Subgroups — C₃₁×#62166 #21518925

Order 7936.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#556	C₂²	1	1	yes	characteristic
23	C₃₁×#554	C₂²	1	2	yes	—
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	C₂²	1	2	yes	—
26	C₃₁×#553	C₂²	1	2	yes	complemented
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#551	—	2	2	no	—
29	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#547	—	2	2	no	—
32	C₃₁×#547	C₂²	1	1	yes	characteristic
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#547	C₂²	1	1	yes	characteristic
35	C₃₁×#546	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#540	C₂²	1	2	yes	complemented
39	C₃₁×#539	—	2	2	no	—
40	C₃₁×#539	—	2	2	no	—
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#532	C₂²	1	1	yes	characteristic
45	C₃₁×#529	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
47	C₃₁×#525	—	2	1	no	—
48	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
49	C₃₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#501	C₂²	1	2	yes	complemented
53	C₃₁×#498	C₂²	1	2	yes	complemented
54	C₃₁×#491	C₂²	1	2	yes	complemented
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#488	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	complemented
58	C₃₁×#484	C₂²	1	2	yes	—
59	C₃₁×#483	C₂²	1	2	yes	—
60	C₃₁×#483	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	—
62	C₃₁×#481	C₂²	1	2	yes	—
63	C₃₁×#481	C₂²	1	2	yes	—
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#479	C₂²	1	2	yes	complemented
68	C₃₁×#479	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	—
70	C₃₁×#478	C₂²	1	2	yes	—
71	C₃₁×#478	C₂²	1	2	yes	—
72	C₃₁×#478	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#476	C₂²	1	1	yes	characteristic
75	C₃₁×#476	C₂²	1	2	yes	—
76	C₃₁×#476	C₂²	1	1	yes	characteristic
77	C₃₁×#476	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	2	yes	complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	complemented
84	C₃₁×#466	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#461	C₂²	1	2	yes	complemented
91	C₃₁×#460	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	1	yes	characteristic
93	C₃₁×#459	C₂²	1	1	yes	characteristic
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#447	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₃₁×#442	C₂²	1	2	yes	—
99	C₃₁×#442	C₂²	1	2	yes	—
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×D₈×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
111	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
112	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₃₁×#417	C₂²	1	2	yes	—
116	C₃₁×#416	C₂²	1	2	yes	—
117	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₃₁	—	2	1	no	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	—	2	1	no	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#127	C₂³	1	1	yes	characteristic
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	D₄	1	2	yes	—
146	C₃₁×#125	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	—	2	1	no	—
150	C₃₁×#125	—	2	1	no	—
151	C₃₁×#125	D₄	1	1	yes	characteristic
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	1	no	—
157	C₃₁×#124	D₄	1	1	yes	characteristic
158	C₃₁×#124	C₂³	1	2	yes	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	D₄	1	2	yes	—
