Subgroups — C₃₁×#3521 #16843454

Order 3968.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#552	C₂	1	2	yes	maximal, complemented
8	C₃₁×#551	C₂	1	2	yes	maximal, complemented
9	C₃₁×#551	C₂	1	2	yes	maximal, complemented
10	C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#539	C₂	1	2	yes	maximal, complemented
16	C₃₁×#538	C₂	1	2	yes	maximal, complemented
17	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	C₂	1	2	yes	maximal, complemented
19	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#126	C₂	1	2	yes	maximal, complemented
21	C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#126	C₂²	1	1	yes	characteristic
30	C₃₁×#126	C₂²	1	2	yes	—
31	C₃₁×#126	C₂²	1	2	yes	—
32	C₃₁×#126	C₂²	1	2	yes	—
33	C₃₁×#126	C₂²	1	2	yes	—
34	C₃₁×#126	C₂²	1	2	yes	complemented
35	C₃₁×#126	C₂²	1	2	yes	complemented
36	C₃₁×#126	C₂²	1	2	yes	complemented
37	C₃₁×#126	C₂²	1	2	yes	complemented
38	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#126	C₂²	1	2	yes	complemented
40	C₃₁×#126	C₂²	1	2	yes	complemented
41	C₃₁×#125	C₂²	1	2	yes	complemented
42	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#125	C₂²	1	2	yes	complemented
45	C₃₁×#125	C₂²	1	2	yes	complemented
46	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#124	C₂²	1	1	yes	characteristic
48	C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₃₁×#124	C₂²	1	2	yes	—
50	C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#124	C₂²	1	2	yes	complemented
52	C₃₁×#123	C₂²	1	2	yes	—
53	C₃₁×#123	C₂²	1	1	yes	characteristic
54	C₃₁×#123	C₂²	1	2	yes	—
55	C₃₁×#123	C₂²	1	2	yes	—
56	C₃₁×#123	C₂²	1	2	yes	complemented
57	C₃₁×#123	C₂²	1	2	yes	complemented
58	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#123	C₂²	1	2	yes	complemented
60	C₃₁×#123	C₂²	1	2	yes	complemented
61	C₃₁×#123	C₂²	1	2	yes	complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
72	C₃₁×#121	C₂²	1	1	yes	characteristic
73	C₃₁×#121	C₂²	1	1	yes	characteristic
74	C₃₁×#121	C₂²	1	2	yes	—
75	C₃₁×#121	C₂²	1	2	yes	—
76	C₃₁×#121	C₂²	1	1	yes	characteristic
77	C₃₁×#121	C₂²	1	2	yes	complemented
78	C₃₁×#121	C₂²	1	2	yes	complemented
79	C₃₁×#120	C₂²	1	2	yes	—
80	C₃₁×#120	C₂²	1	2	yes	—
81	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
83	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
84	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
86	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₃₁	C₂²	1	2	yes	—
90	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₃₁	C₂²	1	2	yes	—
93	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
95	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
96	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
97	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
98	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
99	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
100	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
101	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
103	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
104	C₃₁×#117	C₂²	1	1	yes	characteristic
105	C₃₁×#117	C₂²	1	1	yes	characteristic
106	C₃₁×#117	C₂²	1	2	yes	complemented
107	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#117	C₂²	1	2	yes	complemented
110	C₃₁×#117	C₂²	1	2	yes	complemented
111	C₃₁×#117	C₂²	1	2	yes	complemented
112	C₃₁×#117	C₂²	1	2	yes	complemented
113	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
116	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
121	C₂×C₄²×C₃₁	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₃₁	C₂³	1	2	yes	—
124	#41×C₃₁	—	2	4	no	—
