Subgroups — C₃₁×#60876 #21517635

Order 7936.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3458	C₂	1	1	yes	maximal, characteristic, complemented
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×#3237	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3233	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×#3095	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic
18	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#552	—	2	2	no	—
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#551	—	2	2	no	—
30	C₃₁×#544	—	2	1	no	—
31	C₃₁×#544	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#544	C₂²	1	1	yes	characteristic
34	C₃₁×#544	C₂²	1	1	yes	characteristic
35	C₃₁×#544	C₂²	1	1	yes	characteristic
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#544	C₂²	1	2	yes	—
38	C₃₁×#544	C₂²	1	2	yes	—
39	C₃₁×#543	—	2	2	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#541	C₂²	1	2	yes	—
42	C₃₁×#536	C₂²	1	1	yes	characteristic
43	C₃₁×#533	—	2	2	no	—
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	—	2	1	no	—
46	C₃₁×#533	C₂²	1	2	yes	—
47	C₃₁×#533	C₂²	1	2	yes	—
48	C₃₁×#533	C₂²	1	2	yes	—
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₃₁×#525	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₃₁×#520	C₂²	1	1	yes	characteristic
53	C₃₁×#519	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#501	C₂²	1	2	yes	complemented
61	C₃₁×#500	C₂²	1	2	yes	complemented
62	C₃₁×#499	C₂²	1	2	yes	complemented
63	C₃₁×#499	C₂²	1	2	yes	complemented
64	C₃₁×#498	C₂²	1	2	yes	complemented
65	C₃₁×#491	C₂²	1	2	yes	complemented
66	C₃₁×#491	C₂²	1	2	yes	complemented
67	C₃₁×#489	C₂²	1	2	yes	complemented
68	C₃₁×#489	C₂²	1	2	yes	complemented
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#488	C₂²	1	2	yes	complemented
71	C₃₁×#487	C₂²	1	2	yes	complemented
72	C₃₁×#487	C₂²	1	2	yes	complemented
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	1	yes	characteristic
78	C₃₁×#485	C₂²	1	1	yes	characteristic
79	C₃₁×#485	C₂²	1	2	yes	—
80	C₃₁×#485	C₂²	1	2	yes	—
81	C₃₁×#485	C₂²	1	2	yes	—
82	C₃₁×#485	C₂²	1	2	yes	—
83	C₃₁×#484	C₂²	1	1	yes	characteristic
84	C₃₁×#484	C₂²	1	2	yes	—
85	C₃₁×#483	C₂²	1	1	yes	characteristic
86	C₃₁×#483	C₂²	1	2	yes	—
87	C₃₁×#482	C₂²	1	1	yes	characteristic
88	C₃₁×#482	C₂²	1	1	yes	characteristic
89	C₃₁×#482	C₂²	1	2	yes	—
90	C₃₁×#482	C₂²	1	2	yes	—
91	C₃₁×#481	C₂²	1	1	yes	characteristic
92	C₃₁×#480	C₂²	1	1	yes	characteristic
93	C₃₁×#479	C₂²	1	2	yes	complemented
94	C₃₁×#479	C₂²	1	2	yes	complemented
95	C₃₁×#479	C₂²	1	2	yes	complemented
96	C₃₁×#479	C₂²	1	2	yes	complemented
97	C₃₁×#479	C₂²	1	2	yes	complemented
98	C₃₁×#479	C₂²	1	2	yes	complemented
99	C₃₁×#478	C₂²	1	2	yes	complemented
100	C₃₁×#478	C₂²	1	2	yes	complemented
101	C₃₁×#477	C₂²	1	2	yes	complemented
102	C₃₁×#477	C₂²	1	2	yes	complemented
103	C₃₁×#477	C₂²	1	2	yes	complemented
104	C₃₁×#476	C₂²	1	2	yes	complemented
105	C₃₁×#475	C₂²	1	2	yes	complemented
106	C₃₁×#475	C₂²	1	2	yes	complemented
107	C₃₁×#475	C₂²	1	2	yes	complemented
108	C₃₁×#474	C₂²	1	2	yes	complemented
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×#424	C₂²	1	1	yes	characteristic
