Subgroups — C₃₁×#60890 #21517649

Order 7936.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 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×#3460	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×#3241	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3228	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×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#478	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	2	no	—
28	C₃₁×#554	—	2	1	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	complemented
34	C₃₁×#544	C₂²	1	2	yes	complemented
35	C₃₁×#542	—	2	1	no	—
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#540	—	2	1	no	—
38	C₃₁×#540	C₂²	1	2	yes	—
39	C₃₁×#538	—	2	2	no	—
40	C₃₁×#537	C₂²	1	1	yes	characteristic
41	C₃₁×#535	C₂²	1	1	yes	characteristic
42	C₃₁×#535	C₂²	1	1	yes	characteristic
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#533	C₂²	1	2	yes	complemented
45	C₃₁×#532	—	2	1	no	—
46	C₃₁×#532	C₂²	1	2	yes	—
47	C₃₁×#529	—	2	1	no	—
48	C₃₁×#529	C₂²	1	2	yes	—
49	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	2	no	—
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×D₄×C₃₁	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×#490	C₂²	1	2	yes	—
66	C₃₁×#490	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×#486	C₂²	1	2	yes	—
72	C₃₁×#486	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	complemented
74	C₃₁×#485	C₂²	1	2	yes	complemented
75	C₃₁×#484	C₂²	1	2	yes	complemented
76	C₃₁×#483	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#482	C₂²	1	2	yes	—
80	C₃₁×#482	C₂²	1	2	yes	—
81	C₃₁×#482	C₂²	1	2	yes	complemented
82	C₃₁×#482	C₂²	1	2	yes	complemented
83	C₃₁×#481	C₂²	1	2	yes	—
84	C₃₁×#481	C₂²	1	2	yes	—
85	C₃₁×#481	C₂²	1	2	yes	complemented
86	C₃₁×#480	C₂²	1	2	yes	—
87	C₃₁×#480	C₂²	1	2	yes	—
88	C₃₁×#480	C₂²	1	2	yes	complemented
89	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#479	C₂²	1	2	yes	complemented
92	C₃₁×#479	C₂²	1	2	yes	complemented
93	C₃₁×#478	C₂²	1	2	yes	—
94	C₃₁×#478	C₂²	1	2	yes	—
95	C₃₁×#478	C₂²	1	2	yes	—
96	C₃₁×#478	C₂²	1	2	yes	—
97	C₃₁×#478	C₂²	1	2	yes	—
98	C₃₁×#478	C₂²	1	2	yes	—
99	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#478	C₂²	1	2	yes	complemented
102	C₃₁×#478	C₂²	1	2	yes	complemented
103	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#476	C₂²	1	2	yes	—
105	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#474	C₂²	1	2	yes	—
108	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#433	C₂²	1	2	yes	complemented
111	C₃₁×#432	C₂²	1	2	yes	complemented
112	C₃₁×#431	C₂²	1	2	yes	complemented
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×#418	C₂²	1	1	yes	characteristic
124	C₃₁×#418	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×#102	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	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	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	—	2	1	no	—
140	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	—	2	1	no	—
145	C₃₁×C₄⋊Q₈	—	2	1	no	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
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×#127	—	2	1	no	—
155	C₃₁×#127	C₂³	1	2	yes	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#125	—	2	1	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	—	2	1	no	—
161	C₃₁×#125	—	2	2	no	—
162	C₃₁×#125	—	2	2	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	1	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	1	yes	characteristic
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	2	yes	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#120	—	2	2	no	—