125	#41×C₃₁	—	2	4	no	—
126	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₄×C₃₁	—	2	4	no	—
131	C₂×D₄×C₃₁	C₂³	1	2	yes	—
132	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₃₁	C₂³	1	2	yes	—
134	C₂×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₃₁	C₂³	1	2	yes	—
138	C₂×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
155	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
206	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
213	C₄²×C₃₁	C₂³	1	1	yes	characteristic
214	C₄²×C₃₁	C₂³	1	1	yes	characteristic
215	C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₄²×C₃₁	C₂³	1	2	yes	—
217	C₄²×C₃₁	C₂³	1	2	yes	—
218	C₄²×C₃₁	C₂³	1	1	yes	characteristic
219	C₄²×C₃₁	C₂³	1	2	yes	—
220	C₄²×C₃₁	C₂³	1	2	yes	—
221	C₄²×C₃₁	C₂³	1	1	yes	characteristic
222	C₄²×C₃₁	C₂³	1	2	yes	—
223	C₄²×C₃₁	C₂³	1	2	yes	—
224	C₄²×C₃₁	C₂³	1	1	yes	characteristic
225	C₂³×C₃₁	—	2	4	no	—
226	C₂³×C₃₁	—	4	2	no	—
227	C₂³×C₃₁	—	4	2	no	—
228	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂³×C₃₁	C₂⁴	1	2	yes	—
230	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂³×C₃₁	C₂⁴	1	2	yes	—
233	Q₈×C₃₁	—	2	2	no	—
234	Q₈×C₃₁	—	2	2	no	—
235	Q₈×C₃₁	—	4	1	no	—
236	Q₈×C₃₁	—	4	2	no	—
237	D₄×C₃₁	—	2	4	no	—
238	D₄×C₃₁	—	2	4	no	—
239	D₄×C₃₁	—	2	4	no	—
240	D₄×C₃₁	—	2	2	no	—
241	D₄×C₃₁	—	4	2	no	—
242	D₄×C₃₁	—	4	1	no	—
243	D₄×C₃₁	—	4	1	no	—
244	D₄×C₃₁	—	4	2	no	—
245	D₄×C₃₁	—	4	1	no	—
246	D₄×C₃₁	#41	1	4	yes	—
247	C₂×C₄×C₃₁	—	2	4	no	—
248	C₂×C₄×C₃₁	—	2	4	no	—
249	C₂×C₄×C₃₁	—	2	2	no	—
250	C₂×C₄×C₃₁	—	2	2	no	—
251	C₂×C₄×C₃₁	—	2	2	no	—
252	C₂×C₄×C₃₁	—	4	2	no	—
253	C₂×C₄×C₃₁	—	4	1	no	—
254	C₂×C₄×C₃₁	—	4	2	no	—
255	C₂×C₄×C₃₁	—	4	2	no	—
256	C₂×C₄×C₃₁	—	4	2	no	—
257	C₂×C₄×C₃₁	—	4	2	no	—
258	C₂×C₄×C₃₁	—	4	1	no	—
259	C₂×C₄×C₃₁	—	4	2	no	—
260	C₂×C₄×C₃₁	—	4	2	no	—
261	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	#3521	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂²×C₃₁	—	2	2	no	—
281	C₂²×C₃₁	—	2	2	no	—
282	C₂²×C₃₁	—	2	1	no	—
283	C₂²×C₃₁	—	2	1	no	—
284	C₂²×C₃₁	—	2	1	no	—
285	C₂²×C₃₁	—	2	2	no	—
286	C₂²×C₃₁	—	2	1	no	—
287	C₂²×C₃₁	—	2	1	no	—
288	C₂²×C₃₁	—	2	1	no	—
289	C₂²×C₃₁	—	2	2	no	—
290	C₂²×C₃₁	—	2	2	no	—
291	C₂²×C₃₁	—	2	1	no	—
292	C₂²×C₃₁	—	2	1	no	—
293	C₂²×C₃₁	—	2	1	no	—
294	C₂²×C₃₁	—	8	4	no	—
295	C₂²×C₃₁	C₂×#41	1	4	yes	—
296	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
297	C₄×C₃₁	—	2	1	no	—
298	C₄×C₃₁	—	2	1	no	—
299	C₄×C₃₁	—	2	1	no	—
300	C₄×C₃₁	—	2	2	no	—
301	C₄×C₃₁	—	2	2	no	—
302	C₄×C₃₁	—	2	1	no	—
303	C₄×C₃₁	—	2	2	no	—
304	C₄×C₃₁	—	2	1	no	—
305	C₄×C₃₁	—	2	1	no	—
306	C₄×C₃₁	—	2	2	no	—
307	C₄×C₃₁	—	2	1	no	—
308	C₄×C₃₁	—	2	1	no	—
309	C₄×C₃₁	—	2	1	no	—
310	C₄×C₃₁	—	2	2	no	—
311	C₄×C₃₁	—	2	1	no	—
312	C₄×C₃₁	—	2	2	no	—
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	C₂×#41	1	2	yes	—
315	#556	C₂×C₃₁	1	1	yes	characteristic, complemented
316	#556	C₂×C₃₁	1	1	yes	characteristic, complemented
317	#554	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#553	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#553	C₂×C₃₁	1	2	yes	complemented
320	#552	C₂×C₃₁	1	1	yes	characteristic, complemented
321	#552	C₂×C₃₁	1	2	yes	complemented
322	#551	C₂×C₃₁	1	2	yes	complemented
323	#551	C₂×C₃₁	1	2	yes	complemented
324	#547	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
327	#542	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#541	C₂×C₃₁	1	1	yes	characteristic, complemented
329	#539	C₂×C₃₁	1	2	yes	complemented
330	#538	C₂×C₃₁	1	2	yes	complemented
331	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#529	C₂×C₃₁	1	2	yes	complemented