122	C₃₁×#424	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×#407	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×C₂²⋊C₈	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	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×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	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	—	2	1	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	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	1	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	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	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	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	—	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	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
203	C₃₁×#121	C₂³	1	1	yes	characteristic
204	C₃₁×#121	C₂³	1	1	yes	characteristic
205	C₃₁×#120	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	2	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	1	no	—
223	C₃₁×#117	—	2	1	no	—
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	—	2	1	no	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	—	2	2	no	—
229	C₃₁×#117	D₄	1	1	yes	characteristic
230	C₃₁×#117	D₄	1	2	yes	—
231	C₃₁×#117	D₄	1	1	yes	characteristic
232	C₃₁×#117	C₂³	1	1	yes	characteristic
233	C₃₁×#117	C₂³	1	1	yes	characteristic
234	C₃₁×#117	C₂³	1	1	yes	characteristic
235	C₃₁×#117	C₂³	1	1	yes	characteristic
236	C₃₁×#117	C₂³	1	1	yes	characteristic
237	C₃₁×#117	C₂³	1	2	yes	—
238	C₃₁×#117	C₂³	1	2	yes	—
239	C₃₁×#117	C₂³	1	1	yes	characteristic
240	C₃₁×#117	C₂³	1	1	yes	characteristic
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
254	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
255	C₂×C₄²×C₃₁	—	2	1	no	—
256	C₂×C₄²×C₃₁	—	2	1	no	—
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	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
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	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×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	2	2	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	2	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	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	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₃₁	—	2	1	no	—
326	C₂×D₄×C₃₁	—	2	1	no	—
327	C₂×D₄×C₃₁	—	2	1	no	—
328	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	1	no	—
334	C₂²×C₄×C₃₁	—	2	1	no	—
335	C₂²×C₄×C₃₁	—	2	1	no	—
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	1	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	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	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	2	no	—
386	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	1	no	—
403	C₂²⋊C₄×C₃₁	—	2	1	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₄²×C₃₁	—	2	2	no	—
422	C₄²×C₃₁	—	2	1	no	—
423	C₄²×C₃₁	—	2	1	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	1	no	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	C₂×D₄	1	2	yes	—
432	C₄²×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	C₂⁴	1	2	yes	—
434	C₄²×C₃₁	C₂⁴	1	2	yes	—
435	#60876	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂³×C₃₁	—	2	2	no	—
