Subgroups — C₃₁×#61988 #21518747

Order 7936.

1960 conjugacy classes of subgroups.

The subgroup lattice has 926 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×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3319	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3287	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3268	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3245	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3214	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#555	—	2	2	no	—
24	C₃₁×#555	—	2	1	no	—
25	C₃₁×#555	C₂²	1	2	yes	—
26	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	—	2	1	no	—
29	C₃₁×#550	C₂²	1	2	yes	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	4	yes	—
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	—	2	2	no	—
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₃₁×#532	C₂²	1	1	yes	characteristic
43	C₃₁×#532	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
45	C₃₁×#518	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#496	C₂²	1	4	yes	complemented
51	C₃₁×#493	C₂²	1	2	yes	—
52	C₃₁×#489	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#485	C₂²	1	2	yes	—
55	C₃₁×#482	C₂²	1	4	yes	complemented
56	C₃₁×#477	C₂²	1	2	yes	complemented
57	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#474	C₂²	1	2	yes	complemented
60	C₃₁×#474	C₂²	1	4	yes	complemented
61	C₃₁×#468	C₂²	1	4	yes	—
62	C₃₁×#466	C₂²	1	4	yes	complemented
63	C₃₁×#466	C₂²	1	4	yes	complemented
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#463	C₂²	1	4	yes	complemented
66	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#461	C₂²	1	2	yes	complemented
69	C₃₁×#460	C₂²	1	2	yes	—
70	C₃₁×#460	C₂²	1	2	yes	—
71	C₃₁×#460	C₂²	1	2	yes	complemented
72	C₃₁×#459	C₂²	1	2	yes	—
73	C₃₁×#459	C₂²	1	2	yes	—
74	C₃₁×#459	C₂²	1	2	yes	—
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	4	yes	complemented
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	4	yes	complemented
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#449	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	—
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#442	C₂²	1	4	yes	complemented
84	C₃₁×#440	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic
91	C₃₁×#423	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#418	C₂²	1	2	yes	—
94	C₃₁×#416	C₂²	1	4	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
100	C₂×#41×C₃₁	C₂³	1	2	yes	—
101	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×#41×C₃₁	C₂³	1	4	yes	—
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
106	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
107	C₃₁×#135	—	4	8	no	—
108	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂×D₈×C₃₁	C₂³	1	4	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
116	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
117	C₃₁×C₄⋊Q₈	—	2	1	no	—
118	C₃₁×C₄⋊Q₈	—	2	2	no	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×#127	—	2	2	no	—
124	C₃₁×#127	—	2	1	no	—
125	C₃₁×#127	—	2	2	no	—
126	C₃₁×#127	—	2	1	no	—
127	C₃₁×#127	—	2	1	no	—
128	C₃₁×#127	C₂³	1	2	yes	—
129	C₃₁×#127	C₂³	1	2	yes	—
130	C₃₁×#127	C₂³	1	2	yes	—
131	C₃₁×#127	C₂³	1	1	yes	characteristic
132	C₃₁×#125	—	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	—	2	1	no	—
139	C₃₁×#124	—	2	2	no	—
140	C₃₁×#124	C₂³	1	4	yes	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×#123	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	1	no	—
