Subgroups — C₃₁×#60917 #21517676

Order 7936.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3256	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3250	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3080	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3040	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#533	C₂²	1	1	yes	characteristic
22	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#532	C₂²	1	1	yes	characteristic
25	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#529	—	2	1	no	—
28	C₃₁×#529	—	2	1	no	—
29	C₃₁×#529	—	2	1	no	—
30	C₃₁×#529	—	2	1	no	—
31	C₃₁×#529	—	2	1	no	—
32	C₃₁×#529	—	2	1	no	—
33	C₃₁×#529	—	2	1	no	—
34	C₃₁×#529	—	2	1	no	—
35	C₃₁×#529	C₂²	1	2	yes	—
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#529	C₂²	1	2	yes	—
39	C₃₁×#529	C₂²	1	2	yes	complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#126	—	2	1	no	—
42	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
44	C₃₁×#525	—	2	1	no	—
45	C₃₁×#525	—	2	1	no	—
46	C₃₁×#525	C₂²	1	2	yes	—
47	C₂×C₃₁×#123	—	2	1	no	—
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₁	—	2	1	no	—
51	C₄×#41×C₃₁	—	2	1	no	—
52	C₄×#41×C₃₁	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₃₁	—	2	1	no	—
55	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#117	—	2	1	no	—
57	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
58	C₃₁×#479	C₂²	1	4	yes	complemented
59	C₃₁×#479	C₂²	1	4	yes	complemented
60	C₃₁×#479	C₂²	1	4	yes	complemented
61	C₃₁×#478	C₂²	1	4	yes	complemented
62	C₃₁×#478	C₂²	1	4	yes	complemented
63	C₃₁×#478	C₂²	1	4	yes	complemented
64	C₃₁×#477	C₂²	1	2	yes	complemented
65	C₃₁×#476	C₂²	1	2	yes	complemented
66	C₃₁×#475	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	complemented
68	C₃₁×#470	C₂²	1	4	yes	complemented
69	C₃₁×#469	C₂²	1	4	yes	—
70	C₃₁×#468	C₂²	1	4	yes	—
71	C₃₁×#468	C₂²	1	4	yes	complemented
72	C₃₁×#467	C₂²	1	4	yes	complemented
73	C₃₁×#466	C₂²	1	4	yes	—
74	C₃₁×#465	C₂²	1	4	yes	—
75	C₃₁×#465	C₂²	1	4	yes	complemented
76	C₃₁×#464	C₂²	1	4	yes	complemented
77	C₃₁×#464	C₂²	1	4	yes	complemented
78	C₃₁×#464	C₂²	1	4	yes	complemented
79	C₃₁×#463	C₂²	1	4	yes	complemented
80	C₃₁×#463	C₂²	1	4	yes	complemented
81	C₃₁×#463	C₂²	1	4	yes	complemented
82	C₃₁×#462	C₂²	1	2	yes	complemented
83	C₃₁×#461	C₂²	1	2	yes	complemented
84	C₃₁×#460	C₂²	1	2	yes	complemented
85	C₃₁×#459	C₂²	1	2	yes	complemented
86	C₃₁×#428	C₂²	1	2	yes	—
87	C₃₁×#428	C₂²	1	2	yes	—
88	C₃₁×#423	C₂²	1	1	yes	characteristic
89	C₃₁×#423	C₂²	1	1	yes	characteristic
90	C₃₁×#423	C₂²	1	2	yes	—
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₃₁×#423	C₂²	1	2	yes	complemented
93	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
94	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
95	C₃₁×#419	C₂²	1	2	yes	—
96	C₃₁×#418	C₂²	1	2	yes	—
97	C₃₁×#417	C₂²	1	2	yes	—
98	C₃₁×#417	C₂²	1	2	yes	—
99	C₂×#41×C₃₁	—	2	1	no	—
100	C₂×#41×C₃₁	—	2	1	no	—
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	—	2	1	no	—
106	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×#137	—	4	4	no	—
110	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
111	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₁	—	4	4	no	—
116	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
117	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
118	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×#127	C₂³	1	1	yes	characteristic
