Subgroups — C₃₁×#61327 #21518086

Order 7936.

1802 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3371	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3365	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3362	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#559	C₂²	1	4	yes	—
21	Q₈²×C₃₁	—	2	1	no	—
22	Q₈²×C₃₁	C₂²	1	2	yes	complemented
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#557	—	2	2	no	—
25	C₃₁×#557	C₂²	1	2	yes	complemented
26	C₃₁×#557	C₂²	1	4	yes	complemented
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#555	—	2	1	no	—
29	C₃₁×#553	—	2	2	no	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#544	—	2	2	no	—
33	C₃₁×#544	C₂²	1	2	yes	—
34	C₃₁×#538	—	2	2	no	—
35	C₃₁×#535	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	2	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#525	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₃₁×#519	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#490	C₂²	1	4	yes	—
46	C₃₁×#489	C₂²	1	4	yes	—
47	C₃₁×#488	C₂²	1	4	yes	—
48	C₃₁×#488	C₂²	1	2	yes	complemented
49	C₃₁×#488	C₂²	1	2	yes	complemented
50	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#486	C₂²	1	4	yes	—
53	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#476	C₂²	1	2	yes	—
59	C₃₁×#476	C₂²	1	4	yes	complemented
60	C₃₁×#475	C₂²	1	4	yes	complemented
61	C₃₁×#474	C₂²	1	2	yes	—
62	C₃₁×#464	C₂²	1	4	yes	—
63	C₃₁×#464	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#462	C₂²	1	2	yes	complemented
66	C₃₁×#460	C₂²	1	4	yes	—
67	C₃₁×#460	C₂²	1	4	yes	—
68	C₃₁×#460	C₂²	1	2	yes	complemented
69	C₃₁×#446	C₂²	1	2	yes	complemented
70	C₃₁×#446	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
73	C₃₁×#441	C₂²	1	4	yes	complemented
74	C₃₁×#440	C₂²	1	4	yes	complemented
75	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
76	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
77	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
81	C₃₁×#428	C₂²	1	2	yes	—
82	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
83	C₃₁×#424	C₂²	1	2	yes	—
84	C₃₁×#423	C₂²	1	1	yes	characteristic
85	C₃₁×#418	C₂²	1	2	yes	—
86	C₃₁×#417	C₂²	1	2	yes	—
87	C₃₁×#416	C₂²	1	2	yes	—
88	C₃₁×#416	C₂²	1	2	yes	—
89	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	C₂³	1	2	yes	—
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	—	2	1	no	—
98	C₃₁×#137	—	2	8	no	—
99	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	—	2	4	no	—
101	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	4	no	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	—	2	4	no	—
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×#127	C₂³	1	4	yes	—
119	C₃₁×#127	C₂³	1	1	yes	characteristic
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	D₄	1	2	yes	—
126	C₃₁×#125	C₂³	1	2	yes	—
127	C₃₁×#125	C₂³	1	4	yes	—
128	C₃₁×#124	—	2	4	no	—
129	C₃₁×#124	C₂³	1	4	yes	—
130	C₃₁×#124	C₂³	1	2	yes	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×#123	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
138	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
139	C₃₁×#121	—	2	1	no	—
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	4	no	—
145	C₃₁×#120	—	2	4	no	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	4	no	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	4	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	1	no	—
168	C₄×D₄×C₃₁	C₂³	1	2	yes	—
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	4	yes	—
171	C₃₁×#117	—	2	2	no	—
172	C₃₁×#117	—	2	2	no	—
173	C₃₁×#117	—	2	4	no	—
174	C₃₁×#117	C₂³	1	2	yes	—
175	C₃₁×#117	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	4	yes	—
184	C₃₁×#106	C₂³	1	2	yes	—
185	C₃₁×#106	C₂³	1	2	yes	—
