Subgroups — C₃₁×#62123 #21518882

Order 7936.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3080	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#555	—	2	1	no	—
27	C₃₁×#555	—	2	2	no	—
28	C₃₁×#555	C₂²	1	2	yes	—
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#553	C₂²	1	2	yes	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#550	—	2	1	no	—
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#550	C₂²	1	2	yes	—
39	C₃₁×#550	C₂²	1	1	yes	characteristic
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#539	—	2	2	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#532	—	2	1	no	—
46	C₃₁×#532	—	2	2	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	2	yes	—
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	2	yes	—
51	C₂×C₃₁×#125	C₂²	1	2	yes	—
52	C₃₁×#520	—	2	1	no	—
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#500	C₂²	1	1	yes	characteristic
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#490	C₂²	1	2	yes	—
63	C₃₁×#486	C₂²	1	1	yes	characteristic
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	1	yes	characteristic
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#482	C₂²	1	1	yes	characteristic
68	C₃₁×#482	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#481	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#480	C₂²	1	2	yes	—
74	C₃₁×#480	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#479	C₂²	1	1	yes	characteristic
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	1	yes	characteristic
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	1	yes	characteristic
88	C₃₁×#476	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#475	C₂²	1	1	yes	characteristic
91	C₃₁×#475	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	1	yes	characteristic
93	C₃₁×#474	C₂²	1	2	yes	—
94	C₃₁×#469	C₂²	1	2	yes	—
95	C₃₁×#469	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	—
97	C₃₁×#468	C₂²	1	2	yes	—
98	C₃₁×#466	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#463	C₂²	1	2	yes	—
103	C₃₁×#460	C₂²	1	1	yes	characteristic
104	C₃₁×#460	C₂²	1	2	yes	—
105	C₃₁×#459	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	2	yes	—
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#452	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	—
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#432	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#428	C₂²	1	2	yes	—
129	C₃₁×#427	C₂²	1	2	yes	—
130	C₃₁×#423	C₂²	1	2	yes	—
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×#127	—	2	1	no	—
159	C₃₁×#127	—	2	2	no	—
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#127	C₂³	1	2	yes	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	1	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	C₂³	1	1	yes	characteristic
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	C₂³	1	1	yes	characteristic
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	1	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×#121	—	2	1	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	C₂³	1	1	yes	characteristic
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
233	C₄×D₄×C₃₁	D₄	1	2	yes	—
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	D₄	1	1	yes	characteristic
250	C₃₁×#117	D₄	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄²×C₃₁	—	2	1	no	—
260	C₂×C₄²×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	#41×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	1	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	4	no	—
318	#41×C₃₁	—	4	4	no	—
319	#41×C₃₁	—	8	4	no	—
320	#41×C₃₁	—	8	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	Q₁₆×C₃₁	—	2	2	no	—
361	SD₁₆×C₃₁	—	2	2	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	1	no	—
