Subgroups — C₃₁×#62136 #21518895

Order 7936.

1812 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3347	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3309	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3245	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3235	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#556	—	2	1	no	—
20	C₃₁×#555	—	2	1	no	—
21	C₃₁×#555	—	2	2	no	—
22	C₃₁×#555	C₂²	1	1	yes	characteristic
23	C₃₁×#555	C₂²	1	2	yes	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#553	C₂²	1	4	yes	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	C₂²	1	1	yes	characteristic
29	C₃₁×#550	C₂²	1	2	yes	—
30	C₃₁×#550	C₂²	1	1	yes	characteristic
31	C₃₁×#548	—	2	2	no	—
32	C₃₁×#547	—	2	1	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#537	—	2	1	no	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#532	—	2	1	no	—
37	C₃₁×#532	—	2	2	no	—
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#520	—	2	1	no	—
44	C₄×#41×C₃₁	—	2	1	no	—
45	C₄×#41×C₃₁	C₂²	1	2	yes	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	—
49	C₃₁×#500	C₂²	1	2	yes	—
50	C₃₁×#490	C₂²	1	4	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#482	C₂²	1	4	yes	—
53	C₃₁×#482	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	2	yes	—
55	C₃₁×#482	C₂²	1	4	yes	—
56	C₃₁×#480	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	4	yes	—
58	C₃₁×#478	C₂²	1	4	yes	—
59	C₃₁×#477	C₂²	1	1	yes	characteristic
60	C₃₁×#477	C₂²	1	2	yes	—
61	C₃₁×#476	C₂²	1	2	yes	—
62	C₃₁×#476	C₂²	1	2	yes	—
63	C₃₁×#476	C₂²	1	2	yes	—
64	C₃₁×#476	C₂²	1	1	yes	characteristic
65	C₃₁×#475	C₂²	1	2	yes	—
66	C₃₁×#474	C₂²	1	2	yes	—
67	C₃₁×#474	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	4	yes	—
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#469	C₂²	1	4	yes	—
71	C₃₁×#466	C₂²	1	4	yes	—
72	C₃₁×#466	C₂²	1	4	yes	—
73	C₃₁×#460	C₂²	1	1	yes	characteristic
74	C₃₁×#459	C₂²	1	1	yes	characteristic
75	C₃₁×#459	C₂²	1	4	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	4	yes	—
80	C₃₁×#446	C₂²	1	2	yes	—
81	C₃₁×#442	C₂²	1	4	yes	—
82	C₃₁×#440	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×D₈×C₃₁	C₂²	1	2	yes	—
85	C₃₁×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#432	C₂²	1	2	yes	—
88	C₃₁×#431	C₂²	1	1	yes	characteristic
89	C₃₁×#428	C₂²	1	2	yes	—
90	C₃₁×#427	C₂²	1	4	yes	—
91	C₃₁×#423	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
93	C₃₁×#417	C₂²	1	2	yes	—
94	C₃₁×#416	C₂²	1	4	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₃₁	—	2	1	no	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	2	no	—
111	C₃₁×C₄⋊Q₈	—	2	1	no	—
112	C₃₁×C₄⋊Q₈	—	2	1	no	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×#127	—	2	1	no	—
119	C₃₁×#127	—	2	2	no	—
120	C₃₁×#127	C₂³	1	1	yes	characteristic
121	C₃₁×#127	C₂³	1	1	yes	characteristic
122	C₃₁×#127	C₂³	1	2	yes	—
123	C₃₁×#126	—	2	4	no	—
124	C₃₁×#125	C₂³	1	4	yes	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	—	2	4	no	—
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#123	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×#121	—	2	1	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	1	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	C₂³	1	4	yes	—
152	C₃₁×#121	C₂³	1	2	yes	—
153	C₃₁×#121	C₂³	1	2	yes	—
154	C₃₁×#121	C₂³	1	2	yes	—
155	C₃₁×#121	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	2	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	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	4	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	2	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
176	C₄×D₄×C₃₁	D₄	1	2	yes	—
177	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₃₁	C₂³	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	4	yes	—
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₃₁×#117	—	2	1	no	—
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	—	2	1	no	—