186	C₃₁×#106	C₂³	1	4	yes	—
187	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
188	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
190	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
191	C₃₁×#103	C₂³	1	2	yes	—
192	C₃₁×#103	C₂³	1	2	yes	—
193	C₃₁×#103	C₂³	1	2	yes	—
194	C₃₁×#103	C₂³	1	2	yes	—
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#103	C₂³	1	4	yes	—
198	C₃₁×#102	C₂³	1	2	yes	—
199	C₃₁×#102	C₂³	1	2	yes	—
200	C₃₁×#102	C₂³	1	2	yes	—
201	C₃₁×#102	C₂³	1	2	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	C₂⁴×C₃₁	—	2	1	no	—
214	#41×C₃₁	—	2	4	no	—
215	#41×C₃₁	—	2	4	no	—
216	#41×C₃₁	—	8	4	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	4	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₃₁	#41	1	4	yes	complemented
225	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
227	C₂×D₄×C₃₁	—	2	2	no	—
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	4	no	—
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	—	2	4	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	2	no	—
235	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	—	2	1	no	—
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	8	2	no	—
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₃₁	—	2	8	no	—
249	SD₁₆×C₃₁	—	2	4	no	—
250	SD₁₆×C₃₁	—	2	4	no	—
251	SD₁₆×C₃₁	—	2	8	no	—
252	M₁₆×C₃₁	—	2	4	no	—
253	C₂×C₈×C₃₁	—	2	2	no	—
254	C₂×C₈×C₃₁	—	2	2	no	—
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	—	2	4	no	—
298	C₄²×C₃₁	—	2	4	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	4	yes	—
306	#61327	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂³×C₃₁	—	2	2	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	—	4	2	no	—
310	C₂³×C₃₁	—	8	1	no	—
311	C₂³×C₃₁	—	8	1	no	—
312	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₃₁	—	2	4	no	—
314	Q₈×C₃₁	—	2	4	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	2	2	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	Q₈×C₃₁	—	4	2	no	—
320	Q₈×C₃₁	—	8	1	no	—
321	Q₈×C₃₁	—	8	4	no	—
322	Q₈×C₃₁	C₂×#41	1	4	yes	—
323	D₄×C₃₁	—	2	2	no	—
324	D₄×C₃₁	—	2	2	no	—
325	D₄×C₃₁	—	2	2	no	—
326	D₄×C₃₁	—	2	2	no	—
327	D₄×C₃₁	—	4	4	no	—
328	D₄×C₃₁	—	4	2	no	—
329	D₄×C₃₁	—	4	2	no	—
330	D₄×C₃₁	—	8	1	no	—
331	D₄×C₃₁	—	8	4	no	—
332	D₄×C₃₁	—	8	4	no	—
333	C₂×C₄×C₃₁	—	2	4	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	—	4	1	no	—
342	C₂×C₄×C₃₁	—	4	4	no	—
343	C₂×C₄×C₃₁	—	4	4	no	—
344	C₂×C₄×C₃₁	—	8	2	no	—
345	C₂×C₄×C₃₁	—	8	4	no	—
346	C₂×C₄×C₃₁	—	8	1	no	—
347	C₂×C₄×C₃₁	—	8	1	no	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
356	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
357	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
358	C₈×C₃₁	—	2	1	no	—
359	C₈×C₃₁	—	2	1	no	—
360	C₈×C₃₁	—	2	4	no	—
361	C₈×C₃₁	—	2	1	no	—
362	C₈×C₃₁	—	2	1	no	—
363	#3506	C₂×C₃₁	1	1	yes	characteristic
364	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#3371	C₂×C₃₁	1	4	yes	complemented
366	#3369	C₂×C₃₁	1	2	yes	complemented
367	#3368	C₂×C₃₁	1	2	yes	complemented
368	#3365	C₂×C₃₁	1	4	yes	complemented
369	#3364	C₂×C₃₁	1	2	yes	complemented
370	#3362	C₂×C₃₁	1	2	yes	complemented
371	#3136	C₂×C₃₁	1	2	yes	complemented
372	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#3084	C₂×C₃₁	1	2	yes	complemented
374	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#3043	C₂×C₃₁	1	2	yes	complemented
376	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
378	#2947	C₂×C₃₁	1	2	yes	complemented
379	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	1	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	4	2	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	8	4	no	—
389	C₂²×C₃₁	#548	1	2	yes	—
