Subgroups — C₃₁×#61793 #21518552

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#560	—	2	2	no	—
21	C₃₁×#559	—	2	1	no	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#556	—	2	2	no	—
24	C₃₁×#556	C₂²	1	1	yes	characteristic
25	C₃₁×#556	C₂²	1	2	yes	complemented
26	C₃₁×#554	C₂²	1	2	yes	complemented
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#552	C₂²	1	2	yes	complemented
30	C₃₁×#550	—	2	1	no	—
31	C₃₁×#550	C₂²	1	1	yes	characteristic
32	C₃₁×#547	C₂²	1	1	yes	characteristic
33	C₃₁×#546	—	2	1	no	—
34	C₃₁×#546	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#542	—	2	1	no	—
37	C₃₁×#539	—	2	1	no	—
38	C₃₁×#539	—	2	1	no	—
39	C₃₁×#538	—	2	2	no	—
40	C₃₁×#537	C₂²	1	2	yes	—
41	C₃₁×#536	C₂²	1	2	yes	complemented
42	C₃₁×#535	—	2	1	no	—
43	C₃₁×#535	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#529	—	2	2	no	—
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#490	C₂²	1	2	yes	—
55	C₃₁×#489	C₂²	1	1	yes	characteristic
56	C₃₁×#489	C₂²	1	1	yes	characteristic
57	C₃₁×#485	C₂²	1	2	yes	complemented
58	C₃₁×#485	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#485	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#483	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	—
66	C₃₁×#482	C₂²	1	2	yes	—
67	C₃₁×#482	C₂²	1	2	yes	—
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	1	yes	characteristic
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	—
74	C₃₁×#480	C₂²	1	2	yes	—
75	C₃₁×#480	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	complemented
80	C₃₁×#476	C₂²	1	2	yes	complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#470	C₂²	1	2	yes	complemented
83	C₃₁×#468	C₂²	1	2	yes	—
84	C₃₁×#468	C₂²	1	2	yes	—
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#467	C₂²	1	2	yes	complemented
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#465	C₂²	1	2	yes	—
89	C₃₁×#465	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	—
91	C₃₁×#460	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#452	C₂²	1	2	yes	complemented
94	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	1	yes	characteristic
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#435	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₃₁×#428	C₂²	1	2	yes	complemented
111	C₃₁×#427	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
113	C₃₁×#418	C₂²	1	2	yes	—
114	C₃₁×#417	C₂²	1	2	yes	complemented
115	C₃₁×#416	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#102	C₂²	1	2	yes	—
117	C₃₁×#408	C₂²	1	2	yes	complemented
118	C₃₁×#408	C₂²	1	2	yes	complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	—	2	1	no	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×#127	—	2	1	no	—
140	C₃₁×#127	—	2	2	no	—
141	C₃₁×#127	D₄	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	1	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	1	yes	characteristic
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	1	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	—	2	1	no	—
160	C₃₁×#124	D₄	1	2	yes	—
161	C₃₁×#124	C₂³	1	1	yes	characteristic
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	1	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	1	no	—
172	C₃₁×C₂²⋊Q₈	—	2	1	no	—
173	C₃₁×C₂²⋊Q₈	—	2	1	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
179	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	—	2	2	no	—
184	C₃₁×#121	—	2	2	no	—
185	C₃₁×#121	—	2	2	no	—
186	C₃₁×#121	—	2	1	no	—
187	C₃₁×#121	—	2	1	no	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	D₄	1	2	yes	—
191	C₃₁×#121	D₄	1	1	yes	characteristic
