Subgroups — C₃₁×#61831 #21518590

Order 7936.

1750 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3388	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3376	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3239	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#3105	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#559	C₂²	1	2	yes	complemented
17	C₃₁×#557	C₂²	1	2	yes	complemented
18	C₃₁×#556	—	2	2	no	—
19	C₃₁×#556	C₂²	1	2	yes	complemented
20	C₃₁×#554	—	2	2	no	—
21	C₃₁×#554	—	2	2	no	—
22	C₃₁×#554	C₂²	1	4	yes	—
23	C₃₁×#554	C₂²	1	4	yes	—
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#539	—	2	1	no	—
27	C₃₁×#539	—	2	1	no	—
28	C₃₁×#536	—	2	1	no	—
29	C₃₁×#533	C₂²	1	1	yes	characteristic
30	C₃₁×#532	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃₁×#529	C₂²	1	2	yes	—
33	C₃₁×#529	C₂²	1	2	yes	—
34	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
39	C₃₁×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
45	C₃₁×#501	C₂²	1	2	yes	complemented
46	C₃₁×#501	C₂²	1	4	yes	complemented
47	C₃₁×#501	C₂²	1	2	yes	complemented
48	C₃₁×#499	C₂²	1	4	yes	complemented
49	C₃₁×#491	C₂²	1	2	yes	complemented
50	C₃₁×#490	C₂²	1	2	yes	complemented
51	C₃₁×#489	C₂²	1	4	yes	complemented
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#484	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	2	yes	—
55	C₃₁×#483	C₂²	1	2	yes	—
56	C₃₁×#481	C₂²	1	2	yes	—
57	C₃₁×#481	C₂²	1	2	yes	—
58	C₃₁×#480	C₂²	1	2	yes	—
59	C₃₁×#479	C₂²	1	4	yes	complemented
60	C₃₁×#479	C₂²	1	4	yes	complemented
61	C₃₁×#478	C₂²	1	4	yes	—
62	C₃₁×#478	C₂²	1	4	yes	—
63	C₃₁×#478	C₂²	1	4	yes	complemented
64	C₃₁×#478	C₂²	1	4	yes	complemented
65	C₃₁×#476	C₂²	1	2	yes	—
66	C₃₁×#475	C₂²	1	4	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	4	yes	complemented
69	C₃₁×#463	C₂²	1	4	yes	—
70	C₃₁×#463	C₂²	1	4	yes	—
71	C₃₁×#461	C₂²	1	2	yes	—
72	C₃₁×#459	C₂²	1	2	yes	—
73	C₃₁×#450	C₂²	1	2	yes	—
74	C₃₁×#447	C₂²	1	2	yes	—
75	C₃₁×#446	C₂²	1	4	yes	complemented
76	C₃₁×#446	C₂²	1	4	yes	complemented
77	C₃₁×#442	C₂²	1	4	yes	—
78	C₃₁×#442	C₂²	1	4	yes	—
79	C₃₁×#440	C₂²	1	4	yes	—
80	C₃₁×#440	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
82	C₄×D₈×C₃₁	C₂²	1	4	yes	—
83	C₃₁×#432	C₂²	1	1	yes	characteristic
84	C₃₁×#432	C₂²	1	1	yes	characteristic
85	C₃₁×#432	C₂²	1	2	yes	—
86	C₃₁×#431	C₂²	1	2	yes	—
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂²×Q₈×C₃₁	—	2	1	no	—
89	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂³×C₄×C₃₁	—	2	1	no	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×D₈×C₃₁	C₂³	1	4	yes	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	—	2	2	no	—
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×#127	C₂³	1	1	yes	characteristic
103	C₃₁×#126	—	2	2	no	—
104	C₃₁×#126	—	2	2	no	—
105	C₃₁×#126	—	2	2	no	—
106	C₃₁×#126	—	2	2	no	—
107	C₃₁×#125	—	2	2	no	—
108	C₃₁×#125	—	2	2	no	—
109	C₃₁×#125	—	2	2	no	—
110	C₃₁×#125	—	2	1	no	—
111	C₃₁×#125	—	2	1	no	—
112	C₃₁×#125	—	2	1	no	—
113	C₃₁×#125	C₂³	1	2	yes	—
114	C₃₁×#125	C₂³	1	2	yes	—
115	C₃₁×#125	C₂³	1	2	yes	—
116	C₃₁×#125	C₂³	1	4	yes	—
117	C₃₁×#125	C₂³	1	2	yes	—
118	C₃₁×#124	—	2	2	no	—
119	C₃₁×#124	—	2	1	no	—
120	C₃₁×#124	C₂³	1	2	yes	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#123	—	2	2	no	—
123	C₃₁×#123	—	2	2	no	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#121	—	2	1	no	—
139	C₃₁×#121	C₂³	1	2	yes	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	D₄	1	2	yes	—
