Subgroups — C₃₁×#61791 #21518550

Order 7936.

1774 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3334	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3203	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3098	C₂	1	4	yes	maximal, complemented
17	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#562	—	2	2	no	—
19	C₃₁×#556	C₂²	1	2	yes	—
20	C₃₁×#555	C₂²	1	2	yes	—
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	C₂²	1	2	yes	—
23	C₃₁×#554	C₂²	1	2	yes	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#550	—	2	1	no	—
26	C₃₁×#550	C₂²	1	2	yes	—
27	C₃₁×#548	—	2	2	no	—
28	C₃₁×#547	C₂²	1	2	yes	—
29	C₃₁×#547	C₂²	1	2	yes	—
30	C₃₁×#547	C₂²	1	2	yes	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#540	—	2	2	no	—
33	C₃₁×#537	—	2	2	no	—
34	C₃₁×#537	C₂²	1	4	yes	—
35	C₃₁×#537	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#500	C₂²	1	2	yes	—
45	C₃₁×#500	C₂²	1	2	yes	—
46	C₃₁×#487	C₂²	1	2	yes	—
47	C₃₁×#486	C₂²	1	2	yes	—
48	C₃₁×#485	C₂²	1	2	yes	—
49	C₃₁×#485	C₂²	1	4	yes	—
50	C₃₁×#484	C₂²	1	4	yes	—
51	C₃₁×#484	C₂²	1	4	yes	—
52	C₃₁×#484	C₂²	1	4	yes	—
53	C₃₁×#482	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	2	yes	—
55	C₃₁×#480	C₂²	1	4	yes	—
56	C₃₁×#480	C₂²	1	4	yes	—
57	C₃₁×#480	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#477	C₂²	1	1	yes	characteristic
60	C₃₁×#477	C₂²	1	2	yes	—
61	C₃₁×#476	C₂²	1	1	yes	characteristic
62	C₃₁×#475	C₂²	1	1	yes	characteristic
63	C₃₁×#474	C₂²	1	1	yes	characteristic
64	C₃₁×#474	C₂²	1	2	yes	—
65	C₃₁×#474	C₂²	1	2	yes	—
66	C₃₁×#468	C₂²	1	4	yes	—
67	C₃₁×#468	C₂²	1	4	yes	—
68	C₃₁×#467	C₂²	1	4	yes	—
69	C₃₁×#466	C₂²	1	4	yes	—
70	C₃₁×#462	C₂²	1	1	yes	characteristic
71	C₃₁×#461	C₂²	1	1	yes	characteristic
72	C₃₁×#460	C₂²	1	1	yes	characteristic
73	C₃₁×#459	C₂²	1	1	yes	characteristic
74	C₃₁×#452	C₂²	1	4	yes	—
75	C₃₁×#452	C₂²	1	2	yes	—
76	C₃₁×#449	C₂²	1	2	yes	—
77	C₃₁×#449	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
81	C₄×D₈×C₃₁	C₂²	1	2	yes	—
82	C₃₁×#436	C₂²	1	2	yes	—
83	C₃₁×#436	C₂²	1	2	yes	—
84	C₈×D₄×C₃₁	C₂²	1	2	yes	—
85	C₈×D₄×C₃₁	C₂²	1	2	yes	—
86	C₃₁×#431	C₂²	1	1	yes	characteristic
87	C₃₁×#431	C₂²	1	1	yes	characteristic
88	C₃₁×#428	C₂²	1	4	yes	—
89	C₂×C₃₁×#107	C₂²	1	4	yes	—
90	C₃₁×#417	C₂²	1	4	yes	—
91	C₃₁×#416	C₂²	1	4	yes	—
92	C₃₁×#408	C₂²	1	4	yes	—
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	—	2	2	no	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	4	yes	—
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	—	2	1	no	—
100	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×#127	—	2	2	no	—
115	C₃₁×#127	D₄	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	1	yes	characteristic
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	—	2	1	no	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	4	no	—
123	C₃₁×#124	—	2	1	no	—
124	C₃₁×#124	D₄	1	2	yes	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	4	no	—
144	C₃₁×#121	—	2	4	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	—	2	4	no	—
147	C₃₁×#121	D₄	1	2	yes	—
148	C₃₁×#121	D₄	1	2	yes	—
149	C₃₁×#121	C₂³	1	4	yes	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#121	C₂³	1	4	yes	—
152	C₄×Q₈×C₃₁	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	4	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₃₁×#117	—	2	1	no	—
172	C₃₁×#117	—	2	2	no	—
173	C₃₁×#117	—	2	1	no	—
174	C₃₁×#117	C₂³	1	4	yes	—
