Subgroups — C₃₁×#62569 #21519328

Order 7936.

1712 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×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3329	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#562	—	2	2	no	—
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#555	C₂²	1	2	yes	—
25	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#551	—	2	2	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#548	—	2	1	no	—
33	C₃₁×#548	C₂²	1	2	yes	—
34	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#546	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#543	—	2	1	no	—
38	C₃₁×#542	—	2	2	no	—
39	C₃₁×#542	—	2	2	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#540	C₂²	1	2	yes	complemented
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#537	—	2	1	no	—
44	C₃₁×#536	—	2	1	no	—
45	C₃₁×#536	C₂²	1	2	yes	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#496	C₂²	1	2	yes	—
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#491	C₂²	1	2	yes	complemented
56	C₃₁×#491	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#488	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#480	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#477	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	2	yes	—
79	C₃₁×#469	C₂²	1	2	yes	—
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#463	C₂²	1	2	yes	—
86	C₃₁×#463	C₂²	1	2	yes	—
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#461	C₂²	1	2	yes	complemented
90	C₃₁×#461	C₂²	1	2	yes	complemented
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#448	C₂²	1	1	yes	characteristic
94	C₃₁×#448	C₂²	1	1	yes	characteristic
95	C₃₁×#448	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	complemented
97	C₃₁×#447	C₂²	1	1	yes	characteristic
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×D₈×C₃₁	C₂²	1	2	yes	—
106	C₃₁×#436	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	—
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#432	C₂²	1	1	yes	characteristic
111	C₃₁×#419	C₂²	1	2	yes	—
112	C₃₁×#419	C₂²	1	2	yes	complemented
113	C₃₁×#418	C₂²	1	2	yes	—
114	C₃₁×#417	C₂²	1	2	yes	—
115	C₃₁×#416	C₂²	1	2	yes	—
116	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	—	2	1	no	—
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×SD₁₆×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×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×#127	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	1	no	—
152	C₃₁×#125	D₄	1	1	yes	characteristic
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	—	2	2	no	—
160	C₃₁×#124	—	2	1	no	—
161	C₃₁×#124	—	2	1	no	—
162	C₃₁×#124	—	2	1	no	—
163	C₃₁×#124	D₄	1	1	yes	characteristic
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	2	yes	—
166	C₃₁×#124	C₂³	1	2	yes	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	D₄	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	—	2	1	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	1	no	—
179	C₃₁×C₂²⋊Q₈	—	2	1	no	—
180	C₃₁×C₂²⋊Q₈	—	2	1	no	—
181	C₃₁×C₂²⋊Q₈	—	2	1	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	1	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	D₄	1	1	yes	characteristic
205	C₃₁×#121	C₂³	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	1	yes	characteristic
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₃₁×#117	—	2	1	no	—
229	C₃₁×#117	—	2	1	no	—
230	C₃₁×#117	—	2	2	no	—
231	C₃₁×#117	—	2	2	no	—
232	C₃₁×#117	C₂³	1	2	yes	—
233	C₃₁×#117	C₂³	1	2	yes	—
234	C₃₁×#117	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	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×#103	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	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	2	yes	—
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	2	no	—
