Subgroups — C₃₁×#61953 #21518712

Order 7936.

1932 conjugacy classes of subgroups.

The subgroup lattice has 906 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×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3396	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3297	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3287	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3282	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	—	2	1	no	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#556	—	2	1	no	—
26	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#550	—	2	1	no	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#548	C₂²	1	2	yes	—
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	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₃₁×#532	C₂²	1	1	yes	characteristic
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	2	yes	complemented
49	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#495	C₂²	1	4	yes	complemented
51	C₃₁×#493	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	2	yes	—
55	C₃₁×#482	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#475	C₂²	1	2	yes	complemented
61	C₃₁×#466	C₂²	1	4	yes	complemented
62	C₃₁×#465	C₂²	1	4	yes	—
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#463	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	1	yes	characteristic, complemented
69	C₃₁×#461	C₂²	1	2	yes	complemented
70	C₃₁×#460	C₂²	1	2	yes	—
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	complemented
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#451	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#449	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	—
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
87	C₈×D₄×C₃₁	C₂²	1	4	yes	—
88	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
89	C₃₁×#431	C₂²	1	1	yes	characteristic
90	C₃₁×#431	C₂²	1	2	yes	complemented
91	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#416	C₂²	1	4	yes	complemented
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
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	2	yes	—
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	—	2	1	no	—
103	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
104	C₃₁×#135	—	4	8	no	—
105	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₃₁	—	4	4	no	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×D₈×C₃₁	C₂³	1	4	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
114	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×#127	—	2	1	no	—
120	C₃₁×#127	—	2	2	no	—
121	C₃₁×#127	—	2	1	no	—
122	C₃₁×#127	—	2	1	no	—
123	C₃₁×#127	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	2	yes	—
125	C₃₁×#127	C₂³	1	1	yes	characteristic
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	1	no	—
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	1	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	—	2	1	no	—
138	C₃₁×#124	C₂³	1	2	yes	—
139	C₃₁×#124	C₂³	1	4	yes	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	4	no	—
143	C₃₁×#123	—	2	4	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	4	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#121	C₂³	1	4	yes	—
161	C₃₁×#120	—	2	4	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	1	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	1	yes	characteristic
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	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	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	1	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	D₄	1	2	yes	—
189	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₄×D₄×C₃₁	C₂³	1	4	yes	—
192	C₄×D₄×C₃₁	C₂³	1	2	yes	—
193	C₄×D₄×C₃₁	C₂³	1	2	yes	—
194	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	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	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	2	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×#107	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	2	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	4	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	4	no	—
