Subgroups — C₃₁×#62815 #21519574

Order 7936.

7210 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3512	C₂	1	4	yes	maximal, complemented
2	C₃₁×#3511	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3510	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3509	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3508	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3507	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3506	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3505	C₂	1	8	yes	maximal, complemented
9	C₃₁×#3480	C₂	1	8	yes	maximal, complemented
10	C₃₁×#3475	C₂	1	8	yes	maximal, complemented
11	C₃₁×#3455	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3449	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3444	C₂	1	4	yes	maximal, complemented
14	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3428	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	16	yes	complemented
21	C₃₁×#559	C₂²	1	8	yes	complemented
22	C₃₁×#557	C₂²	1	8	yes	complemented
23	C₃₁×#556	C₂²	1	8	yes	complemented
24	C₃₁×#556	C₂²	1	8	yes	complemented
25	C₃₁×#556	C₂²	1	16	yes	complemented
26	C₃₁×#555	C₂²	1	8	yes	complemented
27	C₃₁×#554	C₂²	1	8	yes	complemented
28	C₃₁×#553	C₂²	1	16	yes	complemented
29	C₃₁×#553	C₂²	1	16	yes	complemented
30	C₃₁×#553	C₂²	1	32	yes	complemented
31	C₃₁×#552	C₂²	1	16	yes	complemented
32	C₃₁×#552	C₂²	1	16	yes	complemented
33	C₃₁×#551	C₂²	1	32	yes	complemented
34	C₃₁×#550	C₂²	1	8	yes	complemented
35	C₃₁×#548	C₂²	1	16	yes	complemented
36	C₃₁×#547	C₂²	1	8	yes	complemented
37	C₃₁×#546	C₂²	1	16	yes	complemented
38	C₃₁×#542	C₂²	1	16	yes	complemented
39	C₃₁×#541	C₂²	1	8	yes	complemented
40	C₃₁×#540	C₂²	1	8	yes	complemented
41	C₃₁×#539	C₂²	1	16	yes	complemented
42	C₃₁×#538	C₂²	1	16	yes	complemented
43	C₃₁×#537	C₂²	1	8	yes	complemented
44	C₃₁×#536	C₂²	1	4	yes	—
45	C₃₁×#536	C₂²	1	4	yes	complemented
46	C₃₁×#535	C₂²	1	4	yes	—
47	C₃₁×#535	C₂²	1	4	yes	complemented
48	C₃₁×#534	C₂²	1	8	yes	—
49	C₃₁×#533	C₂²	1	2	yes	complemented
50	C₃₁×#533	C₂²	1	2	yes	complemented
51	C₃₁×#533	C₂²	1	4	yes	complemented
52	C₃₁×#533	C₂²	1	4	yes	complemented
53	C₃₁×#533	C₂²	1	2	yes	complemented
54	C₃₁×#533	C₂²	1	2	yes	complemented
55	C₃₁×#533	C₂²	1	8	yes	complemented
56	C₃₁×#532	C₂²	1	2	yes	—
57	C₃₁×#532	C₂²	1	2	yes	—
58	C₃₁×#532	C₂²	1	4	yes	—
59	C₃₁×#532	C₂²	1	4	yes	complemented
60	C₃₁×#532	C₂²	1	2	yes	complemented
61	C₃₁×#532	C₂²	1	2	yes	complemented
62	C₃₁×#532	C₂²	1	8	yes	complemented
63	C₃₁×#532	C₂²	1	8	yes	complemented
64	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#529	C₂²	1	16	yes	complemented
68	C₃₁×#529	C₂²	1	16	yes	complemented
69	C₃₁×#529	C₂²	1	16	yes	complemented
70	C₃₁×#529	C₂²	1	32	yes	complemented
71	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
72	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
73	C₃₁×#525	C₂²	1	8	yes	—
74	C₃₁×#525	C₂²	1	8	yes	complemented
75	C₃₁×#525	C₂²	1	16	yes	complemented
76	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
77	C₂×C₃₁×#121	C₂²	1	4	yes	—
78	C₃₁×#520	C₂²	1	8	yes	complemented
79	C₃₁×#520	C₂²	1	8	yes	complemented
80	C₃₁×#519	C₂²	1	4	yes	complemented
81	C₃₁×#518	C₂²	1	8	yes	—
82	C₃₁×#518	C₂²	1	4	yes	complemented
83	C₄×#41×C₃₁	C₂²	1	4	yes	—
84	C₄×#41×C₃₁	C₂²	1	2	yes	—
85	C₄×#41×C₃₁	C₂²	1	2	yes	—
86	C₄×#41×C₃₁	C₂²	1	4	yes	complemented
87	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
88	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
89	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
90	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
91	C₄×#41×C₃₁	C₂²	1	16	yes	complemented
92	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
93	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
94	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
95	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
96	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
97	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
98	C₂×C₃₁×#117	C₂²	1	2	yes	—
99	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
100	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
101	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
102	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
103	C₂×#41×C₃₁	—	2	8	no	—
104	C₂×#41×C₃₁	—	2	16	no	—
105	C₂×#41×C₃₁	C₂³	1	2	yes	—
106	C₂×#41×C₃₁	C₂³	1	2	yes	—
107	C₂×#41×C₃₁	C₂³	1	4	yes	—
108	C₂×#41×C₃₁	C₂³	1	2	yes	—
