Subgroups — C₃₁×#60770 #21517529

Order 7936.

2132 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3202	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3190	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3189	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
19	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₃₁	—	2	2	no	—
24	C₃₁×#548	—	2	2	no	—
25	C₃₁×#547	—	2	4	no	—
26	C₃₁×#547	—	2	2	no	—
27	C₃₁×#546	—	2	4	no	—
28	C₃₁×#546	—	2	2	no	—
29	C₃₁×#537	C₂²	1	2	yes	—
30	C₃₁×#537	C₂²	1	4	yes	—
31	C₃₁×#536	C₂²	1	2	yes	—
32	C₃₁×#536	C₂²	1	4	yes	—
33	C₃₁×#525	C₂²	1	4	yes	—
34	C₃₁×#525	C₂²	1	2	yes	—
35	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃₁×#520	C₂²	1	2	yes	—
38	C₃₁×#485	C₂²	1	4	yes	complemented
39	C₃₁×#485	C₂²	1	4	yes	complemented
40	C₃₁×#485	C₂²	1	4	yes	complemented
41	C₃₁×#484	C₂²	1	4	yes	complemented
42	C₃₁×#484	C₂²	1	4	yes	complemented
43	C₃₁×#483	C₂²	1	4	yes	complemented
44	C₃₁×#482	C₂²	1	4	yes	complemented
45	C₃₁×#480	C₂²	1	4	yes	complemented
46	C₃₁×#470	C₂²	1	4	yes	complemented
47	C₃₁×#468	C₂²	1	4	yes	complemented
48	C₃₁×#467	C₂²	1	1	yes	characteristic
49	C₃₁×#467	C₂²	1	4	yes	—
50	C₃₁×#467	C₂²	1	2	yes	—
51	C₃₁×#467	C₂²	1	2	yes	—
52	C₃₁×#467	C₂²	1	2	yes	complemented
53	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#467	C₂²	1	2	yes	complemented
55	C₃₁×#466	C₂²	1	1	yes	characteristic
56	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#465	C₂²	1	2	yes	—
58	C₃₁×#465	C₂²	1	4	yes	—
59	C₃₁×#465	C₂²	1	2	yes	complemented
60	C₃₁×#452	C₂²	1	4	yes	complemented
61	C₃₁×#452	C₂²	1	4	yes	complemented
62	C₃₁×#452	C₂²	1	4	yes	complemented
63	C₃₁×#451	C₂²	1	4	yes	complemented
64	C₃₁×#451	C₂²	1	4	yes	complemented
65	C₃₁×#451	C₂²	1	4	yes	complemented
66	C₃₁×#449	C₂²	1	4	yes	complemented
67	C₃₁×#448	C₂²	1	4	yes	complemented
68	C₃₁×#428	C₂²	1	2	yes	complemented
69	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#419	C₂²	1	2	yes	complemented
72	C₃₁×#417	C₂²	1	2	yes	complemented
73	C₃₁×#416	C₂²	1	2	yes	complemented
74	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
75	C₃₁×#408	C₂²	1	2	yes	—
76	C₃₁×#408	C₂²	1	2	yes	—
77	C₃₁×#408	C₂²	1	2	yes	—
78	C₃₁×#408	C₂²	1	2	yes	—
79	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
80	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
81	C₃₁×2₋¹⁺⁴	—	4	4	no	—
82	C₃₁×2₋¹⁺⁴	—	4	4	no	—
83	C₂×#41×C₃₁	—	2	4	no	—
84	C₂×#41×C₃₁	—	2	2	no	—
85	C₂×#41×C₃₁	—	4	2	no	—
86	C₂×#41×C₃₁	—	4	2	no	—
87	C₂×#41×C₃₁	D₄	1	2	yes	—
88	C₂×#41×C₃₁	D₄	1	2	yes	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂×#41×C₃₁	C₂³	1	2	yes	—
92	C₂×#41×C₃₁	C₂³	1	2	yes	—
93	C₂²×Q₈×C₃₁	—	2	2	no	—
94	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
95	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
96	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
97	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₃₁	D₄	1	2	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
101	C₃₁×#137	—	4	4	no	—
102	C₃₁×#135	—	4	2	no	—
103	C₂×Q₁₆×C₃₁	—	4	2	no	—
104	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₃₁	—	4	2	no	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
113	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂²×C₈×C₃₁	—	4	2	no	—
115	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₃₁×C₄⋊Q₈	—	2	2	no	—