333	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
334	C₂×#126	C₂×C₃₁	1	2	yes	complemented
335	#520	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#518	C₂×C₃₁	1	1	yes	characteristic, complemented
337	C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
338	C₂×C₃₁	—	2	4	no	—
339	C₂×C₃₁	—	4	1	no	—
340	C₂×C₃₁	—	4	1	no	—
341	C₂×C₃₁	—	4	2	no	—
342	C₂×C₃₁	—	4	1	no	—
343	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
344	C₂×C₃₁	#585	1	1	yes	characteristic
345	C₂×C₃₁	#585	1	1	yes	characteristic
346	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
347	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
348	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
349	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
350	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
351	#126	C₂²×C₃₁	1	1	yes	characteristic
352	#126	C₂²×C₃₁	1	2	yes	—
353	#126	C₂²×C₃₁	1	2	yes	—
354	#126	C₂²×C₃₁	1	2	yes	—
355	#126	C₂²×C₃₁	1	2	yes	—
356	#126	C₂²×C₃₁	1	2	yes	complemented
357	#126	C₂²×C₃₁	1	2	yes	complemented
358	#126	C₂²×C₃₁	1	2	yes	complemented
359	#126	C₂²×C₃₁	1	2	yes	complemented
360	#126	C₂²×C₃₁	1	1	yes	characteristic, complemented
361	#126	C₂²×C₃₁	1	2	yes	complemented
362	#126	C₂²×C₃₁	1	2	yes	complemented
363	#125	C₂²×C₃₁	1	2	yes	complemented
364	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
365	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
366	#125	C₂²×C₃₁	1	2	yes	complemented
367	#125	C₂²×C₃₁	1	2	yes	complemented
368	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	#124	C₂²×C₃₁	1	1	yes	characteristic
370	#124	C₂²×C₃₁	1	1	yes	characteristic
371	#124	C₂²×C₃₁	1	2	yes	—
372	#124	C₂²×C₃₁	1	1	yes	characteristic
373	#124	C₂²×C₃₁	1	2	yes	complemented
374	#123	C₂²×C₃₁	1	2	yes	—
375	#123	C₂²×C₃₁	1	1	yes	characteristic
376	#123	C₂²×C₃₁	1	2	yes	—
377	#123	C₂²×C₃₁	1	2	yes	—
378	#123	C₂²×C₃₁	1	2	yes	complemented
379	#123	C₂²×C₃₁	1	2	yes	complemented
380	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
381	#123	C₂²×C₃₁	1	2	yes	complemented
382	#123	C₂²×C₃₁	1	2	yes	complemented
383	#123	C₂²×C₃₁	1	2	yes	complemented
384	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
386	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
387	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
388	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
389	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
390	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
391	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
392	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
394	#121	C₂²×C₃₁	1	1	yes	characteristic
395	#121	C₂²×C₃₁	1	1	yes	characteristic
396	#121	C₂²×C₃₁	1	2	yes	—
397	#121	C₂²×C₃₁	1	2	yes	—
398	#121	C₂²×C₃₁	1	1	yes	characteristic
399	#121	C₂²×C₃₁	1	2	yes	complemented
400	#121	C₂²×C₃₁	1	2	yes	complemented
401	#120	C₂²×C₃₁	1	2	yes	—
402	#120	C₂²×C₃₁	1	2	yes	—
403	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
408	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
411	C₄×D₄	C₂²×C₃₁	1	2	yes	—
412	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
413	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
414	C₄×D₄	C₂²×C₃₁	1	2	yes	—
415	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
416	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
417	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
418	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
419	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
420	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