143	C₄×Q₈×C₃₁	D₄	1	2	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×D₄×C₃₁	—	2	2	no	—
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	—	2	1	no	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	4	yes	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	4	yes	—
161	C₄×D₄×C₃₁	C₂³	1	2	yes	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₃₁×#117	—	2	1	no	—
165	C₃₁×#117	—	2	2	no	—
166	C₃₁×#117	—	2	2	no	—
167	C₃₁×#117	—	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	4	no	—
174	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
175	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
176	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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×#106	C₂³	1	4	yes	—
192	C₃₁×#106	C₂³	1	4	yes	—
193	C₃₁×#106	C₂³	1	4	yes	—
194	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
196	C₃₁×C₄⋊C₈	C₂³	1	2	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×#102	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	2	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×#97	C₂³	1	2	yes	—
209	C₃₁×#97	C₂³	1	4	yes	—
210	C₃₁×#97	C₂³	1	2	yes	—
211	C₄×C₈×C₃₁	C₂³	1	4	yes	—
212	C₂⁴×C₃₁	—	2	1	no	—
213	#41×C₃₁	—	4	4	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	—	4	2	no	—
218	C₂×Q₈×C₃₁	—	8	2	no	—
219	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
220	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₃₁	—	2	4	no	—
223	C₂×D₄×C₃₁	—	2	2	no	—
224	C₂×D₄×C₃₁	—	2	1	no	—
225	C₂×D₄×C₃₁	—	2	1	no	—
226	C₂×D₄×C₃₁	—	2	1	no	—
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
233	C₂²×C₄×C₃₁	—	2	2	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	2	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	2	2	no	—
238	C₂²×C₄×C₃₁	—	2	2	no	—
239	C₂²×C₄×C₃₁	—	4	4	no	—
240	C₂²×C₄×C₃₁	—	8	2	no	—
241	C₂²×C₄×C₃₁	—	8	2	no	—
242	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	SD₁₆×C₃₁	—	2	8	no	—
250	D₈×C₃₁	—	2	8	no	—
251	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
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	1	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	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	—	2	2	no	—
295	C₂²⋊C₄×C₃₁	—	2	2	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	2	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	2	yes	—
304	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₃₁	C₂⁴	1	2	yes	—
307	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₄²×C₃₁	C₂⁴	1	2	yes	—
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	#61831	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₃₁	—	2	4	no	—
312	C₂³×C₃₁	—	2	2	no	—
313	C₂³×C₃₁	—	2	2	no	—
314	C₂³×C₃₁	—	4	2	no	—
315	C₂³×C₃₁	—	4	2	no	—
316	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₃₁	—	2	4	no	—
318	Q₈×C₃₁	—	4	2	no	—
319	Q₈×C₃₁	—	4	2	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	8	1	no	—
322	Q₈×C₃₁	—	8	4	no	—
323	D₄×C₃₁	—	2	4	no	—
324	D₄×C₃₁	—	2	2	no	—
325	D₄×C₃₁	—	2	4	no	—
326	D₄×C₃₁	—	4	2	no	—
327	D₄×C₃₁	—	4	4	no	—
328	D₄×C₃₁	—	8	1	no	—
329	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
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	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	4	1	no	—
341	C₂×C₄×C₃₁	—	4	1	no	—
342	C₂×C₄×C₃₁	—	4	1	no	—
343	C₂×C₄×C₃₁	—	4	8	no	—
344	C₂×C₄×C₃₁	—	4	4	no	—
345	C₂×C₄×C₃₁	—	4	2	no	—
346	C₂×C₄×C₃₁	—	4	2	no	—
347	C₂×C₄×C₃₁	—	4	2	no	—
