Subgroups — C₃₁×#60922 #21517681

Order 7936.

1932 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3259	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3257	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3253	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3245	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3062	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3058	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
20	C₂×C₃₁×#131	C₂²	1	2	yes	—
21	C₃₁×#559	—	2	1	no	—
22	C₃₁×#559	—	2	1	no	—
23	C₃₁×#550	—	2	1	no	—
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#546	—	2	2	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#544	C₂²	1	1	yes	characteristic
28	C₃₁×#542	—	2	1	no	—
29	C₃₁×#542	C₂²	1	2	yes	complemented
30	C₃₁×#540	—	2	1	no	—
31	C₃₁×#540	C₂²	1	2	yes	complemented
32	C₃₁×#540	C₂²	1	4	yes	complemented
33	C₃₁×#538	—	2	2	no	—
34	C₃₁×#537	C₂²	1	1	yes	characteristic
35	C₃₁×#535	C₂²	1	1	yes	characteristic
36	C₃₁×#535	C₂²	1	1	yes	characteristic
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	2	yes	complemented
41	C₃₁×#532	C₂²	1	2	yes	complemented
42	C₃₁×#532	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
44	C₃₁×#529	—	2	1	no	—
45	C₃₁×#529	C₂²	1	2	yes	complemented
46	C₃₁×#525	—	2	2	no	—
47	C₃₁×#518	C₂²	1	2	yes	—
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#479	C₂²	1	2	yes	complemented
52	C₃₁×#478	C₂²	1	2	yes	complemented
53	C₃₁×#478	C₂²	1	4	yes	complemented
54	C₃₁×#478	C₂²	1	4	yes	complemented
55	C₃₁×#478	C₂²	1	4	yes	complemented
56	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#476	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	4	yes	complemented
60	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#474	C₂²	1	2	yes	complemented
63	C₃₁×#474	C₂²	1	4	yes	complemented
64	C₃₁×#469	C₂²	1	4	yes	complemented
65	C₃₁×#469	C₂²	1	4	yes	complemented
66	C₃₁×#469	C₂²	1	4	yes	complemented
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#466	C₂²	1	4	yes	complemented
69	C₃₁×#466	C₂²	1	4	yes	complemented
70	C₃₁×#466	C₂²	1	4	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#463	C₂²	1	4	yes	complemented
73	C₃₁×#463	C₂²	1	4	yes	complemented
74	C₃₁×#460	C₂²	1	2	yes	complemented
75	C₃₁×#460	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#459	C₂²	1	4	yes	—
79	C₃₁×#459	C₂²	1	2	yes	complemented
80	C₃₁×#459	C₂²	1	4	yes	complemented
81	C₃₁×#459	C₂²	1	4	yes	complemented
82	C₃₁×#459	C₂²	1	2	yes	complemented
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#427	C₂²	1	2	yes	—
85	C₃₁×#424	C₂²	1	2	yes	—
86	C₃₁×#424	C₂²	1	4	yes	complemented
87	C₃₁×#423	C₂²	1	1	yes	characteristic
88	C₃₁×#423	C₂²	1	2	yes	complemented
89	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₃₁×#418	C₂²	1	2	yes	—
92	C₃₁×#418	C₂²	1	2	yes	—
93	C₃₁×#416	C₂²	1	2	yes	—
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	—	2	1	no	—
105	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
106	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×D₈×C₃₁	—	4	4	no	—
108	C₂×D₈×C₃₁	C₂³	1	4	yes	—
109	C₂×D₈×C₃₁	C₂³	1	4	yes	—
110	C₂×D₈×C₃₁	C₂³	1	4	yes	—
111	C₃₁×#131	—	4	4	no	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
