Subgroups — C₃₁×#61959 #21518718

Order 7936.

2178 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3272	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3264	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3038	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
21	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#553	—	2	1	no	—
25	C₃₁×#552	—	2	1	no	—
26	C₃₁×#552	C₂²	1	2	yes	complemented
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#550	—	2	1	no	—
29	C₃₁×#550	C₂²	1	2	yes	complemented
30	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#546	C₂²	1	2	yes	complemented
32	D₄²×C₃₁	—	2	1	no	—
33	D₄²×C₃₁	—	2	2	no	—
34	D₄²×C₃₁	C₂²	1	4	yes	—
35	D₄²×C₃₁	C₂²	1	2	yes	complemented
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	complemented
41	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₃₁×#525	—	2	1	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃₁×#117	—	2	1	no	—
50	C₃₁×#496	C₂²	1	4	yes	complemented
51	C₃₁×#492	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#482	C₂²	1	4	yes	complemented
55	C₃₁×#480	C₂²	1	2	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#476	C₂²	1	2	yes	complemented
58	C₃₁×#475	C₂²	1	2	yes	complemented
59	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#469	C₂²	1	4	yes	complemented
62	C₃₁×#468	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#461	C₂²	1	2	yes	complemented
66	C₃₁×#460	C₂²	1	2	yes	complemented
67	C₃₁×#460	C₂²	1	4	yes	complemented
68	C₃₁×#460	C₂²	1	2	yes	complemented
69	C₃₁×#460	C₂²	1	2	yes	complemented
70	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#459	C₂²	1	4	yes	complemented
73	C₃₁×#459	C₂²	1	2	yes	complemented
74	C₃₁×#459	C₂²	1	2	yes	complemented
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#450	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	4	yes	complemented
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	2	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#442	C₂²	1	4	yes	complemented
84	C₃₁×#440	C₂²	1	4	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#436	C₂²	1	2	yes	complemented
88	C₃₁×#435	C₂²	1	4	yes	complemented
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#418	C₂²	1	4	yes	complemented
94	C₂×C₃₁×#102	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	D₄	1	1	yes	characteristic
100	C₂×#41×C₃₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₃₁	—	2	4	no	—
102	C₂²×D₄×C₃₁	—	2	2	no	—
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	—	2	2	no	—
105	C₂²×D₄×C₃₁	—	2	1	no	—
106	C₂²×D₄×C₃₁	—	2	2	no	—
107	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
110	C₂³×C₄×C₃₁	—	2	1	no	—
111	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
112	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
115	C₂×D₈×C₃₁	—	4	4	no	—
116	C₂×D₈×C₃₁	C₂³	1	2	yes	—
117	C₂×D₈×C₃₁	C₂³	1	4	yes	—
118	C₂×D₈×C₃₁	C₂³	1	2	yes	—
119	C₂×D₈×C₃₁	C₂³	1	4	yes	—
120	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
121	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃₁×#127	—	2	1	no	—
126	C₃₁×#127	—	2	1	no	—
127	C₃₁×#127	—	2	2	no	—
128	C₃₁×#127	—	2	2	no	—
129	C₃₁×#127	C₂³	1	2	yes	—
130	C₃₁×#127	C₂³	1	1	yes	characteristic
131	C₃₁×#127	C₂³	1	2	yes	—
132	C₃₁×#127	C₂³	1	4	yes	—
133	C₃₁×#126	—	2	2	no	—
134	C₃₁×#126	—	2	2	no	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#125	—	2	2	no	—
137	C₃₁×#125	—	2	1	no	—
138	C₃₁×#125	C₂³	1	2	yes	—
139	C₃₁×#124	—	2	2	no	—
140	C₃₁×#124	—	2	1	no	—
141	C₃₁×#124	—	2	2	no	—
