Subgroups — C₃₁×#61997 #21518756

Order 7936.

1904 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3275	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3103	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3037	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#552	C₂²	1	2	yes	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#548	C₂²	1	2	yes	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	4	yes	—
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#535	—	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	2	yes	—
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₃₁×#518	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#495	C₂²	1	4	yes	complemented
51	C₃₁×#492	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	2	yes	—
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#475	C₂²	1	2	yes	complemented
58	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#475	C₂²	1	2	yes	complemented
60	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#470	C₂²	1	4	yes	—
62	C₃₁×#469	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#464	C₂²	1	4	yes	complemented
66	C₃₁×#463	C₂²	1	4	yes	complemented
67	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#462	C₂²	1	2	yes	complemented
69	C₃₁×#462	C₂²	1	2	yes	complemented
70	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#460	C₂²	1	2	yes	—
72	C₃₁×#460	C₂²	1	2	yes	—
73	C₃₁×#460	C₂²	1	2	yes	—
74	C₃₁×#460	C₂²	1	2	yes	—
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#450	C₂²	1	4	yes	—
80	C₃₁×#449	C₂²	1	4	yes	complemented
81	C₃₁×#448	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
86	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
87	C₃₁×#436	C₂²	1	4	yes	—
88	C₃₁×#436	C₂²	1	2	yes	complemented
89	C₃₁×#431	C₂²	1	1	yes	characteristic
90	C₃₁×#431	C₂²	1	2	yes	complemented
91	C₃₁×#423	C₂²	1	1	yes	characteristic
92	C₃₁×#423	C₂²	1	2	yes	complemented
93	C₃₁×#418	C₂²	1	2	yes	—
94	C₃₁×#417	C₂²	1	4	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	—	2	1	no	—
103	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
104	C₃₁×#137	—	4	8	no	—
105	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
106	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×#127	—	2	2	no	—
122	C₃₁×#127	—	2	1	no	—
123	C₃₁×#127	—	2	1	no	—
124	C₃₁×#127	C₂³	1	2	yes	—
125	C₃₁×#127	C₂³	1	2	yes	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	1	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	C₂³	1	2	yes	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	C₂³	1	2	yes	—
138	C₃₁×#124	C₂³	1	4	yes	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×#123	—	2	4	no	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	4	yes	—
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#120	—	2	4	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	—	2	1	no	—
166	C₄×Q₈×C₃₁	—	2	1	no	—
167	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
186	C₄×D₄×C₃₁	D₄	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	4	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	—	2	1	no	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	2	no	—
196	C₃₁×#117	—	2	1	no	—
197	C₃₁×#117	—	2	2	no	—
198	C₃₁×#117	D₄	1	1	yes	characteristic
199	C₃₁×#117	D₄	1	2	yes	—
200	C₃₁×#117	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂×C₄²×C₃₁	—	2	2	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#106	C₂³	1	2	yes	—
210	C₃₁×#106	C₂³	1	4	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	2	no	—
232	#41×C₃₁	—	4	2	no	—
233	#41×C₃₁	—	4	1	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	8	4	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	4	2	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	4	no	—
259	C₂×D₄×C₃₁	—	8	2	no	—
260	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
