Subgroups — C₃₁×#61983 #21518742

Order 7936.

2164 conjugacy classes of subgroups.

The subgroup lattice has 938 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×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3310	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3265	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3112	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#460	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	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	2	yes	complemented
20	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
21	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#556	—	2	1	no	—
23	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#552	—	2	2	no	—
25	C₃₁×#552	C₂²	1	2	yes	complemented
26	C₃₁×#550	—	2	1	no	—
27	C₃₁×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#548	C₂²	1	2	yes	complemented
30	C₃₁×#547	—	2	1	no	—
31	C₃₁×#547	C₂²	1	1	yes	characteristic, 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	—
36	C₃₁×#535	—	2	2	no	—
37	C₃₁×#535	—	2	1	no	—
38	C₃₁×#533	—	2	1	no	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#127	C₂²	1	2	yes	—
44	C₃₁×#529	—	2	2	no	—
45	C₃₁×#529	C₂²	1	2	yes	complemented
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
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	2	yes	complemented
55	C₃₁×#480	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	2	yes	complemented
59	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#474	C₂²	1	2	yes	complemented
61	C₃₁×#468	C₂²	1	4	yes	complemented
62	C₃₁×#466	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	1	yes	characteristic, complemented
67	C₃₁×#460	C₂²	1	2	yes	complemented
68	C₃₁×#460	C₂²	1	2	yes	complemented
69	C₃₁×#460	C₂²	1	4	yes	complemented
70	C₃₁×#460	C₂²	1	2	yes	complemented
71	C₃₁×#460	C₂²	1	4	yes	complemented
72	C₃₁×#460	C₂²	1	2	yes	complemented
73	C₃₁×#460	C₂²	1	2	yes	complemented
74	C₃₁×#459	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
80	C₃₁×#448	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₃₁×#440	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#418	C₂²	1	2	yes	complemented
94	C₂×C₃₁×#102	C₂²	1	4	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	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
103	C₂²×D₄×C₃₁	—	2	4	no	—
104	C₂²×D₄×C₃₁	—	2	2	no	—
105	C₂²×D₄×C₃₁	—	2	2	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	2	no	—
108	C₂²×D₄×C₃₁	—	2	1	no	—
109	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
112	C₂×SD₁₆×C₃₁	—	4	8	no	—
113	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×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	2	yes	—
121	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
122	C₃₁×C₄⋊Q₈	—	2	1	no	—
123	C₃₁×C₄⋊Q₈	—	2	1	no	—
124	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃₁×#127	—	2	1	no	—
128	C₃₁×#127	—	2	2	no	—
129	C₃₁×#127	—	2	1	no	—
130	C₃₁×#127	—	2	2	no	—
131	C₃₁×#127	C₂³	1	1	yes	characteristic
132	C₃₁×#127	C₂³	1	2	yes	—
133	C₃₁×#127	C₂³	1	2	yes	—
134	C₃₁×#127	C₂³	1	4	yes	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#126	—	2	2	no	—
137	C₃₁×#126	—	2	2	no	—
138	C₃₁×#125	—	2	2	no	—
139	C₃₁×#125	—	2	2	no	—
140	C₃₁×#125	—	2	1	no	—
141	C₃₁×#125	C₂³	1	2	yes	—
142	C₃₁×#124	—	2	2	no	—
143	C₃₁×#124	—	2	1	no	—
144	C₃₁×#124	—	2	2	no	—
145	C₃₁×#124	C₂³	1	2	yes	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×#123	—	2	2	no	—
148	C₃₁×#123	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	1	no	—
150	C₃₁×C₂²⋊Q₈	—	2	1	no	—
151	C₃₁×C₂²⋊Q₈	—	2	1	no	—
152	C₃₁×C₂²⋊Q₈	—	2	2	no	—
153	C₃₁×C₂²⋊Q₈	—	2	2	no	—
154	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
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	4	no	—
162	C₃₁×#121	—	2	2	no	—
163	C₃₁×#121	C₂³	1	2	yes	—
164	C₃₁×#121	C₂³	1	4	yes	—
165	C₃₁×#121	C₂³	1	2	yes	—
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	—	2	2	no	—
