Subgroups — C₃₁×#61348 #21518107

Order 7936.

1782 conjugacy classes of subgroups.

The subgroup lattice has 800 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	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3367	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3363	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3046	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2951	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#135	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	2	yes	—
21	Q₈²×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#557	C₂²	1	2	yes	—
23	C₃₁×#557	C₂²	1	2	yes	—
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#556	C₂²	1	4	yes	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#554	—	2	2	no	—
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#552	—	2	2	no	—
30	D₄×Q₈×C₃₁	—	2	2	no	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#544	—	2	2	no	—
33	C₃₁×#544	C₂²	1	2	yes	—
34	C₃₁×#539	—	2	2	no	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃₁×#529	—	2	2	no	—
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₃₁×#520	C₂²	1	2	yes	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#491	C₂²	1	4	yes	—
47	C₃₁×#489	C₂²	1	4	yes	—
48	C₃₁×#489	C₂²	1	4	yes	—
49	C₃₁×#488	C₂²	1	4	yes	—
50	C₃₁×#487	C₂²	1	4	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#486	C₂²	1	2	yes	—
53	C₃₁×#479	C₂²	1	4	yes	—
54	C₃₁×#478	C₂²	1	4	yes	—
55	C₃₁×#477	C₂²	1	4	yes	—
56	C₃₁×#477	C₂²	1	2	yes	—
57	C₃₁×#477	C₂²	1	4	yes	—
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#474	C₂²	1	4	yes	—
60	C₃₁×#464	C₂²	1	4	yes	—
61	C₃₁×#464	C₂²	1	2	yes	—
62	C₃₁×#463	C₂²	1	4	yes	—
63	C₃₁×#463	C₂²	1	2	yes	—
64	C₃₁×#462	C₂²	1	1	yes	characteristic
65	C₃₁×#462	C₂²	1	4	yes	—
66	C₃₁×#461	C₂²	1	4	yes	—
67	C₃₁×#461	C₂²	1	1	yes	characteristic
68	C₃₁×#460	C₂²	1	1	yes	characteristic
69	C₃₁×#459	C₂²	1	1	yes	characteristic
70	C₃₁×#446	C₂²	1	4	yes	—
71	C₃₁×#446	C₂²	1	2	yes	—
72	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
73	C₃₁×#441	C₂²	1	2	yes	—
74	C₃₁×#440	C₂²	1	2	yes	—
75	C₃₁×#440	C₂²	1	4	yes	—
76	C₃₁×#440	C₂²	1	4	yes	—
77	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
79	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×D₈×C₃₁	C₂²	1	4	yes	—
81	C₃₁×#428	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#107	C₂²	1	2	yes	—
83	C₃₁×#424	C₂²	1	2	yes	—
84	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₃₁×#419	C₂²	1	1	yes	characteristic
86	C₃₁×#417	C₂²	1	2	yes	—
87	C₃₁×#417	C₂²	1	2	yes	—
88	C₃₁×#417	C₂²	1	1	yes	characteristic
89	C₃₁×#416	C₂²	1	2	yes	—
90	C₂×C₃₁×#103	C₂²	1	2	yes	—
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	C₂³	1	2	yes	—
94	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₃₁	—	2	2	no	—
96	C₂²×Q₈×C₃₁	—	2	1	no	—
97	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₃₁×#137	—	2	4	no	—
99	C₃₁×#135	—	2	8	no	—
100	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	—	2	2	no	—
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	—	2	4	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
120	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×#127	C₂³	1	1	yes	characteristic
123	C₃₁×#126	—	2	4	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#125	—	2	2	no	—
126	C₃₁×#125	—	2	2	no	—
127	C₃₁×#125	—	2	4	no	—
128	C₃₁×#125	—	2	4	no	—
129	C₃₁×#125	D₄	1	2	yes	—
130	C₃₁×#125	C₂³	1	4	yes	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	C₂³	1	4	yes	—
133	C₃₁×#124	C₂³	1	2	yes	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	—	2	4	no	—
144	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	4	no	—
