Subgroups — C₃₁×#62205 #21518964

Order 7936.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	—	2	1	no	—
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	2	yes	—
33	C₃₁×#553	C₂²	1	2	yes	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	—	2	1	no	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#547	—	2	2	no	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#532	—	2	1	no	—
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#498	C₂²	1	2	yes	—
59	C₃₁×#498	C₂²	1	1	yes	characteristic
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#486	C₂²	1	1	yes	characteristic
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#483	C₂²	1	1	yes	characteristic
67	C₃₁×#483	C₂²	1	2	yes	—
68	C₃₁×#483	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#481	C₂²	1	2	yes	—
71	C₃₁×#481	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#481	C₂²	1	2	yes	—
74	C₃₁×#480	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	1	yes	characteristic
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	1	yes	characteristic
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#477	C₂²	1	1	yes	characteristic
81	C₃₁×#476	C₂²	1	2	yes	—
82	C₃₁×#476	C₂²	1	1	yes	characteristic
83	C₃₁×#476	C₂²	1	2	yes	—
84	C₃₁×#476	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	2	yes	—
86	C₃₁×#475	C₂²	1	1	yes	characteristic
87	C₃₁×#475	C₂²	1	1	yes	characteristic
88	C₃₁×#475	C₂²	1	2	yes	—
89	C₃₁×#475	C₂²	1	2	yes	—
90	C₃₁×#475	C₂²	1	2	yes	—
91	C₃₁×#475	C₂²	1	1	yes	characteristic
92	C₃₁×#475	C₂²	1	1	yes	characteristic
93	C₃₁×#475	C₂²	1	2	yes	—
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#469	C₂²	1	2	yes	—
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#464	C₂²	1	1	yes	characteristic
102	C₃₁×#464	C₂²	1	2	yes	—
103	C₃₁×#463	C₂²	1	2	yes	—
104	C₃₁×#463	C₂²	1	2	yes	—
105	C₃₁×#460	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#451	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#448	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₂×C₃₁×#106	C₂²	1	2	yes	—
129	C₂×C₃₁×#106	C₂²	1	2	yes	—
130	C₃₁×#424	C₂²	1	2	yes	—
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₂×C₃₁×#103	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	—	2	1	no	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	1	no	—
170	C₃₁×#126	D₄	1	2	yes	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	D₄	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	1	yes	characteristic
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	D₄	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	1	yes	characteristic
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	D₄	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	D₄	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	1	yes	characteristic
266	C₃₁×#106	C₂³	1	2	yes	—
267	C₃₁×#106	C₂³	1	1	yes	characteristic
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	2	4	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	#41×C₃₁	—	8	4	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	4	1	no	—
326	C₂×Q₈×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	—	8	2	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
357	Q₁₆×C₃₁	—	2	2	no	—
358	Q₁₆×C₃₁	—	4	1	no	—
359	SD₁₆×C₃₁	—	2	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	2	no	—
362	D₈×C₃₁	—	4	2	no	—
363	M₁₆×C₃₁	—	4	2	no	—
364	C₂×C₈×C₃₁	—	4	2	no	—
365	C₂×C₈×C₃₁	—	4	2	no	—
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	2	yes	—
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#62205	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	2	2	no	—
446	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₃₁	—	2	2	no	—
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	4	2	no	—
455	Q₈×C₃₁	—	4	2	no	—
456	Q₈×C₃₁	—	4	2	no	—
457	Q₈×C₃₁	—	8	2	no	—
458	Q₈×C₃₁	—	8	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
