Subgroups — C₃₁×#62814 #21519573

Order 7936.

7286 conjugacy classes of subgroups.

The subgroup lattice has 768 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	8	yes	maximal, complemented
2	C₃₁×#3494	C₂	1	8	yes	maximal, complemented
3	C₃₁×#3493	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3492	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3491	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3490	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3475	C₂	1	16	yes	maximal, complemented
8	C₃₁×#3458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3455	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3444	C₂	1	4	yes	maximal, complemented
12	C₂×C₃₁×#525	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3428	C₂	1	2	yes	maximal, complemented
14	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#556	C₂²	1	16	yes	complemented
18	C₃₁×#555	C₂²	1	16	yes	complemented
19	C₃₁×#554	C₂²	1	16	yes	complemented
20	C₃₁×#553	C₂²	1	16	yes	complemented
21	C₃₁×#553	C₂²	1	16	yes	complemented
22	C₃₁×#552	C₂²	1	32	yes	complemented
23	C₃₁×#552	C₂²	1	16	yes	complemented
24	C₃₁×#552	C₂²	1	16	yes	complemented
25	C₃₁×#551	C₂²	1	32	yes	complemented
26	C₃₁×#551	C₂²	1	32	yes	complemented
27	C₃₁×#547	C₂²	1	16	yes	complemented
28	C₃₁×#546	C₂²	1	32	yes	complemented
29	C₃₁×#544	C₂²	1	4	yes	complemented
30	C₃₁×#544	C₂²	1	8	yes	complemented
31	C₃₁×#543	C₂²	1	4	yes	—
32	C₃₁×#542	C₂²	1	16	yes	complemented
33	C₃₁×#541	C₂²	1	8	yes	complemented
34	C₃₁×#540	C₂²	1	8	yes	complemented
35	C₃₁×#539	C₂²	1	16	yes	complemented
36	C₃₁×#538	C₂²	1	16	yes	complemented
37	C₃₁×#537	C₂²	1	4	yes	complemented
38	C₃₁×#536	C₂²	1	4	yes	complemented
39	C₃₁×#535	C₂²	1	4	yes	complemented
40	C₃₁×#534	C₂²	1	4	yes	—
41	C₃₁×#533	C₂²	1	4	yes	complemented
42	C₃₁×#533	C₂²	1	8	yes	complemented
43	C₃₁×#533	C₂²	1	8	yes	complemented
44	C₃₁×#532	C₂²	1	4	yes	complemented
45	C₃₁×#532	C₂²	1	8	yes	complemented
46	C₃₁×#529	C₂²	1	16	yes	complemented
47	C₃₁×#529	C₂²	1	16	yes	complemented
48	C₃₁×#529	C₂²	1	16	yes	complemented
49	C₃₁×#529	C₂²	1	32	yes	complemented
50	C₃₁×#525	C₂²	1	8	yes	—
51	C₃₁×#525	C₂²	1	8	yes	—
52	C₃₁×#525	C₂²	1	4	yes	complemented
53	C₃₁×#525	C₂²	1	4	yes	complemented
54	C₃₁×#525	C₂²	1	4	yes	complemented
55	C₃₁×#525	C₂²	1	4	yes	complemented
56	C₃₁×#525	C₂²	1	16	yes	complemented
57	C₃₁×#525	C₂²	1	8	yes	complemented
58	C₂×C₃₁×#123	C₂²	1	4	yes	—
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
61	C₂×C₃₁×#120	C₂²	1	4	yes	—
62	C₃₁×#520	C₂²	1	8	yes	complemented
63	C₃₁×#520	C₂²	1	8	yes	complemented
64	C₃₁×#519	C₂²	1	4	yes	complemented
65	C₃₁×#518	C₂²	1	8	yes	—
66	C₃₁×#518	C₂²	1	4	yes	complemented
67	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
68	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
69	C₄×#41×C₃₁	C₂²	1	16	yes	complemented
70	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
71	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#117	C₂²	1	2	yes	—
74	C₂×C₃₁×#117	C₂²	1	2	yes	—
75	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
76	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
77	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
78	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
79	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
80	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
81	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
83	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
84	C₂×#41×C₃₁	—	2	16	no	—
85	C₂×#41×C₃₁	C₂³	1	4	yes	—
86	C₂×#41×C₃₁	C₂³	1	4	yes	—
87	C₂×#41×C₃₁	C₂³	1	4	yes	—
88	C₂×#41×C₃₁	C₂³	1	4	yes	—
89	C₂×#41×C₃₁	C₂³	1	16	yes	—
90	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
94	C₂³×C₄×C₃₁	—	2	8	no	—
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	complemented
106	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
