Subgroups — C₃₁×#34720 #21491479

Order 7936.

2548 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2477	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2475	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2463	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2460	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2439	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2421	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2415	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2407	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2398	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
20	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#533	—	2	8	no	—
26	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#125	C₂²	1	2	yes	—
29	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
36	C₄×#41×C₃₁	—	2	8	no	—
37	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#117	C₂²	1	2	yes	—
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#117	C₂²	1	2	yes	—
52	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
54	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#400	C₂²	1	2	yes	—
56	C₃₁×#400	C₂²	1	2	yes	—
57	C₃₁×#398	C₂²	1	2	yes	—
58	C₃₁×#397	C₂²	1	2	yes	—
59	C₃₁×#397	C₂²	1	2	yes	—
60	C₃₁×#397	C₂²	1	2	yes	—
61	C₃₁×#396	C₂²	1	2	yes	—
62	C₃₁×#396	C₂²	1	2	yes	—
63	C₃₁×#394	C₂²	1	2	yes	—
64	C₃₁×#394	C₂²	1	2	yes	—
65	C₃₁×#394	C₂²	1	2	yes	—
66	C₃₁×#394	C₂²	1	2	yes	—
67	C₃₁×#394	C₂²	1	2	yes	—
68	C₃₁×#393	C₂²	1	2	yes	—
69	C₃₁×#393	C₂²	1	2	yes	—
70	C₃₁×#392	C₂²	1	2	yes	—
71	C₃₁×#391	C₂²	1	1	yes	characteristic
72	C₃₁×#391	C₂²	1	1	yes	characteristic
73	C₃₁×#391	C₂²	1	1	yes	characteristic
74	C₃₁×#391	C₂²	1	1	yes	characteristic
75	C₃₁×#391	C₂²	1	2	yes	—
76	C₃₁×#390	C₂²	1	1	yes	characteristic
77	C₃₁×#390	C₂²	1	1	yes	characteristic
78	C₃₁×#389	C₂²	1	1	yes	characteristic
79	C₃₁×#389	C₂²	1	2	yes	—
80	C₃₁×#389	C₂²	1	1	yes	characteristic
81	C₃₁×#389	C₂²	1	1	yes	characteristic
82	C₃₁×#389	C₂²	1	1	yes	characteristic
83	C₃₁×#388	C₂²	1	2	yes	—
84	C₃₁×#388	C₂²	1	2	yes	—
85	C₃₁×#388	C₂²	1	2	yes	—
86	C₃₁×#388	C₂²	1	2	yes	—
87	C₃₁×#388	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#387	C₂²	1	2	yes	—
91	C₃₁×#387	C₂²	1	2	yes	—
92	C₃₁×#387	C₂²	1	2	yes	—
93	C₃₁×#387	C₂²	1	2	yes	—
94	C₃₁×#387	C₂²	1	2	yes	—
95	C₃₁×#386	C₂²	1	2	yes	—
96	C₃₁×#386	C₂²	1	2	yes	—
97	C₃₁×#386	C₂²	1	2	yes	—
98	C₃₁×#385	C₂²	1	2	yes	—
99	C₃₁×#385	C₂²	1	2	yes	—
100	C₃₁×#385	C₂²	1	2	yes	—
101	C₃₁×#385	C₂²	1	2	yes	—
102	C₃₁×#385	C₂²	1	2	yes	—
103	C₃₁×#382	C₂²	1	1	yes	characteristic
104	C₃₁×#380	C₂²	1	1	yes	characteristic
105	C₃₁×#380	C₂²	1	1	yes	characteristic
106	C₃₁×#380	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
123	C₃₁×#376	C₂²	1	2	yes	—
124	C₄³×C₃₁	C₂²	1	1	yes	characteristic
125	C₂×#41×C₃₁	—	2	4	no	—
126	C₂×#41×C₃₁	—	2	4	no	—
127	C₂×#41×C₃₁	—	2	4	no	—
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	—	2	4	no	—
145	C₃₁×C₄⋊Q₈	—	2	4	no	—
146	C₃₁×#125	—	2	8	no	—
147	C₃₁×#124	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	2	4	no	—
150	C₃₁×C₂²⋊Q₈	—	2	4	no	—
151	C₃₁×C₂²⋊Q₈	—	2	8	no	—
152	C₃₁×C₂²⋊Q₈	—	2	8	no	—
153	C₃₁×#121	—	2	4	no	—
154	C₄×Q₈×C₃₁	—	2	4	no	—
155	C₄×Q₈×C₃₁	—	2	8	no	—
156	C₄×Q₈×C₃₁	—	2	4	no	—
