	C₂²×C₃₁	1	8	yes	complemented
462	#485	C₂²×C₃₁	1	8	yes	complemented
463	#484	C₂²×C₃₁	1	4	yes	complemented
464	#483	C₂²×C₃₁	1	4	yes	complemented
465	#482	C₂²×C₃₁	1	8	yes	—
466	#481	C₂²×C₃₁	1	4	yes	—
467	#480	C₂²×C₃₁	1	4	yes	—
468	#479	C₂²×C₃₁	1	8	yes	complemented
469	#478	C₂²×C₃₁	1	8	yes	complemented
470	#477	C₂²×C₃₁	1	4	yes	complemented
471	#476	C₂²×C₃₁	1	4	yes	complemented
472	#475	C₂²×C₃₁	1	4	yes	complemented
473	#474	C₂²×C₃₁	1	4	yes	complemented
474	#432	C₂²×C₃₁	1	2	yes	complemented
475	#432	C₂²×C₃₁	1	2	yes	complemented
476	#431	C₂²×C₃₁	1	2	yes	complemented
477	#431	C₂²×C₃₁	1	2	yes	complemented
478	#428	C₂²×C₃₁	1	4	yes	—
479	#428	C₂²×C₃₁	1	4	yes	—
480	#423	C₂²×C₃₁	1	2	yes	—
481	#419	C₂²×C₃₁	1	4	yes	—
482	#418	C₂²×C₃₁	1	4	yes	—
483	#407	C₂²×C₃₁	1	2	yes	—
484	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
485	C₂×C₃₁	—	2	2	no	—
486	C₂×C₃₁	—	2	2	no	—
487	C₂×C₃₁	—	4	1	no	—
488	C₂×C₃₁	—	8	2	no	—
489	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
490	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
491	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
499	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
501	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
502	C₄⋊Q₈	—	2	1	no	—
503	C₄⋊Q₈	—	2	1	no	—
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
510	#126	—	2	2	no	—
511	#126	—	2	2	no	—
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	C₂³×C₃₁	1	2	yes	—
519	#125	C₂³×C₃₁	1	2	yes	—
520	#125	C₂³×C₃₁	1	4	yes	—
521	#125	C₂³×C₃₁	1	4	yes	—
522	#124	—	2	1	no	—
523	#124	—	2	1	no	—
524	#124	C₂³×C₃₁	1	2	yes	—
525	#124	C₂³×C₃₁	1	2	yes	—
526	#123	—	2	2	no	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
541	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	C₂³×C₃₁	1	2	yes	—
545	#121	C₂³×C₃₁	1	2	yes	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
557	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	C₂³×C₃₁	1	2	yes	—
565	C₄×D₄	C₂³×C₃₁	1	2	yes	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	C₂³×C₃₁	1	4	yes	—
573	#117	C₂³×C₃₁	1	4	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	—	2	2	no	—
594	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
595	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
596	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
597	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
598	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
599	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
606	#107	C₂³×C₃₁	1	8	yes	—
607	#107	C₂³×C₃₁	1	8	yes	—
608	#106	C₂³×C₃₁	1	8	yes	—
609	#106	C₂³×C₃₁	1	8	yes	—
610	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
611	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
612	#103	C₂³×C₃₁	1	8	yes	—
613	#103	C₂³×C₃₁	1	8	yes	—
614	#102	C₂³×C₃₁	1	8	yes	—
615	#102	C₂³×C₃₁	1	8	yes	—
616	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
617	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
618	#97	C₂³×C₃₁	1	4	yes	—
619	C₄×C₈	C₂³×C₃₁	1	4	yes	—
620	C₃₁	#60866	1	1	yes	characteristic, direct product factor, Sylow
621	C₂⁴	—	2	1	no	—
622	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	4	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	4	no	—
649	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	M₁₆	—	2	8	no	—
668	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	4	no	—