192	C₃₁×#121	D₄	1	1	yes	characteristic
193	C₃₁×#121	C₂³	1	1	yes	characteristic
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₃₁×#121	C₂³	1	2	yes	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#121	C₂³	1	2	yes	—
198	C₃₁×#120	—	2	2	no	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	—	2	2	no	—
201	C₃₁×#120	—	2	2	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	—	2	2	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	—	2	2	no	—
227	C₃₁×#117	—	2	1	no	—
228	C₃₁×#117	C₂³	1	2	yes	—
229	C₃₁×#117	C₂³	1	2	yes	—
230	C₃₁×#117	C₂³	1	2	yes	—
231	C₃₁×#117	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
238	C₂×C₄²×C₃₁	—	2	1	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×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#107	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×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×C₂²⋊C₈	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	1	yes	characteristic
279	C₃₁×#97	C₂³	1	1	yes	characteristic
280	C₂⁴×C₃₁	—	2	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	8	2	no	—
286	#41×C₃₁	—	8	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×D₄×C₃₁	—	2	1	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	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	1	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	4	2	no	—
305	C₂×D₄×C₃₁	—	4	2	no	—
306	C₂×D₄×C₃₁	—	8	2	no	—
307	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	1	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	2	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	—	2	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	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
328	Q₁₆×C₃₁	—	4	2	no	—
329	SD₁₆×C₃₁	—	4	2	no	—
330	SD₁₆×C₃₁	—	4	2	no	—
331	SD₁₆×C₃₁	—	4	2	no	—
332	M₁₆×C₃₁	—	4	2	no	—
333	M₁₆×C₃₁	—	4	2	no	—
334	C₂×C₈×C₃₁	—	4	2	no	—
335	C₂×C₈×C₃₁	—	4	2	no	—
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	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	1	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	1	no	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
403	#61793	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂³×C₃₁	—	2	1	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	8	2	no	—
407	C₂³×C₃₁	—	8	2	no	—
408	C₂³×C₃₁	—	8	2	no	—
409	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
410	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
411	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	4	2	no	—
416	Q₈×C₃₁	—	4	2	no	—
417	Q₈×C₃₁	—	4	2	no	—
418	Q₈×C₃₁	—	4	2	no	—
419	Q₈×C₃₁	—	8	1	no	—
420	D₄×C₃₁	—	2	2	no	—
421	D₄×C₃₁	—	2	2	no	—
422	D₄×C₃₁	—	2	2	no	—
423	D₄×C₃₁	—	4	1	no	—
424	D₄×C₃₁	—	4	2	no	—
425	D₄×C₃₁	—	4	2	no	—
426	D₄×C₃₁	—	4	2	no	—
427	D₄×C₃₁	—	4	2	no	—
428	D₄×C₃₁	—	4	1	no	—
429	D₄×C₃₁	—	4	2	no	—
430	D₄×C₃₁	—	8	1	no	—
431	D₄×C₃₁	—	8	2	no	—
432	D₄×C₃₁	—	8	1	no	—
433	D₄×C₃₁	—	8	2	no	—
434	D₄×C₃₁	—	8	2	no	—
435	D₄×C₃₁	—	8	2	no	—
436	D₄×C₃₁	—	8	2	no	—
437	D₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	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	2	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	1	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	4	1	no	—
452	C₂×C₄×C₃₁	—	4	1	no	—
453	C₂×C₄×C₃₁	—	4	2	no	—
454	C₂×C₄×C₃₁	—	4	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	2	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	1	yes	characteristic
463	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
469	C₈×C₃₁	—	2	2	no	—
470	C₈×C₃₁	—	2	2	no	—
471	C₈×C₃₁	—	2	2	no	—