123	C₃₁×C₄⋊Q₈	—	2	4	no	—
124	C₃₁×#124	—	2	2	no	—
125	C₃₁×#124	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₃₁×#121	—	2	4	no	—
145	C₃₁×#121	—	2	4	no	—
146	C₃₁×#121	—	2	4	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	4	no	—
149	C₃₁×#121	C₂³	1	4	yes	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#121	C₂³	1	2	yes	—
152	C₃₁×#120	—	2	2	no	—
153	C₃₁×#120	—	2	4	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	4	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	4	no	—
161	C₃₁×#117	C₂³	1	2	yes	—
162	C₃₁×#117	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	1	yes	characteristic
172	C₃₁×#107	C₂³	1	1	yes	characteristic
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#103	C₂³	1	4	yes	—
177	C₃₁×#103	C₂³	1	4	yes	—
178	C₃₁×#103	C₂³	1	2	yes	—
179	C₃₁×#103	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
192	#41×C₃₁	—	2	4	no	—
193	#41×C₃₁	—	2	4	no	—
194	#41×C₃₁	—	2	4	no	—
195	#41×C₃₁	—	2	4	no	—
196	#41×C₃₁	—	4	2	no	—
197	#41×C₃₁	—	4	2	no	—
198	#41×C₃₁	—	4	4	no	—
199	#41×C₃₁	—	4	4	no	—
200	#41×C₃₁	—	4	4	no	—
201	#41×C₃₁	—	4	4	no	—
202	#41×C₃₁	—	4	16	no	—
203	#41×C₃₁	—	4	8	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	2	2	no	—
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	—	2	4	no	—
208	C₂×Q₈×C₃₁	—	4	2	no	—
209	C₂×Q₈×C₃₁	—	4	4	no	—
210	C₂×Q₈×C₃₁	—	4	4	no	—
211	C₂×Q₈×C₃₁	—	4	8	no	—
212	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
215	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₃₁	—	2	2	no	—
217	C₂×D₄×C₃₁	—	2	4	no	—
218	C₂×D₄×C₃₁	—	2	2	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	4	2	no	—
222	C₂×D₄×C₃₁	—	4	4	no	—
223	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	2	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	—	4	2	no	—
237	C₂²×C₄×C₃₁	—	4	2	no	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	Q₁₆×C₃₁	—	4	2	no	—
248	Q₁₆×C₃₁	—	4	2	no	—
249	Q₁₆×C₃₁	—	4	1	no	—
250	Q₁₆×C₃₁	—	4	4	no	—
251	SD₁₆×C₃₁	—	4	2	no	—
252	SD₁₆×C₃₁	—	4	4	no	—
253	D₈×C₃₁	—	4	1	no	—
254	M₁₆×C₃₁	—	2	4	no	—
255	M₁₆×C₃₁	—	4	2	no	—
256	C₂×C₈×C₃₁	—	2	2	no	—
257	C₂×C₈×C₃₁	—	2	2	no	—
258	C₂×C₈×C₃₁	—	4	1	no	—
259	C₂×C₈×C₃₁	—	4	1	no	—
260	C₂×C₈×C₃₁	—	4	1	no	—
261	C₂×C₈×C₃₁	—	4	1	no	—
262	C₂×C₈×C₃₁	—	4	2	no	—
263	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
266	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₄²×C₃₁	—	2	4	no	—
293	C₄²×C₃₁	—	2	2	no	—
294	#60770	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	4	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	4	1	no	—
300	C₂³×C₃₁	—	4	2	no	—
301	C₂³×C₃₁	—	4	2	no	—
302	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
303	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
304	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₃₁	—	2	4	no	—
307	Q₈×C₃₁	—	2	4	no	—
308	Q₈×C₃₁	—	2	2	no	—
309	Q₈×C₃₁	—	2	4	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	4	2	no	—
312	Q₈×C₃₁	—	4	8	no	—
313	Q₈×C₃₁	—	4	4	no	—
314	D₄×C₃₁	—	2	8	no	—
315	D₄×C₃₁	—	2	4	no	—
316	D₄×C₃₁	—	2	2	no	—
317	D₄×C₃₁	—	2	2	no	—
318	D₄×C₃₁	—	4	2	no	—
319	D₄×C₃₁	—	4	4	no	—
320	D₄×C₃₁	—	4	8	no	—
321	D₄×C₃₁	—	4	4	no	—
322	D₄×C₃₁	—	4	4	no	—
323	D₄×C₃₁	—	8	4	no	—
324	D₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	4	no	—