165	C₄×D₄×C₃₁	—	2	4	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	1	no	—
168	C₄×D₄×C₃₁	C₂³	1	4	yes	—
169	C₄×D₄×C₃₁	C₂³	1	4	yes	—
170	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₃₁×#117	—	2	2	no	—
173	C₃₁×#117	—	2	2	no	—
174	C₃₁×#117	—	2	4	no	—
175	C₃₁×#117	—	2	1	no	—
176	C₃₁×#117	C₂³	1	1	yes	characteristic
177	C₃₁×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
181	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	—	2	1	no	—
186	C₂×C₄²×C₃₁	—	2	1	no	—
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	2	yes	—
191	C₃₁×#106	C₂³	1	2	yes	—
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
195	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
196	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
197	C₃₁×#103	C₂³	1	4	yes	—
198	C₃₁×#103	C₂³	1	4	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#103	C₂³	1	2	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#103	C₂³	1	4	yes	—
204	C₃₁×#103	C₂³	1	2	yes	—
205	C₃₁×#103	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	2	yes	—
207	C₃₁×#102	C₂³	1	2	yes	—
208	C₃₁×#102	C₂³	1	2	yes	—
209	C₃₁×#102	C₂³	1	4	yes	—
210	C₃₁×#102	C₂³	1	4	yes	—
211	C₃₁×#97	C₂³	1	2	yes	—
212	C₃₁×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₃₁	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	4	yes	—
215	#41×C₃₁	—	2	2	no	—
216	#41×C₃₁	—	2	4	no	—
217	#41×C₃₁	—	2	4	no	—
218	#41×C₃₁	#41	1	4	yes	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	4	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	—	2	2	no	—
225	C₂×Q₈×C₃₁	—	8	2	no	—
226	C₂×Q₈×C₃₁	—	8	4	no	—
227	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂×D₄×C₃₁	—	2	1	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	1	no	—
235	C₂×D₄×C₃₁	—	2	1	no	—
236	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	1	no	—
243	C₂²×C₄×C₃₁	—	2	1	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	4	no	—
247	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₃₁	—	2	4	no	—
251	Q₁₆×C₃₁	—	2	4	no	—
252	SD₁₆×C₃₁	—	2	4	no	—
253	SD₁₆×C₃₁	—	2	4	no	—
254	SD₁₆×C₃₁	—	2	4	no	—
255	D₈×C₃₁	—	2	4	no	—
256	M₁₆×C₃₁	—	2	2	no	—
257	M₁₆×C₃₁	—	2	2	no	—
258	C₂×C₈×C₃₁	—	2	4	no	—
259	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
260	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
261	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
262	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	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	4	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₃₁	—	2	1	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	1	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	1	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	1	no	—
304	C₄²×C₃₁	—	2	1	no	—
305	C₄²×C₃₁	—	2	4	no	—
306	C₄²×C₃₁	—	2	4	no	—
307	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₃₁	C₂⁴	1	4	yes	—
311	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
312	#61348	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂³×C₃₁	—	2	1	no	—
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₃₁	—	2	4	no	—
317	Q₈×C₃₁	—	2	1	no	—
318	Q₈×C₃₁	—	2	2	no	—
319	Q₈×C₃₁	—	2	2	no	—
320	Q₈×C₃₁	—	2	2	no	—
321	Q₈×C₃₁	—	2	2	no	—
322	Q₈×C₃₁	—	4	2	no	—
323	Q₈×C₃₁	—	4	4	no	—
324	Q₈×C₃₁	—	4	2	no	—
325	Q₈×C₃₁	—	8	2	no	—
326	Q₈×C₃₁	—	8	4	no	—
327	Q₈×C₃₁	C₂×#41	1	2	yes	—
328	D₄×C₃₁	—	2	4	no	—
329	D₄×C₃₁	—	2	2	no	—
330	D₄×C₃₁	—	2	1	no	—
331	D₄×C₃₁	—	2	2	no	—
332	D₄×C₃₁	—	4	4	no	—
333	D₄×C₃₁	—	4	2	no	—
334	D₄×C₃₁	—	8	1	no	—
335	D₄×C₃₁	C₂×#41	1	2	yes	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	4	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	1	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	4	no	—