207	C₃₁×#120	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	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	2	yes	—
229	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
230	C₄×D₄×C₃₁	D₄	1	2	yes	—
231	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	2	no	—
238	C₃₁×#117	C₂³	1	1	yes	characteristic
239	C₃₁×#117	C₂³	1	1	yes	characteristic
240	C₃₁×#117	C₂³	1	1	yes	characteristic
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₃₁×#117	C₂³	1	2	yes	—
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	2	yes	—
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×C₂²⋊C₄×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	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
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	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	8	4	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₃₁	—	2	1	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	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	—	8	2	no	—
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	M₁₆×C₃₁	—	2	2	no	—
356	M₁₆×C₃₁	—	2	2	no	—
357	C₂×C₈×C₃₁	—	2	2	no	—
358	C₂×C₈×C₃₁	—	2	2	no	—
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
420	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₄²×C₃₁	—	2	1	no	—
424	C₄²×C₃₁	—	2	1	no	—
425	C₄²×C₃₁	—	2	1	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₃₁	C₂×D₄	1	2	yes	—
432	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	C₂⁴	1	2	yes	—
435	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
437	#60890	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂³×C₃₁	—	2	2	no	—
439	C₂³×C₃₁	—	2	1	no	—
440	C₂³×C₃₁	—	4	2	no	—
441	C₂³×C₃₁	—	8	1	no	—
442	C₂³×C₃₁	—	8	1	no	—
443	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
444	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	2	1	no	—
448	Q₈×C₃₁	—	8	1	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	Q₈×C₃₁	—	8	1	no	—
451	Q₈×C₃₁	—	8	2	no	—
452	Q₈×C₃₁	—	8	2	no	—
453	D₄×C₃₁	—	2	4	no	—
454	D₄×C₃₁	—	2	2	no	—
455	D₄×C₃₁	—	2	2	no	—
456	D₄×C₃₁	—	2	2	no	—
457	D₄×C₃₁	—	2	1	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	4	2	no	—
460	D₄×C₃₁	—	4	2	no	—
461	D₄×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	8	2	no	—
463	D₄×C₃₁	—	8	2	no	—
464	D₄×C₃₁	—	8	2	no	—
465	D₄×C₃₁	—	8	2	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	4	1	no	—
479	C₂×C₄×C₃₁	—	4	1	no	—
480	C₂×C₄×C₃₁	—	4	2	no	—
481	C₂×C₄×C₃₁	—	4	2	no	—
482	C₂×C₄×C₃₁	—	4	4	no	—
483	C₂×C₄×C₃₁	—	4	2	no	—
484	C₂×C₄×C₃₁	—	4	2	no	—
485	C₂×C₄×C₃₁	—	8	1	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	—	8	1	no	—
488	C₂×C₄×C₃₁	—	8	2	no	—
489	C₂×C₄×C₃₁	—	8	1	no	—
490	C₂×C₄×C₃₁	—	8	2	no	—
491	C₂×C₄×C₃₁	—	8	1	no	—
492	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
501	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
502	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
503	C₈×C₃₁	—	2	1	no	—
504	C₈×C₃₁	—	2	1	no	—
505	C₈×C₃₁	—	2	1	no	—
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	—	2	2	no	—
508	C₈×C₃₁	—	2	2	no	—
509	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3460	C₂×C₃₁	1	1	yes	characteristic
511	#3244	C₂×C₃₁	1	2	yes	complemented
512	#3243	C₂×C₃₁	1	2	yes	complemented
513	#3241	C₂×C₃₁	1	2	yes	complemented
514	#3241	C₂×C₃₁	1	2	yes	complemented
515	#3240	C₂×C₃₁	1	2	yes	complemented
516	#3234	C₂×C₃₁	1	2	yes	complemented
517	#3232	C₂×C₃₁	1	2	yes	complemented
518	#3228	C₂×C₃₁	1	2	yes	complemented
519	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