437	C₂³×C₃₁	—	2	1	no	—
438	C₂³×C₃₁	—	4	1	no	—
439	C₂³×C₃₁	—	4	1	no	—
440	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₃₁	—	2	2	no	—
444	Q₈×C₃₁	—	2	2	no	—
445	Q₈×C₃₁	—	2	1	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	4	2	no	—
448	Q₈×C₃₁	—	8	2	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	Q₈×C₃₁	—	8	2	no	—
451	Q₈×C₃₁	—	8	2	no	—
452	Q₈×C₃₁	—	8	2	no	—
453	D₄×C₃₁	—	2	1	no	—
454	D₄×C₃₁	—	2	1	no	—
455	D₄×C₃₁	—	4	2	no	—
456	D₄×C₃₁	—	4	2	no	—
457	D₄×C₃₁	—	8	1	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	4	2	no	—
477	C₂×C₄×C₃₁	—	4	2	no	—
478	C₂×C₄×C₃₁	—	4	2	no	—
479	C₂×C₄×C₃₁	—	4	2	no	—
480	C₂×C₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	8	1	no	—
482	C₂×C₄×C₃₁	—	8	1	no	—
483	C₂×C₄×C₃₁	—	8	1	no	—
484	C₂×C₄×C₃₁	—	8	1	no	—
485	C₂×C₄×C₃₁	—	8	1	no	—
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	1	yes	characteristic
489	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
496	C₈×C₃₁	—	2	1	no	—
497	C₈×C₃₁	—	2	1	no	—
498	C₈×C₃₁	—	2	1	no	—
499	C₈×C₃₁	—	2	1	no	—
500	C₈×C₃₁	—	2	2	no	—
501	C₈×C₃₁	—	2	2	no	—
502	#3495	C₂×C₃₁	1	1	yes	characteristic
503	#3458	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3244	C₂×C₃₁	1	2	yes	complemented
505	#3243	C₂×C₃₁	1	2	yes	complemented
506	#3242	C₂×C₃₁	1	2	yes	complemented
507	#3242	C₂×C₃₁	1	2	yes	complemented
508	#3240	C₂×C₃₁	1	2	yes	complemented
509	#3237	C₂×C₃₁	1	2	yes	complemented
510	#3233	C₂×C₃₁	1	2	yes	complemented
511	#3231	C₂×C₃₁	1	2	yes	complemented
512	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3093	C₂×C₃₁	1	1	yes	characteristic
518	#3091	C₂×C₃₁	1	1	yes	characteristic
519	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
525	C₂²×C₃₁	—	2	1	no	—
526	C₂²×C₃₁	—	2	1	no	—
527	C₂²×C₃₁	—	2	1	no	—
528	C₂²×C₃₁	—	2	1	no	—
529	C₂²×C₃₁	—	2	1	no	—
530	C₂²×C₃₁	—	2	1	no	—
531	C₂²×C₃₁	—	2	1	no	—
532	C₂²×C₃₁	—	2	1	no	—
533	C₂²×C₃₁	—	4	1	no	—
534	C₂²×C₃₁	—	4	1	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	8	2	no	—
537	C₂²×C₃₁	#536	1	2	yes	—
538	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	2	2	no	—
543	C₄×C₃₁	—	2	1	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	4	2	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	1	no	—
548	C₄×C₃₁	—	4	1	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	1	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	1	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	2	no	—
556	C₄×C₃₁	#536	1	2	yes	—
557	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
559	#556	—	2	1	no	—
560	#554	—	2	1	no	—
561	#552	—	2	2	no	—
562	#552	—	2	1	no	—
563	#552	—	2	1	no	—
564	#551	—	2	2	no	—
565	#544	—	2	1	no	—
566	#544	—	2	1	no	—
567	#544	C₂²×C₃₁	1	1	yes	characteristic
568	#544	C₂²×C₃₁	1	1	yes	characteristic
569	#544	C₂²×C₃₁	1	1	yes	characteristic
570	#544	C₂²×C₃₁	1	1	yes	characteristic
571	#544	C₂²×C₃₁	1	1	yes	characteristic
572	#544	C₂²×C₃₁	1	2	yes	—
573	#544	C₂²×C₃₁	1	2	yes	—
574	#543	—	2	2	no	—
575	#542	C₂²×C₃₁	1	2	yes	—
576	#541	C₂²×C₃₁	1	2	yes	—
577	#536	C₂²×C₃₁	1	1	yes	characteristic
578	#533	—	2	2	no	—
579	#533	—	2	1	no	—
580	#533	—	2	1	no	—
581	#533	C₂²×C₃₁	1	2	yes	—