171	C₄×Q₈×C₃₁	—	2	2	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	2	yes	—
177	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
179	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	1	no	—
183	C₄×D₄×C₃₁	—	2	1	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	1	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₃₁	D₄	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	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	1	yes	characteristic
193	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₃₁	C₂³	1	2	yes	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	1	no	—
197	C₃₁×#117	—	2	2	no	—
198	C₃₁×#117	—	2	1	no	—
199	C₃₁×#117	—	2	2	no	—
200	C₃₁×#117	D₄	1	2	yes	—
201	C₃₁×#117	D₄	1	1	yes	characteristic
202	C₃₁×#117	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
204	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	—	2	1	no	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	4	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	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	2	no	—
232	C₂⁴×C₃₁	—	2	4	no	—
233	#41×C₃₁	—	2	4	no	—
234	#41×C₃₁	—	2	2	no	—
235	#41×C₃₁	—	4	1	no	—
236	#41×C₃₁	—	4	8	no	—
237	#41×C₃₁	—	4	4	no	—
238	#41×C₃₁	—	4	8	no	—
239	#41×C₃₁	—	4	4	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	—	2	1	no	—
243	C₂×Q₈×C₃₁	—	2	4	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	4	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	4	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	—	2	4	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	2	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	2	no	—
266	C₂×D₄×C₃₁	—	4	8	no	—
267	C₂×D₄×C₃₁	—	4	4	no	—
268	C₂×D₄×C₃₁	—	4	16	no	—
269	C₂×D₄×C₃₁	—	4	8	no	—
270	C₂×D₄×C₃₁	—	8	4	no	—
271	C₂×D₄×C₃₁	—	8	2	no	—
272	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
275	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	2	1	no	—
280	C₂²×C₄×C₃₁	—	2	1	no	—
281	C₂²×C₄×C₃₁	—	2	1	no	—
282	C₂²×C₄×C₃₁	—	2	4	no	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	SD₁₆×C₃₁	—	2	4	no	—
291	SD₁₆×C₃₁	—	2	8	no	—
292	SD₁₆×C₃₁	—	4	4	no	—
293	SD₁₆×C₃₁	—	4	4	no	—
294	SD₁₆×C₃₁	—	4	4	no	—
295	D₈×C₃₁	—	4	2	no	—
296	D₈×C₃₁	—	4	4	no	—
297	M₁₆×C₃₁	—	4	2	no	—
298	C₂×C₈×C₃₁	—	4	4	no	—
299	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
300	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
301	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	1	no	—
311	C₄⋊C₄×C₃₁	—	2	1	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	1	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	2	yes	—
318	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	1	no	—
329	C₂²⋊C₄×C₃₁	—	2	1	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	—	2	2	no	—
333	C₂²⋊C₄×C₃₁	—	2	4	no	—
334	C₂²⋊C₄×C₃₁	—	2	4	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	—	2	1	no	—
340	C₄²×C₃₁	—	2	1	no	—
341	C₄²×C₃₁	—	2	2	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	1	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₃₁	C₂×D₄	1	2	yes	—
348	C₄²×C₃₁	C₂×D₄	1	2	yes	—
349	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₄²×C₃₁	C₂⁴	1	2	yes	—
351	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
352	#61983	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	4	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	4	4	no	—
357	C₂³×C₃₁	—	4	8	no	—
358	C₂³×C₃₁	—	8	4	no	—
359	C₂³×C₃₁	—	8	2	no	—
360	C₂³×C₃₁	—	8	4	no	—
361	C₂³×C₃₁	—	8	2	no	—
362	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
364	Q₈×C₃₁	—	2	2	no	—
365	Q₈×C₃₁	—	2	1	no	—
366	Q₈×C₃₁	—	2	2	no	—
367	Q₈×C₃₁	—	2	2	no	—
368	Q₈×C₃₁	—	4	4	no	—
369	Q₈×C₃₁	—	4	2	no	—
370	Q₈×C₃₁	—	4	2	no	—
371	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	complemented
372	D₄×C₃₁	—	2	4	no	—
373	D₄×C₃₁	—	2	1	no	—
374	D₄×C₃₁	—	2	4	no	—
375	D₄×C₃₁	—	2	2	no	—
376	D₄×C₃₁	—	2	1	no	—
377	D₄×C₃₁	—	2	2	no	—
