Subgroups — C₃₁×#62576 #21519335

Order 7936.

2050 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#490	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
19	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#553	C₂²	1	2	yes	complemented
23	C₃₁×#552	—	2	2	no	—
24	C₃₁×#552	—	2	1	no	—
25	C₃₁×#552	C₂²	1	2	yes	complemented
26	C₃₁×#550	—	2	1	no	—
27	C₃₁×#550	C₂²	1	2	yes	—
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
30	D₄²×C₃₁	—	2	1	no	—
31	D₄²×C₃₁	—	2	2	no	—
32	D₄²×C₃₁	C₂²	1	2	yes	—
33	D₄²×C₃₁	C₂²	1	4	yes	—
34	C₃₁×#541	—	2	1	no	—
35	C₃₁×#539	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#535	—	2	2	no	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₂×C₃₁×#127	C₂²	1	2	yes	—
42	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
46	C₃₁×#520	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#496	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	4	yes	complemented
53	C₃₁×#490	C₂²	1	4	yes	complemented
54	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#490	C₂²	1	2	yes	complemented
56	C₃₁×#490	C₂²	1	2	yes	complemented
57	C₃₁×#490	C₂²	1	2	yes	complemented
58	C₃₁×#490	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#486	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	4	yes	complemented
63	C₃₁×#481	C₂²	1	4	yes	complemented
64	C₃₁×#480	C₂²	1	4	yes	complemented
65	C₃₁×#478	C₂²	1	4	yes	complemented
66	C₃₁×#478	C₂²	1	4	yes	complemented
67	C₃₁×#476	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#469	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#466	C₂²	1	4	yes	complemented
72	C₃₁×#465	C₂²	1	4	yes	complemented
73	C₃₁×#460	C₂²	1	2	yes	complemented
74	C₃₁×#460	C₂²	1	4	yes	complemented
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	4	yes	complemented
77	C₃₁×#450	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	2	yes	complemented
79	C₃₁×#447	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	2	yes	complemented
81	C₃₁×#446	C₂²	1	2	yes	complemented
82	C₃₁×#442	C₂²	1	4	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
86	C₃₁×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
88	C₃₁×#432	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#418	C₂²	1	4	yes	complemented
91	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
92	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
95	C₃₁×H(5,𝔽₂)	—	4	8	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	—	2	1	no	—
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₃₁	—	2	4	no	—
102	C₂²×D₄×C₃₁	—	2	2	no	—
103	C₂²×D₄×C₃₁	—	2	2	no	—
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	—	2	2	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×D₈×C₃₁	C₂³	1	2	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂×M₁₆×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	2	no	—
120	C₃₁×#127	—	2	1	no	—
121	C₃₁×#127	—	2	1	no	—
122	C₃₁×#127	—	2	2	no	—
123	C₃₁×#127	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	4	yes	—
125	C₃₁×#127	C₂³	1	1	yes	characteristic
126	C₃₁×#127	C₂³	1	2	yes	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#126	—	2	2	no	—
130	C₃₁×#126	—	2	1	no	—
131	C₃₁×#125	—	2	2	no	—
132	C₃₁×#125	—	2	2	no	—
133	C₃₁×#125	—	2	1	no	—
134	C₃₁×#125	—	2	2	no	—
135	C₃₁×#125	—	2	2	no	—
136	C₃₁×#125	C₂³	1	2	yes	—
137	C₃₁×#125	C₂³	1	2	yes	—
138	C₃₁×#125	C₂³	1	1	yes	characteristic
139	C₃₁×#125	C₂³	1	2	yes	—
140	C₃₁×#124	—	2	2	no	—
141	C₃₁×#124	—	2	1	no	—
142	C₃₁×#124	C₂³	1	1	yes	characteristic
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×#123	—	2	1	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×#123	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	1	no	—
150	C₃₁×C₂²⋊Q₈	—	2	1	no	—
151	C₃₁×C₂²⋊Q₈	—	2	2	no	—
152	C₃₁×C₂²⋊Q₈	—	2	1	no	—
153	C₃₁×C₂²⋊Q₈	—	2	2	no	—