284	#41×C₃₁	—	8	2	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	2	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	4	2	no	—
293	C₂×Q₈×C₃₁	—	4	2	no	—
294	C₂×Q₈×C₃₁	—	4	2	no	—
295	C₂×Q₈×C₃₁	—	8	2	no	—
296	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	1	no	—
305	C₂×D₄×C₃₁	—	2	1	no	—
306	C₂×D₄×C₃₁	—	2	1	no	—
307	C₂×D₄×C₃₁	—	2	1	no	—
308	C₂×D₄×C₃₁	—	4	2	no	—
309	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₃₁	—	2	1	no	—
315	C₂²×C₄×C₃₁	—	2	2	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	2	1	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	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	SD₁₆×C₃₁	—	4	2	no	—
328	SD₁₆×C₃₁	—	4	2	no	—
329	SD₁₆×C₃₁	—	4	2	no	—
330	SD₁₆×C₃₁	—	4	2	no	—
331	D₈×C₃₁	—	4	2	no	—
332	D₈×C₃₁	—	4	2	no	—
333	M₁₆×C₃₁	—	4	2	no	—
334	M₁₆×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	1	no	—
341	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	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	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	1	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	—	2	2	no	—
398	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₃₁	C₂⁴	1	2	yes	—
402	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
403	#62569	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	—	2	1	no	—
407	C₂³×C₃₁	—	4	2	no	—
408	C₂³×C₃₁	—	8	1	no	—
409	C₂³×C₃₁	—	8	1	no	—
410	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	4	1	no	—
417	Q₈×C₃₁	—	4	2	no	—
418	Q₈×C₃₁	—	8	1	no	—
419	Q₈×C₃₁	—	8	1	no	—
420	Q₈×C₃₁	—	8	2	no	—
421	Q₈×C₃₁	—	8	1	no	—
422	Q₈×C₃₁	—	8	2	no	—
423	Q₈×C₃₁	—	8	1	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	2	2	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	4	1	no	—
430	D₄×C₃₁	—	8	1	no	—
431	D₄×C₃₁	—	8	1	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	1	no	—
437	D₄×C₃₁	—	8	1	no	—
438	D₄×C₃₁	—	8	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	1	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	4	1	no	—
450	C₂×C₄×C₃₁	—	4	1	no	—
451	C₂×C₄×C₃₁	—	4	2	no	—
452	C₂×C₄×C₃₁	—	4	2	no	—
453	C₂×C₄×C₃₁	—	8	2	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	2	no	—
458	C₂×C₄×C₃₁	—	8	1	no	—
459	C₂×C₄×C₃₁	—	8	2	no	—
460	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
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	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3376	C₂×C₃₁	1	2	yes	complemented
476	#3367	C₂×C₃₁	1	2	yes	complemented
477	#3329	C₂×C₃₁	1	2	yes	complemented
478	#3322	C₂×C₃₁	1	2	yes	complemented
479	#3321	C₂×C₃₁	1	2	yes	complemented
480	#3320	C₂×C₃₁	1	2	yes	complemented
481	#3319	C₂×C₃₁	1	2	yes	complemented
482	#3308	C₂×C₃₁	1	2	yes	complemented
483	#3243	C₂×C₃₁	1	2	yes	complemented
484	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3221	C₂×C₃₁	1	2	yes	complemented
486	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3179	C₂×C₃₁	1	2	yes	complemented
489	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3137	C₂×C₃₁	1	2	yes	complemented
491	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
492	C₂²×C₃₁	—	2	1	no	—
493	C₂²×C₃₁	—	2	2	no	—
494	C₂²×C₃₁	—	2	1	no	—
495	C₂²×C₃₁	—	2	2	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	1	no	—
498	C₂²×C₃₁	—	4	1	no	—
499	C₂²×C₃₁	—	4	1	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	1	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	1	no	—
506	C₂²×C₃₁	—	4	1	no	—
507	C₂²×C₃₁	—	16	2	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	2	no	—
512	C₄×C₃₁	—	2	1	no	—
513	C₄×C₃₁	—	2	1	no	—
514	C₄×C₃₁	—	2	2	no	—
515	C₄×C₃₁	—	2	2	no	—
516	C₄×C₃₁	—	2	1	no	—
517	C₄×C₃₁	—	4	1	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	2	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	#585	1	2	yes	—