709	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
733	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	4	no	—
737	Q₈	—	4	4	no	—
738	Q₈	—	4	4	no	—
739	Q₈	—	4	2	no	—
740	Q₈	—	4	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
785	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
786	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
787	C₈	—	2	8	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	8	4	no	—
800	C₂²	C₃₁×#536	1	2	yes	—
801	C₂²	C₃₁×#575	1	2	yes	—
802	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	4	no	—
816	C₄	—	4	4	no	—
817	C₄	C₃₁×#536	1	2	yes	—
818	C₄	C₃₁×#575	1	2	yes	—
819	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
820	C₂	—	2	2	no	—
821	C₂	—	2	2	no	—
822	C₂	—	4	1	no	—
823	C₂	—	8	2	no	—
824	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
825	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
826	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#533	C₂	semidirect
3. C₃₁×#3240	C₂	semidirect
4. C₃₁×#3239	C₂	semidirect
5. C₃₁×#3238	C₂	semidirect
6. C₃₁×#3233	C₂	semidirect
7. C₃₁×#3232	C₂	semidirect
8. C₃₁×#3166	C₂	semidirect
9. C₃₁×#3140	C₂	semidirect
10. C₃₁×#3095	C₂	semidirect
12. C₃₁×#3078	C₂	semidirect
13. C₃₁×#3077	C₂	semidirect
14. C₃₁×#2920	C₂	semidirect
21. C₃₁×#533	C₂²	semidirect
22. C₃₁×#533	C₂²	semidirect
23. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₃₁×#125	C₂²	semidirect
50. C₃₁×#501	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#489	C₂²	semidirect
55. C₃₁×#488	C₂²	semidirect
56. C₃₁×#485	C₂²	semidirect
57. C₃₁×#484	C₂²	semidirect
58. C₃₁×#483	C₂²	semidirect
62. C₃₁×#479	C₂²	semidirect
63. C₃₁×#478	C₂²	semidirect
64. C₃₁×#477	C₂²	semidirect
65. C₃₁×#476	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#432	C₂²	semidirect
69. C₃₁×#432	C₂²	semidirect
70. C₃₁×#431	C₂²	semidirect
71. C₃₁×#431	C₂²	semidirect
311. #60866	C₃₁	direct (N × H)
375. C₂×#533	C₂×C₃₁	semidirect
377. #3240	C₂×C₃₁	semidirect
378. #3239	C₂×C₃₁	semidirect
379. #3238	C₂×C₃₁	semidirect
380. #3233	C₂×C₃₁	semidirect
381. #3232	C₂×C₃₁	semidirect
382. #3166	C₂×C₃₁	semidirect
383. #3140	C₂×C₃₁	semidirect
384. #3095	C₂×C₃₁	semidirect
386. #3078	C₂×C₃₁	semidirect
387. #3077	C₂×C₃₁	semidirect
388. #2920	C₂×C₃₁	semidirect
427. #533	C₂²×C₃₁	semidirect
428. #533	C₂²×C₃₁	semidirect
429. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
430. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
441. C₂×#125	C₂²×C₃₁	semidirect
456. #501	C₂²×C₃₁	semidirect
457. #501	C₂²×C₃₁	semidirect
458. #499	C₂²×C₃₁	semidirect
459. #489	C₂²×C₃₁	semidirect
460. #489	C₂²×C₃₁	semidirect
461. #488	C₂²×C₃₁	semidirect
462. #485	C₂²×C₃₁	semidirect
463. #484	C₂²×C₃₁	semidirect
464. #483	C₂²×C₃₁	semidirect
468. #479	C₂²×C₃₁	semidirect
469. #478	C₂²×C₃₁	semidirect
470. #477	C₂²×C₃₁	semidirect
471. #476	C₂²×C₃₁	semidirect
472. #475	C₂²×C₃₁	semidirect
473. #474	C₂²×C₃₁	semidirect
474. #432	C₂²×C₃₁	semidirect
475. #432	C₂²×C₃₁	semidirect
476. #431	C₂²×C₃₁	semidirect
477. #431	C₂²×C₃₁	semidirect
620. C₃₁	#60866	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#533	2
C₂×C₃₁×#529	2
C₃₁×#3240	2
C₃₁×#3239	2
C₃₁×#3238	2
C₃₁×#3233	2
C₃₁×#3232	2
C₃₁×#3166	2
C₃₁×#3140	2
C₃₁×#3095	2
C₃₁×#3094	2
C₃₁×#3078	2
C₃₁×#3077	2
C₃₁×#2920	2
#60866	31

Subgroups — C31×#60866 #21517625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60866 #21517625