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	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#121	C₂³	1	2	yes	—
162	C₃₁×#121	C₂³	1	4	yes	—
163	C₃₁×#120	—	2	4	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	—	2	1	no	—
166	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	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	1	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	D₄	1	2	yes	—
186	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	4	yes	—
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	2	yes	—
192	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₃₁	C₂³	1	2	yes	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	2	no	—
196	C₃₁×#117	—	2	1	no	—
197	C₃₁×#117	—	2	1	no	—
198	C₃₁×#117	—	2	2	no	—
199	C₃₁×#117	D₄	1	1	yes	characteristic
200	C₃₁×#117	D₄	1	2	yes	—
201	C₃₁×#117	C₂³	1	2	yes	—
202	C₃₁×#117	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃₁×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	4	2	no	—
234	#41×C₃₁	—	4	1	no	—
235	#41×C₃₁	—	4	2	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	4	4	no	—
238	#41×C₃₁	—	4	4	no	—
239	#41×C₃₁	—	8	2	no	—
240	#41×C₃₁	—	8	4	no	—
241	#41×C₃₁	—	8	4	no	—
242	C₂×Q₈×C₃₁	—	2	1	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	2	1	no	—
245	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	4	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	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	—	2	1	no	—
262	C₂×D₄×C₃₁	—	2	2	no	—
263	C₂×D₄×C₃₁	—	2	2	no	—
264	C₂×D₄×C₃₁	—	4	2	no	—
265	C₂×D₄×C₃₁	—	4	2	no	—
266	C₂×D₄×C₃₁	—	4	4	no	—
267	C₂×D₄×C₃₁	—	8	2	no	—
268	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
271	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	1	no	—
275	C₂²×C₄×C₃₁	—	2	2	no	—
276	C₂²×C₄×C₃₁	—	2	1	no	—
277	C₂²×C₄×C₃₁	—	2	1	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	2	4	no	—
280	C₂²×C₄×C₃₁	—	2	4	no	—
281	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	Q₁₆×C₃₁	—	2	4	no	—
288	SD₁₆×C₃₁	—	2	8	no	—
289	SD₁₆×C₃₁	—	4	2	no	—
290	SD₁₆×C₃₁	—	4	4	no	—
291	D₈×C₃₁	—	4	4	no	—
292	D₈×C₃₁	—	4	4	no	—
293	D₈×C₃₁	—	4	4	no	—
294	M₁₆×C₃₁	—	4	2	no	—
295	C₂×C₈×C₃₁	—	4	4	no	—
296	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
297	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
298	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	1	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	1	no	—
327	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	1	no	—
339	C₄²×C₃₁	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₄²×C₃₁	C₂⁴	1	2	yes	—
346	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
347	#61988	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	4	no	—
351	C₂³×C₃₁	—	4	4	no	—
352	C₂³×C₃₁	—	8	2	no	—
353	C₂³×C₃₁	—	8	2	no	—
354	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
356	Q₈×C₃₁	—	2	2	no	—
357	Q₈×C₃₁	—	2	1	no	—
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	2	2	no	—
360	Q₈×C₃₁	—	4	2	no	—
361	Q₈×C₃₁	—	8	2	no	—
362	Q₈×C₃₁	—	8	1	no	—
363	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	2	1	no	—
366	D₄×C₃₁	—	2	4	no	—
367	D₄×C₃₁	—	2	2	no	—
368	D₄×C₃₁	—	2	2	no	—
369	D₄×C₃₁	—	2	4	no	—
370	D₄×C₃₁	—	2	1	no	—
371	D₄×C₃₁	—	4	2	no	—
372	D₄×C₃₁	—	4	4	no	—
373	D₄×C₃₁	—	4	2	no	—
374	D₄×C₃₁	—	4	4	no	—
375	D₄×C₃₁	—	4	4	no	—