157	C₄×Q₈×C₃₁	D₄	1	8	yes	complemented
158	C₄×D₄×C₃₁	—	2	4	no	—
159	C₄×D₄×C₃₁	—	2	4	no	—
160	C₄×D₄×C₃₁	—	2	8	no	—
161	C₄×D₄×C₃₁	—	2	8	no	—
162	C₄×D₄×C₃₁	—	2	4	no	—
163	C₄×D₄×C₃₁	—	2	4	no	—
164	C₄×D₄×C₃₁	—	2	4	no	—
165	C₄×D₄×C₃₁	—	2	8	no	—
166	C₃₁×#117	—	2	8	no	—
167	C₃₁×#117	—	2	4	no	—
168	C₃₁×#117	—	2	8	no	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₃₁	—	2	4	no	—
212	C₂×C₄²×C₃₁	—	2	8	no	—
213	C₂×C₄²×C₃₁	—	2	4	no	—
214	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
216	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
228	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	1	yes	characteristic
244	C₃₁×#95	C₂³	1	2	yes	—
245	C₃₁×#95	C₂³	1	2	yes	—
246	C₃₁×#95	C₂³	1	2	yes	—
247	C₃₁×#95	C₂³	1	2	yes	—
248	C₃₁×#95	C₂³	1	1	yes	characteristic
249	C₃₁×#95	C₂³	1	1	yes	characteristic
250	C₃₁×#95	C₂³	1	1	yes	characteristic
251	C₃₁×#95	C₂³	1	1	yes	characteristic
252	C₃₁×#95	C₂³	1	2	yes	—
253	C₃₁×#95	C₂³	1	2	yes	—
254	C₃₁×#95	C₂³	1	2	yes	—
255	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
257	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
258	#41×C₃₁	—	2	32	no	—
259	C₂×Q₈×C₃₁	—	2	4	no	—
260	C₂×Q₈×C₃₁	—	2	2	no	—
261	C₂×Q₈×C₃₁	—	2	2	no	—
262	C₂×Q₈×C₃₁	—	2	2	no	—
263	C₂×Q₈×C₃₁	—	2	4	no	—
264	C₂×Q₈×C₃₁	—	2	2	no	—
265	C₂×Q₈×C₃₁	—	2	2	no	—
266	C₂×Q₈×C₃₁	—	4	2	no	—
267	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
268	C₂×D₄×C₃₁	—	2	2	no	—
269	C₂×D₄×C₃₁	—	2	2	no	—
270	C₂×D₄×C₃₁	—	2	4	no	—
271	C₂×D₄×C₃₁	—	2	4	no	—
272	C₂×D₄×C₃₁	—	2	4	no	—
273	C₂×D₄×C₃₁	—	2	4	no	—
274	C₂×D₄×C₃₁	—	2	4	no	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	4	2	no	—
279	C₂×D₄×C₃₁	#41	1	4	yes	—
280	C₂²×C₄×C₃₁	—	2	4	no	—
281	C₂²×C₄×C₃₁	—	2	2	no	—
282	C₂²×C₄×C₃₁	—	2	4	no	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	—	2	4	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	4	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	4	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	—	2	4	no	—
298	C₂²×C₄×C₃₁	—	2	2	no	—
299	C₂²×C₄×C₃₁	—	2	4	no	—
300	C₂²×C₄×C₃₁	—	2	2	no	—
301	C₂²×C₄×C₃₁	—	2	4	no	—
302	C₂²×C₄×C₃₁	—	4	1	no	—
303	C₂²×C₄×C₃₁	—	4	1	no	—
304	C₂²×C₄×C₃₁	—	4	2	no	—
305	C₂²×C₄×C₃₁	#41	1	4	yes	—
306	C₂²×C₄×C₃₁	#41	1	4	yes	complemented
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₃₁	—	2	4	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	4	no	—
330	C₄⋊C₄×C₃₁	—	2	4	no	—
331	C₄⋊C₄×C₃₁	—	2	4	no	—
332	C₄⋊C₄×C₃₁	—	2	4	no	—
333	C₄⋊C₄×C₃₁	—	2	4	no	—
334	C₄⋊C₄×C₃₁	—	2	4	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	4	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	4	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	4	no	—
343	C₄⋊C₄×C₃₁	—	2	4	no	—
344	C₄⋊C₄×C₃₁	—	4	2	no	—
345	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
346	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
347	C₄⋊C₄×C₃₁	#41	1	4	yes	complemented
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	4	no	—
351	C₂²⋊C₄×C₃₁	—	2	4	no	—
352	C₂²⋊C₄×C₃₁	—	2	4	no	—
353	C₂²⋊C₄×C₃₁	—	2	4	no	—
354	C₂²⋊C₄×C₃₁	—	2	4	no	—
355	C₂²⋊C₄×C₃₁	—	2	4	no	—
356	C₂²⋊C₄×C₃₁	—	2	4	no	—
357	C₂²⋊C₄×C₃₁	—	2	4	no	—
358	C₂²⋊C₄×C₃₁	—	2	4	no	—
359	C₂²⋊C₄×C₃₁	—	2	4	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	4	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	4	no	—
