Subgroups — C₃₁×#61787 #21518546

Order 7936.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3202	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#559	—	2	1	no	—
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#556	—	2	2	no	—
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#555	—	2	1	no	—
31	C₃₁×#555	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	1	yes	characteristic
34	C₃₁×#554	C₂²	1	1	yes	characteristic
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	C₃₁×#552	C₂²	1	2	yes	—
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	2	yes	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#540	—	2	1	no	—
45	C₃₁×#539	—	2	2	no	—
46	C₃₁×#537	C₂²	1	2	yes	—
47	C₃₁×#536	C₂²	1	2	yes	—
48	C₃₁×#536	C₂²	1	2	yes	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	—	2	1	no	—
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#500	C₂²	1	1	yes	characteristic
58	C₃₁×#499	C₂²	1	2	yes	—
59	C₃₁×#498	C₂²	1	1	yes	characteristic
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#487	C₂²	1	1	yes	characteristic
62	C₃₁×#487	C₂²	1	1	yes	characteristic
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#485	C₂²	1	2	yes	—
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	2	yes	—
70	C₃₁×#485	C₂²	1	2	yes	—
71	C₃₁×#484	C₂²	1	2	yes	—
72	C₃₁×#484	C₂²	1	2	yes	—
73	C₃₁×#484	C₂²	1	2	yes	—
74	C₃₁×#484	C₂²	1	2	yes	—
75	C₃₁×#483	C₂²	1	2	yes	—
76	C₃₁×#483	C₂²	1	2	yes	—
77	C₃₁×#483	C₂²	1	1	yes	characteristic
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#482	C₂²	1	2	yes	—
80	C₃₁×#480	C₂²	1	1	yes	characteristic
81	C₃₁×#480	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	1	yes	characteristic
83	C₃₁×#479	C₂²	1	2	yes	—
84	C₃₁×#479	C₂²	1	1	yes	characteristic
85	C₃₁×#479	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	1	yes	characteristic
88	C₃₁×#477	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#475	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	1	yes	characteristic
92	C₃₁×#470	C₂²	1	2	yes	—
93	C₃₁×#470	C₂²	1	2	yes	—
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#467	C₂²	1	2	yes	—
98	C₃₁×#467	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#464	C₂²	1	1	yes	characteristic
102	C₃₁×#462	C₂²	1	1	yes	characteristic
103	C₃₁×#462	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#451	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	1	yes	characteristic
108	C₃₁×#451	C₂²	1	2	yes	—
109	C₃₁×#451	C₂²	1	2	yes	—
110	C₃₁×#448	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#436	C₂²	1	1	yes	characteristic
118	C₃₁×#436	C₂²	1	2	yes	—
119	C₃₁×#436	C₂²	1	1	yes	characteristic
120	C₈×D₄×C₃₁	C₂²	1	2	yes	—
121	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
123	C₃₁×#431	C₂²	1	1	yes	characteristic
124	C₃₁×#431	C₂²	1	1	yes	characteristic
125	C₃₁×#428	C₂²	1	2	yes	—
126	C₃₁×#428	C₂²	1	2	yes	—
127	C₃₁×#427	C₂²	1	2	yes	—
128	C₂×C₃₁×#107	C₂²	1	2	yes	—
129	C₃₁×#419	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#408	C₂²	1	2	yes	—
134	C₃₁×#408	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	C₂³	1	2	yes	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×#127	D₄	1	1	yes	characteristic
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	1	no	—
164	C₃₁×#125	—	2	1	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	1	yes	characteristic
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	D₄	1	2	yes	—
180	C₃₁×#124	C₂³	1	1	yes	characteristic
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	1	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	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	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	D₄	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₃₁	—	2	1	no	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	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	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	4	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	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	—	4	1	no	—