232	#41×C₃₁	—	2	4	no	—
233	#41×C₃₁	—	4	2	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	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	4	1	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	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	4	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	2	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	2	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	4	2	no	—
260	C₂×D₄×C₃₁	—	4	2	no	—
261	C₂×D₄×C₃₁	—	4	4	no	—
262	C₂×D₄×C₃₁	—	8	2	no	—
263	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
266	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	—	2	1	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	2	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	—	2	4	no	—
274	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	Q₁₆×C₃₁	—	2	4	no	—
281	Q₁₆×C₃₁	—	4	2	no	—
282	SD₁₆×C₃₁	—	2	8	no	—
283	SD₁₆×C₃₁	—	4	4	no	—
284	SD₁₆×C₃₁	—	4	4	no	—
285	D₈×C₃₁	—	4	4	no	—
286	D₈×C₃₁	—	4	4	no	—
287	C₂×C₈×C₃₁	—	4	2	no	—
288	C₂×C₈×C₃₁	—	4	4	no	—
289	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
290	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
291	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₄⋊C₄×C₃₁	—	2	2	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	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂×D₄	1	2	yes	—
340	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₃₁	C₂⁴	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	#61953	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂³×C₃₁	—	2	2	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	2	yes	—
352	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₃₁	—	2	2	no	—
354	Q₈×C₃₁	—	2	1	no	—
355	Q₈×C₃₁	—	2	1	no	—
356	Q₈×C₃₁	—	2	2	no	—
357	Q₈×C₃₁	—	2	1	no	—
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	4	2	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	4	no	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	2	2	no	—
366	D₄×C₃₁	—	2	4	no	—
367	D₄×C₃₁	—	2	2	no	—
368	D₄×C₃₁	—	2	4	no	—
369	D₄×C₃₁	—	4	4	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	—	4	2	no	—
375	D₄×C₃₁	—	8	1	no	—
376	D₄×C₃₁	—	8	2	no	—
377	D₄×C₃₁	—	8	2	no	—
378	D₄×C₃₁	—	8	2	no	—
379	D₄×C₃₁	—	8	4	no	—
380	D₄×C₃₁	—	8	4	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	4	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	4	1	no	—
394	C₂×C₄×C₃₁	—	4	2	no	—
395	C₂×C₄×C₃₁	—	4	4	no	—
396	C₂×C₄×C₃₁	—	4	2	no	—
397	C₂×C₄×C₃₁	—	4	4	no	—
398	C₂×C₄×C₃₁	—	8	2	no	—
399	C₂×C₄×C₃₁	—	8	4	no	—
400	C₂×C₄×C₃₁	—	8	4	no	—
401	C₂×C₄×C₃₁	—	8	1	no	—
402	C₂×C₄×C₃₁	#135	1	4	yes	complemented
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	2	yes	—
408	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
412	C₈×C₃₁	—	2	2	no	—
413	C₈×C₃₁	—	2	4	no	—
414	C₈×C₃₁	—	2	2	no	—
415	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#3396	C₂×C₃₁	1	2	yes	complemented
418	#3365	C₂×C₃₁	1	2	yes	complemented
419	#3304	C₂×C₃₁	1	2	yes	complemented
420	#3297	C₂×C₃₁	1	4	yes	complemented
421	#3287	C₂×C₃₁	1	2	yes	complemented
422	#3282	C₂×C₃₁	1	4	yes	complemented
423	#3247	C₂×C₃₁	1	2	yes	complemented
424	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#3212	C₂×C₃₁	1	2	yes	complemented
426	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
427	#3106	C₂×C₃₁	1	2	yes	complemented
428	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#3035	C₂×C₃₁	1	2	yes	complemented
430	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
432	C₂²×C₃₁	—	2	1	no	—
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	2	2	no	—
435	C₂²×C₃₁	—	2	2	no	—
436	C₂²×C₃₁	—	2	2	no	—
437	C₂²×C₃₁	—	4	4	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	4	no	—
441	C₂²×C₃₁	—	4	2	no	—
442	C₂²×C₃₁	—	4	4	no	—
443	C₂²×C₃₁	—	16	4	no	—
444	C₂²×C₃₁	C₂×#135	1	2	yes	—
445	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	2	2	no	—
448	C₄×C₃₁	—	2	1	no	—
449	C₄×C₃₁	—	2	2	no	—
450	C₄×C₃₁	—	2	1	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	2	no	—
453	C₄×C₃₁	—	4	1	no	—