190	C₃₁×#117	D₄	1	1	yes	characteristic
191	C₃₁×#117	D₄	1	2	yes	—
192	C₃₁×#117	C₂³	1	4	yes	—
193	C₃₁×#117	C₂³	1	2	yes	—
194	C₃₁×#117	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	—	2	1	no	—
199	C₂×C₄²×C₃₁	—	2	2	no	—
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	2	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	#41×C₃₁	—	2	4	no	—
229	#41×C₃₁	—	2	2	no	—
230	#41×C₃₁	—	4	2	no	—
231	#41×C₃₁	—	4	2	no	—
232	#41×C₃₁	—	4	1	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	8	2	no	—
236	#41×C₃₁	—	8	4	no	—
237	#41×C₃₁	—	8	4	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	8	2	no	—
244	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	1	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	2	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	SD₁₆×C₃₁	—	2	4	no	—
280	D₈×C₃₁	—	4	2	no	—
281	D₈×C₃₁	—	4	4	no	—
282	M₁₆×C₃₁	—	4	2	no	—
283	C₂×C₈×C₃₁	—	4	4	no	—
284	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	1	no	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	—	2	1	no	—
329	C₄²×C₃₁	—	2	4	no	—
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	C₂×D₄	1	2	yes	—
333	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₄²×C₃₁	C₂⁴	1	2	yes	—
336	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
337	#62136	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
342	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	1	no	—
345	Q₈×C₃₁	—	4	2	no	—
346	Q₈×C₃₁	—	4	4	no	—
347	Q₈×C₃₁	—	8	2	no	—
348	Q₈×C₃₁	—	8	2	no	—
349	Q₈×C₃₁	—	8	1	no	—
350	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	1	no	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	2	1	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	4	2	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	2	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	4	4	no	—
363	D₄×C₃₁	—	4	4	no	—
364	D₄×C₃₁	—	4	2	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	8	2	no	—
367	D₄×C₃₁	—	8	1	no	—
368	D₄×C₃₁	—	8	2	no	—
369	D₄×C₃₁	—	8	2	no	—
370	D₄×C₃₁	—	8	2	no	—
371	D₄×C₃₁	—	8	4	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	4	no	—
385	C₂×C₄×C₃₁	—	4	2	no	—
386	C₂×C₄×C₃₁	—	4	4	no	—
387	C₂×C₄×C₃₁	—	4	2	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	2	no	—
390	C₂×C₄×C₃₁	—	4	4	no	—
391	C₂×C₄×C₃₁	—	4	4	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	8	4	no	—
394	C₂×C₄×C₃₁	—	8	2	no	—
395	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
404	C₈×C₃₁	—	2	2	no	—
405	C₈×C₃₁	—	2	2	no	—
406	C₈×C₃₁	—	2	4	no	—
407	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3385	C₂×C₃₁	1	2	yes	complemented
410	#3366	C₂×C₃₁	1	2	yes	complemented
411	#3347	C₂×C₃₁	1	4	yes	complemented
412	#3341	C₂×C₃₁	1	2	yes	complemented
413	#3309	C₂×C₃₁	1	4	yes	complemented
414	#3305	C₂×C₃₁	1	2	yes	complemented
415	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3245	C₂×C₃₁	1	2	yes	complemented
417	#3235	C₂×C₃₁	1	2	yes	complemented
418	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3115	C₂×C₃₁	1	2	yes	complemented
420	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3076	C₂×C₃₁	1	2	yes	complemented
423	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	2	1	no	—
427	C₂²×C₃₁	—	2	2	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	1	no	—
437	C₂²×C₃₁	—	4	2	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	4	1	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	—	4	1	no	—
451	C₄×C₃₁	—	4	4	no	—
452	C₄×C₃₁	#575	1	2	yes	—
453	C₄×C₃₁	#576	1	2	yes	—
454	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
455	C₄×C₃₁	#585	1	1	yes	characteristic
456	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
457	#556	—	2	1	no	—
458	#555	—	2	1	no	—
459	#555	—	2	2	no	—
460	#555	C₂²×C₃₁	1	1	yes	characteristic
461	#555	C₂²×C₃₁	1	2	yes	—
462	#555	C₂²×C₃₁	1	2	yes	—
463	#554	C₂²×C₃₁	1	2	yes	—
464	#553	C₂²×C₃₁	1	4	yes	—
465	#550	—	2	1	no	—
466	#550	C₂²×C₃₁	1	1	yes	characteristic