582	#533	C₂²×C₃₁	1	2	yes	—
583	#533	C₂²×C₃₁	1	2	yes	—
584	#529	C₂²×C₃₁	1	2	yes	—
585	#525	C₂²×C₃₁	1	1	yes	characteristic
586	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
587	#520	C₂²×C₃₁	1	1	yes	characteristic
588	#519	C₂²×C₃₁	1	1	yes	characteristic
589	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
591	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
592	#501	C₂²×C₃₁	1	2	yes	complemented
593	#501	C₂²×C₃₁	1	2	yes	complemented
594	#501	C₂²×C₃₁	1	2	yes	complemented
595	#501	C₂²×C₃₁	1	2	yes	complemented
596	#500	C₂²×C₃₁	1	2	yes	complemented
597	#499	C₂²×C₃₁	1	2	yes	complemented
598	#499	C₂²×C₃₁	1	2	yes	complemented
599	#498	C₂²×C₃₁	1	2	yes	complemented
600	#491	C₂²×C₃₁	1	2	yes	complemented
601	#491	C₂²×C₃₁	1	2	yes	complemented
602	#489	C₂²×C₃₁	1	2	yes	complemented
603	#489	C₂²×C₃₁	1	2	yes	complemented
604	#488	C₂²×C₃₁	1	2	yes	complemented
605	#488	C₂²×C₃₁	1	2	yes	complemented
606	#487	C₂²×C₃₁	1	2	yes	complemented
607	#487	C₂²×C₃₁	1	2	yes	complemented
608	#485	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
613	#485	C₂²×C₃₁	1	1	yes	characteristic
614	#485	C₂²×C₃₁	1	2	yes	—
615	#485	C₂²×C₃₁	1	2	yes	—
616	#485	C₂²×C₃₁	1	2	yes	—
617	#485	C₂²×C₃₁	1	2	yes	—
618	#484	C₂²×C₃₁	1	1	yes	characteristic
619	#484	C₂²×C₃₁	1	2	yes	—
620	#483	C₂²×C₃₁	1	1	yes	characteristic
621	#483	C₂²×C₃₁	1	2	yes	—
622	#482	C₂²×C₃₁	1	1	yes	characteristic
623	#482	C₂²×C₃₁	1	1	yes	characteristic
624	#482	C₂²×C₃₁	1	2	yes	—
625	#482	C₂²×C₃₁	1	2	yes	—
626	#481	C₂²×C₃₁	1	1	yes	characteristic
627	#480	C₂²×C₃₁	1	1	yes	characteristic
628	#479	C₂²×C₃₁	1	2	yes	complemented
629	#479	C₂²×C₃₁	1	2	yes	complemented
630	#479	C₂²×C₃₁	1	2	yes	complemented
631	#479	C₂²×C₃₁	1	2	yes	complemented
632	#479	C₂²×C₃₁	1	2	yes	complemented
633	#479	C₂²×C₃₁	1	2	yes	complemented
634	#478	C₂²×C₃₁	1	2	yes	complemented
635	#478	C₂²×C₃₁	1	2	yes	complemented
636	#477	C₂²×C₃₁	1	2	yes	complemented
637	#477	C₂²×C₃₁	1	2	yes	complemented
638	#477	C₂²×C₃₁	1	2	yes	complemented
639	#476	C₂²×C₃₁	1	2	yes	complemented
640	#475	C₂²×C₃₁	1	2	yes	complemented
641	#475	C₂²×C₃₁	1	2	yes	complemented
642	#475	C₂²×C₃₁	1	2	yes	complemented
643	#474	C₂²×C₃₁	1	2	yes	complemented
644	#433	C₂²×C₃₁	1	2	yes	—
645	#433	C₂²×C₃₁	1	2	yes	—
646	#432	C₂²×C₃₁	1	2	yes	—
647	#431	C₂²×C₃₁	1	2	yes	—
648	#428	C₂²×C₃₁	1	1	yes	characteristic
649	#428	C₂²×C₃₁	1	1	yes	characteristic
650	#428	C₂²×C₃₁	1	1	yes	characteristic
651	#428	C₂²×C₃₁	1	1	yes	characteristic
652	#427	C₂²×C₃₁	1	1	yes	characteristic
653	#427	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
656	#424	C₂²×C₃₁	1	1	yes	characteristic
657	#424	C₂²×C₃₁	1	1	yes	characteristic
658	#419	C₂²×C₃₁	1	1	yes	characteristic
659	#419	C₂²×C₃₁	1	1	yes	characteristic
660	#417	C₂²×C₃₁	1	1	yes	characteristic
661	#417	C₂²×C₃₁	1	1	yes	characteristic
662	#416	C₂²×C₃₁	1	1	yes	characteristic
663	#416	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
665	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
666	#407	C₂²×C₃₁	1	1	yes	characteristic
667	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
668	#405	C₂²×C₃₁	1	1	yes	characteristic
669	#405	C₂²×C₃₁	1	1	yes	characteristic
