Subgroups — C₃₁×#61209 #21517968

Order 7936.

2078 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3320	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3307	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3303	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3010	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
21	C₂×C₃₁×#131	C₂²	1	2	yes	—
22	C₃₁×#559	—	2	2	no	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#553	C₂²	1	4	yes	—
26	C₃₁×#550	—	2	1	no	—
27	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#547	—	2	2	no	—
30	C₃₁×#547	—	2	2	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#547	C₂²	1	2	yes	complemented
33	C₃₁×#547	C₂²	1	2	yes	complemented
34	C₃₁×#538	—	2	2	no	—
35	C₃₁×#536	—	2	2	no	—
36	C₃₁×#536	C₂²	1	2	yes	—
37	C₃₁×#535	C₂²	1	2	yes	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	—	2	1	no	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#525	—	2	2	no	—
44	C₃₁×#520	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#491	C₂²	1	4	yes	complemented
48	C₃₁×#487	C₂²	1	2	yes	complemented
49	C₃₁×#487	C₂²	1	2	yes	complemented
50	C₃₁×#485	C₂²	1	4	yes	complemented
51	C₃₁×#485	C₂²	1	4	yes	complemented
52	C₃₁×#484	C₂²	1	4	yes	complemented
53	C₃₁×#483	C₂²	1	4	yes	complemented
54	C₃₁×#479	C₂²	1	2	yes	complemented
55	C₃₁×#478	C₂²	1	2	yes	complemented
56	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#468	C₂²	1	4	yes	—
61	C₃₁×#468	C₂²	1	4	yes	—
62	C₃₁×#465	C₂²	1	4	yes	—
63	C₃₁×#465	C₂²	1	4	yes	—
64	C₃₁×#461	C₂²	1	2	yes	—
65	C₃₁×#461	C₂²	1	4	yes	—
66	C₃₁×#461	C₂²	1	2	yes	—
67	C₃₁×#449	C₂²	1	4	yes	—
68	C₃₁×#449	C₂²	1	4	yes	—
69	C₃₁×#448	C₂²	1	4	yes	—
70	C₃₁×#448	C₂²	1	4	yes	—
71	C₃₁×#442	C₂²	1	2	yes	—
72	C₃₁×#440	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
74	C₄×D₈×C₃₁	C₂²	1	2	yes	—
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#428	C₂²	1	1	yes	characteristic
79	C₃₁×#427	C₂²	1	2	yes	—
80	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
81	C₃₁×#419	C₂²	1	2	yes	—
82	C₃₁×#419	C₂²	1	2	yes	—
83	C₃₁×#419	C₂²	1	4	yes	complemented
84	C₃₁×#418	C₂²	1	1	yes	characteristic
85	C₃₁×#417	C₂²	1	1	yes	characteristic
86	C₃₁×#417	C₂²	1	4	yes	complemented
87	C₃₁×#416	C₂²	1	2	yes	—
88	C₃₁×#416	C₂²	1	4	yes	complemented
89	C₂×C₃₁×#103	C₂²	1	2	yes	—
90	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
91	C₃₁×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₃₁×2₋¹⁺⁴	—	2	8	no	—
94	C₃₁×2₋¹⁺⁴	—	4	4	no	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	—	2	4	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	C₂³	1	4	yes	—
99	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×#41×C₃₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₃₁	—	2	2	no	—
102	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
103	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
104	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	—	2	1	no	—
106	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
107	C₂×SD₁₆×C₃₁	—	4	4	no	—
108	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×D₈×C₃₁	C₂³	1	2	yes	—
112	C₃₁×#131	—	4	4	no	—
113	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
117	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
118	C₃₁×C₄⋊Q₈	—	2	2	no	—
119	C₃₁×C₄⋊Q₈	—	2	2	no	—
120	C₃₁×C₄⋊Q₈	—	2	2	no	—
121	C₃₁×C₄⋊Q₈	—	2	1	no	—
122	C₃₁×C₄⋊Q₈	—	2	1	no	—
123	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₃₁×#127	—	2	2	no	—
129	C₃₁×#127	D₄	1	1	yes	characteristic
130	C₃₁×#126	—	2	4	no	—