467	#550	C₂²×C₃₁	1	2	yes	—
468	#550	C₂²×C₃₁	1	1	yes	characteristic
469	#548	—	2	2	no	—
470	#547	—	2	1	no	—
471	#542	—	2	2	no	—
472	#537	—	2	1	no	—
473	#533	C₂²×C₃₁	1	2	yes	—
474	#532	—	2	1	no	—
475	#532	—	2	2	no	—
476	#532	C₂²×C₃₁	1	1	yes	characteristic
477	#532	C₂²×C₃₁	1	2	yes	—
478	#532	C₂²×C₃₁	1	1	yes	characteristic
479	#532	C₂²×C₃₁	1	2	yes	—
480	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
481	#520	—	2	1	no	—
482	C₄×#41	—	2	1	no	—
483	C₄×#41	C₂²×C₃₁	1	2	yes	—
484	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
485	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
486	#501	C₂²×C₃₁	1	4	yes	—
487	#500	C₂²×C₃₁	1	2	yes	—
488	#490	C₂²×C₃₁	1	4	yes	—
489	#486	C₂²×C₃₁	1	2	yes	—
490	#482	C₂²×C₃₁	1	4	yes	—
491	#482	C₂²×C₃₁	1	4	yes	—
492	#482	C₂²×C₃₁	1	2	yes	—
493	#482	C₂²×C₃₁	1	4	yes	—
494	#480	C₂²×C₃₁	1	4	yes	—
495	#479	C₂²×C₃₁	1	4	yes	—
496	#478	C₂²×C₃₁	1	4	yes	—
497	#477	C₂²×C₃₁	1	1	yes	characteristic
498	#477	C₂²×C₃₁	1	2	yes	—
499	#476	C₂²×C₃₁	1	2	yes	—
500	#476	C₂²×C₃₁	1	2	yes	—
501	#476	C₂²×C₃₁	1	2	yes	—
502	#476	C₂²×C₃₁	1	1	yes	characteristic
503	#475	C₂²×C₃₁	1	2	yes	—
504	#474	C₂²×C₃₁	1	2	yes	—
505	#474	C₂²×C₃₁	1	2	yes	—
506	#474	C₂²×C₃₁	1	4	yes	—
507	#474	C₂²×C₃₁	1	2	yes	—
508	#469	C₂²×C₃₁	1	4	yes	—
509	#466	C₂²×C₃₁	1	4	yes	—
510	#466	C₂²×C₃₁	1	4	yes	—
511	#460	C₂²×C₃₁	1	1	yes	characteristic
512	#459	C₂²×C₃₁	1	1	yes	characteristic
513	#459	C₂²×C₃₁	1	4	yes	—
514	#459	C₂²×C₃₁	1	2	yes	—
515	#459	C₂²×C₃₁	1	2	yes	—
516	#449	C₂²×C₃₁	1	2	yes	—
517	#449	C₂²×C₃₁	1	4	yes	—
518	#446	C₂²×C₃₁	1	2	yes	—
519	#442	C₂²×C₃₁	1	4	yes	—
520	#440	C₂²×C₃₁	1	4	yes	—
521	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
522	C₄×D₈	C₂²×C₃₁	1	2	yes	—
523	#435	C₂²×C₃₁	1	4	yes	—
524	C₈×D₄	C₂²×C₃₁	1	2	yes	—
525	#432	C₂²×C₃₁	1	2	yes	—
526	#431	C₂²×C₃₁	1	1	yes	characteristic
527	#428	C₂²×C₃₁	1	2	yes	—
528	#427	C₂²×C₃₁	1	4	yes	—
529	#423	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
531	#417	C₂²×C₃₁	1	2	yes	—
532	#416	C₂²×C₃₁	1	4	yes	—
533	C₂×C₃₁	—	4	1	no	—
534	C₂×C₃₁	—	4	2	no	—
535	C₂×C₃₁	—	8	2	no	—
536	C₂×C₃₁	—	8	1	no	—
537	C₂×C₃₁	—	8	2	no	—
538	C₂×C₃₁	#3489	1	1	yes	characteristic
539	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
540	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
547	C₂×#41	C₂³×C₃₁	1	2	yes	—
548	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
549	C₂²×Q₈	—	2	1	no	—
550	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
551	C₂×D₈	C₂³×C₃₁	1	2	yes	—
552	C₂×D₈	C₂³×C₃₁	1	4	yes	—
553	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
554	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	2	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	#127	—	2	1	no	—
565	#127	—	2	2	no	—
566	#127	C₂³×C₃₁	1	1	yes	characteristic
567	#127	C₂³×C₃₁	1	1	yes	characteristic
568	#127	C₂³×C₃₁	1	2	yes	—
569	#126	—	2	4	no	—
570	#125	C₂³×C₃₁	1	4	yes	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	—	2	4	no	—
575	#124	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	—	2	1	no	—
579	#123	—	2	4	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	4	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₃₁	1	2	yes	—
598	#121	C₂³×C₃₁	1	2	yes	—
599	#121	C₂³×C₃₁	1	2	yes	—
600	#121	C₂³×C₃₁	1	2	yes	—
601	#121	C₂³×C₃₁	1	4	yes	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
609	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
622	C₄×D₄	D₄×C₃₁	1	2	yes	—
623	C₄×D₄	C₂³×C₃₁	1	2	yes	—
624	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₃₁	1	2	yes	—
627	C₄×D₄	C₂³×C₃₁	1	4	yes	—
628	C₄×D₄	C₂³×C₃₁	1	2	yes	—
629	C₄×D₄	C₂³×C₃₁	1	2	yes	—
630	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	—	2	1	no	—
636	#117	D₄×C₃₁	1	1	yes	characteristic
637	#117	D₄×C₃₁	1	2	yes	—
638	#117	C₂³×C₃₁	1	2	yes	—
639	#117	C₂³×C₃₁	1	1	yes	characteristic
640	#117	C₂³×C₃₁	1	4	yes	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	2	no	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	2	no	—