670	C₂×C₃₁	—	2	2	no	—
671	C₂×C₃₁	—	4	1	no	—
672	C₂×C₃₁	—	4	1	no	—
673	C₂×C₃₁	—	8	1	no	—
674	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
675	C₂×C₃₁	#3584	1	1	yes	characteristic
676	C₂×C₃₁	#3586	1	1	yes	characteristic
677	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
678	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
682	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
683	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	1	no	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#125	—	2	1	no	—
702	#125	—	2	1	no	—
703	#125	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	1	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	C₂³×C₃₁	1	2	yes	—
712	#125	C₂³×C₃₁	1	2	yes	—
713	#125	C₂³×C₃₁	1	2	yes	—
714	#125	C₂³×C₃₁	1	2	yes	—
715	#125	C₂³×C₃₁	1	2	yes	—
716	#124	—	2	2	no	—
717	#124	C₂³×C₃₁	1	2	yes	—
718	#123	—	2	1	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
742	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
743	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	#121	C₂³×C₃₁	1	1	yes	characteristic
746	#121	C₂³×C₃₁	1	1	yes	characteristic
747	#120	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	2	no	—
753	C₄×Q₈	—	2	2	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	C₂³×C₃₁	1	2	yes	—
763	#117	—	2	1	no	—
764	#117	—	2	1	no	—
765	#117	—	2	1	no	—
766	#117	—	2	1	no	—
767	#117	—	2	2	no	—
768	#117	—	2	1	no	—
769	#117	—	2	2	no	—
770	#117	—	2	2	no	—
771	#117	D₄×C₃₁	1	1	yes	characteristic
772	#117	D₄×C₃₁	1	2	yes	—
773	#117	D₄×C₃₁	1	1	yes	characteristic
774	#117	C₂³×C₃₁	1	2	yes	—
775	#117	C₂³×C₃₁	1	1	yes	characteristic
776	#117	C₂³×C₃₁	1	1	yes	characteristic
777	#117	C₂³×C₃₁	1	1	yes	characteristic
778	#117	C₂³×C₃₁	1	1	yes	characteristic
779	#117	C₂³×C₃₁	1	2	yes	—
780	#117	C₂³×C₃₁	1	1	yes	characteristic
781	#117	C₂³×C₃₁	1	1	yes	characteristic
782	#117	C₂³×C₃₁	1	1	yes	characteristic
783	#117	C₂³×C₃₁	1	2	yes	—
784	C₂×C₄⋊C₄	—	2	1	no	—
785	C₂×C₄⋊C₄	—	2	1	no	—
786	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
787	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	—	2	1	no	—
794	C₂×C₂²⋊C₄	—	2	1	no	—
795	C₂×C₂²⋊C₄	—	2	1	no	—
796	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
797	C₂×C₄²	—	2	1	no	—
798	C₂×C₄²	—	2	1	no	—
799	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
800	#107	C₂³×C₃₁	1	2	yes	—
801	#107	C₂³×C₃₁	1	2	yes	—
802	#107	C₂³×C₃₁	1	1	yes	characteristic
803	#107	C₂³×C₃₁	1	1	yes	characteristic
804	#107	C₂³×C₃₁	1	1	yes	characteristic
805	#107	C₂³×C₃₁	1	1	yes	characteristic
806	#107	C₂³×C₃₁	1	2	yes	—
807	#107	C₂³×C₃₁	1	2	yes	—
808	#107	C₂³×C₃₁	1	2	yes	—
809	#107	C₂³×C₃₁	1	2	yes	—
810	#106	C₂³×C₃₁	1	2	yes	—
811	#106	C₂³×C₃₁	1	2	yes	—
812	#106	C₂³×C₃₁	1	1	yes	characteristic
813	#106	C₂³×C₃₁	1	1	yes	characteristic
814	#106	C₂³×C₃₁	1	1	yes	characteristic
815	#106	C₂³×C₃₁	1	1	yes	characteristic
816	#106	C₂³×C₃₁	1	2	yes	—
817	#106	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	2	yes	—
819	#106	C₂³×C₃₁	1	2	yes	—
820	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
821	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
824	#103	C₂³×C₃₁	1	2	yes	—
825	#103	C₂³×C₃₁	1	2	yes	—