348	C₂×C₄×C₃₁	—	8	2	no	—
349	C₂×C₄×C₃₁	—	8	2	no	—
350	C₂×C₄×C₃₁	—	8	4	no	—
351	C₂×C₄×C₃₁	—	8	2	no	—
352	C₂×C₄×C₃₁	—	8	2	no	—
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
363	C₈×C₃₁	—	2	4	no	—
364	C₈×C₃₁	—	2	4	no	—
365	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#554	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#3389	C₂×C₃₁	1	4	yes	complemented
368	#3388	C₂×C₃₁	1	4	yes	complemented
369	#3376	C₂×C₃₁	1	4	yes	complemented
370	#3370	C₂×C₃₁	1	4	yes	complemented
371	#3239	C₂×C₃₁	1	2	yes	complemented
372	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#3232	C₂×C₃₁	1	2	yes	complemented
375	#3114	C₂×C₃₁	1	2	yes	complemented
376	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#3109	C₂×C₃₁	1	1	yes	characteristic
378	#3105	C₂×C₃₁	1	2	yes	complemented
379	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	1	no	—
382	C₂²×C₃₁	—	2	4	no	—
383	C₂²×C₃₁	—	4	8	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	4	2	no	—
389	C₂²×C₃₁	#575	1	2	yes	—
390	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₃₁	—	2	2	no	—
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	2	2	no	—
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	2	2	no	—
397	C₄×C₃₁	—	2	1	no	—
398	C₄×C₃₁	—	2	1	no	—
399	C₄×C₃₁	—	2	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	2	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	—	4	2	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
407	#559	C₂²×C₃₁	1	2	yes	complemented
408	#557	C₂²×C₃₁	1	2	yes	complemented
409	#556	—	2	2	no	—
410	#556	C₂²×C₃₁	1	2	yes	complemented
411	#554	—	2	2	no	—
412	#554	—	2	2	no	—
413	#554	C₂²×C₃₁	1	4	yes	—
414	#554	C₂²×C₃₁	1	4	yes	—
415	#554	C₂²×C₃₁	1	2	yes	complemented
416	#552	—	2	2	no	—
417	#539	—	2	1	no	—
418	#539	—	2	1	no	—
419	#536	—	2	1	no	—
420	#533	C₂²×C₃₁	1	1	yes	characteristic
421	#532	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
423	#529	C₂²×C₃₁	1	2	yes	—
424	#529	C₂²×C₃₁	1	2	yes	—
425	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	—	2	1	no	—
428	C₂×C₂²⋊Q₈	—	2	1	no	—
429	C₂×C₂²⋊Q₈	—	2	1	no	—
430	#520	—	2	1	no	—
431	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	—	2	1	no	—
436	#501	C₂²×C₃₁	1	2	yes	complemented
437	#501	C₂²×C₃₁	1	4	yes	complemented
438	#501	C₂²×C₃₁	1	2	yes	complemented
439	#499	C₂²×C₃₁	1	4	yes	complemented
440	#491	C₂²×C₃₁	1	2	yes	complemented
441	#490	C₂²×C₃₁	1	2	yes	complemented
442	#489	C₂²×C₃₁	1	4	yes	complemented
443	#488	C₂²×C₃₁	1	4	yes	complemented
444	#484	C₂²×C₃₁	1	2	yes	—
445	#484	C₂²×C₃₁	1	2	yes	—
446	#483	C₂²×C₃₁	1	2	yes	—
447	#481	C₂²×C₃₁	1	2	yes	—
448	#481	C₂²×C₃₁	1	2	yes	—
449	#480	C₂²×C₃₁	1	2	yes	—
450	#479	C₂²×C₃₁	1	4	yes	complemented
451	#479	C₂²×C₃₁	1	4	yes	complemented
452	#478	C₂²×C₃₁	1	4	yes	—
453	#478	C₂²×C₃₁	1	4	yes	—
454	#478	C₂²×C₃₁	1	4	yes	complemented
455	#478	C₂²×C₃₁	1	4	yes	complemented
456	#476	C₂²×C₃₁	1	2	yes	—
457	#475	C₂²×C₃₁	1	4	yes	complemented
458	#474	C₂²×C₃₁	1	2	yes	—
459	#474	C₂²×C₃₁	1	4	yes	complemented
460	#463	C₂²×C₃₁	1	4	yes	—
461	#463	C₂²×C₃₁	1	4	yes	—
462	#461	C₂²×C₃₁	1	2	yes	—
463	#459	C₂²×C₃₁	1	2	yes	—
464	#450	C₂²×C₃₁	1	2	yes	—
465	#447	C₂²×C₃₁	1	2	yes	—
466	#446	C₂²×C₃₁	1	4	yes	complemented
467	#446	C₂²×C₃₁	1	4	yes	complemented
468	#442	C₂²×C₃₁	1	4	yes	—
469	#442	C₂²×C₃₁	1	4	yes	—
470	#440	C₂²×C₃₁	1	4	yes	—
471	#440	C₂²×C₃₁	1	4	yes	—
472	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
