Subgroups — C₃₁×#61894 #21518653

Order 7936.

1730 conjugacy classes of subgroups.

The subgroup lattice has 802 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×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3376	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3108	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	—	2	2	no	—
20	C₃₁×#556	—	2	2	no	—
21	C₃₁×#556	C₂²	1	4	yes	—
22	C₃₁×#556	C₂²	1	4	yes	—
23	C₃₁×#556	C₂²	1	2	yes	complemented
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×#126	—	2	1	no	—
35	C₂×C₃₁×#126	—	2	1	no	—
36	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
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×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#117	—	2	1	no	—
45	C₃₁×#497	C₂²	1	2	yes	—
46	C₃₁×#497	C₂²	1	4	yes	complemented
47	C₃₁×#496	C₂²	1	2	yes	—
48	C₃₁×#495	C₂²	1	4	yes	—
49	C₃₁×#491	C₂²	1	4	yes	complemented
50	C₃₁×#489	C₂²	1	2	yes	—
51	C₃₁×#489	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	—
53	C₃₁×#483	C₂²	1	2	yes	—
54	C₃₁×#480	C₂²	1	2	yes	—
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	—
57	C₃₁×#477	C₂²	1	2	yes	complemented
58	C₃₁×#475	C₂²	1	2	yes	complemented
59	C₃₁×#464	C₂²	1	4	yes	—
60	C₃₁×#464	C₂²	1	4	yes	—
61	C₃₁×#464	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	—
63	C₃₁×#463	C₂²	1	4	yes	—
64	C₃₁×#463	C₂²	1	4	yes	—
65	C₃₁×#462	C₂²	1	2	yes	complemented
66	C₃₁×#462	C₂²	1	4	yes	complemented
67	C₃₁×#461	C₂²	1	4	yes	complemented
68	C₃₁×#460	C₂²	1	2	yes	complemented
69	C₃₁×#451	C₂²	1	2	yes	—
70	C₃₁×#451	C₂²	1	2	yes	—
71	C₃₁×#450	C₂²	1	2	yes	—
72	C₃₁×#448	C₂²	1	2	yes	—
73	C₃₁×#448	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×#441	C₂²	1	4	yes	complemented
79	C₃₁×#440	C₂²	1	4	yes	—
80	C₃₁×#440	C₂²	1	4	yes	complemented
81	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
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	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×D₈×C₃₁	C₂³	1	4	yes	—
99	C₃₁×C₄⋊Q₈	—	2	2	no	—
100	C₃₁×C₄⋊Q₈	—	2	2	no	—
101	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	4	no	—
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#126	—	2	4	no	—
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#126	—	2	2	no	—
111	C₃₁×#126	—	2	2	no	—
112	C₃₁×#126	—	2	2	no	—
113	C₃₁×#126	—	2	2	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	—	2	2	no	—
116	C₃₁×#125	—	2	1	no	—
117	C₃₁×#125	C₂³	1	2	yes	—
118	C₃₁×#125	C₂³	1	2	yes	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	1	no	—
122	C₃₁×#124	—	2	1	no	—
123	C₃₁×#124	—	2	1	no	—
124	C₃₁×#124	C₂³	1	2	yes	—
125	C₃₁×#124	C₂³	1	2	yes	—
126	C₃₁×#124	C₂³	1	4	yes	—
127	C₃₁×#124	C₂³	1	2	yes	—
128	C₃₁×#124	C₂³	1	2	yes	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	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	—	2	1	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×#121	—	2	1	no	—
142	C₃₁×#121	C₂³	1	2	yes	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	—	2	1	no	—
148	C₄×Q₈×C₃₁	D₄	1	2	yes	—
149	C₄×Q₈×C₃₁	D₄	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	4	yes	—
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₃₁×#117	—	2	1	no	—
168	C₃₁×#117	—	2	4	no	—
169	C₃₁×#117	—	2	4	no	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	2	no	—
172	C₃₁×#117	—	2	2	no	—