113	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×#127	—	2	1	no	—
121	C₃₁×#127	—	2	2	no	—
122	C₃₁×#127	—	2	1	no	—
123	C₃₁×#127	—	2	1	no	—
124	C₃₁×#127	C₂³	1	2	yes	—
125	C₃₁×#127	C₂³	1	2	yes	—
126	C₃₁×#127	C₂³	1	2	yes	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	C₂³	1	2	yes	—
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	C₂³	1	2	yes	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	4	no	—
143	C₃₁×#123	—	2	4	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	1	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	1	no	—
158	C₃₁×#121	—	2	2	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	4	no	—
161	C₃₁×#121	—	2	4	no	—
162	C₃₁×#121	C₂³	1	4	yes	—
163	C₃₁×#121	C₂³	1	4	yes	—
164	C₃₁×#121	C₂³	1	2	yes	—
165	C₃₁×#121	C₂³	1	2	yes	—
166	C₃₁×#121	C₂³	1	2	yes	—
167	C₃₁×#120	—	2	2	no	—
168	C₃₁×#120	—	2	4	no	—
169	C₃₁×#120	—	2	2	no	—
170	C₄×Q₈×C₃₁	—	2	1	no	—
171	C₄×Q₈×C₃₁	—	2	1	no	—
172	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	—	2	1	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	D₄	1	2	yes	—
187	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₃₁	D₄	1	2	yes	—
189	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₄×D₄×C₃₁	C₂³	1	2	yes	—
192	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₃₁	C₂³	1	4	yes	—
195	C₄×D₄×C₃₁	C₂³	1	4	yes	—
196	C₃₁×#117	—	2	1	no	—
197	C₃₁×#117	—	2	2	no	—
198	C₃₁×#117	C₂³	1	2	yes	—
199	C₃₁×#117	C₂³	1	1	yes	characteristic
200	C₃₁×#117	C₂³	1	1	yes	characteristic
201	C₃₁×#117	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×#106	C₂³	1	2	yes	—
213	C₃₁×#106	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
219	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
220	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	2	yes	—
222	C₃₁×#103	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	2	yes	—
226	C₃₁×#102	C₂³	1	2	yes	—
227	C₃₁×#102	C₂³	1	4	yes	—
228	C₃₁×#102	C₂³	1	4	yes	—
229	C₃₁×#102	C₂³	1	4	yes	—
230	C₃₁×#102	C₂³	1	4	yes	—
231	C₂⁴×C₃₁	—	2	2	no	—
232	C₂⁴×C₃₁	—	2	1	no	—
233	#41×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	2	2	no	—
235	#41×C₃₁	—	2	2	no	—
236	#41×C₃₁	—	2	2	no	—
237	#41×C₃₁	—	8	4	no	—
238	#41×C₃₁	—	8	4	no	—
239	#41×C₃₁	—	8	4	no	—
240	C₂×Q₈×C₃₁	—	2	1	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	2	2	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	2	2	no	—
262	C₂×D₄×C₃₁	—	2	4	no	—
263	C₂×D₄×C₃₁	—	8	2	no	—
264	C₂×D₄×C₃₁	—	8	2	no	—
265	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₃₁	—	2	1	no	—
271	C₂²×C₄×C₃₁	—	2	1	no	—
272	C₂²×C₄×C₃₁	—	2	1	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	1	no	—
275	C₂²×C₄×C₃₁	—	2	4	no	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	8	2	no	—
279	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	SD₁₆×C₃₁	—	4	4	no	—
286	D₈×C₃₁	—	4	4	no	—
287	D₈×C₃₁	—	4	4	no	—
288	D₈×C₃₁	—	4	4	no	—
289	M₁₆×C₃₁	—	2	4	no	—
290	M₁₆×C₃₁	—	4	4	no	—
291	C₂×C₈×C₃₁	—	2	4	no	—
292	C₂×C₈×C₃₁	—	4	4	no	—
293	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
294	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	1	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	1	no	—