170	C₃₁×C₂²⋊Q₈	—	2	1	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	1	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	1	no	—
175	C₃₁×C₂²⋊Q₈	—	2	1	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₃₁×#121	—	2	1	no	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	—	2	2	no	—
194	C₃₁×#121	D₄	1	1	yes	characteristic
195	C₃₁×#121	C₂³	1	2	yes	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#121	C₂³	1	2	yes	—
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₃₁×#120	—	2	2	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₃₁×#117	—	2	1	no	—
223	C₃₁×#117	—	2	2	no	—
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	2	4	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	2	no	—
284	#41×C₃₁	—	8	4	no	—
285	#41×C₃₁	—	8	2	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	8	2	no	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	1	no	—
302	C₂×D₄×C₃₁	—	4	1	no	—
303	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	—	2	1	no	—
309	C₂²×C₄×C₃₁	—	2	1	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	2	no	—
313	C₂²×C₄×C₃₁	—	2	2	no	—
314	C₂²×C₄×C₃₁	—	2	1	no	—
315	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	8	2	no	—
323	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
327	SD₁₆×C₃₁	—	4	2	no	—
328	SD₁₆×C₃₁	—	4	2	no	—
329	D₈×C₃₁	—	2	4	no	—
330	D₈×C₃₁	—	4	2	no	—
331	M₁₆×C₃₁	—	4	2	no	—
332	C₂×C₈×C₃₁	—	4	1	no	—
333	C₂×C₈×C₃₁	—	4	2	no	—
334	C₂×C₈×C₃₁	—	4	1	no	—
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
337	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
338	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	1	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	1	no	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₃₁	C₂⁴	1	2	yes	—
400	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	#62166	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	1	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	4	2	no	—
407	C₂³×C₃₁	—	4	2	no	—
408	C₂³×C₃₁	—	8	1	no	—
409	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
410	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	4	1	no	—
414	Q₈×C₃₁	—	4	2	no	—
415	Q₈×C₃₁	—	8	2	no	—
416	Q₈×C₃₁	—	8	1	no	—
417	Q₈×C₃₁	—	8	2	no	—
418	D₄×C₃₁	—	2	4	no	—
419	D₄×C₃₁	—	2	2	no	—
420	D₄×C₃₁	—	2	1	no	—
421	D₄×C₃₁	—	2	1	no	—
422	D₄×C₃₁	—	2	1	no	—
423	D₄×C₃₁	—	2	2	no	—
424	D₄×C₃₁	—	4	1	no	—
425	D₄×C₃₁	—	4	2	no	—
426	D₄×C₃₁	—	4	4	no	—
427	D₄×C₃₁	—	4	4	no	—
428	D₄×C₃₁	—	8	1	no	—
429	D₄×C₃₁	—	8	1	no	—
430	D₄×C₃₁	—	8	2	no	—
431	D₄×C₃₁	—	8	2	no	—
432	D₄×C₃₁	—	8	2	no	—
433	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	2	1	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	4	1	no	—
447	C₂×C₄×C₃₁	—	4	4	no	—
448	C₂×C₄×C₃₁	—	4	2	no	—
449	C₂×C₄×C₃₁	—	4	2	no	—
450	C₂×C₄×C₃₁	—	4	2	no	—
451	C₂×C₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	—	8	1	no	—
453	C₂×C₄×C₃₁	—	8	1	no	—
454	C₂×C₄×C₃₁	—	8	2	no	—
455	C₂×C₄×C₃₁	—	8	2	no	—
456	C₂×C₄×C₃₁	—	8	2	no	—
457	C₂×C₄×C₃₁	—	8	1	no	—
458	C₂×C₄×C₃₁	—	8	1	no	—
459	C₂×C₄×C₃₁	—	8	2	no	—
460	C₂×C₄×C₃₁	—	8	2	no	—
461	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
470	C₈×C₃₁	—	2	2	no	—
471	C₈×C₃₁	—	2	2	no	—
472	C₈×C₃₁	—	2	2	no	—
473	C₈×C₃₁	—	2	2	no	—
474	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
476	#3384	C₂×C₃₁	1	2	yes	complemented
477	#3376	C₂×C₃₁	1	2	yes	complemented