525	#563	—	2	1	no	—
526	#562	—	2	1	no	—
527	#562	—	2	2	no	—
528	#556	C₂²×C₃₁	1	2	yes	—
529	#555	C₂²×C₃₁	1	2	yes	—
530	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#553	C₂²×C₃₁	1	2	yes	—
533	#552	—	2	1	no	—
534	#551	—	2	2	no	—
535	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
536	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
537	#548	—	2	1	no	—
538	#548	C₂²×C₃₁	1	2	yes	—
539	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
540	#546	C₂²×C₃₁	1	2	yes	—
541	#544	C₂²×C₃₁	1	2	yes	complemented
542	#543	—	2	1	no	—
543	#542	—	2	2	no	—
544	#542	—	2	2	no	—
545	#542	C₂²×C₃₁	1	2	yes	—
546	#540	C₂²×C₃₁	1	2	yes	complemented
547	#538	—	2	1	no	—
548	#537	—	2	1	no	—
549	#536	—	2	1	no	—
550	#536	C₂²×C₃₁	1	2	yes	—
551	#533	C₂²×C₃₁	1	1	yes	characteristic
552	#533	C₂²×C₃₁	1	1	yes	characteristic
553	#532	C₂²×C₃₁	1	1	yes	characteristic
554	#529	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
556	#501	C₂²×C₃₁	1	2	yes	complemented
557	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	#496	C₂²×C₃₁	1	2	yes	—
559	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#491	C₂²×C₃₁	1	2	yes	complemented
561	#491	C₂²×C₃₁	1	2	yes	complemented
562	#489	C₂²×C₃₁	1	2	yes	—
563	#489	C₂²×C₃₁	1	2	yes	—
564	#489	C₂²×C₃₁	1	2	yes	—
565	#489	C₂²×C₃₁	1	2	yes	—
566	#488	C₂²×C₃₁	1	2	yes	—
567	#488	C₂²×C₃₁	1	2	yes	—
568	#488	C₂²×C₃₁	1	2	yes	—
569	#487	C₂²×C₃₁	1	2	yes	complemented
570	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#485	C₂²×C₃₁	1	2	yes	—
573	#485	C₂²×C₃₁	1	2	yes	—
574	#485	C₂²×C₃₁	1	2	yes	complemented
575	#484	C₂²×C₃₁	1	2	yes	complemented
576	#482	C₂²×C₃₁	1	2	yes	—
577	#480	C₂²×C₃₁	1	2	yes	—
578	#479	C₂²×C₃₁	1	2	yes	complemented
579	#478	C₂²×C₃₁	1	2	yes	—
580	#477	C₂²×C₃₁	1	2	yes	complemented
581	#477	C₂²×C₃₁	1	2	yes	complemented
582	#475	C₂²×C₃₁	1	2	yes	complemented
583	#474	C₂²×C₃₁	1	2	yes	—
584	#469	C₂²×C₃₁	1	2	yes	—
585	#468	C₂²×C₃₁	1	2	yes	—
586	#468	C₂²×C₃₁	1	2	yes	—
587	#468	C₂²×C₃₁	1	2	yes	complemented
588	#466	C₂²×C₃₁	1	2	yes	—
589	#465	C₂²×C₃₁	1	2	yes	complemented
590	#463	C₂²×C₃₁	1	2	yes	—
591	#463	C₂²×C₃₁	1	2	yes	—
592	#463	C₂²×C₃₁	1	2	yes	—
593	#463	C₂²×C₃₁	1	2	yes	—
594	#461	C₂²×C₃₁	1	2	yes	complemented
595	#461	C₂²×C₃₁	1	2	yes	complemented
596	#449	C₂²×C₃₁	1	2	yes	—
597	#449	C₂²×C₃₁	1	2	yes	—
598	#448	C₂²×C₃₁	1	1	yes	characteristic
599	#448	C₂²×C₃₁	1	1	yes	characteristic
600	#448	C₂²×C₃₁	1	2	yes	complemented
601	#448	C₂²×C₃₁	1	2	yes	complemented
602	#447	C₂²×C₃₁	1	1	yes	characteristic
603	#447	C₂²×C₃₁	1	1	yes	characteristic
604	#446	C₂²×C₃₁	1	2	yes	complemented
605	#442	C₂²×C₃₁	1	2	yes	—
606	#440	C₂²×C₃₁	1	2	yes	complemented
607	#440	C₂²×C₃₁	1	2	yes	complemented
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	#436	C₂²×C₃₁	1	2	yes	—
612	#435	C₂²×C₃₁	1	2	yes	—
613	#435	C₂²×C₃₁	1	2	yes	complemented
614	#433	C₂²×C₃₁	1	2	yes	complemented
615	#432	C₂²×C₃₁	1	1	yes	characteristic
616	#419	C₂²×C₃₁	1	2	yes	—
617	#419	C₂²×C₃₁	1	2	yes	complemented
618	#418	C₂²×C₃₁	1	2	yes	—
619	#417	C₂²×C₃₁	1	2	yes	—
620	#416	C₂²×C₃₁	1	2	yes	—
621	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
622	#405	C₂²×C₃₁	1	2	yes	complemented
623	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
624	C₂×C₃₁	—	4	2	no	—
625	C₂×C₃₁	—	4	1	no	—
626	C₂×C₃₁	—	8	1	no	—
627	C₂×C₃₁	—	8	1	no	—
628	C₂×C₃₁	—	8	2	no	—
629	C₂×C₃₁	#3500	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	C₂²×Q₈	—	2	1	no	—
636	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
638	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×SD₁₆	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×D₈	C₂³×C₃₁	1	2	yes	—
644	C₂×D₈	C₂³×C₃₁	1	2	yes	—
645	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
