Subgroups — C₃₁×#60891 #21517650

Order 7936.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3236	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3231	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	—	2	1	no	—
25	C₃₁×#557	—	2	1	no	—
26	C₃₁×#554	—	2	2	no	—
27	C₃₁×#554	—	2	1	no	—
28	C₃₁×#554	—	2	2	no	—
29	C₃₁×#554	—	2	1	no	—
30	C₃₁×#544	C₂²	1	1	yes	characteristic
31	C₃₁×#544	C₂²	1	1	yes	characteristic
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#544	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	2	yes	—
35	C₃₁×#542	—	2	1	no	—
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#541	—	2	1	no	—
38	C₃₁×#541	C₂²	1	2	yes	—
39	C₃₁×#539	—	2	2	no	—
40	C₃₁×#537	C₂²	1	1	yes	characteristic
41	C₃₁×#536	C₂²	1	1	yes	characteristic
42	C₃₁×#536	C₂²	1	1	yes	characteristic
43	C₃₁×#533	—	2	1	no	—
44	C₃₁×#533	C₂²	1	2	yes	—
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	2	yes	—
47	C₃₁×#529	—	2	2	no	—
48	C₃₁×#529	—	2	1	no	—
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#125	C₂²	1	2	yes	—
52	C₃₁×#520	C₂²	1	1	yes	characteristic
53	C₃₁×#520	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#501	C₂²	1	2	yes	—
61	C₃₁×#500	C₂²	1	2	yes	—
62	C₃₁×#499	C₂²	1	2	yes	—
63	C₃₁×#499	C₂²	1	2	yes	—
64	C₃₁×#498	C₂²	1	2	yes	—
65	C₃₁×#491	C₂²	1	2	yes	—
66	C₃₁×#491	C₂²	1	2	yes	—
67	C₃₁×#489	C₂²	1	2	yes	—
68	C₃₁×#489	C₂²	1	2	yes	—
69	C₃₁×#488	C₂²	1	2	yes	—
70	C₃₁×#488	C₂²	1	2	yes	—
71	C₃₁×#487	C₂²	1	2	yes	—
72	C₃₁×#487	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#485	C₂²	1	2	yes	—
77	C₃₁×#485	C₂²	1	2	yes	—
78	C₃₁×#485	C₂²	1	2	yes	—
79	C₃₁×#484	C₂²	1	2	yes	—
80	C₃₁×#484	C₂²	1	2	yes	—
81	C₃₁×#484	C₂²	1	2	yes	—
82	C₃₁×#483	C₂²	1	2	yes	—
83	C₃₁×#483	C₂²	1	2	yes	—
84	C₃₁×#483	C₂²	1	2	yes	—
85	C₃₁×#482	C₂²	1	2	yes	—
86	C₃₁×#482	C₂²	1	2	yes	—
87	C₃₁×#481	C₂²	1	2	yes	—
88	C₃₁×#480	C₂²	1	2	yes	—
89	C₃₁×#479	C₂²	1	2	yes	—
90	C₃₁×#479	C₂²	1	2	yes	—
91	C₃₁×#479	C₂²	1	2	yes	—
92	C₃₁×#479	C₂²	1	2	yes	—
93	C₃₁×#479	C₂²	1	1	yes	characteristic
94	C₃₁×#479	C₂²	1	1	yes	characteristic
95	C₃₁×#479	C₂²	1	2	yes	—
96	C₃₁×#479	C₂²	1	2	yes	—
97	C₃₁×#479	C₂²	1	2	yes	—
98	C₃₁×#479	C₂²	1	2	yes	—
99	C₃₁×#478	C₂²	1	1	yes	characteristic
100	C₃₁×#478	C₂²	1	1	yes	characteristic
101	C₃₁×#478	C₂²	1	2	yes	—
102	C₃₁×#478	C₂²	1	2	yes	—
103	C₃₁×#477	C₂²	1	1	yes	characteristic
104	C₃₁×#477	C₂²	1	2	yes	—
105	C₃₁×#476	C₂²	1	1	yes	characteristic
106	C₃₁×#475	C₂²	1	1	yes	characteristic
107	C₃₁×#475	C₂²	1	2	yes	—
108	C₃₁×#474	C₂²	1	1	yes	characteristic
109	C₃₁×#433	C₂²	1	2	yes	—
110	C₃₁×#433	C₂²	1	2	yes	—
111	C₃₁×#432	C₂²	1	2	yes	—
112	C₃₁×#431	C₂²	1	2	yes	—
113	C₃₁×#428	C₂²	1	1	yes	characteristic
114	C₃₁×#428	C₂²	1	1	yes	characteristic
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#427	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
120	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
121	C₃₁×#423	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₃₁×#419	C₂²	1	1	yes	characteristic
124	C₃₁×#419	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₃₁×#408	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₃₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	—	2	1	no	—