263	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	2	4	no	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₃₁	—	2	4	no	—
278	Q₁₆×C₃₁	—	4	4	no	—
279	SD₁₆×C₃₁	—	2	8	no	—
280	SD₁₆×C₃₁	—	4	2	no	—
281	SD₁₆×C₃₁	—	4	4	no	—
282	SD₁₆×C₃₁	—	4	4	no	—
283	D₈×C₃₁	—	4	4	no	—
284	M₁₆×C₃₁	—	4	2	no	—
285	M₁₆×C₃₁	—	4	4	no	—
286	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	1	no	—
323	C₂²⋊C₄×C₃₁	—	2	1	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₄²×C₃₁	—	2	1	no	—
332	C₄²×C₃₁	—	2	1	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	1	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	C₂×D₄	1	2	yes	—
342	C₄²×C₃₁	C₂⁴	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	#61997	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	—	2	4	no	—
348	C₂³×C₃₁	—	4	4	no	—
349	C₂³×C₃₁	—	8	2	no	—
350	C₂³×C₃₁	—	8	2	no	—
351	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
353	Q₈×C₃₁	—	2	2	no	—
354	Q₈×C₃₁	—	2	1	no	—
355	Q₈×C₃₁	—	2	2	no	—
356	Q₈×C₃₁	—	2	2	no	—
357	Q₈×C₃₁	—	2	2	no	—
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	4	4	no	—
360	Q₈×C₃₁	—	4	2	no	—
361	Q₈×C₃₁	—	4	2	no	—
362	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	2	1	no	—
365	D₄×C₃₁	—	2	4	no	—
366	D₄×C₃₁	—	2	1	no	—
367	D₄×C₃₁	—	2	4	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	4	2	no	—
370	D₄×C₃₁	—	4	4	no	—
371	D₄×C₃₁	—	4	4	no	—
372	D₄×C₃₁	—	4	4	no	—
373	D₄×C₃₁	—	4	4	no	—
374	D₄×C₃₁	—	8	2	no	—
375	D₄×C₃₁	—	8	2	no	—
376	D₄×C₃₁	—	8	4	no	—
377	D₄×C₃₁	—	8	4	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	4	2	no	—
394	C₂×C₄×C₃₁	—	4	4	no	—
395	C₂×C₄×C₃₁	—	4	4	no	—
396	C₂×C₄×C₃₁	—	4	2	no	—
397	C₂×C₄×C₃₁	—	4	2	no	—
398	C₂×C₄×C₃₁	—	8	4	no	—
399	C₂×C₄×C₃₁	—	8	4	no	—
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	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
409	C₈×C₃₁	—	2	4	no	—
410	C₈×C₃₁	—	2	2	no	—
411	C₈×C₃₁	—	2	2	no	—
412	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3394	C₂×C₃₁	1	2	yes	complemented
415	#3365	C₂×C₃₁	1	2	yes	complemented
416	#3332	C₂×C₃₁	1	2	yes	complemented
417	#3323	C₂×C₃₁	1	4	yes	complemented
418	#3278	C₂×C₃₁	1	2	yes	complemented
419	#3275	C₂×C₃₁	1	4	yes	complemented
420	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3251	C₂×C₃₁	1	2	yes	complemented
422	#3212	C₂×C₃₁	1	2	yes	complemented
423	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#3103	C₂×C₃₁	1	2	yes	complemented
426	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
427	#3037	C₂×C₃₁	1	2	yes	complemented
428	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	1	no	—
432	C₂²×C₃₁	—	2	2	no	—
433	C₂²×C₃₁	—	2	2	no	—
434	C₂²×C₃₁	—	2	1	no	—
435	C₂²×C₃₁	—	4	1	no	—
436	C₂²×C₃₁	—	4	4	no	—
437	C₂²×C₃₁	—	4	1	no	—
438	C₂²×C₃₁	—	4	4	no	—
439	C₂²×C₃₁	—	4	1	no	—
440	C₂²×C₃₁	—	4	4	no	—
441	C₂²×C₃₁	—	16	4	no	—
442	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	2	no	—
448	C₄×C₃₁	—	2	2	no	—
449	C₄×C₃₁	—	2	1	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	—	4	1	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	—	4	1	no	—
455	C₄×C₃₁	—	4	2	no	—
456	C₄×C₃₁	#575	1	2	yes	—
457	C₄×C₃₁	#577	1	2	yes	—
458	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₄×C₃₁	#585	1	1	yes	characteristic
460	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
461	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
462	#559	—	2	1	no	—
463	#559	C₂²×C₃₁	1	2	yes	—
464	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	#556	—	2	1	no	—
466	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#552	—	2	2	no	—
468	#552	C₂²×C₃₁	1	2	yes	—
469	#550	—	2	1	no	—
470	#550	C₂²×C₃₁	1	2	yes	—
471	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	#548	C₂²×C₃₁	1	2	yes	—
473	#547	—	2	1	no	—
474	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#546	—	2	2	no	—