390	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	4	no	—
394	C₄×C₃₁	—	2	4	no	—
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	2	4	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	2	no	—
402	C₄×C₃₁	#548	1	2	yes	—
403	C₄×C₃₁	#577	1	2	yes	—
404	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
405	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₂×#137	C₂²×C₃₁	1	2	yes	—
407	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
408	#559	C₂²×C₃₁	1	4	yes	—
409	Q₈²	—	2	1	no	—
410	Q₈²	C₂²×C₃₁	1	2	yes	complemented
411	#557	—	2	1	no	—
412	#557	—	2	2	no	—
413	#557	C₂²×C₃₁	1	2	yes	complemented
414	#557	C₂²×C₃₁	1	4	yes	complemented
415	#556	C₂²×C₃₁	1	2	yes	—
416	#555	—	2	1	no	—
417	#553	—	2	2	no	—
418	#550	C₂²×C₃₁	1	2	yes	—
419	#547	—	2	1	no	—
420	#544	—	2	2	no	—
421	#544	C₂²×C₃₁	1	2	yes	—
422	#538	—	2	2	no	—
423	#535	C₂²×C₃₁	1	2	yes	—
424	#533	—	2	2	no	—
425	#533	C₂²×C₃₁	1	1	yes	characteristic
426	#533	C₂²×C₃₁	1	1	yes	characteristic
427	#532	C₂²×C₃₁	1	1	yes	characteristic
428	#525	—	2	2	no	—
429	#520	C₂²×C₃₁	1	2	yes	—
430	#519	C₂²×C₃₁	1	2	yes	—
431	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
433	#490	C₂²×C₃₁	1	4	yes	—
434	#489	C₂²×C₃₁	1	4	yes	—
435	#488	C₂²×C₃₁	1	4	yes	—
436	#488	C₂²×C₃₁	1	2	yes	complemented
437	#488	C₂²×C₃₁	1	2	yes	complemented
438	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
439	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	#486	C₂²×C₃₁	1	4	yes	—
441	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
442	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	#479	C₂²×C₃₁	1	4	yes	complemented
444	#478	C₂²×C₃₁	1	4	yes	—
445	#478	C₂²×C₃₁	1	4	yes	complemented
446	#476	C₂²×C₃₁	1	2	yes	—
447	#476	C₂²×C₃₁	1	4	yes	complemented
448	#475	C₂²×C₃₁	1	4	yes	complemented
449	#474	C₂²×C₃₁	1	2	yes	—
450	#464	C₂²×C₃₁	1	4	yes	—
451	#464	C₂²×C₃₁	1	4	yes	—
452	#464	C₂²×C₃₁	1	4	yes	complemented
453	#462	C₂²×C₃₁	1	2	yes	complemented
454	#460	C₂²×C₃₁	1	4	yes	—
455	#460	C₂²×C₃₁	1	4	yes	—
456	#460	C₂²×C₃₁	1	2	yes	complemented
457	#446	C₂²×C₃₁	1	2	yes	complemented
458	#446	C₂²×C₃₁	1	2	yes	complemented
459	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
460	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
461	#441	C₂²×C₃₁	1	4	yes	complemented
462	#440	C₂²×C₃₁	1	4	yes	complemented
463	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
464	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
465	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
466	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
467	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
468	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
469	#428	C₂²×C₃₁	1	2	yes	—
470	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
471	#424	C₂²×C₃₁	1	2	yes	—
472	#423	C₂²×C₃₁	1	1	yes	characteristic
473	#418	C₂²×C₃₁	1	2	yes	—
474	#417	C₂²×C₃₁	1	2	yes	—
475	#416	C₂²×C₃₁	1	2	yes	—
476	#416	C₂²×C₃₁	1	2	yes	—
477	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
479	#405	C₂²×C₃₁	1	2	yes	—
480	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₃₁	—	2	2	no	—
482	C₂×C₃₁	—	8	2	no	—
483	C₂×C₃₁	—	8	2	no	—
484	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
485	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
486	C₂×C₃₁	#3584	1	1	yes	characteristic
487	C₂×#41	—	2	2	no	—
488	C₂×#41	C₂³×C₃₁	1	2	yes	—
489	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	#137	—	2	8	no	—
493	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
494	C₂×SD₁₆	—	2	4	no	—
495	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
498	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