462	D₄×C₃₁	—	2	4	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	4	4	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	4	4	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	8	1	no	—
473	D₄×C₃₁	—	8	2	no	—
474	D₄×C₃₁	—	8	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	4	4	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	2	no	—
501	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
510	C₈×C₃₁	—	2	1	no	—
511	C₈×C₃₁	—	2	1	no	—
512	C₈×C₃₁	—	2	1	no	—
513	C₈×C₃₁	—	2	2	no	—
514	C₈×C₃₁	—	2	2	no	—
515	C₈×C₃₁	—	2	1	no	—
516	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
519	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3345	C₂×C₃₁	1	2	yes	complemented
524	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3335	C₂×C₃₁	1	2	yes	complemented
526	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3316	C₂×C₃₁	1	2	yes	complemented
528	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3301	C₂×C₃₁	1	2	yes	complemented
530	#3263	C₂×C₃₁	1	2	yes	complemented
531	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3244	C₂×C₃₁	1	2	yes	complemented
533	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3125	C₂×C₃₁	1	2	yes	complemented
535	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3084	C₂×C₃₁	1	2	yes	complemented
537	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	4	2	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	2	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	#577	1	2	yes	—
551	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₃₁	—	2	2	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	1	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	#577	1	2	yes	—
570	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	C₄×C₃₁	#585	1	1	yes	characteristic
572	#563	—	2	2	no	—
573	#559	—	2	1	no	—
574	#559	C₂²×C₃₁	1	1	yes	characteristic
575	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
576	#557	C₂²×C₃₁	1	1	yes	characteristic
577	#556	C₂²×C₃₁	1	1	yes	characteristic
578	#554	—	2	1	no	—
579	#554	C₂²×C₃₁	1	1	yes	characteristic
580	#554	C₂²×C₃₁	1	2	yes	—
581	#553	C₂²×C₃₁	1	2	yes	—
582	#550	C₂²×C₃₁	1	1	yes	characteristic
583	D₄×Q₈	—	2	1	no	—
584	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
585	#548	—	2	1	no	—
586	#548	C₂²×C₃₁	1	2	yes	—
587	#547	—	2	2	no	—
588	#547	C₂²×C₃₁	1	1	yes	characteristic
589	#547	C₂²×C₃₁	1	2	yes	—
590	#544	C₂²×C₃₁	1	2	yes	—
591	#542	—	2	2	no	—
592	#542	C₂²×C₃₁	1	2	yes	—
593	#542	C₂²×C₃₁	1	2	yes	—
594	#541	—	2	1	no	—
595	#539	—	2	2	no	—
596	#536	—	2	1	no	—
597	#532	—	2	1	no	—
598	#532	C₂²×C₃₁	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
600	#529	—	2	1	no	—
601	#529	C₂²×C₃₁	1	1	yes	characteristic
602	#529	C₂²×C₃₁	1	1	yes	characteristic
603	#520	C₂²×C₃₁	1	2	yes	—
604	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
605	#501	C₂²×C₃₁	1	2	yes	—
606	#498	C₂²×C₃₁	1	2	yes	—
607	#498	C₂²×C₃₁	1	1	yes	characteristic
608	#498	C₂²×C₃₁	1	1	yes	characteristic
609	#489	C₂²×C₃₁	1	2	yes	—
610	#488	C₂²×C₃₁	1	2	yes	—
611	#486	C₂²×C₃₁	1	1	yes	characteristic
612	#486	C₂²×C₃₁	1	1	yes	characteristic
613	#485	C₂²×C₃₁	1	2	yes	—
614	#483	C₂²×C₃₁	1	1	yes	characteristic
615	#483	C₂²×C₃₁	1	2	yes	—
616	#483	C₂²×C₃₁	1	2	yes	—
617	#482	C₂²×C₃₁	1	2	yes	—
618	#481	C₂²×C₃₁	1	2	yes	—
619	#481	C₂²×C₃₁	1	2	yes	—
620	#481	C₂²×C₃₁	1	2	yes	—
621	#481	C₂²×C₃₁	1	2	yes	—
622	#480	C₂²×C₃₁	1	1	yes	characteristic
623	#479	C₂²×C₃₁	1	1	yes	characteristic
624	#479	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	1	yes	characteristic
626	#478	C₂²×C₃₁	1	2	yes	—
627	#478	C₂²×C₃₁	1	2	yes	—
628	#477	C₂²×C₃₁	1	1	yes	characteristic
629	#476	C₂²×C₃₁	1	2	yes	—
630	#476	C₂²×C₃₁	1	1	yes	characteristic
631	#476	C₂²×C₃₁	1	2	yes	—
632	#476	C₂²×C₃₁	1	2	yes	—
633	#476	C₂²×C₃₁	1	2	yes	—
634	#475	C₂²×C₃₁	1	1	yes	characteristic
635	#475	C₂²×C₃₁	1	1	yes	characteristic
636	#475	C₂²×C₃₁	1	2	yes	—