476	#546	C₂²×C₃₁	1	4	yes	—
477	#540	—	2	2	no	—
478	#535	—	2	1	no	—
479	#533	—	2	1	no	—
480	#533	C₂²×C₃₁	1	1	yes	characteristic
481	#533	C₂²×C₃₁	1	1	yes	characteristic
482	#532	C₂²×C₃₁	1	2	yes	—
483	#532	C₂²×C₃₁	1	2	yes	—
484	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
485	#529	—	2	2	no	—
486	#529	C₂²×C₃₁	1	2	yes	complemented
487	#518	—	2	1	no	—
488	C₄×#41	—	2	1	no	—
489	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
490	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
492	#495	C₂²×C₃₁	1	4	yes	complemented
493	#492	C₂²×C₃₁	1	2	yes	—
494	#488	C₂²×C₃₁	1	4	yes	complemented
495	#486	C₂²×C₃₁	1	2	yes	—
496	#485	C₂²×C₃₁	1	2	yes	—
497	#481	C₂²×C₃₁	1	4	yes	complemented
498	#478	C₂²×C₃₁	1	4	yes	complemented
499	#475	C₂²×C₃₁	1	2	yes	complemented
500	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#475	C₂²×C₃₁	1	2	yes	complemented
502	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
503	#470	C₂²×C₃₁	1	4	yes	—
504	#469	C₂²×C₃₁	1	4	yes	complemented
505	#468	C₂²×C₃₁	1	4	yes	complemented
506	#464	C₂²×C₃₁	1	4	yes	complemented
507	#464	C₂²×C₃₁	1	4	yes	complemented
508	#463	C₂²×C₃₁	1	4	yes	complemented
509	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	#462	C₂²×C₃₁	1	2	yes	complemented
511	#462	C₂²×C₃₁	1	2	yes	complemented
512	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	#460	C₂²×C₃₁	1	2	yes	—
514	#460	C₂²×C₃₁	1	2	yes	—
515	#460	C₂²×C₃₁	1	2	yes	—
516	#460	C₂²×C₃₁	1	2	yes	—
517	#459	C₂²×C₃₁	1	2	yes	—
518	#459	C₂²×C₃₁	1	2	yes	—
519	#452	C₂²×C₃₁	1	2	yes	—
520	#452	C₂²×C₃₁	1	4	yes	complemented
521	#450	C₂²×C₃₁	1	4	yes	—
522	#449	C₂²×C₃₁	1	4	yes	complemented
523	#448	C₂²×C₃₁	1	4	yes	complemented
524	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
525	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
526	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
527	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
528	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
529	#436	C₂²×C₃₁	1	4	yes	—
530	#436	C₂²×C₃₁	1	2	yes	complemented
531	#431	C₂²×C₃₁	1	1	yes	characteristic
532	#431	C₂²×C₃₁	1	2	yes	complemented
533	#423	C₂²×C₃₁	1	1	yes	characteristic
534	#423	C₂²×C₃₁	1	2	yes	complemented
535	#418	C₂²×C₃₁	1	2	yes	—
536	#417	C₂²×C₃₁	1	4	yes	complemented
537	C₂×C₃₁	—	4	2	no	—
538	C₂×C₃₁	—	4	1	no	—
539	C₂×C₃₁	—	8	1	no	—
540	C₂×C₃₁	—	8	4	no	—
541	C₂×C₃₁	#3488	1	1	yes	characteristic
542	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
543	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
547	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
548	C₂×#41	C₂³×C₃₁	1	4	yes	—
549	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
553	#137	—	4	8	no	—
554	AGL(1,ℤ/8)	—	4	4	no	—
555	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
556	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
561	C₂×D₈	C₂³×C₃₁	1	4	yes	—
562	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
563	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
570	#127	—	2	2	no	—
571	#127	—	2	1	no	—
572	#127	—	2	1	no	—
573	#127	C₂³×C₃₁	1	2	yes	—
574	#127	C₂³×C₃₁	1	2	yes	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#125	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	—	2	1	no	—
581	#125	—	2	1	no	—
582	#125	C₂³×C₃₁	1	2	yes	—
583	#124	—	2	2	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	C₂³×C₃₁	1	2	yes	—
587	#124	C₂³×C₃₁	1	4	yes	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	4	no	—
591	#123	—	2	4	no	—
592	#123	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	—	2	4	no	—
608	#121	C₂³×C₃₁	1	2	yes	—
609	#121	C₂³×C₃₁	1	4	yes	—
610	#120	—	2	4	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
619	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