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	4	no	—
135	C₃₁×#124	D₄	1	2	yes	—
136	C₃₁×#123	—	2	4	no	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×#123	—	2	4	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	4	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	4	no	—
152	C₃₁×#121	D₄	1	2	yes	—
153	C₃₁×#121	D₄	1	2	yes	—
154	C₃₁×#121	C₂³	1	4	yes	—
155	C₃₁×#121	C₂³	1	4	yes	—
156	C₃₁×#120	—	2	4	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	1	no	—
168	C₄×D₄×C₃₁	—	2	4	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₄×D₄×C₃₁	C₂³	1	2	yes	—
174	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₄×D₄×C₃₁	C₂³	1	2	yes	—
177	C₃₁×#117	—	2	2	no	—
178	C₃₁×#117	—	2	1	no	—
179	C₃₁×#117	C₂³	1	2	yes	—
180	C₃₁×#117	C₂³	1	4	yes	—
181	C₃₁×#117	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
185	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
188	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₄²×C₃₁	—	2	1	no	—
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₃₁×#107	C₂³	1	2	yes	—
192	C₃₁×#107	C₂³	1	2	yes	—
193	C₃₁×#107	C₂³	1	2	yes	—
194	C₃₁×#106	C₂³	1	2	yes	—
195	C₃₁×#106	C₂³	1	2	yes	—
196	C₃₁×#106	C₂³	1	2	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
199	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₃₁×#103	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	2	yes	—
203	C₃₁×#103	C₂³	1	2	yes	—
204	C₃₁×#103	C₂³	1	4	yes	—
205	C₃₁×#103	C₂³	1	2	yes	—
206	C₃₁×#103	C₂³	1	4	yes	—
207	C₃₁×#103	C₂³	1	4	yes	—
208	C₃₁×#103	C₂³	1	4	yes	—
209	C₃₁×#102	C₂³	1	2	yes	—
210	C₃₁×#102	C₂³	1	2	yes	—
211	C₃₁×#102	C₂³	1	2	yes	—
212	C₃₁×#102	C₂³	1	2	yes	—
213	C₃₁×#102	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₃₁×#97	C₂³	1	2	yes	—
217	C₄×C₈×C₃₁	C₂³	1	2	yes	—
218	C₂⁴×C₃₁	—	2	1	no	—
219	#41×C₃₁	—	2	4	no	—
220	#41×C₃₁	—	2	4	no	—
221	#41×C₃₁	—	2	2	no	—
222	#41×C₃₁	—	2	8	no	—
223	#41×C₃₁	—	4	4	no	—
224	#41×C₃₁	—	4	8	no	—
225	#41×C₃₁	—	4	16	no	—
226	#41×C₃₁	—	8	4	no	—
227	#41×C₃₁	#41	1	4	yes	complemented
228	C₂×Q₈×C₃₁	—	2	1	no	—
229	C₂×Q₈×C₃₁	—	2	4	no	—
230	C₂×Q₈×C₃₁	—	2	2	no	—
231	C₂×Q₈×C₃₁	—	2	1	no	—
232	C₂×Q₈×C₃₁	—	2	8	no	—
233	C₂×Q₈×C₃₁	—	2	4	no	—
234	C₂×Q₈×C₃₁	—	2	4	no	—
235	C₂×Q₈×C₃₁	—	4	4	no	—
236	C₂×Q₈×C₃₁	—	4	8	no	—
237	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₃₁	—	2	1	no	—
241	C₂×D₄×C₃₁	—	2	4	no	—
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	4	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	8	2	no	—
264	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	SD₁₆×C₃₁	—	2	4	no	—
269	SD₁₆×C₃₁	—	4	4	no	—
270	SD₁₆×C₃₁	—	4	4	no	—
271	D₈×C₃₁	—	2	4	no	—
272	M₁₆×C₃₁	—	2	2	no	—
273	M₁₆×C₃₁	—	2	2	no	—
274	M₁₆×C₃₁	—	4	4	no	—
275	C₂×C₈×C₃₁	—	2	4	no	—
276	C₂×C₈×C₃₁	—	4	4	no	—
277	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
280	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	1	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	1	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
314	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
315	C₄²×C₃₁	—	2	1	no	—
316	C₄²×C₃₁	—	2	1	no	—
317	C₄²×C₃₁	—	2	1	no	—
318	C₄²×C₃₁	—	2	4	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
324	#61209	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂³×C₃₁	—	2	1	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	4	2	no	—
328	C₂³×C₃₁	—	8	1	no	—
329	C₂³×C₃₁	—	8	1	no	—
330	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
331	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	Q₈×C₃₁	—	2	4	no	—
333	Q₈×C₃₁	—	2	1	no	—