333	C₂×C₄×C₃₁	—	2	4	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	4	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	4	2	no	—
340	C₂×C₄×C₃₁	—	4	4	no	—
341	C₂×C₄×C₃₁	—	4	8	no	—
342	C₂×C₄×C₃₁	—	4	8	no	—
343	C₂×C₄×C₃₁	—	4	4	no	—
344	C₂×C₄×C₃₁	—	4	4	no	—
345	C₂×C₄×C₃₁	—	8	2	no	—
346	C₂×C₄×C₃₁	—	8	4	no	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
352	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
353	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
354	C₈×C₃₁	—	2	1	no	—
355	C₈×C₃₁	—	2	1	no	—
356	C₈×C₃₁	—	2	1	no	—
357	C₈×C₃₁	—	2	1	no	—
358	C₈×C₃₁	—	2	4	no	—
359	#3489	C₂×C₃₁	1	2	yes	complemented
360	#3203	C₂×C₃₁	1	2	yes	complemented
361	#3202	C₂×C₃₁	1	2	yes	complemented
362	#3201	C₂×C₃₁	1	4	yes	complemented
363	#3191	C₂×C₃₁	1	2	yes	complemented
364	#3190	C₂×C₃₁	1	4	yes	complemented
365	#3189	C₂×C₃₁	1	2	yes	complemented
366	#3098	C₂×C₃₁	1	2	yes	complemented
367	#3097	C₂×C₃₁	1	2	yes	complemented
368	#3056	C₂×C₃₁	1	2	yes	complemented
369	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
370	C₂×#467	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#3013	C₂×C₃₁	1	2	yes	complemented
372	#3011	C₂×C₃₁	1	2	yes	complemented
373	C₂×#408	C₂×C₃₁	1	1	yes	characteristic, complemented
374	C₂²×C₃₁	—	2	1	no	—
375	C₂²×C₃₁	—	2	1	no	—
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	4	no	—
379	C₂²×C₃₁	—	2	1	no	—
380	C₂²×C₃₁	—	2	1	no	—
381	C₂²×C₃₁	—	2	4	no	—
382	C₂²×C₃₁	—	2	1	no	—
383	C₂²×C₃₁	—	2	4	no	—
384	C₂²×C₃₁	—	4	4	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	8	4	no	—
389	C₂²×C₃₁	#534	1	2	yes	—
390	C₂²×C₃₁	#578	1	2	yes	—
391	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	2	4	no	—
395	C₄×C₃₁	—	4	4	no	—
396	C₄×C₃₁	—	4	2	no	—
397	C₄×C₃₁	—	4	4	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	#534	1	2	yes	—
401	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
404	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
405	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
406	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
409	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
410	D₄×Q₈	—	2	2	no	—
411	#548	—	2	2	no	—
412	#547	—	2	4	no	—
413	#547	—	2	2	no	—
414	#546	—	2	4	no	—
415	#546	—	2	2	no	—
416	#537	C₂²×C₃₁	1	2	yes	—
417	#537	C₂²×C₃₁	1	4	yes	—
418	#536	C₂²×C₃₁	1	2	yes	—
419	#536	C₂²×C₃₁	1	4	yes	—
420	#525	C₂²×C₃₁	1	4	yes	—
421	#525	C₂²×C₃₁	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
423	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
424	#520	C₂²×C₃₁	1	2	yes	—
425	#485	C₂²×C₃₁	1	4	yes	complemented
426	#485	C₂²×C₃₁	1	4	yes	complemented
427	#485	C₂²×C₃₁	1	4	yes	complemented
428	#484	C₂²×C₃₁	1	4	yes	complemented
429	#484	C₂²×C₃₁	1	4	yes	complemented
430	#483	C₂²×C₃₁	1	4	yes	complemented
431	#482	C₂²×C₃₁	1	4	yes	complemented
432	#480	C₂²×C₃₁	1	4	yes	complemented
433	#470	C₂²×C₃₁	1	4	yes	complemented
434	#468	C₂²×C₃₁	1	4	yes	complemented
435	#467	C₂²×C₃₁	1	1	yes	characteristic
436	#467	C₂²×C₃₁	1	4	yes	—
437	#467	C₂²×C₃₁	1	2	yes	—
438	#467	C₂²×C₃₁	1	2	yes	—
439	#467	C₂²×C₃₁	1	2	yes	complemented
440	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	#467	C₂²×C₃₁	1	2	yes	complemented
442	#466	C₂²×C₃₁	1	1	yes	characteristic
443	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	#465	C₂²×C₃₁	1	2	yes	—
445	#465	C₂²×C₃₁	1	4	yes	—