421	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
422	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
423	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
425	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
426	#117	C₂²×C₃₁	1	1	yes	characteristic
427	#117	C₂²×C₃₁	1	1	yes	characteristic
428	#117	C₂²×C₃₁	1	2	yes	complemented
429	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
431	#117	C₂²×C₃₁	1	2	yes	complemented
432	#117	C₂²×C₃₁	1	2	yes	complemented
433	#117	C₂²×C₃₁	1	2	yes	complemented
434	#117	C₂²×C₃₁	1	2	yes	complemented
435	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
436	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
438	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
439	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
443	C₂×C₄²	C₂²×C₃₁	1	2	yes	complemented
444	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	C₃₁	#3521	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴	C₂³×C₃₁	1	2	yes	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
451	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
452	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	C₂³×C₃₁	1	2	yes	—
455	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
456	C₂×D₄	C₂³×C₃₁	1	2	yes	—
457	C₂×D₄	C₂³×C₃₁	1	2	yes	—
458	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
459	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
460	C₂×D₄	C₂³×C₃₁	1	2	yes	—
461	C₂×D₄	C₂³×C₃₁	1	2	yes	—
462	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
465	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
467	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
470	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
471	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
474	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
475	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
476	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
477	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
478	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
479	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
481	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
486	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
490	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
492	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
494	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
496	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
499	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
500	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
501	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
502	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
503	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
508	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
511	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
517	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
518	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
519	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
522	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
524	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
525	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
526	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
527	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
536	C₄²	C₂³×C₃₁	1	1	yes	characteristic
537	C₄²	C₂³×C₃₁	1	1	yes	characteristic
538	C₄²	C₂³×C₃₁	1	1	yes	characteristic
539	C₄²	C₂³×C₃₁	1	2	yes	—
540	C₄²	C₂³×C₃₁	1	2	yes	—
541	C₄²	C₂³×C₃₁	1	1	yes	characteristic