124	C₃₁×#126	—	2	2	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#126	—	2	2	no	—
130	C₃₁×#125	—	2	1	no	—
131	C₃₁×#125	—	2	1	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	—	2	1	no	—
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#125	C₂³	1	2	yes	—
136	C₃₁×#125	C₂³	1	2	yes	—
137	C₃₁×#124	—	2	1	no	—
138	C₃₁×#124	—	2	1	no	—
139	C₃₁×#124	—	2	1	no	—
140	C₃₁×#124	—	2	1	no	—
141	C₃₁×#124	C₂³	1	2	yes	—
142	C₃₁×#124	C₂³	1	2	yes	—
143	C₃₁×#124	C₂³	1	2	yes	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×#123	—	2	2	no	—
148	C₃₁×#123	—	2	2	no	—
149	C₃₁×#123	—	2	2	no	—
150	C₃₁×#123	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	—	2	1	no	—
152	C₃₁×C₂²⋊Q₈	—	2	1	no	—
153	C₃₁×C₂²⋊Q₈	—	2	1	no	—
154	C₃₁×C₂²⋊Q₈	—	2	1	no	—
155	C₃₁×C₂²⋊Q₈	—	2	1	no	—
156	C₃₁×C₂²⋊Q₈	—	2	1	no	—
157	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×#121	—	2	1	no	—
162	C₃₁×#121	—	2	1	no	—
163	C₃₁×#121	—	2	1	no	—
164	C₃₁×#121	—	2	1	no	—
165	C₃₁×#121	—	2	1	no	—
166	C₃₁×#121	—	2	1	no	—
167	C₃₁×#121	C₂³	1	2	yes	—
168	C₃₁×#121	C₂³	1	2	yes	—
169	C₃₁×#121	C₂³	1	2	yes	—
170	C₃₁×#121	C₂³	1	2	yes	—
171	C₃₁×#120	—	2	2	no	—
172	C₄×Q₈×C₃₁	—	2	1	no	—
173	C₄×Q₈×C₃₁	—	2	1	no	—
174	C₄×Q₈×C₃₁	—	2	1	no	—
175	C₄×Q₈×C₃₁	—	2	1	no	—
176	C₄×Q₈×C₃₁	—	2	1	no	—
177	C₄×Q₈×C₃₁	—	2	1	no	—
178	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
179	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
180	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
181	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	—	2	2	no	—
189	C₄×D₄×C₃₁	—	2	2	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₄×D₄×C₃₁	—	2	2	no	—
192	C₄×D₄×C₃₁	—	2	1	no	—
193	C₄×D₄×C₃₁	—	2	1	no	—
194	C₄×D₄×C₃₁	—	2	1	no	—
195	C₄×D₄×C₃₁	—	2	1	no	—
196	C₄×D₄×C₃₁	—	2	1	no	—
197	C₄×D₄×C₃₁	—	2	1	no	—
198	C₄×D₄×C₃₁	C₂³	1	2	yes	—
199	C₄×D₄×C₃₁	C₂³	1	2	yes	—
200	C₄×D₄×C₃₁	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#117	—	2	1	no	—
203	C₃₁×#117	—	2	1	no	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	—	2	2	no	—
207	C₃₁×#117	—	2	2	no	—
208	C₃₁×#117	—	2	2	no	—
209	C₃₁×#117	—	2	2	no	—
210	C₃₁×#117	—	2	2	no	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
213	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
214	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
215	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
216	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
219	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
220	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
221	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
223	C₂×C₄²×C₃₁	—	2	1	no	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
237	C₃₁×#107	C₂³	1	4	yes	—
238	C₃₁×#107	C₂³	1	4	yes	—
239	C₃₁×#106	C₂³	1	4	yes	—
240	C₃₁×#106	C₂³	1	4	yes	—
241	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
242	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
243	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
244	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
246	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	4	yes	—
248	C₃₁×#103	C₂³	1	4	yes	—
249	C₃₁×#103	C₂³	1	4	yes	—
250	C₃₁×#103	C₂³	1	4	yes	—
251	C₃₁×#102	C₂³	1	4	yes	—
252	C₃₁×#102	C₂³	1	4	yes	—
253	C₃₁×#102	C₂³	1	4	yes	—
254	C₃₁×#102	C₂³	1	4	yes	—
255	C₂⁴×C₃₁	—	2	1	no	—
256	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