637	#475	C₂²×C₃₁	1	1	yes	characteristic
638	#475	C₂²×C₃₁	1	1	yes	characteristic
639	#475	C₂²×C₃₁	1	2	yes	—
640	#475	C₂²×C₃₁	1	2	yes	—
641	#475	C₂²×C₃₁	1	2	yes	—
642	#470	C₂²×C₃₁	1	2	yes	—
643	#469	C₂²×C₃₁	1	2	yes	—
644	#466	C₂²×C₃₁	1	2	yes	—
645	#465	C₂²×C₃₁	1	2	yes	—
646	#465	C₂²×C₃₁	1	2	yes	—
647	#465	C₂²×C₃₁	1	2	yes	—
648	#464	C₂²×C₃₁	1	1	yes	characteristic
649	#464	C₂²×C₃₁	1	1	yes	characteristic
650	#464	C₂²×C₃₁	1	2	yes	—
651	#463	C₂²×C₃₁	1	2	yes	—
652	#463	C₂²×C₃₁	1	2	yes	—
653	#460	C₂²×C₃₁	1	1	yes	characteristic
654	#459	C₂²×C₃₁	1	1	yes	characteristic
655	#452	C₂²×C₃₁	1	2	yes	—
656	#451	C₂²×C₃₁	1	1	yes	characteristic
657	#449	C₂²×C₃₁	1	2	yes	—
658	#448	C₂²×C₃₁	1	1	yes	characteristic
659	#446	C₂²×C₃₁	1	1	yes	characteristic
660	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
661	#442	C₂²×C₃₁	1	2	yes	—
662	#441	C₂²×C₃₁	1	2	yes	—
663	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
666	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
669	#436	C₂²×C₃₁	1	1	yes	characteristic
670	#435	C₂²×C₃₁	1	2	yes	—
671	C₈×D₄	C₂²×C₃₁	1	2	yes	—
672	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
673	#433	C₂²×C₃₁	1	2	yes	—
674	#431	C₂²×C₃₁	1	1	yes	characteristic
675	#428	C₂²×C₃₁	1	2	yes	—
676	C₂×#106	C₂²×C₃₁	1	2	yes	—
677	C₂×#106	C₂²×C₃₁	1	2	yes	—
678	#424	C₂²×C₃₁	1	2	yes	—
679	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
680	#417	C₂²×C₃₁	1	2	yes	—
681	#416	C₂²×C₃₁	1	2	yes	—
682	C₂×#103	C₂²×C₃₁	1	2	yes	—
683	C₂×C₃₁	—	2	2	no	—
684	C₂×C₃₁	—	4	2	no	—
685	C₂×C₃₁	—	8	2	no	—
686	C₂×C₃₁	—	8	1	no	—
687	C₂×C₃₁	#3489	1	1	yes	characteristic
688	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
689	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
690	C₂×#41	—	2	2	no	—
691	C₂×#41	—	2	1	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	C₂³×C₃₁	1	2	yes	—
694	C₂²×Q₈	—	2	1	no	—
695	C₂²×Q₈	—	2	1	no	—
696	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×D₈	C₂³×C₃₁	1	2	yes	—
703	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
705	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
706	C₄⋊Q₈	—	2	1	no	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	—	2	1	no	—
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
718	#127	—	2	1	no	—
719	#127	C₂³×C₃₁	1	1	yes	characteristic
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	1	no	—
725	#126	D₄×C₃₁	1	2	yes	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	D₄×C₃₁	1	1	yes	characteristic
731	#125	C₂³×C₃₁	1	1	yes	characteristic
732	#125	C₂³×C₃₁	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	1	no	—
739	#124	D₄×C₃₁	1	1	yes	characteristic
740	#124	C₂³×C₃₁	1	1	yes	characteristic
741	#124	C₂³×C₃₁	1	2	yes	—
742	#123	—	2	1	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	D₄×C₃₁	1	2	yes	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	1	no	—
770	#121	—	2	2	no	—
771	#121	D₄×C₃₁	1	1	yes	characteristic
772	#121	C₂³×C₃₁	1	1	yes	characteristic
773	#121	C₂³×C₃₁	1	2	yes	—
774	#121	C₂³×C₃₁	1	2	yes	—
775	#121	C₂³×C₃₁	1	2	yes	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	C₂³×C₃₁	1	2	yes	—
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	2	no	—
812	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
814	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
816	C₂×C₄²	—	2	1	no	—
817	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
818	#107	C₂³×C₃₁	1	1	yes	characteristic
819	#107	C₂³×C₃₁	1	2	yes	—
820	#107	C₂³×C₃₁	1	1	yes	characteristic
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	1	yes	characteristic
823	#106	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	2	yes	—
826	#106	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	2	yes	—
828	#106	C₂³×C₃₁	1	2	yes	—
829	#106	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	1	yes	characteristic
831	#106	C₂³×C₃₁	1	2	yes	—
832	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