366	C₂²⋊C₄×C₃₁	—	2	4	no	—
367	C₂²⋊C₄×C₃₁	—	4	2	no	—
368	C₂²⋊C₄×C₃₁	—	4	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	4	no	—
372	C₄²×C₃₁	—	2	4	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	2	2	no	—
376	C₄²×C₃₁	—	2	2	no	—
377	C₄²×C₃₁	—	2	4	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	—	2	2	no	—
380	C₄²×C₃₁	—	2	2	no	—
381	C₄²×C₃₁	—	2	4	no	—
382	C₄²×C₃₁	—	2	2	no	—
383	C₄²×C₃₁	—	2	2	no	—
384	C₄²×C₃₁	—	4	1	no	—
385	C₄²×C₃₁	C₂×D₄	1	4	yes	—
386	C₄²×C₃₁	C₂×D₄	1	8	yes	—
387	#34720	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂³×C₃₁	—	2	1	no	—
389	C₂³×C₃₁	—	2	2	no	—
390	C₂³×C₃₁	—	2	1	no	—
391	C₂³×C₃₁	—	2	2	no	—
392	C₂³×C₃₁	—	2	1	no	—
393	C₂³×C₃₁	—	2	1	no	—
394	C₂³×C₃₁	—	2	1	no	—
395	C₂³×C₃₁	—	2	1	no	—
396	C₂³×C₃₁	—	2	2	no	—
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	—	2	1	no	—
400	C₂³×C₃₁	—	2	1	no	—
401	C₂³×C₃₁	—	2	1	no	—
402	C₂³×C₃₁	—	2	2	no	—
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	C₂×#41	1	4	yes	—
407	C₂³×C₃₁	C₂×#41	1	2	yes	—
408	C₂³×C₃₁	C₂×#41	1	2	yes	—
409	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
410	Q₈×C₃₁	—	2	8	no	—
411	Q₈×C₃₁	—	4	8	no	—
412	Q₈×C₃₁	—	4	4	no	—
413	D₄×C₃₁	—	2	8	no	—
414	D₄×C₃₁	—	2	16	no	—
415	D₄×C₃₁	—	2	8	no	—
416	D₄×C₃₁	—	4	8	no	—
417	C₂×C₄×C₃₁	—	2	16	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	1	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	8	no	—
435	C₂×C₄×C₃₁	—	2	8	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	1	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	1	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	4	4	no	—
467	C₂×C₄×C₃₁	—	4	8	no	—
468	C₂×C₄×C₃₁	—	4	4	no	—
469	C₂×C₄×C₃₁	—	4	4	no	—
470	C₂×C₄×C₃₁	—	4	4	no	—
471	C₂×C₄×C₃₁	—	4	8	no	—
472	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
479	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
480	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
481	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
483	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
484	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
485	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
486	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
487	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#2477	C₂×C₃₁	1	2	yes	complemented
489	#2475	C₂×C₃₁	1	2	yes	complemented
490	#2463	C₂×C₃₁	1	2	yes	complemented
491	#2460	C₂×C₃₁	1	2	yes	complemented
492	#2452	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#2446	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#2439	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#2432	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#2427	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#2421	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#2415	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#2407	C₂×C₃₁	1	1	yes	characteristic
500	#2398	C₂×C₃₁	1	2	yes	complemented
501	#2392	C₂×C₃₁	1	2	yes	complemented
502	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
503	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
504	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
505	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#2290	C₂×C₃₁	1	2	yes	complemented