345	C₂×C₄×C₃₁	—	4	1	no	—
346	C₂×C₄×C₃₁	—	4	2	no	—
347	C₂×C₄×C₃₁	—	4	2	no	—
348	C₂×C₄×C₃₁	—	4	4	no	—
349	C₂×C₄×C₃₁	—	4	2	no	—
350	C₂×C₄×C₃₁	—	8	4	no	—
351	C₂×C₄×C₃₁	—	8	4	no	—
352	C₂×C₄×C₃₁	—	8	1	no	—
353	C₂×C₄×C₃₁	—	8	2	no	—
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂²×D₄	1	4	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	C₂×#41	1	2	yes	—
362	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
363	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
364	C₈×C₃₁	—	2	2	no	—
365	C₈×C₃₁	—	2	2	no	—
366	C₈×C₃₁	—	2	2	no	—
367	C₈×C₃₁	—	2	2	no	—
368	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#3377	C₂×C₃₁	1	4	yes	complemented
371	#3375	C₂×C₃₁	1	2	yes	complemented
372	#3372	C₂×C₃₁	1	2	yes	complemented
373	#3367	C₂×C₃₁	1	4	yes	complemented
374	#3363	C₂×C₃₁	1	2	yes	complemented
375	#3361	C₂×C₃₁	1	2	yes	complemented
376	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#3137	C₂×C₃₁	1	2	yes	complemented
378	#3083	C₂×C₃₁	1	2	yes	complemented
379	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#3046	C₂×C₃₁	1	2	yes	complemented
381	#3035	C₂×C₃₁	1	1	yes	characteristic
382	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
383	#2951	C₂×C₃₁	1	2	yes	complemented
384	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
385	C₂²×C₃₁	—	2	1	no	—
386	C₂²×C₃₁	—	2	1	no	—
387	C₂²×C₃₁	—	2	2	no	—
388	C₂²×C₃₁	—	4	1	no	—
389	C₂²×C₃₁	—	4	1	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	#548	1	2	yes	—
394	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	2	1	no	—
397	C₄×C₃₁	—	2	4	no	—
398	C₄×C₃₁	—	2	2	no	—
399	C₄×C₃₁	—	2	1	no	—
400	C₄×C₃₁	—	2	4	no	—
401	C₄×C₃₁	—	4	1	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	—	4	4	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	2	no	—
406	C₄×C₃₁	—	4	1	no	—
407	C₄×C₃₁	#548	1	2	yes	—
408	C₄×C₃₁	#578	1	2	yes	—
409	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
410	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
412	C₂×#135	C₂²×C₃₁	1	2	yes	—
413	#559	C₂²×C₃₁	1	2	yes	—
414	Q₈²	C₂²×C₃₁	1	2	yes	—
415	#557	C₂²×C₃₁	1	2	yes	—
416	#557	C₂²×C₃₁	1	2	yes	—
417	#556	—	2	1	no	—
418	#556	C₂²×C₃₁	1	4	yes	—
419	#554	—	2	1	no	—
420	#554	—	2	2	no	—
421	#554	C₂²×C₃₁	1	2	yes	—
422	#552	—	2	2	no	—
423	D₄×Q₈	—	2	2	no	—
424	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
425	#544	—	2	2	no	—
426	#544	C₂²×C₃₁	1	2	yes	—
427	#539	—	2	2	no	—
428	#536	C₂²×C₃₁	1	2	yes	—
429	#533	—	2	1	no	—
430	#533	C₂²×C₃₁	1	1	yes	characteristic
431	#532	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	—	2	1	no	—
433	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
434	#529	—	2	2	no	—
435	#520	C₂²×C₃₁	1	2	yes	—
436	#520	C₂²×C₃₁	1	2	yes	—
437	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
439	#491	C₂²×C₃₁	1	4	yes	—
440	#489	C₂²×C₃₁	1	4	yes	—
441	#489	C₂²×C₃₁	1	4	yes	—
442	#488	C₂²×C₃₁	1	4	yes	—
443	#487	C₂²×C₃₁	1	4	yes	—
444	#487	C₂²×C₃₁	1	2	yes	—
445	#486	C₂²×C₃₁	1	2	yes	—
446	#479	C₂²×C₃₁	1	4	yes	—
447	#478	C₂²×C₃₁	1	4	yes	—
448	#477	C₂²×C₃₁	1	2	yes	—
449	#477	C₂²×C₃₁	1	4	yes	—
450	#477	C₂²×C₃₁	1	2	yes	—
451	#477	C₂²×C₃₁	1	4	yes	—
452	#474	C₂²×C₃₁	1	4	yes	—
453	#464	C₂²×C₃₁	1	4	yes	—
454	#464	C₂²×C₃₁	1	2	yes	—
455	#463	C₂²×C₃₁	1	4	yes	—
456	#463	C₂²×C₃₁	1	2	yes	—
457	#462	C₂²×C₃₁	1	1	yes	characteristic
458	#462	C₂²×C₃₁	1	4	yes	—
459	#461	C₂²×C₃₁	1	4	yes	—
460	#461	C₂²×C₃₁	1	1	yes	characteristic
461	#460	C₂²×C₃₁	1	1	yes	characteristic
462	#459	C₂²×C₃₁	1	1	yes	characteristic
463	#446	C₂²×C₃₁	1	4	yes	—
464	#446	C₂²×C₃₁	1	2	yes	—
465	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
466	#441	C₂²×C₃₁	1	2	yes	—