257	#41×C₃₁	—	2	4	no	—
258	#41×C₃₁	—	2	4	no	—
259	#41×C₃₁	—	4	4	no	—
260	#41×C₃₁	—	4	4	no	—
261	C₂×Q₈×C₃₁	—	2	1	no	—
262	C₂×Q₈×C₃₁	—	2	1	no	—
263	C₂×Q₈×C₃₁	—	2	1	no	—
264	C₂×Q₈×C₃₁	—	2	2	no	—
265	C₂×Q₈×C₃₁	—	2	2	no	—
266	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₃₁	—	2	2	no	—
269	C₂×D₄×C₃₁	—	2	2	no	—
270	C₂×D₄×C₃₁	—	2	2	no	—
271	C₂×D₄×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	2	no	—
273	C₂×D₄×C₃₁	—	2	1	no	—
274	C₂×D₄×C₃₁	—	2	1	no	—
275	C₂×D₄×C₃₁	—	2	1	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	4	4	no	—
279	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	2	no	—
283	C₂²×C₄×C₃₁	—	2	1	no	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	4	2	no	—
292	C₂²×C₄×C₃₁	—	4	2	no	—
293	C₂²×C₄×C₃₁	—	4	4	no	—
294	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	Q₁₆×C₃₁	—	4	4	no	—
313	SD₁₆×C₃₁	—	4	4	no	—
314	SD₁₆×C₃₁	—	4	4	no	—
315	D₈×C₃₁	—	4	4	no	—
316	M₁₆×C₃₁	—	2	4	no	—
317	M₁₆×C₃₁	—	2	4	no	—
318	M₁₆×C₃₁	—	4	4	no	—
319	C₂×C₈×C₃₁	—	4	4	no	—
320	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
321	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
386	#60917	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	2	2	no	—
389	C₂³×C₃₁	—	2	2	no	—
390	C₂³×C₃₁	—	2	2	no	—
391	C₂³×C₃₁	—	4	1	no	—
392	C₂³×C₃₁	—	4	2	no	—
393	C₂³×C₃₁	—	4	2	no	—
394	C₂³×C₃₁	—	4	2	no	—
395	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	Q₈×C₃₁	—	2	2	no	—
399	Q₈×C₃₁	—	2	2	no	—
400	Q₈×C₃₁	—	2	2	no	—
401	Q₈×C₃₁	—	2	2	no	—
402	Q₈×C₃₁	—	4	2	no	—
403	Q₈×C₃₁	—	4	2	no	—
404	Q₈×C₃₁	—	4	2	no	—
405	D₄×C₃₁	—	2	2	no	—
406	D₄×C₃₁	—	2	2	no	—
407	D₄×C₃₁	—	2	2	no	—
408	D₄×C₃₁	—	2	2	no	—
409	D₄×C₃₁	—	4	2	no	—
410	D₄×C₃₁	—	4	4	no	—
411	D₄×C₃₁	—	4	4	no	—
412	D₄×C₃₁	—	4	4	no	—
413	D₄×C₃₁	—	4	4	no	—
414	D₄×C₃₁	—	4	4	no	—
415	D₄×C₃₁	—	4	2	no	—
416	D₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	4	1	no	—
436	C₂×C₄×C₃₁	—	4	1	no	—
437	C₂×C₄×C₃₁	—	4	1	no	—
438	C₂×C₄×C₃₁	—	4	1	no	—
439	C₂×C₄×C₃₁	—	4	1	no	—
440	C₂×C₄×C₃₁	—	4	1	no	—
441	C₂×C₄×C₃₁	—	4	1	no	—
442	C₂×C₄×C₃₁	—	4	4	no	—
443	C₂×C₄×C₃₁	—	4	4	no	—
444	C₂×C₄×C₃₁	—	4	4	no	—
445	C₂×C₄×C₃₁	—	4	2	no	—
446	C₂×C₄×C₃₁	—	4	2	no	—
447	C₂×C₄×C₃₁	—	4	2	no	—
448	C₂×C₄×C₃₁	—	4	4	no	—
449	C₂×C₄×C₃₁	—	4	4	no	—
450	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
462	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
463	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
464	C₈×C₃₁	—	2	4	no	—
465	C₈×C₃₁	—	2	4	no	—
466	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
467	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3256	C₂×C₃₁	1	4	yes	complemented
469	#3252	C₂×C₃₁	1	2	yes	complemented
470	#3251	C₂×C₃₁	1	2	yes	complemented
471	#3250	C₂×C₃₁	1	4	yes	complemented
472	#3248	C₂×C₃₁	1	2	yes	complemented
473	#3247	C₂×C₃₁	1	2	yes	complemented
474	#3080	C₂×C₃₁	1	2	yes	complemented
475	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
476	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3056	C₂×C₃₁	1	2	yes	complemented
478	#3055	C₂×C₃₁	1	2	yes	complemented
479	#3040	C₂×C₃₁	1	2	yes	complemented
480	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
481	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
482	C₂×#423	C₂×C₃₁	1	1	yes	characteristic, complemented
483	C₂²×C₃₁	—	2	1	no	—
484	C₂²×C₃₁	—	2	1	no	—
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	1	no	—