508	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
509	C₂²×C₃₁	—	2	4	no	—
510	C₂²×C₃₁	—	2	2	no	—
511	C₂²×C₃₁	—	2	2	no	—
512	C₂²×C₃₁	—	2	2	no	—
513	C₂²×C₃₁	—	2	2	no	—
514	C₂²×C₃₁	—	2	2	no	—
515	C₂²×C₃₁	—	2	2	no	—
516	C₂²×C₃₁	—	2	4	no	—
517	C₂²×C₃₁	—	2	4	no	—
518	C₂²×C₃₁	—	4	1	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	4	1	no	—
521	C₂²×C₃₁	—	4	2	no	—
522	C₂²×C₃₁	—	4	1	no	—
523	C₂²×C₃₁	—	4	2	no	—
524	C₂²×C₃₁	—	4	1	no	—
525	C₂²×C₃₁	—	4	2	no	—
526	C₂²×C₃₁	—	4	1	no	—
527	C₂²×C₃₁	—	4	1	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	4	1	no	—
530	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
531	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
532	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
533	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
534	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
535	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂²×C₃₁	#585	1	1	yes	characteristic
537	C₄×C₃₁	—	2	2	no	—
538	C₄×C₃₁	—	2	4	no	—
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	2	2	no	—
543	C₄×C₃₁	—	2	4	no	—
544	C₄×C₃₁	—	2	2	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	—	4	1	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	2	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	#525	1	4	yes	—
556	C₄×C₃₁	#548	1	4	yes	—
557	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
558	#533	—	2	8	no	—
559	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
561	C₂×#125	C₂²×C₃₁	1	2	yes	—
562	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
563	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
564	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
565	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
566	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
567	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
568	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×#41	—	2	8	no	—
570	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
571	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
572	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
573	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
575	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
576	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
577	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
578	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
579	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×#117	C₂²×C₃₁	1	2	yes	—
583	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
584	C₂×#117	C₂²×C₃₁	1	2	yes	—
585	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
586	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
587	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
588	#400	C₂²×C₃₁	1	2	yes	—
589	#400	C₂²×C₃₁	1	2	yes	—
590	#398	C₂²×C₃₁	1	2	yes	—
591	#397	C₂²×C₃₁	1	2	yes	—
592	#397	C₂²×C₃₁	1	2	yes	—
593	#397	C₂²×C₃₁	1	2	yes	—
594	#396	C₂²×C₃₁	1	2	yes	—
595	#396	C₂²×C₃₁	1	2	yes	—
596	#394	C₂²×C₃₁	1	2	yes	—
597	#394	C₂²×C₃₁	1	2	yes	—
598	#394	C₂²×C₃₁	1	2	yes	—
599	#394	C₂²×C₃₁	1	2	yes	—
600	#394	C₂²×C₃₁	1	2	yes	—
601	#393	C₂²×C₃₁	1	2	yes	—
602	#393	C₂²×C₃₁	1	2	yes	—
603	#392	C₂²×C₃₁	1	2	yes	—
604	#391	C₂²×C₃₁	1	1	yes	characteristic