542	C₄²	C₂³×C₃₁	1	2	yes	—
543	C₄²	C₂³×C₃₁	1	2	yes	—
544	C₄²	C₂³×C₃₁	1	1	yes	characteristic
545	C₄²	C₂³×C₃₁	1	2	yes	—
546	C₄²	C₂³×C₃₁	1	2	yes	—
547	C₄²	C₂³×C₃₁	1	1	yes	characteristic
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
552	C₂³	C₂⁴×C₃₁	1	2	yes	—
553	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
555	C₂³	C₂⁴×C₃₁	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	1	no	—
569	D₄	#41×C₃₁	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
585	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
586	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
587	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
588	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
589	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
591	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
592	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
593	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
594	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
595	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
596	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
597	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
598	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
599	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
600	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	8	4	no	—
617	C₂²	C₂×#41×C₃₁	1	4	yes	—
618	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	C₂×#41×C₃₁	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	4	1	no	—
642	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic
643	C₂	C₃₁×#585	1	1	yes	characteristic
644	C₂	C₃₁×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#556	C₂	semidirect
2. C₃₁×#556	C₂	semidirect
3. C₃₁×#554	C₂	semidirect
4. C₃₁×#553	C₂	semidirect
5. C₃₁×#553	C₂	semidirect
6. C₃₁×#552	C₂	semidirect
7. C₃₁×#552	C₂	semidirect
8. C₃₁×#551	C₂	semidirect
9. C₃₁×#551	C₂	semidirect
10. C₃₁×#547	C₂	semidirect
11. C₃₁×#546	C₂	semidirect
12. C₃₁×#546	C₂	semidirect
13. C₃₁×#542	C₂	semidirect
14. C₃₁×#541	C₂	semidirect
15. C₃₁×#539	C₂	semidirect
16. C₃₁×#538	C₂	semidirect
17. C₃₁×#529	C₂	semidirect
18. C₃₁×#529	C₂	semidirect
19. C₃₁×#529	C₂	semidirect
20. C₂×C₃₁×#126	C₂	semidirect
21. C₃₁×#520	C₂	semidirect
22. C₃₁×#518	C₂	semidirect
23. C₄×#41×C₃₁	C₂	semidirect
27. C₃₁×C₄⋊Q₈	C₂²	semidirect
28. C₃₁×C₄⋊Q₈	C₂²	semidirect
34. C₃₁×#126	C₂²	semidirect
35. C₃₁×#126	C₂²	semidirect
36. C₃₁×#126	C₂²	semidirect
37. C₃₁×#126	C₂²	semidirect
38. C₃₁×#126	C₂²	semidirect
39. C₃₁×#126	C₂²	semidirect
40. C₃₁×#126	C₂²	semidirect
41. C₃₁×#125	C₂²	semidirect
42. C₃₁×#125	C₂²	semidirect
43. C₃₁×#125	C₂²	semidirect
44. C₃₁×#125	C₂²	semidirect
45. C₃₁×#125	C₂²	semidirect
46. C₃₁×#125	C₂²	semidirect
51. C₃₁×#124	C₂²	semidirect
56. C₃₁×#123	C₂²	semidirect
57. C₃₁×#123	C₂²	semidirect
58. C₃₁×#123	C₂²	semidirect
59. C₃₁×#123	C₂²	semidirect
60. C₃₁×#123	C₂²	semidirect
61. C₃₁×#123	C₂²	semidirect
64. C₃₁×C₂²⋊Q₈	C₂²	semidirect
65. C₃₁×C₂²⋊Q₈	C₂²	semidirect
66. C₃₁×C₂²⋊Q₈	C₂²	semidirect
67. C₃₁×C₂²⋊Q₈	C₂²	semidirect
68. C₃₁×C₂²⋊Q₈	C₂²	semidirect
69. C₃₁×C₂²⋊Q₈	C₂²	semidirect
70. C₃₁×C₂²⋊Q₈	C₂²	semidirect
71. C₃₁×C₂²⋊Q₈	C₂²	semidirect
77. C₃₁×#121	C₂²	semidirect
78. C₃₁×#121	C₂²	semidirect
81. C₄×Q₈×C₃₁	C₂²	semidirect
82. C₄×Q₈×C₃₁	C₂²	semidirect
83. C₄×Q₈×C₃₁	C₂²	semidirect
84. C₄×Q₈×C₃₁	C₂²	semidirect
85. C₄×Q₈×C₃₁	C₂²	semidirect
86. C₄×Q₈×C₃₁	C₂²	semidirect
97. C₄×D₄×C₃₁	C₂²	semidirect
98. C₄×D₄×C₃₁	C₂²	semidirect
99. C₄×D₄×C₃₁	C₂²	semidirect
100. C₄×D₄×C₃₁	C₂²	semidirect