109	C₂×#41×C₃₁	C₂³	1	4	yes	—
110	C₂×#41×C₃₁	C₂³	1	2	yes	—
111	C₂×#41×C₃₁	C₂³	1	4	yes	—
112	C₂×#41×C₃₁	C₂³	1	4	yes	—
113	C₂×#41×C₃₁	C₂³	1	16	yes	—
114	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
120	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
130	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
135	C₃₁×#127	C₂³	1	2	yes	—
136	C₃₁×#127	C₂³	1	2	yes	—
137	C₃₁×#127	C₂³	1	4	yes	—
138	C₃₁×#127	C₂³	1	8	yes	—
139	C₃₁×#126	C₂³	1	32	yes	—
140	C₃₁×#126	C₂³	1	32	yes	—
141	C₃₁×#126	C₂³	1	32	yes	—
142	C₃₁×#125	C₂³	1	4	yes	—
143	C₃₁×#125	C₂³	1	4	yes	—
144	C₃₁×#125	C₂³	1	8	yes	—
145	C₃₁×#125	C₂³	1	16	yes	—
146	C₃₁×#125	C₂³	1	32	yes	—
147	C₃₁×#124	C₂³	1	4	yes	—
148	C₃₁×#124	C₂³	1	4	yes	—
149	C₃₁×#124	C₂³	1	8	yes	—
150	C₃₁×#124	C₂³	1	16	yes	—
151	C₃₁×#124	C₂³	1	32	yes	—
152	C₃₁×#124	C₂³	1	8	yes	—
153	C₃₁×#124	C₂³	1	8	yes	—
154	C₃₁×#123	C₂³	1	16	yes	—
155	C₃₁×#123	C₂³	1	16	yes	—
156	C₃₁×#123	C₂³	1	32	yes	—
157	C₃₁×#123	C₂³	1	32	yes	—
158	C₃₁×#123	C₂³	1	32	yes	—
159	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
160	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
161	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
162	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
163	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
164	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
165	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
166	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
167	C₃₁×#121	C₂³	1	8	yes	—
168	C₃₁×#121	C₂³	1	8	yes	—
169	C₃₁×#121	C₂³	1	8	yes	—
170	C₃₁×#121	C₂³	1	8	yes	—
171	C₃₁×#121	C₂³	1	16	yes	—
172	C₃₁×#121	C₂³	1	16	yes	—
173	C₃₁×#121	C₂³	1	16	yes	—
174	C₃₁×#121	C₂³	1	32	yes	—
175	C₃₁×#121	C₂³	1	32	yes	—
176	C₃₁×#120	C₂³	1	16	yes	—
177	C₃₁×#120	C₂³	1	16	yes	—
178	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
179	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
180	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
181	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
182	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
183	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
184	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
185	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
186	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
187	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
188	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
189	C₄×D₄×C₃₁	C₂³	1	8	yes	—
190	C₄×D₄×C₃₁	C₂³	1	8	yes	—
191	C₄×D₄×C₃₁	C₂³	1	8	yes	—
192	C₄×D₄×C₃₁	C₂³	1	8	yes	—
193	C₄×D₄×C₃₁	C₂³	1	4	yes	—
194	C₄×D₄×C₃₁	C₂³	1	4	yes	—
195	C₄×D₄×C₃₁	C₂³	1	4	yes	—
196	C₄×D₄×C₃₁	C₂³	1	4	yes	—
197	C₄×D₄×C₃₁	C₂³	1	8	yes	—
198	C₄×D₄×C₃₁	C₂³	1	8	yes	—
199	C₄×D₄×C₃₁	C₂³	1	8	yes	—
200	C₄×D₄×C₃₁	C₂³	1	8	yes	—
201	C₄×D₄×C₃₁	C₂³	1	32	yes	—
202	C₄×D₄×C₃₁	C₂³	1	32	yes	—
203	C₄×D₄×C₃₁	C₂³	1	16	yes	—
204	C₄×D₄×C₃₁	C₂³	1	16	yes	—
205	C₄×D₄×C₃₁	C₂³	1	32	yes	—
206	C₄×D₄×C₃₁	C₂³	1	32	yes	—
207	C₄×D₄×C₃₁	C₂³	1	16	yes	—
208	C₃₁×#117	C₂³	1	2	yes	—
209	C₃₁×#117	C₂³	1	4	yes	—
210	C₃₁×#117	C₂³	1	2	yes	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₃₁×#117	C₂³	1	2	yes	—
213	C₃₁×#117	C₂³	1	4	yes	—
214	C₃₁×#117	C₂³	1	4	yes	—
215	C₃₁×#117	C₂³	1	4	yes	—
216	C₃₁×#117	C₂³	1	8	yes	—
217	C₃₁×#117	C₂³	1	4	yes	—
218	C₃₁×#117	C₂³	1	4	yes	—
219	C₃₁×#117	C₂³	1	16	yes	—
220	C₃₁×#117	C₂³	1	16	yes	—
221	C₃₁×#117	C₂³	1	16	yes	—
222	C₃₁×#117	C₂³	1	16	yes	—
223	C₃₁×#117	C₂³	1	32	yes	—
224	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
226	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
227	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
228	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
231	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
233	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
234	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
235	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
236	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
239	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
240	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
241	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
246	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
247	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
248	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
249	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