143	C₃₁×C₄⋊Q₈	—	2	1	no	—
144	C₃₁×C₄⋊Q₈	—	2	1	no	—
145	C₃₁×C₄⋊Q₈	—	2	2	no	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	2	no	—
148	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#126	—	2	2	no	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#125	—	2	2	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	—	2	2	no	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	—	2	2	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	C₂³	1	1	yes	characteristic
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	C₂³	1	2	yes	—
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	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
229	C₄×D₄×C₃₁	D₄	1	2	yes	—
230	C₄×D₄×C₃₁	D₄	1	2	yes	—
231	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	1	no	—
236	C₃₁×#117	—	2	2	no	—
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₃₁×#117	C₂³	1	1	yes	characteristic
239	C₃₁×#117	C₂³	1	1	yes	characteristic
240	C₃₁×#117	C₂³	1	2	yes	—
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₃₁×#117	C₂³	1	1	yes	characteristic
243	C₃₁×#117	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
245	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
254	C₂×C₄²×C₃₁	—	2	1	no	—
255	C₂×C₄²×C₃₁	—	2	1	no	—
256	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
258	C₃₁×#107	C₂³	1	2	yes	—
259	C₃₁×#107	C₂³	1	2	yes	—
260	C₃₁×#107	C₂³	1	1	yes	characteristic
261	C₃₁×#107	C₂³	1	1	yes	characteristic
262	C₃₁×#107	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	1	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	1	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	M₁₆×C₃₁	—	2	2	no	—
348	M₁₆×C₃₁	—	2	2	no	—
349	C₂×C₈×C₃₁	—	2	2	no	—
350	C₂×C₈×C₃₁	—	2	2	no	—
351	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
354	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₄²×C₃₁	—	2	2	no	—
420	C₄²×C₃₁	—	2	1	no	—
421	C₄²×C₃₁	—	2	1	no	—
422	C₄²×C₃₁	—	2	1	no	—
423	C₄²×C₃₁	—	2	2	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₃₁	C₂×D₄	1	2	yes	—
430	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₃₁	C₂×D₄	1	2	yes	—
432	C₄²×C₃₁	C₂⁴	1	2	yes	—
433	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
434	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
435	#60891	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂³×C₃₁	—	2	1	no	—
437	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
438	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₃₁	—	2	2	no	—
440	Q₈×C₃₁	—	2	2	no	—
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	2	1	no	—
443	Q₈×C₃₁	—	2	1	no	—
444	Q₈×C₃₁	—	4	2	no	—
445	Q₈×C₃₁	—	8	1	no	—
446	Q₈×C₃₁	—	8	2	no	—
447	Q₈×C₃₁	—	8	2	no	—
448	Q₈×C₃₁	—	8	1	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	2	4	no	—
451	D₄×C₃₁	—	2	2	no	—
452	D₄×C₃₁	—	2	1	no	—
453	D₄×C₃₁	—	2	1	no	—
454	D₄×C₃₁	—	4	2	no	—
455	D₄×C₃₁	—	8	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	4	1	no	—
470	C₂×C₄×C₃₁	—	4	2	no	—
471	C₂×C₄×C₃₁	—	4	1	no	—
472	C₂×C₄×C₃₁	—	4	2	no	—
473	C₂×C₄×C₃₁	—	4	2	no	—
474	C₂×C₄×C₃₁	—	4	2	no	—
475	C₂×C₄×C₃₁	—	4	2	no	—