376	D₄×C₃₁	—	4	4	no	—
377	D₄×C₃₁	—	4	2	no	—
378	D₄×C₃₁	—	4	4	no	—
379	D₄×C₃₁	—	8	2	no	—
380	D₄×C₃₁	—	8	2	no	—
381	D₄×C₃₁	—	8	2	no	—
382	D₄×C₃₁	—	8	1	no	—
383	D₄×C₃₁	—	8	4	no	—
384	D₄×C₃₁	—	8	2	no	—
385	D₄×C₃₁	—	8	2	no	—
386	D₄×C₃₁	—	8	2	no	—
387	D₄×C₃₁	—	8	4	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	4	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	4	2	no	—
402	C₂×C₄×C₃₁	—	4	4	no	—
403	C₂×C₄×C₃₁	—	4	2	no	—
404	C₂×C₄×C₃₁	—	4	4	no	—
405	C₂×C₄×C₃₁	—	4	2	no	—
406	C₂×C₄×C₃₁	—	4	2	no	—
407	C₂×C₄×C₃₁	—	4	4	no	—
408	C₂×C₄×C₃₁	—	8	4	no	—
409	C₂×C₄×C₃₁	—	8	4	no	—
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	2	yes	—
413	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
419	C₈×C₃₁	—	2	2	no	—
420	C₈×C₃₁	—	2	4	no	—
421	C₈×C₃₁	—	2	2	no	—
422	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3399	C₂×C₃₁	1	2	yes	complemented
425	#3375	C₂×C₃₁	1	2	yes	complemented
426	#3319	C₂×C₃₁	1	4	yes	complemented
427	#3305	C₂×C₃₁	1	2	yes	complemented
428	#3287	C₂×C₃₁	1	2	yes	complemented
429	#3268	C₂×C₃₁	1	4	yes	complemented
430	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#3245	C₂×C₃₁	1	2	yes	complemented
432	#3214	C₂×C₃₁	1	2	yes	complemented
433	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3115	C₂×C₃₁	1	2	yes	complemented
435	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#3035	C₂×C₃₁	1	2	yes	complemented
438	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
439	C₂²×C₃₁	—	2	2	no	—
440	C₂²×C₃₁	—	2	1	no	—
441	C₂²×C₃₁	—	2	1	no	—
442	C₂²×C₃₁	—	2	2	no	—
443	C₂²×C₃₁	—	2	2	no	—
444	C₂²×C₃₁	—	2	1	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	—	4	1	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	4	4	no	—
454	C₂²×C₃₁	—	16	4	no	—
455	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	2	no	—
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	1	no	—
465	C₄×C₃₁	—	4	1	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₄×C₃₁	#575	1	2	yes	—
469	C₄×C₃₁	#576	1	2	yes	—
470	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₄×C₃₁	#585	1	1	yes	characteristic
472	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
473	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
474	#559	—	2	1	no	—
475	#559	C₂²×C₃₁	1	2	yes	—
476	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#555	—	2	2	no	—
478	#555	—	2	1	no	—
479	#555	C₂²×C₃₁	1	2	yes	—
480	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
481	#550	—	2	1	no	—
482	#550	—	2	1	no	—
483	#550	C₂²×C₃₁	1	2	yes	—
484	#550	C₂²×C₃₁	1	2	yes	—
485	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
487	#546	—	2	2	no	—
488	#546	C₂²×C₃₁	1	4	yes	—
489	#540	—	2	2	no	—
490	#535	—	2	1	no	—
491	#533	C₂²×C₃₁	1	1	yes	characteristic
492	#532	—	2	1	no	—
493	#532	—	2	2	no	—
494	#532	C₂²×C₃₁	1	2	yes	—
495	#532	C₂²×C₃₁	1	2	yes	—
496	#532	C₂²×C₃₁	1	1	yes	characteristic
497	#532	C₂²×C₃₁	1	2	yes	complemented
498	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
499	#518	—	2	1	no	—
500	C₄×#41	—	2	1	no	—
501	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
502	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
503	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
504	#496	C₂²×C₃₁	1	4	yes	complemented
505	#493	C₂²×C₃₁	1	2	yes	—
506	#489	C₂²×C₃₁	1	4	yes	complemented
507	#486	C₂²×C₃₁	1	2	yes	—
508	#485	C₂²×C₃₁	1	2	yes	—
509	#482	C₂²×C₃₁	1	4	yes	complemented