530	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
532	C₂²×C₃₁	—	2	1	no	—
533	C₂²×C₃₁	—	2	1	no	—
534	C₂²×C₃₁	—	2	2	no	—
535	C₂²×C₃₁	—	2	2	no	—
536	C₂²×C₃₁	—	2	2	no	—
537	C₂²×C₃₁	—	4	1	no	—
538	C₂²×C₃₁	—	4	2	no	—
539	C₂²×C₃₁	—	4	2	no	—
540	C₂²×C₃₁	—	4	1	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	—	8	4	no	—
544	C₂²×C₃₁	#536	1	2	yes	—
545	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
546	C₄×C₃₁	—	2	1	no	—
547	C₄×C₃₁	—	2	1	no	—
548	C₄×C₃₁	—	2	2	no	—
549	C₄×C₃₁	—	2	1	no	—
550	C₄×C₃₁	—	2	1	no	—
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	2	2	no	—
553	C₄×C₃₁	—	4	2	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	1	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	2	no	—
558	C₄×C₃₁	—	4	1	no	—
559	C₄×C₃₁	—	4	2	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	#536	1	2	yes	—
564	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
565	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	#557	—	2	1	no	—
567	#557	—	2	1	no	—
568	#554	—	2	2	no	—
569	#554	—	2	2	no	—
570	#554	—	2	1	no	—
571	#554	—	2	1	no	—
572	#544	C₂²×C₃₁	1	1	yes	characteristic
573	#544	C₂²×C₃₁	1	1	yes	characteristic
574	#544	C₂²×C₃₁	1	1	yes	characteristic
575	#544	C₂²×C₃₁	1	2	yes	complemented
576	#544	C₂²×C₃₁	1	2	yes	complemented
577	#542	—	2	1	no	—
578	#542	C₂²×C₃₁	1	2	yes	—
579	#540	—	2	1	no	—
580	#540	C₂²×C₃₁	1	2	yes	—
581	#538	—	2	2	no	—
582	#537	C₂²×C₃₁	1	1	yes	characteristic
583	#535	C₂²×C₃₁	1	1	yes	characteristic
584	#535	C₂²×C₃₁	1	1	yes	characteristic
585	#533	C₂²×C₃₁	1	1	yes	characteristic
586	#533	C₂²×C₃₁	1	2	yes	complemented
587	#532	—	2	1	no	—
588	#532	C₂²×C₃₁	1	2	yes	—
589	#529	—	2	1	no	—
590	#529	C₂²×C₃₁	1	2	yes	—
591	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
593	#525	—	2	2	no	—
594	#520	C₂²×C₃₁	1	1	yes	characteristic
595	#520	C₂²×C₃₁	1	1	yes	characteristic
596	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
597	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
599	#501	C₂²×C₃₁	1	2	yes	complemented
600	#501	C₂²×C₃₁	1	2	yes	complemented
601	#501	C₂²×C₃₁	1	2	yes	complemented
602	#501	C₂²×C₃₁	1	2	yes	complemented
603	#500	C₂²×C₃₁	1	2	yes	complemented
604	#499	C₂²×C₃₁	1	2	yes	complemented
605	#499	C₂²×C₃₁	1	2	yes	complemented
606	#498	C₂²×C₃₁	1	2	yes	complemented
607	#490	C₂²×C₃₁	1	2	yes	—
608	#490	C₂²×C₃₁	1	2	yes	—
609	#489	C₂²×C₃₁	1	2	yes	—
610	#489	C₂²×C₃₁	1	2	yes	—
611	#488	C₂²×C₃₁	1	2	yes	—
612	#488	C₂²×C₃₁	1	2	yes	—
613	#486	C₂²×C₃₁	1	2	yes	—
614	#486	C₂²×C₃₁	1	2	yes	—
615	#485	C₂²×C₃₁	1	2	yes	complemented
616	#485	C₂²×C₃₁	1	2	yes	complemented
617	#484	C₂²×C₃₁	1	2	yes	complemented
618	#483	C₂²×C₃₁	1	2	yes	complemented
619	#482	C₂²×C₃₁	1	2	yes	—
620	#482	C₂²×C₃₁	1	2	yes	—
621	#482	C₂²×C₃₁	1	2	yes	—
622	#482	C₂²×C₃₁	1	2	yes	—
623	#482	C₂²×C₃₁	1	2	yes	complemented
624	#482	C₂²×C₃₁	1	2	yes	complemented
625	#481	C₂²×C₃₁	1	2	yes	—
626	#481	C₂²×C₃₁	1	2	yes	—
627	#481	C₂²×C₃₁	1	2	yes	complemented
628	#480	C₂²×C₃₁	1	2	yes	—
629	#480	C₂²×C₃₁	1	2	yes	—
630	#480	C₂²×C₃₁	1	2	yes	complemented
631	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#479	C₂²×C₃₁	1	2	yes	complemented
634	#479	C₂²×C₃₁	1	2	yes	complemented
635	#478	C₂²×C₃₁	1	2	yes	—
636	#478	C₂²×C₃₁	1	2	yes	—
637	#478	C₂²×C₃₁	1	2	yes	—
638	#478	C₂²×C₃₁	1	2	yes	—
639	#478	C₂²×C₃₁	1	2	yes	—
640	#478	C₂²×C₃₁	1	2	yes	—
641	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#478	C₂²×C₃₁	1	2	yes	complemented
644	#478	C₂²×C₃₁	1	2	yes	complemented
645	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#476	C₂²×C₃₁	1	2	yes	—