476	C₂×C₄×C₃₁	—	8	1	no	—
477	C₂×C₄×C₃₁	—	8	1	no	—
478	C₂×C₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	—	8	1	no	—
480	C₂×C₄×C₃₁	—	8	1	no	—
481	C₂×C₄×C₃₁	—	8	2	no	—
482	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
491	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
492	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
493	C₈×C₃₁	—	2	1	no	—
494	C₈×C₃₁	—	2	1	no	—
495	C₈×C₃₁	—	2	1	no	—
496	C₈×C₃₁	—	2	1	no	—
497	C₈×C₃₁	—	2	2	no	—
498	C₈×C₃₁	—	2	2	no	—
499	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3461	C₂×C₃₁	1	1	yes	characteristic
501	#3244	C₂×C₃₁	1	2	yes	complemented
502	#3243	C₂×C₃₁	1	2	yes	complemented
503	#3242	C₂×C₃₁	1	2	yes	complemented
504	#3242	C₂×C₃₁	1	2	yes	complemented
505	#3240	C₂×C₃₁	1	2	yes	complemented
506	#3236	C₂×C₃₁	1	2	yes	complemented
507	#3232	C₂×C₃₁	1	2	yes	complemented
508	#3231	C₂×C₃₁	1	2	yes	complemented
509	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3099	C₂×C₃₁	1	1	yes	characteristic
514	#3098	C₂×C₃₁	1	1	yes	characteristic
515	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
520	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
522	C₂²×C₃₁	—	2	1	no	—
523	C₂²×C₃₁	—	2	1	no	—
524	C₂²×C₃₁	—	2	2	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	2	no	—
527	C₂²×C₃₁	—	4	1	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	4	1	no	—
530	C₂²×C₃₁	#536	1	2	yes	—
531	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₃₁	—	2	1	no	—
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	1	no	—
536	C₄×C₃₁	—	2	1	no	—
537	C₄×C₃₁	—	2	2	no	—
538	C₄×C₃₁	—	2	2	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	2	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	—	4	1	no	—
545	C₄×C₃₁	—	4	2	no	—
546	C₄×C₃₁	—	4	1	no	—
547	C₄×C₃₁	—	4	1	no	—
548	C₄×C₃₁	—	4	1	no	—
549	C₄×C₃₁	—	4	2	no	—
550	C₄×C₃₁	#536	1	2	yes	—
551	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	#557	—	2	1	no	—
554	#557	—	2	1	no	—
555	#554	—	2	2	no	—
556	#554	—	2	1	no	—
557	#554	—	2	2	no	—
558	#554	—	2	1	no	—
559	#544	C₂²×C₃₁	1	1	yes	characteristic
560	#544	C₂²×C₃₁	1	1	yes	characteristic
561	#544	C₂²×C₃₁	1	1	yes	characteristic
562	#544	C₂²×C₃₁	1	2	yes	—
563	#544	C₂²×C₃₁	1	2	yes	—
564	#542	—	2	1	no	—
565	#542	C₂²×C₃₁	1	2	yes	—
566	#541	—	2	1	no	—
567	#541	C₂²×C₃₁	1	2	yes	—
568	#539	—	2	2	no	—
569	#537	C₂²×C₃₁	1	1	yes	characteristic
570	#536	C₂²×C₃₁	1	1	yes	characteristic
571	#536	C₂²×C₃₁	1	1	yes	characteristic
572	#533	—	2	1	no	—
573	#533	C₂²×C₃₁	1	2	yes	—
574	#533	C₂²×C₃₁	1	1	yes	characteristic
575	#533	C₂²×C₃₁	1	2	yes	—
576	#529	—	2	2	no	—
577	#529	—	2	1	no	—
578	#529	C₂²×C₃₁	1	2	yes	—
579	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×#125	C₂²×C₃₁	1	2	yes	—
581	#520	C₂²×C₃₁	1	1	yes	characteristic
582	#520	C₂²×C₃₁	1	1	yes	characteristic
583	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
584	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
585	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
586	#501	C₂²×C₃₁	1	2	yes	—
587	#501	C₂²×C₃₁	1	2	yes	—
588	#501	C₂²×C₃₁	1	2	yes	—
589	#501	C₂²×C₃₁	1	2	yes	—
590	#500	C₂²×C₃₁	1	2	yes	—
