Subgroups — C₃₁×#60867 #21517626

Order 7936.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3455	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3244	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3243	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3242	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3241	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3093	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3092	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3080	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3079	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#544	—	2	2	no	—
17	C₃₁×#544	—	2	2	no	—
18	C₃₁×#544	C₂²	1	4	yes	—
19	C₃₁×#544	C₂²	1	4	yes	—
20	C₃₁×#542	C₂²	1	2	yes	—
21	C₃₁×#542	C₂²	1	2	yes	—
22	C₃₁×#541	C₂²	1	2	yes	—
23	C₃₁×#540	C₂²	1	2	yes	—
24	C₃₁×#539	—	2	1	no	—
25	C₃₁×#539	—	2	1	no	—
26	C₃₁×#538	—	2	1	no	—
27	C₃₁×#538	—	2	1	no	—
28	C₃₁×#533	C₂²	1	1	yes	characteristic
29	C₃₁×#532	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃₁×#529	—	2	2	no	—
34	C₃₁×#529	—	2	2	no	—
35	C₂×C₃₁×#125	—	2	1	no	—
36	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
38	C₃₁×#525	C₂²	1	2	yes	—
39	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
41	C₄×#41×C₃₁	C₂²	1	2	yes	—
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#501	C₂²	1	4	yes	complemented
46	C₃₁×#501	C₂²	1	2	yes	complemented
47	C₃₁×#501	C₂²	1	2	yes	complemented
48	C₃₁×#500	C₂²	1	2	yes	complemented
49	C₃₁×#499	C₂²	1	4	yes	complemented
50	C₃₁×#498	C₂²	1	2	yes	complemented
51	C₃₁×#491	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	2	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	complemented
54	C₃₁×#488	C₂²	1	4	yes	complemented
55	C₃₁×#487	C₂²	1	2	yes	complemented
56	C₃₁×#486	C₂²	1	2	yes	complemented
57	C₃₁×#485	C₂²	1	4	yes	—
58	C₃₁×#485	C₂²	1	4	yes	—
59	C₃₁×#484	C₂²	1	4	yes	—
60	C₃₁×#483	C₂²	1	4	yes	—
61	C₃₁×#482	C₂²	1	4	yes	—
62	C₃₁×#482	C₂²	1	4	yes	—
63	C₃₁×#481	C₂²	1	4	yes	—
64	C₃₁×#480	C₂²	1	4	yes	—
65	C₃₁×#479	C₂²	1	4	yes	complemented
66	C₃₁×#479	C₂²	1	4	yes	complemented
67	C₃₁×#478	C₂²	1	4	yes	complemented
68	C₃₁×#478	C₂²	1	4	yes	complemented
69	C₃₁×#477	C₂²	1	4	yes	complemented
70	C₃₁×#476	C₂²	1	4	yes	complemented
71	C₃₁×#475	C₂²	1	4	yes	complemented
72	C₃₁×#474	C₂²	1	4	yes	complemented
73	C₃₁×#433	C₂²	1	4	yes	—
74	C₃₁×#433	C₂²	1	4	yes	—
75	C₃₁×#428	C₂²	1	2	yes	—
76	C₃₁×#428	C₂²	1	2	yes	—
77	C₃₁×#428	C₂²	1	2	yes	—
78	C₃₁×#428	C₂²	1	2	yes	—
79	C₃₁×#423	C₂²	1	2	yes	—
80	C₃₁×#417	C₂²	1	2	yes	—
81	C₃₁×#417	C₂²	1	2	yes	—
82	C₃₁×#417	C₂²	1	2	yes	—
83	C₃₁×#417	C₂²	1	2	yes	—
84	C₃₁×#407	C₂²	1	2	yes	—
85	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
87	C₂×#41×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	—	2	1	no	—
89	C₂²×Q₈×C₃₁	—	2	1	no	—
90	C₂³×C₄×C₃₁	—	2	1	no	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
93	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
94	C₃₁×C₄⋊Q₈	—	2	4	no	—
95	C₃₁×C₄⋊Q₈	—	2	4	no	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	—	2	1	no	—
98	C₃₁×C₄⋊Q₈	—	2	1	no	—
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×#127	C₂³	1	1	yes	characteristic
106	C₃₁×#126	—	2	2	no	—
107	C₃₁×#126	—	2	2	no	—
108	C₃₁×#126	—	2	2	no	—
109	C₃₁×#126	—	2	2	no	—
110	C₃₁×#125	—	2	4	no	—
111	C₃₁×#125	—	2	4	no	—
112	C₃₁×#125	—	2	2	no	—
113	C₃₁×#125	—	2	2	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	—	2	1	no	—