250	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
251	C₂×C₄²×C₃₁	C₂³	1	16	yes	—
252	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
253	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
254	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
255	#41×C₃₁	—	2	8	no	—
256	#41×C₃₁	—	2	16	no	—
257	#41×C₃₁	—	2	8	no	—
258	#41×C₃₁	—	2	16	no	—
259	#41×C₃₁	—	2	8	no	—
260	#41×C₃₁	—	2	16	no	—
261	#41×C₃₁	—	2	8	no	—
262	#41×C₃₁	—	2	16	no	—
263	#41×C₃₁	—	4	32	no	—
264	C₂×Q₈×C₃₁	—	2	8	no	—
265	C₂×Q₈×C₃₁	—	2	4	no	—
266	C₂×Q₈×C₃₁	—	4	8	no	—
267	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
269	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
270	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
273	C₂×D₄×C₃₁	—	2	8	no	—
274	C₂×D₄×C₃₁	—	2	16	no	—
275	C₂×D₄×C₃₁	—	2	8	no	—
276	C₂×D₄×C₃₁	—	2	4	no	—
277	C₂×D₄×C₃₁	—	4	8	no	—
278	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
279	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
280	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
281	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
282	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
284	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
285	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
287	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
288	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₃₁	—	2	16	no	—
290	C₂²×C₄×C₃₁	—	2	8	no	—
291	C₂²×C₄×C₃₁	—	4	4	no	—
292	C₂²×C₄×C₃₁	—	4	8	no	—
293	C₂²×C₄×C₃₁	#41	1	8	yes	complemented
294	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	—
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
319	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
321	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
322	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
323	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
325	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
326	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
329	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
330	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
331	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
332	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
334	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
337	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
341	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₃₁	C₂⁴	1	4	yes	—
345	C₄²×C₃₁	C₂⁴	1	8	yes	—
346	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₄²×C₃₁	C₂⁴	1	2	yes	—
349	C₄²×C₃₁	C₂⁴	1	2	yes	—
350	C₄²×C₃₁	C₂⁴	1	8	yes	—
351	C₄²×C₃₁	C₂⁴	1	2	yes	—
352	C₄²×C₃₁	C₂⁴	1	2	yes	—
353	C₄²×C₃₁	C₂⁴	1	32	yes	—
354	C₄²×C₃₁	C₂⁴	1	8	yes	—
355	C₄²×C₃₁	C₂⁴	1	4	yes	—
356	C₄²×C₃₁	C₂⁴	1	2	yes	—
357	C₄²×C₃₁	C₂⁴	1	2	yes	—
358	C₄²×C₃₁	C₂⁴	1	8	yes	—
359	#62815	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂³×C₃₁	—	2	4	no	—
361	C₂³×C₃₁	—	2	8	no	—
362	C₂³×C₃₁	—	4	2	no	—
363	C₂³×C₃₁	—	4	4	no	—
364	C₂³×C₃₁	—	4	8	no	—
365	C₂³×C₃₁	C₂×#41	1	4	yes	—
366	C₂³×C₃₁	C₂⁵	1	4	yes	—
367	C₂³×C₃₁	C₂⁵	1	8	yes	—
368	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
369	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
370	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
371	Q₈×C₃₁	—	2	4	no	—
372	Q₈×C₃₁	—	2	8	no	—
373	Q₈×C₃₁	—	2	8	no	—
374	Q₈×C₃₁	—	2	4	no	—
375	Q₈×C₃₁	—	2	16	no	—
376	Q₈×C₃₁	—	4	8	no	—
377	D₄×C₃₁	—	2	8	no	—
378	D₄×C₃₁	—	2	16	no	—
379	D₄×C₃₁	—	2	8	no	—
380	D₄×C₃₁	—	2	16	no	—
381	D₄×C₃₁	—	2	4	no	—
382	D₄×C₃₁	—	2	8	no	—
383	D₄×C₃₁	—	2	4	no	—
384	D₄×C₃₁	—	2	8	no	—
385	D₄×C₃₁	—	2	16	no	—
386	D₄×C₃₁	—	4	8	no	—
387	D₄×C₃₁	—	4	32	no	—
388	C₂×C₄×C₃₁	—	2	8	no	—
389	C₂×C₄×C₃₁	—	2	4	no	—
390	C₂×C₄×C₃₁	—	2	8	no	—
391	C₂×C₄×C₃₁	—	2	16	no	—
392	C₂×C₄×C₃₁	—	2	16	no	—
393	C₂×C₄×C₃₁	—	2	8	no	—
394	C₂×C₄×C₃₁	—	2	4	no	—
395	C₂×C₄×C₃₁	—	2	4	no	—
396	C₂×C₄×C₃₁	—	2	4	no	—
397	C₂×C₄×C₃₁	—	2	16	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	—	4	8	no	—
400	C₂×C₄×C₃₁	—	4	2	no	—
401	C₂×C₄×C₃₁	—	4	2	no	—
402	C₂×C₄×C₃₁	—	4	2	no	—
403	C₂×C₄×C₃₁	—	4	8	no	—
404	C₂×C₄×C₃₁	—	4	32	no	—
405	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
406	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
407	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
408	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
409	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