322	C₂×Q₈×C₃₁	—	4	1	no	—
323	C₂×Q₈×C₃₁	—	4	2	no	—
324	C₂×Q₈×C₃₁	—	4	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
353	Q₁₆×C₃₁	—	4	1	no	—
354	Q₁₆×C₃₁	—	4	2	no	—
355	Q₁₆×C₃₁	—	4	1	no	—
356	Q₁₆×C₃₁	—	4	2	no	—
357	SD₁₆×C₃₁	—	4	1	no	—
358	SD₁₆×C₃₁	—	4	1	no	—
359	M₁₆×C₃₁	—	4	2	no	—
360	M₁₆×C₃₁	—	4	2	no	—
361	C₂×C₈×C₃₁	—	4	2	no	—
362	C₂×C₈×C₃₁	—	4	2	no	—
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	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	2	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	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#61787	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
446	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₃₁	—	2	1	no	—
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	4	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	1	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	2	2	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	8	1	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	4	1	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	8	2	no	—
495	C₂×C₄×C₃₁	—	8	1	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
508	C₈×C₃₁	—	2	1	no	—
509	C₈×C₃₁	—	2	2	no	—
510	C₈×C₃₁	—	2	1	no	—
511	C₈×C₃₁	—	2	1	no	—
512	C₈×C₃₁	—	2	1	no	—
513	C₈×C₃₁	—	2	2	no	—
514	#3547	C₂×C₃₁	1	1	yes	characteristic
515	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3352	C₂×C₃₁	1	2	yes	complemented
519	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3336	C₂×C₃₁	1	2	yes	complemented
522	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3327	C₂×C₃₁	1	2	yes	complemented
525	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3300	C₂×C₃₁	1	2	yes	complemented
527	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3202	C₂×C₃₁	1	2	yes	complemented
531	#3201	C₂×C₃₁	1	2	yes	complemented
532	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3098	C₂×C₃₁	1	2	yes	complemented
535	#3097	C₂×C₃₁	1	2	yes	complemented
536	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	2	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
550	C₄×C₃₁	—	2	1	no	—
551	C₄×C₃₁	—	2	1	no	—
552	C₄×C₃₁	—	2	2	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	1	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	—	4	1	no	—
559	C₄×C₃₁	—	4	2	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	#578	1	2	yes	—
568	C₄×C₃₁	#585	1	1	yes	characteristic
569	C₄×C₃₁	#585	1	1	yes	characteristic
570	#562	—	2	2	no	—
571	#559	—	2	1	no	—
572	#557	—	2	1	no	—
573	#556	—	2	2	no	—
574	#556	C₂²×C₃₁	1	1	yes	characteristic
575	#556	C₂²×C₃₁	1	1	yes	characteristic
576	#555	—	2	1	no	—
577	#555	C₂²×C₃₁	1	1	yes	characteristic
578	#554	C₂²×C₃₁	1	1	yes	characteristic
579	#554	C₂²×C₃₁	1	1	yes	characteristic
580	#554	C₂²×C₃₁	1	1	yes	characteristic
581	#553	—	2	1	no	—
582	#552	C₂²×C₃₁	1	2	yes	—
583	#552	C₂²×C₃₁	1	2	yes	—
584	#552	C₂²×C₃₁	1	2	yes	—
585	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
586	#548	C₂²×C₃₁	1	2	yes	—
587	#547	C₂²×C₃₁	1	1	yes	characteristic
588	#544	—	2	1	no	—
589	#542	—	2	2	no	—
590	#540	—	2	1	no	—
591	#539	—	2	2	no	—
592	#537	C₂²×C₃₁	1	2	yes	—
593	#536	C₂²×C₃₁	1	2	yes	—
594	#536	C₂²×C₃₁	1	2	yes	—
595	#533	C₂²×C₃₁	1	1	yes	characteristic
596	#533	C₂²×C₃₁	1	1	yes	characteristic
597	#532	C₂²×C₃₁	1	1	yes	characteristic
598	#529	—	2	1	no	—
599	#529	—	2	1	no	—
600	#529	C₂²×C₃₁	1	1	yes	characteristic
601	#520	C₂²×C₃₁	1	2	yes	—
602	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
603	#500	C₂²×C₃₁	1	1	yes	characteristic
604	#499	C₂²×C₃₁	1	2	yes	—
605	#498	C₂²×C₃₁	1	1	yes	characteristic
606	#488	C₂²×C₃₁	1	2	yes	—
607	#487	C₂²×C₃₁	1	1	yes	characteristic
608	#487	C₂²×C₃₁	1	1	yes	characteristic
609	#485	C₂²×C₃₁	1	2	yes	—
610	#485	C₂²×C₃₁	1	2	yes	—
611	#485	C₂²×C₃₁	1	2	yes	—
612	#485	C₂²×C₃₁	1	2	yes	—
613	#485	C₂²×C₃₁	1	2	yes	—
614	#485	C₂²×C₃₁	1	2	yes	—
615	#485	C₂²×C₃₁	1	2	yes	—
616	#485	C₂²×C₃₁	1	2	yes	—
617	#484	C₂²×C₃₁	1	2	yes	—