175	C₃₁×#117	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	2	yes	—
185	C₃₁×#107	C₂³	1	4	yes	—
186	C₃₁×#107	C₂³	1	4	yes	—
187	C₃₁×#107	C₂³	1	4	yes	—
188	C₃₁×#107	C₂³	1	4	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	2	yes	—
191	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	4	yes	—
197	C₃₁×#103	C₂³	1	2	yes	—
198	C₃₁×#103	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#102	C₂³	1	2	yes	—
202	C₃₁×#102	C₂³	1	4	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	2	yes	—
213	#41×C₃₁	—	4	2	no	—
214	#41×C₃₁	—	4	2	no	—
215	#41×C₃₁	—	4	1	no	—
216	#41×C₃₁	—	4	1	no	—
217	#41×C₃₁	—	4	4	no	—
218	#41×C₃₁	—	4	4	no	—
219	#41×C₃₁	—	8	2	no	—
220	#41×C₃₁	—	8	4	no	—
221	#41×C₃₁	—	8	4	no	—
222	C₂×Q₈×C₃₁	—	2	1	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	—	2	1	no	—
225	C₂×Q₈×C₃₁	—	2	2	no	—
226	C₂×Q₈×C₃₁	—	8	2	no	—
227	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	4	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	1	no	—
236	C₂×D₄×C₃₁	—	2	1	no	—
237	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
240	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	4	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	1	no	—
247	C₂²×C₄×C₃₁	—	2	1	no	—
248	C₂²×C₄×C₃₁	—	2	1	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	4	no	—
251	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
255	Q₁₆×C₃₁	—	4	2	no	—
256	SD₁₆×C₃₁	—	4	2	no	—
257	SD₁₆×C₃₁	—	4	2	no	—
258	D₈×C₃₁	—	4	2	no	—
259	M₁₆×C₃₁	—	4	4	no	—
260	C₂×C₈×C₃₁	—	4	4	no	—
261	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
262	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
263	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
264	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	1	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	1	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
299	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
300	C₄²×C₃₁	—	2	1	no	—
301	C₄²×C₃₁	—	2	1	no	—
302	C₄²×C₃₁	—	2	1	no	—
303	C₄²×C₃₁	—	2	4	no	—
304	C₄²×C₃₁	—	2	2	no	—
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	#61791	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₂³×C₃₁	—	2	1	no	—
311	C₂³×C₃₁	—	2	2	no	—
312	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
313	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₃₁	—	2	1	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	2	1	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	Q₈×C₃₁	—	4	4	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	8	2	no	—
322	Q₈×C₃₁	—	8	1	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	4	no	—
325	D₄×C₃₁	—	2	1	no	—
326	D₄×C₃₁	—	2	2	no	—
327	D₄×C₃₁	—	2	1	no	—
328	D₄×C₃₁	—	2	2	no	—
329	D₄×C₃₁	—	4	2	no	—
330	D₄×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	4	2	no	—
332	D₄×C₃₁	—	4	2	no	—
333	D₄×C₃₁	—	8	1	no	—
334	D₄×C₃₁	—	8	4	no	—
335	D₄×C₃₁	—	8	2	no	—
336	D₄×C₃₁	—	8	4	no	—
337	D₄×C₃₁	—	8	4	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	4	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	1	no	—
345	C₂×C₄×C₃₁	—	2	1	no	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	4	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	4	2	no	—
352	C₂×C₄×C₃₁	—	4	2	no	—
353	C₂×C₄×C₃₁	—	4	4	no	—
354	C₂×C₄×C₃₁	—	4	2	no	—
355	C₂×C₄×C₃₁	—	8	4	no	—
356	C₂×C₄×C₃₁	—	8	2	no	—
357	C₂×C₄×C₃₁	—	8	4	no	—