378	D₄×C₃₁	—	2	4	no	—
379	D₄×C₃₁	—	4	2	no	—
380	D₄×C₃₁	—	4	4	no	—
381	D₄×C₃₁	—	4	2	no	—
382	D₄×C₃₁	—	4	8	no	—
383	D₄×C₃₁	—	4	4	no	—
384	D₄×C₃₁	—	4	8	no	—
385	D₄×C₃₁	—	4	4	no	—
386	D₄×C₃₁	—	4	4	no	—
387	D₄×C₃₁	—	4	2	no	—
388	D₄×C₃₁	—	4	4	no	—
389	D₄×C₃₁	—	8	2	no	—
390	D₄×C₃₁	—	8	4	no	—
391	D₄×C₃₁	—	8	4	no	—
392	D₄×C₃₁	—	8	2	no	—
393	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
394	C₂×C₄×C₃₁	—	2	4	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	4	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	1	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	4	2	no	—
409	C₂×C₄×C₃₁	—	4	4	no	—
410	C₂×C₄×C₃₁	—	4	8	no	—
411	C₂×C₄×C₃₁	—	4	4	no	—
412	C₂×C₄×C₃₁	—	4	4	no	—
413	C₂×C₄×C₃₁	—	4	2	no	—
414	C₂×C₄×C₃₁	—	4	2	no	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
424	C₈×C₃₁	—	2	2	no	—
425	C₈×C₃₁	—	2	4	no	—
426	C₈×C₃₁	—	2	2	no	—
427	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#3397	C₂×C₃₁	1	2	yes	complemented
430	#3368	C₂×C₃₁	1	2	yes	complemented
431	#3310	C₂×C₃₁	1	4	yes	complemented
432	#3294	C₂×C₃₁	1	2	yes	complemented
433	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
434	#3265	C₂×C₃₁	1	4	yes	complemented
435	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#3247	C₂×C₃₁	1	2	yes	complemented
437	#3217	C₂×C₃₁	1	2	yes	complemented
438	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#3112	C₂×C₃₁	1	2	yes	complemented
440	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
442	C₂×#460	C₂×C₃₁	1	2	yes	complemented
443	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
444	C₂²×C₃₁	—	2	2	no	—
445	C₂²×C₃₁	—	2	2	no	—
446	C₂²×C₃₁	—	2	1	no	—
447	C₂²×C₃₁	—	2	1	no	—
448	C₂²×C₃₁	—	2	1	no	—
449	C₂²×C₃₁	—	4	1	no	—
450	C₂²×C₃₁	—	4	4	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	4	no	—
453	C₂²×C₃₁	—	4	2	no	—
454	C₂²×C₃₁	—	4	1	no	—
455	C₂²×C₃₁	—	4	1	no	—
456	C₂²×C₃₁	—	4	2	no	—
457	C₂²×C₃₁	—	4	4	no	—
458	C₂²×C₃₁	—	16	8	no	—
459	C₂²×C₃₁	—	16	4	no	—
460	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
461	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	2	no	—
465	C₄×C₃₁	—	2	1	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	1	no	—
469	C₄×C₃₁	—	4	2	no	—
470	C₄×C₃₁	—	4	1	no	—
471	C₄×C₃₁	—	4	2	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	1	no	—
474	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
475	C₄×C₃₁	#577	1	2	yes	—
476	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₄×C₃₁	#585	1	1	yes	characteristic
478	C₂×H(5,𝔽₂)	—	2	1	no	—
479	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
480	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
481	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	#556	—	2	1	no	—
483	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
484	#552	—	2	2	no	—
485	#552	C₂²×C₃₁	1	2	yes	complemented
486	#550	—	2	1	no	—
487	#550	C₂²×C₃₁	1	2	yes	—
488	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#548	C₂²×C₃₁	1	2	yes	complemented
490	#547	—	2	1	no	—
491	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
492	D₄²	—	2	1	no	—
493	D₄²	—	2	2	no	—
494	D₄²	C₂²×C₃₁	1	4	yes	—
495	D₄²	C₂²×C₃₁	1	2	yes	—
496	#535	—	2	2	no	—
497	#535	—	2	1	no	—
498	#533	—	2	1	no	—
499	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#532	C₂²×C₃₁	1	1	yes	characteristic
501	#532	C₂²×C₃₁	1	2	yes	—
502	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#127	C₂²×C₃₁	1	2	yes	—
504	#529	—	2	2	no	—
505	#529	C₂²×C₃₁	1	2	yes	complemented
506	C₄×#41	—	2	1	no	—
507	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
508	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
509	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
510	#496	C₂²×C₃₁	1	4	yes	complemented
511	#492	C₂²×C₃₁	1	2	yes	complemented
512	#490	C₂²×C₃₁	1	4	yes	complemented
513	#486	C₂²×C₃₁	1	2	yes	complemented
514	#482	C₂²×C₃₁	1	2	yes	complemented
515	#480	C₂²×C₃₁	1	4	yes	complemented