478	#3346	C₂×C₃₁	1	2	yes	complemented
479	#3345	C₂×C₃₁	1	2	yes	complemented
480	#3335	C₂×C₃₁	1	2	yes	complemented
481	#3307	C₂×C₃₁	1	2	yes	complemented
482	#3306	C₂×C₃₁	1	2	yes	complemented
483	#3297	C₂×C₃₁	1	2	yes	complemented
484	#3257	C₂×C₃₁	1	2	yes	complemented
485	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3244	C₂×C₃₁	1	2	yes	complemented
487	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3119	C₂×C₃₁	1	2	yes	complemented
489	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3084	C₂×C₃₁	1	2	yes	complemented
491	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
492	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
493	C₂²×C₃₁	—	2	1	no	—
494	C₂²×C₃₁	—	2	1	no	—
495	C₂²×C₃₁	—	2	2	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	2	no	—
499	C₂²×C₃₁	—	4	1	no	—
500	C₂²×C₃₁	—	4	1	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	1	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	1	no	—
507	C₂²×C₃₁	—	8	4	no	—
508	C₂²×C₃₁	#577	1	2	yes	—
509	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₃₁	—	2	1	no	—
511	C₄×C₃₁	—	2	1	no	—
512	C₄×C₃₁	—	2	2	no	—
513	C₄×C₃₁	—	2	2	no	—
514	C₄×C₃₁	—	2	1	no	—
515	C₄×C₃₁	—	2	1	no	—
516	C₄×C₃₁	—	2	1	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	1	no	—
520	C₄×C₃₁	—	4	2	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	2	no	—
525	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄×C₃₁	#585	1	1	yes	characteristic
527	#563	—	2	1	no	—
528	#562	—	2	1	no	—
529	#556	C₂²×C₃₁	1	1	yes	characteristic
530	#554	C₂²×C₃₁	1	2	yes	—
531	#554	C₂²×C₃₁	1	2	yes	complemented
532	#553	C₂²×C₃₁	1	2	yes	—
533	#553	C₂²×C₃₁	1	2	yes	complemented
534	#552	—	2	1	no	—
535	#551	—	2	2	no	—
536	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
537	#548	—	2	1	no	—
538	#547	—	2	2	no	—
539	#547	C₂²×C₃₁	1	1	yes	characteristic
540	#547	C₂²×C₃₁	1	2	yes	—
541	#547	C₂²×C₃₁	1	1	yes	characteristic
542	#546	C₂²×C₃₁	1	2	yes	—
543	#544	C₂²×C₃₁	1	2	yes	complemented
544	#542	C₂²×C₃₁	1	2	yes	—
545	#540	C₂²×C₃₁	1	2	yes	complemented
546	#539	—	2	2	no	—
547	#539	—	2	2	no	—
548	#539	—	2	1	no	—
549	#537	—	2	1	no	—
550	#533	C₂²×C₃₁	1	1	yes	characteristic
551	#532	C₂²×C₃₁	1	1	yes	characteristic
552	#529	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
554	#525	—	2	1	no	—
555	C₂×C₂²⋊Q₈	—	2	1	no	—
556	#520	C₂²×C₃₁	1	2	yes	—
557	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
558	#501	C₂²×C₃₁	1	2	yes	complemented
559	#501	C₂²×C₃₁	1	2	yes	complemented
560	#498	C₂²×C₃₁	1	2	yes	complemented
561	#491	C₂²×C₃₁	1	2	yes	complemented
562	#489	C₂²×C₃₁	1	2	yes	—
563	#488	C₂²×C₃₁	1	2	yes	—
564	#485	C₂²×C₃₁	1	2	yes	complemented
565	#484	C₂²×C₃₁	1	2	yes	—
566	#483	C₂²×C₃₁	1	2	yes	—
567	#483	C₂²×C₃₁	1	2	yes	complemented
568	#482	C₂²×C₃₁	1	2	yes	—
569	#481	C₂²×C₃₁	1	2	yes	—
570	#481	C₂²×C₃₁	1	2	yes	—
571	#481	C₂²×C₃₁	1	2	yes	complemented
572	#480	C₂²×C₃₁	1	2	yes	complemented
573	#479	C₂²×C₃₁	1	2	yes	complemented
574	#479	C₂²×C₃₁	1	2	yes	complemented
575	#479	C₂²×C₃₁	1	2	yes	complemented
576	#478	C₂²×C₃₁	1	2	yes	—
577	#478	C₂²×C₃₁	1	2	yes	—
578	#478	C₂²×C₃₁	1	2	yes	—
579	#478	C₂²×C₃₁	1	2	yes	—
580	#478	C₂²×C₃₁	1	2	yes	—
581	#476	C₂²×C₃₁	1	1	yes	characteristic
582	#476	C₂²×C₃₁	1	2	yes	—
583	#476	C₂²×C₃₁	1	1	yes	characteristic