473	C₄×D₈	C₂²×C₃₁	1	4	yes	—
474	#432	C₂²×C₃₁	1	1	yes	characteristic
475	#432	C₂²×C₃₁	1	1	yes	characteristic
476	#432	C₂²×C₃₁	1	2	yes	—
477	#431	C₂²×C₃₁	1	2	yes	—
478	C₂×C₃₁	—	2	2	no	—
479	C₂×C₃₁	—	4	4	no	—
480	C₂×C₃₁	—	8	2	no	—
481	C₂×C₃₁	#3486	1	1	yes	characteristic
482	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
483	C₂×C₃₁	#3585	1	1	yes	characteristic
484	C₂×#41	—	2	1	no	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
492	C₂×D₈	C₂³×C₃₁	1	4	yes	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
497	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
499	#127	C₂³×C₃₁	1	1	yes	characteristic
500	#126	—	2	2	no	—
501	#126	—	2	2	no	—
502	#126	—	2	2	no	—
503	#126	—	2	2	no	—
504	#125	—	2	2	no	—
505	#125	—	2	2	no	—
506	#125	—	2	2	no	—
507	#125	—	2	1	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	C₂³×C₃₁	1	2	yes	—
511	#125	C₂³×C₃₁	1	4	yes	—
512	#125	C₂³×C₃₁	1	2	yes	—
513	#125	C₂³×C₃₁	1	2	yes	—
514	#125	C₂³×C₃₁	1	2	yes	—
515	#124	—	2	2	no	—
516	#124	—	2	1	no	—
517	#124	C₂³×C₃₁	1	2	yes	—
518	#124	C₂³×C₃₁	1	2	yes	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
535	#121	—	2	1	no	—
536	#121	C₂³×C₃₁	1	2	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	D₄×C₃₁	1	2	yes	—
540	C₄×Q₈	D₄×C₃₁	1	2	yes	—
541	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
545	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	C₂³×C₃₁	1	4	yes	—
555	C₄×D₄	C₂³×C₃₁	1	2	yes	—
556	C₄×D₄	C₂³×C₃₁	1	4	yes	—
557	C₄×D₄	C₂³×C₃₁	1	2	yes	—
558	C₄×D₄	C₂³×C₃₁	1	2	yes	—
559	C₄×D₄	C₂³×C₃₁	1	2	yes	—
560	C₄×D₄	C₂³×C₃₁	1	2	yes	—
561	#117	—	2	1	no	—
562	#117	—	2	2	no	—
563	#117	—	2	2	no	—
564	#117	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	—	2	4	no	—
572	C₂×C₄⋊C₄	—	2	2	no	—
573	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
574	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
585	#107	C₂³×C₃₁	1	4	yes	—
586	#107	C₂³×C₃₁	1	4	yes	—
587	#107	C₂³×C₃₁	1	4	yes	—
588	#106	C₂³×C₃₁	1	4	yes	—
589	#106	C₂³×C₃₁	1	4	yes	—
590	#106	C₂³×C₃₁	1	4	yes	—
591	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
592	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
593	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
594	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
595	#103	C₂³×C₃₁	1	4	yes	—
596	#103	C₂³×C₃₁	1	4	yes	—
597	#103	C₂³×C₃₁	1	4	yes	—
598	#102	C₂³×C₃₁	1	4	yes	—
599	#102	C₂³×C₃₁	1	4	yes	—
600	#102	C₂³×C₃₁	1	4	yes	—
601	#102	C₂³×C₃₁	1	4	yes	—
602	#102	C₂³×C₃₁	1	4	yes	—
603	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
604	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
605	#97	C₂³×C₃₁	1	2	yes	—
606	#97	C₂³×C₃₁	1	4	yes	—
607	#97	C₂³×C₃₁	1	2	yes	—
608	C₄×C₈	C₂³×C₃₁	1	4	yes	—
609	C₃₁	#61831	1	1	yes	characteristic, direct product factor, Sylow
610	C₂⁴	—	2	1	no	—
611	#41	—	4	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	8	2	no	—
617	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
626	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	8	2	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
647	SD₁₆	—	2	8	no	—
648	D₈	—	2	8	no	—
649	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
650	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	C₂×D₄×C₃₁	1	2	yes	—
701	C₄²	C₂×D₄×C₃₁	1	2	yes	—
702	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₃₁	1	2	yes	—
705	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
706	C₄²	C₂⁴×C₃₁	1	2	yes	—
