Subgroups — C₃₁×#61480 #21518239

Order 7936.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3519	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
9	D₄×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3122	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2948	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#555	C₂²	1	2	yes	complemented
21	C₃₁×#554	C₂²	1	2	yes	complemented
22	C₃₁×#553	—	2	2	no	—
23	C₃₁×#553	C₂²	1	4	yes	complemented
24	C₃₁×#550	C₂²	1	2	yes	complemented
25	C₃₁×#546	—	2	2	no	—
26	C₃₁×#546	—	2	4	no	—
27	D₄²×C₃₁	C₂²	1	4	yes	complemented
28	D₄²×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#540	C₂²	1	4	yes	complemented
30	C₃₁×#538	—	2	4	no	—
31	C₃₁×#532	C₂²	1	2	yes	complemented
32	C₃₁×#529	C₂²	1	1	yes	characteristic
33	C₃₁×#525	—	2	2	no	—
34	C₂×C₃₁×#121	—	2	2	no	—
35	C₃₁×#518	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#499	C₂²	1	2	yes	complemented
39	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#493	C₂²	1	2	yes	complemented
41	C₃₁×#490	C₂²	1	4	yes	complemented
42	C₃₁×#486	C₂²	1	2	yes	complemented
43	C₃₁×#482	C₂²	1	4	yes	complemented
44	C₃₁×#482	C₂²	1	4	yes	complemented
45	C₃₁×#481	C₂²	1	4	yes	complemented
46	C₃₁×#478	C₂²	1	4	yes	complemented
47	C₃₁×#478	C₂²	1	4	yes	complemented
48	C₃₁×#476	C₂²	1	2	yes	complemented
49	C₃₁×#476	C₂²	1	2	yes	complemented
50	C₃₁×#469	C₂²	1	4	yes	complemented
51	C₃₁×#466	C₂²	1	2	yes	complemented
52	C₃₁×#466	C₂²	1	2	yes	complemented
53	C₃₁×#466	C₂²	1	2	yes	complemented
54	C₃₁×#466	C₂²	1	2	yes	complemented
55	C₃₁×#459	C₂²	1	2	yes	complemented
56	C₃₁×#459	C₂²	1	2	yes	complemented
57	C₃₁×#459	C₂²	1	4	yes	complemented
58	C₃₁×#459	C₂²	1	4	yes	complemented
59	C₃₁×#447	C₂²	1	4	yes	complemented
60	C₃₁×#447	C₂²	1	4	yes	complemented
61	C₃₁×#447	C₂²	1	4	yes	complemented
62	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#442	C₂²	1	4	yes	complemented
65	C₃₁×#442	C₂²	1	4	yes	complemented
66	C₃₁×#442	C₂²	1	4	yes	complemented
67	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×D₈×C₃₁	C₂²	1	2	yes	—
69	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
71	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
73	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
75	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
76	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#435	C₂²	1	2	yes	complemented
79	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
80	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#433	C₂²	1	2	yes	complemented
82	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#427	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#418	C₂²	1	4	yes	complemented
86	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
87	C₃₁×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	—	2	2	no	—
91	C₂²×D₄×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	—	2	4	no	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₃₁	—	2	2	no	—
96	C₂×D₈×C₃₁	—	2	4	no	—
97	C₂×D₈×C₃₁	—	2	8	no	—
98	C₂×D₈×C₃₁	C₂³	1	2	yes	—
99	C₂×D₈×C₃₁	C₂³	1	2	yes	—
100	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	C₂³	1	2	yes	—
103	C₂×D₈×C₃₁	C₂³	1	4	yes	—
104	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#127	C₂³	1	4	yes	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#126	D₄	1	2	yes	—
114	C₃₁×#125	D₄	1	1	yes	characteristic
115	C₃₁×#125	C₂³	1	4	yes	—
116	C₃₁×#124	—	2	4	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	D₄	1	1	yes	characteristic
