Subgroups — C₃₁×#34877 #21491636

Order 7936.

2646 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2611	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2610	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2601	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2539	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2413	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2411	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2396	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2392	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#120	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2293	C₂	1	4	yes	maximal, complemented
17	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#529	—	2	8	no	—
20	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#120	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×#117	—	2	8	no	—
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂×C₃₁×#117	C₂²	1	2	yes	—
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	C₂²	1	2	yes	—
38	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#400	C₂²	1	2	yes	complemented
46	C₃₁×#399	C₂²	1	2	yes	—
47	C₃₁×#398	C₂²	1	2	yes	complemented
48	C₃₁×#398	C₂²	1	4	yes	complemented
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#396	C₂²	1	4	yes	—
51	C₃₁×#396	C₂²	1	4	yes	complemented
52	C₃₁×#395	C₂²	1	2	yes	complemented
53	C₃₁×#394	C₂²	1	4	yes	—
54	C₃₁×#394	C₂²	1	2	yes	complemented
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#392	C₂²	1	2	yes	—
57	C₃₁×#390	C₂²	1	4	yes	—
58	C₃₁×#390	C₂²	1	4	yes	—
59	C₃₁×#389	C₂²	1	4	yes	complemented
60	C₃₁×#389	C₂²	1	4	yes	complemented
61	C₃₁×#388	C₂²	1	4	yes	—
62	C₃₁×#388	C₂²	1	4	yes	—
63	C₃₁×#388	C₂²	1	4	yes	complemented
64	C₃₁×#388	C₂²	1	4	yes	complemented
65	C₃₁×#388	C₂²	1	4	yes	complemented
66	C₃₁×#387	C₂²	1	4	yes	complemented
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	4	yes	—
70	C₃₁×#385	C₂²	1	2	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	4	yes	—
73	C₃₁×#381	C₂²	1	2	yes	—
74	C₃₁×#379	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
76	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
83	C₃₁×#376	C₂²	1	2	yes	complemented
84	C₄³×C₃₁	C₂²	1	2	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	—	2	4	no	—
91	C₂³×C₄×C₃₁	—	2	8	no	—
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×#126	—	2	8	no	—
102	C₃₁×#125	—	2	4	no	—
103	C₃₁×#124	—	2	4	no	—
104	C₃₁×#123	—	2	8	no	—
105	C₃₁×#123	—	2	8	no	—
106	C₃₁×C₂²⋊Q₈	—	2	4	no	—
107	C₃₁×#121	—	2	4	no	—
108	C₃₁×#120	—	2	8	no	—
109	C₄×Q₈×C₃₁	—	2	4	no	—
110	C₄×D₄×C₃₁	—	2	8	no	—
111	C₄×D₄×C₃₁	—	2	16	no	—
112	C₄×D₄×C₃₁	—	2	4	no	—
113	C₃₁×#117	—	2	8	no	—
114	C₃₁×#117	—	2	8	no	—
115	C₃₁×#117	—	2	8	no	—
116	C₃₁×#117	—	2	8	no	—
117	C₃₁×#117	—	2	8	no	—
118	C₃₁×#117	—	2	8	no	—
119	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄²×C₃₁	—	2	4	no	—
155	C₂×C₄²×C₃₁	D₄	1	8	yes	complemented
156	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
158	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×#95	C₂³	1	2	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₃₁×#95	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	2	yes	—
172	C₃₁×#95	C₂³	1	4	yes	—
173	C₃₁×#95	C₂³	1	4	yes	—
174	C₃₁×#95	C₂³	1	4	yes	—
175	C₃₁×#95	C₂³	1	4	yes	—
176	C₂⁴×C₃₁	—	2	2	no	—
177	C₂⁴×C₃₁	—	2	4	no	—
178	C₂⁴×C₃₁	—	2	4	no	—
179	C₂⁴×C₃₁	—	4	2	no	—
180	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