647	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#474	C₂²×C₃₁	1	2	yes	—
650	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#433	C₂²×C₃₁	1	2	yes	complemented
652	#433	C₂²×C₃₁	1	2	yes	complemented
653	#432	C₂²×C₃₁	1	2	yes	complemented
654	#431	C₂²×C₃₁	1	2	yes	complemented
655	#428	C₂²×C₃₁	1	1	yes	characteristic
656	#428	C₂²×C₃₁	1	1	yes	characteristic
657	#428	C₂²×C₃₁	1	1	yes	characteristic
658	#428	C₂²×C₃₁	1	1	yes	characteristic
659	#427	C₂²×C₃₁	1	1	yes	characteristic
660	#427	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
662	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
663	#423	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
665	#418	C₂²×C₃₁	1	1	yes	characteristic
666	#418	C₂²×C₃₁	1	1	yes	characteristic
667	#417	C₂²×C₃₁	1	1	yes	characteristic
668	#417	C₂²×C₃₁	1	1	yes	characteristic
669	#416	C₂²×C₃₁	1	1	yes	characteristic
670	#416	C₂²×C₃₁	1	1	yes	characteristic
671	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
672	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
673	#408	C₂²×C₃₁	1	1	yes	characteristic
674	#408	C₂²×C₃₁	1	1	yes	characteristic
675	#405	C₂²×C₃₁	1	1	yes	characteristic
676	#405	C₂²×C₃₁	1	1	yes	characteristic
677	C₂×C₃₁	—	2	2	no	—
678	C₂×C₃₁	—	4	2	no	—
679	C₂×C₃₁	—	8	1	no	—
680	C₂×C₃₁	—	8	2	no	—
681	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
682	C₂×C₃₁	#3584	1	1	yes	characteristic
683	C₂×C₃₁	#3585	1	1	yes	characteristic
684	C₂×#41	—	2	2	no	—
685	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
687	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
688	C₂³×C₄	—	2	1	no	—
689	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
703	#127	—	2	1	no	—
704	#127	C₂³×C₃₁	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#125	—	2	1	no	—
708	#125	—	2	1	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	1	no	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	C₂³×C₃₁	1	2	yes	—
717	#125	C₂³×C₃₁	1	2	yes	—
718	#125	C₂³×C₃₁	1	1	yes	characteristic
719	#125	C₂³×C₃₁	1	2	yes	—
720	#125	C₂³×C₃₁	1	2	yes	—
721	#125	C₂³×C₃₁	1	2	yes	—
722	#125	C₂³×C₃₁	1	1	yes	characteristic
723	#124	—	2	1	no	—
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	C₂³×C₃₁	1	2	yes	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
745	#121	—	2	2	no	—
746	#121	—	2	1	no	—
747	#121	—	2	2	no	—
748	#121	—	2	1	no	—
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	C₂³×C₃₁	1	2	yes	—
753	#121	C₂³×C₃₁	1	2	yes	—
754	#121	C₂³×C₃₁	1	2	yes	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	2	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	D₄×C₃₁	1	2	yes	—
778	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
779	C₄×D₄	D₄×C₃₁	1	2	yes	—
780	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₃₁	1	2	yes	—
782	C₄×D₄	C₂³×C₃₁	1	2	yes	—
783	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
785	#117	—	2	1	no	—
786	#117	—	2	2	no	—
787	#117	C₂³×C₃₁	1	1	yes	characteristic
788	#117	C₂³×C₃₁	1	1	yes	characteristic
789	#117	C₂³×C₃₁	1	1	yes	characteristic
790	#117	C₂³×C₃₁	1	2	yes	—
791	#117	C₂³×C₃₁	1	2	yes	—
792	#117	C₂³×C₃₁	1	1	yes	characteristic
793	#117	C₂³×C₃₁	1	2	yes	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
803	C₂×C₂²⋊C₄	—	2	1	no	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
807	#107	C₂³×C₃₁	1	2	yes	—
808	#107	C₂³×C₃₁	1	2	yes	—
809	#107	C₂³×C₃₁	1	1	yes	characteristic
810	#107	C₂³×C₃₁	1	1	yes	characteristic
811	#107	C₂³×C₃₁	1	1	yes	characteristic
812	#107	C₂³×C₃₁	1	1	yes	characteristic
813	#107	C₂³×C₃₁	1	2	yes	—