707	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	8	1	no	—
719	Q₈	—	8	4	no	—
720	D₄	—	2	4	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	4	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	4	no	—
725	D₄	—	8	1	no	—
726	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	8	2	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	—	8	2	no	—
750	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
753	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
759	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
760	C₈	—	2	4	no	—
761	C₈	—	2	4	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	8	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	C₃₁×#575	1	2	yes	—
772	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
773	C₄	—	2	1	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	2	no	—
792	C₂	C₃₁×#3486	1	1	yes	characteristic
793	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
794	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3109	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
2. C₂×C₃₁×#554	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3376	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3239	C₂	semidirect
8. C₃₁×#3236	C₂	semidirect
9. C₃₁×#3234	C₂	semidirect
10. C₃₁×#3232	C₂	semidirect
11. C₃₁×#3114	C₂	semidirect
12. C₃₁×#3110	C₂	semidirect
14. C₃₁×#3105	C₂	semidirect
15. C₃₁×#2983	C₂	semidirect
16. C₃₁×#559	C₂²	semidirect
17. C₃₁×#557	C₂²	semidirect
19. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#501	C₂²	semidirect
47. C₃₁×#501	C₂²	semidirect
48. C₃₁×#499	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
50. C₃₁×#490	C₂²	semidirect
51. C₃₁×#489	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
59. C₃₁×#479	C₂²	semidirect
60. C₃₁×#479	C₂²	semidirect
63. C₃₁×#478	C₂²	semidirect
64. C₃₁×#478	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
75. C₃₁×#446	C₂²	semidirect
76. C₃₁×#446	C₂²	semidirect
310. #61831	C₃₁	direct (N × H)
365. #3507	C₂×C₃₁	semidirect
366. C₂×#554	C₂×C₃₁	semidirect
367. #3389	C₂×C₃₁	semidirect
368. #3388	C₂×C₃₁	semidirect
369. #3376	C₂×C₃₁	semidirect
370. #3370	C₂×C₃₁	semidirect
371. #3239	C₂×C₃₁	semidirect
372. #3236	C₂×C₃₁	semidirect
373. #3234	C₂×C₃₁	semidirect
374. #3232	C₂×C₃₁	semidirect
375. #3114	C₂×C₃₁	semidirect
376. #3110	C₂×C₃₁	semidirect
378. #3105	C₂×C₃₁	semidirect
379. #2983	C₂×C₃₁	semidirect
407. #559	C₂²×C₃₁	semidirect
408. #557	C₂²×C₃₁	semidirect
410. #556	C₂²×C₃₁	semidirect
415. #554	C₂²×C₃₁	semidirect
436. #501	C₂²×C₃₁	semidirect
437. #501	C₂²×C₃₁	semidirect
438. #501	C₂²×C₃₁	semidirect
439. #499	C₂²×C₃₁	semidirect
440. #491	C₂²×C₃₁	semidirect
441. #490	C₂²×C₃₁	semidirect
442. #489	C₂²×C₃₁	semidirect
443. #488	C₂²×C₃₁	semidirect
450. #479	C₂²×C₃₁	semidirect
451. #479	C₂²×C₃₁	semidirect
454. #478	C₂²×C₃₁	semidirect
455. #478	C₂²×C₃₁	semidirect
457. #475	C₂²×C₃₁	semidirect
459. #474	C₂²×C₃₁	semidirect
466. #446	C₂²×C₃₁	semidirect
467. #446	C₂²×C₃₁	semidirect
609. C₃₁	#61831	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×#3507	2
C₂×C₃₁×#554	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3376	2
C₃₁×#3370	2
C₃₁×#3239	2
C₃₁×#3236	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3114	2
C₃₁×#3110	2
C₃₁×#3109	2
C₃₁×#3105	2
C₃₁×#2983	2
#61831	31

Subgroups — C31×#61831 #21518590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61831 #21518590