181	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
182	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
183	C₂×Q₈×C₃₁	—	2	2	no	—
184	C₂×Q₈×C₃₁	—	4	2	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	8	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	2	no	—
190	C₂×D₄×C₃₁	—	2	8	no	—
191	C₂×D₄×C₃₁	—	4	4	no	—
192	C₂×D₄×C₃₁	—	4	2	no	—
193	C₂²×C₄×C₃₁	—	2	32	no	—
194	C₂²×C₄×C₃₁	—	2	2	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	4	no	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	4	no	—
202	C₂²×C₄×C₃₁	—	2	4	no	—
203	C₂²×C₄×C₃₁	—	2	2	no	—
204	C₂²×C₄×C₃₁	—	2	2	no	—
205	C₂²×C₄×C₃₁	—	2	4	no	—
206	C₂²×C₄×C₃₁	—	2	4	no	—
207	C₂²×C₄×C₃₁	—	2	8	no	—
208	C₂²×C₄×C₃₁	—	4	2	no	—
209	C₂²×C₄×C₃₁	—	4	2	no	—
210	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₃₁	#41	1	8	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	4	no	—
236	C₄⋊C₄×C₃₁	—	2	2	no	—
237	C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₄⋊C₄×C₃₁	—	2	8	no	—
239	C₄⋊C₄×C₃₁	—	2	8	no	—
240	C₄⋊C₄×C₃₁	—	2	8	no	—
241	C₄⋊C₄×C₃₁	—	4	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	8	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₃₁	—	2	4	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	4	no	—
252	C₂²⋊C₄×C₃₁	—	2	4	no	—
253	C₂²⋊C₄×C₃₁	—	2	8	no	—
254	C₂²⋊C₄×C₃₁	—	2	8	no	—
255	C₂²⋊C₄×C₃₁	—	2	8	no	—
256	C₂²⋊C₄×C₃₁	—	4	4	no	—
257	C₂²⋊C₄×C₃₁	—	4	4	no	—
258	C₂²⋊C₄×C₃₁	#41	1	8	yes	—
259	C₄²×C₃₁	—	2	4	no	—
260	C₄²×C₃₁	—	2	4	no	—
261	C₄²×C₃₁	—	2	4	no	—
262	C₄²×C₃₁	—	2	8	no	—
263	C₄²×C₃₁	—	2	8	no	—
264	C₄²×C₃₁	—	4	2	no	—
265	C₄²×C₃₁	—	4	2	no	—
266	C₄²×C₃₁	C₂×D₄	1	4	yes	—
267	C₄²×C₃₁	C₂×D₄	1	4	yes	—
268	C₄²×C₃₁	C₂×D₄	1	4	yes	—
269	C₄²×C₃₁	C₂×D₄	1	4	yes	—
270	#34877	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	8	no	—
274	C₂³×C₃₁	—	2	2	no	—
275	C₂³×C₃₁	—	2	4	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	4	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	2	4	no	—
281	C₂³×C₃₁	—	2	2	no	—
282	C₂³×C₃₁	—	2	4	no	—
283	C₂³×C₃₁	—	4	16	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	—	4	4	no	—
286	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
287	C₂³×C₃₁	C₂×#41	1	4	yes	—
288	C₂³×C₃₁	C₂×#41	1	4	yes	—
289	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
290	Q₈×C₃₁	—	4	4	no	—
291	D₄×C₃₁	—	4	16	no	—
292	D₄×C₃₁	—	4	4	no	—
293	D₄×C₃₁	—	4	8	no	—
294	C₂×C₄×C₃₁	—	2	16	no	—
295	C₂×C₄×C₃₁	—	2	8	no	—
296	C₂×C₄×C₃₁	—	2	8	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	4	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	8	no	—
307	C₂×C₄×C₃₁	—	2	16	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	4	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	4	4	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	8	no	—
326	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
333	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
334	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
335	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
336	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#2611	C₂×C₃₁	1	2	yes	complemented
338	#2610	C₂×C₃₁	1	2	yes	complemented
339	#2601	C₂×C₃₁	1	4	yes	complemented
340	#2591	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#2583	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#2561	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#2539	C₂×C₃₁	1	1	yes	characteristic
344	#2413	C₂×C₃₁	1	2	yes	complemented
345	#2411	C₂×C₃₁	1	2	yes	complemented