467	#440	C₂²×C₃₁	1	2	yes	—
468	#440	C₂²×C₃₁	1	4	yes	—
469	#440	C₂²×C₃₁	1	4	yes	—
470	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
471	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
472	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
473	C₄×D₈	C₂²×C₃₁	1	4	yes	—
474	#428	C₂²×C₃₁	1	1	yes	characteristic
475	C₂×#107	C₂²×C₃₁	1	2	yes	—
476	#424	C₂²×C₃₁	1	2	yes	—
477	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
478	#419	C₂²×C₃₁	1	1	yes	characteristic
479	#417	C₂²×C₃₁	1	2	yes	—
480	#417	C₂²×C₃₁	1	2	yes	—
481	#417	C₂²×C₃₁	1	1	yes	characteristic
482	#416	C₂²×C₃₁	1	2	yes	—
483	C₂×#103	C₂²×C₃₁	1	2	yes	—
484	#405	C₂²×C₃₁	1	2	yes	—
485	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×C₃₁	—	2	2	no	—
487	C₂×C₃₁	—	4	2	no	—
488	C₂×C₃₁	—	8	2	no	—
489	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
490	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
491	C₂×C₃₁	#3585	1	1	yes	characteristic
492	C₂×#41	C₂³×C₃₁	1	2	yes	—
493	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×Q₈	—	2	2	no	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
497	#137	—	2	4	no	—
498	#135	—	2	8	no	—
499	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
500	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
504	C₂×D₈	C₂³×C₃₁	1	2	yes	—
505	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
506	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	4	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
515	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
518	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
521	#127	C₂³×C₃₁	1	1	yes	characteristic
522	#126	—	2	4	no	—
523	#126	—	2	4	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	D₄×C₃₁	1	2	yes	—
529	#125	C₂³×C₃₁	1	4	yes	—
530	#124	—	2	2	no	—
531	#124	C₂³×C₃₁	1	2	yes	—
532	#124	C₂³×C₃₁	1	4	yes	—
533	#123	—	2	4	no	—
534	#123	—	2	4	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
544	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
553	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
554	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
555	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
556	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
557	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
558	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
559	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
569	C₄×D₄	C₂³×C₃₁	1	4	yes	—
570	C₄×D₄	C₂³×C₃₁	1	4	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	4	no	—
574	#117	—	2	1	no	—
575	#117	C₂³×C₃₁	1	1	yes	characteristic
576	#117	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	2	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄²	—	2	1	no	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
587	#107	C₂³×C₃₁	1	4	yes	—
588	#107	C₂³×C₃₁	1	4	yes	—
589	#107	C₂³×C₃₁	1	2	yes	—
590	#106	C₂³×C₃₁	1	2	yes	—
591	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
594	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
595	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
596	#103	C₂³×C₃₁	1	4	yes	—
597	#103	C₂³×C₃₁	1	4	yes	—
598	#103	C₂³×C₃₁	1	2	yes	—
599	#103	C₂³×C₃₁	1	2	yes	—
600	#103	C₂³×C₃₁	1	2	yes	—
601	#103	C₂³×C₃₁	1	4	yes	—
602	#103	C₂³×C₃₁	1	4	yes	—
603	#103	C₂³×C₃₁	1	2	yes	—
604	#103	C₂³×C₃₁	1	2	yes	—
605	#102	C₂³×C₃₁	1	2	yes	—
606	#102	C₂³×C₃₁	1	2	yes	—
607	#102	C₂³×C₃₁	1	2	yes	—
608	#102	C₂³×C₃₁	1	4	yes	—
609	#102	C₂³×C₃₁	1	4	yes	—
610	#97	C₂³×C₃₁	1	2	yes	—
611	#97	C₂³×C₃₁	1	4	yes	—
612	C₄×C₈	C₂³×C₃₁	1	2	yes	—
613	C₄×C₈	C₂³×C₃₁	1	4	yes	—
614	C₃₁	#61348	1	1	yes	characteristic, direct product factor, Sylow