605	#391	C₂²×C₃₁	1	1	yes	characteristic
606	#391	C₂²×C₃₁	1	1	yes	characteristic
607	#391	C₂²×C₃₁	1	1	yes	characteristic
608	#391	C₂²×C₃₁	1	2	yes	—
609	#390	C₂²×C₃₁	1	1	yes	characteristic
610	#390	C₂²×C₃₁	1	1	yes	characteristic
611	#389	C₂²×C₃₁	1	1	yes	characteristic
612	#389	C₂²×C₃₁	1	2	yes	—
613	#389	C₂²×C₃₁	1	1	yes	characteristic
614	#389	C₂²×C₃₁	1	1	yes	characteristic
615	#389	C₂²×C₃₁	1	1	yes	characteristic
616	#388	C₂²×C₃₁	1	2	yes	—
617	#388	C₂²×C₃₁	1	2	yes	—
618	#388	C₂²×C₃₁	1	2	yes	—
619	#388	C₂²×C₃₁	1	2	yes	—
620	#388	C₂²×C₃₁	1	2	yes	—
621	#387	C₂²×C₃₁	1	2	yes	—
622	#387	C₂²×C₃₁	1	2	yes	—
623	#387	C₂²×C₃₁	1	2	yes	—
624	#387	C₂²×C₃₁	1	2	yes	—
625	#387	C₂²×C₃₁	1	2	yes	—
626	#387	C₂²×C₃₁	1	2	yes	—
627	#387	C₂²×C₃₁	1	2	yes	—
628	#386	C₂²×C₃₁	1	2	yes	—
629	#386	C₂²×C₃₁	1	2	yes	—
630	#386	C₂²×C₃₁	1	2	yes	—
631	#385	C₂²×C₃₁	1	2	yes	—
632	#385	C₂²×C₃₁	1	2	yes	—
633	#385	C₂²×C₃₁	1	2	yes	—
634	#385	C₂²×C₃₁	1	2	yes	—
635	#385	C₂²×C₃₁	1	2	yes	—
636	#382	C₂²×C₃₁	1	1	yes	characteristic
637	#380	C₂²×C₃₁	1	1	yes	characteristic
638	#380	C₂²×C₃₁	1	1	yes	characteristic
639	#380	C₂²×C₃₁	1	2	yes	—
640	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
641	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
643	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
644	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
645	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
647	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
648	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
649	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
650	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
651	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
652	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
653	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
654	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
655	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
656	#376	C₂²×C₃₁	1	2	yes	—
657	C₄³	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×C₃₁	—	4	2	no	—
659	C₂×C₃₁	—	4	4	no	—
660	C₂×C₃₁	—	4	2	no	—
661	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
662	C₂×C₃₁	#3444	1	1	yes	characteristic
663	C₂×C₃₁	#3461	1	1	yes	characteristic
664	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
665	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
666	C₂×C₃₁	#3475	1	1	yes	characteristic
667	C₂×C₃₁	#3482	1	1	yes	characteristic
668	C₂×#41	—	2	4	no	—
669	C₂×#41	—	2	4	no	—
670	C₂×#41	—	2	4	no	—
671	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
673	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
676	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
677	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
679	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
681	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
684	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₄⋊Q₈	—	2	4	no	—
688	C₄⋊Q₈	—	2	4	no	—
689	#125	—	2	8	no	—
690	#124	—	2	4	no	—
691	C₂²⋊Q₈	—	2	4	no	—
692	C₂²⋊Q₈	—	2	4	no	—
693	C₂²⋊Q₈	—	2	4	no	—
694	C₂²⋊Q₈	—	2	8	no	—
695	C₂²⋊Q₈	—	2	8	no	—
696	#121	—	2	4	no	—
697	C₄×Q₈	—	2	4	no	—
698	C₄×Q₈	—	2	8	no	—
699	C₄×Q₈	—	2	4	no	—
700	C₄×Q₈	D₄×C₃₁	1	8	yes	complemented