154	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	—	2	1	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	4	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	—	2	4	no	—
163	C₃₁×#121	C₂³	1	2	yes	—
164	C₃₁×#121	C₂³	1	1	yes	characteristic
165	C₃₁×#121	C₂³	1	4	yes	—
166	C₃₁×#121	C₂³	1	2	yes	—
167	C₃₁×#120	—	2	4	no	—
168	C₃₁×#120	—	2	4	no	—
169	C₃₁×#120	—	2	4	no	—
170	C₄×Q₈×C₃₁	—	2	1	no	—
171	C₄×Q₈×C₃₁	—	2	1	no	—
172	C₄×Q₈×C₃₁	—	2	1	no	—
173	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
176	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
184	C₄×D₄×C₃₁	D₄	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	4	yes	—
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	D₄	1	1	yes	characteristic
195	C₃₁×#117	D₄	1	2	yes	—
196	C₃₁×#117	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
210	C₃₁×#103	C₂³	1	2	yes	—
211	C₃₁×#102	C₂³	1	2	yes	—
212	C₃₁×#102	C₂³	1	2	yes	—
213	C₃₁×#102	C₂³	1	4	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	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	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₃₁×#97	C₂³	1	1	yes	characteristic
225	C₃₁×#97	C₂³	1	2	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₃₁×#97	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₂⁴×C₃₁	—	2	2	no	—
230	C₂⁴×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	4	8	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	8	no	—
235	#41×C₃₁	—	4	4	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	4	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	4	4	no	—
256	C₂×D₄×C₃₁	—	4	4	no	—
257	C₂×D₄×C₃₁	—	4	4	no	—
258	C₂×D₄×C₃₁	—	4	8	no	—
259	C₂×D₄×C₃₁	—	4	4	no	—
260	C₂×D₄×C₃₁	—	4	16	no	—
261	C₂×D₄×C₃₁	—	4	8	no	—
262	C₂×D₄×C₃₁	—	8	4	no	—
263	C₂×D₄×C₃₁	—	8	2	no	—
264	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
268	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	1	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	2	no	—
275	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	SD₁₆×C₃₁	—	4	4	no	—
282	SD₁₆×C₃₁	—	4	2	no	—
283	D₈×C₃₁	—	4	4	no	—
284	D₈×C₃₁	—	4	2	no	—
285	M₁₆×C₃₁	—	4	2	no	—
286	C₂×C₈×C₃₁	—	4	4	no	—
287	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
289	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₄⋊C₄×C₃₁	—	2	1	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	2	yes	—
309	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	1	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	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	1	no	—
329	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	C₂×D₄	1	2	yes	—
336	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₃₁	C₂⁴	1	2	yes	—
342	#62576	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	2	4	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	—	4	4	no	—
347	C₂³×C₃₁	—	4	8	no	—
348	C₂³×C₃₁	—	8	4	no	—
349	C₂³×C₃₁	—	8	2	no	—
350	C₂³×C₃₁	—	8	4	no	—
351	C₂³×C₃₁	—	8	2	no	—
352	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
354	Q₈×C₃₁	—	2	2	no	—
355	Q₈×C₃₁	—	2	2	no	—
356	Q₈×C₃₁	—	4	2	no	—
357	Q₈×C₃₁	—	4	2	no	—
358	Q₈×C₃₁	—	8	1	no	—
359	D₄×C₃₁	—	2	4	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	4	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	4	no	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	4	4	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	4	8	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	4	4	no	—
371	D₄×C₃₁	—	4	8	no	—
372	D₄×C₃₁	—	4	4	no	—
373	D₄×C₃₁	—	4	4	no	—
374	D₄×C₃₁	—	8	4	no	—
375	D₄×C₃₁	—	8	2	no	—
376	D₄×C₃₁	—	8	4	no	—
377	D₄×C₃₁	—	8	2	no	—
378	D₄×C₃₁	—	8	1	no	—
379	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
380	C₂×C₄×C₃₁	—	2	4	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	4	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	2	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	1	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	1	no	—