826	#103	C₂³×C₃₁	1	2	yes	—
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	1	yes	characteristic
829	#103	C₂³×C₃₁	1	1	yes	characteristic
830	#103	C₂³×C₃₁	1	1	yes	characteristic
831	#103	C₂³×C₃₁	1	1	yes	characteristic
832	#103	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#102	C₂³×C₃₁	1	1	yes	characteristic
839	#102	C₂³×C₃₁	1	1	yes	characteristic
840	#102	C₂³×C₃₁	1	1	yes	characteristic
841	#102	C₂³×C₃₁	1	1	yes	characteristic
842	#102	C₂³×C₃₁	1	2	yes	—
843	#102	C₂³×C₃₁	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
850	#97	C₂³×C₃₁	1	2	yes	—
851	#97	C₂³×C₃₁	1	2	yes	—
852	C₄×C₈	C₂³×C₃₁	1	2	yes	—
853	C₄×C₈	C₂³×C₃₁	1	2	yes	—
854	C₃₁	#60876	1	1	yes	characteristic, direct product factor, Sylow
855	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
867	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
883	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
884	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
886	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
890	M₁₆	—	2	2	no	—
891	M₁₆	—	2	2	no	—
892	C₂×C₈	—	2	2	no	—
893	C₂×C₈	—	2	2	no	—
894	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
897	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
898	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	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	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
931	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
932	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
941	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
942	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	C₂×D₄×C₃₁	1	2	yes	—
975	C₄²	C₂×D₄×C₃₁	1	2	yes	—
976	C₄²	C₂⁴×C₃₁	1	2	yes	—
977	C₄²	C₂⁴×C₃₁	1	2	yes	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	1	no	—
982	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
983	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
984	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	8	2	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	—	8	2	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	8	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	1	no	—
1024	C₂×C₄	—	8	1	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1034	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1035	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1036	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1037	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	2	2	no	—
1043	C₈	—	2	2	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	8	2	no	—
1056	C₂²	C₃₁×#536	1	2	yes	—
1057	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	C₃₁×#536	1	2	yes	—
1076	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1077	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1078	C₂	—	2	2	no	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	1	no	—
1081	C₂	—	8	1	no	—
1082	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
1083	C₂	C₃₁×#3584	1	1	yes	characteristic
1084	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×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3458	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×#3237	C₂	semidirect