510	#477	C₂²×C₃₁	1	2	yes	complemented
511	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	#474	C₂²×C₃₁	1	2	yes	complemented
514	#474	C₂²×C₃₁	1	4	yes	complemented
515	#468	C₂²×C₃₁	1	4	yes	—
516	#466	C₂²×C₃₁	1	4	yes	complemented
517	#466	C₂²×C₃₁	1	4	yes	complemented
518	#464	C₂²×C₃₁	1	4	yes	complemented
519	#463	C₂²×C₃₁	1	4	yes	complemented
520	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
522	#461	C₂²×C₃₁	1	2	yes	complemented
523	#460	C₂²×C₃₁	1	2	yes	—
524	#460	C₂²×C₃₁	1	2	yes	—
525	#460	C₂²×C₃₁	1	2	yes	complemented
526	#459	C₂²×C₃₁	1	2	yes	—
527	#459	C₂²×C₃₁	1	2	yes	—
528	#459	C₂²×C₃₁	1	2	yes	—
529	#459	C₂²×C₃₁	1	2	yes	—
530	#459	C₂²×C₃₁	1	4	yes	complemented
531	#452	C₂²×C₃₁	1	2	yes	—
532	#449	C₂²×C₃₁	1	4	yes	complemented
533	#449	C₂²×C₃₁	1	4	yes	complemented
534	#449	C₂²×C₃₁	1	4	yes	complemented
535	#447	C₂²×C₃₁	1	4	yes	—
536	#446	C₂²×C₃₁	1	2	yes	complemented
537	#442	C₂²×C₃₁	1	4	yes	complemented
538	#440	C₂²×C₃₁	1	4	yes	complemented
539	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
540	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
541	#435	C₂²×C₃₁	1	4	yes	—
542	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
543	#432	C₂²×C₃₁	1	2	yes	complemented
544	#431	C₂²×C₃₁	1	1	yes	characteristic
545	#423	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
547	#418	C₂²×C₃₁	1	2	yes	—
548	#416	C₂²×C₃₁	1	4	yes	complemented
549	C₂×C₃₁	—	4	2	no	—
550	C₂×C₃₁	—	4	1	no	—
551	C₂×C₃₁	—	8	1	no	—
552	C₂×C₃₁	—	8	2	no	—
553	C₂×C₃₁	—	8	4	no	—
554	C₂×C₃₁	#3488	1	1	yes	characteristic
555	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
556	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
562	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×#41	C₂³×C₃₁	1	2	yes	—
564	C₂×#41	C₂³×C₃₁	1	4	yes	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
568	AGL(1,ℤ/8)	—	4	4	no	—
569	#135	—	4	8	no	—
570	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
571	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
574	C₂×D₈	C₂³×C₃₁	1	4	yes	—
575	C₂×D₈	C₂³×C₃₁	1	4	yes	—
576	C₂×D₈	C₂³×C₃₁	1	4	yes	—
577	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
578	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
579	C₄⋊Q₈	—	2	1	no	—
580	C₄⋊Q₈	—	2	2	no	—
581	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
585	#127	—	2	2	no	—
586	#127	—	2	1	no	—
587	#127	—	2	2	no	—
588	#127	—	2	1	no	—
589	#127	—	2	1	no	—
590	#127	C₂³×C₃₁	1	2	yes	—
591	#127	C₂³×C₃₁	1	2	yes	—
592	#127	C₂³×C₃₁	1	1	yes	characteristic
593	#127	C₂³×C₃₁	1	2	yes	—
594	#125	—	2	1	no	—
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	—	2	2	no	—
600	#124	—	2	1	no	—
601	#124	—	2	2	no	—
602	#124	C₂³×C₃₁	1	4	yes	—
603	#123	—	2	4	no	—
604	#123	—	2	4	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	#121	—	2	1	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	4	no	—
620	#121	—	2	4	no	—
621	#121	C₂³×C₃₁	1	4	yes	—
622	#121	C₂³×C₃₁	1	2	yes	—
623	#121	C₂³×C₃₁	1	2	yes	—
624	#121	C₂³×C₃₁	1	2	yes	—
625	#120	—	2	4	no	—
626	C₄×Q₈	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
629	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
632	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
633	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	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	C₂³×C₃₁	1	1	yes	characteristic
650	C₄×D₄	C₂³×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	4	yes	—
