Subgroups — C₃₁×#61934 #21518693

Order 7936.

1690 conjugacy classes of subgroups.

The subgroup lattice has 784 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×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3398	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3393	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3363	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3359	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3225	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3121	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	C₃₁×#557	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×#556	C₂²	1	2	yes	—
26	C₃₁×#556	C₂²	1	2	yes	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	—	2	2	no	—
29	D₄×Q₈×C₃₁	—	2	1	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#542	C₂²	1	4	yes	—
33	C₃₁×#541	—	2	2	no	—
34	C₃₁×#536	—	2	2	no	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	—	2	1	no	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#533	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×#519	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#497	C₂²	1	4	yes	—
45	C₃₁×#495	C₂²	1	4	yes	—
46	C₃₁×#494	C₂²	1	2	yes	—
47	C₃₁×#492	C₂²	1	2	yes	—
48	C₃₁×#489	C₂²	1	4	yes	—
49	C₃₁×#487	C₂²	1	4	yes	—
50	C₃₁×#487	C₂²	1	2	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#482	C₂²	1	2	yes	—
54	C₃₁×#477	C₂²	1	1	yes	characteristic
55	C₃₁×#477	C₂²	1	4	yes	—
56	C₃₁×#476	C₂²	1	1	yes	characteristic
57	C₃₁×#475	C₂²	1	1	yes	characteristic
58	C₃₁×#475	C₂²	1	4	yes	—
59	C₃₁×#474	C₂²	1	1	yes	characteristic
60	C₃₁×#464	C₂²	1	4	yes	—
61	C₃₁×#464	C₂²	1	4	yes	—
62	C₃₁×#464	C₂²	1	4	yes	—
63	C₃₁×#463	C₂²	1	4	yes	—
64	C₃₁×#462	C₂²	1	1	yes	characteristic
65	C₃₁×#462	C₂²	1	2	yes	—
66	C₃₁×#462	C₂²	1	4	yes	—
67	C₃₁×#462	C₂²	1	2	yes	—
68	C₃₁×#461	C₂²	1	2	yes	—
69	C₃₁×#461	C₂²	1	4	yes	—
70	C₃₁×#461	C₂²	1	1	yes	characteristic
71	C₃₁×#461	C₂²	1	2	yes	—
72	C₃₁×#460	C₂²	1	1	yes	characteristic
73	C₃₁×#459	C₂²	1	1	yes	characteristic
74	C₃₁×#452	C₂²	1	2	yes	—
75	C₃₁×#451	C₂²	1	4	yes	—
76	C₃₁×#449	C₂²	1	2	yes	—
77	C₃₁×#448	C₂²	1	4	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×#441	C₂²	1	4	yes	—
83	C₃₁×#440	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
85	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
88	C₄×SD₁₆×C₃₁	C₂²	1	2	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	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
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×D₈×C₃₁	C₂³	1	2	yes	—
105	C₃₁×C₄⋊Q₈	—	2	4	no	—
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#126	—	2	4	no	—
122	C₃₁×#126	—	2	4	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	—	2	4	no	—
126	C₃₁×#125	—	2	4	no	—
127	C₃₁×#125	—	2	1	no	—
128	C₃₁×#125	D₄	1	2	yes	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	—	2	4	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	C₂³	1	4	yes	—
133	C₃₁×#124	C₂³	1	4	yes	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×#123	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	1	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	4	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×#121	—	2	1	no	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	—	2	2	no	—
152	C₄×Q₈×C₃₁	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	C₂³	1	4	yes	—
173	C₃₁×#117	—	2	1	no	—
174	C₃₁×#117	—	2	2	no	—
175	C₃₁×#117	—	2	2	no	—
176	C₃₁×#117	—	2	2	no	—
177	C₃₁×#117	—	2	4	no	—
178	C₃₁×#117	—	2	1	no	—
179	C₃₁×#117	C₂³	1	1	yes	characteristic
180	C₃₁×#117	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₄²×C₃₁	—	2	1	no	—
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#106	C₂³	1	2	yes	—
188	C₃₁×#106	C₂³	1	2	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	4	yes	—
198	C₃₁×#103	C₂³	1	2	yes	—
199	C₃₁×#103	C₂³	1	4	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	2	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×#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	—	4	1	no	—