446	#465	C₂²×C₃₁	1	2	yes	complemented
447	#452	C₂²×C₃₁	1	4	yes	complemented
448	#452	C₂²×C₃₁	1	4	yes	complemented
449	#452	C₂²×C₃₁	1	4	yes	complemented
450	#451	C₂²×C₃₁	1	4	yes	complemented
451	#451	C₂²×C₃₁	1	4	yes	complemented
452	#451	C₂²×C₃₁	1	4	yes	complemented
453	#449	C₂²×C₃₁	1	4	yes	complemented
454	#448	C₂²×C₃₁	1	4	yes	complemented
455	#428	C₂²×C₃₁	1	2	yes	complemented
456	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
457	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	#419	C₂²×C₃₁	1	2	yes	complemented
459	#417	C₂²×C₃₁	1	2	yes	complemented
460	#416	C₂²×C₃₁	1	2	yes	complemented
461	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
462	#408	C₂²×C₃₁	1	2	yes	—
463	#408	C₂²×C₃₁	1	2	yes	—
464	#408	C₂²×C₃₁	1	2	yes	—
465	#408	C₂²×C₃₁	1	2	yes	—
466	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
467	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
468	C₂×C₃₁	—	2	2	no	—
469	C₂×C₃₁	—	2	2	no	—
470	C₂×C₃₁	—	4	1	no	—
471	C₂×C₃₁	—	4	4	no	—
472	C₂×C₃₁	—	8	2	no	—
473	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
474	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
475	C₂×C₃₁	#3584	1	1	yes	characteristic
476	2₋¹⁺⁴	—	4	4	no	—
477	2₋¹⁺⁴	—	4	4	no	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	4	2	no	—
481	C₂×#41	—	4	2	no	—
482	C₂×#41	D₄×C₃₁	1	2	yes	—
483	C₂×#41	D₄×C₃₁	1	2	yes	—
484	C₂×#41	C₂³×C₃₁	1	2	yes	—
485	C₂×#41	C₂³×C₃₁	1	4	yes	—
486	C₂×#41	C₂³×C₃₁	1	2	yes	—
487	C₂×#41	C₂³×C₃₁	1	2	yes	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
491	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
492	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
493	C₂²×D₄	D₄×C₃₁	1	2	yes	—
494	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
496	#137	—	4	4	no	—
497	#135	—	4	2	no	—
498	C₂×Q₁₆	—	4	2	no	—
499	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
500	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
501	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
502	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
505	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
506	C₂×M₁₆	—	4	2	no	—
507	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
508	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
509	C₂²×C₈	—	4	2	no	—
510	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	4	no	—
519	#124	—	2	2	no	—
520	#124	—	2	4	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	2	no	—
525	#123	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
537	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
538	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
539	#121	—	2	4	no	—
540	#121	—	2	4	no	—
541	#121	—	2	4	no	—
542	#121	—	2	2	no	—
543	#121	—	2	4	no	—
544	#121	C₂³×C₃₁	1	2	yes	—
545	#121	C₂³×C₃₁	1	4	yes	—
546	#121	C₂³×C₃₁	1	2	yes	—
547	#120	—	2	2	no	—
548	#120	—	2	4	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	4	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	4	no	—
556	#117	C₂³×C₃₁	1	2	yes	—
557	#117	C₂³×C₃₁	1	4	yes	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
562	C₂×C₂²⋊C₄	—	2	2	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	#107	C₂³×C₃₁	1	2	yes	—
565	#107	C₂³×C₃₁	1	2	yes	—
566	#107	C₂³×C₃₁	1	1	yes	characteristic
567	#107	C₂³×C₃₁	1	1	yes	characteristic