591	#499	C₂²×C₃₁	1	2	yes	—
592	#499	C₂²×C₃₁	1	2	yes	—
593	#498	C₂²×C₃₁	1	2	yes	—
594	#491	C₂²×C₃₁	1	2	yes	—
595	#491	C₂²×C₃₁	1	2	yes	—
596	#489	C₂²×C₃₁	1	2	yes	—
597	#489	C₂²×C₃₁	1	2	yes	—
598	#488	C₂²×C₃₁	1	2	yes	—
599	#488	C₂²×C₃₁	1	2	yes	—
600	#487	C₂²×C₃₁	1	2	yes	—
601	#487	C₂²×C₃₁	1	2	yes	—
602	#485	C₂²×C₃₁	1	2	yes	—
603	#485	C₂²×C₃₁	1	2	yes	—
604	#485	C₂²×C₃₁	1	2	yes	—
605	#485	C₂²×C₃₁	1	2	yes	—
606	#485	C₂²×C₃₁	1	2	yes	—
607	#485	C₂²×C₃₁	1	2	yes	—
608	#484	C₂²×C₃₁	1	2	yes	—
609	#484	C₂²×C₃₁	1	2	yes	—
610	#484	C₂²×C₃₁	1	2	yes	—
611	#483	C₂²×C₃₁	1	2	yes	—
612	#483	C₂²×C₃₁	1	2	yes	—
613	#483	C₂²×C₃₁	1	2	yes	—
614	#482	C₂²×C₃₁	1	2	yes	—
615	#482	C₂²×C₃₁	1	2	yes	—
616	#481	C₂²×C₃₁	1	2	yes	—
617	#480	C₂²×C₃₁	1	2	yes	—
618	#479	C₂²×C₃₁	1	2	yes	—
619	#479	C₂²×C₃₁	1	2	yes	—
620	#479	C₂²×C₃₁	1	2	yes	—
621	#479	C₂²×C₃₁	1	2	yes	—
622	#479	C₂²×C₃₁	1	1	yes	characteristic
623	#479	C₂²×C₃₁	1	1	yes	characteristic
624	#479	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	2	yes	—
626	#479	C₂²×C₃₁	1	2	yes	—
627	#479	C₂²×C₃₁	1	2	yes	—
628	#478	C₂²×C₃₁	1	1	yes	characteristic
629	#478	C₂²×C₃₁	1	1	yes	characteristic
630	#478	C₂²×C₃₁	1	2	yes	—
631	#478	C₂²×C₃₁	1	2	yes	—
632	#477	C₂²×C₃₁	1	1	yes	characteristic
633	#477	C₂²×C₃₁	1	2	yes	—
634	#476	C₂²×C₃₁	1	1	yes	characteristic
635	#475	C₂²×C₃₁	1	1	yes	characteristic
636	#475	C₂²×C₃₁	1	2	yes	—
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#433	C₂²×C₃₁	1	2	yes	—
639	#433	C₂²×C₃₁	1	2	yes	—
640	#432	C₂²×C₃₁	1	2	yes	—
641	#431	C₂²×C₃₁	1	2	yes	—
642	#428	C₂²×C₃₁	1	1	yes	characteristic
643	#428	C₂²×C₃₁	1	1	yes	characteristic
644	#428	C₂²×C₃₁	1	1	yes	characteristic
645	#428	C₂²×C₃₁	1	1	yes	characteristic
646	#427	C₂²×C₃₁	1	1	yes	characteristic
647	#427	C₂²×C₃₁	1	1	yes	characteristic
648	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
650	#423	C₂²×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
652	#419	C₂²×C₃₁	1	1	yes	characteristic
653	#419	C₂²×C₃₁	1	1	yes	characteristic
654	#417	C₂²×C₃₁	1	1	yes	characteristic
655	#417	C₂²×C₃₁	1	1	yes	characteristic
656	#416	C₂²×C₃₁	1	1	yes	characteristic
657	#416	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
659	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
660	#408	C₂²×C₃₁	1	1	yes	characteristic
661	#408	C₂²×C₃₁	1	1	yes	characteristic
662	#405	C₂²×C₃₁	1	1	yes	characteristic
663	#405	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×C₃₁	—	2	2	no	—
665	C₂×C₃₁	—	4	2	no	—
666	C₂×C₃₁	—	8	1	no	—
667	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
668	C₂×C₃₁	#3584	1	1	yes	characteristic
669	C₂×C₃₁	#3586	1	1	yes	characteristic
670	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
671	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
676	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
684	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	1	no	—
695	#125	—	2	2	no	—
696	#125	—	2	1	no	—
697	#125	—	2	2	no	—
698	#125	—	2	1	no	—
699	#125	—	2	2	no	—
700	#125	—	2	1	no	—
701	#125	—	2	1	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	C₂³×C₃₁	1	2	yes	—
706	#125	C₂³×C₃₁	1	1	yes	characteristic