214	#41×C₃₁	—	4	1	no	—
215	#41×C₃₁	—	8	2	no	—
216	C₂×Q₈×C₃₁	—	2	2	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	2	4	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	4	2	no	—
221	C₂×Q₈×C₃₁	—	4	2	no	—
222	C₂×Q₈×C₃₁	—	8	4	no	—
223	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
226	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	—	2	1	no	—
236	C₂²×C₄×C₃₁	—	2	1	no	—
237	C₂²×C₄×C₃₁	—	2	1	no	—
238	C₂²×C₄×C₃₁	—	2	2	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₃₁	—	4	4	no	—
244	Q₁₆×C₃₁	—	4	2	no	—
245	Q₁₆×C₃₁	—	4	4	no	—
246	SD₁₆×C₃₁	—	4	4	no	—
247	SD₁₆×C₃₁	—	4	2	no	—
248	SD₁₆×C₃₁	—	4	4	no	—
249	SD₁₆×C₃₁	—	4	2	no	—
250	D₈×C₃₁	—	4	2	no	—
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	4	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₃₁	—	2	1	no	—
284	C₂²⋊C₄×C₃₁	—	2	2	no	—
285	C₂²⋊C₄×C₃₁	—	2	1	no	—
286	C₂²⋊C₄×C₃₁	—	2	1	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
295	C₄²×C₃₁	—	2	1	no	—
296	C₄²×C₃₁	—	2	1	no	—
297	C₄²×C₃₁	—	2	1	no	—
298	C₄²×C₃₁	—	2	4	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	4	no	—
302	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₃₁	C₂⁴	1	4	yes	—
307	#61934	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂³×C₃₁	—	2	1	no	—
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₃₁	—	2	4	no	—
312	Q₈×C₃₁	—	2	4	no	—
313	Q₈×C₃₁	—	2	1	no	—
314	Q₈×C₃₁	—	2	2	no	—
315	Q₈×C₃₁	—	2	4	no	—
316	Q₈×C₃₁	—	2	4	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	2	1	no	—
319	Q₈×C₃₁	—	4	4	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	8	4	no	—
322	Q₈×C₃₁	—	8	1	no	—
323	D₄×C₃₁	—	2	1	no	—
324	D₄×C₃₁	—	2	2	no	—
325	D₄×C₃₁	—	2	2	no	—
326	D₄×C₃₁	—	2	1	no	—
327	D₄×C₃₁	—	4	2	no	—
328	D₄×C₃₁	—	4	2	no	—
329	D₄×C₃₁	—	8	1	no	—
330	D₄×C₃₁	—	8	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	4	2	no	—
343	C₂×C₄×C₃₁	—	4	4	no	—
344	C₂×C₄×C₃₁	—	4	2	no	—
345	C₂×C₄×C₃₁	—	4	4	no	—
346	C₂×C₄×C₃₁	—	4	2	no	—
347	C₂×C₄×C₃₁	—	8	4	no	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
356	C₈×C₃₁	—	2	2	no	—
357	C₈×C₃₁	—	2	2	no	—
358	C₈×C₃₁	—	2	2	no	—
359	C₈×C₃₁	—	2	2	no	—
360	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
361	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3400	C₂×C₃₁	1	2	yes	complemented
363	#3398	C₂×C₃₁	1	2	yes	complemented
364	#3394	C₂×C₃₁	1	2	yes	complemented
365	#3393	C₂×C₃₁	1	2	yes	complemented
366	#3369	C₂×C₃₁	1	2	yes	complemented
367	#3367	C₂×C₃₁	1	2	yes	complemented
368	#3363	C₂×C₃₁	1	2	yes	complemented
369	#3359	C₂×C₃₁	1	2	yes	complemented
370	#3225	C₂×C₃₁	1	4	yes	complemented
371	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#3121	C₂×C₃₁	1	4	yes	complemented
374	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#3106	C₂×C₃₁	1	1	yes	characteristic
376	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	1	no	—
379	C₂²×C₃₁	—	2	1	no	—
380	C₂²×C₃₁	—	4	1	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	4	1	no	—
384	C₂²×C₃₁	—	4	1	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	1	no	—
389	C₄×C₃₁	—	2	4	no	—
390	C₄×C₃₁	—	2	1	no	—
391	C₄×C₃₁	—	2	4	no	—
392	C₄×C₃₁	—	4	1	no	—
393	C₄×C₃₁	—	4	4	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	1	no	—
396	C₄×C₃₁	—	4	2	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	1	no	—
399	C₄×C₃₁	#577	1	2	yes	—
400	C₄×C₃₁	#578	1	2	yes	—
401	C₄×C₃₁	#585	1	1	yes	characteristic
402	C₄×C₃₁	#585	1	1	yes	characteristic
403	#563	—	2	2	no	—
404	#559	C₂²×C₃₁	1	2	yes	—
405	Q₈²	C₂²×C₃₁	1	2	yes	—
406	#557	C₂²×C₃₁	1	2	yes	—
407	#557	C₂²×C₃₁	1	2	yes	—
408	#556	—	2	1	no	—
409	#556	C₂²×C₃₁	1	2	yes	—
410	#556	C₂²×C₃₁	1	2	yes	—
411	#556	C₂²×C₃₁	1	2	yes	—
412	#552	—	2	2	no	—
413	#552	—	2	2	no	—
414	D₄×Q₈	—	2	1	no	—
415	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
416	#542	—	2	2	no	—
417	#542	C₂²×C₃₁	1	4	yes	—
418	#541	—	2	2	no	—
419	#536	—	2	2	no	—
420	#536	C₂²×C₃₁	1	2	yes	—
421	#533	—	2	1	no	—
422	#533	—	2	1	no	—