487	C₂²×C₃₁	—	2	1	no	—
488	C₂²×C₃₁	—	2	1	no	—
489	C₂²×C₃₁	—	2	1	no	—
490	C₂²×C₃₁	—	4	4	no	—
491	C₂²×C₃₁	—	4	2	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	8	4	no	—
498	C₂²×C₃₁	#537	1	2	yes	—
499	C₂²×C₃₁	#575	1	2	yes	—
500	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	2	1	no	—
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	1	no	—
506	C₄×C₃₁	—	2	1	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	2	1	no	—
509	C₄×C₃₁	—	2	1	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	2	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	#537	1	2	yes	—
517	C₄×C₃₁	#575	1	2	yes	—
518	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×#137	C₂²×C₃₁	1	2	yes	—
521	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
522	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
523	#533	C₂²×C₃₁	1	1	yes	characteristic
524	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
525	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	#532	C₂²×C₃₁	1	1	yes	characteristic
527	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
529	#529	—	2	1	no	—
530	#529	—	2	1	no	—
531	#529	—	2	1	no	—
532	#529	—	2	1	no	—
533	#529	—	2	1	no	—
534	#529	—	2	1	no	—
535	#529	—	2	1	no	—
536	#529	—	2	1	no	—
537	#529	C₂²×C₃₁	1	2	yes	—
538	#529	C₂²×C₃₁	1	2	yes	—
539	#529	C₂²×C₃₁	1	2	yes	—
540	#529	C₂²×C₃₁	1	2	yes	—
541	#529	C₂²×C₃₁	1	2	yes	complemented
542	#529	C₂²×C₃₁	1	2	yes	complemented
543	C₂×#126	—	2	1	no	—
544	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
545	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
546	#525	—	2	1	no	—
547	#525	—	2	1	no	—
548	#525	C₂²×C₃₁	1	2	yes	—
549	C₂×#123	—	2	1	no	—
550	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
552	C₄×#41	—	2	1	no	—
553	C₄×#41	—	2	1	no	—
554	C₄×#41	C₂²×C₃₁	1	2	yes	—
555	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
556	C₂×C₄×D₄	—	2	1	no	—
557	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
558	C₂×#117	—	2	1	no	—
559	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
560	#479	C₂²×C₃₁	1	4	yes	complemented
561	#479	C₂²×C₃₁	1	4	yes	complemented
562	#479	C₂²×C₃₁	1	4	yes	complemented
563	#478	C₂²×C₃₁	1	4	yes	complemented
564	#478	C₂²×C₃₁	1	4	yes	complemented
565	#478	C₂²×C₃₁	1	4	yes	complemented
566	#477	C₂²×C₃₁	1	2	yes	complemented
567	#476	C₂²×C₃₁	1	2	yes	complemented
568	#475	C₂²×C₃₁	1	2	yes	complemented
569	#474	C₂²×C₃₁	1	2	yes	complemented
570	#470	C₂²×C₃₁	1	4	yes	complemented
571	#469	C₂²×C₃₁	1	4	yes	—
572	#468	C₂²×C₃₁	1	4	yes	—
573	#468	C₂²×C₃₁	1	4	yes	complemented
574	#467	C₂²×C₃₁	1	4	yes	complemented
575	#466	C₂²×C₃₁	1	4	yes	—
576	#465	C₂²×C₃₁	1	4	yes	—
577	#465	C₂²×C₃₁	1	4	yes	complemented
578	#464	C₂²×C₃₁	1	4	yes	complemented
579	#464	C₂²×C₃₁	1	4	yes	complemented
580	#464	C₂²×C₃₁	1	4	yes	complemented
581	#463	C₂²×C₃₁	1	4	yes	complemented
582	#463	C₂²×C₃₁	1	4	yes	complemented
583	#463	C₂²×C₃₁	1	4	yes	complemented
584	#462	C₂²×C₃₁	1	2	yes	complemented
585	#461	C₂²×C₃₁	1	2	yes	complemented
586	#460	C₂²×C₃₁	1	2	yes	complemented
587	#459	C₂²×C₃₁	1	2	yes	complemented
588	#428	C₂²×C₃₁	1	2	yes	—
589	#428	C₂²×C₃₁	1	2	yes	—
590	#423	C₂²×C₃₁	1	1	yes	characteristic
591	#423	C₂²×C₃₁	1	1	yes	characteristic
592	#423	C₂²×C₃₁	1	2	yes	—
593	#423	C₂²×C₃₁	1	2	yes	complemented
594	#423	C₂²×C₃₁	1	2	yes	complemented
595	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