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	8	no	—
704	C₄×D₄	—	2	8	no	—
705	C₄×D₄	—	2	4	no	—
706	C₄×D₄	—	2	4	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	8	no	—
709	#117	—	2	8	no	—
710	#117	—	2	4	no	—
711	#117	—	2	8	no	—
712	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
754	C₂×C₄²	—	2	4	no	—
755	C₂×C₄²	—	2	8	no	—
756	C₂×C₄²	—	2	4	no	—
757	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
759	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
760	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
762	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
766	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
774	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
775	#95	C₂³×C₃₁	1	2	yes	—
776	#95	C₂³×C₃₁	1	2	yes	—
777	#95	C₂³×C₃₁	1	2	yes	—
778	#95	C₂³×C₃₁	1	2	yes	—
779	#95	C₂³×C₃₁	1	1	yes	characteristic
780	#95	C₂³×C₃₁	1	1	yes	characteristic
781	#95	C₂³×C₃₁	1	1	yes	characteristic
782	#95	C₂³×C₃₁	1	1	yes	characteristic
783	#95	C₂³×C₃₁	1	1	yes	characteristic
784	#95	C₂³×C₃₁	1	1	yes	characteristic
785	#95	C₂³×C₃₁	1	2	yes	—
786	#95	C₂³×C₃₁	1	2	yes	—
787	#95	C₂³×C₃₁	1	2	yes	—
788	#95	C₂³×C₃₁	1	2	yes	—
789	#95	C₂³×C₃₁	1	2	yes	—
790	#95	C₂³×C₃₁	1	2	yes	—
791	#95	C₂³×C₃₁	1	2	yes	—
792	#95	C₂³×C₃₁	1	2	yes	—
793	#95	C₂³×C₃₁	1	2	yes	—
794	#95	C₂³×C₃₁	1	2	yes	—
795	#95	C₂³×C₃₁	1	2	yes	—
796	#95	C₂³×C₃₁	1	2	yes	—
797	#95	C₂³×C₃₁	1	2	yes	—
798	C₃₁	#34720	1	1	yes	characteristic, direct product factor, Sylow
799	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
801	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
802	#41	—	2	32	no	—
803	C₂×Q₈	—	2	4	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	2	no	—
807	C₂×Q₈	—	2	4	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	#41×C₃₁	1	4	yes	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	#41×C₃₁	1	4	yes	—
850	C₂²×C₄	#41×C₃₁	1	4	yes	complemented
851	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	4	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
890	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
891	C₄⋊C₄	#41×C₃₁	1	4	yes	complemented
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	4	no	—
916	C₄²	—	2	4	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	4	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	4	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	4	1	no	—
929	C₄²	C₂×D₄×C₃₁	1	4	yes	—
930	C₄²	C₂×D₄×C₃₁	1	8	yes	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	1	no	—
949	C₂³	C₂×#41×C₃₁	1	4	yes	—
950	C₂³	C₂×#41×C₃₁	1	2	yes	—
951	C₂³	C₂×#41×C₃₁	1	2	yes	—
952	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
953	Q₈	—	2	8	no	—
954	Q₈	—	4	8	no	—
955	Q₈	—	4	4	no	—
956	D₄	—	2	8	no	—
957	D₄	—	2	16	no	—
958	D₄	—	2	8	no	—
959	D₄	—	4	8	no	—
960	C₂×C₄	—	2	16	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	8	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
1017	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
1018	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1022	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1023	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1025	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1026	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1027	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1028	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1029	C₂²	—	2	4	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	4	no	—