516	#478	C₂²×C₃₁	1	4	yes	complemented
517	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	#477	C₂²×C₃₁	1	2	yes	complemented
519	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#474	C₂²×C₃₁	1	2	yes	complemented
521	#468	C₂²×C₃₁	1	4	yes	complemented
522	#466	C₂²×C₃₁	1	4	yes	complemented
523	#465	C₂²×C₃₁	1	4	yes	complemented
524	#463	C₂²×C₃₁	1	4	yes	complemented
525	#461	C₂²×C₃₁	1	2	yes	complemented
526	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
527	#460	C₂²×C₃₁	1	2	yes	complemented
528	#460	C₂²×C₃₁	1	2	yes	complemented
529	#460	C₂²×C₃₁	1	4	yes	complemented
530	#460	C₂²×C₃₁	1	2	yes	complemented
531	#460	C₂²×C₃₁	1	4	yes	complemented
532	#460	C₂²×C₃₁	1	2	yes	complemented
533	#460	C₂²×C₃₁	1	2	yes	complemented
534	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
535	#459	C₂²×C₃₁	1	2	yes	complemented
536	#459	C₂²×C₃₁	1	2	yes	complemented
537	#450	C₂²×C₃₁	1	4	yes	complemented
538	#450	C₂²×C₃₁	1	4	yes	complemented
539	#449	C₂²×C₃₁	1	2	yes	complemented
540	#448	C₂²×C₃₁	1	4	yes	complemented
541	#447	C₂²×C₃₁	1	4	yes	complemented
542	#446	C₂²×C₃₁	1	2	yes	complemented
543	#440	C₂²×C₃₁	1	4	yes	complemented
544	#440	C₂²×C₃₁	1	4	yes	complemented
545	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
546	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
547	#435	C₂²×C₃₁	1	4	yes	complemented
548	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
549	#432	C₂²×C₃₁	1	2	yes	complemented
550	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
552	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
553	#418	C₂²×C₃₁	1	2	yes	complemented
554	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
555	C₂×C₃₁	—	2	4	no	—
556	C₂×C₃₁	—	4	1	no	—
557	C₂×C₃₁	—	8	1	no	—
558	C₂×C₃₁	—	8	2	no	—
559	C₂×C₃₁	—	8	4	no	—
560	C₂×C₃₁	#3488	1	1	yes	characteristic
561	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
562	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
563	H(5,𝔽₂)	—	4	8	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
569	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
570	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
571	C₂²×D₄	—	2	4	no	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
578	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
579	AGL(1,ℤ/8)	—	4	4	no	—
580	C₂×SD₁₆	—	4	8	no	—
581	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
586	C₂×D₈	C₂³×C₃₁	1	4	yes	—
587	C₂×D₈	C₂³×C₃₁	1	2	yes	—
588	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
589	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
590	C₄⋊Q₈	—	2	1	no	—
591	C₄⋊Q₈	—	2	1	no	—
592	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
595	#127	—	2	1	no	—
596	#127	—	2	2	no	—
597	#127	—	2	1	no	—
598	#127	—	2	2	no	—
599	#127	C₂³×C₃₁	1	2	yes	—
600	#127	C₂³×C₃₁	1	1	yes	characteristic
601	#127	C₂³×C₃₁	1	2	yes	—
602	#127	C₂³×C₃₁	1	4	yes	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	—	2	1	no	—
609	#125	C₂³×C₃₁	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	—	2	1	no	—
612	#124	—	2	2	no	—
613	#124	C₂³×C₃₁	1	2	yes	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	4	no	—
629	#121	—	2	4	no	—
630	#121	—	2	2	no	—
631	#121	C₂³×C₃₁	1	2	yes	—
632	#121	C₂³×C₃₁	1	4	yes	—
633	#121	C₂³×C₃₁	1	2	yes	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	—	2	2	no	—
639	C₄×Q₈	—	2	2	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
642	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
643	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
644	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
645	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
646	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
656	C₄×D₄	D₄×C₃₁	1	2	yes	—
657	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₃₁	1	2	yes	—
660	C₄×D₄	C₂³×C₃₁	1	4	yes	—
661	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₃₁	1	2	yes	—