454	C₄×C₃₁	—	4	2	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	1	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	—	4	2	no	—
459	C₄×C₃₁	C₂×#135	1	2	yes	—
460	C₄×C₃₁	C₂×#135	1	2	yes	—
461	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₄×C₃₁	#585	1	1	yes	characteristic
463	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
464	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
465	#559	—	2	1	no	—
466	#559	—	2	1	no	—
467	#559	C₂²×C₃₁	1	2	yes	—
468	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	#556	—	2	1	no	—
471	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	#553	—	2	2	no	—
473	#553	C₂²×C₃₁	1	2	yes	—
474	#550	—	2	1	no	—
475	#550	C₂²×C₃₁	1	2	yes	—
476	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#548	C₂²×C₃₁	1	2	yes	—
478	#546	—	2	2	no	—
479	#546	C₂²×C₃₁	1	4	yes	—
480	#540	—	2	2	no	—
481	#535	—	2	1	no	—
482	#533	C₂²×C₃₁	1	1	yes	characteristic
483	#532	—	2	1	no	—
484	#532	C₂²×C₃₁	1	2	yes	—
485	#532	C₂²×C₃₁	1	2	yes	—
486	#532	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
488	#529	—	2	2	no	—
489	#529	C₂²×C₃₁	1	2	yes	complemented
490	#518	—	2	1	no	—
491	C₄×#41	—	2	1	no	—
492	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
493	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
494	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
495	#495	C₂²×C₃₁	1	4	yes	complemented
496	#493	C₂²×C₃₁	1	2	yes	—
497	#488	C₂²×C₃₁	1	4	yes	complemented
498	#486	C₂²×C₃₁	1	2	yes	—
499	#484	C₂²×C₃₁	1	2	yes	—
500	#482	C₂²×C₃₁	1	4	yes	complemented
501	#478	C₂²×C₃₁	1	4	yes	complemented
502	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
503	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
504	#476	C₂²×C₃₁	1	2	yes	complemented
505	#475	C₂²×C₃₁	1	2	yes	complemented
506	#466	C₂²×C₃₁	1	4	yes	complemented
507	#465	C₂²×C₃₁	1	4	yes	—
508	#465	C₂²×C₃₁	1	4	yes	complemented
509	#464	C₂²×C₃₁	1	4	yes	complemented
510	#463	C₂²×C₃₁	1	4	yes	complemented
511	#463	C₂²×C₃₁	1	4	yes	complemented
512	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#461	C₂²×C₃₁	1	2	yes	complemented
515	#460	C₂²×C₃₁	1	2	yes	—
516	#460	C₂²×C₃₁	1	2	yes	—
517	#460	C₂²×C₃₁	1	2	yes	—
518	#460	C₂²×C₃₁	1	2	yes	—
519	#460	C₂²×C₃₁	1	2	yes	complemented
520	#459	C₂²×C₃₁	1	2	yes	—
521	#459	C₂²×C₃₁	1	2	yes	—
522	#452	C₂²×C₃₁	1	4	yes	complemented
523	#451	C₂²×C₃₁	1	2	yes	—
524	#449	C₂²×C₃₁	1	4	yes	complemented
525	#449	C₂²×C₃₁	1	4	yes	complemented
526	#447	C₂²×C₃₁	1	4	yes	—
527	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
528	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
529	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
530	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
531	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
532	C₈×D₄	C₂²×C₃₁	1	4	yes	—
533	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
534	#431	C₂²×C₃₁	1	1	yes	characteristic
535	#431	C₂²×C₃₁	1	2	yes	complemented
536	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
537	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
538	#416	C₂²×C₃₁	1	4	yes	complemented
539	C₂×#102	C₂²×C₃₁	1	2	yes	—
540	C₂×C₃₁	—	2	2	no	—
541	C₂×C₃₁	—	4	2	no	—
542	C₂×C₃₁	—	8	2	no	—
543	C₂×C₃₁	—	8	4	no	—
544	C₂×C₃₁	#3488	1	1	yes	characteristic
545	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
546	C₂×C₃₁	#3585	1	1	yes	characteristic
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
550	C₂×#41	C₂³×C₃₁	1	2	yes	—
551	C₂×#41	C₂³×C₃₁	1	4	yes	—
552	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
556	#135	—	4	8	no	—
557	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
558	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
559	C₂×SD₁₆	—	4	4	no	—
560	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
561	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
562	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
563	C₂×D₈	C₂³×C₃₁	1	4	yes	—
564	C₂×D₈	C₂³×C₃₁	1	4	yes	—
565	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
566	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
567	C₄⋊Q₈	—	2	1	no	—
568	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