1037	C₂²	—	2	4	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1051	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1052	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1053	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1054	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1055	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1056	C₂²	C₃₁×#585	1	1	yes	characteristic
1057	C₄	—	2	2	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	C₃₁×#525	1	4	yes	—
1076	C₄	C₃₁×#548	1	4	yes	—
1077	C₂	—	4	2	no	—
1078	C₂	—	4	4	no	—
1079	C₂	—	4	2	no	—
1080	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1081	C₂	C₃₁×#3444	1	1	yes	characteristic
1082	C₂	C₃₁×#3461	1	1	yes	characteristic
1083	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1084	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1085	C₂	C₃₁×#3475	1	1	yes	characteristic
1086	C₂	C₃₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#2407	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×#533	C₂	semidirect
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#2477	C₂	semidirect
4. C₃₁×#2475	C₂	semidirect
5. C₃₁×#2463	C₂	semidirect
6. C₃₁×#2460	C₂	semidirect
7. C₃₁×#2452	C₂	semidirect
8. C₃₁×#2446	C₂	semidirect
9. C₃₁×#2439	C₂	semidirect
10. C₃₁×#2432	C₂	semidirect
11. C₃₁×#2427	C₂	semidirect
12. C₃₁×#2421	C₂	semidirect
13. C₃₁×#2415	C₂	semidirect
15. C₃₁×#2398	C₂	semidirect
16. C₃₁×#2392	C₂	semidirect
17. C₄×C₃₁×#124	C₂	semidirect
18. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
20. C₄×C₃₁×#121	C₂	semidirect
21. C₃₁×#2295	C₂	semidirect
22. C₃₁×#2290	C₂	semidirect
23. C₄²×D₄×C₃₁	C₂	semidirect
157. C₄×Q₈×C₃₁	D₄	semidirect
306. C₂²×C₄×C₃₁	#41	semidirect
347. C₄⋊C₄×C₃₁	#41	semidirect
387. #34720	C₃₁	direct (N × H)
486. C₂×#533	C₂×C₃₁	semidirect
487. C₂×C₄×#41	C₂×C₃₁	semidirect
488. #2477	C₂×C₃₁	semidirect
489. #2475	C₂×C₃₁	semidirect
490. #2463	C₂×C₃₁	semidirect
491. #2460	C₂×C₃₁	semidirect
492. #2452	C₂×C₃₁	semidirect
493. #2446	C₂×C₃₁	semidirect
494. #2439	C₂×C₃₁	semidirect
495. #2432	C₂×C₃₁	semidirect
496. #2427	C₂×C₃₁	semidirect
497. #2421	C₂×C₃₁	semidirect
498. #2415	C₂×C₃₁	semidirect
500. #2398	C₂×C₃₁	semidirect
501. #2392	C₂×C₃₁	semidirect
502. C₄×#124	C₂×C₃₁	semidirect
503. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
504. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
505. C₄×#121	C₂×C₃₁	semidirect
506. #2295	C₂×C₃₁	semidirect
507. #2290	C₂×C₃₁	semidirect
508. C₄²×D₄	C₂×C₃₁	semidirect
700. C₄×Q₈	D₄×C₃₁	semidirect
798. C₃₁	#34720	direct (N × H)
850. C₂²×C₄	#41×C₃₁	semidirect
891. C₄⋊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
C₂×C₃₁×#533	2
C₂×C₄×#41×C₃₁	2
C₃₁×#2477	2
C₃₁×#2475	2
C₃₁×#2463	2
C₃₁×#2460	2
C₃₁×#2452	2
C₃₁×#2446	2
C₃₁×#2439	2
C₃₁×#2432	2
C₃₁×#2427	2
C₃₁×#2421	2
C₃₁×#2415	2
C₃₁×#2407	2
C₃₁×#2398	2
C₃₁×#2392	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₃₁×#2295	2
C₃₁×#2290	2
C₄²×D₄×C₃₁	2
#34720	31

Subgroups — C31×#34720 #21491479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34720 #21491479