116	C₃₁×#125	—	2	1	no	—
117	C₃₁×#125	C₂³	1	4	yes	—
118	C₃₁×#125	C₂³	1	2	yes	—
119	C₃₁×#125	C₂³	1	2	yes	—
120	C₃₁×#125	C₂³	1	2	yes	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	C₂³	1	2	yes	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	2	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	2	no	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	1	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×#121	—	2	1	no	—
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	C₂³	1	2	yes	—
144	C₃₁×#121	C₂³	1	2	yes	—
145	C₃₁×#120	—	2	2	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	—	2	1	no	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	—	2	2	no	—
160	C₃₁×#117	D₄	1	2	yes	—
161	C₃₁×#117	D₄	1	2	yes	—
162	C₃₁×#117	C₂³	1	2	yes	—
163	C₃₁×#117	C₂³	1	4	yes	—
164	C₃₁×#117	C₂³	1	2	yes	—
165	C₃₁×#117	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	—	2	1	no	—
185	C₂×C₄²×C₃₁	—	2	2	no	—
186	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×#107	C₂³	1	4	yes	—
189	C₃₁×#107	C₂³	1	4	yes	—
190	C₃₁×#107	C₂³	1	4	yes	—
191	C₃₁×#107	C₂³	1	4	yes	—
192	C₃₁×#106	C₂³	1	4	yes	—
193	C₃₁×#106	C₂³	1	4	yes	—
194	C₃₁×#106	C₂³	1	4	yes	—
195	C₃₁×#106	C₂³	1	4	yes	—
196	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
198	C₃₁×#103	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	4	yes	—
200	C₃₁×#103	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#102	C₂³	1	4	yes	—
203	C₃₁×#102	C₂³	1	4	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₃₁×#97	C₂³	1	2	yes	—
209	C₃₁×#97	C₂³	1	2	yes	—
210	C₄×C₈×C₃₁	C₂³	1	2	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
213	#41×C₃₁	—	2	8	no	—
214	C₂×Q₈×C₃₁	—	2	1	no	—
215	C₂×Q₈×C₃₁	—	2	1	no	—
216	C₂×Q₈×C₃₁	—	2	4	no	—
217	C₂×Q₈×C₃₁	—	2	2	no	—
218	C₂×Q₈×C₃₁	—	2	2	no	—
219	C₂×Q₈×C₃₁	—	8	2	no	—
220	C₂×Q₈×C₃₁	—	8	2	no	—
221	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₃₁	—	2	2	no	—
223	C₂×D₄×C₃₁	—	2	2	no	—
224	C₂×D₄×C₃₁	—	2	2	no	—
225	C₂×D₄×C₃₁	—	2	1	no	—
226	C₂×D₄×C₃₁	—	2	1	no	—
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	2	1	no	—
230	C₂²×C₄×C₃₁	—	2	1	no	—
231	C₂²×C₄×C₃₁	—	2	1	no	—
232	C₂²×C₄×C₃₁	—	2	1	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	—	2	2	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	8	2	no	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	M₁₆×C₃₁	—	2	4	no	—
247	M₁₆×C₃₁	—	2	4	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	C₂×D₄	1	2	yes	—
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₄²×C₃₁	C₂⁴	1	2	yes	—
308	#60867	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	2	no	—
311	C₂³×C₃₁	—	4	1	no	—
312	C₂³×C₃₁	—	4	1	no	—
313	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
314	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₃₁	—	2	4	no	—
316	Q₈×C₃₁	—	8	1	no	—
317	Q₈×C₃₁	—	8	1	no	—
318	Q₈×C₃₁	—	8	4	no	—
319	Q₈×C₃₁	—	8	2	no	—
320	Q₈×C₃₁	—	8	2	no	—
321	D₄×C₃₁	—	2	4	no	—
322	D₄×C₃₁	—	4	4	no	—
323	D₄×C₃₁	—	8	1	no	—
324	D₄×C₃₁	—	8	1	no	—
325	D₄×C₃₁	—	8	2	no	—
326	D₄×C₃₁	—	8	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	4	no	—
329	C₂×C₄×C₃₁	—	2	4	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	4	1	no	—
338	C₂×C₄×C₃₁	—	4	1	no	—
339	C₂×C₄×C₃₁	—	4	1	no	—
340	C₂×C₄×C₃₁	—	4	1	no	—
341	C₂×C₄×C₃₁	—	4	2	no	—
342	C₂×C₄×C₃₁	—	4	2	no	—
343	C₂×C₄×C₃₁	—	4	2	no	—
344	C₂×C₄×C₃₁	—	4	2	no	—
345	C₂×C₄×C₃₁	—	4	4	no	—
346	C₂×C₄×C₃₁	—	8	2	no	—