568	#107	C₂³×C₃₁	1	4	yes	—
569	#106	C₂³×C₃₁	1	2	yes	—
570	#106	C₂³×C₃₁	1	4	yes	—
571	#103	C₂³×C₃₁	1	4	yes	—
572	#103	C₂³×C₃₁	1	4	yes	—
573	#103	C₂³×C₃₁	1	2	yes	—
574	#103	C₂³×C₃₁	1	2	yes	—
575	#103	C₂³×C₃₁	1	4	yes	—
576	#103	C₂³×C₃₁	1	4	yes	—
577	#103	C₂³×C₃₁	1	4	yes	—
578	#102	C₂³×C₃₁	1	2	yes	—
579	#102	C₂³×C₃₁	1	2	yes	—
580	#102	C₂³×C₃₁	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
584	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
585	C₃₁	#60770	1	1	yes	characteristic, direct product factor, Sylow
586	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
587	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
588	#41	—	2	4	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	4	2	no	—
593	#41	—	4	2	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	16	no	—
599	#41	—	4	8	no	—
600	C₂×Q₈	—	2	4	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	—	4	8	no	—
608	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
609	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
610	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
611	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
620	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
621	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
622	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
623	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
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	4	yes	—
638	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
643	Q₁₆	—	4	2	no	—
644	Q₁₆	—	4	2	no	—
645	Q₁₆	—	4	1	no	—
646	Q₁₆	—	4	4	no	—
647	SD₁₆	—	4	2	no	—
648	SD₁₆	—	4	4	no	—
649	D₈	—	4	1	no	—
650	M₁₆	—	2	4	no	—
651	M₁₆	—	4	2	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	4	1	no	—
655	C₂×C₈	—	4	1	no	—
656	C₂×C₈	—	4	1	no	—
657	C₂×C₈	—	4	1	no	—
658	C₂×C₈	—	4	2	no	—
659	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
660	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
662	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
698	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
699	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
700	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
701	Q₈	—	2	4	no	—
702	Q₈	—	2	4	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	4	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	4	2	no	—
707	Q₈	—	4	8	no	—
708	Q₈	—	4	4	no	—
709	D₄	—	2	8	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	8	2	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
747	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
748	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
749	C₈	—	2	1	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	4	no	—
769	C₂²	C₃₁×#534	1	2	yes	—
770	C₂²	C₃₁×#578	1	2	yes	—
771	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	4	4	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	4	no	—
779	C₄	—	4	2	no	—
780	C₄	C₃₁×#534	1	2	yes	—
781	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
782	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂	—	2	2	no	—
784	C₂	—	2	2	no	—
785	C₂	—	4	1	no	—
786	C₂	—	4	4	no	—
787	C₂	—	8	2	no	—
788	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
789	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
790	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3489	C₂	semidirect