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	D₄	1	2	yes	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×C₂²⋊Q₈	—	2	4	no	—
125	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
126	C₃₁×#121	—	2	4	no	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	2	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	D₄	1	1	yes	characteristic
136	C₃₁×#121	C₂³	1	4	yes	—
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#120	—	2	4	no	—
140	C₃₁×#120	—	2	4	no	—
141	C₃₁×#120	—	2	4	no	—
142	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	2	4	no	—
145	C₄×D₄×C₃₁	—	2	4	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	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	C₂³	1	4	yes	—
160	C₃₁×#117	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
164	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
165	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	1	yes	characteristic
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#106	C₂³	1	4	yes	—
173	C₃₁×#106	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×#102	C₂³	1	2	yes	—
179	C₃₁×#102	C₂³	1	2	yes	—
180	C₃₁×#102	C₂³	1	2	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×#97	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	C₂⁴×C₃₁	—	2	2	no	—
199	C₂⁴×C₃₁	—	2	4	no	—
200	#41×C₃₁	—	8	4	no	—
201	#41×C₃₁	—	8	4	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	8	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	4	2	no	—
216	C₂×D₄×C₃₁	—	4	4	no	—
217	C₂×D₄×C₃₁	—	8	4	no	—
218	C₂×D₄×C₃₁	—	8	8	no	—
219	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	8	4	no	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	D₈×C₃₁	—	2	4	no	—
238	D₈×C₃₁	—	2	8	no	—
239	D₈×C₃₁	—	2	2	no	—
240	D₈×C₃₁	—	2	4	no	—
241	D₈×C₃₁	—	4	2	no	—
242	D₈×C₃₁	—	4	4	no	—
243	D₈×C₃₁	#41	1	4	yes	complemented
244	M₁₆×C₃₁	—	4	2	no	—
245	C₂×C₈×C₃₁	—	2	2	no	—
246	C₂×C₈×C₃₁	—	2	4	no	—
247	C₂×C₈×C₃₁	—	4	1	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₄²×C₃₁	—	2	4	no	—
284	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₄²×C₃₁	C₂⁴	1	2	yes	—
289	#61480	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	4	no	—
293	C₂³×C₃₁	—	4	4	no	—
294	C₂³×C₃₁	—	4	8	no	—
295	C₂³×C₃₁	—	4	4	no	—
296	C₂³×C₃₁	—	8	2	no	—
297	C₂³×C₃₁	—	8	4	no	—
298	C₂³×C₃₁	—	8	4	no	—
299	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₃₁	—	2	2	no	—
302	Q₈×C₃₁	—	8	2	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	2	4	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	2	2	no	—
309	D₄×C₃₁	—	2	4	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	8	no	—
312	D₄×C₃₁	—	4	8	no	—
313	D₄×C₃₁	—	4	4	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	2	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	—	8	4	no	—
318	D₄×C₃₁	—	8	4	no	—
319	D₄×C₃₁	C₂×#41	1	4	yes	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	1	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	4	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	8	2	no	—
332	C₂×C₄×C₃₁	—	8	2	no	—
333	C₂×C₄×C₃₁	—	8	4	no	—
334	C₂×C₄×C₃₁	—	8	4	no	—
335	C₂×C₄×C₃₁	—	8	4	no	—
336	C₂×C₄×C₃₁	—	8	2	no	—
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
346	C₈×C₃₁	—	2	1	no	—
347	C₈×C₃₁	—	2	2	no	—
348	C₈×C₃₁	—	2	1	no	—
349	C₈×C₃₁	—	2	1	no	—
350	C₈×C₃₁	—	2	2	no	—
351	C₈×C₃₁	C₂×#41	1	2	yes	—
352	#3519	C₂×C₃₁	1	2	yes	complemented
353	#3391	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3366	C₂×C₃₁	1	2	yes	complemented