107	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
108	C₃₁×#127	C₂³	1	4	yes	complemented
109	C₃₁×#126	C₂³	1	32	yes	—
110	C₃₁×#126	C₂³	1	32	yes	complemented
111	C₃₁×#126	C₂³	1	32	yes	complemented
112	C₃₁×#125	C₂³	1	8	yes	complemented
113	C₃₁×#125	C₂³	1	16	yes	complemented
114	C₃₁×#125	C₂³	1	32	yes	complemented
115	C₃₁×#125	C₂³	1	16	yes	complemented
116	C₃₁×#124	C₂³	1	32	yes	—
117	C₃₁×#124	C₂³	1	8	yes	complemented
118	C₃₁×#124	C₂³	1	16	yes	complemented
119	C₃₁×#123	C₂³	1	16	yes	—
120	C₃₁×#123	C₂³	1	8	yes	—
121	C₃₁×#123	C₂³	1	8	yes	—
122	C₃₁×#123	C₂³	1	32	yes	—
123	C₃₁×#123	C₂³	1	16	yes	—
124	C₃₁×#123	C₂³	1	32	yes	—
125	C₃₁×#123	C₂³	1	32	yes	complemented
126	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
127	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
129	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
130	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
131	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
134	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
135	C₃₁×#121	C₂³	1	8	yes	—
136	C₃₁×#121	C₂³	1	8	yes	—
137	C₃₁×#121	C₂³	1	8	yes	—
138	C₃₁×#121	C₂³	1	8	yes	—
139	C₃₁×#121	C₂³	1	16	yes	—
140	C₃₁×#121	C₂³	1	16	yes	—
141	C₃₁×#121	C₂³	1	32	yes	—
142	C₃₁×#121	C₂³	1	16	yes	complemented
143	C₃₁×#120	C₂³	1	16	yes	—
144	C₃₁×#120	C₂³	1	8	yes	—
145	C₃₁×#120	C₂³	1	8	yes	—
146	C₃₁×#120	C₂³	1	16	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
148	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
149	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
150	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
151	C₄×D₄×C₃₁	C₂³	1	16	yes	—
152	C₄×D₄×C₃₁	C₂³	1	16	yes	—
153	C₄×D₄×C₃₁	C₂³	1	16	yes	—
154	C₄×D₄×C₃₁	C₂³	1	16	yes	—
155	C₄×D₄×C₃₁	C₂³	1	32	yes	—
156	C₄×D₄×C₃₁	C₂³	1	32	yes	—
157	C₄×D₄×C₃₁	C₂³	1	32	yes	—
158	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
159	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
160	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
161	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
162	C₃₁×#117	C₂³	1	4	yes	—
163	C₃₁×#117	C₂³	1	4	yes	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₃₁×#117	C₂³	1	4	yes	—
166	C₃₁×#117	C₂³	1	4	yes	—
167	C₃₁×#117	C₂³	1	16	yes	—
168	C₃₁×#117	C₂³	1	4	yes	—
169	C₃₁×#117	C₂³	1	4	yes	—
170	C₃₁×#117	C₂³	1	4	yes	—
171	C₃₁×#117	C₂³	1	8	yes	—
172	C₃₁×#117	C₂³	1	8	yes	—
173	C₃₁×#117	C₂³	1	8	yes	—
174	C₃₁×#117	C₂³	1	8	yes	—
175	C₃₁×#117	C₂³	1	16	yes	—
176	C₃₁×#117	C₂³	1	16	yes	—
177	C₃₁×#117	C₂³	1	16	yes	complemented
178	C₃₁×#117	C₂³	1	16	yes	complemented
179	C₃₁×#117	C₂³	1	32	yes	complemented
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
196	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	16	yes	complemented
203	C₂⁴×C₃₁	—	2	4	no	—
204	C₂⁴×C₃₁	—	4	4	no	—
205	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
207	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
208	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
210	#41×C₃₁	—	2	16	no	—
211	#41×C₃₁	—	2	16	no	—
212	#41×C₃₁	—	2	16	no	—
213	#41×C₃₁	—	2	16	no	—
214	#41×C₃₁	—	4	32	no	—
215	C₂×Q₈×C₃₁	—	2	8	no	—
216	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
217	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
218	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
219	C₂×D₄×C₃₁	—	2	16	no	—
220	C₂×D₄×C₃₁	—	2	8	no	—
221	C₂×D₄×C₃₁	—	4	16	no	—
222	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
224	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
225	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
226	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
227	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
228	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	—	2	16	no	—
231	C₂²×C₄×C₃₁	—	2	16	no	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	4	no	—