584	#476	C₂²×C₃₁	1	2	yes	complemented
585	#476	C₂²×C₃₁	1	2	yes	complemented
586	#475	C₂²×C₃₁	1	2	yes	complemented
587	#475	C₂²×C₃₁	1	2	yes	complemented
588	#474	C₂²×C₃₁	1	2	yes	complemented
589	#469	C₂²×C₃₁	1	2	yes	—
590	#468	C₂²×C₃₁	1	2	yes	complemented
591	#466	C₂²×C₃₁	1	2	yes	—
592	#465	C₂²×C₃₁	1	2	yes	—
593	#465	C₂²×C₃₁	1	2	yes	—
594	#465	C₂²×C₃₁	1	2	yes	complemented
595	#463	C₂²×C₃₁	1	2	yes	—
596	#463	C₂²×C₃₁	1	2	yes	—
597	#461	C₂²×C₃₁	1	2	yes	complemented
598	#460	C₂²×C₃₁	1	2	yes	complemented
599	#459	C₂²×C₃₁	1	1	yes	characteristic
600	#459	C₂²×C₃₁	1	1	yes	characteristic
601	#449	C₂²×C₃₁	1	2	yes	—
602	#449	C₂²×C₃₁	1	2	yes	—
603	#447	C₂²×C₃₁	1	2	yes	—
604	#446	C₂²×C₃₁	1	2	yes	complemented
605	#442	C₂²×C₃₁	1	2	yes	—
606	#442	C₂²×C₃₁	1	2	yes	—
607	#442	C₂²×C₃₁	1	2	yes	—
608	#440	C₂²×C₃₁	1	2	yes	complemented
609	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
610	C₄×D₈	C₂²×C₃₁	1	2	yes	—
611	#435	C₂²×C₃₁	1	2	yes	—
612	#435	C₂²×C₃₁	1	2	yes	complemented
613	C₈×D₄	C₂²×C₃₁	1	2	yes	—
614	#433	C₂²×C₃₁	1	2	yes	complemented
615	#432	C₂²×C₃₁	1	1	yes	characteristic
616	#428	C₂²×C₃₁	1	2	yes	complemented
617	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
618	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
620	#424	C₂²×C₃₁	1	2	yes	complemented
621	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
622	#417	C₂²×C₃₁	1	2	yes	—
623	#416	C₂²×C₃₁	1	2	yes	—
624	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
625	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
626	C₂×C₃₁	—	2	2	no	—
627	C₂×C₃₁	—	4	2	no	—
628	C₂×C₃₁	—	4	2	no	—
629	C₂×C₃₁	—	8	2	no	—
630	C₂×C₃₁	—	8	1	no	—
631	C₂×C₃₁	#3489	1	1	yes	characteristic
632	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
633	C₂×C₃₁	#3585	1	1	yes	characteristic
634	C₂×#41	—	2	1	no	—
635	C₂×#41	—	2	2	no	—
636	C₂×#41	—	2	1	no	—
637	C₂×#41	C₂³×C₃₁	1	2	yes	—
638	C₂²×Q₈	—	2	1	no	—
639	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂³×C₄	—	2	1	no	—
641	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
643	C₂×D₈	C₂³×C₃₁	1	2	yes	—
644	C₂×D₈	C₂³×C₃₁	1	2	yes	—
645	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
646	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
655	#127	C₂³×C₃₁	1	1	yes	characteristic
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	D₄×C₃₁	1	2	yes	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	1	no	—
664	#125	—	2	1	no	—
665	#125	—	2	1	no	—
666	#125	D₄×C₃₁	1	1	yes	characteristic
667	#125	C₂³×C₃₁	1	2	yes	—
668	#125	C₂³×C₃₁	1	2	yes	—
669	#125	C₂³×C₃₁	1	2	yes	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	D₄×C₃₁	1	1	yes	characteristic
673	#124	C₂³×C₃₁	1	2	yes	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	D₄×C₃₁	1	2	yes	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
702	#121	—	2	1	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	D₄×C₃₁	1	1	yes	characteristic
710	#121	C₂³×C₃₁	1	2	yes	—
711	#121	C₂³×C₃₁	1	2	yes	—
712	#121	C₂³×C₃₁	1	2	yes	—
713	#121	C₂³×C₃₁	1	2	yes	—
714	#120	—	2	2	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
717	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
718	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
728	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₃₁	1	2	yes	—