410	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
411	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
412	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
413	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
414	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
415	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
416	C₂×C₄×C₃₁	C₂⁵	1	16	yes	—
417	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
418	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
419	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
420	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
421	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
422	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
423	#3512	C₂×C₃₁	1	4	yes	complemented
424	#3511	C₂×C₃₁	1	4	yes	complemented
425	#3510	C₂×C₃₁	1	4	yes	complemented
426	#3509	C₂×C₃₁	1	2	yes	complemented
427	#3508	C₂×C₃₁	1	2	yes	complemented
428	#3507	C₂×C₃₁	1	4	yes	complemented
429	#3506	C₂×C₃₁	1	4	yes	complemented
430	#3505	C₂×C₃₁	1	8	yes	complemented
431	#3480	C₂×C₃₁	1	8	yes	complemented
432	#3475	C₂×C₃₁	1	8	yes	complemented
433	#3455	C₂×C₃₁	1	4	yes	complemented
434	#3449	C₂×C₃₁	1	2	yes	complemented
435	#3444	C₂×C₃₁	1	4	yes	complemented
436	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
437	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3428	C₂×C₃₁	1	2	yes	complemented
439	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
440	C₂²×C₃₁	—	2	2	no	—
441	C₂²×C₃₁	—	2	2	no	—
442	C₂²×C₃₁	—	2	2	no	—
443	C₂²×C₃₁	—	2	4	no	—
444	C₂²×C₃₁	—	2	8	no	—
445	C₂²×C₃₁	—	2	8	no	—
446	C₂²×C₃₁	—	2	16	no	—
447	C₂²×C₃₁	—	4	4	no	—
448	C₂²×C₃₁	—	4	8	no	—
449	C₂²×C₃₁	—	8	8	no	—
450	C₂²×C₃₁	C₂²×#41	1	2	yes	—
451	C₂²×C₃₁	C₂²×#41	1	2	yes	—
452	C₂²×C₃₁	C₂²×#41	1	2	yes	—
453	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
454	C₄×C₃₁	—	2	8	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	8	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	2	no	—
460	C₄×C₃₁	—	2	16	no	—
461	C₄×C₃₁	C₂²×#41	1	2	yes	—
462	C₄×C₃₁	C₂²×#41	1	2	yes	—
463	C₄×C₃₁	C₂²×#41	1	2	yes	—
464	C₄×C₃₁	C₂²×#41	1	2	yes	—
465	C₄×C₃₁	#585	1	4	yes	—
466	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
467	C₂²×#41	C₂²×C₃₁	1	2	yes	—
468	#559	C₂²×C₃₁	1	16	yes	complemented
469	#559	C₂²×C₃₁	1	8	yes	complemented
470	#557	C₂²×C₃₁	1	8	yes	complemented
471	#556	C₂²×C₃₁	1	8	yes	complemented
472	#556	C₂²×C₃₁	1	8	yes	complemented
473	#556	C₂²×C₃₁	1	16	yes	complemented
474	#555	C₂²×C₃₁	1	8	yes	complemented
475	#554	C₂²×C₃₁	1	8	yes	complemented
476	#553	C₂²×C₃₁	1	16	yes	complemented
477	#553	C₂²×C₃₁	1	16	yes	complemented
478	#553	C₂²×C₃₁	1	32	yes	complemented
479	#552	C₂²×C₃₁	1	16	yes	complemented
480	#552	C₂²×C₃₁	1	16	yes	complemented
481	#551	C₂²×C₃₁	1	32	yes	complemented
482	#550	C₂²×C₃₁	1	8	yes	complemented
483	#548	C₂²×C₃₁	1	16	yes	complemented
484	#547	C₂²×C₃₁	1	8	yes	complemented
485	#546	C₂²×C₃₁	1	16	yes	complemented
486	#542	C₂²×C₃₁	1	16	yes	complemented
487	#541	C₂²×C₃₁	1	8	yes	complemented
488	#540	C₂²×C₃₁	1	8	yes	complemented
489	#539	C₂²×C₃₁	1	16	yes	complemented
490	#538	C₂²×C₃₁	1	16	yes	complemented
491	#537	C₂²×C₃₁	1	8	yes	complemented
492	#536	C₂²×C₃₁	1	4	yes	—
493	#536	C₂²×C₃₁	1	4	yes	complemented
494	#535	C₂²×C₃₁	1	4	yes	—
495	#535	C₂²×C₃₁	1	4	yes	complemented
496	#534	C₂²×C₃₁	1	8	yes	—
497	#533	C₂²×C₃₁	1	2	yes	complemented
498	#533	C₂²×C₃₁	1	2	yes	complemented
499	#533	C₂²×C₃₁	1	4	yes	complemented
500	#533	C₂²×C₃₁	1	4	yes	complemented
501	#533	C₂²×C₃₁	1	2	yes	complemented
502	#533	C₂²×C₃₁	1	2	yes	complemented
503	#533	C₂²×C₃₁	1	8	yes	complemented
504	#532	C₂²×C₃₁	1	2	yes	—
505	#532	C₂²×C₃₁	1	2	yes	—
506	#532	C₂²×C₃₁	1	4	yes	—
507	#532	C₂²×C₃₁	1	4	yes	complemented
508	#532	C₂²×C₃₁	1	2	yes	complemented
509	#532	C₂²×C₃₁	1	2	yes	complemented
510	#532	C₂²×C₃₁	1	8	yes	complemented
511	#532	C₂²×C₃₁	1	8	yes	complemented
512	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
514	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#529	C₂²×C₃₁	1	16	yes	complemented
516	#529	C₂²×C₃₁	1	16	yes	complemented
517	#529	C₂²×C₃₁	1	16	yes	complemented
518	#529	C₂²×C₃₁	1	32	yes	complemented
519	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
520	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
521	#525	C₂²×C₃₁	1	8	yes	—
522	#525	C₂²×C₃₁	1	8	yes	complemented
523	#525	C₂²×C₃₁	1	16	yes	complemented