347	C₂×C₄×C₃₁	—	8	2	no	—
348	C₂×C₄×C₃₁	—	8	4	no	—
349	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
358	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
359	C₈×C₃₁	—	2	4	no	—
360	C₈×C₃₁	—	2	4	no	—
361	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3455	C₂×C₃₁	1	1	yes	characteristic
363	#3244	C₂×C₃₁	1	4	yes	complemented
364	#3243	C₂×C₃₁	1	4	yes	complemented
365	#3242	C₂×C₃₁	1	4	yes	complemented
366	#3241	C₂×C₃₁	1	4	yes	complemented
367	#3166	C₂×C₃₁	1	1	yes	characteristic, complemented
368	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#3093	C₂×C₃₁	1	2	yes	complemented
372	#3092	C₂×C₃₁	1	2	yes	complemented
373	#3080	C₂×C₃₁	1	2	yes	complemented
374	#3079	C₂×C₃₁	1	2	yes	complemented
375	#2921	C₂×C₃₁	1	1	yes	characteristic, complemented
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	2	no	—
379	C₂²×C₃₁	—	2	2	no	—
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	4	4	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	4	2	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	#536	1	2	yes	—
386	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₃₁	—	2	2	no	—
388	C₄×C₃₁	—	2	1	no	—
389	C₄×C₃₁	—	2	1	no	—
390	C₄×C₃₁	—	2	2	no	—
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	2	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	—	4	2	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	#536	1	2	yes	—
402	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
403	#544	—	2	2	no	—
404	#544	—	2	2	no	—
405	#544	C₂²×C₃₁	1	4	yes	—
406	#544	C₂²×C₃₁	1	4	yes	—
407	#542	C₂²×C₃₁	1	2	yes	—
408	#542	C₂²×C₃₁	1	2	yes	—
409	#541	C₂²×C₃₁	1	2	yes	—
410	#540	C₂²×C₃₁	1	2	yes	—
411	#539	—	2	1	no	—
412	#539	—	2	1	no	—
413	#538	—	2	1	no	—
414	#538	—	2	1	no	—
415	#533	C₂²×C₃₁	1	1	yes	characteristic
416	#532	C₂²×C₃₁	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	—	2	1	no	—
418	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
420	#529	—	2	2	no	—
421	#529	—	2	2	no	—
422	C₂×#125	—	2	1	no	—
423	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
424	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
425	#525	C₂²×C₃₁	1	2	yes	—
426	C₂×C₂²⋊Q₈	—	2	1	no	—
427	C₂×C₂²⋊Q₈	—	2	1	no	—
428	C₄×#41	C₂²×C₃₁	1	2	yes	—
429	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
432	#501	C₂²×C₃₁	1	4	yes	complemented
433	#501	C₂²×C₃₁	1	2	yes	complemented
434	#501	C₂²×C₃₁	1	2	yes	complemented
435	#500	C₂²×C₃₁	1	2	yes	complemented
436	#499	C₂²×C₃₁	1	4	yes	complemented
437	#498	C₂²×C₃₁	1	2	yes	complemented
438	#491	C₂²×C₃₁	1	2	yes	complemented
439	#490	C₂²×C₃₁	1	2	yes	complemented
440	#489	C₂²×C₃₁	1	4	yes	complemented
441	#488	C₂²×C₃₁	1	4	yes	complemented
442	#487	C₂²×C₃₁	1	2	yes	complemented
443	#486	C₂²×C₃₁	1	2	yes	complemented
444	#485	C₂²×C₃₁	1	4	yes	—
445	#485	C₂²×C₃₁	1	4	yes	—
446	#484	C₂²×C₃₁	1	4	yes	—
447	#483	C₂²×C₃₁	1	4	yes	—
448	#482	C₂²×C₃₁	1	4	yes	—
449	#482	C₂²×C₃₁	1	4	yes	—
450	#481	C₂²×C₃₁	1	4	yes	—
451	#480	C₂²×C₃₁	1	4	yes	—
452	#479	C₂²×C₃₁	1	4	yes	complemented
453	#479	C₂²×C₃₁	1	4	yes	complemented
454	#478	C₂²×C₃₁	1	4	yes	complemented
455	#478	C₂²×C₃₁	1	4	yes	complemented
456	#477	C₂²×C₃₁	1	4	yes	complemented
457	#476	C₂²×C₃₁	1	4	yes	complemented
458	#475	C₂²×C₃₁	1	4	yes	complemented
459	#474	C₂²×C₃₁	1	4	yes	complemented
460	#433	C₂²×C₃₁	1	4	yes	—
461	#433	C₂²×C₃₁	1	4	yes	—
462	#428	C₂²×C₃₁	1	2	yes	—
463	#428	C₂²×C₃₁	1	2	yes	—
464	#428	C₂²×C₃₁	1	2	yes	—