499	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	—	2	4	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	4	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
507	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
512	#127	C₂³×C₃₁	1	1	yes	characteristic
513	#127	C₂³×C₃₁	1	4	yes	—
514	#126	—	2	4	no	—
515	#125	—	2	4	no	—
516	#125	—	2	4	no	—
517	#125	—	2	4	no	—
518	#125	—	2	2	no	—
519	#125	D₄×C₃₁	1	2	yes	—
520	#125	C₂³×C₃₁	1	2	yes	—
521	#125	C₂³×C₃₁	1	4	yes	—
522	#124	—	2	4	no	—
523	#124	C₂³×C₃₁	1	2	yes	—
524	#124	C₂³×C₃₁	1	4	yes	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
532	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	4	no	—
539	#120	—	2	4	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	4	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
550	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
551	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
552	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
553	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
554	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
555	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₃₁	1	2	yes	—
563	C₄×D₄	C₂³×C₃₁	1	2	yes	—
564	C₄×D₄	C₂³×C₃₁	1	4	yes	—
565	#117	—	2	2	no	—
566	#117	—	2	2	no	—
567	#117	—	2	4	no	—
568	#117	C₂³×C₃₁	1	2	yes	—
569	#117	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
577	#107	C₂³×C₃₁	1	4	yes	—
578	#106	C₂³×C₃₁	1	2	yes	—
579	#106	C₂³×C₃₁	1	2	yes	—
580	#106	C₂³×C₃₁	1	4	yes	—
581	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
582	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
583	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
584	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
585	#103	C₂³×C₃₁	1	2	yes	—
586	#103	C₂³×C₃₁	1	2	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	2	yes	—
589	#103	C₂³×C₃₁	1	2	yes	—
590	#103	C₂³×C₃₁	1	2	yes	—
591	#103	C₂³×C₃₁	1	4	yes	—
592	#102	C₂³×C₃₁	1	2	yes	—
593	#102	C₂³×C₃₁	1	2	yes	—
594	#102	C₂³×C₃₁	1	2	yes	—
595	#102	C₂³×C₃₁	1	2	yes	—
596	#102	C₂³×C₃₁	1	2	yes	—
597	#102	C₂³×C₃₁	1	2	yes	—
598	#102	C₂³×C₃₁	1	4	yes	—
599	#102	C₂³×C₃₁	1	4	yes	—
600	#102	C₂³×C₃₁	1	4	yes	—
601	#97	C₂³×C₃₁	1	4	yes	—
602	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₃₁	1	4	yes	—
607	C₃₁	#61327	1	1	yes	characteristic, direct product factor, Sylow
608	C₂⁴	—	2	1	no	—
609	#41	—	2	4	no	—
610	#41	—	2	4	no	—
611	#41	—	8	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	4	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
619	C₂×Q₈	#41×C₃₁	1	4	yes	complemented
620	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
631	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
643	Q₁₆	—	2	8	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	2	4	no	—
646	SD₁₆	—	2	8	no	—
647	M₁₆	—	2	4	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	2	2	no	—
650	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
675	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
676	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₄²	C₂⁴×C₃₁	1	4	yes	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	4	2	no	—
704	C₂³	—	8	1	no	—
705	C₂³	—	8	1	no	—
706	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	Q₈	—	2	4	no	—
708	Q₈	—	2	4	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	4	2	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	8	1	no	—
715	Q₈	—	8	4	no	—
716	Q₈	C₂×#41×C₃₁	1	4	yes	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	2	no	—
724	D₄	—	8	1	no	—
725	D₄	—	8	4	no	—
726	D₄	—	8	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	8	2	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	1	no	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