356	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3339	C₂×C₃₁	1	2	yes	complemented
358	#3325	C₂×C₃₁	1	2	yes	complemented
359	#3318	C₂×C₃₁	1	4	yes	complemented
360	D₄×D₈	C₂×C₃₁	1	2	yes	complemented
361	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3176	C₂×C₃₁	1	2	yes	complemented
363	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#3122	C₂×C₃₁	1	4	yes	complemented
365	#3109	C₂×C₃₁	1	2	yes	complemented
366	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#2948	C₂×C₃₁	1	2	yes	complemented
368	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	2	2	no	—
372	C₂²×C₃₁	—	2	4	no	—
373	C₂²×C₃₁	—	2	2	no	—
374	C₂²×C₃₁	—	2	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	4	4	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	4	no	—
381	C₂²×C₃₁	—	4	4	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	8	8	no	—
384	C₂²×C₃₁	—	16	8	no	—
385	C₂²×C₃₁	#576	1	2	yes	—
386	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	—	2	1	no	—
390	C₄×C₃₁	—	2	1	no	—
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	2	no	—
393	C₄×C₃₁	—	2	2	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	—	4	4	no	—
397	C₄×C₃₁	#576	1	2	yes	—
398	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
399	C₄×C₃₁	#585	1	1	yes	characteristic
400	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
402	#555	C₂²×C₃₁	1	2	yes	complemented
403	#554	C₂²×C₃₁	1	2	yes	complemented
404	#553	—	2	2	no	—
405	#553	C₂²×C₃₁	1	4	yes	complemented
406	#550	C₂²×C₃₁	1	2	yes	complemented
407	#546	—	2	2	no	—
408	#546	—	2	4	no	—
409	D₄²	C₂²×C₃₁	1	4	yes	complemented
410	D₄²	C₂²×C₃₁	1	2	yes	complemented
411	#540	C₂²×C₃₁	1	4	yes	complemented
412	#538	—	2	4	no	—
413	#532	C₂²×C₃₁	1	2	yes	complemented
414	#529	C₂²×C₃₁	1	1	yes	characteristic
415	#525	—	2	2	no	—
416	C₂×#121	—	2	2	no	—
417	#518	C₂²×C₃₁	1	4	yes	complemented
418	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
419	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
420	#499	C₂²×C₃₁	1	2	yes	complemented
421	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	#493	C₂²×C₃₁	1	2	yes	complemented
423	#490	C₂²×C₃₁	1	4	yes	complemented
424	#486	C₂²×C₃₁	1	2	yes	complemented
425	#482	C₂²×C₃₁	1	4	yes	complemented
426	#482	C₂²×C₃₁	1	4	yes	complemented
427	#481	C₂²×C₃₁	1	4	yes	complemented
428	#478	C₂²×C₃₁	1	4	yes	complemented
429	#478	C₂²×C₃₁	1	4	yes	complemented
430	#476	C₂²×C₃₁	1	2	yes	complemented
431	#476	C₂²×C₃₁	1	2	yes	complemented
432	#469	C₂²×C₃₁	1	4	yes	complemented
433	#466	C₂²×C₃₁	1	2	yes	complemented
434	#466	C₂²×C₃₁	1	2	yes	complemented
435	#466	C₂²×C₃₁	1	2	yes	complemented
436	#466	C₂²×C₃₁	1	2	yes	complemented
437	#459	C₂²×C₃₁	1	2	yes	complemented
438	#459	C₂²×C₃₁	1	2	yes	complemented
439	#459	C₂²×C₃₁	1	4	yes	complemented
440	#459	C₂²×C₃₁	1	4	yes	complemented
441	#447	C₂²×C₃₁	1	4	yes	complemented
442	#447	C₂²×C₃₁	1	4	yes	complemented
443	#447	C₂²×C₃₁	1	4	yes	complemented
444	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#442	C₂²×C₃₁	1	4	yes	complemented
447	#442	C₂²×C₃₁	1	4	yes	complemented
448	#442	C₂²×C₃₁	1	4	yes	complemented
449	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
450	C₄×D₈	C₂²×C₃₁	1	2	yes	—
451	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
452	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
453	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
455	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
456	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