465	#428	C₂²×C₃₁	1	2	yes	—
466	#423	C₂²×C₃₁	1	2	yes	—
467	#417	C₂²×C₃₁	1	2	yes	—
468	#417	C₂²×C₃₁	1	2	yes	—
469	#417	C₂²×C₃₁	1	2	yes	—
470	#417	C₂²×C₃₁	1	2	yes	—
471	#407	C₂²×C₃₁	1	2	yes	—
472	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
473	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
474	C₂×C₃₁	—	2	2	no	—
475	C₂×C₃₁	—	4	2	no	—
476	C₂×C₃₁	—	8	2	no	—
477	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
478	C₂×C₃₁	#3585	1	1	yes	characteristic
479	C₂×C₃₁	#3586	1	1	yes	characteristic
480	C₂×#41	C₂³×C₃₁	1	2	yes	—
481	C₂²×Q₈	—	2	1	no	—
482	C₂²×Q₈	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
486	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
487	C₄⋊Q₈	—	2	4	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
494	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
498	#127	C₂³×C₃₁	1	1	yes	characteristic
499	#126	—	2	2	no	—
500	#126	—	2	2	no	—
501	#126	—	2	2	no	—
502	#126	—	2	2	no	—
503	#125	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	2	no	—
506	#125	—	2	2	no	—
507	#125	—	2	2	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	C₂³×C₃₁	1	4	yes	—
511	#125	C₂³×C₃₁	1	2	yes	—
512	#125	C₂³×C₃₁	1	2	yes	—
513	#125	C₂³×C₃₁	1	2	yes	—
514	#124	—	2	2	no	—
515	#124	—	2	2	no	—
516	#124	C₂³×C₃₁	1	2	yes	—
517	#123	—	2	2	no	—
518	#123	—	2	2	no	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
531	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	C₂³×C₃₁	1	2	yes	—
537	#121	C₂³×C₃₁	1	2	yes	—
538	#120	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	C₂³×C₃₁	1	2	yes	—
550	C₄×D₄	C₂³×C₃₁	1	2	yes	—
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	D₄×C₃₁	1	2	yes	—
554	#117	D₄×C₃₁	1	2	yes	—
555	#117	C₂³×C₃₁	1	4	yes	—
556	#117	C₂³×C₃₁	1	2	yes	—
557	#117	C₂³×C₃₁	1	2	yes	—
558	#117	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
568	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
577	C₂×C₄²	—	2	1	no	—
578	C₂×C₄²	—	2	2	no	—
579	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
581	#107	C₂³×C₃₁	1	4	yes	—
582	#107	C₂³×C₃₁	1	4	yes	—
583	#107	C₂³×C₃₁	1	4	yes	—
584	#107	C₂³×C₃₁	1	4	yes	—
585	#106	C₂³×C₃₁	1	4	yes	—
586	#106	C₂³×C₃₁	1	4	yes	—
587	#106	C₂³×C₃₁	1	4	yes	—
588	#106	C₂³×C₃₁	1	4	yes	—
589	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
590	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
591	#103	C₂³×C₃₁	1	4	yes	—
592	#103	C₂³×C₃₁	1	4	yes	—
593	#103	C₂³×C₃₁	1	4	yes	—
594	#103	C₂³×C₃₁	1	4	yes	—
595	#102	C₂³×C₃₁	1	4	yes	—
596	#102	C₂³×C₃₁	1	4	yes	—
597	#102	C₂³×C₃₁	1	4	yes	—
598	#102	C₂³×C₃₁	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
601	#97	C₂³×C₃₁	1	2	yes	—
602	#97	C₂³×C₃₁	1	2	yes	—
603	C₄×C₈	C₂³×C₃₁	1	2	yes	—
604	C₄×C₈	C₂³×C₃₁	1	2	yes	—
605	C₃₁	#60867	1	1	yes	characteristic, direct product factor, Sylow
606	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
607	#41	—	2	8	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	8	2	no	—
614	C₂×Q₈	—	8	2	no	—
615	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	8	2	no	—
632	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	M₁₆	—	2	4	no	—
641	M₁₆	—	2	4	no	—
642	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
643	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
670	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
689	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
690	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