618	#484	C₂²×C₃₁	1	2	yes	—
619	#484	C₂²×C₃₁	1	2	yes	—
620	#484	C₂²×C₃₁	1	2	yes	—
621	#483	C₂²×C₃₁	1	2	yes	—
622	#483	C₂²×C₃₁	1	2	yes	—
623	#483	C₂²×C₃₁	1	1	yes	characteristic
624	#482	C₂²×C₃₁	1	2	yes	—
625	#482	C₂²×C₃₁	1	2	yes	—
626	#480	C₂²×C₃₁	1	1	yes	characteristic
627	#480	C₂²×C₃₁	1	2	yes	—
628	#479	C₂²×C₃₁	1	1	yes	characteristic
629	#479	C₂²×C₃₁	1	2	yes	—
630	#479	C₂²×C₃₁	1	1	yes	characteristic
631	#479	C₂²×C₃₁	1	2	yes	—
632	#477	C₂²×C₃₁	1	1	yes	characteristic
633	#477	C₂²×C₃₁	1	1	yes	characteristic
634	#477	C₂²×C₃₁	1	1	yes	characteristic
635	#476	C₂²×C₃₁	1	1	yes	characteristic
636	#475	C₂²×C₃₁	1	1	yes	characteristic
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#470	C₂²×C₃₁	1	2	yes	—
639	#470	C₂²×C₃₁	1	2	yes	—
640	#470	C₂²×C₃₁	1	2	yes	—
641	#468	C₂²×C₃₁	1	2	yes	—
642	#467	C₂²×C₃₁	1	2	yes	—
643	#467	C₂²×C₃₁	1	2	yes	—
644	#467	C₂²×C₃₁	1	2	yes	—
645	#465	C₂²×C₃₁	1	2	yes	—
646	#464	C₂²×C₃₁	1	1	yes	characteristic
647	#464	C₂²×C₃₁	1	1	yes	characteristic
648	#462	C₂²×C₃₁	1	1	yes	characteristic
649	#462	C₂²×C₃₁	1	1	yes	characteristic
650	#452	C₂²×C₃₁	1	2	yes	—
651	#452	C₂²×C₃₁	1	2	yes	—
652	#451	C₂²×C₃₁	1	2	yes	—
653	#451	C₂²×C₃₁	1	2	yes	—
654	#451	C₂²×C₃₁	1	1	yes	characteristic
655	#451	C₂²×C₃₁	1	2	yes	—
656	#448	C₂²×C₃₁	1	1	yes	characteristic
657	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
659	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
661	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	#436	C₂²×C₃₁	1	1	yes	characteristic
664	#436	C₂²×C₃₁	1	1	yes	characteristic
665	#436	C₂²×C₃₁	1	2	yes	—
666	C₈×D₄	C₂²×C₃₁	1	2	yes	—
667	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
668	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
669	#431	C₂²×C₃₁	1	1	yes	characteristic
670	#431	C₂²×C₃₁	1	1	yes	characteristic
671	#428	C₂²×C₃₁	1	2	yes	—
672	#428	C₂²×C₃₁	1	2	yes	—
673	#427	C₂²×C₃₁	1	2	yes	—
674	C₂×#107	C₂²×C₃₁	1	2	yes	—
675	#419	C₂²×C₃₁	1	2	yes	—
676	#417	C₂²×C₃₁	1	2	yes	—
677	#416	C₂²×C₃₁	1	2	yes	—
678	C₂×#103	C₂²×C₃₁	1	2	yes	—
679	#408	C₂²×C₃₁	1	2	yes	—
680	#408	C₂²×C₃₁	1	2	yes	—
681	C₂×C₃₁	—	4	1	no	—
682	C₂×C₃₁	—	4	2	no	—
683	C₂×C₃₁	—	4	2	no	—
684	C₂×C₃₁	—	8	1	no	—
685	C₂×C₃₁	#3485	1	1	yes	characteristic
686	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
687	C₂×C₃₁	#3584	1	1	yes	characteristic
688	C₂×#41	C₂³×C₃₁	1	2	yes	—
689	C₂×#41	C₂³×C₃₁	1	2	yes	—
690	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
695	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
699	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
700	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
701	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	#127	D₄×C₃₁	1	1	yes	characteristic
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	1	no	—
724	#125	C₂³×C₃₁	1	1	yes	characteristic
725	#125	C₂³×C₃₁	1	2	yes	—
726	#124	—	2	1	no	—
727	#124	—	2	1	no	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	D₄×C₃₁	1	2	yes	—
733	#124	C₂³×C₃₁	1	1	yes	characteristic
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	1	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	D₄×C₃₁	1	1	yes	characteristic
768	#121	D₄×C₃₁	1	1	yes	characteristic
769	#121	D₄×C₃₁	1	2	yes	—
770	#121	C₂³×C₃₁	1	1	yes	characteristic
771	#121	C₂³×C₃₁	1	2	yes	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₃₁	1	2	yes	—
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	#117	—	2	1	no	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₃₁	1	2	yes	—
806	#117	C₂³×C₃₁	1	2	yes	—
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
813	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
814	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
815	C₂×C₄²	—	2	1	no	—
816	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
817	#107	C₂³×C₃₁	1	1	yes	characteristic
818	#107	C₂³×C₃₁	1	2	yes	—
819	#107	C₂³×C₃₁	1	2	yes	—
820	#107	C₂³×C₃₁	1	2	yes	—
821	#107	C₂³×C₃₁	1	2	yes	—
822	#107	C₂³×C₃₁	1	2	yes	—