324	C₂²⋊C₄×C₃₁	—	2	1	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	4	no	—
330	C₂²⋊C₄×C₃₁	—	2	4	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₄²×C₃₁	—	2	1	no	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	—	2	1	no	—
338	C₄²×C₃₁	—	2	2	no	—
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₃₁	C₂×D₄	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	2	yes	—
345	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
346	#60922	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂³×C₃₁	—	2	2	no	—
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	4	no	—
350	C₂³×C₃₁	—	4	2	no	—
351	C₂³×C₃₁	—	4	4	no	—
352	C₂³×C₃₁	—	8	1	no	—
353	C₂³×C₃₁	—	8	1	no	—
354	C₂³×C₃₁	—	8	2	no	—
355	C₂³×C₃₁	—	8	2	no	—
356	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
357	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	2	1	no	—
360	Q₈×C₃₁	—	2	1	no	—
361	Q₈×C₃₁	—	4	2	no	—
362	Q₈×C₃₁	—	4	2	no	—
363	Q₈×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	2	4	no	—
365	D₄×C₃₁	—	2	2	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	2	1	no	—
368	D₄×C₃₁	—	2	4	no	—
369	D₄×C₃₁	—	2	2	no	—
370	D₄×C₃₁	—	2	4	no	—
371	D₄×C₃₁	—	2	1	no	—
372	D₄×C₃₁	—	4	4	no	—
373	D₄×C₃₁	—	4	2	no	—
374	D₄×C₃₁	—	4	2	no	—
375	D₄×C₃₁	—	4	4	no	—
376	D₄×C₃₁	—	4	4	no	—
377	D₄×C₃₁	—	8	2	no	—
378	D₄×C₃₁	—	8	2	no	—
379	D₄×C₃₁	—	8	2	no	—
380	D₄×C₃₁	—	8	2	no	—
381	D₄×C₃₁	—	8	2	no	—
382	D₄×C₃₁	—	8	4	no	—
383	D₄×C₃₁	—	8	2	no	—
384	D₄×C₃₁	—	8	2	no	—
385	D₄×C₃₁	—	8	4	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	4	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	4	1	no	—
397	C₂×C₄×C₃₁	—	4	2	no	—
398	C₂×C₄×C₃₁	—	4	2	no	—
399	C₂×C₄×C₃₁	—	4	4	no	—
400	C₂×C₄×C₃₁	—	4	2	no	—
401	C₂×C₄×C₃₁	—	8	1	no	—
402	C₂×C₄×C₃₁	—	8	2	no	—
403	C₂×C₄×C₃₁	—	8	4	no	—
404	C₂×C₄×C₃₁	—	8	4	no	—
405	C₂×C₄×C₃₁	—	8	1	no	—
406	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
417	C₈×C₃₁	—	2	2	no	—
418	C₈×C₃₁	—	2	2	no	—
419	C₈×C₃₁	—	2	4	no	—
420	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3460	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3259	C₂×C₃₁	1	4	yes	complemented
423	#3257	C₂×C₃₁	1	4	yes	complemented
424	#3253	C₂×C₃₁	1	2	yes	complemented
425	#3251	C₂×C₃₁	1	2	yes	complemented
426	#3247	C₂×C₃₁	1	2	yes	complemented
427	#3245	C₂×C₃₁	1	2	yes	complemented
428	#3081	C₂×C₃₁	1	2	yes	complemented
429	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
430	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#3062	C₂×C₃₁	1	2	yes	complemented
432	#3058	C₂×C₃₁	1	2	yes	complemented
433	#3041	C₂×C₃₁	1	2	yes	complemented
434	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
435	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#2906	C₂×C₃₁	1	1	yes	characteristic, complemented
437	C₂²×C₃₁	—	2	1	no	—
438	C₂²×C₃₁	—	2	1	no	—
439	C₂²×C₃₁	—	2	2	no	—
440	C₂²×C₃₁	—	2	2	no	—
441	C₂²×C₃₁	—	2	2	no	—
442	C₂²×C₃₁	—	4	4	no	—
443	C₂²×C₃₁	—	4	1	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	4	1	no	—
446	C₂²×C₃₁	—	4	2	no	—
447	C₂²×C₃₁	—	4	4	no	—
448	C₂²×C₃₁	—	4	2	no	—
449	C₂²×C₃₁	—	4	1	no	—
450	C₂²×C₃₁	—	4	4	no	—
451	C₂²×C₃₁	—	8	4	no	—
452	C₂²×C₃₁	—	16	4	no	—
453	C₂²×C₃₁	#537	1	2	yes	—