392	C₂×C₄×C₃₁	—	4	8	no	—
393	C₂×C₄×C₃₁	—	4	4	no	—
394	C₂×C₄×C₃₁	—	4	4	no	—
395	C₂×C₄×C₃₁	—	4	2	no	—
396	C₂×C₄×C₃₁	—	8	2	no	—
397	C₂×C₄×C₃₁	—	8	2	no	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₃₁	—	2	2	no	—
408	C₈×C₃₁	—	2	4	no	—
409	C₈×C₃₁	—	2	2	no	—
410	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3368	C₂×C₃₁	1	2	yes	complemented
413	#3366	C₂×C₃₁	1	2	yes	complemented
414	#3318	C₂×C₃₁	1	4	yes	complemented
415	#3310	C₂×C₃₁	1	4	yes	complemented
416	#3295	C₂×C₃₁	1	2	yes	complemented
417	#3294	C₂×C₃₁	1	2	yes	complemented
418	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3234	C₂×C₃₁	1	2	yes	complemented
420	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3217	C₂×C₃₁	1	2	yes	complemented
422	#3180	C₂×C₃₁	1	2	yes	complemented
423	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
425	C₂×#490	C₂×C₃₁	1	2	yes	complemented
426	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
427	C₂²×C₃₁	—	2	2	no	—
428	C₂²×C₃₁	—	2	2	no	—
429	C₂²×C₃₁	—	2	1	no	—
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	1	no	—
432	C₂²×C₃₁	—	4	1	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	4	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	4	no	—
437	C₂²×C₃₁	—	4	1	no	—
438	C₂²×C₃₁	—	4	4	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	16	8	no	—
442	C₂²×C₃₁	—	16	4	no	—
443	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
444	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₃₁	—	2	1	no	—
446	C₄×C₃₁	—	2	2	no	—
447	C₄×C₃₁	—	2	1	no	—
448	C₄×C₃₁	—	2	2	no	—
449	C₄×C₃₁	—	2	1	no	—
450	C₄×C₃₁	—	2	1	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	4	1	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	—	4	1	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
459	C₄×C₃₁	#585	1	2	yes	—
460	C₂×H(5,𝔽₂)	—	2	1	no	—
461	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
462	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
464	#553	C₂²×C₃₁	1	2	yes	complemented
465	#552	—	2	2	no	—
466	#552	—	2	1	no	—
467	#552	C₂²×C₃₁	1	2	yes	complemented
468	#550	—	2	1	no	—
469	#550	C₂²×C₃₁	1	2	yes	—
470	#547	—	2	1	no	—
471	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
472	D₄²	—	2	1	no	—
473	D₄²	—	2	2	no	—
474	D₄²	C₂²×C₃₁	1	2	yes	—
475	D₄²	C₂²×C₃₁	1	4	yes	—
476	#541	—	2	1	no	—
477	#539	—	2	2	no	—
478	#535	—	2	1	no	—
479	#535	—	2	2	no	—
480	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
481	#532	C₂²×C₃₁	1	1	yes	characteristic
482	#532	C₂²×C₃₁	1	2	yes	—
483	C₂×#127	C₂²×C₃₁	1	2	yes	—
484	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
485	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#529	C₂²×C₃₁	1	2	yes	complemented
487	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
488	#520	—	2	1	no	—
489	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
490	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
491	#501	C₂²×C₃₁	1	2	yes	complemented
492	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
493	#496	C₂²×C₃₁	1	2	yes	complemented
494	#490	C₂²×C₃₁	1	4	yes	complemented
495	#490	C₂²×C₃₁	1	4	yes	complemented
496	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#490	C₂²×C₃₁	1	2	yes	complemented
498	#490	C₂²×C₃₁	1	2	yes	complemented
499	#490	C₂²×C₃₁	1	2	yes	complemented
500	#490	C₂²×C₃₁	1	2	yes	complemented
501	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
502	#486	C₂²×C₃₁	1	2	yes	complemented
503	#486	C₂²×C₃₁	1	2	yes	complemented
504	#482	C₂²×C₃₁	1	4	yes	complemented
505	#481	C₂²×C₃₁	1	4	yes	complemented
506	#480	C₂²×C₃₁	1	4	yes	complemented
507	#478	C₂²×C₃₁	1	4	yes	complemented
508	#478	C₂²×C₃₁	1	4	yes	complemented
509	#476	C₂²×C₃₁	1	2	yes	complemented
510	#474	C₂²×C₃₁	1	2	yes	complemented
511	#469	C₂²×C₃₁	1	2	yes	complemented
512	#468	C₂²×C₃₁	1	2	yes	complemented