236	C₂²×C₄×C₃₁	—	2	16	no	—
237	C₂²×C₄×C₃₁	—	4	8	no	—
238	C₂²×C₄×C₃₁	#41	1	8	yes	complemented
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
256	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
269	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
270	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
271	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
272	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
273	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
274	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
275	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
276	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
277	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
280	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
281	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
282	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
283	C₄²×C₃₁	C₂⁴	1	8	yes	—
284	C₄²×C₃₁	C₂⁴	1	4	yes	—
285	C₄²×C₃₁	C₂⁴	1	8	yes	—
286	C₄²×C₃₁	C₂⁴	1	4	yes	—
287	C₄²×C₃₁	C₂⁴	1	8	yes	—
288	C₄²×C₃₁	C₂⁴	1	32	yes	—
289	C₄²×C₃₁	C₂⁴	1	4	yes	—
290	C₄²×C₃₁	C₂⁴	1	4	yes	—
291	C₄²×C₃₁	C₂⁴	1	8	yes	—
292	#62814	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	4	no	—
295	C₂³×C₃₁	—	2	8	no	—
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	8	no	—
298	C₂³×C₃₁	—	2	8	no	—
299	C₂³×C₃₁	—	4	2	no	—
300	C₂³×C₃₁	—	4	4	no	—
301	C₂³×C₃₁	—	4	2	no	—
302	C₂³×C₃₁	—	4	8	no	—
303	C₂³×C₃₁	—	4	16	no	—
304	C₂³×C₃₁	C₂×#41	1	4	yes	—
305	C₂³×C₃₁	C₂⁵	1	2	yes	—
306	C₂³×C₃₁	C₂⁵	1	8	yes	—
307	C₂³×C₃₁	C₂⁵	1	2	yes	—
308	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
309	C₂³×C₃₁	C₂⁵	1	2	yes	—
310	Q₈×C₃₁	—	2	8	no	—
311	Q₈×C₃₁	—	2	8	no	—
312	Q₈×C₃₁	—	4	16	no	—
313	D₄×C₃₁	—	2	16	no	—
314	D₄×C₃₁	—	2	16	no	—
315	D₄×C₃₁	—	2	32	no	—
316	D₄×C₃₁	—	2	8	no	—
317	D₄×C₃₁	—	2	8	no	—
318	D₄×C₃₁	—	4	16	no	—
319	D₄×C₃₁	—	4	16	no	—
320	C₂×C₄×C₃₁	—	2	8	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	16	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	4	no	—
327	C₂×C₄×C₃₁	—	2	8	no	—
328	C₂×C₄×C₃₁	—	2	8	no	—
329	C₂×C₄×C₃₁	—	2	4	no	—
330	C₂×C₄×C₃₁	—	2	4	no	—
331	C₂×C₄×C₃₁	—	2	16	no	—
332	C₂×C₄×C₃₁	—	2	16	no	—
333	C₂×C₄×C₃₁	—	4	4	no	—
334	C₂×C₄×C₃₁	—	4	8	no	—
335	C₂×C₄×C₃₁	—	4	4	no	—
336	C₂×C₄×C₃₁	—	4	8	no	—
337	C₂×C₄×C₃₁	—	4	32	no	—
338	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
339	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
340	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
341	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
342	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
343	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
344	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
345	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
346	C₂×C₄×C₃₁	C₂⁵	1	16	yes	—
347	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
348	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
350	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
351	#3495	C₂×C₃₁	1	8	yes	complemented
352	#3494	C₂×C₃₁	1	8	yes	complemented
353	#3493	C₂×C₃₁	1	4	yes	complemented
354	#3492	C₂×C₃₁	1	4	yes	complemented
355	#3491	C₂×C₃₁	1	4	yes	complemented
356	#3490	C₂×C₃₁	1	4	yes	complemented
357	#3475	C₂×C₃₁	1	16	yes	complemented
358	#3458	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#3455	C₂×C₃₁	1	4	yes	complemented
360	#3449	C₂×C₃₁	1	1	yes	characteristic, complemented
361	#3444	C₂×C₃₁	1	4	yes	complemented
362	C₂×#525	C₂×C₃₁	1	2	yes	complemented
363	#3428	C₂×C₃₁	1	2	yes	complemented
364	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂²×C₃₁	—	2	8	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	2	2	no	—
368	C₂²×C₃₁	—	2	2	no	—
369	C₂²×C₃₁	—	2	4	no	—
370	C₂²×C₃₁	—	2	2	no	—
371	C₂²×C₃₁	—	2	8	no	—
372	C₂²×C₃₁	—	2	16	no	—