524	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
525	C₂×#121	C₂²×C₃₁	1	4	yes	—
526	#520	C₂²×C₃₁	1	8	yes	complemented
527	#520	C₂²×C₃₁	1	8	yes	complemented
528	#519	C₂²×C₃₁	1	4	yes	complemented
529	#518	C₂²×C₃₁	1	8	yes	—
530	#518	C₂²×C₃₁	1	4	yes	complemented
531	C₄×#41	C₂²×C₃₁	1	4	yes	—
532	C₄×#41	C₂²×C₃₁	1	2	yes	—
533	C₄×#41	C₂²×C₃₁	1	2	yes	—
534	C₄×#41	C₂²×C₃₁	1	4	yes	complemented
535	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
536	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
537	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
538	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
539	C₄×#41	C₂²×C₃₁	1	16	yes	complemented
540	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
541	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
542	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
543	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
544	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
545	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×#117	C₂²×C₃₁	1	2	yes	—
547	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
548	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
549	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
550	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
551	C₂×C₃₁	—	2	2	no	—
552	C₂×C₃₁	—	2	2	no	—
553	C₂×C₃₁	—	2	2	no	—
554	C₂×C₃₁	—	4	4	no	—
555	C₂×C₃₁	—	4	8	no	—
556	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
557	C₂×C₃₁	C₂×#585	1	2	yes	—
558	C₂×#41	—	2	8	no	—
559	C₂×#41	—	2	16	no	—
560	C₂×#41	C₂³×C₃₁	1	2	yes	—
561	C₂×#41	C₂³×C₃₁	1	2	yes	—
562	C₂×#41	C₂³×C₃₁	1	4	yes	—
563	C₂×#41	C₂³×C₃₁	1	2	yes	—
564	C₂×#41	C₂³×C₃₁	1	4	yes	—
565	C₂×#41	C₂³×C₃₁	1	2	yes	—
566	C₂×#41	C₂³×C₃₁	1	4	yes	—
567	C₂×#41	C₂³×C₃₁	1	4	yes	—
568	C₂×#41	C₂³×C₃₁	1	16	yes	—
569	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
571	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
572	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
573	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
575	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
576	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
577	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
578	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
581	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
585	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
586	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
587	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
588	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
589	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
590	#127	C₂³×C₃₁	1	2	yes	—
591	#127	C₂³×C₃₁	1	2	yes	—
592	#127	C₂³×C₃₁	1	4	yes	—
593	#127	C₂³×C₃₁	1	8	yes	—
594	#126	C₂³×C₃₁	1	32	yes	—
595	#126	C₂³×C₃₁	1	32	yes	—
596	#126	C₂³×C₃₁	1	32	yes	—
597	#125	C₂³×C₃₁	1	4	yes	—
598	#125	C₂³×C₃₁	1	4	yes	—
599	#125	C₂³×C₃₁	1	8	yes	—
600	#125	C₂³×C₃₁	1	16	yes	—
601	#125	C₂³×C₃₁	1	32	yes	—
602	#124	C₂³×C₃₁	1	4	yes	—
603	#124	C₂³×C₃₁	1	4	yes	—
604	#124	C₂³×C₃₁	1	8	yes	—
605	#124	C₂³×C₃₁	1	16	yes	—
606	#124	C₂³×C₃₁	1	32	yes	—
607	#124	C₂³×C₃₁	1	8	yes	—
608	#124	C₂³×C₃₁	1	8	yes	—
609	#123	C₂³×C₃₁	1	16	yes	—
610	#123	C₂³×C₃₁	1	16	yes	—
611	#123	C₂³×C₃₁	1	32	yes	—
612	#123	C₂³×C₃₁	1	32	yes	—
613	#123	C₂³×C₃₁	1	32	yes	—
614	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
615	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
616	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
617	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
618	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
619	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
620	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
621	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
622	#121	C₂³×C₃₁	1	8	yes	—
623	#121	C₂³×C₃₁	1	8	yes	—
624	#121	C₂³×C₃₁	1	8	yes	—
625	#121	C₂³×C₃₁	1	8	yes	—
626	#121	C₂³×C₃₁	1	16	yes	—
627	#121	C₂³×C₃₁	1	16	yes	—
628	#121	C₂³×C₃₁	1	16	yes	—
629	#121	C₂³×C₃₁	1	32	yes	—
630	#121	C₂³×C₃₁	1	32	yes	—
631	#120	C₂³×C₃₁	1	16	yes	—
632	#120	C₂³×C₃₁	1	16	yes	—
633	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
634	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
635	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
636	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
637	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