142	C₃₁×#124	C₂³	1	2	yes	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	1	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	—	2	4	no	—
160	C₃₁×#121	—	2	2	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	C₂³	1	2	yes	—
163	C₃₁×#121	C₂³	1	2	yes	—
164	C₃₁×#121	C₂³	1	4	yes	—
165	C₃₁×#120	—	2	2	no	—
166	C₃₁×#120	—	2	4	no	—
167	C₃₁×#120	—	2	4	no	—
168	C₃₁×#120	—	2	4	no	—
169	C₄×Q₈×C₃₁	—	2	1	no	—
170	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	2	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	1	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	D₄	1	2	yes	—
182	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	4	yes	—
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	—	2	1	no	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	—	2	2	no	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	2	yes	—
211	C₃₁×#106	C₂³	1	4	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	2	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃₁×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	2	yes	—
231	C₂⁴×C₃₁	—	2	1	no	—
232	C₂⁴×C₃₁	—	2	4	no	—
233	C₂⁴×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	2	4	no	—
235	#41×C₃₁	—	2	4	no	—
236	#41×C₃₁	—	4	2	no	—
237	#41×C₃₁	—	4	8	no	—
238	#41×C₃₁	—	4	8	no	—
239	#41×C₃₁	—	4	4	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	1	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	2	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	2	no	—
258	C₂×D₄×C₃₁	—	2	4	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	4	1	no	—
261	C₂×D₄×C₃₁	—	4	2	no	—
262	C₂×D₄×C₃₁	—	4	4	no	—
263	C₂×D₄×C₃₁	—	4	2	no	—
264	C₂×D₄×C₃₁	—	4	4	no	—
265	C₂×D₄×C₃₁	—	4	8	no	—
266	C₂×D₄×C₃₁	—	4	16	no	—
267	C₂×D₄×C₃₁	—	4	8	no	—
268	C₂×D₄×C₃₁	—	4	4	no	—
269	C₂×D₄×C₃₁	—	8	2	no	—
270	C₂×D₄×C₃₁	—	8	4	no	—
271	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
274	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	—	2	1	no	—
278	C₂²×C₄×C₃₁	—	2	1	no	—
279	C₂²×C₄×C₃₁	—	2	2	no	—
280	C₂²×C₄×C₃₁	—	2	1	no	—
281	C₂²×C₄×C₃₁	—	2	1	no	—
282	C₂²×C₄×C₃₁	—	2	1	no	—
283	C₂²×C₄×C₃₁	—	2	4	no	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	4	4	no	—
287	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	SD₁₆×C₃₁	—	4	4	no	—
294	SD₁₆×C₃₁	—	4	4	no	—
295	SD₁₆×C₃₁	—	4	4	no	—
296	D₈×C₃₁	—	2	8	no	—
297	D₈×C₃₁	—	2	4	no	—
298	D₈×C₃₁	—	4	4	no	—
299	D₈×C₃₁	—	4	2	no	—
300	M₁₆×C₃₁	—	4	4	no	—
301	C₂×C₈×C₃₁	—	4	2	no	—
302	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
303	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₃₁	—	2	1	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	1	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	1	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	1	no	—
316	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	1	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	1	no	—
331	C₂²⋊C₄×C₃₁	—	2	1	no	—
332	C₂²⋊C₄×C₃₁	—	2	1	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	4	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	2	no	—
337	C₂²⋊C₄×C₃₁	—	2	4	no	—
338	C₂²⋊C₄×C₃₁	—	2	2	no	—
339	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	2	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	C₂×D₄	1	2	yes	—
346	C₄²×C₃₁	C₂×D₄	1	2	yes	—
347	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₄²×C₃₁	C₂⁴	1	2	yes	—
351	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
352	#61959	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	1	no	—