423	#533	C₂²×C₃₁	1	1	yes	characteristic
424	#533	C₂²×C₃₁	1	1	yes	characteristic
425	#532	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
427	#519	C₂²×C₃₁	1	2	yes	—
428	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
429	#497	C₂²×C₃₁	1	4	yes	—
430	#495	C₂²×C₃₁	1	4	yes	—
431	#494	C₂²×C₃₁	1	2	yes	—
432	#492	C₂²×C₃₁	1	2	yes	—
433	#489	C₂²×C₃₁	1	4	yes	—
434	#487	C₂²×C₃₁	1	4	yes	—
435	#487	C₂²×C₃₁	1	2	yes	—
436	#487	C₂²×C₃₁	1	2	yes	—
437	#485	C₂²×C₃₁	1	2	yes	—
438	#482	C₂²×C₃₁	1	2	yes	—
439	#477	C₂²×C₃₁	1	1	yes	characteristic
440	#477	C₂²×C₃₁	1	4	yes	—
441	#476	C₂²×C₃₁	1	1	yes	characteristic
442	#475	C₂²×C₃₁	1	1	yes	characteristic
443	#475	C₂²×C₃₁	1	4	yes	—
444	#474	C₂²×C₃₁	1	1	yes	characteristic
445	#464	C₂²×C₃₁	1	4	yes	—
446	#464	C₂²×C₃₁	1	4	yes	—
447	#464	C₂²×C₃₁	1	4	yes	—
448	#463	C₂²×C₃₁	1	4	yes	—
449	#462	C₂²×C₃₁	1	1	yes	characteristic
450	#462	C₂²×C₃₁	1	2	yes	—
451	#462	C₂²×C₃₁	1	4	yes	—
452	#462	C₂²×C₃₁	1	2	yes	—
453	#461	C₂²×C₃₁	1	2	yes	—
454	#461	C₂²×C₃₁	1	4	yes	—
455	#461	C₂²×C₃₁	1	1	yes	characteristic
456	#461	C₂²×C₃₁	1	2	yes	—
457	#460	C₂²×C₃₁	1	1	yes	characteristic
458	#459	C₂²×C₃₁	1	1	yes	characteristic
459	#452	C₂²×C₃₁	1	2	yes	—
460	#451	C₂²×C₃₁	1	4	yes	—
461	#449	C₂²×C₃₁	1	2	yes	—
462	#448	C₂²×C₃₁	1	4	yes	—
463	#446	C₂²×C₃₁	1	2	yes	—
464	#446	C₂²×C₃₁	1	2	yes	—
465	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
466	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
467	#441	C₂²×C₃₁	1	4	yes	—
468	#440	C₂²×C₃₁	1	4	yes	—
469	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
470	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
471	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
472	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
473	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
474	C₄×D₈	C₂²×C₃₁	1	2	yes	—
475	#433	C₂²×C₃₁	1	4	yes	—
476	#431	C₂²×C₃₁	1	1	yes	characteristic
477	#431	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×C₃₁	—	4	1	no	—
479	C₂×C₃₁	—	8	1	no	—
480	C₂×C₃₁	—	8	2	no	—
481	C₂×C₃₁	#3487	1	1	yes	characteristic
482	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
483	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
484	C₂×#41	—	2	1	no	—
485	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
486	C₂²×Q₈	—	2	2	no	—
487	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
488	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
489	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
490	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
493	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
495	C₂×D₈	C₂³×C₃₁	1	2	yes	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
501	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
506	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
509	#127	C₂³×C₃₁	1	1	yes	characteristic
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#125	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	—	2	4	no	—
517	#125	—	2	4	no	—
518	#125	—	2	1	no	—
519	#125	D₄×C₃₁	1	2	yes	—
520	#124	—	2	2	no	—
521	#124	—	2	4	no	—
522	#124	—	2	1	no	—
523	#124	C₂³×C₃₁	1	4	yes	—
524	#124	C₂³×C₃₁	1	4	yes	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
538	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
539	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
540	#121	—	2	1	no	—
541	#121	C₂³×C₃₁	1	2	yes	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
551	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
552	C₄×Q₈	C₂³×C₃₁	1	2	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	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₃₁	1	2	yes	—
563	C₄×D₄	C₂³×C₃₁	1	4	yes	—
564	#117	—	2	1	no	—
565	#117	—	2	2	no	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	2	4	no	—
569	#117	—	2	1	no	—
570	#117	C₂³×C₃₁	1	1	yes	characteristic
571	#117	C₂³×C₃₁	1	2	yes	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
576	#107	C₂³×C₃₁	1	2	yes	—
577	#107	C₂³×C₃₁	1	2	yes	—