663	#117	—	2	1	no	—
664	#117	—	2	1	no	—
665	#117	—	2	2	no	—
666	#117	—	2	1	no	—
667	#117	—	2	2	no	—
668	#117	D₄×C₃₁	1	2	yes	—
669	#117	D₄×C₃₁	1	1	yes	characteristic
670	#117	C₂³×C₃₁	1	1	yes	characteristic
671	C₂×C₄⋊C₄	—	2	2	no	—
672	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₄²	—	2	2	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
676	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
677	#107	C₂³×C₃₁	1	2	yes	—
678	#107	C₂³×C₃₁	1	4	yes	—
679	#106	C₂³×C₃₁	1	2	yes	—
680	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
681	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
682	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
683	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
684	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
685	#103	C₂³×C₃₁	1	2	yes	—
686	#103	C₂³×C₃₁	1	4	yes	—
687	#102	C₂³×C₃₁	1	2	yes	—
688	#102	C₂³×C₃₁	1	4	yes	—
689	#102	C₂³×C₃₁	1	4	yes	—
690	#102	C₂³×C₃₁	1	4	yes	—
691	#102	C₂³×C₃₁	1	4	yes	—
692	#102	C₂³×C₃₁	1	2	yes	—
693	#102	C₂³×C₃₁	1	2	yes	—
694	#102	C₂³×C₃₁	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
697	#97	C₂³×C₃₁	1	4	yes	—
698	C₄×C₈	C₂³×C₃₁	1	2	yes	—
699	C₃₁	#61983	1	1	yes	characteristic, direct product factor, Sylow
700	C₂⁴	—	2	2	no	—
701	C₂⁴	—	2	4	no	—
702	#41	—	2	4	no	—
703	#41	—	2	2	no	—
704	#41	—	4	1	no	—
705	#41	—	4	8	no	—
706	#41	—	4	4	no	—
707	#41	—	4	8	no	—
708	#41	—	4	4	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	4	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	8	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	16	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	—	8	4	no	—
740	C₂×D₄	—	8	2	no	—
741	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
744	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
745	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	4	no	—
763	SD₁₆	—	4	4	no	—
764	D₈	—	4	2	no	—
765	D₈	—	4	4	no	—
766	M₁₆	—	4	2	no	—
767	C₂×C₈	—	4	4	no	—
768	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
769	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
770	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
787	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₃₁	1	2	yes	—
817	C₄²	C₂×D₄×C₃₁	1	2	yes	—
818	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
819	C₄²	C₂⁴×C₃₁	1	2	yes	—
820	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
821	C₂³	—	2	1	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	4	4	no	—
825	C₂³	—	4	8	no	—
826	C₂³	—	8	4	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	4	2	no	—
838	Q₈	—	4	2	no	—
839	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	complemented
840	D₄	—	2	4	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	4	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	4	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	4	no	—
894	C₈	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	4	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	4	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	4	no	—
909	C₂²	—	16	8	no	—
910	C₂²	—	16	4	no	—
911	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
912	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
926	C₄	C₃₁×#577	1	2	yes	—
927	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
928	C₄	C₃₁×#585	1	1	yes	characteristic
929	C₂	—	2	4	no	—
930	C₂	—	4	1	no	—
931	C₂	—	8	2	no	—
932	C₂	—	8	4	no	—
933	C₂	—	8	1	no	—
934	C₂	C₃₁×#3488	1	1	yes	characteristic
935	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
936	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3498	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3368	C₂	semidirect
5. C₃₁×#3310	C₂	semidirect
6. C₃₁×#3294	C₂	semidirect
7. D₄×SD₁₆×C₃₁	C₂	semidirect
8. C₃₁×#3265	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3247	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3112	C₂	semidirect