373	C₂²×C₃₁	—	2	4	no	—
374	C₂²×C₃₁	—	4	4	no	—
375	C₂²×C₃₁	—	4	16	no	—
376	C₂²×C₃₁	—	4	4	no	—
377	C₂²×C₃₁	—	8	8	no	—
378	C₂²×C₃₁	C₂²×#41	1	4	yes	—
379	C₂²×C₃₁	C₂²×#41	1	2	yes	—
380	C₂²×C₃₁	#585	1	4	yes	—
381	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
382	C₄×C₃₁	—	2	2	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	8	no	—
385	C₄×C₃₁	—	2	8	no	—
386	C₄×C₃₁	—	2	8	no	—
387	C₄×C₃₁	—	2	16	no	—
388	C₄×C₃₁	C₂²×#41	1	2	yes	—
389	C₄×C₃₁	C₂²×#41	1	4	yes	—
390	C₄×C₃₁	C₂²×#41	1	2	yes	—
391	C₂²×#41	C₂²×C₃₁	1	2	yes	—
392	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
393	#556	C₂²×C₃₁	1	16	yes	complemented
394	#555	C₂²×C₃₁	1	16	yes	complemented
395	#554	C₂²×C₃₁	1	16	yes	complemented
396	#553	C₂²×C₃₁	1	16	yes	complemented
397	#553	C₂²×C₃₁	1	16	yes	complemented
398	#552	C₂²×C₃₁	1	32	yes	complemented
399	#552	C₂²×C₃₁	1	16	yes	complemented
400	#552	C₂²×C₃₁	1	16	yes	complemented
401	#551	C₂²×C₃₁	1	32	yes	complemented
402	#551	C₂²×C₃₁	1	32	yes	complemented
403	#547	C₂²×C₃₁	1	16	yes	complemented
404	#546	C₂²×C₃₁	1	32	yes	complemented
405	#544	C₂²×C₃₁	1	4	yes	complemented
406	#544	C₂²×C₃₁	1	8	yes	complemented
407	#543	C₂²×C₃₁	1	4	yes	—
408	#542	C₂²×C₃₁	1	16	yes	complemented
409	#541	C₂²×C₃₁	1	8	yes	complemented
410	#540	C₂²×C₃₁	1	8	yes	complemented
411	#539	C₂²×C₃₁	1	16	yes	complemented
412	#538	C₂²×C₃₁	1	16	yes	complemented
413	#537	C₂²×C₃₁	1	4	yes	complemented
414	#536	C₂²×C₃₁	1	4	yes	complemented
415	#535	C₂²×C₃₁	1	4	yes	complemented
416	#534	C₂²×C₃₁	1	4	yes	—
417	#533	C₂²×C₃₁	1	4	yes	complemented
418	#533	C₂²×C₃₁	1	8	yes	complemented
419	#533	C₂²×C₃₁	1	8	yes	complemented
420	#532	C₂²×C₃₁	1	4	yes	complemented
421	#532	C₂²×C₃₁	1	8	yes	complemented
422	#529	C₂²×C₃₁	1	16	yes	complemented
423	#529	C₂²×C₃₁	1	16	yes	complemented
424	#529	C₂²×C₃₁	1	16	yes	complemented
425	#529	C₂²×C₃₁	1	32	yes	complemented
426	#525	C₂²×C₃₁	1	8	yes	—
427	#525	C₂²×C₃₁	1	8	yes	—
428	#525	C₂²×C₃₁	1	4	yes	complemented
429	#525	C₂²×C₃₁	1	4	yes	complemented
430	#525	C₂²×C₃₁	1	4	yes	complemented
431	#525	C₂²×C₃₁	1	4	yes	complemented
432	#525	C₂²×C₃₁	1	16	yes	complemented
433	#525	C₂²×C₃₁	1	8	yes	complemented
434	C₂×#123	C₂²×C₃₁	1	4	yes	—
435	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
436	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
437	C₂×#120	C₂²×C₃₁	1	4	yes	—
438	#520	C₂²×C₃₁	1	8	yes	complemented
439	#520	C₂²×C₃₁	1	8	yes	complemented
440	#519	C₂²×C₃₁	1	4	yes	complemented
441	#518	C₂²×C₃₁	1	8	yes	—
442	#518	C₂²×C₃₁	1	4	yes	complemented
443	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
444	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
445	C₄×#41	C₂²×C₃₁	1	16	yes	complemented
446	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
447	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×#117	C₂²×C₃₁	1	2	yes	—
450	C₂×#117	C₂²×C₃₁	1	2	yes	—
451	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
452	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
453	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
454	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
455	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
456	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
457	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
458	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
459	C₂×C₃₁	—	2	2	no	—
460	C₂×C₃₁	—	2	4	no	—
461	C₂×C₃₁	—	2	4	no	—
462	C₂×C₃₁	—	4	2	no	—
463	C₂×C₃₁	—	4	8	no	—
464	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
465	C₂×C₃₁	C₂×#585	1	2	yes	—
466	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
467	C₂×#41	—	2	16	no	—
468	C₂×#41	C₂³×C₃₁	1	4	yes	—
469	C₂×#41	C₂³×C₃₁	1	4	yes	—
470	C₂×#41	C₂³×C₃₁	1	4	yes	—
471	C₂×#41	C₂³×C₃₁	1	4	yes	—
472	C₂×#41	C₂³×C₃₁	1	16	yes	—
473	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