707	#125	C₂³×C₃₁	1	2	yes	—
708	#125	C₂³×C₃₁	1	2	yes	—
709	#125	C₂³×C₃₁	1	2	yes	—
710	#125	C₂³×C₃₁	1	2	yes	—
711	#125	C₂³×C₃₁	1	1	yes	characteristic
712	#124	—	2	1	no	—
713	#124	—	2	2	no	—
714	#124	C₂³×C₃₁	1	2	yes	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
736	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
737	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	#121	—	2	2	no	—
739	#121	—	2	1	no	—
740	#121	C₂³×C₃₁	1	2	yes	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	2	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
751	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
753	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
764	C₄×D₄	D₄×C₃₁	1	2	yes	—
765	C₄×D₄	D₄×C₃₁	1	2	yes	—
766	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	#117	—	2	2	no	—
770	#117	—	2	1	no	—
771	#117	—	2	2	no	—
772	#117	C₂³×C₃₁	1	1	yes	characteristic
773	#117	C₂³×C₃₁	1	1	yes	characteristic
774	#117	C₂³×C₃₁	1	1	yes	characteristic
775	#117	C₂³×C₃₁	1	2	yes	—
776	#117	C₂³×C₃₁	1	2	yes	—
777	#117	C₂³×C₃₁	1	1	yes	characteristic
778	#117	C₂³×C₃₁	1	2	yes	—
779	C₂×C₄⋊C₄	—	2	1	no	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	2	no	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
789	C₂×C₄²	—	2	1	no	—
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
793	#107	C₂³×C₃₁	1	2	yes	—
794	#107	C₂³×C₃₁	1	2	yes	—
795	#107	C₂³×C₃₁	1	1	yes	characteristic
796	#107	C₂³×C₃₁	1	1	yes	characteristic
797	#107	C₂³×C₃₁	1	1	yes	characteristic
798	#107	C₂³×C₃₁	1	1	yes	characteristic
799	#107	C₂³×C₃₁	1	2	yes	—
800	#107	C₂³×C₃₁	1	2	yes	—
801	#107	C₂³×C₃₁	1	2	yes	—
802	#107	C₂³×C₃₁	1	2	yes	—
803	#106	C₂³×C₃₁	1	2	yes	—
804	#106	C₂³×C₃₁	1	2	yes	—
805	#106	C₂³×C₃₁	1	1	yes	characteristic
806	#106	C₂³×C₃₁	1	1	yes	characteristic
807	#106	C₂³×C₃₁	1	1	yes	characteristic
808	#106	C₂³×C₃₁	1	1	yes	characteristic
809	#106	C₂³×C₃₁	1	2	yes	—
810	#106	C₂³×C₃₁	1	2	yes	—
811	#106	C₂³×C₃₁	1	2	yes	—
812	#106	C₂³×C₃₁	1	2	yes	—
813	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
818	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
819	#103	C₂³×C₃₁	1	2	yes	—
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	1	yes	characteristic
824	#103	C₂³×C₃₁	1	1	yes	characteristic
825	#103	C₂³×C₃₁	1	1	yes	characteristic
826	#103	C₂³×C₃₁	1	1	yes	characteristic
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#102	C₂³×C₃₁	1	1	yes	characteristic
834	#102	C₂³×C₃₁	1	1	yes	characteristic
835	#102	C₂³×C₃₁	1	1	yes	characteristic
836	#102	C₂³×C₃₁	1	1	yes	characteristic
837	#102	C₂³×C₃₁	1	2	yes	—
838	#102	C₂³×C₃₁	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
843	#97	C₂³×C₃₁	1	2	yes	—
844	#97	C₂³×C₃₁	1	2	yes	—
845	C₄×C₈	C₂³×C₃₁	1	2	yes	—
846	C₄×C₈	C₂³×C₃₁	1	2	yes	—
847	C₃₁	#60891	1	1	yes	characteristic, direct product factor, Sylow
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	#41	—	2	2	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
862	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
867	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
879	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	M₁₆	—	2	2	no	—