334	Q₈×C₃₁	—	2	4	no	—
335	Q₈×C₃₁	—	2	4	no	—
336	Q₈×C₃₁	—	4	8	no	—
337	Q₈×C₃₁	—	4	4	no	—
338	Q₈×C₃₁	—	4	2	no	—
339	Q₈×C₃₁	—	8	1	no	—
340	Q₈×C₃₁	C₂×#41	1	2	yes	—
341	D₄×C₃₁	—	2	4	no	—
342	D₄×C₃₁	—	2	8	no	—
343	D₄×C₃₁	—	2	4	no	—
344	D₄×C₃₁	—	2	4	no	—
345	D₄×C₃₁	—	2	2	no	—
346	D₄×C₃₁	—	2	1	no	—
347	D₄×C₃₁	—	2	2	no	—
348	D₄×C₃₁	—	4	2	no	—
349	D₄×C₃₁	—	4	8	no	—
350	D₄×C₃₁	—	4	2	no	—
351	D₄×C₃₁	—	8	4	no	—
352	D₄×C₃₁	—	8	4	no	—
353	D₄×C₃₁	C₂×#41	1	2	yes	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	4	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	4	no	—
358	C₂×C₄×C₃₁	—	2	4	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	4	no	—
365	C₂×C₄×C₃₁	—	4	1	no	—
366	C₂×C₄×C₃₁	—	4	8	no	—
367	C₂×C₄×C₃₁	—	4	8	no	—
368	C₂×C₄×C₃₁	—	4	2	no	—
369	C₂×C₄×C₃₁	—	4	4	no	—
370	C₂×C₄×C₃₁	—	4	2	no	—
371	C₂×C₄×C₃₁	—	4	4	no	—
372	C₂×C₄×C₃₁	—	8	2	no	—
373	C₂×C₄×C₃₁	—	8	1	no	—
374	C₂×C₄×C₃₁	—	8	4	no	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
382	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
384	C₈×C₃₁	—	2	2	no	—
385	C₈×C₃₁	—	2	2	no	—
386	C₈×C₃₁	—	2	2	no	—
387	C₈×C₃₁	—	2	2	no	—
388	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#3330	C₂×C₃₁	1	2	yes	complemented
391	#3329	C₂×C₃₁	1	2	yes	complemented
392	#3320	C₂×C₃₁	1	4	yes	complemented
393	#3307	C₂×C₃₁	1	4	yes	complemented
394	#3303	C₂×C₃₁	1	2	yes	complemented
395	#3298	C₂×C₃₁	1	2	yes	complemented
396	#3139	C₂×C₃₁	1	1	yes	characteristic, complemented
397	#3097	C₂×C₃₁	1	2	yes	complemented
398	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
399	#3057	C₂×C₃₁	1	2	yes	complemented
400	C₂×#461	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3010	C₂×C₃₁	1	2	yes	complemented
402	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#2935	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#2898	C₂×C₃₁	1	2	yes	complemented
405	C₂²×C₃₁	—	2	1	no	—
406	C₂²×C₃₁	—	2	1	no	—
407	C₂²×C₃₁	—	2	4	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	—	2	4	no	—
410	C₂²×C₃₁	—	2	4	no	—
411	C₂²×C₃₁	—	4	1	no	—
412	C₂²×C₃₁	—	4	1	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	8	4	no	—
417	C₂²×C₃₁	#546	1	2	yes	—
418	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₃₁	—	2	1	no	—
420	C₄×C₃₁	—	2	1	no	—
421	C₄×C₃₁	—	2	2	no	—
422	C₄×C₃₁	—	2	4	no	—
423	C₄×C₃₁	—	2	1	no	—
424	C₄×C₃₁	—	4	1	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	4	no	—
427	C₄×C₃₁	—	4	1	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	#546	1	2	yes	—
431	C₄×C₃₁	#577	1	2	yes	—
432	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
433	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
435	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
436	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
437	C₂×#131	C₂²×C₃₁	1	2	yes	—
438	#559	—	2	2	no	—
439	#556	—	2	1	no	—
440	#555	C₂²×C₃₁	1	2	yes	—
441	#553	C₂²×C₃₁	1	4	yes	—
442	#550	—	2	1	no	—
443	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
444	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
445	#547	—	2	2	no	—
446	#547	—	2	2	no	—
447	#547	C₂²×C₃₁	1	2	yes	—
448	#547	C₂²×C₃₁	1	2	yes	complemented
449	#547	C₂²×C₃₁	1	2	yes	complemented
450	#538	—	2	2	no	—
451	#536	—	2	2	no	—
452	#536	C₂²×C₃₁	1	2	yes	—
453	#535	C₂²×C₃₁	1	2	yes	—
454	#533	C₂²×C₃₁	1	1	yes	characteristic
455	#532	—	2	1	no	—
456	#532	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	—	2	1	no	—
458	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	#525	—	2	2	no	—
460	#520	C₂²×C₃₁	1	2	yes	—