620	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
621	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
635	C₄×D₄	D₄×C₃₁	1	2	yes	—
636	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₄×D₄	C₂³×C₃₁	1	4	yes	—
639	C₄×D₄	C₂³×C₃₁	1	2	yes	—
640	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
641	#117	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	—	2	1	no	—
644	#117	—	2	2	no	—
645	#117	—	2	1	no	—
646	#117	—	2	2	no	—
647	#117	D₄×C₃₁	1	1	yes	characteristic
648	#117	D₄×C₃₁	1	2	yes	—
649	#117	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	—	2	2	no	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₂²⋊C₄	—	2	4	no	—
653	C₂×C₄²	—	2	2	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
657	#107	C₂³×C₃₁	1	2	yes	—
658	#106	C₂³×C₃₁	1	2	yes	—
659	#106	C₂³×C₃₁	1	4	yes	—
660	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
661	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
662	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
663	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
664	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
665	#103	C₂³×C₃₁	1	2	yes	—
666	#103	C₂³×C₃₁	1	4	yes	—
667	#103	C₂³×C₃₁	1	2	yes	—
668	#103	C₂³×C₃₁	1	4	yes	—
669	#103	C₂³×C₃₁	1	2	yes	—
670	#102	C₂³×C₃₁	1	4	yes	—
671	#102	C₂³×C₃₁	1	4	yes	—
672	#102	C₂³×C₃₁	1	4	yes	—
673	#102	C₂³×C₃₁	1	4	yes	—
674	#102	C₂³×C₃₁	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
677	C₄×C₈	C₂³×C₃₁	1	2	yes	—
678	C₄×C₈	C₂³×C₃₁	1	4	yes	—
679	C₃₁	#61997	1	1	yes	characteristic, direct product factor, Sylow
680	C₂⁴	—	2	2	no	—
681	#41	—	2	2	no	—
682	#41	—	4	2	no	—
683	#41	—	4	1	no	—
684	#41	—	4	4	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	8	4	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	4	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
694	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
696	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	8	2	no	—
710	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
712	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
713	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
727	Q₁₆	—	2	4	no	—
728	Q₁₆	—	4	4	no	—
729	SD₁₆	—	2	8	no	—
730	SD₁₆	—	4	2	no	—
731	SD₁₆	—	4	4	no	—
732	SD₁₆	—	4	4	no	—
733	D₈	—	4	4	no	—
734	M₁₆	—	4	2	no	—
735	M₁₆	—	4	4	no	—
736	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
737	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
738	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
760	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
763	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	—	2	1	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
790	C₄²	C₂×D₄×C₃₁	1	2	yes	—
791	C₄²	C₂×D₄×C₃₁	1	2	yes	—
792	C₄²	C₂⁴×C₃₁	1	2	yes	—
793	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
795	C₂³	—	2	1	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	4	4	no	—
798	C₂³	—	8	2	no	—
799	C₂³	—	8	2	no	—
800	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
801	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	4	4	no	—
809	Q₈	—	4	2	no	—
810	Q₈	—	4	2	no	—
811	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
812	D₄	—	2	2	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	4	no	—
815	D₄	—	2	1	no	—
816	D₄	—	2	4	no	—
817	D₄	—	4	2	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	8	2	no	—
824	D₄	—	8	2	no	—
825	D₄	—	8	4	no	—
826	D₄	—	8	4	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	8	4	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
854	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
857	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₈	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	16	4	no	—
874	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	1	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	C₃₁×#575	1	2	yes	—