884	M₁₆	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
890	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
891	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
929	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
930	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₄²	C₂×D₄×C₃₁	1	2	yes	—
966	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₄²	C₂×D₄×C₃₁	1	2	yes	—
968	C₄²	C₂⁴×C₃₁	1	2	yes	—
969	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂³	—	2	1	no	—
972	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
973	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	4	2	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	2	no	—
982	Q₈	—	8	2	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	D₄	—	2	4	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	1	no	—
988	D₄	—	2	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	4	2	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	—	8	1	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1026	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	C₃₁×#536	1	2	yes	—
1043	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	C₃₁×#536	1	2	yes	—
1063	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1064	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
1069	C₂	C₃₁×#3584	1	1	yes	characteristic
1070	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×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3504	C₂	semidirect
3. C₃₁×#3244	C₂	semidirect
4. C₃₁×#3243	C₂	semidirect
5. C₃₁×#3242	C₂	semidirect
6. C₃₁×#3242	C₂	semidirect
7. C₃₁×#3240	C₂	semidirect
8. C₃₁×#3236	C₂	semidirect
9. C₃₁×#3232	C₂	semidirect
10. C₃₁×#3231	C₂	semidirect
11. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3163	C₂	semidirect
13. C₃₁×#3137	C₂	semidirect
14. C₃₁×#3137	C₂	semidirect
17. C₃₁×#3097	C₂	semidirect
18. C₃₁×#3097	C₂	semidirect
19. C₃₁×#3080	C₂	semidirect
20. C₃₁×#3078	C₂	semidirect
21. C₃₁×#3076	C₂	semidirect
22. C₂×C₃₁×#479	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
435. #60891	C₃₁	direct (N × H)
499. #3504	C₂×C₃₁	semidirect
501. #3244	C₂×C₃₁	semidirect
502. #3243	C₂×C₃₁	semidirect
503. #3242	C₂×C₃₁	semidirect
504. #3242	C₂×C₃₁	semidirect
505. #3240	C₂×C₃₁	semidirect
506. #3236	C₂×C₃₁	semidirect
507. #3232	C₂×C₃₁	semidirect
508. #3231	C₂×C₃₁	semidirect
509. #3164	C₂×C₃₁	semidirect
510. #3163	C₂×C₃₁	semidirect
511. #3137	C₂×C₃₁	semidirect
512. #3137	C₂×C₃₁	semidirect
515. #3097	C₂×C₃₁	semidirect
516. #3097	C₂×C₃₁	semidirect
517. #3080	C₂×C₃₁	semidirect
518. #3078	C₂×C₃₁	semidirect
519. #3076	C₂×C₃₁	semidirect
520. C₂×#479	C₂×C₃₁	semidirect
521. #2925	C₂×C₃₁	semidirect
847. C₃₁	#60891	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×#3504	2
C₃₁×#3461	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3240	2
C₃₁×#3236	2
C₃₁×#3232	2
C₃₁×#3231	2
C₃₁×#3164	2
C₃₁×#3163	2
C₃₁×#3137	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3080	2
C₃₁×#3078	2
C₃₁×#3076	2
C₂×C₃₁×#479	2
C₃₁×#2925	2
#60891	31

Subgroups — C31×#60891 #21517650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60891 #21517650