654	C₄×D₄	C₂³×C₃₁	1	2	yes	—
655	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
656	#117	—	2	1	no	—
657	#117	—	2	2	no	—
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	2	2	no	—
661	#117	D₄×C₃₁	1	1	yes	characteristic
662	#117	D₄×C₃₁	1	2	yes	—
663	#117	C₂³×C₃₁	1	1	yes	characteristic
664	#117	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	—	2	4	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	2	no	—
668	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄²	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
674	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
676	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
677	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
678	#103	C₂³×C₃₁	1	2	yes	—
679	#103	C₂³×C₃₁	1	4	yes	—
680	#103	C₂³×C₃₁	1	2	yes	—
681	#103	C₂³×C₃₁	1	2	yes	—
682	#102	C₂³×C₃₁	1	4	yes	—
683	#102	C₂³×C₃₁	1	4	yes	—
684	#102	C₂³×C₃₁	1	4	yes	—
685	#102	C₂³×C₃₁	1	2	yes	—
686	#102	C₂³×C₃₁	1	4	yes	—
687	#102	C₂³×C₃₁	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
690	#97	C₂³×C₃₁	1	4	yes	—
691	C₄×C₈	C₂³×C₃₁	1	2	yes	—
692	C₃₁	#61988	1	1	yes	characteristic, direct product factor, Sylow
693	C₂⁴	—	2	2	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	1	no	—
698	#41	—	4	2	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	8	2	no	—
703	#41	—	8	4	no	—
704	#41	—	8	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	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	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	8	2	no	—
731	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
732	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
733	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
734	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
750	Q₁₆	—	2	4	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	4	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	D₈	—	4	4	no	—
757	M₁₆	—	4	2	no	—
758	C₂×C₈	—	4	4	no	—
759	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
760	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
761	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	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	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	C₂×D₄×C₃₁	1	2	yes	—
804	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₃₁	1	2	yes	—
806	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₄²	C₂⁴×C₃₁	1	2	yes	—
809	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	8	2	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	1	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	8	2	no	—
824	Q₈	—	8	1	no	—
825	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	1	no	—
833	D₄	—	4	2	no	—
834	D₄	—	4	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	2	no	—
840	D₄	—	4	4	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	1	no	—
845	D₄	—	8	4	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	C₃₁×#575	1	2	yes	—
914	C₄	C₃₁×#576	1	2	yes	—
915	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
916	C₄	C₃₁×#585	1	1	yes	characteristic
917	C₂	—	4	1	no	—
918	C₂	—	4	2	no	—
919	C₂	—	8	4	no	—
920	C₂	—	8	1	no	—
921	C₂	—	8	2	no	—
922	C₂	C₃₁×#3488	1	1	yes	characteristic
923	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
924	C₂	C₂×C₃₁×#576	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×#3483	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3319	C₂	semidirect