173	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	D₄	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×C₂²⋊C₄×C₃₁	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₄²×C₃₁	—	2	1	no	—
188	C₂×C₄²×C₃₁	—	2	1	no	—
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₃₁×#107	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	4	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	2	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×#103	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	4	yes	—
209	C₃₁×#97	C₂³	1	2	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	1	no	—
217	C₂×Q₈×C₃₁	—	2	1	no	—
218	C₂×Q₈×C₃₁	—	4	2	no	—
219	C₂×Q₈×C₃₁	—	4	2	no	—
220	C₂×Q₈×C₃₁	—	4	2	no	—
221	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	2	1	no	—
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	4	2	no	—
231	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
232	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	—	2	1	no	—
234	C₂²×C₄×C₃₁	—	2	1	no	—
235	C₂²×C₄×C₃₁	—	2	1	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	2	4	no	—
238	C₂²×C₄×C₃₁	—	2	2	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	4	4	no	—
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	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	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₃₁	—	4	4	no	—
249	Q₁₆×C₃₁	—	4	4	no	—
250	SD₁₆×C₃₁	—	4	4	no	—
251	SD₁₆×C₃₁	—	4	4	no	—
252	SD₁₆×C₃₁	—	4	4	no	—
253	D₈×C₃₁	—	4	4	no	—
254	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
255	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
256	C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₄⋊C₄×C₃₁	—	2	4	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	4	no	—
264	C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	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	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	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	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	2	no	—
304	C₄²×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	C₂×D₄	1	2	yes	—
306	C₄²×C₃₁	C₂×D₄	1	2	yes	—
307	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	2	yes	—
310	C₄²×C₃₁	C₂⁴	1	2	yes	—
311	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
313	#61894	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	4	2	no	—
317	C₂³×C₃₁	—	4	2	no	—
318	C₂³×C₃₁	—	4	2	no	—
319	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₃₁	—	2	2	no	—
321	Q₈×C₃₁	—	2	4	no	—
322	Q₈×C₃₁	—	2	4	no	—
323	Q₈×C₃₁	—	2	2	no	—
324	Q₈×C₃₁	—	4	2	no	—
325	Q₈×C₃₁	—	4	2	no	—
326	Q₈×C₃₁	—	4	2	no	—
327	Q₈×C₃₁	—	4	2	no	—
328	Q₈×C₃₁	—	4	2	no	—
329	Q₈×C₃₁	—	8	1	no	—
330	D₄×C₃₁	—	2	4	no	—
331	D₄×C₃₁	—	2	4	no	—
332	D₄×C₃₁	—	4	2	no	—
333	D₄×C₃₁	—	4	2	no	—
334	D₄×C₃₁	—	4	4	no	—
335	D₄×C₃₁	—	8	1	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	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	4	1	no	—
347	C₂×C₄×C₃₁	—	4	1	no	—
348	C₂×C₄×C₃₁	—	4	1	no	—
349	C₂×C₄×C₃₁	—	4	8	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	4	2	no	—
352	C₂×C₄×C₃₁	—	4	2	no	—
353	C₂×C₄×C₃₁	—	4	2	no	—
354	C₂×C₄×C₃₁	—	8	2	no	—
355	C₂×C₄×C₃₁	—	8	2	no	—
356	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
366	C₈×C₃₁	—	2	4	no	—
367	C₈×C₃₁	—	2	4	no	—
368	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