889	C₄	C₃₁×#577	1	2	yes	—
890	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
891	C₄	C₃₁×#585	1	1	yes	characteristic
892	C₂	—	4	1	no	—
893	C₂	—	4	2	no	—
894	C₂	—	8	4	no	—
895	C₂	—	8	1	no	—
896	C₂	C₃₁×#3488	1	1	yes	characteristic
897	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
898	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. C₃₁×#3365	C₂	semidirect
5. C₃₁×#3332	C₂	semidirect
6. C₃₁×#3323	C₂	semidirect
7. C₃₁×#3278	C₂	semidirect
8. C₃₁×#3275	C₂	semidirect
9. C₃₁×#3255	C₂	semidirect
10. C₃₁×#3251	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3107	C₂	semidirect
14. C₃₁×#3103	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₃₁×#3037	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
18. C₂×C₃₁×#137	C₂²	semidirect
22. C₃₁×#557	C₂²	semidirect
24. C₃₁×#556	C₂²	semidirect
29. D₄×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#547	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
49. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
50. C₃₁×#495	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#475	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
59. C₃₁×#475	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
62. C₃₁×#469	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#464	C₂²	semidirect
66. C₃₁×#463	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#462	C₂²	semidirect
69. C₃₁×#462	C₂²	semidirect
70. C₃₁×#461	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
80. C₃₁×#449	C₂²	semidirect
81. C₃₁×#448	C₂²	semidirect
82. C₈×Q₈×C₃₁	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₃₁×#436	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
94. C₃₁×#417	C₂²	semidirect
345. #61997	C₃₁	direct (N × H)
412. #3508	C₂×C₃₁	semidirect
413. #3482	C₂×C₃₁	semidirect
414. #3394	C₂×C₃₁	semidirect
415. #3365	C₂×C₃₁	semidirect
416. #3332	C₂×C₃₁	semidirect
417. #3323	C₂×C₃₁	semidirect
418. #3278	C₂×C₃₁	semidirect
419. #3275	C₂×C₃₁	semidirect
420. #3255	C₂×C₃₁	semidirect
421. #3251	C₂×C₃₁	semidirect
422. #3212	C₂×C₃₁	semidirect
423. #3208	C₂×C₃₁	semidirect
424. #3107	C₂×C₃₁	semidirect
425. #3103	C₂×C₃₁	semidirect
426. #3038	C₂×C₃₁	semidirect
427. #3037	C₂×C₃₁	semidirect
428. #2991	C₂×C₃₁	semidirect
460. C₂×#137	C₂²×C₃₁	semidirect
464. #557	C₂²×C₃₁	semidirect
466. #556	C₂²×C₃₁	semidirect
471. D₄×Q₈	C₂²×C₃₁	semidirect
474. #547	C₂²×C₃₁	semidirect
486. #529	C₂²×C₃₁	semidirect
491. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
492. #495	C₂²×C₃₁	semidirect
494. #488	C₂²×C₃₁	semidirect
497. #481	C₂²×C₃₁	semidirect
498. #478	C₂²×C₃₁	semidirect
499. #475	C₂²×C₃₁	semidirect
500. #475	C₂²×C₃₁	semidirect
501. #475	C₂²×C₃₁	semidirect
502. #474	C₂²×C₃₁	semidirect
504. #469	C₂²×C₃₁	semidirect
505. #468	C₂²×C₃₁	semidirect
506. #464	C₂²×C₃₁	semidirect
507. #464	C₂²×C₃₁	semidirect
508. #463	C₂²×C₃₁	semidirect
509. #462	C₂²×C₃₁	semidirect
510. #462	C₂²×C₃₁	semidirect
511. #462	C₂²×C₃₁	semidirect
512. #461	C₂²×C₃₁	semidirect
520. #452	C₂²×C₃₁	semidirect
522. #449	C₂²×C₃₁	semidirect
523. #448	C₂²×C₃₁	semidirect
524. C₈×Q₈	C₂²×C₃₁	semidirect
525. C₄×Q₁₆	C₂²×C₃₁	semidirect
526. C₄×SD₁₆	C₂²×C₃₁	semidirect
527. C₄×SD₁₆	C₂²×C₃₁	semidirect
528. C₄×SD₁₆	C₂²×C₃₁	semidirect
530. #436	C₂²×C₃₁	semidirect
532. #431	C₂²×C₃₁	semidirect
534. #423	C₂²×C₃₁	semidirect
536. #417	C₂²×C₃₁	semidirect
679. C₃₁	#61997	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×#3508	2
C₃₁×#3482	2
C₃₁×#3394	2
C₃₁×#3365	2
C₃₁×#3332	2
C₃₁×#3323	2
C₃₁×#3278	2
C₃₁×#3275	2
C₃₁×#3255	2
C₃₁×#3251	2
C₃₁×#3212	2
C₃₁×#3208	2
C₃₁×#3107	2
C₃₁×#3103	2
C₃₁×#3038	2
C₃₁×#3037	2
C₃₁×#2991	2
#61997	31

Subgroups — C31×#61997 #21518756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61997 #21518756