Subgroups — C₃₁×#61871 #21518630

Order 7936.

1700 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
5	Q₈×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
6	Q₈×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3125	C₂	1	4	yes	maximal, complemented
15	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#563	—	2	2	no	—
19	C₃₁×#559	C₂²	1	2	yes	—
20	Q₈²×C₃₁	C₂²	1	2	yes	—
21	Q₈²×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#557	C₂²	1	2	yes	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#554	—	2	2	no	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	D₄×Q₈×C₃₁	—	2	1	no	—
28	D₄×Q₈×C₃₁	—	2	2	no	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#544	—	2	2	no	—
32	C₃₁×#544	C₂²	1	2	yes	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#542	C₂²	1	4	yes	—
35	C₃₁×#536	—	2	2	no	—
36	C₃₁×#533	—	2	1	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	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
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×#501	C₂²	1	4	yes	—
45	C₃₁×#498	C₂²	1	4	yes	—
46	C₃₁×#498	C₂²	1	2	yes	—
47	C₃₁×#498	C₂²	1	2	yes	—
48	C₃₁×#489	C₂²	1	4	yes	—
49	C₃₁×#488	C₂²	1	4	yes	—
50	C₃₁×#487	C₂²	1	2	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#483	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	2	yes	—
55	C₃₁×#481	C₂²	1	4	yes	—
56	C₃₁×#479	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	1	yes	characteristic
59	C₃₁×#476	C₂²	1	2	yes	—
60	C₃₁×#476	C₂²	1	1	yes	characteristic
61	C₃₁×#476	C₂²	1	2	yes	—
62	C₃₁×#476	C₂²	1	4	yes	—
63	C₃₁×#476	C₂²	1	4	yes	—
64	C₃₁×#475	C₂²	1	1	yes	characteristic
65	C₃₁×#475	C₂²	1	2	yes	—
66	C₃₁×#475	C₂²	1	4	yes	—
67	C₃₁×#475	C₂²	1	2	yes	—
68	C₃₁×#475	C₂²	1	4	yes	—
69	C₃₁×#474	C₂²	1	1	yes	characteristic
70	C₃₁×#464	C₂²	1	4	yes	—
71	C₃₁×#463	C₂²	1	4	yes	—
72	C₃₁×#462	C₂²	1	1	yes	characteristic
73	C₃₁×#461	C₂²	1	1	yes	characteristic
74	C₃₁×#460	C₂²	1	1	yes	characteristic
75	C₃₁×#459	C₂²	1	1	yes	characteristic
76	C₃₁×#452	C₂²	1	2	yes	—
77	C₃₁×#449	C₂²	1	2	yes	—
78	C₃₁×#446	C₂²	1	2	yes	—
79	C₃₁×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
82	C₃₁×#442	C₂²	1	4	yes	—
83	C₃₁×#441	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
89	C₄×D₈×C₃₁	C₂²	1	2	yes	—
90	C₃₁×#433	C₂²	1	4	yes	—
91	C₃₁×#431	C₂²	1	1	yes	characteristic
92	C₃₁×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	1	no	—
94	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₃₁	—	2	2	no	—
96	C₂²×Q₈×C₃₁	—	2	2	no	—
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂×D₈×C₃₁	C₂³	1	2	yes	—
102	C₃₁×C₄⋊Q₈	—	2	2	no	—
103	C₃₁×C₄⋊Q₈	—	2	2	no	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	—	2	4	no	—
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	—	2	4	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×#127	C₂³	1	1	yes	characteristic
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#126	—	2	4	no	—
122	C₃₁×#125	—	2	2	no	—
123	C₃₁×#125	—	2	4	no	—
124	C₃₁×#125	—	2	1	no	—
125	C₃₁×#125	D₄	1	2	yes	—
126	C₃₁×#125	C₂³	1	4	yes	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	—	2	4	no	—
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	C₂³	1	4	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	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	1	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	C₂³	1	4	yes	—