358	C₂×C₄×C₃₁	—	8	4	no	—
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
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	C₂⁵	1	1	yes	characteristic
366	C₈×C₃₁	—	2	2	no	—
367	C₈×C₃₁	—	2	2	no	—
368	C₈×C₃₁	—	2	2	no	—
369	C₈×C₃₁	—	2	2	no	—
370	#3548	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#3357	C₂×C₃₁	1	2	yes	complemented
373	#3353	C₂×C₃₁	1	2	yes	complemented
374	#3338	C₂×C₃₁	1	2	yes	complemented
375	#3334	C₂×C₃₁	1	2	yes	complemented
376	#3333	C₂×C₃₁	1	2	yes	complemented
377	#3330	C₂×C₃₁	1	2	yes	complemented
378	#3305	C₂×C₃₁	1	2	yes	complemented
379	#3302	C₂×C₃₁	1	2	yes	complemented
380	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
382	#3203	C₂×C₃₁	1	4	yes	complemented
383	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
385	#3098	C₂×C₃₁	1	4	yes	complemented
386	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
387	C₂²×C₃₁	—	2	1	no	—
388	C₂²×C₃₁	—	2	4	no	—
389	C₂²×C₃₁	—	2	1	no	—
390	C₂²×C₃₁	—	2	4	no	—
391	C₂²×C₃₁	—	2	1	no	—
392	C₂²×C₃₁	—	2	4	no	—
393	C₂²×C₃₁	—	4	1	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	1	no	—
397	C₂²×C₃₁	—	4	1	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₃₁	—	2	1	no	—
401	C₄×C₃₁	—	2	4	no	—
402	C₄×C₃₁	—	2	1	no	—
403	C₄×C₃₁	—	2	1	no	—
404	C₄×C₃₁	—	4	1	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	—	4	1	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	—	4	4	no	—
410	C₄×C₃₁	—	4	1	no	—
411	C₄×C₃₁	#576	1	2	yes	—
412	C₄×C₃₁	#578	1	2	yes	—
413	C₄×C₃₁	#585	1	1	yes	characteristic
414	C₄×C₃₁	#585	1	1	yes	characteristic
415	#562	—	2	2	no	—
416	#556	C₂²×C₃₁	1	2	yes	—
417	#555	C₂²×C₃₁	1	2	yes	—
418	#554	—	2	1	no	—
419	#554	C₂²×C₃₁	1	2	yes	—
420	#554	C₂²×C₃₁	1	2	yes	—
421	#553	—	2	2	no	—
422	#550	—	2	1	no	—
423	#550	C₂²×C₃₁	1	2	yes	—
424	#548	—	2	2	no	—
425	#547	C₂²×C₃₁	1	2	yes	—
426	#547	C₂²×C₃₁	1	2	yes	—
427	#547	C₂²×C₃₁	1	2	yes	—
428	#542	—	2	2	no	—
429	#540	—	2	2	no	—
430	#537	—	2	2	no	—
431	#537	C₂²×C₃₁	1	4	yes	—
432	#537	C₂²×C₃₁	1	2	yes	—
433	#533	—	2	1	no	—
434	#533	C₂²×C₃₁	1	1	yes	characteristic
435	#532	—	2	1	no	—
436	#532	C₂²×C₃₁	1	1	yes	characteristic
437	#532	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
439	#520	C₂²×C₃₁	1	2	yes	—
440	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
441	#500	C₂²×C₃₁	1	2	yes	—
442	#500	C₂²×C₃₁	1	2	yes	—
443	#487	C₂²×C₃₁	1	2	yes	—
444	#486	C₂²×C₃₁	1	2	yes	—
445	#485	C₂²×C₃₁	1	2	yes	—
446	#485	C₂²×C₃₁	1	4	yes	—
447	#484	C₂²×C₃₁	1	4	yes	—
448	#484	C₂²×C₃₁	1	4	yes	—
449	#484	C₂²×C₃₁	1	4	yes	—
450	#482	C₂²×C₃₁	1	4	yes	—
451	#482	C₂²×C₃₁	1	2	yes	—
452	#480	C₂²×C₃₁	1	4	yes	—
453	#480	C₂²×C₃₁	1	4	yes	—
454	#480	C₂²×C₃₁	1	4	yes	—
455	#477	C₂²×C₃₁	1	2	yes	—
456	#477	C₂²×C₃₁	1	1	yes	characteristic
457	#477	C₂²×C₃₁	1	2	yes	—
458	#476	C₂²×C₃₁	1	1	yes	characteristic
459	#475	C₂²×C₃₁	1	1	yes	characteristic
460	#474	C₂²×C₃₁	1	2	yes	—
461	#474	C₂²×C₃₁	1	1	yes	characteristic
462	#474	C₂²×C₃₁	1	2	yes	—
463	#468	C₂²×C₃₁	1	4	yes	—
464	#468	C₂²×C₃₁	1	4	yes	—
465	#467	C₂²×C₃₁	1	4	yes	—
466	#466	C₂²×C₃₁	1	4	yes	—
467	#462	C₂²×C₃₁	1	1	yes	characteristic
468	#461	C₂²×C₃₁	1	1	yes	characteristic
469	#460	C₂²×C₃₁	1	1	yes	characteristic
470	#459	C₂²×C₃₁	1	1	yes	characteristic
471	#452	C₂²×C₃₁	1	4	yes	—
472	#452	C₂²×C₃₁	1	2	yes	—
473	#449	C₂²×C₃₁	1	4	yes	—
474	#449	C₂²×C₃₁	1	2	yes	—
475	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