474	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
475	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
476	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
477	C₂³×C₄	—	2	8	no	—
478	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
481	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
482	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
483	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
487	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	complemented
489	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
490	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
491	#127	C₂³×C₃₁	1	4	yes	complemented
492	#126	C₂³×C₃₁	1	32	yes	—
493	#126	C₂³×C₃₁	1	32	yes	complemented
494	#126	C₂³×C₃₁	1	32	yes	complemented
495	#125	C₂³×C₃₁	1	8	yes	complemented
496	#125	C₂³×C₃₁	1	16	yes	complemented
497	#125	C₂³×C₃₁	1	32	yes	complemented
498	#125	C₂³×C₃₁	1	16	yes	complemented
499	#124	C₂³×C₃₁	1	32	yes	—
500	#124	C₂³×C₃₁	1	8	yes	complemented
501	#124	C₂³×C₃₁	1	16	yes	complemented
502	#123	C₂³×C₃₁	1	16	yes	—
503	#123	C₂³×C₃₁	1	8	yes	—
504	#123	C₂³×C₃₁	1	8	yes	—
505	#123	C₂³×C₃₁	1	32	yes	—
506	#123	C₂³×C₃₁	1	16	yes	—
507	#123	C₂³×C₃₁	1	32	yes	—
508	#123	C₂³×C₃₁	1	32	yes	complemented
509	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
510	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
513	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
514	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
515	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
516	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
517	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
518	#121	C₂³×C₃₁	1	8	yes	—
519	#121	C₂³×C₃₁	1	8	yes	—
520	#121	C₂³×C₃₁	1	8	yes	—
521	#121	C₂³×C₃₁	1	8	yes	—
522	#121	C₂³×C₃₁	1	16	yes	—
523	#121	C₂³×C₃₁	1	16	yes	—
524	#121	C₂³×C₃₁	1	32	yes	—
525	#121	C₂³×C₃₁	1	16	yes	complemented
526	#120	C₂³×C₃₁	1	16	yes	—
527	#120	C₂³×C₃₁	1	8	yes	—
528	#120	C₂³×C₃₁	1	8	yes	—
529	#120	C₂³×C₃₁	1	16	yes	—
530	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
531	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
532	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
533	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
534	C₄×D₄	C₂³×C₃₁	1	16	yes	—
535	C₄×D₄	C₂³×C₃₁	1	16	yes	—
536	C₄×D₄	C₂³×C₃₁	1	16	yes	—
537	C₄×D₄	C₂³×C₃₁	1	16	yes	—
538	C₄×D₄	C₂³×C₃₁	1	32	yes	—
539	C₄×D₄	C₂³×C₃₁	1	32	yes	—
540	C₄×D₄	C₂³×C₃₁	1	32	yes	—
541	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
542	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
543	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
544	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
545	#117	C₂³×C₃₁	1	4	yes	—
546	#117	C₂³×C₃₁	1	4	yes	—
547	#117	C₂³×C₃₁	1	4	yes	—
548	#117	C₂³×C₃₁	1	4	yes	—
549	#117	C₂³×C₃₁	1	4	yes	—
550	#117	C₂³×C₃₁	1	16	yes	—
551	#117	C₂³×C₃₁	1	4	yes	—
552	#117	C₂³×C₃₁	1	4	yes	—
553	#117	C₂³×C₃₁	1	4	yes	—
554	#117	C₂³×C₃₁	1	8	yes	—
555	#117	C₂³×C₃₁	1	8	yes	—
556	#117	C₂³×C₃₁	1	8	yes	—
557	#117	C₂³×C₃₁	1	8	yes	—
558	#117	C₂³×C₃₁	1	16	yes	—
559	#117	C₂³×C₃₁	1	16	yes	—
560	#117	C₂³×C₃₁	1	16	yes	complemented
561	#117	C₂³×C₃₁	1	16	yes	complemented
562	#117	C₂³×C₃₁	1	32	yes	complemented
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
579	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
581	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
583	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
584	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
585	C₂×C₄²	C₂³×C₃₁	1	16	yes	complemented
586	C₃₁	#62814	1	1	yes	characteristic, direct product factor, Sylow
587	C₂⁴	—	2	4	no	—
588	C₂⁴	—	4	4	no	—
589	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
590	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