814	#107	C₂³×C₃₁	1	2	yes	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	2	yes	—
817	#106	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	2	yes	—
819	#106	C₂³×C₃₁	1	1	yes	characteristic
820	#106	C₂³×C₃₁	1	1	yes	characteristic
821	#106	C₂³×C₃₁	1	1	yes	characteristic
822	#106	C₂³×C₃₁	1	1	yes	characteristic
823	#106	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	2	yes	—
826	#106	C₂³×C₃₁	1	2	yes	—
827	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
832	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	1	yes	characteristic
834	#103	C₂³×C₃₁	1	1	yes	characteristic
835	#103	C₂³×C₃₁	1	1	yes	characteristic
836	#103	C₂³×C₃₁	1	1	yes	characteristic
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#102	C₂³×C₃₁	1	2	yes	—
840	#102	C₂³×C₃₁	1	2	yes	—
841	#102	C₂³×C₃₁	1	2	yes	—
842	#102	C₂³×C₃₁	1	2	yes	—
843	#102	C₂³×C₃₁	1	1	yes	characteristic
844	#102	C₂³×C₃₁	1	1	yes	characteristic
845	#102	C₂³×C₃₁	1	1	yes	characteristic
846	#102	C₂³×C₃₁	1	1	yes	characteristic
847	#102	C₂³×C₃₁	1	2	yes	—
848	#102	C₂³×C₃₁	1	2	yes	—
849	#102	C₂³×C₃₁	1	2	yes	—
850	#102	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
857	#97	C₂³×C₃₁	1	2	yes	—
858	#97	C₂³×C₃₁	1	2	yes	—
859	C₄×C₈	C₂³×C₃₁	1	2	yes	—
860	C₄×C₈	C₂³×C₃₁	1	2	yes	—
861	C₃₁	#60890	1	1	yes	characteristic, direct product factor, Sylow
862	C₂⁴	—	2	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	8	4	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
885	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
887	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	8	2	no	—
899	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
905	M₁₆	—	2	2	no	—
906	M₁₆	—	2	2	no	—
907	C₂×C₈	—	2	2	no	—
908	C₂×C₈	—	2	2	no	—
909	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
912	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
913	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	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	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₄²	C₂×D₄×C₃₁	1	2	yes	—
982	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₃₁	1	2	yes	—
984	C₄²	C₂⁴×C₃₁	1	2	yes	—
985	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂³	—	2	2	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	4	2	no	—
990	C₂³	—	8	1	no	—
991	C₂³	—	8	1	no	—
992	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
993	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	4	1	no	—
1028	C₂×C₄	—	4	1	no	—
1029	C₂×C₄	—	4	2	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	8	1	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	1	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	1	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	1	no	—
1041	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1050	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1051	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	2	no	—
1057	C₈	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	8	4	no	—
1070	C₂²	C₃₁×#536	1	2	yes	—
1071	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1072	C₄	—	2	2	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	C₃₁×#536	1	2	yes	—
1090	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1091	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	1	no	—
1096	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
1097	C₂	C₃₁×#3584	1	1	yes	characteristic
1098	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3460	C₂
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×#3241	C₂	semidirect
6. C₃₁×#3241	C₂	semidirect
7. C₃₁×#3240	C₂	semidirect
8. C₃₁×#3234	C₂	semidirect