472	C₈×C₃₁	—	2	2	no	—
473	#3546	C₂×C₃₁	1	1	yes	characteristic
474	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3350	C₂×C₃₁	1	2	yes	complemented
476	#3349	C₂×C₃₁	1	2	yes	complemented
477	#3346	C₂×C₃₁	1	2	yes	complemented
478	#3343	C₂×C₃₁	1	2	yes	complemented
479	#3317	C₂×C₃₁	1	2	yes	complemented
480	#3314	C₂×C₃₁	1	2	yes	complemented
481	#3311	C₂×C₃₁	1	2	yes	complemented
482	#3310	C₂×C₃₁	1	2	yes	complemented
483	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3201	C₂×C₃₁	1	2	yes	complemented
486	#3200	C₂×C₃₁	1	2	yes	complemented
487	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3098	C₂×C₃₁	1	2	yes	complemented
490	#3096	C₂×C₃₁	1	2	yes	complemented
491	#2980	C₂×C₃₁	1	1	yes	characteristic, complemented
492	C₂²×C₃₁	—	2	1	no	—
493	C₂²×C₃₁	—	2	2	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	2	1	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	1	no	—
499	C₂²×C₃₁	—	2	2	no	—
500	C₂²×C₃₁	—	2	2	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	1	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	1	no	—
507	C₂²×C₃₁	—	16	4	no	—
508	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₃₁	—	2	1	no	—
510	C₄×C₃₁	—	2	1	no	—
511	C₄×C₃₁	—	2	1	no	—
512	C₄×C₃₁	—	2	1	no	—
513	C₄×C₃₁	—	2	2	no	—
514	C₄×C₃₁	—	2	1	no	—
515	C₄×C₃₁	—	2	2	no	—
516	C₄×C₃₁	—	4	1	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	2	no	—
519	C₄×C₃₁	—	4	2	no	—
520	C₄×C₃₁	—	4	1	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	1	no	—
524	C₄×C₃₁	#585	1	2	yes	—
525	#560	—	2	2	no	—
526	#559	—	2	1	no	—
527	#557	—	2	1	no	—
528	#556	—	2	2	no	—
529	#556	C₂²×C₃₁	1	1	yes	characteristic
530	#556	C₂²×C₃₁	1	2	yes	complemented
531	#554	C₂²×C₃₁	1	2	yes	complemented
532	#553	C₂²×C₃₁	1	2	yes	—
533	#552	C₂²×C₃₁	1	2	yes	—
534	#552	C₂²×C₃₁	1	2	yes	complemented
535	#550	—	2	1	no	—
536	#550	C₂²×C₃₁	1	1	yes	characteristic
537	#547	C₂²×C₃₁	1	1	yes	characteristic
538	#546	—	2	1	no	—
539	#546	C₂²×C₃₁	1	2	yes	—
540	D₄²	C₂²×C₃₁	1	1	yes	characteristic
541	#542	—	2	1	no	—
542	#539	—	2	1	no	—
543	#539	—	2	1	no	—
544	#538	—	2	2	no	—
545	#537	C₂²×C₃₁	1	2	yes	—
546	#536	C₂²×C₃₁	1	2	yes	complemented
547	#535	—	2	1	no	—
548	#535	C₂²×C₃₁	1	2	yes	—
549	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	#532	C₂²×C₃₁	1	1	yes	characteristic
551	#532	C₂²×C₃₁	1	1	yes	characteristic
552	#529	—	2	2	no	—
553	#529	C₂²×C₃₁	1	1	yes	characteristic
554	#520	C₂²×C₃₁	1	2	yes	complemented
555	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	#501	C₂²×C₃₁	1	2	yes	complemented
557	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#490	C₂²×C₃₁	1	2	yes	—
560	#489	C₂²×C₃₁	1	1	yes	characteristic
561	#489	C₂²×C₃₁	1	1	yes	characteristic
562	#485	C₂²×C₃₁	1	2	yes	complemented
563	#485	C₂²×C₃₁	1	2	yes	complemented
564	#485	C₂²×C₃₁	1	2	yes	complemented
565	#485	C₂²×C₃₁	1	2	yes	complemented
566	#484	C₂²×C₃₁	1	2	yes	complemented
567	#484	C₂²×C₃₁	1	2	yes	complemented
568	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#483	C₂²×C₃₁	1	2	yes	complemented
570	#482	C₂²×C₃₁	1	2	yes	—
571	#482	C₂²×C₃₁	1	2	yes	—
572	#482	C₂²×C₃₁	1	2	yes	—
573	#482	C₂²×C₃₁	1	2	yes	complemented
574	#482	C₂²×C₃₁	1	2	yes	complemented
575	#482	C₂²×C₃₁	1	2	yes	complemented
576	#481	C₂²×C₃₁	1	1	yes	characteristic
577	#481	C₂²×C₃₁	1	2	yes	complemented
578	#480	C₂²×C₃₁	1	2	yes	—
579	#480	C₂²×C₃₁	1	2	yes	—
580	#480	C₂²×C₃₁	1	2	yes	complemented
581	#479	C₂²×C₃₁	1	2	yes	complemented
582	#479	C₂²×C₃₁	1	2	yes	complemented
583	#478	C₂²×C₃₁	1	2	yes	—
584	#477	C₂²×C₃₁	1	2	yes	complemented