646	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
647	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
652	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
657	#127	C₂³×C₃₁	1	1	yes	characteristic
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	D₄×C₃₁	1	2	yes	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	D₄×C₃₁	1	1	yes	characteristic
666	#125	C₂³×C₃₁	1	2	yes	—
667	#125	C₂³×C₃₁	1	2	yes	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	1	no	—
674	#124	—	2	1	no	—
675	#124	—	2	1	no	—
676	#124	D₄×C₃₁	1	1	yes	characteristic
677	#124	C₂³×C₃₁	1	2	yes	—
678	#124	C₂³×C₃₁	1	2	yes	—
679	#124	C₂³×C₃₁	1	2	yes	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	D₄×C₃₁	1	2	yes	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	1	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
707	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	1	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	D₄×C₃₁	1	1	yes	characteristic
718	#121	C₂³×C₃₁	1	1	yes	characteristic
719	#121	C₂³×C₃₁	1	1	yes	characteristic
720	#121	C₂³×C₃₁	1	2	yes	—
721	#121	C₂³×C₃₁	1	2	yes	—
722	#121	C₂³×C₃₁	1	2	yes	—
723	#120	—	2	2	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	—	2	1	no	—
727	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
728	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₃₁	1	2	yes	—
737	C₄×D₄	C₂³×C₃₁	1	2	yes	—
738	C₄×D₄	C₂³×C₃₁	1	2	yes	—
739	C₄×D₄	C₂³×C₃₁	1	2	yes	—
740	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
741	#117	—	2	1	no	—
742	#117	—	2	1	no	—
743	#117	—	2	2	no	—
744	#117	—	2	2	no	—
745	#117	C₂³×C₃₁	1	2	yes	—
746	#117	C₂³×C₃₁	1	2	yes	—
747	#117	C₂³×C₃₁	1	2	yes	—
748	C₂×C₄⋊C₄	—	2	1	no	—
749	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	#106	C₂³×C₃₁	1	2	yes	—
759	#106	C₂³×C₃₁	1	2	yes	—
760	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
761	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
762	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#103	C₂³×C₃₁	1	2	yes	—
766	#103	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	#103	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	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
787	#97	C₂³×C₃₁	1	2	yes	—
788	#97	C₂³×C₃₁	1	2	yes	—
789	#97	C₂³×C₃₁	1	2	yes	—
790	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×C₈	C₂³×C₃₁	1	2	yes	—
793	C₃₁	#62569	1	1	yes	characteristic, direct product factor, Sylow
794	C₂⁴	—	2	1	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	8	2	no	—
798	#41	—	8	2	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	8	2	no	—
810	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
811	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
812	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
824	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
825	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
826	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	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	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	D₈	—	4	2	no	—
846	D₈	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	M₁₆	—	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	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	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	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
875	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	2	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	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₄²	C₂⁴×C₃₁	1	2	yes	—
916	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	8	1	no	—
922	C₂³	—	8	1	no	—
923	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	8	1	no	—
932	Q₈	—	8	1	no	—