454	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₃₁	—	2	1	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	1	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	1	no	—
460	C₄×C₃₁	—	2	2	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	1	no	—
463	C₄×C₃₁	—	4	1	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	1	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	#537	1	2	yes	—
468	C₄×C₃₁	#576	1	2	yes	—
469	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
472	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
473	C₂×#131	C₂²×C₃₁	1	2	yes	—
474	#559	—	2	1	no	—
475	#559	—	2	1	no	—
476	#550	—	2	1	no	—
477	#550	—	2	1	no	—
478	#546	—	2	2	no	—
479	#546	—	2	2	no	—
480	#544	C₂²×C₃₁	1	1	yes	characteristic
481	#542	—	2	1	no	—
482	#542	C₂²×C₃₁	1	2	yes	complemented
483	#540	—	2	1	no	—
484	#540	C₂²×C₃₁	1	2	yes	complemented
485	#540	C₂²×C₃₁	1	4	yes	complemented
486	#538	—	2	2	no	—
487	#537	C₂²×C₃₁	1	1	yes	characteristic
488	#535	C₂²×C₃₁	1	1	yes	characteristic
489	#535	C₂²×C₃₁	1	1	yes	characteristic
490	#535	C₂²×C₃₁	1	2	yes	—
491	#533	C₂²×C₃₁	1	1	yes	characteristic
492	#532	—	2	1	no	—
493	#532	C₂²×C₃₁	1	2	yes	complemented
494	#532	C₂²×C₃₁	1	2	yes	complemented
495	#532	C₂²×C₃₁	1	2	yes	complemented
496	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
497	#529	—	2	1	no	—
498	#529	C₂²×C₃₁	1	2	yes	complemented
499	#525	—	2	2	no	—
500	#518	C₂²×C₃₁	1	2	yes	—
501	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
502	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
504	#479	C₂²×C₃₁	1	2	yes	complemented
505	#478	C₂²×C₃₁	1	2	yes	complemented
506	#478	C₂²×C₃₁	1	4	yes	complemented
507	#478	C₂²×C₃₁	1	4	yes	complemented
508	#478	C₂²×C₃₁	1	4	yes	complemented
509	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	#476	C₂²×C₃₁	1	2	yes	complemented
512	#476	C₂²×C₃₁	1	4	yes	complemented
513	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#474	C₂²×C₃₁	1	2	yes	complemented
516	#474	C₂²×C₃₁	1	4	yes	complemented
517	#469	C₂²×C₃₁	1	4	yes	complemented
518	#469	C₂²×C₃₁	1	4	yes	complemented
519	#469	C₂²×C₃₁	1	4	yes	complemented
520	#468	C₂²×C₃₁	1	4	yes	complemented
521	#466	C₂²×C₃₁	1	4	yes	complemented
522	#466	C₂²×C₃₁	1	4	yes	complemented
523	#466	C₂²×C₃₁	1	4	yes	complemented
524	#465	C₂²×C₃₁	1	4	yes	complemented
525	#463	C₂²×C₃₁	1	4	yes	complemented
526	#463	C₂²×C₃₁	1	4	yes	complemented
527	#460	C₂²×C₃₁	1	2	yes	complemented
528	#460	C₂²×C₃₁	1	2	yes	complemented
529	#459	C₂²×C₃₁	1	2	yes	—
530	#459	C₂²×C₃₁	1	2	yes	—
531	#459	C₂²×C₃₁	1	4	yes	—
532	#459	C₂²×C₃₁	1	2	yes	complemented
533	#459	C₂²×C₃₁	1	4	yes	complemented
534	#459	C₂²×C₃₁	1	4	yes	complemented
535	#459	C₂²×C₃₁	1	2	yes	complemented
536	#428	C₂²×C₃₁	1	2	yes	—
537	#427	C₂²×C₃₁	1	2	yes	—
538	#424	C₂²×C₃₁	1	2	yes	—
539	#424	C₂²×C₃₁	1	4	yes	complemented
540	#423	C₂²×C₃₁	1	1	yes	characteristic
541	#423	C₂²×C₃₁	1	2	yes	complemented
542	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
543	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
544	#418	C₂²×C₃₁	1	2	yes	—
545	#418	C₂²×C₃₁	1	2	yes	—
546	#416	C₂²×C₃₁	1	2	yes	—
547	C₂×#102	C₂²×C₃₁	1	2	yes	—
548	C₂×C₃₁	—	2	2	no	—
549	C₂×C₃₁	—	4	2	no	—
550	C₂×C₃₁	—	8	1	no	—
551	C₂×C₃₁	—	8	2	no	—