101. C₄×D₄×C₃₁	C₂²	semidirect
102. C₄×D₄×C₃₁	C₂²	semidirect
103. C₄×D₄×C₃₁	C₂²	semidirect
106. C₃₁×#117	C₂²	semidirect
107. C₃₁×#117	C₂²	semidirect
108. C₃₁×#117	C₂²	semidirect
109. C₃₁×#117	C₂²	semidirect
110. C₃₁×#117	C₂²	semidirect
111. C₃₁×#117	C₂²	semidirect
112. C₃₁×#117	C₂²	semidirect
113. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
114. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
115. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
116. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
121. C₂×C₄²×C₃₁	C₂²	semidirect
122. C₂×C₄²×C₃₁	C₂²	semidirect
279. #3521	C₃₁	direct (N × H)
315. #556	C₂×C₃₁	semidirect
316. #556	C₂×C₃₁	semidirect
317. #554	C₂×C₃₁	semidirect
318. #553	C₂×C₃₁	semidirect
319. #553	C₂×C₃₁	semidirect
320. #552	C₂×C₃₁	semidirect
321. #552	C₂×C₃₁	semidirect
322. #551	C₂×C₃₁	semidirect
323. #551	C₂×C₃₁	semidirect
324. #547	C₂×C₃₁	semidirect
325. #546	C₂×C₃₁	semidirect
326. #546	C₂×C₃₁	semidirect
327. #542	C₂×C₃₁	semidirect
328. #541	C₂×C₃₁	semidirect
329. #539	C₂×C₃₁	semidirect
330. #538	C₂×C₃₁	semidirect
331. #529	C₂×C₃₁	semidirect
332. #529	C₂×C₃₁	semidirect
333. #529	C₂×C₃₁	semidirect
334. C₂×#126	C₂×C₃₁	semidirect
335. #520	C₂×C₃₁	semidirect
336. #518	C₂×C₃₁	semidirect
337. C₄×#41	C₂×C₃₁	semidirect
349. C₄⋊Q₈	C₂²×C₃₁	semidirect
350. C₄⋊Q₈	C₂²×C₃₁	semidirect
356. #126	C₂²×C₃₁	semidirect
357. #126	C₂²×C₃₁	semidirect
358. #126	C₂²×C₃₁	semidirect
359. #126	C₂²×C₃₁	semidirect
360. #126	C₂²×C₃₁	semidirect
361. #126	C₂²×C₃₁	semidirect
362. #126	C₂²×C₃₁	semidirect
363. #125	C₂²×C₃₁	semidirect
364. #125	C₂²×C₃₁	semidirect
365. #125	C₂²×C₃₁	semidirect
366. #125	C₂²×C₃₁	semidirect
367. #125	C₂²×C₃₁	semidirect
368. #125	C₂²×C₃₁	semidirect
373. #124	C₂²×C₃₁	semidirect
378. #123	C₂²×C₃₁	semidirect
379. #123	C₂²×C₃₁	semidirect
380. #123	C₂²×C₃₁	semidirect
381. #123	C₂²×C₃₁	semidirect
382. #123	C₂²×C₃₁	semidirect
383. #123	C₂²×C₃₁	semidirect
386. C₂²⋊Q₈	C₂²×C₃₁	semidirect
387. C₂²⋊Q₈	C₂²×C₃₁	semidirect
388. C₂²⋊Q₈	C₂²×C₃₁	semidirect
389. C₂²⋊Q₈	C₂²×C₃₁	semidirect
390. C₂²⋊Q₈	C₂²×C₃₁	semidirect
391. C₂²⋊Q₈	C₂²×C₃₁	semidirect
392. C₂²⋊Q₈	C₂²×C₃₁	semidirect
393. C₂²⋊Q₈	C₂²×C₃₁	semidirect
399. #121	C₂²×C₃₁	semidirect
400. #121	C₂²×C₃₁	semidirect
403. C₄×Q₈	C₂²×C₃₁	semidirect
404. C₄×Q₈	C₂²×C₃₁	semidirect
405. C₄×Q₈	C₂²×C₃₁	semidirect
406. C₄×Q₈	C₂²×C₃₁	semidirect
407. C₄×Q₈	C₂²×C₃₁	semidirect
408. C₄×Q₈	C₂²×C₃₁	semidirect
419. C₄×D₄	C₂²×C₃₁	semidirect
420. C₄×D₄	C₂²×C₃₁	semidirect
421. C₄×D₄	C₂²×C₃₁	semidirect
422. C₄×D₄	C₂²×C₃₁	semidirect
423. C₄×D₄	C₂²×C₃₁	semidirect
424. C₄×D₄	C₂²×C₃₁	semidirect
425. C₄×D₄	C₂²×C₃₁	semidirect
428. #117	C₂²×C₃₁	semidirect
429. #117	C₂²×C₃₁	semidirect
430. #117	C₂²×C₃₁	semidirect
431. #117	C₂²×C₃₁	semidirect
432. #117	C₂²×C₃₁	semidirect
433. #117	C₂²×C₃₁	semidirect
434. #117	C₂²×C₃₁	semidirect
435. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
436. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
437. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
438. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
443. C₂×C₄²	C₂²×C₃₁	semidirect
444. C₂×C₄²	C₂²×C₃₁	semidirect
445. C₃₁	#3521	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#556	2
C₃₁×#554	2
C₃₁×#553	2
C₃₁×#552	2
C₃₁×#551	2
C₃₁×#547	2
C₃₁×#546	2
C₃₁×#542	2
C₃₁×#541	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#529	2
C₂×C₃₁×#126	2
C₃₁×#520	2
C₃₁×#518	2
C₄×#41×C₃₁	2
#3521	31

Subgroups — C31×#3521 #16843454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3521 #16843454