461	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
463	#491	C₂²×C₃₁	1	4	yes	complemented
464	#487	C₂²×C₃₁	1	2	yes	complemented
465	#487	C₂²×C₃₁	1	2	yes	complemented
466	#485	C₂²×C₃₁	1	4	yes	complemented
467	#485	C₂²×C₃₁	1	4	yes	complemented
468	#484	C₂²×C₃₁	1	4	yes	complemented
469	#483	C₂²×C₃₁	1	4	yes	complemented
470	#479	C₂²×C₃₁	1	2	yes	complemented
471	#478	C₂²×C₃₁	1	2	yes	complemented
472	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
473	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
474	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	#468	C₂²×C₃₁	1	4	yes	—
477	#468	C₂²×C₃₁	1	4	yes	—
478	#465	C₂²×C₃₁	1	4	yes	—
479	#465	C₂²×C₃₁	1	4	yes	—
480	#461	C₂²×C₃₁	1	2	yes	—
481	#461	C₂²×C₃₁	1	2	yes	—
482	#461	C₂²×C₃₁	1	4	yes	—
483	#449	C₂²×C₃₁	1	4	yes	—
484	#449	C₂²×C₃₁	1	4	yes	—
485	#448	C₂²×C₃₁	1	4	yes	—
486	#448	C₂²×C₃₁	1	4	yes	—
487	#442	C₂²×C₃₁	1	2	yes	—
488	#440	C₂²×C₃₁	1	2	yes	—
489	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
490	C₄×D₈	C₂²×C₃₁	1	2	yes	—
491	#436	C₂²×C₃₁	1	2	yes	complemented
492	#435	C₂²×C₃₁	1	4	yes	complemented
493	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
494	#428	C₂²×C₃₁	1	1	yes	characteristic
495	#427	C₂²×C₃₁	1	2	yes	—
496	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
497	#419	C₂²×C₃₁	1	2	yes	—
498	#419	C₂²×C₃₁	1	2	yes	—
499	#419	C₂²×C₃₁	1	4	yes	complemented
500	#418	C₂²×C₃₁	1	1	yes	characteristic
501	#417	C₂²×C₃₁	1	1	yes	characteristic
502	#417	C₂²×C₃₁	1	4	yes	complemented
503	#416	C₂²×C₃₁	1	2	yes	—
504	#416	C₂²×C₃₁	1	4	yes	complemented
505	C₂×#103	C₂²×C₃₁	1	2	yes	—
506	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
507	#408	C₂²×C₃₁	1	2	yes	—
508	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
509	C₂×C₃₁	—	2	2	no	—
510	C₂×C₃₁	—	4	4	no	—
511	C₂×C₃₁	—	4	2	no	—
512	C₂×C₃₁	—	8	2	no	—
513	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
514	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
515	C₂×C₃₁	#3586	1	1	yes	characteristic
516	2₋¹⁺⁴	—	2	8	no	—
517	2₋¹⁺⁴	—	4	4	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	C₂³×C₃₁	1	4	yes	—
522	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
523	C₂×#41	C₂³×C₃₁	1	2	yes	—
524	C₂²×Q₈	—	2	2	no	—
525	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
526	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
527	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂³×C₄	—	2	1	no	—
529	AGL(1,ℤ/8)	—	2	4	no	—
530	C₂×SD₁₆	—	4	4	no	—
531	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
534	C₂×D₈	C₂³×C₃₁	1	2	yes	—
535	#131	—	4	4	no	—
536	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
537	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
538	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
539	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
540	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
551	#127	—	2	2	no	—
552	#127	D₄×C₃₁	1	1	yes	characteristic
553	#126	—	2	4	no	—
554	#125	C₂³×C₃₁	1	2	yes	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	4	no	—
558	#124	D₄×C₃₁	1	2	yes	—
559	#123	—	2	4	no	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
570	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	4	no	—
575	#121	D₄×C₃₁	1	2	yes	—
576	#121	D₄×C₃₁	1	2	yes	—
577	#121	C₂³×C₃₁	1	4	yes	—
578	#121	C₂³×C₃₁	1	4	yes	—
579	#120	—	2	4	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	C₂³×C₃₁	1	2	yes	—
595	C₄×D₄	C₂³×C₃₁	1	2	yes	—
596	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₃₁	1	2	yes	—