346	#2396	C₂×C₃₁	1	2	yes	complemented
347	#2392	C₂×C₃₁	1	2	yes	complemented
348	C₄×#123	C₂×C₃₁	1	2	yes	complemented
349	C₄×#120	C₂×C₃₁	1	2	yes	complemented
350	#2293	C₂×C₃₁	1	4	yes	complemented
351	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
352	C₂²×C₃₁	—	2	2	no	—
353	C₂²×C₃₁	—	2	2	no	—
354	C₂²×C₃₁	—	2	8	no	—
355	C₂²×C₃₁	—	2	4	no	—
356	C₂²×C₃₁	—	2	8	no	—
357	C₂²×C₃₁	—	4	16	no	—
358	C₂²×C₃₁	—	4	2	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	4	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	4	2	no	—
364	C₂²×C₃₁	—	4	4	no	—
365	C₂²×C₃₁	—	4	4	no	—
366	C₂²×C₃₁	#532	1	4	yes	—
367	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
368	C₂²×C₃₁	C₂²×#41	1	2	yes	—
369	C₂²×C₃₁	C₂²×#41	1	2	yes	—
370	C₂²×C₃₁	#585	1	2	yes	—
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	2	4	no	—
373	C₄×C₃₁	—	2	2	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	2	2	no	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	8	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	2	no	—
383	C₄×C₃₁	—	4	4	no	—
384	C₄×C₃₁	#525	1	4	yes	—
385	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
386	#529	—	2	8	no	—
387	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
388	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
389	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
390	C₂×#123	C₂²×C₃₁	1	2	yes	—
391	C₂×#123	C₂²×C₃₁	1	2	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
394	C₂×#120	C₂²×C₃₁	1	2	yes	—
395	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
397	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
399	C₂×#117	—	2	8	no	—
400	C₂×#117	C₂²×C₃₁	1	2	yes	—
401	C₂×#117	C₂²×C₃₁	1	2	yes	—
402	C₂×#117	C₂²×C₃₁	1	2	yes	—
403	C₂×#117	C₂²×C₃₁	1	2	yes	—
404	C₂×#117	C₂²×C₃₁	1	2	yes	—
405	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
406	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
412	#400	C₂²×C₃₁	1	2	yes	complemented
413	#399	C₂²×C₃₁	1	2	yes	—
414	#398	C₂²×C₃₁	1	2	yes	complemented
415	#398	C₂²×C₃₁	1	4	yes	complemented
416	#397	C₂²×C₃₁	1	2	yes	—
417	#396	C₂²×C₃₁	1	4	yes	—
418	#396	C₂²×C₃₁	1	4	yes	complemented
419	#395	C₂²×C₃₁	1	2	yes	complemented
420	#394	C₂²×C₃₁	1	4	yes	—
421	#394	C₂²×C₃₁	1	2	yes	complemented
422	#393	C₂²×C₃₁	1	2	yes	—
423	#392	C₂²×C₃₁	1	2	yes	—
424	#390	C₂²×C₃₁	1	4	yes	—
425	#390	C₂²×C₃₁	1	4	yes	—
426	#389	C₂²×C₃₁	1	4	yes	complemented
427	#389	C₂²×C₃₁	1	4	yes	complemented
428	#388	C₂²×C₃₁	1	4	yes	—
429	#388	C₂²×C₃₁	1	4	yes	—
430	#388	C₂²×C₃₁	1	4	yes	complemented
431	#388	C₂²×C₃₁	1	4	yes	complemented
432	#388	C₂²×C₃₁	1	4	yes	complemented
433	#387	C₂²×C₃₁	1	4	yes	complemented
434	#386	C₂²×C₃₁	1	2	yes	—
435	#386	C₂²×C₃₁	1	2	yes	—
436	#386	C₂²×C₃₁	1	4	yes	—
437	#385	C₂²×C₃₁	1	2	yes	—
438	#385	C₂²×C₃₁	1	2	yes	—
439	#385	C₂²×C₃₁	1	4	yes	—
440	#381	C₂²×C₃₁	1	2	yes	—
441	#379	C₂²×C₃₁	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
443	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
444	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
445	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
450	#376	C₂²×C₃₁	1	2	yes	complemented
451	C₄³	C₂²×C₃₁	1	2	yes	complemented
452	C₂×C₃₁	—	2	4	no	—
453	C₂×C₃₁	—	4	4	no	—
454	C₂×C₃₁	—	8	2	no	—
455	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
456	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
457	C₂×C₃₁	#3449	1	1	yes	characteristic
458	C₂×C₃₁	#3475	1	4	yes	—
459	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