9. C₃₁×#3232	C₂	semidirect
10. C₃₁×#3228	C₂	semidirect
11. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3163	C₂	semidirect
13. C₃₁×#3136	C₂	semidirect
14. C₃₁×#3136	C₂	semidirect
15. C₃₁×#3099	C₂	semidirect
16. C₃₁×#3098	C₂	semidirect
17. C₃₁×#3096	C₂	semidirect
18. C₃₁×#3096	C₂	semidirect
19. C₃₁×#3080	C₂	semidirect
20. C₃₁×#3077	C₂	semidirect
21. C₃₁×#3076	C₂	semidirect
22. C₂×C₃₁×#478	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
33. C₃₁×#544	C₂²	semidirect
34. C₃₁×#544	C₂²	semidirect
44. C₃₁×#533	C₂²	semidirect
50. C₂×C₃₁×#125	C₂²	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
73. C₃₁×#485	C₂²	semidirect
74. C₃₁×#485	C₂²	semidirect
75. C₃₁×#484	C₂²	semidirect
76. C₃₁×#483	C₂²	semidirect
81. C₃₁×#482	C₂²	semidirect
82. C₃₁×#482	C₂²	semidirect
85. C₃₁×#481	C₂²	semidirect
88. C₃₁×#480	C₂²	semidirect
89. C₃₁×#479	C₂²	semidirect
90. C₃₁×#479	C₂²	semidirect
91. C₃₁×#479	C₂²	semidirect
92. C₃₁×#479	C₂²	semidirect
99. C₃₁×#478	C₂²	semidirect
100. C₃₁×#478	C₂²	semidirect
101. C₃₁×#478	C₂²	semidirect
102. C₃₁×#478	C₂²	semidirect
103. C₃₁×#477	C₂²	semidirect
105. C₃₁×#476	C₂²	semidirect
106. C₃₁×#475	C₂²	semidirect
108. C₃₁×#474	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#433	C₂²	semidirect
111. C₃₁×#432	C₂²	semidirect
112. C₃₁×#431	C₂²	semidirect
437. #60890	C₃₁	direct (N × H)
509. #3504	C₂×C₃₁	semidirect
511. #3244	C₂×C₃₁	semidirect
512. #3243	C₂×C₃₁	semidirect
513. #3241	C₂×C₃₁	semidirect
514. #3241	C₂×C₃₁	semidirect
515. #3240	C₂×C₃₁	semidirect
516. #3234	C₂×C₃₁	semidirect
517. #3232	C₂×C₃₁	semidirect
518. #3228	C₂×C₃₁	semidirect
519. #3164	C₂×C₃₁	semidirect
520. #3163	C₂×C₃₁	semidirect
521. #3136	C₂×C₃₁	semidirect
522. #3136	C₂×C₃₁	semidirect
523. #3099	C₂×C₃₁	semidirect
524. #3098	C₂×C₃₁	semidirect
525. #3096	C₂×C₃₁	semidirect
526. #3096	C₂×C₃₁	semidirect
527. #3080	C₂×C₃₁	semidirect
528. #3077	C₂×C₃₁	semidirect
529. #3076	C₂×C₃₁	semidirect
530. C₂×#478	C₂×C₃₁	semidirect
531. #2925	C₂×C₃₁	semidirect
575. #544	C₂²×C₃₁	semidirect
576. #544	C₂²×C₃₁	semidirect
586. #533	C₂²×C₃₁	semidirect
592. C₂×#125	C₂²×C₃₁	semidirect
599. #501	C₂²×C₃₁	semidirect
600. #501	C₂²×C₃₁	semidirect
601. #501	C₂²×C₃₁	semidirect
602. #501	C₂²×C₃₁	semidirect
603. #500	C₂²×C₃₁	semidirect
604. #499	C₂²×C₃₁	semidirect
605. #499	C₂²×C₃₁	semidirect
606. #498	C₂²×C₃₁	semidirect
615. #485	C₂²×C₃₁	semidirect
616. #485	C₂²×C₃₁	semidirect
617. #484	C₂²×C₃₁	semidirect
618. #483	C₂²×C₃₁	semidirect
623. #482	C₂²×C₃₁	semidirect
624. #482	C₂²×C₃₁	semidirect
627. #481	C₂²×C₃₁	semidirect
630. #480	C₂²×C₃₁	semidirect
631. #479	C₂²×C₃₁	semidirect
632. #479	C₂²×C₃₁	semidirect
633. #479	C₂²×C₃₁	semidirect
634. #479	C₂²×C₃₁	semidirect
641. #478	C₂²×C₃₁	semidirect
642. #478	C₂²×C₃₁	semidirect
643. #478	C₂²×C₃₁	semidirect
644. #478	C₂²×C₃₁	semidirect
645. #477	C₂²×C₃₁	semidirect
647. #476	C₂²×C₃₁	semidirect
648. #475	C₂²×C₃₁	semidirect
650. #474	C₂²×C₃₁	semidirect
651. #433	C₂²×C₃₁	semidirect
652. #433	C₂²×C₃₁	semidirect
653. #432	C₂²×C₃₁	semidirect
654. #431	C₂²×C₃₁	semidirect
861. C₃₁	#60890	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×#3460	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3241	2
C₃₁×#3240	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3228	2
C₃₁×#3164	2
C₃₁×#3163	2
C₃₁×#3136	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#3080	2
C₃₁×#3077	2
C₃₁×#3076	2
C₂×C₃₁×#478	2
C₃₁×#2925	2
#60890	31

Subgroups — C31×#60890 #21517649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60890 #21517649