571	#127	—	2	1	no	—
572	#127	—	2	2	no	—
573	#127	—	2	1	no	—
574	#127	—	2	1	no	—
575	#127	C₂³×C₃₁	1	2	yes	—
576	#127	C₂³×C₃₁	1	2	yes	—
577	#127	C₂³×C₃₁	1	1	yes	characteristic
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#125	—	2	2	no	—
582	#125	—	2	1	no	—
583	#125	C₂³×C₃₁	1	2	yes	—
584	#124	—	2	1	no	—
585	#124	—	2	2	no	—
586	#124	—	2	1	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	1	no	—
590	#124	C₂³×C₃₁	1	2	yes	—
591	#124	C₂³×C₃₁	1	4	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	2	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	—	2	4	no	—
609	#121	—	2	4	no	—
610	#121	C₂³×C₃₁	1	2	yes	—
611	#121	C₂³×C₃₁	1	4	yes	—
612	#121	C₂³×C₃₁	1	2	yes	—
613	#120	—	2	4	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
625	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
626	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	D₄×C₃₁	1	2	yes	—
641	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₃₁	1	2	yes	—
643	C₄×D₄	C₂³×C₃₁	1	2	yes	—
644	C₄×D₄	C₂³×C₃₁	1	4	yes	—
645	C₄×D₄	C₂³×C₃₁	1	2	yes	—
646	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
647	#117	—	2	1	no	—
648	#117	—	2	2	no	—
649	#117	—	2	2	no	—
650	#117	D₄×C₃₁	1	1	yes	characteristic
651	#117	D₄×C₃₁	1	2	yes	—
652	#117	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	—	2	4	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	2	no	—
658	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
660	#107	C₂³×C₃₁	1	2	yes	—
661	#107	C₂³×C₃₁	1	2	yes	—
662	#106	C₂³×C₃₁	1	4	yes	—
663	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
664	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
665	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
667	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
668	#103	C₂³×C₃₁	1	2	yes	—
669	#103	C₂³×C₃₁	1	4	yes	—
670	#103	C₂³×C₃₁	1	2	yes	—
671	#103	C₂³×C₃₁	1	2	yes	—
672	#103	C₂³×C₃₁	1	2	yes	—
673	#102	C₂³×C₃₁	1	4	yes	—
674	#102	C₂³×C₃₁	1	4	yes	—
675	#102	C₂³×C₃₁	1	4	yes	—
676	#102	C₂³×C₃₁	1	4	yes	—
677	#102	C₂³×C₃₁	1	4	yes	—
678	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
680	C₄×C₈	C₂³×C₃₁	1	2	yes	—
681	C₄×C₈	C₂³×C₃₁	1	4	yes	—
682	C₃₁	#61953	1	1	yes	characteristic, direct product factor, Sylow
683	C₂⁴	—	2	2	no	—
684	#41	—	2	4	no	—
685	#41	—	2	4	no	—
686	#41	—	4	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	#41	—	8	4	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
698	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	8	2	no	—
716	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
719	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
733	Q₁₆	—	2	4	no	—
734	Q₁₆	—	4	2	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	4	4	no	—
737	SD₁₆	—	4	4	no	—
738	D₈	—	4	4	no	—
739	D₈	—	4	4	no	—
740	C₂×C₈	—	4	2	no	—
741	C₂×C₈	—	4	4	no	—
742	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
743	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
744	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	2	no	—
791	C₄²	C₂×D₄×C₃₁	1	2	yes	—
792	C₄²	C₂×D₄×C₃₁	1	2	yes	—
793	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
794	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₄²	C₂⁴×C₃₁	1	2	yes	—
796	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
798	C₂³	—	2	2	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	8	2	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
804	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
805	Q₈	—	2	2	no	—
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	1	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	4	2	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	4	2	no	—
814	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
815	D₄	—	2	4	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	4	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	4	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	4	4	no	—
826	D₄	—	4	2	no	—
827	D₄	—	8	1	no	—
828	D₄	—	8	2	no	—
829	D₄	—	8	2	no	—
830	D₄	—	8	2	no	—
831	D₄	—	8	4	no	—
832	D₄	—	8	4	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	4	no	—