364	D₈×C₃₁	—	4	2	no	—
365	D₈×C₃₁	—	4	1	no	—
366	M₁₆×C₃₁	—	4	2	no	—
367	M₁₆×C₃₁	—	4	2	no	—
368	C₂×C₈×C₃₁	—	4	2	no	—
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₃₁	C₂×D₄	1	2	yes	—
438	C₄²×C₃₁	C₂×D₄	1	2	yes	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	2	yes	—
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#62123	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	2	2	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	4	2	no	—
454	Q₈×C₃₁	—	8	1	no	—
455	Q₈×C₃₁	—	8	2	no	—
456	Q₈×C₃₁	—	8	1	no	—
457	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
458	D₄×C₃₁	—	2	2	no	—
459	D₄×C₃₁	—	2	1	no	—
460	D₄×C₃₁	—	2	1	no	—
461	D₄×C₃₁	—	2	2	no	—
462	D₄×C₃₁	—	2	1	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	4	2	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	4	4	no	—
468	D₄×C₃₁	—	4	4	no	—
469	D₄×C₃₁	—	4	4	no	—
470	D₄×C₃₁	—	4	2	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	—	8	1	no	—
473	D₄×C₃₁	—	8	1	no	—
474	D₄×C₃₁	—	8	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	4	1	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	4	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	4	no	—
499	C₂×C₄×C₃₁	—	4	4	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
513	C₈×C₃₁	—	2	1	no	—
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	2	no	—
516	C₈×C₃₁	—	2	2	no	—
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	1	no	—
519	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3348	C₂×C₃₁	1	2	yes	complemented
528	#3347	C₂×C₃₁	1	2	yes	complemented
529	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3317	C₂×C₃₁	1	2	yes	complemented
532	#3309	C₂×C₃₁	1	2	yes	complemented
533	#3251	C₂×C₃₁	1	2	yes	complemented
534	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3234	C₂×C₃₁	1	2	yes	complemented
536	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3111	C₂×C₃₁	1	2	yes	complemented
538	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3080	C₂×C₃₁	1	2	yes	complemented
540	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	#575	1	2	yes	—
575	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
576	C₄×C₃₁	#585	1	1	yes	characteristic
577	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
578	#557	C₂²×C₃₁	1	1	yes	characteristic
579	#555	—	2	1	no	—
580	#555	—	2	2	no	—
581	#555	C₂²×C₃₁	1	2	yes	—
582	#555	C₂²×C₃₁	1	1	yes	characteristic
583	#554	C₂²×C₃₁	1	1	yes	characteristic
584	#554	C₂²×C₃₁	1	1	yes	characteristic
585	#553	C₂²×C₃₁	1	2	yes	—
586	#552	—	2	2	no	—
587	#552	—	2	1	no	—
588	#552	C₂²×C₃₁	1	2	yes	—
589	#550	—	2	1	no	—
590	#550	C₂²×C₃₁	1	1	yes	characteristic
591	#550	C₂²×C₃₁	1	2	yes	—
592	#550	C₂²×C₃₁	1	1	yes	characteristic
593	#547	—	2	1	no	—
594	#547	C₂²×C₃₁	1	1	yes	characteristic
595	#541	—	2	1	no	—
596	#539	—	2	2	no	—
597	#533	C₂²×C₃₁	1	1	yes	characteristic
598	#532	—	2	1	no	—
599	#532	—	2	2	no	—
600	#532	C₂²×C₃₁	1	1	yes	characteristic
601	#532	C₂²×C₃₁	1	2	yes	—
602	#529	C₂²×C₃₁	1	1	yes	characteristic
603	#529	C₂²×C₃₁	1	2	yes	—
604	C₂×#125	C₂²×C₃₁	1	2	yes	—
605	#520	—	2	1	no	—
606	C₄×#41	—	2	1	no	—
607	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
608	C₄×#41	C₂²×C₃₁	1	2	yes	—
609	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
610	#501	C₂²×C₃₁	1	2	yes	—
611	#501	C₂²×C₃₁	1	2	yes	—
612	#500	C₂²×C₃₁	1	1	yes	characteristic
613	#498	C₂²×C₃₁	1	1	yes	characteristic
614	#490	C₂²×C₃₁	1	2	yes	—
615	#490	C₂²×C₃₁	1	2	yes	—
616	#486	C₂²×C₃₁	1	1	yes	characteristic
617	#486	C₂²×C₃₁	1	1	yes	characteristic
618	#485	C₂²×C₃₁	1	1	yes	characteristic
619	#485	C₂²×C₃₁	1	2	yes	—
620	#482	C₂²×C₃₁	1	1	yes	characteristic
621	#482	C₂²×C₃₁	1	2	yes	—
622	#482	C₂²×C₃₁	1	2	yes	—