168	C₄×D₄×C₃₁	C₂³	1	4	yes	—
169	C₃₁×#117	—	2	1	no	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	2	no	—
172	C₃₁×#117	—	2	1	no	—
173	C₃₁×#117	C₂³	1	1	yes	characteristic
174	C₃₁×#117	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₃₁	—	2	1	no	—
180	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₃₁×#107	C₂³	1	2	yes	—
182	C₃₁×#107	C₂³	1	2	yes	—
183	C₃₁×#106	C₂³	1	2	yes	—
184	C₃₁×#106	C₂³	1	2	yes	—
185	C₃₁×#106	C₂³	1	4	yes	—
186	C₃₁×#106	C₂³	1	4	yes	—
187	C₃₁×#106	C₂³	1	4	yes	—
188	C₃₁×#106	C₂³	1	4	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
194	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	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	4	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	2	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₃₁×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₃₁	C₂³	1	2	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	#41×C₃₁	—	2	2	no	—
214	#41×C₃₁	—	2	2	no	—
215	#41×C₃₁	—	8	2	no	—
216	C₂×Q₈×C₃₁	—	2	1	no	—
217	C₂×Q₈×C₃₁	—	2	2	no	—
218	C₂×Q₈×C₃₁	—	2	4	no	—
219	C₂×Q₈×C₃₁	—	2	4	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	8	2	no	—
223	C₂×Q₈×C₃₁	—	8	4	no	—
224	C₂×Q₈×C₃₁	—	8	4	no	—
225	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	—	2	1	no	—
233	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
234	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	—	2	1	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	2	1	no	—
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	4	no	—
242	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	Q₁₆×C₃₁	—	2	4	no	—
246	SD₁₆×C₃₁	—	2	4	no	—
247	SD₁₆×C₃₁	—	2	4	no	—
248	D₈×C₃₁	—	2	4	no	—
249	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
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	—	2	1	no	—
259	C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	4	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₃₁	—	2	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	1	no	—
283	C₂²⋊C₄×C₃₁	—	2	1	no	—
284	C₂²⋊C₄×C₃₁	—	2	1	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
292	C₄²×C₃₁	—	2	1	no	—
293	C₄²×C₃₁	—	2	1	no	—
294	C₄²×C₃₁	—	2	1	no	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	4	no	—
297	C₄²×C₃₁	—	2	4	no	—
298	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄²×C₃₁	C₂⁴	1	4	yes	—
303	#61871	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₃₁	—	2	1	no	—
305	C₂³×C₃₁	—	2	2	no	—
306	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
307	Q₈×C₃₁	—	2	4	no	—
308	Q₈×C₃₁	—	2	4	no	—
309	Q₈×C₃₁	—	2	1	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	2	2	no	—
312	Q₈×C₃₁	—	4	2	no	—
313	Q₈×C₃₁	—	4	4	no	—
314	Q₈×C₃₁	—	8	2	no	—
315	Q₈×C₃₁	—	8	4	no	—
316	Q₈×C₃₁	—	8	4	no	—
317	Q₈×C₃₁	—	8	1	no	—
318	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
319	D₄×C₃₁	—	2	4	no	—
320	D₄×C₃₁	—	2	1	no	—
321	D₄×C₃₁	—	2	2	no	—
322	D₄×C₃₁	—	2	2	no	—
323	D₄×C₃₁	—	4	2	no	—
324	D₄×C₃₁	—	8	1	no	—
325	D₄×C₃₁	—	8	2	no	—
326	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
327	C₂×C₄×C₃₁	—	2	4	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	4	no	—
339	C₂×C₄×C₃₁	—	4	2	no	—
340	C₂×C₄×C₃₁	—	4	2	no	—
341	C₂×C₄×C₃₁	—	4	4	no	—