513	#466	C₂²×C₃₁	1	4	yes	complemented
514	#465	C₂²×C₃₁	1	4	yes	complemented
515	#460	C₂²×C₃₁	1	2	yes	complemented
516	#460	C₂²×C₃₁	1	4	yes	complemented
517	#459	C₂²×C₃₁	1	2	yes	complemented
518	#459	C₂²×C₃₁	1	4	yes	complemented
519	#450	C₂²×C₃₁	1	4	yes	complemented
520	#450	C₂²×C₃₁	1	2	yes	complemented
521	#447	C₂²×C₃₁	1	4	yes	complemented
522	#447	C₂²×C₃₁	1	2	yes	complemented
523	#446	C₂²×C₃₁	1	2	yes	complemented
524	#442	C₂²×C₃₁	1	4	yes	complemented
525	#440	C₂²×C₃₁	1	4	yes	complemented
526	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
527	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
528	#435	C₂²×C₃₁	1	4	yes	complemented
529	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
530	#432	C₂²×C₃₁	1	2	yes	complemented
531	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#418	C₂²×C₃₁	1	4	yes	complemented
533	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
534	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
535	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
536	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
537	C₂×C₃₁	—	2	4	no	—
538	C₂×C₃₁	—	4	1	no	—
539	C₂×C₃₁	—	8	1	no	—
540	C₂×C₃₁	—	8	2	no	—
541	C₂×C₃₁	—	8	4	no	—
542	C₂×C₃₁	#3500	1	1	yes	characteristic
543	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
544	C₂×C₃₁	#3585	1	1	yes	characteristic
545	H(5,𝔽₂)	—	4	8	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
551	C₂²×D₄	—	2	4	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	2	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
558	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
561	C₂×D₈	C₂³×C₃₁	1	2	yes	—
562	C₂×D₈	C₂³×C₃₁	1	4	yes	—
563	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
564	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
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	#127	—	2	2	no	—
570	#127	—	2	1	no	—
571	#127	—	2	1	no	—
572	#127	—	2	2	no	—
573	#127	C₂³×C₃₁	1	1	yes	characteristic
574	#127	C₂³×C₃₁	1	2	yes	—
575	#127	C₂³×C₃₁	1	2	yes	—
576	#127	C₂³×C₃₁	1	4	yes	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	1	no	—
581	#125	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	—	2	1	no	—
584	#125	—	2	2	no	—
585	#125	—	2	2	no	—
586	#125	C₂³×C₃₁	1	1	yes	characteristic
587	#125	C₂³×C₃₁	1	2	yes	—
588	#125	C₂³×C₃₁	1	2	yes	—
589	#125	C₂³×C₃₁	1	2	yes	—
590	#124	—	2	2	no	—
591	#124	—	2	1	no	—
592	#124	C₂³×C₃₁	1	1	yes	characteristic
593	#123	—	2	2	no	—
594	#123	—	2	1	no	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	4	no	—
611	#121	—	2	2	no	—
612	#121	—	2	4	no	—
613	#121	C₂³×C₃₁	1	2	yes	—
614	#121	C₂³×C₃₁	1	1	yes	characteristic
615	#121	C₂³×C₃₁	1	4	yes	—
616	#121	C₂³×C₃₁	1	2	yes	—
617	#120	—	2	4	no	—
618	#120	—	2	4	no	—
619	#120	—	2	4	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
625	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
626	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
634	C₄×D₄	D₄×C₃₁	1	2	yes	—
635	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₃₁	1	2	yes	—
637	C₄×D₄	C₂³×C₃₁	1	2	yes	—
638	C₄×D₄	C₂³×C₃₁	1	4	yes	—
639	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₄×D₄	C₂³×C₃₁	1	2	yes	—
641	#117	—	2	2	no	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	D₄×C₃₁	1	1	yes	characteristic
645	#117	D₄×C₃₁	1	2	yes	—
646	#117	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	#107	C₂³×C₃₁	1	2	yes	—
655	#107	C₂³×C₃₁	1	4	yes	—
656	#106	C₂³×C₃₁	1	2	yes	—
657	#106	C₂³×C₃₁	1	4	yes	—
658	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
660	#103	C₂³×C₃₁	1	2	yes	—
661	#102	C₂³×C₃₁	1	2	yes	—
662	#102	C₂³×C₃₁	1	2	yes	—
663	#102	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	4	yes	—
665	#102	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	4	yes	—
667	#102	C₂³×C₃₁	1	4	yes	—
668	#102	C₂³×C₃₁	1	4	yes	—
669	#102	C₂³×C₃₁	1	4	yes	—