457	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
458	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	#435	C₂²×C₃₁	1	2	yes	complemented
461	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
462	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	#433	C₂²×C₃₁	1	2	yes	complemented
464	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	#427	C₂²×C₃₁	1	2	yes	complemented
466	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#418	C₂²×C₃₁	1	4	yes	complemented
468	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
469	#405	C₂²×C₃₁	1	2	yes	complemented
470	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	C₂×C₃₁	—	2	2	no	—
472	C₂×C₃₁	—	4	2	no	—
473	C₂×C₃₁	—	4	4	no	—
474	C₂×C₃₁	—	8	2	no	—
475	C₂×C₃₁	—	8	4	no	—
476	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
477	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
478	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	—	2	4	no	—
483	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
484	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
485	C₂³×C₄	—	2	2	no	—
486	C₂×D₈	—	2	4	no	—
487	C₂×D₈	—	2	8	no	—
488	C₂×D₈	C₂³×C₃₁	1	2	yes	—
489	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
490	C₂×D₈	C₂³×C₃₁	1	2	yes	—
491	C₂×D₈	C₂³×C₃₁	1	4	yes	—
492	C₂×D₈	C₂³×C₃₁	1	2	yes	—
493	C₂×D₈	C₂³×C₃₁	1	4	yes	—
494	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
498	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
500	#127	C₂³×C₃₁	1	2	yes	—
501	#127	C₂³×C₃₁	1	4	yes	—
502	#126	—	2	4	no	—
503	#126	D₄×C₃₁	1	2	yes	—
504	#125	D₄×C₃₁	1	1	yes	characteristic
505	#125	C₂³×C₃₁	1	4	yes	—
506	#124	—	2	4	no	—
507	#124	—	2	2	no	—
508	#124	D₄×C₃₁	1	1	yes	characteristic
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	—	2	4	no	—
512	#123	D₄×C₃₁	1	2	yes	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
516	#121	—	2	4	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	—	2	4	no	—
525	#121	D₄×C₃₁	1	1	yes	characteristic
526	#121	C₂³×C₃₁	1	4	yes	—
527	#121	C₂³×C₃₁	1	4	yes	—
528	#121	C₂³×C₃₁	1	4	yes	—
529	#120	—	2	4	no	—
530	#120	—	2	4	no	—
531	#120	—	2	4	no	—
532	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	C₂³×C₃₁	1	2	yes	—
540	C₄×D₄	C₂³×C₃₁	1	2	yes	—
541	C₄×D₄	C₂³×C₃₁	1	2	yes	—
542	C₄×D₄	C₂³×C₃₁	1	2	yes	—
543	C₄×D₄	C₂³×C₃₁	1	4	yes	—
544	C₄×D₄	C₂³×C₃₁	1	4	yes	—
545	C₄×D₄	C₂³×C₃₁	1	4	yes	—
546	C₄×D₄	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
548	#117	—	2	2	no	—
549	#117	C₂³×C₃₁	1	4	yes	—
550	#117	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₂²⋊C₄	—	2	2	no	—
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
557	#107	C₂³×C₃₁	1	1	yes	characteristic
558	#107	C₂³×C₃₁	1	1	yes	characteristic
559	#107	C₂³×C₃₁	1	2	yes	—
560	#107	C₂³×C₃₁	1	2	yes	—
561	#107	C₂³×C₃₁	1	2	yes	—
562	#106	C₂³×C₃₁	1	4	yes	—
563	#106	C₂³×C₃₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
567	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
568	#102	C₂³×C₃₁	1	2	yes	—
569	#102	C₂³×C₃₁	1	2	yes	—
570	#102	C₂³×C₃₁	1	2	yes	—
571	#102	C₂³×C₃₁	1	2	yes	—
572	#102	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	4	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	4	yes	—
577	#102	C₂³×C₃₁	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
581	#97	C₂³×C₃₁	1	2	yes	—
582	#97	C₂³×C₃₁	1	2	yes	—
583	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
584	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₄×C₈	C₂³×C₃₁	1	2	yes	—