732	C₄×D₄	C₂³×C₃₁	1	2	yes	—
733	C₄×D₄	C₂³×C₃₁	1	2	yes	—
734	C₄×D₄	C₂³×C₃₁	1	2	yes	—
735	C₄×D₄	C₂³×C₃₁	1	2	yes	—
736	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
737	#117	—	2	1	no	—
738	#117	—	2	2	no	—
739	#117	—	2	1	no	—
740	#117	C₂³×C₃₁	1	2	yes	—
741	#117	C₂³×C₃₁	1	2	yes	—
742	C₂×C₄⋊C₄	—	2	1	no	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	2	no	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	2	no	—
747	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
755	#107	C₂³×C₃₁	1	2	yes	—
756	#107	C₂³×C₃₁	1	2	yes	—
757	#107	C₂³×C₃₁	1	2	yes	—
758	#107	C₂³×C₃₁	1	2	yes	—
759	#106	C₂³×C₃₁	1	2	yes	—
760	#106	C₂³×C₃₁	1	2	yes	—
761	#106	C₂³×C₃₁	1	2	yes	—
762	#106	C₂³×C₃₁	1	2	yes	—
763	#106	C₂³×C₃₁	1	2	yes	—
764	#106	C₂³×C₃₁	1	2	yes	—
765	#106	C₂³×C₃₁	1	2	yes	—
766	#106	C₂³×C₃₁	1	2	yes	—
767	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
768	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
769	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
771	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
772	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
773	#103	C₂³×C₃₁	1	2	yes	—
774	#103	C₂³×C₃₁	1	2	yes	—
775	#103	C₂³×C₃₁	1	2	yes	—
776	#103	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#103	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	#102	C₂³×C₃₁	1	2	yes	—
781	#102	C₂³×C₃₁	1	2	yes	—
782	#102	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	#102	C₂³×C₃₁	1	2	yes	—
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
792	#97	C₂³×C₃₁	1	2	yes	—
793	#97	C₂³×C₃₁	1	2	yes	—
794	C₄×C₈	C₂³×C₃₁	1	2	yes	—
795	C₃₁	#62166	1	1	yes	characteristic, direct product factor, Sylow
796	C₂⁴	—	2	1	no	—
797	#41	—	2	4	no	—
798	#41	—	4	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	4	no	—
801	#41	—	8	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	8	2	no	—
807	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
820	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
823	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	8	2	no	—
839	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	D₈	—	2	4	no	—
846	D₈	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	1	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
852	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
853	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
854	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
881	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₄²	C₂⁴×C₃₁	1	2	yes	—
916	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	8	1	no	—
924	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
925	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	1	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	8	2	no	—
931	Q₈	—	8	1	no	—
932	Q₈	—	8	2	no	—
933	D₄	—	2	4	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	1	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	1	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	—	8	1	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
984	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	C₃₁×#577	1	2	yes	—
1005	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1006	C₄	—	2	2	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1022	C₄	C₃₁×#585	1	1	yes	characteristic