670	#102	C₂³×C₃₁	1	4	yes	—
671	#102	C₂³×C₃₁	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
674	#97	C₂³×C₃₁	1	1	yes	characteristic
675	#97	C₂³×C₃₁	1	2	yes	—
676	#97	C₂³×C₃₁	1	4	yes	—
677	#97	C₂³×C₃₁	1	1	yes	characteristic
678	C₄×C₈	C₂³×C₃₁	1	2	yes	—
679	C₃₁	#62576	1	1	yes	characteristic, direct product factor, Sylow
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	4	8	no	—
684	#41	—	4	4	no	—
685	#41	—	4	8	no	—
686	#41	—	4	4	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	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	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	4	8	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	16	no	—
712	C₂×D₄	—	4	8	no	—
713	C₂×D₄	—	8	4	no	—
714	C₂×D₄	—	8	2	no	—
715	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
716	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
718	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
719	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	SD₁₆	—	4	4	no	—
733	SD₁₆	—	4	2	no	—
734	D₈	—	4	4	no	—
735	D₈	—	4	2	no	—
736	M₁₆	—	4	2	no	—
737	C₂×C₈	—	4	4	no	—
738	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
739	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
740	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	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	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
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	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
781	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	1	no	—
786	C₄²	C₂×D₄×C₃₁	1	2	yes	—
787	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₄²	C₂×D₄×C₃₁	1	2	yes	—
790	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₄²	C₂⁴×C₃₁	1	2	yes	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	4	8	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	2	no	—
800	C₂³	—	8	4	no	—
801	C₂³	—	8	2	no	—
802	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
803	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	1	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	8	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	4	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	1	no	—
829	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	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	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
856	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
857	C₈	—	2	2	no	—
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	16	8	no	—
875	C₂²	—	16	4	no	—
876	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
877	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
892	C₄	C₃₁×#585	1	2	yes	—
893	C₂	—	2	4	no	—
894	C₂	—	4	1	no	—
895	C₂	—	8	2	no	—
896	C₂	—	8	4	no	—
897	C₂	—	8	1	no	—
898	C₂	C₃₁×#3500	1	1	yes	characteristic
899	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
900	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×#3515	C₂	semidirect
2. C₃₁×#3498	C₂	semidirect
3. C₃₁×#3368	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3318	C₂	semidirect
6. C₃₁×#3310	C₂	semidirect
7. C₃₁×#3295	C₂	semidirect
8. C₃₁×#3294	C₂	semidirect
9. C₃₁×#3235	C₂	semidirect
10. C₃₁×#3234	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3217	C₂	semidirect
13. C₃₁×#3180	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3138	C₂	semidirect
16. C₂×C₃₁×#490	C₂	semidirect
17. C₃₁×#2970	C₂	semidirect
19. C₃₁×#557	C₂²	semidirect
20. C₃₁×#554	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
22. C₃₁×#553	C₂²	semidirect
25. C₃₁×#552	C₂²	semidirect
29. C₃₁×#547	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
43. C₃₁×#529	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
45. C₂×C₃₁×#125	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