596	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
597	#419	C₂²×C₃₁	1	2	yes	—
598	#418	C₂²×C₃₁	1	2	yes	—
599	#417	C₂²×C₃₁	1	2	yes	—
600	#417	C₂²×C₃₁	1	2	yes	—
601	C₂×C₃₁	—	2	2	no	—
602	C₂×C₃₁	—	2	2	no	—
603	C₂×C₃₁	—	4	1	no	—
604	C₂×C₃₁	—	8	2	no	—
605	C₂×C₃₁	—	8	2	no	—
606	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
607	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
608	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	C₂³×C₃₁	1	2	yes	—
612	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
613	C₂²×D₄	—	2	1	no	—
614	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₂³×C₄	—	2	1	no	—
616	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
617	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
619	#137	—	4	4	no	—
620	AGL(1,ℤ/8)	—	4	4	no	—
621	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
622	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
623	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
624	C₂×D₈	C₂³×C₃₁	1	4	yes	—
625	C₂×M₁₆	—	4	4	no	—
626	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
627	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
628	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
629	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
630	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	#127	C₂³×C₃₁	1	1	yes	characteristic
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#125	—	2	1	no	—
641	#125	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#125	C₂³×C₃₁	1	2	yes	—
645	#125	C₂³×C₃₁	1	2	yes	—
646	#125	C₂³×C₃₁	1	2	yes	—
647	#124	—	2	1	no	—
648	#124	—	2	1	no	—
649	#124	—	2	1	no	—
650	#124	—	2	1	no	—
651	#124	C₂³×C₃₁	1	2	yes	—
652	#124	C₂³×C₃₁	1	2	yes	—
653	#124	C₂³×C₃₁	1	2	yes	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	C₂²⋊Q₈	—	2	1	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
668	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
669	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
670	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
671	#121	—	2	1	no	—
672	#121	—	2	1	no	—
673	#121	—	2	1	no	—
674	#121	—	2	1	no	—
675	#121	—	2	1	no	—
676	#121	—	2	1	no	—
677	#121	C₂³×C₃₁	1	2	yes	—
678	#121	C₂³×C₃₁	1	2	yes	—
679	#121	C₂³×C₃₁	1	2	yes	—
680	#121	C₂³×C₃₁	1	2	yes	—
681	#120	—	2	2	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	—	2	1	no	—
685	C₄×Q₈	—	2	1	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	1	no	—
688	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
689	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
691	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	—	2	1	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	C₂³×C₃₁	1	2	yes	—
709	C₄×D₄	C₂³×C₃₁	1	2	yes	—
710	C₄×D₄	C₂³×C₃₁	1	2	yes	—
711	C₄×D₄	C₂³×C₃₁	1	2	yes	—
712	#117	—	2	1	no	—
713	#117	—	2	1	no	—
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	—	2	2	no	—
718	#117	—	2	2	no	—
719	#117	—	2	2	no	—
720	#117	—	2	2	no	—
721	#117	C₂³×C₃₁	1	2	yes	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	1	no	—
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	—	2	1	no	—
729	C₂×C₂²⋊C₄	—	2	1	no	—
730	C₂×C₂²⋊C₄	—	2	1	no	—
731	C₂×C₂²⋊C₄	—	2	1	no	—
732	C₂×C₂²⋊C₄	—	2	1	no	—
733	C₂×C₄²	—	2	1	no	—
734	C₂×C₄²	—	2	2	no	—
735	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
736	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