585	#476	C₂²×C₃₁	1	2	yes	complemented
586	#474	C₂²×C₃₁	1	2	yes	complemented
587	#470	C₂²×C₃₁	1	2	yes	complemented
588	#468	C₂²×C₃₁	1	2	yes	—
589	#468	C₂²×C₃₁	1	2	yes	—
590	#468	C₂²×C₃₁	1	2	yes	complemented
591	#467	C₂²×C₃₁	1	2	yes	complemented
592	#465	C₂²×C₃₁	1	2	yes	—
593	#465	C₂²×C₃₁	1	2	yes	—
594	#465	C₂²×C₃₁	1	2	yes	complemented
595	#464	C₂²×C₃₁	1	2	yes	—
596	#460	C₂²×C₃₁	1	2	yes	—
597	#452	C₂²×C₃₁	1	2	yes	complemented
598	#452	C₂²×C₃₁	1	2	yes	complemented
599	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#450	C₂²×C₃₁	1	2	yes	—
601	#450	C₂²×C₃₁	1	2	yes	—
602	#448	C₂²×C₃₁	1	1	yes	characteristic
603	#448	C₂²×C₃₁	1	2	yes	complemented
604	#441	C₂²×C₃₁	1	2	yes	complemented
605	#440	C₂²×C₃₁	1	2	yes	—
606	#440	C₂²×C₃₁	1	2	yes	complemented
607	#440	C₂²×C₃₁	1	2	yes	complemented
608	#435	C₂²×C₃₁	1	2	yes	—
609	#435	C₂²×C₃₁	1	2	yes	complemented
610	#435	C₂²×C₃₁	1	2	yes	complemented
611	#435	C₂²×C₃₁	1	2	yes	complemented
612	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#428	C₂²×C₃₁	1	2	yes	complemented
615	#428	C₂²×C₃₁	1	2	yes	complemented
616	#427	C₂²×C₃₁	1	2	yes	complemented
617	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
618	#418	C₂²×C₃₁	1	2	yes	—
619	#417	C₂²×C₃₁	1	2	yes	complemented
620	#416	C₂²×C₃₁	1	2	yes	complemented
621	C₂×#102	C₂²×C₃₁	1	2	yes	—
622	#408	C₂²×C₃₁	1	2	yes	complemented
623	#408	C₂²×C₃₁	1	2	yes	complemented
624	C₂×C₃₁	—	4	1	no	—
625	C₂×C₃₁	—	4	2	no	—
626	C₂×C₃₁	—	4	2	no	—
627	C₂×C₃₁	—	8	2	no	—
628	C₂×C₃₁	—	8	1	no	—
629	C₂×C₃₁	#3485	1	1	yes	characteristic
630	C₂×C₃₁	#3585	1	1	yes	characteristic
631	C₂×C₃₁	#3586	1	1	yes	characteristic
632	C₂×#41	—	2	1	no	—
633	C₂×#41	—	2	1	no	—
634	C₂×#41	C₂³×C₃₁	1	2	yes	—
635	C₂×#41	C₂³×C₃₁	1	2	yes	—
636	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₂²×D₄	—	2	1	no	—
638	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
639	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
643	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
644	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
645	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
646	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
652	#127	—	2	1	no	—
653	#127	—	2	2	no	—
654	#127	D₄×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	1	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	C₂³×C₃₁	1	1	yes	characteristic
667	#125	C₂³×C₃₁	1	2	yes	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	1	no	—
671	#124	—	2	2	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₃₁	1	2	yes	—
674	#124	C₂³×C₃₁	1	1	yes	characteristic
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	1	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	D₄×C₃₁	1	2	yes	—
704	#121	D₄×C₃₁	1	1	yes	characteristic
705	#121	D₄×C₃₁	1	1	yes	characteristic
706	#121	C₂³×C₃₁	1	1	yes	characteristic
707	#121	C₂³×C₃₁	1	2	yes	—
708	#121	C₂³×C₃₁	1	2	yes	—
709	#121	C₂³×C₃₁	1	2	yes	—
710	#121	C₂³×C₃₁	1	2	yes	—
711	#120	—	2	2	no	—
712	#120	—	2	2	no	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	C₄×Q₈	—	2	2	no	—
716	C₄×Q₈	—	2	2	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
724	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₃₁	1	2	yes	—
735	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₃₁	1	2	yes	—
737	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
738	#117	—	2	2	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	C₂³×C₃₁	1	2	yes	—
742	#117	C₂³×C₃₁	1	2	yes	—
743	#117	C₂³×C₃₁	1	2	yes	—
744	#117	C₂³×C₃₁	1	2	yes	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	—	2	2	no	—