14. C₃₁×#3106	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₂×C₃₁×#460	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×SD₁₆×C₃₁	C₂²	semidirect
21. C₃₁×#557	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
25. C₃₁×#552	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
29. C₃₁×#548	C₂²	semidirect
31. C₃₁×#547	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
45. C₃₁×#529	C₂²	semidirect
48. C₄×#41×C₃₁	C₂²	semidirect
49. C₂×C₄×Q₈×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×#477	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#468	C₂²	semidirect
62. C₃₁×#466	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×#460	C₂²	semidirect
71. C₃₁×#460	C₂²	semidirect
72. C₃₁×#460	C₂²	semidirect
73. C₃₁×#460	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×#448	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₃₁×#440	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#435	C₂²	semidirect
88. C₈×D₄×C₃₁	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. #61983	C₃₁	direct (N × H)
371. Q₈×C₃₁	H(5,𝔽₂)	semidirect
393. D₄×C₃₁	AGL(1,ℤ/8)	semidirect
427. #3498	C₂×C₃₁	semidirect
428. #3482	C₂×C₃₁	semidirect
429. #3397	C₂×C₃₁	semidirect
430. #3368	C₂×C₃₁	semidirect
431. #3310	C₂×C₃₁	semidirect
432. #3294	C₂×C₃₁	semidirect
433. D₄×SD₁₆	C₂×C₃₁	semidirect
434. #3265	C₂×C₃₁	semidirect
435. #3254	C₂×C₃₁	semidirect
436. #3247	C₂×C₃₁	semidirect
437. #3217	C₂×C₃₁	semidirect
438. #3208	C₂×C₃₁	semidirect
439. #3112	C₂×C₃₁	semidirect
440. #3106	C₂×C₃₁	semidirect
441. #3038	C₂×C₃₁	semidirect
442. C₂×#460	C₂×C₃₁	semidirect
443. #2990	C₂×C₃₁	semidirect
479. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
480. C₂²×SD₁₆	C₂²×C₃₁	semidirect
481. #557	C₂²×C₃₁	semidirect
483. #556	C₂²×C₃₁	semidirect
485. #552	C₂²×C₃₁	semidirect
488. D₄×Q₈	C₂²×C₃₁	semidirect
489. #548	C₂²×C₃₁	semidirect
491. #547	C₂²×C₃₁	semidirect
499. #533	C₂²×C₃₁	semidirect
505. #529	C₂²×C₃₁	semidirect
508. C₄×#41	C₂²×C₃₁	semidirect
509. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
510. #496	C₂²×C₃₁	semidirect
511. #492	C₂²×C₃₁	semidirect
512. #490	C₂²×C₃₁	semidirect
513. #486	C₂²×C₃₁	semidirect
514. #482	C₂²×C₃₁	semidirect
515. #480	C₂²×C₃₁	semidirect
516. #478	C₂²×C₃₁	semidirect
517. #477	C₂²×C₃₁	semidirect
518. #477	C₂²×C₃₁	semidirect
519. #476	C₂²×C₃₁	semidirect
520. #474	C₂²×C₃₁	semidirect
521. #468	C₂²×C₃₁	semidirect
522. #466	C₂²×C₃₁	semidirect
523. #465	C₂²×C₃₁	semidirect
524. #463	C₂²×C₃₁	semidirect
525. #461	C₂²×C₃₁	semidirect
526. #460	C₂²×C₃₁	semidirect
527. #460	C₂²×C₃₁	semidirect
528. #460	C₂²×C₃₁	semidirect
529. #460	C₂²×C₃₁	semidirect
530. #460	C₂²×C₃₁	semidirect
531. #460	C₂²×C₃₁	semidirect
532. #460	C₂²×C₃₁	semidirect
533. #460	C₂²×C₃₁	semidirect
534. #459	C₂²×C₃₁	semidirect
535. #459	C₂²×C₃₁	semidirect
536. #459	C₂²×C₃₁	semidirect
537. #450	C₂²×C₃₁	semidirect
538. #450	C₂²×C₃₁	semidirect
539. #449	C₂²×C₃₁	semidirect
540. #448	C₂²×C₃₁	semidirect
541. #447	C₂²×C₃₁	semidirect
542. #446	C₂²×C₃₁	semidirect
543. #440	C₂²×C₃₁	semidirect
544. #440	C₂²×C₃₁	semidirect
545. C₄×SD₁₆	C₂²×C₃₁	semidirect
546. C₄×D₈	C₂²×C₃₁	semidirect
547. #435	C₂²×C₃₁	semidirect
548. C₈×D₄	C₂²×C₃₁	semidirect
549. #432	C₂²×C₃₁	semidirect
550. #431	C₂²×C₃₁	semidirect
551. #423	C₂²×C₃₁	semidirect
552. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
553. #418	C₂²×C₃₁	semidirect
554. C₂×#102	C₂²×C₃₁	semidirect
699. C₃₁	#61983	direct (N × H)
839. Q₈	C₃₁×H(5,𝔽₂)	semidirect
861. D₄	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×#3482	2
C₃₁×#3397	2
C₃₁×#3368	2
C₃₁×#3310	2
C₃₁×#3294	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3265	2
C₃₁×#3254	2
C₃₁×#3247	2
C₃₁×#3217	2
C₃₁×#3208	2
C₃₁×#3112	2
C₃₁×#3106	2
C₃₁×#3038	2
C₂×C₃₁×#460	2
C₃₁×#2990	2
#61983	31

Subgroups — C31×#61983 #21518742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61983 #21518742