591	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
592	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
593	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
594	#41	—	2	16	no	—
595	#41	—	2	16	no	—
596	#41	—	2	16	no	—
597	#41	—	2	16	no	—
598	#41	—	4	32	no	—
599	C₂×Q₈	—	2	8	no	—
600	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
601	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
602	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
603	C₂×D₄	—	2	16	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	4	16	no	—
606	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
607	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
608	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
609	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
610	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
611	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
612	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	16	no	—
615	C₂²×C₄	—	2	16	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	16	no	—
621	C₂²×C₄	—	4	8	no	—
622	C₂²×C₄	#41×C₃₁	1	8	yes	complemented
623	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
627	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
628	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
633	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
638	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
640	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	—
641	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
646	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
648	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
649	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
650	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
651	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
652	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
654	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
655	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
656	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
657	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
658	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
659	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
660	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
661	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
662	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
663	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
664	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
665	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
666	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
667	C₄²	C₂⁴×C₃₁	1	4	yes	—
668	C₄²	C₂⁴×C₃₁	1	8	yes	—
669	C₄²	C₂⁴×C₃₁	1	4	yes	—
670	C₄²	C₂⁴×C₃₁	1	4	yes	—
671	C₄²	C₂⁴×C₃₁	1	8	yes	—
672	C₄²	C₂⁴×C₃₁	1	4	yes	—
673	C₄²	C₂⁴×C₃₁	1	8	yes	—
674	C₄²	C₂⁴×C₃₁	1	8	yes	—
675	C₄²	C₂⁴×C₃₁	1	32	yes	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	8	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	8	no	—
686	C₂³	—	4	16	no	—
687	C₂³	C₂×#41×C₃₁	1	4	yes	—
688	C₂³	C₂⁵×C₃₁	1	2	yes	—
689	C₂³	C₂⁵×C₃₁	1	8	yes	—
690	C₂³	C₂⁵×C₃₁	1	2	yes	—
691	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
692	C₂³	C₂⁵×C₃₁	1	2	yes	—
693	Q₈	—	2	8	no	—
694	Q₈	—	2	8	no	—
695	Q₈	—	4	16	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	16	no	—
698	D₄	—	2	32	no	—
699	D₄	—	2	8	no	—
700	D₄	—	2	8	no	—
701	D₄	—	4	16	no	—
702	D₄	—	4	16	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	16	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	16	no	—
715	C₂×C₄	—	2	16	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	32	no	—
721	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
722	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
723	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