751	C₂×C₄²	—	2	1	no	—
752	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
753	#107	C₂³×C₃₁	1	2	yes	—
754	#107	C₂³×C₃₁	1	2	yes	—
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	#107	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	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
766	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
767	#103	C₂³×C₃₁	1	2	yes	—
768	#103	C₂³×C₃₁	1	2	yes	—
769	#103	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#103	C₂³×C₃₁	1	2	yes	—
773	#103	C₂³×C₃₁	1	2	yes	—
774	#102	C₂³×C₃₁	1	2	yes	—
775	#102	C₂³×C₃₁	1	2	yes	—
776	#102	C₂³×C₃₁	1	2	yes	—
777	#102	C₂³×C₃₁	1	2	yes	—
778	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
790	#97	C₂³×C₃₁	1	2	yes	—
791	#97	C₂³×C₃₁	1	1	yes	characteristic
792	#97	C₂³×C₃₁	1	1	yes	characteristic
793	C₃₁	#61793	1	1	yes	characteristic, direct product factor, Sylow
794	C₂⁴	—	2	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	4	2	no	—
798	#41	—	4	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×D₄	—	2	1	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	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	8	2	no	—
821	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
822	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
824	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
825	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
826	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
842	Q₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	SD₁₆	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
875	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	1	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	1	yes	characteristic
916	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	8	2	no	—
920	C₂³	—	8	2	no	—
921	C₂³	—	8	2	no	—
922	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
923	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
924	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	2	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	4	2	no	—
932	Q₈	—	8	1	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	1	no	—
942	D₄	—	4	2	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	1	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
981	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₈	—	2	2	no	—
985	C₈	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	2	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	—	16	4	no	—
1002	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₃₁×#585	1	2	yes	—
1019	C₂	—	4	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	2	no	—
1022	C₂	—	8	1	no	—
1023	C₂	—	8	2	no	—
1024	C₂	C₃₁×#3485	1	1	yes	characteristic
1025	C₂	C₃₁×#3585	1	1	yes	characteristic
1026	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3350	C₂	semidirect
4. C₃₁×#3349	C₂	semidirect
5. C₃₁×#3346	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3317	C₂	semidirect
8. C₃₁×#3314	C₂	semidirect
9. C₃₁×#3311	C₂	semidirect
10. C₃₁×#3310	C₂	semidirect
11. C₃₁×#3240	C₂	semidirect
12. C₃₁×#3235	C₂	semidirect
13. C₃₁×#3201	C₂	semidirect
14. C₃₁×#3200	C₂	semidirect
15. C₃₁×#3117	C₂	semidirect
16. C₃₁×#3112	C₂	semidirect
17. C₃₁×#3098	C₂	semidirect
18. C₃₁×#3096	C₂	semidirect
19. C₃₁×#2980	C₂	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
41. C₃₁×#536	C₂²	semidirect
44. C₃₁×#533	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#501	C₂²	semidirect
57. C₃₁×#485	C₂²	semidirect