355	C₂³×C₃₁	—	2	4	no	—
356	C₂³×C₃₁	—	2	2	no	—
357	C₂³×C₃₁	—	4	2	no	—
358	C₂³×C₃₁	—	4	8	no	—
359	C₂³×C₃₁	—	4	2	no	—
360	C₂³×C₃₁	—	4	4	no	—
361	C₂³×C₃₁	—	8	1	no	—
362	C₂³×C₃₁	—	8	2	no	—
363	C₂³×C₃₁	—	8	4	no	—
364	C₂³×C₃₁	—	8	2	no	—
365	C₂³×C₃₁	—	8	4	no	—
366	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
367	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₃₁	—	2	2	no	—
369	Q₈×C₃₁	—	2	2	no	—
370	Q₈×C₃₁	—	2	2	no	—
371	Q₈×C₃₁	—	4	2	no	—
372	Q₈×C₃₁	—	8	1	no	—
373	D₄×C₃₁	—	2	4	no	—
374	D₄×C₃₁	—	2	2	no	—
375	D₄×C₃₁	—	2	4	no	—
376	D₄×C₃₁	—	2	2	no	—
377	D₄×C₃₁	—	2	1	no	—
378	D₄×C₃₁	—	2	1	no	—
379	D₄×C₃₁	—	2	1	no	—
380	D₄×C₃₁	—	2	2	no	—
381	D₄×C₃₁	—	2	4	no	—
382	D₄×C₃₁	—	4	2	no	—
383	D₄×C₃₁	—	4	8	no	—
384	D₄×C₃₁	—	4	2	no	—
385	D₄×C₃₁	—	4	4	no	—
386	D₄×C₃₁	—	4	4	no	—
387	D₄×C₃₁	—	4	8	no	—
388	D₄×C₃₁	—	4	4	no	—
389	D₄×C₃₁	—	4	2	no	—
390	D₄×C₃₁	—	4	4	no	—
391	D₄×C₃₁	—	4	4	no	—
392	D₄×C₃₁	—	8	4	no	—
393	D₄×C₃₁	—	8	2	no	—
394	D₄×C₃₁	—	8	4	no	—
395	D₄×C₃₁	—	8	2	no	—
396	D₄×C₃₁	—	8	2	no	—
397	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	complemented
398	C₂×C₄×C₃₁	—	2	4	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	4	2	no	—
409	C₂×C₄×C₃₁	—	4	1	no	—
410	C₂×C₄×C₃₁	—	4	4	no	—
411	C₂×C₄×C₃₁	—	4	8	no	—
412	C₂×C₄×C₃₁	—	4	2	no	—
413	C₂×C₄×C₃₁	—	4	2	no	—
414	C₂×C₄×C₃₁	—	4	2	no	—
415	C₂×C₄×C₃₁	—	4	2	no	—
416	C₂×C₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
420	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
429	C₈×C₃₁	—	2	4	no	—
430	C₈×C₃₁	—	2	2	no	—
431	C₈×C₃₁	—	2	2	no	—
432	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
433	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3397	C₂×C₃₁	1	2	yes	complemented
435	#3366	C₂×C₃₁	1	2	yes	complemented
436	#3325	C₂×C₃₁	1	2	yes	complemented
437	#3310	C₂×C₃₁	1	4	yes	complemented
438	#3272	C₂×C₃₁	1	2	yes	complemented
439	#3264	C₂×C₃₁	1	4	yes	complemented
440	#3251	C₂×C₃₁	1	2	yes	complemented
441	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#3217	C₂×C₃₁	1	2	yes	complemented
443	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#3115	C₂×C₃₁	1	2	yes	complemented
445	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3038	C₂×C₃₁	1	2	yes	complemented
447	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
449	C₂²×C₃₁	—	2	1	no	—
450	C₂²×C₃₁	—	2	1	no	—
451	C₂²×C₃₁	—	2	2	no	—
452	C₂²×C₃₁	—	2	2	no	—
453	C₂²×C₃₁	—	2	2	no	—
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	4	1	no	—
456	C₂²×C₃₁	—	4	1	no	—
457	C₂²×C₃₁	—	4	4	no	—
458	C₂²×C₃₁	—	4	2	no	—
459	C₂²×C₃₁	—	4	1	no	—
460	C₂²×C₃₁	—	4	1	no	—
461	C₂²×C₃₁	—	4	4	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	4	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	8	4	no	—
467	C₂²×C₃₁	—	16	4	no	—
468	C₂²×C₃₁	—	16	8	no	—
469	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
470	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
471	C₄×C₃₁	—	2	1	no	—
472	C₄×C₃₁	—	2	2	no	—
473	C₄×C₃₁	—	2	1	no	—
474	C₄×C₃₁	—	2	2	no	—
475	C₄×C₃₁	—	2	1	no	—
476	C₄×C₃₁	—	2	2	no	—
477	C₄×C₃₁	—	4	2	no	—
478	C₄×C₃₁	—	4	2	no	—
479	C₄×C₃₁	—	4	1	no	—
480	C₄×C₃₁	—	4	1	no	—
481	C₄×C₃₁	—	4	2	no	—
482	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
483	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
484	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₄×C₃₁	#585	1	1	yes	characteristic
486	C₂×H(5,𝔽₂)	—	2	1	no	—
487	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
488	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