638	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
639	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
640	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
641	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
642	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
643	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
644	C₄×D₄	C₂³×C₃₁	1	8	yes	—
645	C₄×D₄	C₂³×C₃₁	1	8	yes	—
646	C₄×D₄	C₂³×C₃₁	1	8	yes	—
647	C₄×D₄	C₂³×C₃₁	1	8	yes	—
648	C₄×D₄	C₂³×C₃₁	1	4	yes	—
649	C₄×D₄	C₂³×C₃₁	1	4	yes	—
650	C₄×D₄	C₂³×C₃₁	1	4	yes	—
651	C₄×D₄	C₂³×C₃₁	1	4	yes	—
652	C₄×D₄	C₂³×C₃₁	1	8	yes	—
653	C₄×D₄	C₂³×C₃₁	1	8	yes	—
654	C₄×D₄	C₂³×C₃₁	1	8	yes	—
655	C₄×D₄	C₂³×C₃₁	1	8	yes	—
656	C₄×D₄	C₂³×C₃₁	1	32	yes	—
657	C₄×D₄	C₂³×C₃₁	1	32	yes	—
658	C₄×D₄	C₂³×C₃₁	1	16	yes	—
659	C₄×D₄	C₂³×C₃₁	1	16	yes	—
660	C₄×D₄	C₂³×C₃₁	1	32	yes	—
661	C₄×D₄	C₂³×C₃₁	1	32	yes	—
662	C₄×D₄	C₂³×C₃₁	1	16	yes	—
663	#117	C₂³×C₃₁	1	2	yes	—
664	#117	C₂³×C₃₁	1	4	yes	—
665	#117	C₂³×C₃₁	1	2	yes	—
666	#117	C₂³×C₃₁	1	2	yes	—
667	#117	C₂³×C₃₁	1	2	yes	—
668	#117	C₂³×C₃₁	1	4	yes	—
669	#117	C₂³×C₃₁	1	4	yes	—
670	#117	C₂³×C₃₁	1	4	yes	—
671	#117	C₂³×C₃₁	1	8	yes	—
672	#117	C₂³×C₃₁	1	4	yes	—
673	#117	C₂³×C₃₁	1	4	yes	—
674	#117	C₂³×C₃₁	1	16	yes	—
675	#117	C₂³×C₃₁	1	16	yes	—
676	#117	C₂³×C₃₁	1	16	yes	—
677	#117	C₂³×C₃₁	1	16	yes	—
678	#117	C₂³×C₃₁	1	32	yes	—
679	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
691	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	16	yes	—
695	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
696	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
702	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
703	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
704	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
707	C₃₁	#62815	1	1	yes	characteristic, direct product factor, Sylow
708	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
709	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
710	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
711	#41	—	2	8	no	—
712	#41	—	2	16	no	—
713	#41	—	2	8	no	—
714	#41	—	2	16	no	—
715	#41	—	2	8	no	—
716	#41	—	2	16	no	—
717	#41	—	2	8	no	—
718	#41	—	2	16	no	—
719	#41	—	4	32	no	—
720	C₂×Q₈	—	2	8	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	4	8	no	—
723	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
725	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
726	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
728	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
729	C₂×D₄	—	2	8	no	—
730	C₂×D₄	—	2	16	no	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	4	8	no	—
734	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
735	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
736	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
737	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
738	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
739	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
740	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
741	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
742	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
743	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
744	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
745	C₂²×C₄	—	2	16	no	—
746	C₂²×C₄	—	2	8	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	4	8	no	—
749	C₂²×C₄	#41×C₃₁	1	8	yes	complemented
750	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
755	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
759	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
760	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
762	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
766	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	—
767	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
774	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
776	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
779	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
780	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
781	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
783	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
784	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
785	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
787	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
788	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