342	C₂×C₄×C₃₁	—	8	4	no	—
343	C₂×C₄×C₃₁	—	8	4	no	—
344	C₂×C₄×C₃₁	—	8	2	no	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
353	C₈×C₃₁	—	2	2	no	—
354	C₈×C₃₁	—	2	2	no	—
355	C₈×C₃₁	—	2	2	no	—
356	C₈×C₃₁	—	2	2	no	—
357	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#3387	C₂×C₃₁	1	2	yes	complemented
360	#3384	C₂×C₃₁	1	2	yes	complemented
361	Q₈×SD₁₆	C₂×C₃₁	1	2	yes	complemented
362	Q₈×SD₁₆	C₂×C₃₁	1	2	yes	complemented
363	#3373	C₂×C₃₁	1	2	yes	complemented
364	#3369	C₂×C₃₁	1	2	yes	complemented
365	#3365	C₂×C₃₁	1	2	yes	complemented
366	#3360	C₂×C₃₁	1	2	yes	complemented
367	#3244	C₂×C₃₁	1	4	yes	complemented
368	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#3125	C₂×C₃₁	1	4	yes	complemented
371	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#3106	C₂×C₃₁	1	1	yes	characteristic
373	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
374	C₂²×C₃₁	—	2	1	no	—
375	C₂²×C₃₁	—	2	2	no	—
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	4	1	no	—
379	C₂²×C₃₁	—	4	1	no	—
380	C₂²×C₃₁	—	4	2	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	2	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	4	no	—
389	C₄×C₃₁	—	2	4	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	1	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	1	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	4	no	—
396	C₄×C₃₁	#577	1	2	yes	—
397	C₄×C₃₁	#577	1	2	yes	—
398	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	#563	—	2	2	no	—
401	#559	C₂²×C₃₁	1	2	yes	—
402	Q₈²	C₂²×C₃₁	1	2	yes	—
403	Q₈²	C₂²×C₃₁	1	2	yes	—
404	#557	C₂²×C₃₁	1	2	yes	—
405	#556	—	2	1	no	—
406	#556	C₂²×C₃₁	1	2	yes	—
407	#554	—	2	2	no	—
408	#554	C₂²×C₃₁	1	2	yes	—
409	D₄×Q₈	—	2	1	no	—
410	D₄×Q₈	—	2	2	no	—
411	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
412	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
413	#544	—	2	2	no	—
414	#544	C₂²×C₃₁	1	2	yes	—
415	#542	—	2	2	no	—
416	#542	C₂²×C₃₁	1	4	yes	—
417	#536	—	2	2	no	—
418	#533	—	2	1	no	—
419	#533	C₂²×C₃₁	1	1	yes	characteristic
420	#533	C₂²×C₃₁	1	1	yes	characteristic
421	#532	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×C₄⋊Q₈	—	2	1	no	—
423	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
424	#520	C₂²×C₃₁	1	2	yes	—
425	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
426	#501	C₂²×C₃₁	1	4	yes	—
427	#498	C₂²×C₃₁	1	4	yes	—
428	#498	C₂²×C₃₁	1	2	yes	—
429	#498	C₂²×C₃₁	1	2	yes	—
430	#489	C₂²×C₃₁	1	4	yes	—
431	#488	C₂²×C₃₁	1	4	yes	—
432	#487	C₂²×C₃₁	1	2	yes	—
433	#486	C₂²×C₃₁	1	2	yes	—
434	#485	C₂²×C₃₁	1	2	yes	—
435	#483	C₂²×C₃₁	1	4	yes	—
436	#482	C₂²×C₃₁	1	2	yes	—
437	#481	C₂²×C₃₁	1	4	yes	—
438	#479	C₂²×C₃₁	1	4	yes	—
439	#478	C₂²×C₃₁	1	4	yes	—
440	#477	C₂²×C₃₁	1	1	yes	characteristic
441	#476	C₂²×C₃₁	1	2	yes	—
442	#476	C₂²×C₃₁	1	1	yes	characteristic
443	#476	C₂²×C₃₁	1	2	yes	—
444	#476	C₂²×C₃₁	1	4	yes	—
445	#476	C₂²×C₃₁	1	4	yes	—
446	#475	C₂²×C₃₁	1	1	yes	characteristic
447	#475	C₂²×C₃₁	1	2	yes	—
448	#475	C₂²×C₃₁	1	4	yes	—
449	#475	C₂²×C₃₁	1	2	yes	—
450	#475	C₂²×C₃₁	1	4	yes	—
451	#474	C₂²×C₃₁	1	1	yes	characteristic
452	#464	C₂²×C₃₁	1	4	yes	—
453	#463	C₂²×C₃₁	1	4	yes	—
454	#462	C₂²×C₃₁	1	1	yes	characteristic
455	#461	C₂²×C₃₁	1	1	yes	characteristic
456	#460	C₂²×C₃₁	1	1	yes	characteristic