552	C₂×C₃₁	—	8	4	no	—
553	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
554	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
555	C₂×C₃₁	#3585	1	1	yes	characteristic
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
560	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
565	C₂³×C₄	—	2	1	no	—
566	AGL(1,ℤ/8)	—	4	4	no	—
567	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
568	C₂×D₈	—	4	4	no	—
569	C₂×D₈	C₂³×C₃₁	1	4	yes	—
570	C₂×D₈	C₂³×C₃₁	1	4	yes	—
571	C₂×D₈	C₂³×C₃₁	1	4	yes	—
572	#131	—	4	4	no	—
573	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
574	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
575	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
576	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
581	#127	—	2	1	no	—
582	#127	—	2	2	no	—
583	#127	—	2	1	no	—
584	#127	—	2	1	no	—
585	#127	C₂³×C₃₁	1	2	yes	—
586	#127	C₂³×C₃₁	1	2	yes	—
587	#127	C₂³×C₃₁	1	2	yes	—
588	#126	—	2	2	no	—
589	#126	—	2	2	no	—
590	#125	—	2	1	no	—
591	#125	C₂³×C₃₁	1	2	yes	—
592	#125	C₂³×C₃₁	1	2	yes	—
593	#124	—	2	1	no	—
594	#124	—	2	2	no	—
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	C₂³×C₃₁	1	2	yes	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	4	no	—
604	#123	—	2	4	no	—
605	#123	—	2	2	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	2	no	—
620	#121	—	2	2	no	—
621	#121	—	2	4	no	—
622	#121	—	2	4	no	—
623	#121	C₂³×C₃₁	1	2	yes	—
624	#121	C₂³×C₃₁	1	4	yes	—
625	#121	C₂³×C₃₁	1	4	yes	—
626	#121	C₂³×C₃₁	1	2	yes	—
627	#121	C₂³×C₃₁	1	2	yes	—
628	#120	—	2	2	no	—
629	#120	—	2	4	no	—
630	#120	—	2	2	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
634	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	D₄×C₃₁	1	2	yes	—
648	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
649	C₄×D₄	D₄×C₃₁	1	2	yes	—
650	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₃₁	1	2	yes	—
652	C₄×D₄	C₂³×C₃₁	1	2	yes	—
653	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₃₁	1	4	yes	—
656	C₄×D₄	C₂³×C₃₁	1	4	yes	—
657	#117	—	2	1	no	—
658	#117	—	2	2	no	—
659	#117	C₂³×C₃₁	1	1	yes	characteristic
660	#117	C₂³×C₃₁	1	2	yes	—
661	#117	C₂³×C₃₁	1	1	yes	characteristic
662	#117	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	4	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
669	#107	C₂³×C₃₁	1	2	yes	—
670	#107	C₂³×C₃₁	1	2	yes	—
671	#107	C₂³×C₃₁	1	4	yes	—
672	#106	C₂³×C₃₁	1	2	yes	—
673	#106	C₂³×C₃₁	1	2	yes	—
674	#106	C₂³×C₃₁	1	4	yes	—
675	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
676	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
677	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
678	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
679	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
680	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
681	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
682	#103	C₂³×C₃₁	1	2	yes	—
683	#103	C₂³×C₃₁	1	2	yes	—
684	#102	C₂³×C₃₁	1	4	yes	—
685	#102	C₂³×C₃₁	1	4	yes	—
686	#102	C₂³×C₃₁	1	2	yes	—
687	#102	C₂³×C₃₁	1	2	yes	—
688	#102	C₂³×C₃₁	1	4	yes	—
689	#102	C₂³×C₃₁	1	4	yes	—
690	#102	C₂³×C₃₁	1	4	yes	—
691	#102	C₂³×C₃₁	1	4	yes	—
692	C₃₁	#60922	1	1	yes	characteristic, direct product factor, Sylow