750	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
751	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
752	C₈	—	2	1	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	4	no	—
755	C₈	—	2	1	no	—
756	C₈	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₃₁×#548	1	2	yes	—
767	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
768	C₄	—	2	4	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	4	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	4	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	C₃₁×#548	1	2	yes	—
780	C₄	C₃₁×#577	1	2	yes	—
781	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
782	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
783	C₂	—	2	2	no	—
784	C₂	—	8	2	no	—
785	C₂	—	8	2	no	—
786	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
787	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
788	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3371	C₂	semidirect
4. C₃₁×#3369	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3365	C₂	semidirect
7. C₃₁×#3364	C₂	semidirect
8. C₃₁×#3362	C₂	semidirect
9. C₃₁×#3136	C₂	semidirect
10. C₃₁×#3131	C₂	semidirect
11. C₃₁×#3084	C₂	semidirect
12. C₃₁×#3077	C₂	semidirect
13. C₃₁×#3043	C₂	semidirect
14. C₃₁×#3037	C₂	semidirect
15. C₃₁×#2960	C₂	semidirect
16. C₃₁×#2947	C₂	semidirect
17. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
22. Q₈²×C₃₁	C₂²	semidirect
25. C₃₁×#557	C₂²	semidirect
26. C₃₁×#557	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#487	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#486	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#462	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
69. C₃₁×#446	C₂²	semidirect
70. C₃₁×#446	C₂²	semidirect
71. C₈×Q₈×C₃₁	C₂²	semidirect
72. C₈×Q₈×C₃₁	C₂²	semidirect
73. C₃₁×#441	C₂²	semidirect
74. C₃₁×#440	C₂²	semidirect
75. C₄×Q₁₆×C₃₁	C₂²	semidirect
80. C₄×SD₁₆×C₃₁	C₂²	semidirect
224. C₂×Q₈×C₃₁	#41	semidirect
306. #61327	C₃₁	direct (N × H)
364. #3502	C₂×C₃₁	semidirect
365. #3371	C₂×C₃₁	semidirect
366. #3369	C₂×C₃₁	semidirect
367. #3368	C₂×C₃₁	semidirect
368. #3365	C₂×C₃₁	semidirect
369. #3364	C₂×C₃₁	semidirect
370. #3362	C₂×C₃₁	semidirect
371. #3136	C₂×C₃₁	semidirect
372. #3131	C₂×C₃₁	semidirect
373. #3084	C₂×C₃₁	semidirect
374. #3077	C₂×C₃₁	semidirect
375. #3043	C₂×C₃₁	semidirect
376. #3037	C₂×C₃₁	semidirect
377. #2960	C₂×C₃₁	semidirect
378. #2947	C₂×C₃₁	semidirect
379. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
410. Q₈²	C₂²×C₃₁	semidirect
413. #557	C₂²×C₃₁	semidirect
414. #557	C₂²×C₃₁	semidirect
436. #488	C₂²×C₃₁	semidirect
437. #488	C₂²×C₃₁	semidirect
438. #487	C₂²×C₃₁	semidirect
439. #487	C₂²×C₃₁	semidirect
441. #486	C₂²×C₃₁	semidirect
442. #486	C₂²×C₃₁	semidirect
443. #479	C₂²×C₃₁	semidirect
445. #478	C₂²×C₃₁	semidirect
447. #476	C₂²×C₃₁	semidirect
448. #475	C₂²×C₃₁	semidirect
452. #464	C₂²×C₃₁	semidirect
453. #462	C₂²×C₃₁	semidirect
456. #460	C₂²×C₃₁	semidirect
457. #446	C₂²×C₃₁	semidirect
458. #446	C₂²×C₃₁	semidirect
459. C₈×Q₈	C₂²×C₃₁	semidirect
460. C₈×Q₈	C₂²×C₃₁	semidirect
461. #441	C₂²×C₃₁	semidirect
462. #440	C₂²×C₃₁	semidirect
463. C₄×Q₁₆	C₂²×C₃₁	semidirect
468. C₄×SD₁₆	C₂²×C₃₁	semidirect
607. C₃₁	#61327	direct (N × H)
619. C₂×Q₈	#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×#3506	2
C₃₁×#3502	2
C₃₁×#3371	2
C₃₁×#3369	2
C₃₁×#3368	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3362	2
C₃₁×#3136	2
C₃₁×#3131	2
C₃₁×#3084	2
C₃₁×#3077	2
C₃₁×#3043	2
C₃₁×#3037	2
C₃₁×#2960	2
C₃₁×#2947	2
C₂×C₄×SD₁₆×C₃₁	2
#61327	31

Subgroups — C31×#61327 #21518086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61327 #21518086