578	#106	C₂³×C₃₁	1	2	yes	—
579	#106	C₂³×C₃₁	1	2	yes	—
580	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
582	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
583	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
584	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
585	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
586	#103	C₂³×C₃₁	1	2	yes	—
587	#103	C₂³×C₃₁	1	2	yes	—
588	#103	C₂³×C₃₁	1	4	yes	—
589	#103	C₂³×C₃₁	1	2	yes	—
590	#103	C₂³×C₃₁	1	4	yes	—
591	#103	C₂³×C₃₁	1	2	yes	—
592	#103	C₂³×C₃₁	1	4	yes	—
593	#103	C₂³×C₃₁	1	4	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
599	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
600	#97	C₂³×C₃₁	1	4	yes	—
601	C₄×C₈	C₂³×C₃₁	1	2	yes	—
602	C₄×C₈	C₂³×C₃₁	1	2	yes	—
603	C₄×C₈	C₂³×C₃₁	1	4	yes	—
604	C₃₁	#61934	1	1	yes	characteristic, direct product factor, Sylow
605	#41	—	4	1	no	—
606	#41	—	4	1	no	—
607	#41	—	8	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	8	4	no	—
615	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
616	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
618	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
635	Q₁₆	—	4	4	no	—
636	Q₁₆	—	4	2	no	—
637	Q₁₆	—	4	4	no	—
638	SD₁₆	—	4	4	no	—
639	SD₁₆	—	4	2	no	—
640	SD₁₆	—	4	4	no	—
641	SD₁₆	—	4	2	no	—
642	D₈	—	4	2	no	—
643	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
644	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
645	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
646	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
667	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
670	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
696	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₄²	C₂⁴×C₃₁	1	4	yes	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
702	Q₈	—	2	4	no	—
703	Q₈	—	2	4	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	4	4	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	4	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	1	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	8	1	no	—
721	D₄	—	8	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
740	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	4	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	C₃₁×#577	1	2	yes	—
774	C₄	C₃₁×#578	1	2	yes	—
775	C₄	C₃₁×#585	1	1	yes	characteristic
776	C₄	C₃₁×#585	1	1	yes	characteristic
777	C₂	—	4	1	no	—
778	C₂	—	8	1	no	—
779	C₂	—	8	2	no	—
780	C₂	C₃₁×#3487	1	1	yes	characteristic
781	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
782	C₂	C₂×C₃₁×#578	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×#3509	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3398	C₂	semidirect
5. C₃₁×#3394	C₂	semidirect
6. C₃₁×#3393	C₂	semidirect
7. C₃₁×#3369	C₂	semidirect
8. C₃₁×#3367	C₂	semidirect
9. C₃₁×#3363	C₂	semidirect
10. C₃₁×#3359	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3209	C₂	semidirect
13. C₃₁×#3206	C₂	semidirect
14. C₃₁×#3121	C₂	semidirect
15. C₃₁×#3107	C₂	semidirect
17. C₃₁×#2986	C₂	semidirect
307. #61934	C₃₁	direct (N × H)
360. #3550	C₂×C₃₁	semidirect
361. #3509	C₂×C₃₁	semidirect
362. #3400	C₂×C₃₁	semidirect
363. #3398	C₂×C₃₁	semidirect
364. #3394	C₂×C₃₁	semidirect
365. #3393	C₂×C₃₁	semidirect
366. #3369	C₂×C₃₁	semidirect
367. #3367	C₂×C₃₁	semidirect
368. #3363	C₂×C₃₁	semidirect
369. #3359	C₂×C₃₁	semidirect
370. #3225	C₂×C₃₁	semidirect
371. #3209	C₂×C₃₁	semidirect
372. #3206	C₂×C₃₁	semidirect
373. #3121	C₂×C₃₁	semidirect
374. #3107	C₂×C₃₁	semidirect
376. #2986	C₂×C₃₁	semidirect
604. C₃₁	#61934	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×#3509	2
C₃₁×#3400	2
C₃₁×#3398	2
C₃₁×#3394	2
C₃₁×#3393	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3363	2
C₃₁×#3359	2
C₃₁×#3225	2
C₃₁×#3209	2
C₃₁×#3206	2
C₃₁×#3121	2
C₃₁×#3107	2
C₃₁×#3106	2
C₃₁×#2986	2
#61934	31

Subgroups — C31×#61934 #21518693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61934 #21518693