615	#41	—	2	2	no	—
616	#41	—	2	4	no	—
617	#41	—	2	4	no	—
618	#41	#41×C₃₁	1	4	yes	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	8	2	no	—
626	C₂×Q₈	—	8	4	no	—
627	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
628	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
650	Q₁₆	—	2	4	no	—
651	Q₁₆	—	2	4	no	—
652	SD₁₆	—	2	4	no	—
653	SD₁₆	—	2	4	no	—
654	SD₁₆	—	2	4	no	—
655	D₈	—	2	4	no	—
656	M₁₆	—	2	2	no	—
657	M₁₆	—	2	2	no	—
658	C₂×C₈	—	2	4	no	—
659	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
660	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
661	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
662	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
681	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
682	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
683	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
684	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
688	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
689	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
710	C₄²	C₂⁴×C₃₁	1	4	yes	—
711	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₂³	—	2	1	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	4	no	—
723	Q₈	—	4	2	no	—
724	Q₈	—	8	2	no	—
725	Q₈	—	8	4	no	—
726	Q₈	C₂×#41×C₃₁	1	2	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	C₂×#41×C₃₁	1	2	yes	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	1	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
755	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
758	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
760	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
761	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
762	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
763	C₈	—	2	2	no	—
764	C₈	—	2	2	no	—
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	C₃₁×#548	1	2	yes	—
776	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
777	C₄	—	2	2	no	—
778	C₄	—	2	1	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	4	no	—
789	C₄	C₃₁×#548	1	2	yes	—
790	C₄	C₃₁×#578	1	2	yes	—
791	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
792	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂	—	2	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
797	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
798	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×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3363	C₂	semidirect
8. C₃₁×#3361	C₂	semidirect
9. C₃₁×#3141	C₂	semidirect
10. C₃₁×#3137	C₂	semidirect
11. C₃₁×#3083	C₂	semidirect
12. C₂×C₃₁×#477	C₂	semidirect
13. C₃₁×#3046	C₂	semidirect
15. C₃₁×#2962	C₂	semidirect
16. C₃₁×#2951	C₂	semidirect
17. C₄×C₃₁×#137	C₂	semidirect
312. #61348	C₃₁	direct (N × H)
368. #3507	C₂×C₃₁	semidirect
369. #3503	C₂×C₃₁	semidirect
370. #3377	C₂×C₃₁	semidirect
371. #3375	C₂×C₃₁	semidirect
372. #3372	C₂×C₃₁	semidirect
373. #3367	C₂×C₃₁	semidirect
374. #3363	C₂×C₃₁	semidirect
375. #3361	C₂×C₃₁	semidirect
376. #3141	C₂×C₃₁	semidirect
377. #3137	C₂×C₃₁	semidirect
378. #3083	C₂×C₃₁	semidirect
379. C₂×#477	C₂×C₃₁	semidirect
380. #3046	C₂×C₃₁	semidirect
382. #2962	C₂×C₃₁	semidirect
383. #2951	C₂×C₃₁	semidirect
384. C₄×#137	C₂×C₃₁	semidirect
614. C₃₁	#61348	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
C₃₁×#3503	2
C₃₁×#3377	2
C₃₁×#3375	2
C₃₁×#3372	2
C₃₁×#3367	2
C₃₁×#3363	2
C₃₁×#3361	2
C₃₁×#3141	2
C₃₁×#3137	2
C₃₁×#3083	2
C₂×C₃₁×#477	2
C₃₁×#3046	2
C₃₁×#3035	2
C₃₁×#2962	2
C₃₁×#2951	2
C₄×C₃₁×#137	2
#61348	31

Subgroups — C31×#61348 #21518107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61348 #21518107