489	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
490	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
491	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
492	#553	—	2	1	no	—
493	#552	—	2	1	no	—
494	#552	C₂²×C₃₁	1	2	yes	complemented
495	#551	—	2	2	no	—
496	#550	—	2	1	no	—
497	#550	C₂²×C₃₁	1	2	yes	complemented
498	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
499	#546	C₂²×C₃₁	1	2	yes	complemented
500	D₄²	—	2	1	no	—
501	D₄²	—	2	2	no	—
502	D₄²	C₂²×C₃₁	1	4	yes	—
503	D₄²	C₂²×C₃₁	1	2	yes	complemented
504	#535	—	2	1	no	—
505	#535	—	2	2	no	—
506	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	#532	C₂²×C₃₁	1	1	yes	characteristic
508	#532	C₂²×C₃₁	1	2	yes	complemented
509	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
511	#529	—	2	2	no	—
512	#529	C₂²×C₃₁	1	2	yes	complemented
513	#525	—	2	1	no	—
514	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
515	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
516	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
517	C₂×#117	—	2	1	no	—
518	#496	C₂²×C₃₁	1	4	yes	complemented
519	#492	C₂²×C₃₁	1	2	yes	complemented
520	#490	C₂²×C₃₁	1	4	yes	complemented
521	#486	C₂²×C₃₁	1	2	yes	complemented
522	#482	C₂²×C₃₁	1	4	yes	complemented
523	#480	C₂²×C₃₁	1	2	yes	complemented
524	#478	C₂²×C₃₁	1	4	yes	complemented
525	#476	C₂²×C₃₁	1	2	yes	complemented
526	#475	C₂²×C₃₁	1	2	yes	complemented
527	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
529	#469	C₂²×C₃₁	1	4	yes	complemented
530	#468	C₂²×C₃₁	1	4	yes	complemented
531	#465	C₂²×C₃₁	1	4	yes	complemented
532	#463	C₂²×C₃₁	1	4	yes	complemented
533	#461	C₂²×C₃₁	1	2	yes	complemented
534	#460	C₂²×C₃₁	1	2	yes	complemented
535	#460	C₂²×C₃₁	1	4	yes	complemented
536	#460	C₂²×C₃₁	1	2	yes	complemented
537	#460	C₂²×C₃₁	1	2	yes	complemented
538	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
539	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
540	#459	C₂²×C₃₁	1	4	yes	complemented
541	#459	C₂²×C₃₁	1	2	yes	complemented
542	#459	C₂²×C₃₁	1	2	yes	complemented
543	#459	C₂²×C₃₁	1	2	yes	complemented
544	#459	C₂²×C₃₁	1	2	yes	complemented
545	#450	C₂²×C₃₁	1	4	yes	complemented
546	#450	C₂²×C₃₁	1	4	yes	complemented
547	#449	C₂²×C₃₁	1	4	yes	complemented
548	#447	C₂²×C₃₁	1	2	yes	complemented
549	#447	C₂²×C₃₁	1	4	yes	complemented
550	#446	C₂²×C₃₁	1	2	yes	complemented
551	#442	C₂²×C₃₁	1	4	yes	complemented
552	#440	C₂²×C₃₁	1	4	yes	complemented
553	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
554	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
555	#436	C₂²×C₃₁	1	2	yes	complemented
556	#435	C₂²×C₃₁	1	4	yes	complemented
557	#432	C₂²×C₃₁	1	2	yes	complemented
558	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#423	C₂²×C₃₁	1	2	yes	complemented
560	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	#418	C₂²×C₃₁	1	4	yes	complemented
562	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
563	C₂×C₃₁	—	2	2	no	—
564	C₂×C₃₁	—	4	2	no	—
565	C₂×C₃₁	—	4	2	no	—
566	C₂×C₃₁	—	8	1	no	—
567	C₂×C₃₁	—	8	4	no	—
568	C₂×C₃₁	—	8	2	no	—
569	C₂×C₃₁	#3488	1	1	yes	characteristic
570	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
571	C₂×C₃₁	#3585	1	1	yes	characteristic
572	H(5,𝔽₂)	—	4	8	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	1	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
577	C₂×#41	C₂³×C₃₁	1	2	yes	—
578	C₂²×D₄	—	2	4	no	—