457	#459	C₂²×C₃₁	1	1	yes	characteristic
458	#452	C₂²×C₃₁	1	2	yes	—
459	#449	C₂²×C₃₁	1	2	yes	—
460	#446	C₂²×C₃₁	1	2	yes	—
461	#446	C₂²×C₃₁	1	2	yes	—
462	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
463	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
464	#442	C₂²×C₃₁	1	4	yes	—
465	#441	C₂²×C₃₁	1	4	yes	—
466	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
467	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
468	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
469	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
470	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
471	C₄×D₈	C₂²×C₃₁	1	2	yes	—
472	#433	C₂²×C₃₁	1	4	yes	—
473	#431	C₂²×C₃₁	1	1	yes	characteristic
474	#431	C₂²×C₃₁	1	1	yes	characteristic
475	C₂×C₃₁	—	4	1	no	—
476	C₂×C₃₁	—	4	2	no	—
477	C₂×C₃₁	—	8	2	no	—
478	C₂×C₃₁	#3486	1	1	yes	characteristic
479	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
480	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
481	C₂×#41	—	2	1	no	—
482	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×Q₈	—	2	2	no	—
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
488	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
489	C₂×D₈	C₂³×C₃₁	1	2	yes	—
490	C₄⋊Q₈	—	2	2	no	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	2	4	no	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	4	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
499	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
506	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
507	#127	C₂³×C₃₁	1	1	yes	characteristic
508	#126	—	2	4	no	—
509	#126	—	2	4	no	—
510	#125	—	2	2	no	—
511	#125	—	2	4	no	—
512	#125	—	2	1	no	—
513	#125	D₄×C₃₁	1	2	yes	—
514	#125	C₂³×C₃₁	1	4	yes	—
515	#124	—	2	2	no	—
516	#124	—	2	4	no	—
517	#124	—	2	1	no	—
518	#124	C₂³×C₃₁	1	4	yes	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
532	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
534	#121	—	2	1	no	—
535	#121	C₂³×C₃₁	1	2	yes	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
542	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
543	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
545	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
546	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₃₁	1	4	yes	—
555	C₄×D₄	C₂³×C₃₁	1	2	yes	—
556	C₄×D₄	C₂³×C₃₁	1	4	yes	—
557	#117	—	2	1	no	—
558	#117	—	2	2	no	—
559	#117	—	2	2	no	—
560	#117	—	2	1	no	—
561	#117	C₂³×C₃₁	1	1	yes	characteristic
562	#117	C₂³×C₃₁	1	2	yes	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
569	#107	C₂³×C₃₁	1	2	yes	—
570	#107	C₂³×C₃₁	1	2	yes	—
571	#106	C₂³×C₃₁	1	2	yes	—
572	#106	C₂³×C₃₁	1	2	yes	—
573	#106	C₂³×C₃₁	1	4	yes	—
574	#106	C₂³×C₃₁	1	4	yes	—
575	#106	C₂³×C₃₁	1	4	yes	—
576	#106	C₂³×C₃₁	1	4	yes	—
577	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
578	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
582	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
583	#103	C₂³×C₃₁	1	2	yes	—
584	#103	C₂³×C₃₁	1	2	yes	—
585	#103	C₂³×C₃₁	1	2	yes	—
586	#103	C₂³×C₃₁	1	4	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	4	yes	—
589	#102	C₂³×C₃₁	1	2	yes	—
590	#102	C₂³×C₃₁	1	2	yes	—
591	#102	C₂³×C₃₁	1	2	yes	—
592	#102	C₂³×C₃₁	1	2	yes	—
593	#102	C₂³×C₃₁	1	4	yes	—
594	#102	C₂³×C₃₁	1	4	yes	—