476	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
477	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
478	C₄×D₈	C₂²×C₃₁	1	2	yes	—
479	#436	C₂²×C₃₁	1	2	yes	—
480	#436	C₂²×C₃₁	1	2	yes	—
481	C₈×D₄	C₂²×C₃₁	1	2	yes	—
482	C₈×D₄	C₂²×C₃₁	1	2	yes	—
483	#431	C₂²×C₃₁	1	1	yes	characteristic
484	#431	C₂²×C₃₁	1	1	yes	characteristic
485	#428	C₂²×C₃₁	1	4	yes	—
486	C₂×#107	C₂²×C₃₁	1	4	yes	—
487	#417	C₂²×C₃₁	1	4	yes	—
488	#416	C₂²×C₃₁	1	4	yes	—
489	#408	C₂²×C₃₁	1	4	yes	—
490	C₂×C₃₁	—	4	1	no	—
491	C₂×C₃₁	—	4	4	no	—
492	C₂×C₃₁	—	8	1	no	—
493	C₂×C₃₁	—	8	2	no	—
494	C₂×C₃₁	#3485	1	1	yes	characteristic
495	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
496	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	1	no	—
500	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
501	C₂×#41	C₂³×C₃₁	1	4	yes	—
502	C₂×#41	C₂³×C₃₁	1	2	yes	—
503	C₂²×Q₈	—	2	1	no	—
504	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
505	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
506	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
507	C₂×D₈	C₂³×C₃₁	1	2	yes	—
508	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
509	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
518	#127	—	2	2	no	—
519	#127	D₄×C₃₁	1	1	yes	characteristic
520	#127	C₂³×C₃₁	1	1	yes	characteristic
521	#126	—	2	4	no	—
522	#125	—	2	2	no	—
523	#125	—	2	2	no	—
524	#125	—	2	1	no	—
525	#124	—	2	2	no	—
526	#124	—	2	4	no	—
527	#124	—	2	1	no	—
528	#124	D₄×C₃₁	1	2	yes	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
540	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
541	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	—	2	4	no	—
545	#121	—	2	4	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	—	2	4	no	—
549	#121	—	2	1	no	—
550	#121	—	2	4	no	—
551	#121	D₄×C₃₁	1	2	yes	—
552	#121	D₄×C₃₁	1	2	yes	—
553	#121	C₂³×C₃₁	1	2	yes	—
554	#121	C₂³×C₃₁	1	4	yes	—
555	#121	C₂³×C₃₁	1	4	yes	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
560	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₄×D₄	C₂³×C₃₁	1	2	yes	—
573	C₄×D₄	C₂³×C₃₁	1	2	yes	—
574	C₄×D₄	C₂³×C₃₁	1	2	yes	—
575	#117	—	2	1	no	—
576	#117	—	2	2	no	—
577	#117	—	2	1	no	—
578	#117	C₂³×C₃₁	1	1	yes	characteristic
579	#117	C₂³×C₃₁	1	4	yes	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
587	#107	C₂³×C₃₁	1	2	yes	—
588	#107	C₂³×C₃₁	1	2	yes	—
589	#107	C₂³×C₃₁	1	4	yes	—
590	#107	C₂³×C₃₁	1	4	yes	—
591	#107	C₂³×C₃₁	1	4	yes	—
592	#107	C₂³×C₃₁	1	4	yes	—
593	#106	C₂³×C₃₁	1	2	yes	—
594	#106	C₂³×C₃₁	1	2	yes	—
595	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
596	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
599	#103	C₂³×C₃₁	1	2	yes	—
600	#103	C₂³×C₃₁	1	4	yes	—
601	#103	C₂³×C₃₁	1	2	yes	—
602	#103	C₂³×C₃₁	1	4	yes	—
603	#103	C₂³×C₃₁	1	2	yes	—
604	#103	C₂³×C₃₁	1	2	yes	—
605	#102	C₂³×C₃₁	1	2	yes	—
606	#102	C₂³×C₃₁	1	4	yes	—
607	#102	C₂³×C₃₁	1	2	yes	—
608	#102	C₂³×C₃₁	1	4	yes	—
609	#102	C₂³×C₃₁	1	2	yes	—
610	#102	C₂³×C₃₁	1	2	yes	—
611	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
613	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
614	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
615	C₄×C₈	C₂³×C₃₁	1	2	yes	—
616	C₄×C₈	C₂³×C₃₁	1	2	yes	—
617	C₃₁	#61791	1	1	yes	characteristic, direct product factor, Sylow
618	#41	—	4	2	no	—
619	#41	—	4	2	no	—
620	#41	—	4	1	no	—