623	#482	C₂²×C₃₁	1	2	yes	—
624	#481	C₂²×C₃₁	1	2	yes	—
625	#481	C₂²×C₃₁	1	2	yes	—
626	#480	C₂²×C₃₁	1	2	yes	—
627	#480	C₂²×C₃₁	1	2	yes	—
628	#479	C₂²×C₃₁	1	2	yes	—
629	#479	C₂²×C₃₁	1	1	yes	characteristic
630	#479	C₂²×C₃₁	1	2	yes	—
631	#479	C₂²×C₃₁	1	2	yes	—
632	#478	C₂²×C₃₁	1	2	yes	—
633	#478	C₂²×C₃₁	1	2	yes	—
634	#478	C₂²×C₃₁	1	2	yes	—
635	#478	C₂²×C₃₁	1	2	yes	—
636	#478	C₂²×C₃₁	1	2	yes	—
637	#478	C₂²×C₃₁	1	1	yes	characteristic
638	#478	C₂²×C₃₁	1	2	yes	—
639	#477	C₂²×C₃₁	1	1	yes	characteristic
640	#477	C₂²×C₃₁	1	1	yes	characteristic
641	#476	C₂²×C₃₁	1	1	yes	characteristic
642	#476	C₂²×C₃₁	1	1	yes	characteristic
643	#475	C₂²×C₃₁	1	1	yes	characteristic
644	#475	C₂²×C₃₁	1	2	yes	—
645	#474	C₂²×C₃₁	1	1	yes	characteristic
646	#474	C₂²×C₃₁	1	2	yes	—
647	#469	C₂²×C₃₁	1	2	yes	—
648	#469	C₂²×C₃₁	1	2	yes	—
649	#468	C₂²×C₃₁	1	2	yes	—
650	#468	C₂²×C₃₁	1	2	yes	—
651	#466	C₂²×C₃₁	1	2	yes	—
652	#465	C₂²×C₃₁	1	2	yes	—
653	#464	C₂²×C₃₁	1	1	yes	characteristic
654	#463	C₂²×C₃₁	1	1	yes	characteristic
655	#463	C₂²×C₃₁	1	2	yes	—
656	#460	C₂²×C₃₁	1	1	yes	characteristic
657	#460	C₂²×C₃₁	1	2	yes	—
658	#459	C₂²×C₃₁	1	1	yes	characteristic
659	#459	C₂²×C₃₁	1	2	yes	—
660	#452	C₂²×C₃₁	1	2	yes	—
661	#452	C₂²×C₃₁	1	1	yes	characteristic
662	#449	C₂²×C₃₁	1	2	yes	—
663	#449	C₂²×C₃₁	1	1	yes	characteristic
664	#446	C₂²×C₃₁	1	1	yes	characteristic
665	#446	C₂²×C₃₁	1	1	yes	characteristic
666	#442	C₂²×C₃₁	1	2	yes	—
667	#441	C₂²×C₃₁	1	2	yes	—
668	#440	C₂²×C₃₁	1	2	yes	—
669	#440	C₂²×C₃₁	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
674	#436	C₂²×C₃₁	1	1	yes	characteristic
675	#436	C₂²×C₃₁	1	1	yes	characteristic
676	#435	C₂²×C₃₁	1	2	yes	—
677	#435	C₂²×C₃₁	1	2	yes	—
678	#432	C₂²×C₃₁	1	2	yes	—
679	#431	C₂²×C₃₁	1	1	yes	characteristic
680	#428	C₂²×C₃₁	1	2	yes	—
681	#428	C₂²×C₃₁	1	2	yes	—
682	#427	C₂²×C₃₁	1	2	yes	—
683	#423	C₂²×C₃₁	1	2	yes	—
684	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
685	#417	C₂²×C₃₁	1	2	yes	—
686	#417	C₂²×C₃₁	1	2	yes	—
687	#416	C₂²×C₃₁	1	2	yes	—
688	C₂×C₃₁	—	4	2	no	—
689	C₂×C₃₁	—	4	1	no	—
690	C₂×C₃₁	—	8	2	no	—
691	C₂×C₃₁	—	8	1	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	#3489	1	1	yes	characteristic
694	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
695	C₂×C₃₁	#3585	1	1	yes	characteristic
696	C₂×#41	—	2	1	no	—
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	2	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
701	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×#41	C₂³×C₃₁	1	2	yes	—
703	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₃₁	1	2	yes	—
709	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	#127	—	2	1	no	—
720	#127	—	2	2	no	—
721	#127	C₂³×C₃₁	1	1	yes	characteristic
722	#127	C₂³×C₃₁	1	2	yes	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	C₂³×C₃₁	1	1	yes	characteristic
733	#125	C₂³×C₃₁	1	2	yes	—
734	#125	C₂³×C₃₁	1	2	yes	—
735	#125	C₂³×C₃₁	1	2	yes	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	C₂³×C₃₁	1	1	yes	characteristic
742	#123	—	2	2	no	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
755	#121	—	2	1	no	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	C₂³×C₃₁	1	2	yes	—
766	#121	C₂³×C₃₁	1	1	yes	characteristic
767	#121	C₂³×C₃₁	1	2	yes	—
768	#121	C₂³×C₃₁	1	2	yes	—
769	#121	C₂³×C₃₁	1	2	yes	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
794	C₄×D₄	D₄×C₃₁	1	2	yes	—
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	2	yes	—
797	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₃₁	1	2	yes	—
799	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	D₄×C₃₁	1	1	yes	characteristic
811	#117	D₄×C₃₁	1	2	yes	—
812	#117	C₂³×C₃₁	1	1	yes	characteristic
813	#117	C₂³×C₃₁	1	2	yes	—