9. C₃₁×#3233	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
15. C₃₁×#3095	C₂	semidirect
18. C₂×C₃₁×#485	C₂	semidirect
19. C₃₁×#3084	C₂	semidirect
20. C₃₁×#3083	C₂	semidirect
21. C₃₁×#3082	C₂	semidirect
22. C₃₁×#3082	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#501	C₂²	semidirect
61. C₃₁×#500	C₂²	semidirect
62. C₃₁×#499	C₂²	semidirect
63. C₃₁×#499	C₂²	semidirect
64. C₃₁×#498	C₂²	semidirect
65. C₃₁×#491	C₂²	semidirect
66. C₃₁×#491	C₂²	semidirect
67. C₃₁×#489	C₂²	semidirect
68. C₃₁×#489	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#488	C₂²	semidirect
71. C₃₁×#487	C₂²	semidirect
72. C₃₁×#487	C₂²	semidirect
93. C₃₁×#479	C₂²	semidirect
94. C₃₁×#479	C₂²	semidirect
95. C₃₁×#479	C₂²	semidirect
96. C₃₁×#479	C₂²	semidirect
97. C₃₁×#479	C₂²	semidirect
98. C₃₁×#479	C₂²	semidirect
99. C₃₁×#478	C₂²	semidirect
100. C₃₁×#478	C₂²	semidirect
101. C₃₁×#477	C₂²	semidirect
102. C₃₁×#477	C₂²	semidirect
103. C₃₁×#477	C₂²	semidirect
104. C₃₁×#476	C₂²	semidirect
105. C₃₁×#475	C₂²	semidirect
106. C₃₁×#475	C₂²	semidirect
107. C₃₁×#475	C₂²	semidirect
108. C₃₁×#474	C₂²	semidirect
435. #60876	C₃₁	direct (N × H)
503. #3458	C₂×C₃₁	semidirect
504. #3244	C₂×C₃₁	semidirect
505. #3243	C₂×C₃₁	semidirect
506. #3242	C₂×C₃₁	semidirect
507. #3242	C₂×C₃₁	semidirect
508. #3240	C₂×C₃₁	semidirect
509. #3237	C₂×C₃₁	semidirect
510. #3233	C₂×C₃₁	semidirect
511. #3231	C₂×C₃₁	semidirect
512. #3164	C₂×C₃₁	semidirect
513. #3163	C₂×C₃₁	semidirect
514. #3137	C₂×C₃₁	semidirect
515. #3137	C₂×C₃₁	semidirect
516. #3095	C₂×C₃₁	semidirect
519. C₂×#485	C₂×C₃₁	semidirect
520. #3084	C₂×C₃₁	semidirect
521. #3083	C₂×C₃₁	semidirect
522. #3082	C₂×C₃₁	semidirect
523. #3082	C₂×C₃₁	semidirect
524. #2924	C₂×C₃₁	semidirect
592. #501	C₂²×C₃₁	semidirect
593. #501	C₂²×C₃₁	semidirect
594. #501	C₂²×C₃₁	semidirect
595. #501	C₂²×C₃₁	semidirect
596. #500	C₂²×C₃₁	semidirect
597. #499	C₂²×C₃₁	semidirect
598. #499	C₂²×C₃₁	semidirect
599. #498	C₂²×C₃₁	semidirect
600. #491	C₂²×C₃₁	semidirect
601. #491	C₂²×C₃₁	semidirect
602. #489	C₂²×C₃₁	semidirect
603. #489	C₂²×C₃₁	semidirect
604. #488	C₂²×C₃₁	semidirect
605. #488	C₂²×C₃₁	semidirect
606. #487	C₂²×C₃₁	semidirect
607. #487	C₂²×C₃₁	semidirect
628. #479	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
631. #479	C₂²×C₃₁	semidirect
632. #479	C₂²×C₃₁	semidirect
633. #479	C₂²×C₃₁	semidirect
634. #478	C₂²×C₃₁	semidirect
635. #478	C₂²×C₃₁	semidirect
636. #477	C₂²×C₃₁	semidirect
637. #477	C₂²×C₃₁	semidirect
638. #477	C₂²×C₃₁	semidirect
639. #476	C₂²×C₃₁	semidirect
640. #475	C₂²×C₃₁	semidirect
641. #475	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
643. #474	C₂²×C₃₁	semidirect
854. C₃₁	#60876	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×#3495	2
C₃₁×#3458	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3240	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3164	2
C₃₁×#3163	2
C₃₁×#3137	2
C₃₁×#3095	2
C₃₁×#3093	2
C₃₁×#3091	2
C₂×C₃₁×#485	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3082	2
C₃₁×#2924	2
#60876	31

Subgroups — C31×#60876 #21517635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60876 #21517635