621	#41	—	4	1	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	8	2	no	—
625	#41	—	8	4	no	—
626	#41	—	8	4	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	8	2	no	—
632	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
647	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
660	Q₁₆	—	4	2	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	2	no	—
663	D₈	—	4	2	no	—
664	M₁₆	—	4	4	no	—
665	C₂×C₈	—	4	4	no	—
666	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
667	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
668	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
669	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	4	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	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
688	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
689	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
704	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	1	no	—
707	C₄²	—	2	1	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
717	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
718	Q₈	—	2	1	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	1	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	4	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	8	2	no	—
726	Q₈	—	8	1	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	4	no	—
741	D₄	—	8	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	2	no	—
761	C₂×C₄	—	8	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
769	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	4	no	—
797	C₄	—	4	1	no	—
798	C₄	C₃₁×#576	1	2	yes	—
799	C₄	C₃₁×#578	1	2	yes	—
800	C₄	C₃₁×#585	1	1	yes	characteristic
801	C₄	C₃₁×#585	1	1	yes	characteristic
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	2	no	—
806	C₂	C₃₁×#3485	1	1	yes	characteristic
807	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
808	C₂	C₂×C₃₁×#578	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3548	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3353	C₂	semidirect
5. C₃₁×#3338	C₂	semidirect
6. C₃₁×#3334	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3330	C₂	semidirect
9. C₃₁×#3305	C₂	semidirect
10. C₃₁×#3302	C₂	semidirect
11. C₃₁×#3230	C₂	semidirect
12. C₃₁×#3226	C₂	semidirect
13. C₃₁×#3203	C₂	semidirect
14. C₃₁×#3107	C₂	semidirect
15. C₃₁×#3106	C₂	semidirect
16. C₃₁×#3098	C₂	semidirect
17. C₃₁×#2979	C₂	semidirect
309. #61791	C₃₁	direct (N × H)
370. #3548	C₂×C₃₁	semidirect
371. #3511	C₂×C₃₁	semidirect
372. #3357	C₂×C₃₁	semidirect
373. #3353	C₂×C₃₁	semidirect
374. #3338	C₂×C₃₁	semidirect
375. #3334	C₂×C₃₁	semidirect
376. #3333	C₂×C₃₁	semidirect
377. #3330	C₂×C₃₁	semidirect
378. #3305	C₂×C₃₁	semidirect
379. #3302	C₂×C₃₁	semidirect
380. #3230	C₂×C₃₁	semidirect
381. #3226	C₂×C₃₁	semidirect
382. #3203	C₂×C₃₁	semidirect
383. #3107	C₂×C₃₁	semidirect
384. #3106	C₂×C₃₁	semidirect
385. #3098	C₂×C₃₁	semidirect
386. #2979	C₂×C₃₁	semidirect
617. C₃₁	#61791	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×#3548	2
C₃₁×#3511	2
C₃₁×#3357	2
C₃₁×#3353	2
C₃₁×#3338	2
C₃₁×#3334	2
C₃₁×#3333	2
C₃₁×#3330	2
C₃₁×#3305	2
C₃₁×#3302	2
C₃₁×#3230	2
C₃₁×#3226	2
C₃₁×#3203	2
C₃₁×#3107	2
C₃₁×#3106	2
C₃₁×#3098	2
C₃₁×#2979	2
#61791	31

Subgroups — C31×#61791 #21518550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61791 #21518550