588	C₃₁	#61480	1	1	yes	characteristic, direct product factor, Sylow
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	4	no	—
591	#41	—	8	4	no	—
592	#41	—	8	4	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	8	4	no	—
609	C₂×D₄	—	8	8	no	—
610	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
611	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
612	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
614	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	4	no	—
624	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
628	D₈	—	2	4	no	—
629	D₈	—	2	8	no	—
630	D₈	—	2	2	no	—
631	D₈	—	2	4	no	—
632	D₈	—	4	2	no	—
633	D₈	—	4	4	no	—
634	D₈	#41×C₃₁	1	4	yes	complemented
635	M₁₆	—	4	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	4	1	no	—
639	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
643	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
644	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
673	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₄²	—	2	4	no	—
675	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₄²	C₂⁴×C₃₁	1	2	yes	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
690	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	Q₈	—	2	2	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	C₂×#41×C₃₁	1	4	yes	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
736	C₈	—	2	1	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×#41×C₃₁	1	2	yes	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	8	8	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₃₁×#576	1	2	yes	—
759	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
760	C₄	—	2	1	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	C₃₁×#576	1	2	yes	—
771	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
772	C₄	C₃₁×#585	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	4	no	—
778	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
779	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
780	C₂	C₂×C₃₁×#576	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×#3519	C₂	semidirect
2. C₃₁×#3391	C₂	semidirect
3. C₃₁×#3380	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3318	C₂	semidirect
9. D₄×D₈×C₃₁	C₂	semidirect
10. D₄×D₈×C₃₁	C₂	semidirect
11. C₃₁×#3176	C₂	semidirect
12. C₃₁×#3169	C₂	semidirect
13. C₃₁×#3122	C₂	semidirect
14. C₃₁×#3109	C₂	semidirect
15. C₃₁×#2966	C₂	semidirect
16. C₃₁×#2948	C₂	semidirect
17. C₂×C₄×D₈×C₃₁	C₂	semidirect
20. C₃₁×#555	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
23. C₃₁×#553	C₂²	semidirect
24. C₃₁×#550	C₂²	semidirect
27. D₄²×C₃₁	C₂²	semidirect
28. D₄²×C₃₁	C₂²	semidirect
29. C₃₁×#540	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
35. C₃₁×#518	C₂²	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₃₁×#500	C₂²	semidirect
38. C₃₁×#499	C₂²	semidirect
39. C₃₁×#493	C₂²	semidirect
40. C₃₁×#493	C₂²	semidirect
41. C₃₁×#490	C₂²	semidirect
42. C₃₁×#486	C₂²	semidirect
43. C₃₁×#482	C₂²	semidirect
44. C₃₁×#482	C₂²	semidirect
45. C₃₁×#481	C₂²	semidirect
46. C₃₁×#478	C₂²	semidirect
47. C₃₁×#478	C₂²	semidirect
48. C₃₁×#476	C₂²	semidirect
49. C₃₁×#476	C₂²	semidirect
50. C₃₁×#469	C₂²	semidirect
51. C₃₁×#466	C₂²	semidirect
52. C₃₁×#466	C₂²	semidirect
53. C₃₁×#466	C₂²	semidirect
54. C₃₁×#466	C₂²	semidirect
55. C₃₁×#459	C₂²	semidirect
56. C₃₁×#459	C₂²	semidirect
57. C₃₁×#459	C₂²	semidirect
58. C₃₁×#459	C₂²	semidirect
59. C₃₁×#447	C₂²	semidirect
60. C₃₁×#447	C₂²	semidirect
61. C₃₁×#447	C₂²	semidirect