462	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
463	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂³×C₄	—	2	4	no	—
465	C₂³×C₄	—	2	8	no	—
466	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
469	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
470	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
473	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
475	#126	—	2	8	no	—
476	#125	—	2	4	no	—
477	#124	—	2	4	no	—
478	#123	—	2	8	no	—
479	#123	—	2	8	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	#121	—	2	4	no	—
482	#120	—	2	8	no	—
483	C₄×Q₈	—	2	4	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	16	no	—
486	C₄×D₄	—	2	4	no	—
487	#117	—	2	8	no	—
488	#117	—	2	8	no	—
489	#117	—	2	8	no	—
490	#117	—	2	8	no	—
491	#117	—	2	8	no	—
492	#117	—	2	8	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	—	2	4	no	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂×C₄²	—	2	4	no	—
529	C₂×C₄²	D₄×C₃₁	1	8	yes	complemented
530	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
531	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
532	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
533	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
535	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
541	#95	C₂³×C₃₁	1	4	yes	—
542	#95	C₂³×C₃₁	1	2	yes	—
543	#95	C₂³×C₃₁	1	2	yes	—
544	#95	C₂³×C₃₁	1	4	yes	—
545	#95	C₂³×C₃₁	1	4	yes	—
546	#95	C₂³×C₃₁	1	4	yes	—
547	#95	C₂³×C₃₁	1	4	yes	—
548	#95	C₂³×C₃₁	1	4	yes	—
549	#95	C₂³×C₃₁	1	4	yes	—
550	C₃₁	#34877	1	1	yes	characteristic, direct product factor, Sylow
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
556	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
557	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂²×C₄	—	2	32	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
586	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
587	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
588	C₂²×C₄	#41×C₃₁	1	8	yes	—
589	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	2	8	no	—
616	C₄⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	—	4	4	no	—
633	C₂²⋊C₄	#41×C₃₁	1	8	yes	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	8	no	—
638	C₄²	—	2	8	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	4	2	no	—
641	C₄²	C₂×D₄×C₃₁	1	4	yes	—
642	C₄²	C₂×D₄×C₃₁	1	4	yes	—
643	C₄²	C₂×D₄×C₃₁	1	4	yes	—
644	C₄²	C₂×D₄×C₃₁	1	4	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	8	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	4	16	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
661	C₂³	C₂×#41×C₃₁	1	4	yes	—
662	C₂³	C₂×#41×C₃₁	1	4	yes	—
663	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
664	Q₈	—	4	4	no	—
665	D₄	—	4	16	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	C₂×C₄	—	2	16	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	16	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
706	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
707	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
708	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	8	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	4	16	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	C₃₁×#532	1	4	yes	—
724	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₃₁	1	2	yes	—
726	C₂²	C₂²×#41×C₃₁	1	2	yes	—
727	C₂²	C₃₁×#585	1	2	yes	—
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	4	no	—