58. C₃₁×#485	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
60. C₃₁×#485	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#484	C₂²	semidirect
64. C₃₁×#483	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
75. C₃₁×#480	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
79. C₃₁×#477	C₂²	semidirect
80. C₃₁×#476	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#470	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#467	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#452	C₂²	semidirect
94. C₃₁×#451	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
104. C₃₁×#435	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#432	C₂²	semidirect
108. C₃₁×#432	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
110. C₃₁×#428	C₂²	semidirect
111. C₃₁×#427	C₂²	semidirect
112. C₂×C₃₁×#107	C₂²	semidirect
114. C₃₁×#417	C₂²	semidirect
115. C₃₁×#416	C₂²	semidirect
117. C₃₁×#408	C₂²	semidirect
118. C₃₁×#408	C₂²	semidirect
403. #61793	C₃₁	direct (N × H)
474. #3507	C₂×C₃₁	semidirect
475. #3350	C₂×C₃₁	semidirect
476. #3349	C₂×C₃₁	semidirect
477. #3346	C₂×C₃₁	semidirect
478. #3343	C₂×C₃₁	semidirect
479. #3317	C₂×C₃₁	semidirect
480. #3314	C₂×C₃₁	semidirect
481. #3311	C₂×C₃₁	semidirect
482. #3310	C₂×C₃₁	semidirect
483. #3240	C₂×C₃₁	semidirect
484. #3235	C₂×C₃₁	semidirect
485. #3201	C₂×C₃₁	semidirect
486. #3200	C₂×C₃₁	semidirect
487. #3117	C₂×C₃₁	semidirect
488. #3112	C₂×C₃₁	semidirect
489. #3098	C₂×C₃₁	semidirect
490. #3096	C₂×C₃₁	semidirect
491. #2980	C₂×C₃₁	semidirect
530. #556	C₂²×C₃₁	semidirect
531. #554	C₂²×C₃₁	semidirect
534. #552	C₂²×C₃₁	semidirect
546. #536	C₂²×C₃₁	semidirect
549. #533	C₂²×C₃₁	semidirect
554. #520	C₂²×C₃₁	semidirect
555. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
556. #501	C₂²×C₃₁	semidirect
557. #501	C₂²×C₃₁	semidirect
558. #501	C₂²×C₃₁	semidirect
562. #485	C₂²×C₃₁	semidirect
563. #485	C₂²×C₃₁	semidirect
564. #485	C₂²×C₃₁	semidirect
565. #485	C₂²×C₃₁	semidirect
566. #484	C₂²×C₃₁	semidirect
567. #484	C₂²×C₃₁	semidirect
568. #484	C₂²×C₃₁	semidirect
569. #483	C₂²×C₃₁	semidirect
573. #482	C₂²×C₃₁	semidirect
574. #482	C₂²×C₃₁	semidirect
575. #482	C₂²×C₃₁	semidirect
577. #481	C₂²×C₃₁	semidirect
580. #480	C₂²×C₃₁	semidirect
581. #479	C₂²×C₃₁	semidirect
582. #479	C₂²×C₃₁	semidirect
584. #477	C₂²×C₃₁	semidirect
585. #476	C₂²×C₃₁	semidirect
586. #474	C₂²×C₃₁	semidirect
587. #470	C₂²×C₃₁	semidirect
590. #468	C₂²×C₃₁	semidirect
591. #467	C₂²×C₃₁	semidirect
594. #465	C₂²×C₃₁	semidirect
597. #452	C₂²×C₃₁	semidirect
598. #452	C₂²×C₃₁	semidirect
599. #451	C₂²×C₃₁	semidirect
603. #448	C₂²×C₃₁	semidirect
604. #441	C₂²×C₃₁	semidirect
606. #440	C₂²×C₃₁	semidirect
607. #440	C₂²×C₃₁	semidirect
609. #435	C₂²×C₃₁	semidirect
610. #435	C₂²×C₃₁	semidirect
611. #435	C₂²×C₃₁	semidirect
612. #432	C₂²×C₃₁	semidirect
613. #432	C₂²×C₃₁	semidirect
614. #428	C₂²×C₃₁	semidirect
615. #428	C₂²×C₃₁	semidirect
616. #427	C₂²×C₃₁	semidirect
617. C₂×#107	C₂²×C₃₁	semidirect
619. #417	C₂²×C₃₁	semidirect
620. #416	C₂²×C₃₁	semidirect
622. #408	C₂²×C₃₁	semidirect
623. #408	C₂²×C₃₁	semidirect
793. C₃₁	#61793	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×#3546	2
C₃₁×#3507	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3346	2
C₃₁×#3343	2
C₃₁×#3317	2
C₃₁×#3314	2
C₃₁×#3311	2
C₃₁×#3310	2
C₃₁×#3240	2
C₃₁×#3235	2
C₃₁×#3201	2
C₃₁×#3200	2
C₃₁×#3117	2
C₃₁×#3112	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#2980	2
#61793	31

Subgroups — C31×#61793 #21518552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61793 #21518552