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	1	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	1	no	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
586	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
587	C₂³×C₄	—	2	1	no	—
588	AGL(1,ℤ/8)	—	4	8	no	—
589	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
590	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
592	C₂×D₈	—	4	4	no	—
593	C₂×D₈	C₂³×C₃₁	1	4	yes	—
594	C₂×D₈	C₂³×C₃₁	1	2	yes	—
595	C₂×D₈	C₂³×C₃₁	1	4	yes	—
596	C₂×D₈	C₂³×C₃₁	1	2	yes	—
597	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
598	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
599	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
602	#127	—	2	1	no	—
603	#127	—	2	1	no	—
604	#127	—	2	2	no	—
605	#127	—	2	2	no	—
606	#127	C₂³×C₃₁	1	2	yes	—
607	#127	C₂³×C₃₁	1	2	yes	—
608	#127	C₂³×C₃₁	1	1	yes	characteristic
609	#127	C₂³×C₃₁	1	4	yes	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	1	no	—
615	#125	C₂³×C₃₁	1	2	yes	—
616	#124	—	2	2	no	—
617	#124	—	2	1	no	—
618	#124	—	2	2	no	—
619	#124	C₂³×C₃₁	1	2	yes	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	C₂²⋊Q₈	—	2	1	no	—
625	C₂²⋊Q₈	—	2	1	no	—
626	C₂²⋊Q₈	—	2	1	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
629	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	1	no	—
633	#121	—	2	2	no	—
634	#121	—	2	2	no	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	#121	—	2	2	no	—
638	#121	—	2	2	no	—
639	#121	C₂³×C₃₁	1	2	yes	—
640	#121	C₂³×C₃₁	1	2	yes	—
641	#121	C₂³×C₃₁	1	4	yes	—
642	#120	—	2	2	no	—
643	#120	—	2	4	no	—
644	#120	—	2	4	no	—
645	#120	—	2	4	no	—
646	C₄×Q₈	—	2	1	no	—
647	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
648	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
649	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
650	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	D₄×C₃₁	1	2	yes	—
659	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
663	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₃₁	1	2	yes	—
665	C₄×D₄	C₂³×C₃₁	1	2	yes	—
666	C₄×D₄	C₂³×C₃₁	1	4	yes	—
667	C₄×D₄	C₂³×C₃₁	1	2	yes	—
668	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
669	#117	—	2	1	no	—
670	#117	—	2	1	no	—
671	#117	—	2	1	no	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	D₄×C₃₁	1	1	yes	characteristic
676	#117	D₄×C₃₁	1	2	yes	—
677	#117	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄⋊C₄	—	2	1	no	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₄²	—	2	2	no	—
684	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
686	#107	C₂³×C₃₁	1	2	yes	—
687	#107	C₂³×C₃₁	1	2	yes	—
688	#106	C₂³×C₃₁	1	4	yes	—
689	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
690	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
691	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
693	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
694	#103	C₂³×C₃₁	1	4	yes	—
695	#102	C₂³×C₃₁	1	4	yes	—
696	#102	C₂³×C₃₁	1	4	yes	—
697	#102	C₂³×C₃₁	1	2	yes	—
698	#102	C₂³×C₃₁	1	4	yes	—
699	#102	C₂³×C₃₁	1	4	yes	—
700	#102	C₂³×C₃₁	1	2	yes	—
701	#102	C₂³×C₃₁	1	2	yes	—
702	#102	C₂³×C₃₁	1	2	yes	—
703	#102	C₂³×C₃₁	1	4	yes	—
704	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
706	#97	C₂³×C₃₁	1	4	yes	—
707	C₄×C₈	C₂³×C₃₁	1	2	yes	—
708	C₃₁	#61959	1	1	yes	characteristic, direct product factor, Sylow
709	C₂⁴	—	2	1	no	—
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	2	2	no	—
712	#41	—	2	4	no	—
713	#41	—	2	4	no	—
714	#41	—	4	2	no	—
715	#41	—	4	8	no	—
716	#41	—	4	8	no	—