724	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
725	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
726	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
727	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
728	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
729	C₂×C₄	C₂⁵×C₃₁	1	16	yes	—
730	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
731	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
732	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
733	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
734	C₂²	—	2	8	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	16	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	16	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	8	8	no	—
747	C₂²	C₂²×#41×C₃₁	1	4	yes	—
748	C₂²	C₂²×#41×C₃₁	1	2	yes	—
749	C₂²	C₃₁×#585	1	4	yes	—
750	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	8	no	—
754	C₄	—	2	8	no	—
755	C₄	—	2	8	no	—
756	C₄	—	2	16	no	—
757	C₄	C₂²×#41×C₃₁	1	2	yes	—
758	C₄	C₂²×#41×C₃₁	1	4	yes	—
759	C₄	C₂²×#41×C₃₁	1	2	yes	—
760	C₂	—	2	2	no	—
761	C₂	—	2	4	no	—
762	C₂	—	2	4	no	—
763	C₂	—	4	2	no	—
764	C₂	—	4	8	no	—
765	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
766	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×#3495	C₂	semidirect
2. C₃₁×#3494	C₂	semidirect
3. C₃₁×#3493	C₂	semidirect
4. C₃₁×#3492	C₂	semidirect
5. C₃₁×#3491	C₂	semidirect
6. C₃₁×#3490	C₂	semidirect
7. C₃₁×#3475	C₂	semidirect
8. C₃₁×#3458	C₂	semidirect
9. C₃₁×#3455	C₂	semidirect
10. C₃₁×#3449	C₂	semidirect
11. C₃₁×#3444	C₂	semidirect
12. C₂×C₃₁×#525	C₂	semidirect
13. C₃₁×#3428	C₂	semidirect
14. C₂²×C₃₁×#117	C₂	semidirect
17. C₃₁×#556	C₂²	semidirect
18. C₃₁×#555	C₂²	semidirect
19. C₃₁×#554	C₂²	semidirect
20. C₃₁×#553	C₂²	semidirect
21. C₃₁×#553	C₂²	semidirect
22. C₃₁×#552	C₂²	semidirect
23. C₃₁×#552	C₂²	semidirect
24. C₃₁×#552	C₂²	semidirect
25. C₃₁×#551	C₂²	semidirect
26. C₃₁×#551	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
28. C₃₁×#546	C₂²	semidirect
29. C₃₁×#544	C₂²	semidirect
30. C₃₁×#544	C₂²	semidirect
32. C₃₁×#542	C₂²	semidirect
33. C₃₁×#541	C₂²	semidirect
34. C₃₁×#540	C₂²	semidirect
35. C₃₁×#539	C₂²	semidirect
36. C₃₁×#538	C₂²	semidirect
37. C₃₁×#537	C₂²	semidirect
38. C₃₁×#536	C₂²	semidirect
39. C₃₁×#535	C₂²	semidirect
41. C₃₁×#533	C₂²	semidirect
42. C₃₁×#533	C₂²	semidirect
43. C₃₁×#533	C₂²	semidirect
44. C₃₁×#532	C₂²	semidirect
45. C₃₁×#532	C₂²	semidirect
46. C₃₁×#529	C₂²	semidirect
47. C₃₁×#529	C₂²	semidirect
48. C₃₁×#529	C₂²	semidirect
49. C₃₁×#529	C₂²	semidirect
52. C₃₁×#525	C₂²	semidirect
53. C₃₁×#525	C₂²	semidirect
54. C₃₁×#525	C₂²	semidirect
55. C₃₁×#525	C₂²	semidirect
56. C₃₁×#525	C₂²	semidirect
57. C₃₁×#525	C₂²	semidirect
59. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₃₁×#121	C₂²	semidirect
62. C₃₁×#520	C₂²	semidirect
63. C₃₁×#520	C₂²	semidirect
64. C₃₁×#519	C₂²	semidirect
66. C₃₁×#518	C₂²	semidirect
67. C₄×#41×C₃₁	C₂²	semidirect
68. C₄×#41×C₃₁	C₂²	semidirect
69. C₄×#41×C₃₁	C₂²	semidirect
70. C₂×C₄×D₄×C₃₁	C₂²	semidirect
75. C₂×C₃₁×#117	C₂²	semidirect
76. C₂×C₃₁×#117	C₂²	semidirect
77. C₂×C₃₁×#117	C₂²	semidirect
78. C₂×C₃₁×#117	C₂²	semidirect
79. C₂×C₃₁×#117	C₂²	semidirect
80. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
82. C₂²×C₄²×C₃₁	C₂²	semidirect
105. C₃₁×C₄⋊Q₈	C₂³	semidirect
106. C₃₁×C₄⋊Q₈	C₂³	semidirect
107. C₃₁×C₄⋊Q₈	C₂³	semidirect
108. C₃₁×#127	C₂³	semidirect
110. C₃₁×#126	C₂³	semidirect
111. C₃₁×#126	C₂³	semidirect
112. C₃₁×#125	C₂³	semidirect
113. C₃₁×#125	C₂³	semidirect
114. C₃₁×#125	C₂³	semidirect
115. C₃₁×#125	C₂³	semidirect
117. C₃₁×#124	C₂³	semidirect
118. C₃₁×#124	C₂³	semidirect
125. C₃₁×#123	C₂³	semidirect
133. C₃₁×C₂²⋊Q₈	C₂³	semidirect
134. C₃₁×C₂²⋊Q₈	C₂³	semidirect
142. C₃₁×#121	C₂³	semidirect
147. C₄×Q₈×C₃₁	C₂³	semidirect
148. C₄×Q₈×C₃₁	C₂³	semidirect