852	C₂×C₄	—	8	4	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	C₃₁×#135	1	4	yes	complemented
855	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
863	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
864	C₈	—	2	2	no	—
865	C₈	—	2	4	no	—
866	C₈	—	2	2	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	16	4	no	—
879	C₂²	C₂×C₃₁×#135	1	2	yes	—
880	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	C₂×C₃₁×#135	1	2	yes	—
895	C₄	C₂×C₃₁×#135	1	2	yes	—
896	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
897	C₄	C₃₁×#585	1	1	yes	characteristic
898	C₂	—	2	2	no	—
899	C₂	—	4	2	no	—
900	C₂	—	8	4	no	—
901	C₂	—	8	2	no	—
902	C₂	C₃₁×#3488	1	1	yes	characteristic
903	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
904	C₂	C₃₁×#3585	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×#3480	C₂	semidirect
3. C₃₁×#3396	C₂	semidirect
4. C₃₁×#3365	C₂	semidirect
5. C₃₁×#3304	C₂	semidirect
6. C₃₁×#3297	C₂	semidirect
7. C₃₁×#3287	C₂	semidirect
8. C₃₁×#3282	C₂	semidirect
9. C₃₁×#3247	C₂	semidirect
10. C₃₁×#3246	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3104	C₂	semidirect
15. C₃₁×#3035	C₂	semidirect
16. C₂×C₃₁×#460	C₂	semidirect
17. C₃₁×#2988	C₂	semidirect
18. C₂×C₃₁×#135	C₂²	semidirect
23. C₃₁×#559	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
31. C₃₁×#550	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
48. C₄×#41×C₃₁	C₂²	semidirect
50. C₃₁×#495	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#466	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#463	C₂²	semidirect
66. C₃₁×#463	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#462	C₂²	semidirect
69. C₃₁×#461	C₂²	semidirect
74. C₃₁×#460	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#449	C₂²	semidirect
82. C₈×Q₈×C₃₁	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×Q₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
88. C₈×D₄×C₃₁	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
93. C₃₁×#416	C₂²	semidirect
345. #61953	C₃₁	direct (N × H)
402. C₂×C₄×C₃₁	#135	semidirect
415. #3508	C₂×C₃₁	semidirect
416. #3480	C₂×C₃₁	semidirect
417. #3396	C₂×C₃₁	semidirect
418. #3365	C₂×C₃₁	semidirect
419. #3304	C₂×C₃₁	semidirect
420. #3297	C₂×C₃₁	semidirect
421. #3287	C₂×C₃₁	semidirect
422. #3282	C₂×C₃₁	semidirect
423. #3247	C₂×C₃₁	semidirect
424. #3246	C₂×C₃₁	semidirect
425. #3212	C₂×C₃₁	semidirect
426. #3205	C₂×C₃₁	semidirect
427. #3106	C₂×C₃₁	semidirect
428. #3104	C₂×C₃₁	semidirect
429. #3035	C₂×C₃₁	semidirect
430. C₂×#460	C₂×C₃₁	semidirect
431. #2988	C₂×C₃₁	semidirect
463. C₂×#135	C₂²×C₃₁	semidirect
468. #559	C₂²×C₃₁	semidirect
469. #557	C₂²×C₃₁	semidirect
471. #556	C₂²×C₃₁	semidirect
476. #550	C₂²×C₃₁	semidirect
489. #529	C₂²×C₃₁	semidirect
493. C₄×#41	C₂²×C₃₁	semidirect
495. #495	C₂²×C₃₁	semidirect
497. #488	C₂²×C₃₁	semidirect
500. #482	C₂²×C₃₁	semidirect
501. #478	C₂²×C₃₁	semidirect
502. #477	C₂²×C₃₁	semidirect
503. #477	C₂²×C₃₁	semidirect
504. #476	C₂²×C₃₁	semidirect
505. #475	C₂²×C₃₁	semidirect
506. #466	C₂²×C₃₁	semidirect
508. #465	C₂²×C₃₁	semidirect
509. #464	C₂²×C₃₁	semidirect
510. #463	C₂²×C₃₁	semidirect
511. #463	C₂²×C₃₁	semidirect
512. #462	C₂²×C₃₁	semidirect
513. #462	C₂²×C₃₁	semidirect
514. #461	C₂²×C₃₁	semidirect
519. #460	C₂²×C₃₁	semidirect
522. #452	C₂²×C₃₁	semidirect
524. #449	C₂²×C₃₁	semidirect
525. #449	C₂²×C₃₁	semidirect
527. C₈×Q₈	C₂²×C₃₁	semidirect
528. C₄×Q₁₆	C₂²×C₃₁	semidirect
529. C₄×Q₁₆	C₂²×C₃₁	semidirect
530. C₄×SD₁₆	C₂²×C₃₁	semidirect
531. C₄×D₈	C₂²×C₃₁	semidirect
533. C₈×D₄	C₂²×C₃₁	semidirect
535. #431	C₂²×C₃₁	semidirect
537. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
538. #416	C₂²×C₃₁	semidirect
682. C₃₁	#61953	direct (N × H)
854. C₂×C₄	C₃₁×#135	semidirect

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×#3480	2
C₃₁×#3396	2
C₃₁×#3365	2
C₃₁×#3304	2
C₃₁×#3297	2
C₃₁×#3287	2
C₃₁×#3282	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3212	2
C₃₁×#3205	2
C₃₁×#3106	2
C₃₁×#3104	2
C₃₁×#3035	2
C₂×C₃₁×#460	2
C₃₁×#2988	2
#61953	31

Subgroups — C31×#61953 #21518712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61953 #21518712