741	C₄	C₃₁×#525	1	4	yes	—
742	C₂	—	2	4	no	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
746	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
747	C₂	C₃₁×#3449	1	1	yes	characteristic
748	C₂	C₃₁×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#2539	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#529	C₂	semidirect
2. C₂²×C₃₁×#117	C₂	semidirect
3. C₃₁×#2611	C₂	semidirect
4. C₃₁×#2610	C₂	semidirect
5. C₃₁×#2601	C₂	semidirect
6. C₃₁×#2591	C₂	semidirect
7. C₃₁×#2583	C₂	semidirect
8. C₃₁×#2561	C₂	semidirect
10. C₃₁×#2413	C₂	semidirect
11. C₃₁×#2411	C₂	semidirect
12. C₃₁×#2396	C₂	semidirect
13. C₃₁×#2392	C₂	semidirect
14. C₄×C₃₁×#123	C₂	semidirect
15. C₄×C₃₁×#120	C₂	semidirect
16. C₃₁×#2293	C₂	semidirect
17. C₄×C₃₁×#117	C₂	semidirect
20. C₂×C₃₁×#126	C₂²	semidirect
21. C₂×C₃₁×#125	C₂²	semidirect
22. C₂×C₃₁×#124	C₂²	semidirect
28. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
31. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₃₁×#117	C₂²	semidirect
45. C₃₁×#400	C₂²	semidirect
47. C₃₁×#398	C₂²	semidirect
48. C₃₁×#398	C₂²	semidirect
51. C₃₁×#396	C₂²	semidirect
52. C₃₁×#395	C₂²	semidirect
54. C₃₁×#394	C₂²	semidirect
59. C₃₁×#389	C₂²	semidirect
60. C₃₁×#389	C₂²	semidirect
63. C₃₁×#388	C₂²	semidirect
64. C₃₁×#388	C₂²	semidirect
65. C₃₁×#388	C₂²	semidirect
66. C₃₁×#387	C₂²	semidirect
75. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
76. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
77. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
83. C₃₁×#376	C₂²	semidirect
84. C₄³×C₃₁	C₂²	semidirect
155. C₂×C₄²×C₃₁	D₄	semidirect
270. #34877	C₃₁	direct (N × H)
335. C₂×#529	C₂×C₃₁	semidirect
336. C₂²×#117	C₂×C₃₁	semidirect
337. #2611	C₂×C₃₁	semidirect
338. #2610	C₂×C₃₁	semidirect
339. #2601	C₂×C₃₁	semidirect
340. #2591	C₂×C₃₁	semidirect
341. #2583	C₂×C₃₁	semidirect
342. #2561	C₂×C₃₁	semidirect
344. #2413	C₂×C₃₁	semidirect
345. #2411	C₂×C₃₁	semidirect
346. #2396	C₂×C₃₁	semidirect
347. #2392	C₂×C₃₁	semidirect
348. C₄×#123	C₂×C₃₁	semidirect
349. C₄×#120	C₂×C₃₁	semidirect
350. #2293	C₂×C₃₁	semidirect
351. C₄×#117	C₂×C₃₁	semidirect
387. C₂×#126	C₂²×C₃₁	semidirect
388. C₂×#125	C₂²×C₃₁	semidirect
389. C₂×#124	C₂²×C₃₁	semidirect
395. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
398. C₂×C₄×D₄	C₂²×C₃₁	semidirect
405. C₂×#117	C₂²×C₃₁	semidirect
412. #400	C₂²×C₃₁	semidirect
414. #398	C₂²×C₃₁	semidirect
415. #398	C₂²×C₃₁	semidirect
418. #396	C₂²×C₃₁	semidirect
419. #395	C₂²×C₃₁	semidirect
421. #394	C₂²×C₃₁	semidirect
426. #389	C₂²×C₃₁	semidirect
427. #389	C₂²×C₃₁	semidirect
430. #388	C₂²×C₃₁	semidirect
431. #388	C₂²×C₃₁	semidirect
432. #388	C₂²×C₃₁	semidirect
433. #387	C₂²×C₃₁	semidirect
442. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
443. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
444. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
449. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
450. #376	C₂²×C₃₁	semidirect
451. C₄³	C₂²×C₃₁	semidirect
529. C₂×C₄²	D₄×C₃₁	semidirect
550. C₃₁	#34877	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#529	2
C₂²×C₃₁×#117	2
C₃₁×#2611	2
C₃₁×#2610	2
C₃₁×#2601	2
C₃₁×#2591	2
C₃₁×#2583	2
C₃₁×#2561	2
C₃₁×#2539	2
C₃₁×#2413	2
C₃₁×#2411	2
C₃₁×#2396	2
C₃₁×#2392	2
C₄×C₃₁×#123	2
C₄×C₃₁×#120	2
C₃₁×#2293	2
C₄×C₃₁×#117	2
#34877	31

Subgroups — C31×#34877 #21491636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34877 #21491636