149. C₄×Q₈×C₃₁	C₂³	semidirect
150. C₄×Q₈×C₃₁	C₂³	semidirect
158. C₄×D₄×C₃₁	C₂³	semidirect
159. C₄×D₄×C₃₁	C₂³	semidirect
160. C₄×D₄×C₃₁	C₂³	semidirect
161. C₄×D₄×C₃₁	C₂³	semidirect
177. C₃₁×#117	C₂³	semidirect
178. C₃₁×#117	C₂³	semidirect
179. C₃₁×#117	C₂³	semidirect
187. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
202. C₂×C₄²×C₃₁	C₂³	semidirect
238. C₂²×C₄×C₃₁	#41	semidirect
292. #62814	C₃₁	direct (N × H)
351. #3495	C₂×C₃₁	semidirect
352. #3494	C₂×C₃₁	semidirect
353. #3493	C₂×C₃₁	semidirect
354. #3492	C₂×C₃₁	semidirect
355. #3491	C₂×C₃₁	semidirect
356. #3490	C₂×C₃₁	semidirect
357. #3475	C₂×C₃₁	semidirect
358. #3458	C₂×C₃₁	semidirect
359. #3455	C₂×C₃₁	semidirect
360. #3449	C₂×C₃₁	semidirect
361. #3444	C₂×C₃₁	semidirect
362. C₂×#525	C₂×C₃₁	semidirect
363. #3428	C₂×C₃₁	semidirect
364. C₂²×#117	C₂×C₃₁	semidirect
393. #556	C₂²×C₃₁	semidirect
394. #555	C₂²×C₃₁	semidirect
395. #554	C₂²×C₃₁	semidirect
396. #553	C₂²×C₃₁	semidirect
397. #553	C₂²×C₃₁	semidirect
398. #552	C₂²×C₃₁	semidirect
399. #552	C₂²×C₃₁	semidirect
400. #552	C₂²×C₃₁	semidirect
401. #551	C₂²×C₃₁	semidirect
402. #551	C₂²×C₃₁	semidirect
403. #547	C₂²×C₃₁	semidirect
404. #546	C₂²×C₃₁	semidirect
405. #544	C₂²×C₃₁	semidirect
406. #544	C₂²×C₃₁	semidirect
408. #542	C₂²×C₃₁	semidirect
409. #541	C₂²×C₃₁	semidirect
410. #540	C₂²×C₃₁	semidirect
411. #539	C₂²×C₃₁	semidirect
412. #538	C₂²×C₃₁	semidirect
413. #537	C₂²×C₃₁	semidirect
414. #536	C₂²×C₃₁	semidirect
415. #535	C₂²×C₃₁	semidirect
417. #533	C₂²×C₃₁	semidirect
418. #533	C₂²×C₃₁	semidirect
419. #533	C₂²×C₃₁	semidirect
420. #532	C₂²×C₃₁	semidirect
421. #532	C₂²×C₃₁	semidirect
422. #529	C₂²×C₃₁	semidirect
423. #529	C₂²×C₃₁	semidirect
424. #529	C₂²×C₃₁	semidirect
425. #529	C₂²×C₃₁	semidirect
428. #525	C₂²×C₃₁	semidirect
429. #525	C₂²×C₃₁	semidirect
430. #525	C₂²×C₃₁	semidirect
431. #525	C₂²×C₃₁	semidirect
432. #525	C₂²×C₃₁	semidirect
433. #525	C₂²×C₃₁	semidirect
435. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
436. C₂×#121	C₂²×C₃₁	semidirect
438. #520	C₂²×C₃₁	semidirect
439. #520	C₂²×C₃₁	semidirect
440. #519	C₂²×C₃₁	semidirect
442. #518	C₂²×C₃₁	semidirect
443. C₄×#41	C₂²×C₃₁	semidirect
444. C₄×#41	C₂²×C₃₁	semidirect
445. C₄×#41	C₂²×C₃₁	semidirect
446. C₂×C₄×D₄	C₂²×C₃₁	semidirect
451. C₂×#117	C₂²×C₃₁	semidirect
452. C₂×#117	C₂²×C₃₁	semidirect
453. C₂×#117	C₂²×C₃₁	semidirect
454. C₂×#117	C₂²×C₃₁	semidirect
455. C₂×#117	C₂²×C₃₁	semidirect
456. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
458. C₂²×C₄²	C₂²×C₃₁	semidirect
488. C₄⋊Q₈	C₂³×C₃₁	semidirect
489. C₄⋊Q₈	C₂³×C₃₁	semidirect
490. C₄⋊Q₈	C₂³×C₃₁	semidirect
491. #127	C₂³×C₃₁	semidirect
493. #126	C₂³×C₃₁	semidirect
494. #126	C₂³×C₃₁	semidirect
495. #125	C₂³×C₃₁	semidirect
496. #125	C₂³×C₃₁	semidirect
497. #125	C₂³×C₃₁	semidirect
498. #125	C₂³×C₃₁	semidirect
500. #124	C₂³×C₃₁	semidirect
501. #124	C₂³×C₃₁	semidirect
508. #123	C₂³×C₃₁	semidirect
516. C₂²⋊Q₈	C₂³×C₃₁	semidirect
517. C₂²⋊Q₈	C₂³×C₃₁	semidirect
525. #121	C₂³×C₃₁	semidirect
530. C₄×Q₈	C₂³×C₃₁	semidirect
531. C₄×Q₈	C₂³×C₃₁	semidirect
532. C₄×Q₈	C₂³×C₃₁	semidirect
533. C₄×Q₈	C₂³×C₃₁	semidirect
541. C₄×D₄	C₂³×C₃₁	semidirect
542. C₄×D₄	C₂³×C₃₁	semidirect
543. C₄×D₄	C₂³×C₃₁	semidirect
544. C₄×D₄	C₂³×C₃₁	semidirect
560. #117	C₂³×C₃₁	semidirect
561. #117	C₂³×C₃₁	semidirect
562. #117	C₂³×C₃₁	semidirect
570. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
585. C₂×C₄²	C₂³×C₃₁	semidirect
586. C₃₁	#62814	direct (N × H)
622. 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×#3495	2
C₃₁×#3494	2
C₃₁×#3493	2
C₃₁×#3492	2
C₃₁×#3491	2
C₃₁×#3490	2
C₃₁×#3475	2
C₃₁×#3458	2
C₃₁×#3455	2
C₃₁×#3449	2
C₃₁×#3444	2
C₂×C₃₁×#525	2
C₃₁×#3428	2
C₂²×C₃₁×#117	2
#62814	31

Subgroups — C31×#62814 #21519573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62814 #21519573