737	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
738	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
739	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
740	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
747	#107	C₂³×C₃₁	1	4	yes	—
748	#107	C₂³×C₃₁	1	4	yes	—
749	#106	C₂³×C₃₁	1	4	yes	—
750	#106	C₂³×C₃₁	1	4	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
754	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
755	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
756	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	4	yes	—
758	#103	C₂³×C₃₁	1	4	yes	—
759	#103	C₂³×C₃₁	1	4	yes	—
760	#103	C₂³×C₃₁	1	4	yes	—
761	#102	C₂³×C₃₁	1	4	yes	—
762	#102	C₂³×C₃₁	1	4	yes	—
763	#102	C₂³×C₃₁	1	4	yes	—
764	#102	C₂³×C₃₁	1	4	yes	—
765	C₃₁	#60917	1	1	yes	characteristic, direct product factor, Sylow
766	C₂⁴	—	2	1	no	—
767	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
768	#41	—	2	4	no	—
769	#41	—	2	4	no	—
770	#41	—	4	4	no	—
771	#41	—	4	4	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	—	2	2	no	—
777	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
778	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	4	4	no	—
790	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
791	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	4	no	—
805	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
806	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
812	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
813	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
815	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
823	Q₁₆	—	4	4	no	—
824	SD₁₆	—	4	4	no	—
825	SD₁₆	—	4	4	no	—
826	D₈	—	4	4	no	—
827	M₁₆	—	2	4	no	—
828	M₁₆	—	2	4	no	—
829	M₁₆	—	4	4	no	—
830	C₂×C₈	—	4	4	no	—
831	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
832	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
883	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
884	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	4	1	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	2	no	—
904	C₂³	—	4	2	no	—
905	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
906	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
907	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	4	2	no	—
913	Q₈	—	4	2	no	—
914	Q₈	—	4	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
969	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
970	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
971	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
972	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
973	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
974	C₈	—	2	4	no	—
975	C₈	—	2	4	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	4	4	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	8	4	no	—
991	C₂²	C₃₁×#537	1	2	yes	—
992	C₂²	C₃₁×#575	1	2	yes	—
993	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	C₃₁×#537	1	2	yes	—
1010	C₄	C₃₁×#575	1	2	yes	—
1011	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1013	C₂	—	2	2	no	—
1014	C₂	—	2	2	no	—
1015	C₂	—	4	1	no	—
1016	C₂	—	8	2	no	—
1017	C₂	—	8	2	no	—
1018	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
1019	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1020	C₂	C₂×C₃₁×#575	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 ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3444	C₂	semidirect