717	#41	—	4	4	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	4	16	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	—	8	2	no	—
748	C₂×D₄	—	8	4	no	—
749	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
750	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
752	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
753	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
766	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	SD₁₆	—	4	4	no	—
774	D₈	—	2	8	no	—
775	D₈	—	2	4	no	—
776	D₈	—	4	4	no	—
777	D₈	—	4	2	no	—
778	M₁₆	—	4	4	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
782	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
797	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×D₄×C₃₁	1	2	yes	—
824	C₄²	C₂×D₄×C₃₁	1	2	yes	—
825	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
826	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₄²	C₂⁴×C₃₁	1	2	yes	—
829	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	8	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	4	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	4	no	—
843	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
844	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	Q₈	—	2	2	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	1	no	—
855	D₄	—	2	1	no	—
856	D₄	—	2	1	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	4	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	complemented
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
897	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
905	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
906	C₈	—	2	4	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	4	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	4	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
930	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
943	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
944	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
945	C₄	C₃₁×#585	1	1	yes	characteristic
946	C₂	—	2	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	1	no	—
950	C₂	—	8	4	no	—
951	C₂	—	8	2	no	—
952	C₂	C₃₁×#3488	1	1	yes	characteristic
953	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
954	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×#3498	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3325	C₂	semidirect
6. C₃₁×#3310	C₂	semidirect
7. C₃₁×#3272	C₂	semidirect
8. C₃₁×#3264	C₂	semidirect
9. C₃₁×#3251	C₂	semidirect
10. C₃₁×#3246	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3115	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₂×C₃₁×#459	C₂	semidirect
17. C₃₁×#2989	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×D₈×C₃₁	C₂²	semidirect
21. C₃₁×#556	C₂²	semidirect
22. C₃₁×#555	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
26. C₃₁×#552	C₂²	semidirect
29. C₃₁×#550	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
35. D₄²×C₃₁	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
42. C₂×C₃₁×#127	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
47. C₄×#41×C₃₁	C₂²	semidirect
48. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
51. C₃₁×#492	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
59. C₃₁×#474	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#469	C₂²	semidirect
62. C₃₁×#468	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
66. C₃₁×#460	C₂²	semidirect
67. C₃₁×#460	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