693	C₂⁴	—	2	2	no	—
694	C₂⁴	—	2	1	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	2	2	no	—
699	#41	—	8	4	no	—
700	#41	—	8	4	no	—
701	#41	—	8	4	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
728	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
731	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	8	2	no	—
741	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
747	SD₁₆	—	4	4	no	—
748	D₈	—	4	4	no	—
749	D₈	—	4	4	no	—
750	D₈	—	4	4	no	—
751	M₁₆	—	2	4	no	—
752	M₁₆	—	4	4	no	—
753	C₂×C₈	—	2	4	no	—
754	C₂×C₈	—	4	4	no	—
755	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
756	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
757	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
771	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₄²	C₂×D₄×C₃₁	1	2	yes	—
803	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
804	C₄²	C₂×D₄×C₃₁	1	2	yes	—
805	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
806	C₄²	C₂⁴×C₃₁	1	2	yes	—
807	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂³	—	2	2	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	—	8	2	no	—
816	C₂³	—	8	2	no	—
817	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
818	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	1	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	4	2	no	—
824	Q₈	—	8	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	1	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	1	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	—	8	2	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	4	no	—
846	D₄	—	8	4	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	8	1	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	—	8	4	no	—
866	C₂×C₄	—	8	1	no	—
867	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
875	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
876	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
877	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
878	C₈	—	2	2	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	4	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	4	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	8	4	no	—
896	C₂²	—	16	4	no	—
897	C₂²	C₃₁×#537	1	2	yes	—
898	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
899	C₄	—	2	2	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	C₃₁×#537	1	2	yes	—
912	C₄	C₃₁×#576	1	2	yes	—
913	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
914	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	4	no	—
919	C₂	—	8	1	no	—
920	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
921	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
922	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3460	C₂	semidirect
3. C₃₁×#3259	C₂	semidirect
4. C₃₁×#3257	C₂	semidirect
5. C₃₁×#3253	C₂	semidirect
6. C₃₁×#3251	C₂	semidirect
7. C₃₁×#3247	C₂	semidirect
8. C₃₁×#3245	C₂	semidirect
9. C₃₁×#3081	C₂	semidirect
10. C₃₁×#3077	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3062	C₂	semidirect
13. C₃₁×#3058	C₂	semidirect
14. C₃₁×#3041	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₂×C₃₁×#459	C₂	semidirect
17. C₃₁×#2906	C₂	semidirect