51. C₃₁×#496	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#490	C₂²	semidirect
54. C₃₁×#490	C₂²	semidirect
55. C₃₁×#490	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#490	C₂²	semidirect
58. C₃₁×#490	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#486	C₂²	semidirect
61. C₃₁×#486	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#480	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#476	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#469	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
71. C₃₁×#466	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#460	C₂²	semidirect
74. C₃₁×#460	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#450	C₂²	semidirect
78. C₃₁×#450	C₂²	semidirect
79. C₃₁×#447	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#446	C₂²	semidirect
82. C₃₁×#442	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
86. C₃₁×#435	C₂²	semidirect
87. C₈×D₄×C₃₁	C₂²	semidirect
88. C₃₁×#432	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#418	C₂²	semidirect
91. C₂×C₃₁×#102	C₂²	semidirect
92. C₂×C₃₁×#102	C₂²	semidirect
93. C₄×M₁₆×C₃₁	C₂²	semidirect
94. C₂×C₃₁×#97	C₂²	semidirect
342. #62576	C₃₁	direct (N × H)
410. #3515	C₂×C₃₁	semidirect
411. #3498	C₂×C₃₁	semidirect
412. #3368	C₂×C₃₁	semidirect
413. #3366	C₂×C₃₁	semidirect
414. #3318	C₂×C₃₁	semidirect
415. #3310	C₂×C₃₁	semidirect
416. #3295	C₂×C₃₁	semidirect
417. #3294	C₂×C₃₁	semidirect
418. #3235	C₂×C₃₁	semidirect
419. #3234	C₂×C₃₁	semidirect
420. #3217	C₂×C₃₁	semidirect
421. #3217	C₂×C₃₁	semidirect
422. #3180	C₂×C₃₁	semidirect
423. #3171	C₂×C₃₁	semidirect
424. #3138	C₂×C₃₁	semidirect
425. C₂×#490	C₂×C₃₁	semidirect
426. #2970	C₂×C₃₁	semidirect
461. #557	C₂²×C₃₁	semidirect
462. #554	C₂²×C₃₁	semidirect
463. #554	C₂²×C₃₁	semidirect
464. #553	C₂²×C₃₁	semidirect
467. #552	C₂²×C₃₁	semidirect
471. #547	C₂²×C₃₁	semidirect
480. #533	C₂²×C₃₁	semidirect
485. #529	C₂²×C₃₁	semidirect
486. #529	C₂²×C₃₁	semidirect
487. C₂×#125	C₂²×C₃₁	semidirect
490. #501	C₂²×C₃₁	semidirect
491. #501	C₂²×C₃₁	semidirect
492. #496	C₂²×C₃₁	semidirect
493. #496	C₂²×C₃₁	semidirect
494. #490	C₂²×C₃₁	semidirect
495. #490	C₂²×C₃₁	semidirect
496. #490	C₂²×C₃₁	semidirect
497. #490	C₂²×C₃₁	semidirect
498. #490	C₂²×C₃₁	semidirect
499. #490	C₂²×C₃₁	semidirect
500. #490	C₂²×C₃₁	semidirect
501. #489	C₂²×C₃₁	semidirect
502. #486	C₂²×C₃₁	semidirect
503. #486	C₂²×C₃₁	semidirect
504. #482	C₂²×C₃₁	semidirect
505. #481	C₂²×C₃₁	semidirect
506. #480	C₂²×C₃₁	semidirect
507. #478	C₂²×C₃₁	semidirect
508. #478	C₂²×C₃₁	semidirect
509. #476	C₂²×C₃₁	semidirect
510. #474	C₂²×C₃₁	semidirect
511. #469	C₂²×C₃₁	semidirect
512. #468	C₂²×C₃₁	semidirect
513. #466	C₂²×C₃₁	semidirect
514. #465	C₂²×C₃₁	semidirect
515. #460	C₂²×C₃₁	semidirect
516. #460	C₂²×C₃₁	semidirect
517. #459	C₂²×C₃₁	semidirect
518. #459	C₂²×C₃₁	semidirect
519. #450	C₂²×C₃₁	semidirect
520. #450	C₂²×C₃₁	semidirect
521. #447	C₂²×C₃₁	semidirect
522. #447	C₂²×C₃₁	semidirect
523. #446	C₂²×C₃₁	semidirect
524. #442	C₂²×C₃₁	semidirect
525. #440	C₂²×C₃₁	semidirect
526. C₄×SD₁₆	C₂²×C₃₁	semidirect
527. C₄×D₈	C₂²×C₃₁	semidirect
528. #435	C₂²×C₃₁	semidirect
529. C₈×D₄	C₂²×C₃₁	semidirect
530. #432	C₂²×C₃₁	semidirect
531. #432	C₂²×C₃₁	semidirect
532. #418	C₂²×C₃₁	semidirect
533. C₂×#102	C₂²×C₃₁	semidirect
534. C₂×#102	C₂²×C₃₁	semidirect
535. C₄×M₁₆	C₂²×C₃₁	semidirect
536. C₂×#97	C₂²×C₃₁	semidirect
679. C₃₁	#62576	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×#3515	2
C₃₁×#3498	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3318	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3235	2
C₃₁×#3234	2
C₃₁×#3217	2
C₃₁×#3180	2
C₃₁×#3171	2
C₃₁×#3138	2
C₂×C₃₁×#490	2
C₃₁×#2970	2
#62576	31

Subgroups — C31×#62576 #21519335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62576 #21519335