2. C₃₁×#3203	C₂	semidirect
3. C₃₁×#3202	C₂	semidirect
4. C₃₁×#3201	C₂	semidirect
5. C₃₁×#3191	C₂	semidirect
6. C₃₁×#3190	C₂	semidirect
7. C₃₁×#3189	C₂	semidirect
8. C₃₁×#3098	C₂	semidirect
9. C₃₁×#3097	C₂	semidirect
10. C₃₁×#3056	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₂×C₃₁×#467	C₂	semidirect
13. C₃₁×#3013	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₂×C₃₁×#408	C₂	semidirect
18. C₂×C₃₁×#137	C₂²	semidirect
19. C₂×C₃₁×#135	C₂²	semidirect
20. C₂²×Q₁₆×C₃₁	C₂²	semidirect
38. C₃₁×#485	C₂²	semidirect
39. C₃₁×#485	C₂²	semidirect
40. C₃₁×#485	C₂²	semidirect
41. C₃₁×#484	C₂²	semidirect
42. C₃₁×#484	C₂²	semidirect
43. C₃₁×#483	C₂²	semidirect
44. C₃₁×#482	C₂²	semidirect
45. C₃₁×#480	C₂²	semidirect
46. C₃₁×#470	C₂²	semidirect
47. C₃₁×#468	C₂²	semidirect
52. C₃₁×#467	C₂²	semidirect
53. C₃₁×#467	C₂²	semidirect
54. C₃₁×#467	C₂²	semidirect
56. C₃₁×#466	C₂²	semidirect
59. C₃₁×#465	C₂²	semidirect
60. C₃₁×#452	C₂²	semidirect
61. C₃₁×#452	C₂²	semidirect
62. C₃₁×#452	C₂²	semidirect
63. C₃₁×#451	C₂²	semidirect
64. C₃₁×#451	C₂²	semidirect
65. C₃₁×#451	C₂²	semidirect
66. C₃₁×#449	C₂²	semidirect
67. C₃₁×#448	C₂²	semidirect
68. C₃₁×#428	C₂²	semidirect
69. C₃₁×#427	C₂²	semidirect
70. C₂×C₃₁×#107	C₂²	semidirect
71. C₃₁×#419	C₂²	semidirect
72. C₃₁×#417	C₂²	semidirect
73. C₃₁×#416	C₂²	semidirect
74. C₂×C₃₁×#103	C₂²	semidirect
294. #60770	C₃₁	direct (N × H)
359. #3489	C₂×C₃₁	semidirect
360. #3203	C₂×C₃₁	semidirect
361. #3202	C₂×C₃₁	semidirect
362. #3201	C₂×C₃₁	semidirect
363. #3191	C₂×C₃₁	semidirect
364. #3190	C₂×C₃₁	semidirect
365. #3189	C₂×C₃₁	semidirect
366. #3098	C₂×C₃₁	semidirect
367. #3097	C₂×C₃₁	semidirect
368. #3056	C₂×C₃₁	semidirect
369. #3050	C₂×C₃₁	semidirect
370. C₂×#467	C₂×C₃₁	semidirect
371. #3013	C₂×C₃₁	semidirect
372. #3011	C₂×C₃₁	semidirect
373. C₂×#408	C₂×C₃₁	semidirect
405. C₂×#137	C₂²×C₃₁	semidirect
406. C₂×#135	C₂²×C₃₁	semidirect
407. C₂²×Q₁₆	C₂²×C₃₁	semidirect
425. #485	C₂²×C₃₁	semidirect
426. #485	C₂²×C₃₁	semidirect
427. #485	C₂²×C₃₁	semidirect
428. #484	C₂²×C₃₁	semidirect
429. #484	C₂²×C₃₁	semidirect
430. #483	C₂²×C₃₁	semidirect
431. #482	C₂²×C₃₁	semidirect
432. #480	C₂²×C₃₁	semidirect
433. #470	C₂²×C₃₁	semidirect
434. #468	C₂²×C₃₁	semidirect
439. #467	C₂²×C₃₁	semidirect
440. #467	C₂²×C₃₁	semidirect
441. #467	C₂²×C₃₁	semidirect
443. #466	C₂²×C₃₁	semidirect
446. #465	C₂²×C₃₁	semidirect
447. #452	C₂²×C₃₁	semidirect
448. #452	C₂²×C₃₁	semidirect
449. #452	C₂²×C₃₁	semidirect
450. #451	C₂²×C₃₁	semidirect
451. #451	C₂²×C₃₁	semidirect
452. #451	C₂²×C₃₁	semidirect
453. #449	C₂²×C₃₁	semidirect
454. #448	C₂²×C₃₁	semidirect
455. #428	C₂²×C₃₁	semidirect
456. #427	C₂²×C₃₁	semidirect
457. C₂×#107	C₂²×C₃₁	semidirect
458. #419	C₂²×C₃₁	semidirect
459. #417	C₂²×C₃₁	semidirect
460. #416	C₂²×C₃₁	semidirect
461. C₂×#103	C₂²×C₃₁	semidirect
585. C₃₁	#60770	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×#3489	2
C₃₁×#3203	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3191	2
C₃₁×#3190	2
C₃₁×#3189	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3056	2
C₃₁×#3050	2
C₂×C₃₁×#467	2
C₃₁×#3013	2
C₃₁×#3011	2
C₂×C₃₁×#408	2
#60770	31

Subgroups — C31×#60770 #21517529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60770 #21517529