369	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#3402	C₂×C₃₁	1	4	yes	complemented
371	#3401	C₂×C₃₁	1	4	yes	complemented
372	#3377	C₂×C₃₁	1	4	yes	complemented
373	#3376	C₂×C₃₁	1	4	yes	complemented
374	#3218	C₂×C₃₁	1	2	yes	complemented
375	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#3213	C₂×C₃₁	1	1	yes	characteristic
377	#3211	C₂×C₃₁	1	2	yes	complemented
378	#3114	C₂×C₃₁	1	2	yes	complemented
379	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3108	C₂×C₃₁	1	2	yes	complemented
382	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
383	C₂²×C₃₁	—	2	1	no	—
384	C₂²×C₃₁	—	2	1	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	—	4	2	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	8	4	no	—
392	C₂²×C₃₁	#575	1	2	yes	—
393	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
394	C₄×C₃₁	—	2	2	no	—
395	C₄×C₃₁	—	2	2	no	—
396	C₄×C₃₁	—	2	1	no	—
397	C₄×C₃₁	—	2	1	no	—
398	C₄×C₃₁	—	2	1	no	—
399	C₄×C₃₁	—	2	2	no	—
400	C₄×C₃₁	—	2	1	no	—
401	C₄×C₃₁	—	2	1	no	—
402	C₄×C₃₁	—	2	2	no	—
403	C₄×C₃₁	—	4	2	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	—	4	2	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	#585	1	2	yes	—
410	#559	C₂²×C₃₁	1	2	yes	complemented
411	#557	C₂²×C₃₁	1	2	yes	complemented
412	#556	—	2	2	no	—
413	#556	—	2	2	no	—
414	#556	—	2	2	no	—
415	#556	C₂²×C₃₁	1	4	yes	—
416	#556	C₂²×C₃₁	1	4	yes	—
417	#556	C₂²×C₃₁	1	2	yes	complemented
418	#554	C₂²×C₃₁	1	2	yes	complemented
419	#552	—	2	2	no	—
420	#539	—	2	1	no	—
421	#539	—	2	1	no	—
422	#536	—	2	1	no	—
423	#533	C₂²×C₃₁	1	1	yes	characteristic
424	#532	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
426	#529	C₂²×C₃₁	1	2	yes	—
427	#529	C₂²×C₃₁	1	2	yes	—
428	C₂×#126	—	2	1	no	—
429	C₂×#126	—	2	1	no	—
430	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	—	2	1	no	—
433	#520	—	2	1	no	—
434	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×#117	—	2	1	no	—
439	#497	C₂²×C₃₁	1	2	yes	—
440	#497	C₂²×C₃₁	1	4	yes	complemented
441	#496	C₂²×C₃₁	1	2	yes	—
442	#495	C₂²×C₃₁	1	4	yes	—
443	#491	C₂²×C₃₁	1	4	yes	complemented
444	#489	C₂²×C₃₁	1	2	yes	—
445	#489	C₂²×C₃₁	1	2	yes	—
446	#488	C₂²×C₃₁	1	4	yes	—
447	#483	C₂²×C₃₁	1	2	yes	—
448	#480	C₂²×C₃₁	1	2	yes	—
449	#479	C₂²×C₃₁	1	4	yes	complemented
450	#478	C₂²×C₃₁	1	4	yes	—
451	#477	C₂²×C₃₁	1	2	yes	complemented
452	#475	C₂²×C₃₁	1	2	yes	complemented
453	#464	C₂²×C₃₁	1	4	yes	—
454	#464	C₂²×C₃₁	1	4	yes	—
455	#464	C₂²×C₃₁	1	4	yes	complemented
456	#463	C₂²×C₃₁	1	4	yes	—
457	#463	C₂²×C₃₁	1	4	yes	—
458	#463	C₂²×C₃₁	1	4	yes	—
459	#462	C₂²×C₃₁	1	2	yes	complemented
460	#462	C₂²×C₃₁	1	4	yes	complemented
461	#461	C₂²×C₃₁	1	4	yes	complemented
462	#460	C₂²×C₃₁	1	2	yes	complemented
463	#451	C₂²×C₃₁	1	2	yes	—
464	#451	C₂²×C₃₁	1	2	yes	—
465	#450	C₂²×C₃₁	1	2	yes	—
466	#448	C₂²×C₃₁	1	2	yes	—
467	#448	C₂²×C₃₁	1	2	yes	—
468	#447	C₂²×C₃₁	1	2	yes	—
469	#446	C₂²×C₃₁	1	4	yes	complemented
470	#446	C₂²×C₃₁	1	4	yes	complemented
471	#442	C₂²×C₃₁	1	4	yes	—
472	#441	C₂²×C₃₁	1	4	yes	complemented
473	#440	C₂²×C₃₁	1	4	yes	—
474	#440	C₂²×C₃₁	1	4	yes	complemented
475	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
476	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
477	#432	C₂²×C₃₁	1	1	yes	characteristic
478	#432	C₂²×C₃₁	1	1	yes	characteristic
479	#432	C₂²×C₃₁	1	2	yes	—
480	#431	C₂²×C₃₁	1	2	yes	—