814	#117	C₂³×C₃₁	1	2	yes	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
823	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
824	#107	C₂³×C₃₁	1	2	yes	—
825	#107	C₂³×C₃₁	1	2	yes	—
826	#107	C₂³×C₃₁	1	1	yes	characteristic
827	#107	C₂³×C₃₁	1	2	yes	—
828	#107	C₂³×C₃₁	1	2	yes	—
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#107	C₂³×C₃₁	1	2	yes	—
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	1	yes	characteristic
834	#106	C₂³×C₃₁	1	2	yes	—
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	#97	C₂³×C₃₁	1	2	yes	—
870	#97	C₂³×C₃₁	1	2	yes	—
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₃₁	#62123	1	1	yes	characteristic, direct product factor, Sylow
874	#41	—	2	2	no	—
875	#41	—	2	4	no	—
876	#41	—	4	2	no	—
877	#41	—	4	1	no	—
878	#41	—	4	2	no	—
879	#41	—	4	4	no	—
880	#41	—	4	4	no	—
881	#41	—	8	4	no	—
882	#41	—	8	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
905	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	Q₁₆	—	2	2	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	1	no	—
926	D₈	—	4	2	no	—
927	D₈	—	4	1	no	—
928	M₁₆	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	C₂×C₈	—	4	2	no	—
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1000	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1001	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₃₁	1	2	yes	—
1004	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1009	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	4	2	no	—
1015	Q₈	—	8	1	no	—
1016	Q₈	—	8	2	no	—
1017	Q₈	—	8	1	no	—
1018	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	C₃₁×#575	1	2	yes	—
1113	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₄	C₃₁×#585	1	1	yes	characteristic
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	2	no	—
1118	C₂	—	8	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₃₁×#3489	1	1	yes	characteristic
1121	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1122	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×#3515	C₂	semidirect
2. C₃₁×#3483	C₂	semidirect
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3354	C₂	semidirect
9. C₃₁×#3348	C₂	semidirect
10. C₃₁×#3347	C₂	semidirect
11. C₃₁×#3333	C₂	semidirect
12. C₃₁×#3332	C₂	semidirect
13. C₃₁×#3317	C₂	semidirect
14. C₃₁×#3309	C₂	semidirect
15. C₃₁×#3251	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3234	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3080	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
443. #62123	C₃₁	direct (N × H)
519. #3515	C₂×C₃₁	semidirect
520. #3483	C₂×C₃₁	semidirect
521. #3387	C₂×C₃₁	semidirect
522. #3385	C₂×C₃₁	semidirect
523. #3368	C₂×C₃₁	semidirect
524. #3366	C₂×C₃₁	semidirect
525. #3357	C₂×C₃₁	semidirect
526. #3354	C₂×C₃₁	semidirect
527. #3348	C₂×C₃₁	semidirect
528. #3347	C₂×C₃₁	semidirect
529. #3333	C₂×C₃₁	semidirect
530. #3332	C₂×C₃₁	semidirect
531. #3317	C₂×C₃₁	semidirect
532. #3309	C₂×C₃₁	semidirect
533. #3251	C₂×C₃₁	semidirect
534. #3247	C₂×C₃₁	semidirect
535. #3234	C₂×C₃₁	semidirect
536. #3228	C₂×C₃₁	semidirect
537. #3111	C₂×C₃₁	semidirect
538. #3102	C₂×C₃₁	semidirect
539. #3080	C₂×C₃₁	semidirect
540. #3076	C₂×C₃₁	semidirect
541. #2989	C₂×C₃₁	semidirect
873. C₃₁	#62123	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×#3515	2
C₃₁×#3483	2
C₃₁×#3387	2
C₃₁×#3385	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3357	2
C₃₁×#3354	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3317	2
C₃₁×#3309	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3234	2
C₃₁×#3228	2
C₃₁×#3111	2
C₃₁×#3102	2
C₃₁×#3080	2
C₃₁×#3076	2
C₃₁×#2989	2
#62123	31

Subgroups — C31×#62123 #21518882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62123 #21518882