833	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	#103	C₂³×C₃₁	1	2	yes	—
840	#103	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	1	yes	characteristic
844	#103	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	2	yes	—
850	#102	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	C₂³×C₃₁	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
863	#97	C₂³×C₃₁	1	2	yes	—
864	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₃₁	1	2	yes	—
867	C₃₁	#62205	1	1	yes	characteristic, direct product factor, Sylow
868	#41	—	2	4	no	—
869	#41	—	4	2	no	—
870	#41	—	8	2	no	—
871	#41	—	8	4	no	—
872	#41	—	8	2	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	4	1	no	—
882	C₂×Q₈	—	8	2	no	—
883	C₂×Q₈	—	8	2	no	—
884	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
897	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
898	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
913	Q₁₆	—	2	2	no	—
914	Q₁₆	—	4	1	no	—
915	SD₁₆	—	2	2	no	—
916	SD₁₆	—	4	1	no	—
917	SD₁₆	—	4	2	no	—
918	D₈	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	2	no	—
922	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
927	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄²	C₂⁴×C₃₁	1	2	yes	—
998	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1002	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	8	2	no	—
1013	Q₈	—	8	2	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1017	D₄	—	2	4	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	2	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	8	1	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	C₃₁×#577	1	2	yes	—
1083	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	C₃₁×#577	1	2	yes	—
1102	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1103	C₄	C₃₁×#585	1	1	yes	characteristic
1104	C₂	—	2	2	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	1	no	—
1108	C₂	C₃₁×#3489	1	1	yes	characteristic
1109	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1110	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3552	C₂	semidirect
2. C₃₁×#3522	C₂	semidirect
3. C₃₁×#3387	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3365	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3345	C₂	semidirect
9. C₃₁×#3335	C₂	semidirect
10. C₃₁×#3335	C₂	semidirect
11. C₃₁×#3332	C₂	semidirect
12. C₃₁×#3316	C₂	semidirect
13. C₃₁×#3304	C₂	semidirect
14. C₃₁×#3301	C₂	semidirect
15. C₃₁×#3263	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3244	C₂	semidirect
18. C₃₁×#3227	C₂	semidirect
19. C₃₁×#3125	C₂	semidirect
20. C₃₁×#3108	C₂	semidirect
21. C₃₁×#3084	C₂	semidirect
22. C₂×C₃₁×#475	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
443. #62205	C₃₁	direct (N × H)
516. #3552	C₂×C₃₁	semidirect
517. #3522	C₂×C₃₁	semidirect
518. #3387	C₂×C₃₁	semidirect
519. Q₈×SD₁₆	C₂×C₃₁	semidirect
520. #3373	C₂×C₃₁	semidirect
521. #3365	C₂×C₃₁	semidirect
522. #3356	C₂×C₃₁	semidirect
523. #3345	C₂×C₃₁	semidirect
524. #3335	C₂×C₃₁	semidirect
525. #3335	C₂×C₃₁	semidirect
526. #3332	C₂×C₃₁	semidirect
527. #3316	C₂×C₃₁	semidirect
528. #3304	C₂×C₃₁	semidirect
529. #3301	C₂×C₃₁	semidirect
530. #3263	C₂×C₃₁	semidirect
531. #3247	C₂×C₃₁	semidirect
532. #3244	C₂×C₃₁	semidirect
533. #3227	C₂×C₃₁	semidirect
534. #3125	C₂×C₃₁	semidirect
535. #3108	C₂×C₃₁	semidirect
536. #3084	C₂×C₃₁	semidirect
537. C₂×#475	C₂×C₃₁	semidirect
538. #2994	C₂×C₃₁	semidirect
867. C₃₁	#62205	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×#3552	2
C₃₁×#3522	2
C₃₁×#3387	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3373	2
C₃₁×#3365	2
C₃₁×#3356	2
C₃₁×#3345	2
C₃₁×#3335	2
C₃₁×#3332	2
C₃₁×#3316	2
C₃₁×#3304	2
C₃₁×#3301	2
C₃₁×#3263	2
C₃₁×#3247	2
C₃₁×#3244	2
C₃₁×#3227	2
C₃₁×#3125	2
C₃₁×#3108	2
C₃₁×#3084	2
C₂×C₃₁×#475	2
C₃₁×#2994	2
#62205	31

Subgroups — C31×#62205 #21518964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62205 #21518964