595	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
596	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
597	#97	C₂³×C₃₁	1	4	yes	—
598	C₄×C₈	C₂³×C₃₁	1	2	yes	—
599	C₄×C₈	C₂³×C₃₁	1	2	yes	—
600	C₄×C₈	C₂³×C₃₁	1	4	yes	—
601	C₃₁	#61871	1	1	yes	characteristic, direct product factor, Sylow
602	#41	—	2	2	no	—
603	#41	—	2	2	no	—
604	#41	—	8	2	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	8	2	no	—
612	C₂×Q₈	—	8	4	no	—
613	C₂×Q₈	—	8	4	no	—
614	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
615	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
623	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
634	Q₁₆	—	2	4	no	—
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	4	no	—
637	D₈	—	2	4	no	—
638	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
639	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
640	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
641	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
664	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
665	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
668	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₄²	C₂⁴×C₃₁	1	4	yes	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	4	no	—
702	Q₈	—	8	2	no	—
703	Q₈	—	8	4	no	—
704	Q₈	—	8	4	no	—
705	Q₈	—	8	1	no	—
706	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
707	D₄	—	2	4	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	8	1	no	—
713	D₄	—	8	2	no	—
714	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	4	no	—
767	C₄	C₃₁×#577	1	2	yes	—
768	C₄	C₃₁×#577	1	2	yes	—
769	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
770	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	2	no	—
774	C₂	C₃₁×#3486	1	1	yes	characteristic
775	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
776	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3106	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
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. Q₈×SD₁₆×C₃₁	C₂	semidirect
6. Q₈×SD₁₆×C₃₁	C₂	semidirect
7. C₃₁×#3373	C₂	semidirect
8. C₃₁×#3369	C₂	semidirect
9. C₃₁×#3365	C₂	semidirect
10. C₃₁×#3360	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3229	C₂	semidirect
13. C₃₁×#3227	C₂	semidirect
14. C₃₁×#3125	C₂	semidirect
15. C₃₁×#3107	C₂	semidirect
17. C₃₁×#2986	C₂	semidirect
303. #61871	C₃₁	direct (N × H)
357. #3550	C₂×C₃₁	semidirect
358. #3503	C₂×C₃₁	semidirect
359. #3387	C₂×C₃₁	semidirect
360. #3384	C₂×C₃₁	semidirect
361. Q₈×SD₁₆	C₂×C₃₁	semidirect
362. Q₈×SD₁₆	C₂×C₃₁	semidirect
363. #3373	C₂×C₃₁	semidirect
364. #3369	C₂×C₃₁	semidirect
365. #3365	C₂×C₃₁	semidirect
366. #3360	C₂×C₃₁	semidirect
367. #3244	C₂×C₃₁	semidirect
368. #3229	C₂×C₃₁	semidirect
369. #3227	C₂×C₃₁	semidirect
370. #3125	C₂×C₃₁	semidirect
371. #3107	C₂×C₃₁	semidirect
373. #2986	C₂×C₃₁	semidirect
601. C₃₁	#61871	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×#3550	2
C₃₁×#3503	2
C₃₁×#3387	2
C₃₁×#3384	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3373	2
C₃₁×#3369	2
C₃₁×#3365	2
C₃₁×#3360	2
C₃₁×#3244	2
C₃₁×#3229	2
C₃₁×#3227	2
C₃₁×#3125	2
C₃₁×#3107	2
C₃₁×#3106	2
C₃₁×#2986	2
#61871	31

Subgroups — C31×#61871 #21518630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61871 #21518630