823	#107	C₂³×C₃₁	1	1	yes	characteristic
824	#107	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	1	yes	characteristic
826	#106	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	1	yes	characteristic
828	#106	C₂³×C₃₁	1	2	yes	—
829	#106	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	2	yes	—
831	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	#103	C₂³×C₃₁	1	1	yes	characteristic
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#103	C₂³×C₃₁	1	2	yes	—
840	#103	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	1	yes	characteristic
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₃₁	1	2	yes	—
865	C₃₁	#61787	1	1	yes	characteristic, direct product factor, Sylow
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	4	1	no	—
876	C₂×Q₈	—	4	1	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	—	4	2	no	—
879	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
890	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
907	Q₁₆	—	4	1	no	—
908	Q₁₆	—	4	2	no	—
909	Q₁₆	—	4	1	no	—
910	Q₁₆	—	4	2	no	—
911	SD₁₆	—	4	1	no	—
912	SD₁₆	—	4	1	no	—
913	M₁₆	—	4	2	no	—
914	M₁₆	—	4	2	no	—
915	C₂×C₈	—	4	2	no	—
916	C₂×C₈	—	4	2	no	—
917	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
919	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₂³	—	2	1	no	—
998	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
999	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	8	1	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	1	no	—
1024	D₄	—	8	2	no	—
1025	D₄	—	8	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	1	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1060	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1061	C₈	—	2	1	no	—
1062	C₈	—	2	2	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1080	C₄	—	2	2	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	C₃₁×#578	1	2	yes	—
1098	C₄	C₃₁×#585	1	1	yes	characteristic
1099	C₄	C₃₁×#585	1	1	yes	characteristic
1100	C₂	—	4	1	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	1	no	—
1104	C₂	C₃₁×#3485	1	1	yes	characteristic
1105	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1106	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3547	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×#3357	C₂	semidirect
4. C₃₁×#3356	C₂	semidirect
5. C₃₁×#3352	C₂	semidirect
6. C₃₁×#3340	C₂	semidirect
7. C₃₁×#3338	C₂	semidirect
8. C₃₁×#3336	C₂	semidirect
9. C₃₁×#3331	C₂	semidirect
10. C₃₁×#3328	C₂	semidirect
11. C₃₁×#3327	C₂	semidirect
12. C₃₁×#3302	C₂	semidirect
13. C₃₁×#3300	C₂	semidirect
14. C₃₁×#3299	C₂	semidirect
15. C₃₁×#3233	C₂	semidirect
16. C₃₁×#3231	C₂	semidirect
17. C₃₁×#3202	C₂	semidirect
18. C₃₁×#3201	C₂	semidirect
19. C₃₁×#3108	C₂	semidirect
20. C₃₁×#3104	C₂	semidirect
21. C₃₁×#3098	C₂	semidirect
22. C₃₁×#3097	C₂	semidirect
23. C₃₁×#2979	C₂	semidirect
443. #61787	C₃₁	direct (N × H)
515. #3507	C₂×C₃₁	semidirect
516. #3357	C₂×C₃₁	semidirect
517. #3356	C₂×C₃₁	semidirect
518. #3352	C₂×C₃₁	semidirect
519. #3340	C₂×C₃₁	semidirect
520. #3338	C₂×C₃₁	semidirect
521. #3336	C₂×C₃₁	semidirect
522. #3331	C₂×C₃₁	semidirect
523. #3328	C₂×C₃₁	semidirect
524. #3327	C₂×C₃₁	semidirect
525. #3302	C₂×C₃₁	semidirect
526. #3300	C₂×C₃₁	semidirect
527. #3299	C₂×C₃₁	semidirect
528. #3233	C₂×C₃₁	semidirect
529. #3231	C₂×C₃₁	semidirect
530. #3202	C₂×C₃₁	semidirect
531. #3201	C₂×C₃₁	semidirect
532. #3108	C₂×C₃₁	semidirect
533. #3104	C₂×C₃₁	semidirect
534. #3098	C₂×C₃₁	semidirect
535. #3097	C₂×C₃₁	semidirect
536. #2979	C₂×C₃₁	semidirect
865. C₃₁	#61787	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×#3547	2
C₃₁×#3507	2
C₃₁×#3357	2
C₃₁×#3356	2
C₃₁×#3352	2
C₃₁×#3340	2
C₃₁×#3338	2
C₃₁×#3336	2
C₃₁×#3331	2
C₃₁×#3328	2
C₃₁×#3327	2
C₃₁×#3302	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3108	2
C₃₁×#3104	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#2979	2
#61787	31

Subgroups — C31×#61787 #21518546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61787 #21518546