790	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
793	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
794	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
795	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
797	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
798	C₄²	C₂⁴×C₃₁	1	4	yes	—
799	C₄²	C₂⁴×C₃₁	1	2	yes	—
800	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
802	C₄²	C₂⁴×C₃₁	1	4	yes	—
803	C₄²	C₂⁴×C₃₁	1	2	yes	—
804	C₄²	C₂⁴×C₃₁	1	8	yes	—
805	C₄²	C₂⁴×C₃₁	1	8	yes	—
806	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
807	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₄²	C₂⁴×C₃₁	1	2	yes	—
809	C₄²	C₂⁴×C₃₁	1	2	yes	—
810	C₄²	C₂⁴×C₃₁	1	8	yes	—
811	C₄²	C₂⁴×C₃₁	1	2	yes	—
812	C₄²	C₂⁴×C₃₁	1	2	yes	—
813	C₄²	C₂⁴×C₃₁	1	32	yes	—
814	C₄²	C₂⁴×C₃₁	1	8	yes	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	C₂×#41×C₃₁	1	4	yes	—
821	C₂³	C₂⁵×C₃₁	1	4	yes	—
822	C₂³	C₂⁵×C₃₁	1	8	yes	—
823	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
824	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
825	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
826	Q₈	—	2	4	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	16	no	—
831	Q₈	—	4	8	no	—
832	D₄	—	2	8	no	—
833	D₄	—	2	16	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	16	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	8	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	32	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	16	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	32	no	—
860	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
861	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
862	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
863	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
864	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
865	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
866	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
867	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
868	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
869	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
870	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
871	C₂×C₄	C₂⁵×C₃₁	1	16	yes	—
872	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
873	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
874	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
876	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	16	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂²×#41×C₃₁	1	2	yes	—
889	C₂²	C₂²×#41×C₃₁	1	2	yes	—
890	C₂²	C₂²×#41×C₃₁	1	2	yes	—
891	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
892	C₄	—	2	8	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	8	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	16	no	—
899	C₄	C₂²×#41×C₃₁	1	2	yes	—
900	C₄	C₂²×#41×C₃₁	1	2	yes	—
901	C₄	C₂²×#41×C₃₁	1	2	yes	—
902	C₄	C₂²×#41×C₃₁	1	2	yes	—
903	C₄	C₃₁×#585	1	4	yes	—
904	C₂	—	2	2	no	—
905	C₂	—	2	2	no	—
906	C₂	—	2	2	no	—
907	C₂	—	4	4	no	—
908	C₂	—	4	8	no	—
909	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
910	C₂	C₂×C₃₁×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂²×C₃₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3512	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3510	C₂	semidirect
4. C₃₁×#3509	C₂	semidirect
5. C₃₁×#3508	C₂	semidirect
6. C₃₁×#3507	C₂	semidirect
7. C₃₁×#3506	C₂	semidirect
8. C₃₁×#3505	C₂	semidirect
9. C₃₁×#3480	C₂	semidirect
10. C₃₁×#3475	C₂	semidirect
11. C₃₁×#3455	C₂	semidirect
12. C₃₁×#3449	C₂	semidirect
13. C₃₁×#3444	C₂	semidirect
14. C₂×C₃₁×#533	C₂	semidirect
15. C₂×C₃₁×#532	C₂	semidirect
16. C₃₁×#3428	C₂	semidirect
17. C₂×C₄×#41×C₃₁	C₂	semidirect
20. C₃₁×#559	C₂²	semidirect
21. C₃₁×#559	C₂²	semidirect
22. C₃₁×#557	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#556	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#555	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
29. C₃₁×#553	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
32. C₃₁×#552	C₂²	semidirect
33. C₃₁×#551	C₂²	semidirect
34. C₃₁×#550	C₂²	semidirect
35. C₃₁×#548	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
37. C₃₁×#546	C₂²	semidirect
38. C₃₁×#542	C₂²	semidirect
39. C₃₁×#541	C₂²	semidirect
40. C₃₁×#540	C₂²	semidirect
41. C₃₁×#539	C₂²	semidirect
42. C₃₁×#538	C₂²	semidirect
43. C₃₁×#537	C₂²	semidirect