62. C₃₁×#446	C₂²	semidirect
63. C₈×Q₈×C₃₁	C₂²	semidirect
64. C₃₁×#442	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₃₁×#442	C₂²	semidirect
70. C₄×D₈×C₃₁	C₂²	semidirect
71. C₄×D₈×C₃₁	C₂²	semidirect
72. C₄×D₈×C₃₁	C₂²	semidirect
73. C₄×D₈×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₄×D₈×C₃₁	C₂²	semidirect
76. C₄×D₈×C₃₁	C₂²	semidirect
77. C₃₁×#436	C₂²	semidirect
78. C₃₁×#435	C₂²	semidirect
79. C₈×D₄×C₃₁	C₂²	semidirect
80. C₈×D₄×C₃₁	C₂²	semidirect
81. C₃₁×#433	C₂²	semidirect
82. C₃₁×#432	C₂²	semidirect
83. C₃₁×#427	C₂²	semidirect
84. C₂×C₃₁×#107	C₂²	semidirect
85. C₃₁×#418	C₂²	semidirect
86. C₂×C₃₁×#102	C₂²	semidirect
87. C₃₁×#405	C₂²	semidirect
88. C₂×C₄×C₈×C₃₁	C₂²	semidirect
243. D₈×C₃₁	#41	semidirect
289. #61480	C₃₁	direct (N × H)
352. #3519	C₂×C₃₁	semidirect
353. #3391	C₂×C₃₁	semidirect
354. #3380	C₂×C₃₁	semidirect
355. #3366	C₂×C₃₁	semidirect
356. #3341	C₂×C₃₁	semidirect
357. #3339	C₂×C₃₁	semidirect
358. #3325	C₂×C₃₁	semidirect
359. #3318	C₂×C₃₁	semidirect
360. D₄×D₈	C₂×C₃₁	semidirect
361. D₄×D₈	C₂×C₃₁	semidirect
362. #3176	C₂×C₃₁	semidirect
363. #3169	C₂×C₃₁	semidirect
364. #3122	C₂×C₃₁	semidirect
365. #3109	C₂×C₃₁	semidirect
366. #2966	C₂×C₃₁	semidirect
367. #2948	C₂×C₃₁	semidirect
368. C₂×C₄×D₈	C₂×C₃₁	semidirect
402. #555	C₂²×C₃₁	semidirect
403. #554	C₂²×C₃₁	semidirect
405. #553	C₂²×C₃₁	semidirect
406. #550	C₂²×C₃₁	semidirect
409. D₄²	C₂²×C₃₁	semidirect
410. D₄²	C₂²×C₃₁	semidirect
411. #540	C₂²×C₃₁	semidirect
413. #532	C₂²×C₃₁	semidirect
417. #518	C₂²×C₃₁	semidirect
418. C₂×C₄×D₄	C₂²×C₃₁	semidirect
419. #500	C₂²×C₃₁	semidirect
420. #499	C₂²×C₃₁	semidirect
421. #493	C₂²×C₃₁	semidirect
422. #493	C₂²×C₃₁	semidirect
423. #490	C₂²×C₃₁	semidirect
424. #486	C₂²×C₃₁	semidirect
425. #482	C₂²×C₃₁	semidirect
426. #482	C₂²×C₃₁	semidirect
427. #481	C₂²×C₃₁	semidirect
428. #478	C₂²×C₃₁	semidirect
429. #478	C₂²×C₃₁	semidirect
430. #476	C₂²×C₃₁	semidirect
431. #476	C₂²×C₃₁	semidirect
432. #469	C₂²×C₃₁	semidirect
433. #466	C₂²×C₃₁	semidirect
434. #466	C₂²×C₃₁	semidirect
435. #466	C₂²×C₃₁	semidirect
436. #466	C₂²×C₃₁	semidirect
437. #459	C₂²×C₃₁	semidirect
438. #459	C₂²×C₃₁	semidirect
439. #459	C₂²×C₃₁	semidirect
440. #459	C₂²×C₃₁	semidirect
441. #447	C₂²×C₃₁	semidirect
442. #447	C₂²×C₃₁	semidirect
443. #447	C₂²×C₃₁	semidirect
444. #446	C₂²×C₃₁	semidirect
445. C₈×Q₈	C₂²×C₃₁	semidirect
446. #442	C₂²×C₃₁	semidirect
447. #442	C₂²×C₃₁	semidirect
448. #442	C₂²×C₃₁	semidirect
452. C₄×D₈	C₂²×C₃₁	semidirect
453. C₄×D₈	C₂²×C₃₁	semidirect
454. C₄×D₈	C₂²×C₃₁	semidirect
455. C₄×D₈	C₂²×C₃₁	semidirect
456. C₄×D₈	C₂²×C₃₁	semidirect
457. C₄×D₈	C₂²×C₃₁	semidirect
458. C₄×D₈	C₂²×C₃₁	semidirect
459. #436	C₂²×C₃₁	semidirect
460. #435	C₂²×C₃₁	semidirect
461. C₈×D₄	C₂²×C₃₁	semidirect
462. C₈×D₄	C₂²×C₃₁	semidirect
463. #433	C₂²×C₃₁	semidirect
464. #432	C₂²×C₃₁	semidirect
465. #427	C₂²×C₃₁	semidirect
466. C₂×#107	C₂²×C₃₁	semidirect
467. #418	C₂²×C₃₁	semidirect
468. C₂×#102	C₂²×C₃₁	semidirect
469. #405	C₂²×C₃₁	semidirect
470. C₂×C₄×C₈	C₂²×C₃₁	semidirect
588. C₃₁	#61480	direct (N × H)
634. D₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3519	2
C₃₁×#3391	2
C₃₁×#3380	2
C₃₁×#3366	2
C₃₁×#3341	2
C₃₁×#3339	2
C₃₁×#3325	2
C₃₁×#3318	2
D₄×D₈×C₃₁	2
C₃₁×#3176	2
C₃₁×#3169	2
C₃₁×#3122	2
C₃₁×#3109	2
C₃₁×#2966	2
C₃₁×#2948	2
C₂×C₄×D₈×C₃₁	2
#61480	31

Subgroups — C31×#61480 #21518239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61480 #21518239