599	C₄×D₄	C₂³×C₃₁	1	2	yes	—
600	#117	—	2	2	no	—
601	#117	—	2	1	no	—
602	#117	C₂³×C₃₁	1	1	yes	characteristic
603	#117	C₂³×C₃₁	1	2	yes	—
604	#117	C₂³×C₃₁	1	4	yes	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
614	#107	C₂³×C₃₁	1	2	yes	—
615	#107	C₂³×C₃₁	1	2	yes	—
616	#107	C₂³×C₃₁	1	2	yes	—
617	#106	C₂³×C₃₁	1	2	yes	—
618	#106	C₂³×C₃₁	1	2	yes	—
619	#106	C₂³×C₃₁	1	2	yes	—
620	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
622	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
623	#103	C₂³×C₃₁	1	4	yes	—
624	#103	C₂³×C₃₁	1	4	yes	—
625	#103	C₂³×C₃₁	1	2	yes	—
626	#103	C₂³×C₃₁	1	2	yes	—
627	#103	C₂³×C₃₁	1	4	yes	—
628	#103	C₂³×C₃₁	1	2	yes	—
629	#103	C₂³×C₃₁	1	4	yes	—
630	#103	C₂³×C₃₁	1	4	yes	—
631	#103	C₂³×C₃₁	1	4	yes	—
632	#102	C₂³×C₃₁	1	2	yes	—
633	#102	C₂³×C₃₁	1	2	yes	—
634	#102	C₂³×C₃₁	1	2	yes	—
635	#102	C₂³×C₃₁	1	2	yes	—
636	#102	C₂³×C₃₁	1	2	yes	—
637	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
638	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
639	#97	C₂³×C₃₁	1	2	yes	—
640	C₄×C₈	C₂³×C₃₁	1	2	yes	—
641	C₃₁	#61209	1	1	yes	characteristic, direct product factor, Sylow
642	C₂⁴	—	2	1	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	8	no	—
649	#41	—	4	16	no	—
650	#41	—	8	4	no	—
651	#41	#41×C₃₁	1	4	yes	complemented
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	8	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	—	4	8	no	—
661	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
662	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
663	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
673	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
675	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
676	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	8	2	no	—
688	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
691	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	D₈	—	2	4	no	—
696	M₁₆	—	2	2	no	—
697	M₁₆	—	2	2	no	—
698	M₁₆	—	4	4	no	—
699	C₂×C₈	—	2	4	no	—
700	C₂×C₈	—	4	4	no	—
701	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
702	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
703	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
704	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
738	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	2	no	—
744	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	8	1	no	—
752	C₂³	—	8	1	no	—
753	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
754	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
755	Q₈	—	2	4	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	4	8	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	8	1	no	—
763	Q₈	C₂×#41×C₃₁	1	2	yes	—
764	D₄	—	2	4	no	—
765	D₄	—	2	8	no	—
766	D₄	—	2	4	no	—
767	D₄	—	2	4	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	2	no	—
774	D₄	—	8	4	no	—
775	D₄	—	8	4	no	—
776	D₄	C₂×#41×C₃₁	1	2	yes	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	—	8	1	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
800	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
804	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
805	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
806	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
807	C₈	—	2	2	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	2	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	4	no	—
823	C₂²	C₃₁×#546	1	2	yes	—
824	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
825	C₄	—	2	2	no	—