2. C₂×C₃₁×#529	C₂	semidirect
3. C₃₁×#3256	C₂	semidirect
4. C₃₁×#3252	C₂	semidirect
5. C₃₁×#3251	C₂	semidirect
6. C₃₁×#3250	C₂	semidirect
7. C₃₁×#3248	C₂	semidirect
8. C₃₁×#3247	C₂	semidirect
9. C₃₁×#3080	C₂	semidirect
10. C₃₁×#3078	C₂	semidirect
11. C₃₁×#3077	C₂	semidirect
12. C₃₁×#3056	C₂	semidirect
13. C₃₁×#3055	C₂	semidirect
14. C₃₁×#3040	C₂	semidirect
15. C₃₁×#3037	C₂	semidirect
16. C₃₁×#3036	C₂	semidirect
17. C₂×C₃₁×#423	C₂	semidirect
22. C₃₁×#533	C₂²	semidirect
23. C₃₁×#533	C₂²	semidirect
25. C₃₁×#532	C₂²	semidirect
26. C₃₁×#532	C₂²	semidirect
39. C₃₁×#529	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
58. C₃₁×#479	C₂²	semidirect
59. C₃₁×#479	C₂²	semidirect
60. C₃₁×#479	C₂²	semidirect
61. C₃₁×#478	C₂²	semidirect
62. C₃₁×#478	C₂²	semidirect
63. C₃₁×#478	C₂²	semidirect
64. C₃₁×#477	C₂²	semidirect
65. C₃₁×#476	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#470	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#467	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#462	C₂²	semidirect
83. C₃₁×#461	C₂²	semidirect
84. C₃₁×#460	C₂²	semidirect
85. C₃₁×#459	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
93. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
94. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
386. #60917	C₃₁	direct (N × H)
466. #3444	C₂×C₃₁	semidirect
467. C₂×#529	C₂×C₃₁	semidirect
468. #3256	C₂×C₃₁	semidirect
469. #3252	C₂×C₃₁	semidirect
470. #3251	C₂×C₃₁	semidirect
471. #3250	C₂×C₃₁	semidirect
472. #3248	C₂×C₃₁	semidirect
473. #3247	C₂×C₃₁	semidirect
474. #3080	C₂×C₃₁	semidirect
475. #3078	C₂×C₃₁	semidirect
476. #3077	C₂×C₃₁	semidirect
477. #3056	C₂×C₃₁	semidirect
478. #3055	C₂×C₃₁	semidirect
479. #3040	C₂×C₃₁	semidirect
480. #3037	C₂×C₃₁	semidirect
481. #3036	C₂×C₃₁	semidirect
482. C₂×#423	C₂×C₃₁	semidirect
524. #533	C₂²×C₃₁	semidirect
525. #533	C₂²×C₃₁	semidirect
527. #532	C₂²×C₃₁	semidirect
528. #532	C₂²×C₃₁	semidirect
541. #529	C₂²×C₃₁	semidirect
542. #529	C₂²×C₃₁	semidirect
560. #479	C₂²×C₃₁	semidirect
561. #479	C₂²×C₃₁	semidirect
562. #479	C₂²×C₃₁	semidirect
563. #478	C₂²×C₃₁	semidirect
564. #478	C₂²×C₃₁	semidirect
565. #478	C₂²×C₃₁	semidirect
566. #477	C₂²×C₃₁	semidirect
567. #476	C₂²×C₃₁	semidirect
568. #475	C₂²×C₃₁	semidirect
569. #474	C₂²×C₃₁	semidirect
570. #470	C₂²×C₃₁	semidirect
573. #468	C₂²×C₃₁	semidirect
574. #467	C₂²×C₃₁	semidirect
577. #465	C₂²×C₃₁	semidirect
578. #464	C₂²×C₃₁	semidirect
579. #464	C₂²×C₃₁	semidirect
580. #464	C₂²×C₃₁	semidirect
581. #463	C₂²×C₃₁	semidirect
582. #463	C₂²×C₃₁	semidirect
583. #463	C₂²×C₃₁	semidirect
584. #462	C₂²×C₃₁	semidirect
585. #461	C₂²×C₃₁	semidirect
586. #460	C₂²×C₃₁	semidirect
587. #459	C₂²×C₃₁	semidirect
593. #423	C₂²×C₃₁	semidirect
594. #423	C₂²×C₃₁	semidirect
595. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
596. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
765. C₃₁	#60917	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×#3444	2
C₂×C₃₁×#529	2
C₃₁×#3256	2
C₃₁×#3252	2
C₃₁×#3251	2
C₃₁×#3250	2
C₃₁×#3248	2
C₃₁×#3247	2
C₃₁×#3080	2
C₃₁×#3078	2
C₃₁×#3077	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3040	2
C₃₁×#3037	2
C₃₁×#3036	2
C₂×C₃₁×#423	2
#60917	31

Subgroups — C31×#60917 #21517676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60917 #21517676