691	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₃₁	1	2	yes	—
697	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
699	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₄²	C₂⁴×C₃₁	1	2	yes	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
707	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	Q₈	—	2	4	no	—
709	Q₈	—	8	1	no	—
710	Q₈	—	8	1	no	—
711	Q₈	—	8	4	no	—
712	Q₈	—	8	2	no	—
713	Q₈	—	8	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	2	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
743	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
750	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
751	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
752	C₈	—	2	4	no	—
753	C₈	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	C₃₁×#536	1	2	yes	—
764	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	C₃₁×#536	1	2	yes	—
780	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
781	C₂	—	2	2	no	—
782	C₂	—	4	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
785	C₂	C₃₁×#3585	1	1	yes	characteristic
786	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#544	C₂	semidirect
3. C₃₁×#3244	C₂	semidirect
4. C₃₁×#3243	C₂	semidirect
5. C₃₁×#3242	C₂	semidirect
6. C₃₁×#3241	C₂	semidirect
7. C₃₁×#3166	C₂	semidirect
8. C₃₁×#3165	C₂	semidirect
9. C₃₁×#3142	C₂	semidirect
10. C₃₁×#3141	C₂	semidirect
11. C₃₁×#3093	C₂	semidirect
12. C₃₁×#3092	C₂	semidirect
13. C₃₁×#3080	C₂	semidirect
14. C₃₁×#3079	C₂	semidirect
15. C₃₁×#2921	C₂	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#501	C₂²	semidirect
47. C₃₁×#501	C₂²	semidirect
48. C₃₁×#500	C₂²	semidirect
49. C₃₁×#499	C₂²	semidirect
50. C₃₁×#498	C₂²	semidirect
51. C₃₁×#491	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
55. C₃₁×#487	C₂²	semidirect
56. C₃₁×#486	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#477	C₂²	semidirect
70. C₃₁×#476	C₂²	semidirect
71. C₃₁×#475	C₂²	semidirect
72. C₃₁×#474	C₂²	semidirect
308. #60867	C₃₁	direct (N × H)
361. C₂×#544	C₂×C₃₁	semidirect
363. #3244	C₂×C₃₁	semidirect
364. #3243	C₂×C₃₁	semidirect
365. #3242	C₂×C₃₁	semidirect
366. #3241	C₂×C₃₁	semidirect
367. #3166	C₂×C₃₁	semidirect
368. #3165	C₂×C₃₁	semidirect
369. #3142	C₂×C₃₁	semidirect
370. #3141	C₂×C₃₁	semidirect
371. #3093	C₂×C₃₁	semidirect
372. #3092	C₂×C₃₁	semidirect
373. #3080	C₂×C₃₁	semidirect
374. #3079	C₂×C₃₁	semidirect
375. #2921	C₂×C₃₁	semidirect
432. #501	C₂²×C₃₁	semidirect
433. #501	C₂²×C₃₁	semidirect
434. #501	C₂²×C₃₁	semidirect
435. #500	C₂²×C₃₁	semidirect
436. #499	C₂²×C₃₁	semidirect
437. #498	C₂²×C₃₁	semidirect
438. #491	C₂²×C₃₁	semidirect
439. #490	C₂²×C₃₁	semidirect
440. #489	C₂²×C₃₁	semidirect
441. #488	C₂²×C₃₁	semidirect
442. #487	C₂²×C₃₁	semidirect
443. #486	C₂²×C₃₁	semidirect
452. #479	C₂²×C₃₁	semidirect
453. #479	C₂²×C₃₁	semidirect
454. #478	C₂²×C₃₁	semidirect
455. #478	C₂²×C₃₁	semidirect
456. #477	C₂²×C₃₁	semidirect
457. #476	C₂²×C₃₁	semidirect
458. #475	C₂²×C₃₁	semidirect
459. #474	C₂²×C₃₁	semidirect
605. C₃₁	#60867	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#544	2
C₃₁×#3455	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3241	2
C₃₁×#3166	2
C₃₁×#3165	2
C₃₁×#3142	2
C₃₁×#3141	2
C₃₁×#3093	2
C₃₁×#3092	2
C₃₁×#3080	2
C₃₁×#3079	2
C₃₁×#2921	2
#60867	31

Subgroups — C31×#60867 #21517626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60867 #21517626