646	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
648	#107	C₂³×C₃₁	1	2	yes	—
649	#107	C₂³×C₃₁	1	4	yes	—
650	#107	C₂³×C₃₁	1	4	yes	—
651	#107	C₂³×C₃₁	1	4	yes	—
652	#106	C₂³×C₃₁	1	4	yes	—
653	#106	C₂³×C₃₁	1	4	yes	—
654	#106	C₂³×C₃₁	1	2	yes	—
655	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
658	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
660	#103	C₂³×C₃₁	1	2	yes	—
661	#103	C₂³×C₃₁	1	4	yes	—
662	#102	C₂³×C₃₁	1	4	yes	—
663	#102	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	4	yes	—
665	#102	C₂³×C₃₁	1	2	yes	—
666	#102	C₂³×C₃₁	1	2	yes	—
667	#102	C₂³×C₃₁	1	2	yes	—
668	#102	C₂³×C₃₁	1	4	yes	—
669	#102	C₂³×C₃₁	1	4	yes	—
670	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
672	#97	C₂³×C₃₁	1	4	yes	—
673	C₄×C₈	C₂³×C₃₁	1	2	yes	—
674	C₃₁	#62136	1	1	yes	characteristic, direct product factor, Sylow
675	#41	—	2	4	no	—
676	#41	—	2	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	#41	—	8	2	no	—
683	#41	—	8	4	no	—
684	#41	—	8	4	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	8	2	no	—
691	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
708	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
709	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	SD₁₆	—	2	4	no	—
727	D₈	—	4	2	no	—
728	D₈	—	4	4	no	—
729	M₁₆	—	4	2	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
733	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
748	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₃₁	1	2	yes	—
779	C₄²	C₂×D₄×C₃₁	1	2	yes	—
780	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₄²	C₂⁴×C₃₁	1	2	yes	—
783	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
788	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
789	Q₈	—	2	2	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	8	2	no	—
794	Q₈	—	8	2	no	—
795	Q₈	—	8	1	no	—
796	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	4	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	2	no	—
852	C₈	—	2	4	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	4	no	—
881	C₄	C₃₁×#575	1	2	yes	—
882	C₄	C₃₁×#576	1	2	yes	—
883	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
884	C₄	C₃₁×#585	1	1	yes	characteristic
885	C₂	—	4	1	no	—
886	C₂	—	4	2	no	—
887	C₂	—	8	2	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	2	no	—
890	C₂	C₃₁×#3489	1	1	yes	characteristic
891	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
892	C₂	C₂×C₃₁×#576	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3483	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3347	C₂	semidirect
6. C₃₁×#3341	C₂	semidirect
7. C₃₁×#3309	C₂	semidirect
8. C₃₁×#3305	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3245	C₂	semidirect
11. C₃₁×#3235	C₂	semidirect
12. C₃₁×#3226	C₂	semidirect
13. C₃₁×#3115	C₂	semidirect
14. C₃₁×#3106	C₂	semidirect
15. C₃₁×#3079	C₂	semidirect
16. C₃₁×#3076	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
337. #62136	C₃₁	direct (N × H)
407. #3511	C₂×C₃₁	semidirect
408. #3483	C₂×C₃₁	semidirect
409. #3385	C₂×C₃₁	semidirect
410. #3366	C₂×C₃₁	semidirect
411. #3347	C₂×C₃₁	semidirect
412. #3341	C₂×C₃₁	semidirect
413. #3309	C₂×C₃₁	semidirect
414. #3305	C₂×C₃₁	semidirect
415. #3253	C₂×C₃₁	semidirect
416. #3245	C₂×C₃₁	semidirect
417. #3235	C₂×C₃₁	semidirect
418. #3226	C₂×C₃₁	semidirect
419. #3115	C₂×C₃₁	semidirect
420. #3106	C₂×C₃₁	semidirect
421. #3079	C₂×C₃₁	semidirect
422. #3076	C₂×C₃₁	semidirect
423. #2990	C₂×C₃₁	semidirect
674. C₃₁	#62136	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×#3511	2
C₃₁×#3483	2
C₃₁×#3385	2
C₃₁×#3366	2
C₃₁×#3347	2
C₃₁×#3341	2
C₃₁×#3309	2
C₃₁×#3305	2
C₃₁×#3253	2
C₃₁×#3245	2
C₃₁×#3235	2
C₃₁×#3226	2
C₃₁×#3115	2
C₃₁×#3106	2
C₃₁×#3079	2
C₃₁×#3076	2
C₃₁×#2990	2
#62136	31

Subgroups — C31×#62136 #21518895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62136 #21518895