481	C₂×C₃₁	—	2	2	no	—
482	C₂×C₃₁	—	8	2	no	—
483	C₂×C₃₁	—	8	2	no	—
484	C₂×C₃₁	#3487	1	1	yes	characteristic
485	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
486	C₂×C₃₁	#3586	1	1	yes	characteristic
487	C₂×#41	—	2	1	no	—
488	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
494	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
498	C₂×D₈	C₂³×C₃₁	1	4	yes	—
499	C₄⋊Q₈	—	2	2	no	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
502	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
505	#127	C₂³×C₃₁	1	1	yes	characteristic
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#126	—	2	4	no	—
509	#126	—	2	4	no	—
510	#126	—	2	2	no	—
511	#126	—	2	2	no	—
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#125	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	—	2	1	no	—
517	#125	C₂³×C₃₁	1	2	yes	—
518	#125	C₂³×C₃₁	1	2	yes	—
519	#124	—	2	2	no	—
520	#124	—	2	2	no	—
521	#124	—	2	1	no	—
522	#124	—	2	1	no	—
523	#124	—	2	1	no	—
524	#124	C₂³×C₃₁	1	2	yes	—
525	#124	C₂³×C₃₁	1	4	yes	—
526	#124	C₂³×C₃₁	1	2	yes	—
527	#124	C₂³×C₃₁	1	2	yes	—
528	#124	C₂³×C₃₁	1	2	yes	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
541	#121	—	2	1	no	—
542	#121	C₂³×C₃₁	1	2	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	D₄×C₃₁	1	2	yes	—
549	C₄×Q₈	D₄×C₃₁	1	2	yes	—
550	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
551	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
552	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
553	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
554	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
555	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
557	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	C₂³×C₃₁	1	4	yes	—
564	C₄×D₄	C₂³×C₃₁	1	2	yes	—
565	C₄×D₄	C₂³×C₃₁	1	2	yes	—
566	C₄×D₄	C₂³×C₃₁	1	2	yes	—
567	#117	—	2	1	no	—
568	#117	—	2	4	no	—
569	#117	—	2	4	no	—
570	#117	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₄²	—	2	1	no	—
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
592	#107	C₂³×C₃₁	1	4	yes	—
593	#106	C₂³×C₃₁	1	4	yes	—
594	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
595	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
596	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
597	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
598	#103	C₂³×C₃₁	1	4	yes	—
599	#103	C₂³×C₃₁	1	4	yes	—
600	#103	C₂³×C₃₁	1	4	yes	—
601	#103	C₂³×C₃₁	1	4	yes	—
602	#103	C₂³×C₃₁	1	4	yes	—
603	#102	C₂³×C₃₁	1	4	yes	—
604	#102	C₂³×C₃₁	1	4	yes	—
605	#102	C₂³×C₃₁	1	4	yes	—
606	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
607	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
608	#97	C₂³×C₃₁	1	4	yes	—
609	#97	C₂³×C₃₁	1	2	yes	—
610	#97	C₂³×C₃₁	1	2	yes	—
611	C₄×C₈	C₂³×C₃₁	1	4	yes	—
612	C₃₁	#61894	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	—	2	1	no	—
614	#41	—	4	4	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×Q₈	—	4	2	no	—
622	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
623	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
633	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	4	4	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
649	Q₁₆	—	4	4	no	—
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	4	no	—
654	D₈	—	4	4	no	—
655	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