1023	C₂	—	2	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	2	no	—
1026	C₂	—	8	1	no	—
1027	C₂	—	8	2	no	—
1028	C₂	C₃₁×#3489	1	1	yes	characteristic
1029	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1030	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3559	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3346	C₂	semidirect
6. C₃₁×#3345	C₂	semidirect
7. C₃₁×#3335	C₂	semidirect
8. C₃₁×#3307	C₂	semidirect
9. C₃₁×#3306	C₂	semidirect
10. C₃₁×#3297	C₂	semidirect
11. C₃₁×#3257	C₂	semidirect
12. C₃₁×#3246	C₂	semidirect
13. C₃₁×#3244	C₂	semidirect
14. C₃₁×#3236	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3109	C₂	semidirect
17. C₃₁×#3084	C₂	semidirect
18. C₂×C₃₁×#478	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
24. C₃₁×#554	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
38. C₃₁×#540	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#498	C₂²	semidirect
54. C₃₁×#491	C₂²	semidirect
57. C₃₁×#485	C₂²	semidirect
60. C₃₁×#483	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#479	C₂²	semidirect
68. C₃₁×#479	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
83. C₃₁×#468	C₂²	semidirect
87. C₃₁×#465	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
112. C₂×C₃₁×#106	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
402. #62166	C₃₁	direct (N × H)
474. #3559	C₂×C₃₁	semidirect
475. #3520	C₂×C₃₁	semidirect
476. #3384	C₂×C₃₁	semidirect
477. #3376	C₂×C₃₁	semidirect
478. #3346	C₂×C₃₁	semidirect
479. #3345	C₂×C₃₁	semidirect
480. #3335	C₂×C₃₁	semidirect
481. #3307	C₂×C₃₁	semidirect
482. #3306	C₂×C₃₁	semidirect
483. #3297	C₂×C₃₁	semidirect
484. #3257	C₂×C₃₁	semidirect
485. #3246	C₂×C₃₁	semidirect
486. #3244	C₂×C₃₁	semidirect
487. #3236	C₂×C₃₁	semidirect
488. #3119	C₂×C₃₁	semidirect
489. #3109	C₂×C₃₁	semidirect
490. #3084	C₂×C₃₁	semidirect
491. C₂×#478	C₂×C₃₁	semidirect
492. #2992	C₂×C₃₁	semidirect
531. #554	C₂²×C₃₁	semidirect
533. #553	C₂²×C₃₁	semidirect
543. #544	C₂²×C₃₁	semidirect
545. #540	C₂²×C₃₁	semidirect
558. #501	C₂²×C₃₁	semidirect
559. #501	C₂²×C₃₁	semidirect
560. #498	C₂²×C₃₁	semidirect
561. #491	C₂²×C₃₁	semidirect
564. #485	C₂²×C₃₁	semidirect
567. #483	C₂²×C₃₁	semidirect
571. #481	C₂²×C₃₁	semidirect
572. #480	C₂²×C₃₁	semidirect
573. #479	C₂²×C₃₁	semidirect
574. #479	C₂²×C₃₁	semidirect
575. #479	C₂²×C₃₁	semidirect
584. #476	C₂²×C₃₁	semidirect
585. #476	C₂²×C₃₁	semidirect
586. #475	C₂²×C₃₁	semidirect
587. #475	C₂²×C₃₁	semidirect
588. #474	C₂²×C₃₁	semidirect
590. #468	C₂²×C₃₁	semidirect
594. #465	C₂²×C₃₁	semidirect
597. #461	C₂²×C₃₁	semidirect
598. #460	C₂²×C₃₁	semidirect
604. #446	C₂²×C₃₁	semidirect
608. #440	C₂²×C₃₁	semidirect
609. C₄×SD₁₆	C₂²×C₃₁	semidirect
612. #435	C₂²×C₃₁	semidirect
614. #433	C₂²×C₃₁	semidirect
616. #428	C₂²×C₃₁	semidirect
619. C₂×#106	C₂²×C₃₁	semidirect
620. #424	C₂²×C₃₁	semidirect
795. C₃₁	#62166	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×#3559	2
C₃₁×#3520	2
C₃₁×#3384	2
C₃₁×#3376	2
C₃₁×#3346	2
C₃₁×#3345	2
C₃₁×#3335	2
C₃₁×#3307	2
C₃₁×#3306	2
C₃₁×#3297	2
C₃₁×#3257	2
C₃₁×#3246	2
C₃₁×#3244	2
C₃₁×#3236	2
C₃₁×#3119	2
C₃₁×#3109	2
C₃₁×#3084	2
C₂×C₃₁×#478	2
C₃₁×#2992	2
#62166	31

Subgroups — C31×#62166 #21518925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62166 #21518925