826	C₄	—	2	4	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	4	4	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	C₃₁×#546	1	2	yes	—
837	C₄	C₃₁×#577	1	2	yes	—
838	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
839	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
840	C₂	—	2	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	4	2	no	—
843	C₂	—	8	2	no	—
844	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
845	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
846	C₂	C₃₁×#3586	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3506	C₂	semidirect
2. C₃₁×#3499	C₂	semidirect
3. C₃₁×#3330	C₂	semidirect
4. C₃₁×#3329	C₂	semidirect
5. C₃₁×#3320	C₂	semidirect
6. C₃₁×#3307	C₂	semidirect
7. C₃₁×#3303	C₂	semidirect
8. C₃₁×#3298	C₂	semidirect
9. C₃₁×#3139	C₂	semidirect
10. C₃₁×#3097	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3057	C₂	semidirect
13. C₂×C₃₁×#461	C₂	semidirect
14. C₃₁×#3010	C₂	semidirect
15. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
16. C₃₁×#2935	C₂	semidirect
17. C₃₁×#2898	C₂	semidirect
27. D₄×Q₈×C₃₁	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#547	C₂²	semidirect
33. C₃₁×#547	C₂²	semidirect
47. C₃₁×#491	C₂²	semidirect
48. C₃₁×#487	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
50. C₃₁×#485	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#484	C₂²	semidirect
53. C₃₁×#483	C₂²	semidirect
54. C₃₁×#479	C₂²	semidirect
55. C₃₁×#478	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
59. C₃₁×#474	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#435	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
83. C₃₁×#419	C₂²	semidirect
86. C₃₁×#417	C₂²	semidirect
88. C₃₁×#416	C₂²	semidirect
90. C₂×C₃₁×#103	C₂²	semidirect
227. #41×C₃₁	#41	semidirect
324. #61209	C₃₁	direct (N × H)
388. #3506	C₂×C₃₁	semidirect
389. #3499	C₂×C₃₁	semidirect
390. #3330	C₂×C₃₁	semidirect
391. #3329	C₂×C₃₁	semidirect
392. #3320	C₂×C₃₁	semidirect
393. #3307	C₂×C₃₁	semidirect
394. #3303	C₂×C₃₁	semidirect
395. #3298	C₂×C₃₁	semidirect
396. #3139	C₂×C₃₁	semidirect
397. #3097	C₂×C₃₁	semidirect
398. #3076	C₂×C₃₁	semidirect
399. #3057	C₂×C₃₁	semidirect
400. C₂×#461	C₂×C₃₁	semidirect
401. #3010	C₂×C₃₁	semidirect
402. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
403. #2935	C₂×C₃₁	semidirect
404. #2898	C₂×C₃₁	semidirect
443. D₄×Q₈	C₂²×C₃₁	semidirect
444. D₄×Q₈	C₂²×C₃₁	semidirect
448. #547	C₂²×C₃₁	semidirect
449. #547	C₂²×C₃₁	semidirect
463. #491	C₂²×C₃₁	semidirect
464. #487	C₂²×C₃₁	semidirect
465. #487	C₂²×C₃₁	semidirect
466. #485	C₂²×C₃₁	semidirect
467. #485	C₂²×C₃₁	semidirect
468. #484	C₂²×C₃₁	semidirect
469. #483	C₂²×C₃₁	semidirect
470. #479	C₂²×C₃₁	semidirect
471. #478	C₂²×C₃₁	semidirect
472. #477	C₂²×C₃₁	semidirect
473. #476	C₂²×C₃₁	semidirect
474. #475	C₂²×C₃₁	semidirect
475. #474	C₂²×C₃₁	semidirect
491. #436	C₂²×C₃₁	semidirect
492. #435	C₂²×C₃₁	semidirect
493. C₈×D₄	C₂²×C₃₁	semidirect
499. #419	C₂²×C₃₁	semidirect
502. #417	C₂²×C₃₁	semidirect
504. #416	C₂²×C₃₁	semidirect
506. C₂×#103	C₂²×C₃₁	semidirect
641. C₃₁	#61209	direct (N × H)
651. #41	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3506	2
C₃₁×#3499	2
C₃₁×#3330	2
C₃₁×#3329	2
C₃₁×#3320	2
C₃₁×#3307	2
C₃₁×#3303	2
C₃₁×#3298	2
C₃₁×#3139	2
C₃₁×#3097	2
C₃₁×#3076	2
C₃₁×#3057	2
C₂×C₃₁×#461	2
C₃₁×#3010	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2935	2
C₃₁×#2898	2
#61209	31

Subgroups — C31×#61209 #21517968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61209 #21517968