656	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×C₃₁	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×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	2	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	C₂×D₄×C₃₁	1	2	yes	—
707	C₄²	C₂×D₄×C₃₁	1	2	yes	—
708	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₄²	C₂⁴×C₃₁	1	2	yes	—
711	C₄²	C₂⁴×C₃₁	1	2	yes	—
712	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	2	4	no	—
722	Q₈	—	2	4	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
765	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
766	C₈	—	2	4	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	8	4	no	—
777	C₂²	C₃₁×#575	1	2	yes	—
778	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	C₃₁×#585	1	2	yes	—
795	C₂	—	2	2	no	—
796	C₂	—	8	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₃₁×#3487	1	1	yes	characteristic
799	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
800	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×#3213	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×#556	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3377	C₂	semidirect
6. C₃₁×#3376	C₂	semidirect
7. C₃₁×#3218	C₂	semidirect
8. C₃₁×#3215	C₂	semidirect
10. C₃₁×#3211	C₂	semidirect
11. C₃₁×#3114	C₂	semidirect
12. C₃₁×#3113	C₂	semidirect
13. C₃₁×#3112	C₂	semidirect
14. C₃₁×#3108	C₂	semidirect
15. C₃₁×#2983	C₂	semidirect
16. C₃₁×#559	C₂²	semidirect
17. C₃₁×#557	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
46. C₃₁×#497	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
61. C₃₁×#464	C₂²	semidirect
65. C₃₁×#462	C₂²	semidirect
66. C₃₁×#462	C₂²	semidirect
67. C₃₁×#461	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
75. C₃₁×#446	C₂²	semidirect
76. C₃₁×#446	C₂²	semidirect
78. C₃₁×#441	C₂²	semidirect
80. C₃₁×#440	C₂²	semidirect
81. C₄×Q₁₆×C₃₁	C₂²	semidirect
82. C₄×SD₁₆×C₃₁	C₂²	semidirect
313. #61894	C₃₁	direct (N × H)
368. #3507	C₂×C₃₁	semidirect
369. C₂×#556	C₂×C₃₁	semidirect
370. #3402	C₂×C₃₁	semidirect
371. #3401	C₂×C₃₁	semidirect
372. #3377	C₂×C₃₁	semidirect
373. #3376	C₂×C₃₁	semidirect
374. #3218	C₂×C₃₁	semidirect
375. #3215	C₂×C₃₁	semidirect
377. #3211	C₂×C₃₁	semidirect
378. #3114	C₂×C₃₁	semidirect
379. #3113	C₂×C₃₁	semidirect
380. #3112	C₂×C₃₁	semidirect
381. #3108	C₂×C₃₁	semidirect
382. #2983	C₂×C₃₁	semidirect
410. #559	C₂²×C₃₁	semidirect
411. #557	C₂²×C₃₁	semidirect
417. #556	C₂²×C₃₁	semidirect
418. #554	C₂²×C₃₁	semidirect
440. #497	C₂²×C₃₁	semidirect
443. #491	C₂²×C₃₁	semidirect
449. #479	C₂²×C₃₁	semidirect
451. #477	C₂²×C₃₁	semidirect
452. #475	C₂²×C₃₁	semidirect
455. #464	C₂²×C₃₁	semidirect
459. #462	C₂²×C₃₁	semidirect
460. #462	C₂²×C₃₁	semidirect
461. #461	C₂²×C₃₁	semidirect
462. #460	C₂²×C₃₁	semidirect
469. #446	C₂²×C₃₁	semidirect
470. #446	C₂²×C₃₁	semidirect
472. #441	C₂²×C₃₁	semidirect
474. #440	C₂²×C₃₁	semidirect
475. C₄×Q₁₆	C₂²×C₃₁	semidirect
476. C₄×SD₁₆	C₂²×C₃₁	semidirect
612. C₃₁	#61894	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×#556	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3218	2
C₃₁×#3215	2
C₃₁×#3213	2
C₃₁×#3211	2
C₃₁×#3114	2
C₃₁×#3113	2
C₃₁×#3112	2
C₃₁×#3108	2
C₃₁×#2983	2
#61894	31

Subgroups — C31×#61894 #21518653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61894 #21518653