29. C₃₁×#542	C₂²	semidirect
31. C₃₁×#540	C₂²	semidirect
32. C₃₁×#540	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₃₁×#532	C₂²	semidirect
42. C₃₁×#532	C₂²	semidirect
45. C₃₁×#529	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#478	C₂²	semidirect
53. C₃₁×#478	C₂²	semidirect
54. C₃₁×#478	C₂²	semidirect
55. C₃₁×#478	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
62. C₃₁×#474	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#469	C₂²	semidirect
65. C₃₁×#469	C₂²	semidirect
66. C₃₁×#469	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#466	C₂²	semidirect
69. C₃₁×#466	C₂²	semidirect
70. C₃₁×#466	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#463	C₂²	semidirect
73. C₃₁×#463	C₂²	semidirect
74. C₃₁×#460	C₂²	semidirect
75. C₃₁×#460	C₂²	semidirect
79. C₃₁×#459	C₂²	semidirect
80. C₃₁×#459	C₂²	semidirect
81. C₃₁×#459	C₂²	semidirect
82. C₃₁×#459	C₂²	semidirect
86. C₃₁×#424	C₂²	semidirect
88. C₃₁×#423	C₂²	semidirect
90. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
346. #60922	C₃₁	direct (N × H)
420. #3508	C₂×C₃₁	semidirect
421. #3460	C₂×C₃₁	semidirect
422. #3259	C₂×C₃₁	semidirect
423. #3257	C₂×C₃₁	semidirect
424. #3253	C₂×C₃₁	semidirect
425. #3251	C₂×C₃₁	semidirect
426. #3247	C₂×C₃₁	semidirect
427. #3245	C₂×C₃₁	semidirect
428. #3081	C₂×C₃₁	semidirect
429. #3077	C₂×C₃₁	semidirect
430. #3076	C₂×C₃₁	semidirect
431. #3062	C₂×C₃₁	semidirect
432. #3058	C₂×C₃₁	semidirect
433. #3041	C₂×C₃₁	semidirect
434. #3038	C₂×C₃₁	semidirect
435. C₂×#459	C₂×C₃₁	semidirect
436. #2906	C₂×C₃₁	semidirect
482. #542	C₂²×C₃₁	semidirect
484. #540	C₂²×C₃₁	semidirect
485. #540	C₂²×C₃₁	semidirect
493. #532	C₂²×C₃₁	semidirect
494. #532	C₂²×C₃₁	semidirect
495. #532	C₂²×C₃₁	semidirect
498. #529	C₂²×C₃₁	semidirect
504. #479	C₂²×C₃₁	semidirect
505. #478	C₂²×C₃₁	semidirect
506. #478	C₂²×C₃₁	semidirect
507. #478	C₂²×C₃₁	semidirect
508. #478	C₂²×C₃₁	semidirect
509. #477	C₂²×C₃₁	semidirect
510. #476	C₂²×C₃₁	semidirect
511. #476	C₂²×C₃₁	semidirect
512. #476	C₂²×C₃₁	semidirect
513. #475	C₂²×C₃₁	semidirect
514. #474	C₂²×C₃₁	semidirect
515. #474	C₂²×C₃₁	semidirect
516. #474	C₂²×C₃₁	semidirect
517. #469	C₂²×C₃₁	semidirect
518. #469	C₂²×C₃₁	semidirect
519. #469	C₂²×C₃₁	semidirect
520. #468	C₂²×C₃₁	semidirect
521. #466	C₂²×C₃₁	semidirect
522. #466	C₂²×C₃₁	semidirect
523. #466	C₂²×C₃₁	semidirect
524. #465	C₂²×C₃₁	semidirect
525. #463	C₂²×C₃₁	semidirect
526. #463	C₂²×C₃₁	semidirect
527. #460	C₂²×C₃₁	semidirect
528. #460	C₂²×C₃₁	semidirect
532. #459	C₂²×C₃₁	semidirect
533. #459	C₂²×C₃₁	semidirect
534. #459	C₂²×C₃₁	semidirect
535. #459	C₂²×C₃₁	semidirect
539. #424	C₂²×C₃₁	semidirect
541. #423	C₂²×C₃₁	semidirect
543. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
692. C₃₁	#60922	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×#3508	2
C₃₁×#3460	2
C₃₁×#3259	2
C₃₁×#3257	2
C₃₁×#3253	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3245	2
C₃₁×#3081	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#3062	2
C₃₁×#3058	2
C₃₁×#3041	2
C₃₁×#3038	2
C₂×C₃₁×#459	2
C₃₁×#2906	2
#60922	31

Subgroups — C31×#60922 #21517681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60922 #21517681