69. C₃₁×#460	C₂²	semidirect
70. C₃₁×#459	C₂²	semidirect
71. C₃₁×#459	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#459	C₂²	semidirect
74. C₃₁×#459	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#450	C₂²	semidirect
78. C₃₁×#450	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#442	C₂²	semidirect
84. C₃₁×#440	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
88. C₃₁×#435	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
93. C₃₁×#418	C₂²	semidirect
94. C₂×C₃₁×#102	C₂²	semidirect
352. #61959	C₃₁	direct (N × H)
397. D₄×C₃₁	H(5,𝔽₂)	semidirect
419. C₂×C₄×C₃₁	AGL(1,ℤ/8)	semidirect
432. #3498	C₂×C₃₁	semidirect
433. #3475	C₂×C₃₁	semidirect
434. #3397	C₂×C₃₁	semidirect
435. #3366	C₂×C₃₁	semidirect
436. #3325	C₂×C₃₁	semidirect
437. #3310	C₂×C₃₁	semidirect
438. #3272	C₂×C₃₁	semidirect
439. #3264	C₂×C₃₁	semidirect
440. #3251	C₂×C₃₁	semidirect
441. #3246	C₂×C₃₁	semidirect
442. #3217	C₂×C₃₁	semidirect
443. #3208	C₂×C₃₁	semidirect
444. #3115	C₂×C₃₁	semidirect
445. #3100	C₂×C₃₁	semidirect
446. #3038	C₂×C₃₁	semidirect
447. C₂×#459	C₂×C₃₁	semidirect
448. #2989	C₂×C₃₁	semidirect
487. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
488. C₂²×D₈	C₂²×C₃₁	semidirect
489. #556	C₂²×C₃₁	semidirect
490. #555	C₂²×C₃₁	semidirect
491. #554	C₂²×C₃₁	semidirect
494. #552	C₂²×C₃₁	semidirect
497. #550	C₂²×C₃₁	semidirect
498. #547	C₂²×C₃₁	semidirect
499. #546	C₂²×C₃₁	semidirect
503. D₄²	C₂²×C₃₁	semidirect
506. #533	C₂²×C₃₁	semidirect
508. #532	C₂²×C₃₁	semidirect
510. C₂×#127	C₂²×C₃₁	semidirect
512. #529	C₂²×C₃₁	semidirect
515. C₄×#41	C₂²×C₃₁	semidirect
516. C₂×C₄×D₄	C₂²×C₃₁	semidirect
518. #496	C₂²×C₃₁	semidirect
519. #492	C₂²×C₃₁	semidirect
520. #490	C₂²×C₃₁	semidirect
521. #486	C₂²×C₃₁	semidirect
522. #482	C₂²×C₃₁	semidirect
523. #480	C₂²×C₃₁	semidirect
524. #478	C₂²×C₃₁	semidirect
525. #476	C₂²×C₃₁	semidirect
526. #475	C₂²×C₃₁	semidirect
527. #474	C₂²×C₃₁	semidirect
528. #474	C₂²×C₃₁	semidirect
529. #469	C₂²×C₃₁	semidirect
530. #468	C₂²×C₃₁	semidirect
531. #465	C₂²×C₃₁	semidirect
532. #463	C₂²×C₃₁	semidirect
533. #461	C₂²×C₃₁	semidirect
534. #460	C₂²×C₃₁	semidirect
535. #460	C₂²×C₃₁	semidirect
536. #460	C₂²×C₃₁	semidirect
537. #460	C₂²×C₃₁	semidirect
538. #459	C₂²×C₃₁	semidirect
539. #459	C₂²×C₃₁	semidirect
540. #459	C₂²×C₃₁	semidirect
541. #459	C₂²×C₃₁	semidirect
542. #459	C₂²×C₃₁	semidirect
543. #459	C₂²×C₃₁	semidirect
544. #459	C₂²×C₃₁	semidirect
545. #450	C₂²×C₃₁	semidirect
546. #450	C₂²×C₃₁	semidirect
547. #449	C₂²×C₃₁	semidirect
548. #447	C₂²×C₃₁	semidirect
549. #447	C₂²×C₃₁	semidirect
550. #446	C₂²×C₃₁	semidirect
551. #442	C₂²×C₃₁	semidirect
552. #440	C₂²×C₃₁	semidirect
553. C₄×D₈	C₂²×C₃₁	semidirect
554. C₄×D₈	C₂²×C₃₁	semidirect
555. #436	C₂²×C₃₁	semidirect
556. #435	C₂²×C₃₁	semidirect
557. #432	C₂²×C₃₁	semidirect
558. #431	C₂²×C₃₁	semidirect
559. #423	C₂²×C₃₁	semidirect
560. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
561. #418	C₂²×C₃₁	semidirect
562. C₂×#102	C₂²×C₃₁	semidirect
708. C₃₁	#61959	direct (N × H)
874. D₄	C₃₁×H(5,𝔽₂)	semidirect
896. C₂×C₄	C₃₁×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3498	2
C₃₁×#3475	2
C₃₁×#3397	2
C₃₁×#3366	2
C₃₁×#3325	2
C₃₁×#3310	2
C₃₁×#3272	2
C₃₁×#3264	2
C₃₁×#3251	2
C₃₁×#3246	2
C₃₁×#3217	2
C₃₁×#3208	2
C₃₁×#3115	2
C₃₁×#3100	2
C₃₁×#3038	2
C₂×C₃₁×#459	2
C₃₁×#2989	2
#61959	31

Subgroups — C31×#61959 #21518718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61959 #21518718