933	Q₈	—	8	2	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	2	no	—
936	Q₈	—	8	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	1	no	—
950	D₄	—	8	1	no	—
951	D₄	—	8	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	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	2	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	16	2	no	—
1002	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₃₁×#585	1	2	yes	—
1019	C₂	—	4	1	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	8	2	no	—
1022	C₂	—	8	1	no	—
1023	C₂	—	8	1	no	—
1024	C₂	C₃₁×#3500	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
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×#3561	C₂	semidirect
2. C₃₁×#3547	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3329	C₂	semidirect
6. C₃₁×#3322	C₂	semidirect
7. C₃₁×#3321	C₂	semidirect
8. C₃₁×#3320	C₂	semidirect
9. C₃₁×#3319	C₂	semidirect
10. C₃₁×#3308	C₂	semidirect
11. C₃₁×#3243	C₂	semidirect
12. C₃₁×#3237	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3179	C₂	semidirect
17. C₃₁×#3140	C₂	semidirect
18. C₃₁×#3137	C₂	semidirect
19. C₃₁×#2967	C₂	semidirect
25. C₃₁×#555	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
31. D₄×Q₈×C₃₁	C₂²	semidirect
34. C₃₁×#547	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
41. C₃₁×#540	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#500	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
89. C₃₁×#461	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
95. C₃₁×#448	C₂²	semidirect
96. C₃₁×#448	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
112. C₃₁×#419	C₂²	semidirect
116. C₂×C₃₁×#103	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
403. #62569	C₃₁	direct (N × H)
473. #3561	C₂×C₃₁	semidirect
474. #3547	C₂×C₃₁	semidirect
475. #3376	C₂×C₃₁	semidirect
476. #3367	C₂×C₃₁	semidirect
477. #3329	C₂×C₃₁	semidirect
478. #3322	C₂×C₃₁	semidirect
479. #3321	C₂×C₃₁	semidirect
480. #3320	C₂×C₃₁	semidirect
481. #3319	C₂×C₃₁	semidirect
482. #3308	C₂×C₃₁	semidirect
483. #3243	C₂×C₃₁	semidirect
484. #3237	C₂×C₃₁	semidirect
485. #3221	C₂×C₃₁	semidirect
486. #3213	C₂×C₃₁	semidirect
487. #3182	C₂×C₃₁	semidirect
488. #3179	C₂×C₃₁	semidirect
489. #3140	C₂×C₃₁	semidirect
490. #3137	C₂×C₃₁	semidirect
491. #2967	C₂×C₃₁	semidirect
530. #555	C₂²×C₃₁	semidirect
531. #554	C₂²×C₃₁	semidirect
536. D₄×Q₈	C₂²×C₃₁	semidirect
539. #547	C₂²×C₃₁	semidirect
541. #544	C₂²×C₃₁	semidirect
546. #540	C₂²×C₃₁	semidirect
556. #501	C₂²×C₃₁	semidirect
557. #500	C₂²×C₃₁	semidirect
559. #492	C₂²×C₃₁	semidirect
560. #491	C₂²×C₃₁	semidirect
561. #491	C₂²×C₃₁	semidirect
569. #487	C₂²×C₃₁	semidirect
570. #487	C₂²×C₃₁	semidirect
571. #486	C₂²×C₃₁	semidirect
574. #485	C₂²×C₃₁	semidirect
575. #484	C₂²×C₃₁	semidirect
578. #479	C₂²×C₃₁	semidirect
580. #477	C₂²×C₃₁	semidirect
581. #477	C₂²×C₃₁	semidirect
582. #475	C₂²×C₃₁	semidirect
587. #468	C₂²×C₃₁	semidirect
589. #465	C₂²×C₃₁	semidirect
594. #461	C₂²×C₃₁	semidirect
595. #461	C₂²×C₃₁	semidirect
600. #448	C₂²×C₃₁	semidirect
601. #448	C₂²×C₃₁	semidirect
604. #446	C₂²×C₃₁	semidirect
606. #440	C₂²×C₃₁	semidirect
607. #440	C₂²×C₃₁	semidirect
608. #440	C₂²×C₃₁	semidirect
609. C₄×SD₁₆	C₂²×C₃₁	semidirect
613. #435	C₂²×C₃₁	semidirect
614. #433	C₂²×C₃₁	semidirect
617. #419	C₂²×C₃₁	semidirect
621. C₂×#103	C₂²×C₃₁	semidirect
622. #405	C₂²×C₃₁	semidirect
793. C₃₁	#62569	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×#3561	2
C₃₁×#3547	2
C₃₁×#3376	2
C₃₁×#3367	2
C₃₁×#3329	2
C₃₁×#3322	2
C₃₁×#3321	2
C₃₁×#3320	2
C₃₁×#3319	2
C₃₁×#3308	2
C₃₁×#3243	2
C₃₁×#3237	2
C₃₁×#3221	2
C₃₁×#3213	2
C₃₁×#3182	2
C₃₁×#3179	2
C₃₁×#3140	2
C₃₁×#3137	2
C₃₁×#2967	2
#62569	31

Subgroups — C31×#62569 #21519328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62569 #21519328