6. C₃₁×#3305	C₂	semidirect
7. C₃₁×#3287	C₂	semidirect
8. C₃₁×#3268	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3245	C₂	semidirect
11. C₃₁×#3214	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3115	C₂	semidirect
14. C₃₁×#3107	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₃₁×#3035	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
19. C₂×C₃₁×#135	C₂²	semidirect
22. Q₈²×C₃₁	C₂²	semidirect
26. C₃₁×#555	C₂²	semidirect
31. C₃₁×#550	C₂²	semidirect
32. C₃₁×#550	C₂²	semidirect
43. C₃₁×#532	C₂²	semidirect
49. C₄×#41×C₃₁	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#475	C₂²	semidirect
58. C₃₁×#474	C₂²	semidirect
59. C₃₁×#474	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
62. C₃₁×#466	C₂²	semidirect
63. C₃₁×#466	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#463	C₂²	semidirect
66. C₃₁×#462	C₂²	semidirect
67. C₃₁×#461	C₂²	semidirect
68. C₃₁×#461	C₂²	semidirect
71. C₃₁×#460	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
80. C₃₁×#449	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#442	C₂²	semidirect
84. C₃₁×#440	C₂²	semidirect
85. C₄×Q₁₆×C₃₁	C₂²	semidirect
86. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₈×D₄×C₃₁	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
94. C₃₁×#416	C₂²	semidirect
347. #61988	C₃₁	direct (N × H)
422. #3508	C₂×C₃₁	semidirect
423. #3483	C₂×C₃₁	semidirect
424. #3399	C₂×C₃₁	semidirect
425. #3375	C₂×C₃₁	semidirect
426. #3319	C₂×C₃₁	semidirect
427. #3305	C₂×C₃₁	semidirect
428. #3287	C₂×C₃₁	semidirect
429. #3268	C₂×C₃₁	semidirect
430. #3254	C₂×C₃₁	semidirect
431. #3245	C₂×C₃₁	semidirect
432. #3214	C₂×C₃₁	semidirect
433. #3205	C₂×C₃₁	semidirect
434. #3115	C₂×C₃₁	semidirect
435. #3107	C₂×C₃₁	semidirect
436. #3038	C₂×C₃₁	semidirect
437. #3035	C₂×C₃₁	semidirect
438. #2990	C₂×C₃₁	semidirect
473. C₂×#135	C₂²×C₃₁	semidirect
476. Q₈²	C₂²×C₃₁	semidirect
480. #555	C₂²×C₃₁	semidirect
485. #550	C₂²×C₃₁	semidirect
486. #550	C₂²×C₃₁	semidirect
497. #532	C₂²×C₃₁	semidirect
503. C₄×#41	C₂²×C₃₁	semidirect
504. #496	C₂²×C₃₁	semidirect
506. #489	C₂²×C₃₁	semidirect
509. #482	C₂²×C₃₁	semidirect
510. #477	C₂²×C₃₁	semidirect
511. #475	C₂²×C₃₁	semidirect
512. #474	C₂²×C₃₁	semidirect
513. #474	C₂²×C₃₁	semidirect
514. #474	C₂²×C₃₁	semidirect
516. #466	C₂²×C₃₁	semidirect
517. #466	C₂²×C₃₁	semidirect
518. #464	C₂²×C₃₁	semidirect
519. #463	C₂²×C₃₁	semidirect
520. #462	C₂²×C₃₁	semidirect
521. #461	C₂²×C₃₁	semidirect
522. #461	C₂²×C₃₁	semidirect
525. #460	C₂²×C₃₁	semidirect
530. #459	C₂²×C₃₁	semidirect
532. #449	C₂²×C₃₁	semidirect
533. #449	C₂²×C₃₁	semidirect
534. #449	C₂²×C₃₁	semidirect
536. #446	C₂²×C₃₁	semidirect
537. #442	C₂²×C₃₁	semidirect
538. #440	C₂²×C₃₁	semidirect
539. C₄×Q₁₆	C₂²×C₃₁	semidirect
540. C₄×SD₁₆	C₂²×C₃₁	semidirect
542. C₈×D₄	C₂²×C₃₁	semidirect
543. #432	C₂²×C₃₁	semidirect
546. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
548. #416	C₂²×C₃₁	semidirect
692. C₃₁	#61988	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×#3483	2
C₃₁×#3399	2
C₃₁×#3375	2
C₃₁×#3319	2
C₃₁×#3305	2
C₃₁×#3287	2
C₃₁×#3268	2
C₃₁×#3254	2
C₃₁×#3245	2
C₃₁×#3214	2
C₃₁×#3205	2
C₃₁×#3115	2
C₃₁×#3107	2
C₃₁×#3038	2
C₃₁×#3035	2
C₃₁×#2990	2
#61988	31

Subgroups — C31×#61988 #21518747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61988 #21518747