45. C₃₁×#536	C₂²	semidirect
47. C₃₁×#535	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
53. C₃₁×#533	C₂²	semidirect
54. C₃₁×#533	C₂²	semidirect
55. C₃₁×#533	C₂²	semidirect
59. C₃₁×#532	C₂²	semidirect
60. C₃₁×#532	C₂²	semidirect
61. C₃₁×#532	C₂²	semidirect
62. C₃₁×#532	C₂²	semidirect
63. C₃₁×#532	C₂²	semidirect
64. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
65. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
66. C₂×C₃₁×#127	C₂²	semidirect
67. C₃₁×#529	C₂²	semidirect
68. C₃₁×#529	C₂²	semidirect
69. C₃₁×#529	C₂²	semidirect
70. C₃₁×#529	C₂²	semidirect
71. C₂×C₃₁×#125	C₂²	semidirect
72. C₂×C₃₁×#124	C₂²	semidirect
74. C₃₁×#525	C₂²	semidirect
75. C₃₁×#525	C₂²	semidirect
78. C₃₁×#520	C₂²	semidirect
79. C₃₁×#520	C₂²	semidirect
80. C₃₁×#519	C₂²	semidirect
82. C₃₁×#518	C₂²	semidirect
86. C₄×#41×C₃₁	C₂²	semidirect
87. C₄×#41×C₃₁	C₂²	semidirect
88. C₄×#41×C₃₁	C₂²	semidirect
89. C₄×#41×C₃₁	C₂²	semidirect
90. C₄×#41×C₃₁	C₂²	semidirect
91. C₄×#41×C₃₁	C₂²	semidirect
92. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
93. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
95. C₂×C₄×D₄×C₃₁	C₂²	semidirect
96. C₂×C₄×D₄×C₃₁	C₂²	semidirect
99. C₂×C₃₁×#117	C₂²	semidirect
100. C₂×C₃₁×#117	C₂²	semidirect
102. C₂²×C₄²×C₃₁	C₂²	semidirect
293. C₂²×C₄×C₃₁	#41	semidirect
359. #62815	C₃₁	direct (N × H)
423. #3512	C₂×C₃₁	semidirect
424. #3511	C₂×C₃₁	semidirect
425. #3510	C₂×C₃₁	semidirect
426. #3509	C₂×C₃₁	semidirect
427. #3508	C₂×C₃₁	semidirect
428. #3507	C₂×C₃₁	semidirect
429. #3506	C₂×C₃₁	semidirect
430. #3505	C₂×C₃₁	semidirect
431. #3480	C₂×C₃₁	semidirect
432. #3475	C₂×C₃₁	semidirect
433. #3455	C₂×C₃₁	semidirect
434. #3449	C₂×C₃₁	semidirect
435. #3444	C₂×C₃₁	semidirect
436. C₂×#533	C₂×C₃₁	semidirect
437. C₂×#532	C₂×C₃₁	semidirect
438. #3428	C₂×C₃₁	semidirect
439. C₂×C₄×#41	C₂×C₃₁	semidirect
468. #559	C₂²×C₃₁	semidirect
469. #559	C₂²×C₃₁	semidirect
470. #557	C₂²×C₃₁	semidirect
471. #556	C₂²×C₃₁	semidirect
472. #556	C₂²×C₃₁	semidirect
473. #556	C₂²×C₃₁	semidirect
474. #555	C₂²×C₃₁	semidirect
475. #554	C₂²×C₃₁	semidirect
476. #553	C₂²×C₃₁	semidirect
477. #553	C₂²×C₃₁	semidirect
478. #553	C₂²×C₃₁	semidirect
479. #552	C₂²×C₃₁	semidirect
480. #552	C₂²×C₃₁	semidirect
481. #551	C₂²×C₃₁	semidirect
482. #550	C₂²×C₃₁	semidirect
483. #548	C₂²×C₃₁	semidirect
484. #547	C₂²×C₃₁	semidirect
485. #546	C₂²×C₃₁	semidirect
486. #542	C₂²×C₃₁	semidirect
487. #541	C₂²×C₃₁	semidirect
488. #540	C₂²×C₃₁	semidirect
489. #539	C₂²×C₃₁	semidirect
490. #538	C₂²×C₃₁	semidirect
491. #537	C₂²×C₃₁	semidirect
493. #536	C₂²×C₃₁	semidirect
495. #535	C₂²×C₃₁	semidirect
497. #533	C₂²×C₃₁	semidirect
498. #533	C₂²×C₃₁	semidirect
499. #533	C₂²×C₃₁	semidirect
500. #533	C₂²×C₃₁	semidirect
501. #533	C₂²×C₃₁	semidirect
502. #533	C₂²×C₃₁	semidirect
503. #533	C₂²×C₃₁	semidirect
507. #532	C₂²×C₃₁	semidirect
508. #532	C₂²×C₃₁	semidirect
509. #532	C₂²×C₃₁	semidirect
510. #532	C₂²×C₃₁	semidirect
511. #532	C₂²×C₃₁	semidirect
512. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
513. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
514. C₂×#127	C₂²×C₃₁	semidirect
515. #529	C₂²×C₃₁	semidirect
516. #529	C₂²×C₃₁	semidirect
517. #529	C₂²×C₃₁	semidirect
518. #529	C₂²×C₃₁	semidirect
519. C₂×#125	C₂²×C₃₁	semidirect
520. C₂×#124	C₂²×C₃₁	semidirect
522. #525	C₂²×C₃₁	semidirect
523. #525	C₂²×C₃₁	semidirect
526. #520	C₂²×C₃₁	semidirect
527. #520	C₂²×C₃₁	semidirect
528. #519	C₂²×C₃₁	semidirect
530. #518	C₂²×C₃₁	semidirect
534. C₄×#41	C₂²×C₃₁	semidirect
535. C₄×#41	C₂²×C₃₁	semidirect
536. C₄×#41	C₂²×C₃₁	semidirect
537. C₄×#41	C₂²×C₃₁	semidirect
538. C₄×#41	C₂²×C₃₁	semidirect
539. C₄×#41	C₂²×C₃₁	semidirect
540. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
541. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
543. C₂×C₄×D₄	C₂²×C₃₁	semidirect
544. C₂×C₄×D₄	C₂²×C₃₁	semidirect
547. C₂×#117	C₂²×C₃₁	semidirect
548. C₂×#117	C₂²×C₃₁	semidirect
550. C₂²×C₄²	C₂²×C₃₁	semidirect
707. C₃₁	#62815	direct (N × H)
749. C₂²×C₄	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3512	2
C₃₁×#3511	2
C₃₁×#3510	2
C₃₁×#3509	2
C₃₁×#3508	2
C₃₁×#3507	2
C₃₁×#3506	2
C₃₁×#3505	2
C₃₁×#3480	2
C₃₁×#3475	2
C₃₁×#3455	2
C₃₁×#3449	2
C₃₁×#3444	2
C₂×C₃₁×#533	2
C₂×C₃₁×#532	2
C₃₁×#3428	2
C₂×C₄×#41×C₃₁	2
#62815	31

Subgroups — C31×#62815 #21519574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62815 #21519574