Subgroups — C₃₁×#3560 #16843493

Order 3968.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#563	C₂	1	2	yes	maximal, complemented
2	C₃₁×#560	C₂	1	2	yes	maximal, complemented
3	C₃₁×#553	C₂	1	2	yes	maximal, complemented
4	C₃₁×#553	C₂	1	2	yes	maximal, complemented
5	C₃₁×#551	C₂	1	2	yes	maximal, complemented
6	C₃₁×#547	C₂	1	2	yes	maximal, complemented
7	C₃₁×#546	C₂	1	2	yes	maximal, complemented
8	C₃₁×#546	C₂	1	2	yes	maximal, complemented
9	C₃₁×#542	C₂	1	2	yes	maximal, complemented
10	C₃₁×#539	C₂	1	2	yes	maximal, complemented
11	C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#538	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#538	C₂	1	2	yes	maximal, complemented
14	C₃₁×#538	C₂	1	2	yes	maximal, complemented
15	C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
21	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
23	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#126	C₂²	1	2	yes	complemented
27	C₃₁×#126	C₂²	1	2	yes	complemented
28	C₃₁×#126	C₂²	1	2	yes	complemented
29	C₃₁×#126	C₂²	1	2	yes	complemented
30	C₃₁×#126	C₂²	1	2	yes	complemented
31	C₃₁×#126	C₂²	1	2	yes	complemented
32	C₃₁×#126	C₂²	1	2	yes	complemented
33	C₃₁×#126	C₂²	1	2	yes	complemented
34	C₃₁×#126	C₂²	1	2	yes	complemented
35	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#125	C₂²	1	2	yes	complemented
37	C₃₁×#125	C₂²	1	2	yes	complemented
38	C₃₁×#124	C₂²	1	2	yes	—
39	C₃₁×#124	C₂²	1	2	yes	—
40	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#124	C₂²	1	2	yes	complemented
42	C₃₁×#124	C₂²	1	2	yes	complemented
43	C₃₁×#123	C₂²	1	2	yes	—
44	C₃₁×#123	C₂²	1	2	yes	—
45	C₃₁×#123	C₂²	1	2	yes	—
46	C₃₁×#123	C₂²	1	2	yes	—
47	C₃₁×#123	C₂²	1	2	yes	complemented
48	C₃₁×#123	C₂²	1	2	yes	complemented
49	C₃₁×#123	C₂²	1	2	yes	complemented
50	C₃₁×#123	C₂²	1	2	yes	complemented
51	C₃₁×#123	C₂²	1	2	yes	complemented
52	C₃₁×#123	C₂²	1	2	yes	complemented
53	C₃₁×#123	C₂²	1	2	yes	complemented
54	C₃₁×#123	C₂²	1	2	yes	complemented
55	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃₁×#121	C₂²	1	1	yes	characteristic
64	C₃₁×#121	C₂²	1	1	yes	characteristic
65	C₃₁×#121	C₂²	1	2	yes	—
66	C₃₁×#121	C₂²	1	2	yes	—
67	C₃₁×#121	C₂²	1	2	yes	—
68	C₃₁×#121	C₂²	1	2	yes	—
69	C₃₁×#121	C₂²	1	2	yes	—
70	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#121	C₂²	1	2	yes	complemented
72	C₃₁×#121	C₂²	1	2	yes	complemented
73	C₃₁×#121	C₂²	1	2	yes	complemented
74	C₃₁×#121	C₂²	1	2	yes	complemented
75	C₃₁×#121	C₂²	1	2	yes	complemented
76	C₃₁×#121	C₂²	1	2	yes	complemented
77	C₃₁×#121	C₂²	1	2	yes	complemented
78	C₃₁×#120	C₂²	1	2	yes	—
79	C₃₁×#120	C₂²	1	2	yes	—
80	C₃₁×#120	C₂²	1	2	yes	—
81	C₃₁×#120	C₂²	1	2	yes	complemented
82	C₃₁×#120	C₂²	1	2	yes	complemented
83	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
86	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
87	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
90	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
91	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
92	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
93	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
94	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
95	C₃₁×#117	C₂²	1	2	yes	complemented
96	C₃₁×#117	C₂²	1	2	yes	complemented
97	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
101	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
108	C₂⁴×C₃₁	C₂³	1	2	yes	—
109	#41×C₃₁	—	4	4	no	—
110	#41×C₃₁	—	4	4	no	—
111	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
114	C₂×D₄×C₃₁	—	4	4	no	—
115	C₂×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂×D₄×C₃₁	C₂³	1	2	yes	—
117	C₂×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×D₄×C₃₁	C₂³	1	2	yes	—
122	C₂×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂×D₄×C₃₁	C₂³	1	2	yes	—
124	C₂×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂×D₄×C₃₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
143	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
144	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
164	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₄²×C₃₁	C₂³	1	2	yes	—
195	C₄²×C₃₁	C₂³	1	2	yes	—
196	C₄²×C₃₁	C₂³	1	2	yes	—
197	C₂³×C₃₁	—	2	2	no	—
198	C₂³×C₃₁	—	4	2	no	—
199	C₂³×C₃₁	—	4	1	no	—
200	C₂³×C₃₁	—	4	1	no	—
201	C₂³×C₃₁	—	4	2	no	—
202	C₂³×C₃₁	—	4	2	no	—
203	C₂³×C₃₁	C₂⁴	1	2	yes	—
204	C₂³×C₃₁	C₂⁴	1	2	yes	—
205	C₂³×C₃₁	C₂⁴	1	2	yes	—
206	C₂³×C₃₁	C₂⁴	1	2	yes	—
207	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
208	Q₈×C₃₁	—	4	1	no	—
209	Q₈×C₃₁	—	4	2	no	—
210	Q₈×C₃₁	—	4	2	no	—
211	D₄×C₃₁	—	2	4	no	—
212	D₄×C₃₁	—	2	4	no	—
213	D₄×C₃₁	—	2	4	no	—
214	D₄×C₃₁	—	4	2	no	—
215	D₄×C₃₁	—	4	2	no	—
216	D₄×C₃₁	—	4	2	no	—
217	D₄×C₃₁	—	4	2	no	—
218	D₄×C₃₁	—	4	2	no	—
219	D₄×C₃₁	—	4	2	no	—
220	D₄×C₃₁	—	4	1	no	—
221	D₄×C₃₁	—	4	1	no	—
222	D₄×C₃₁	—	4	2	no	—
223	D₄×C₃₁	—	4	1	no	—
224	D₄×C₃₁	—	4	2	no	—
225	D₄×C₃₁	—	4	2	no	—
226	C₂×C₄×C₃₁	—	2	2	no	—
227	C₂×C₄×C₃₁	—	2	2	no	—
228	C₂×C₄×C₃₁	—	4	2	no	—
229	C₂×C₄×C₃₁	—	4	1	no	—
230	C₂×C₄×C₃₁	—	4	1	no	—
231	C₂×C₄×C₃₁	—	4	1	no	—
232	C₂×C₄×C₃₁	—	4	2	no	—
233	C₂×C₄×C₃₁	—	4	2	no	—
234	C₂×C₄×C₃₁	—	4	1	no	—
235	C₂×C₄×C₃₁	—	4	2	no	—
236	C₂×C₄×C₃₁	—	4	2	no	—
237	C₂×C₄×C₃₁	—	4	2	no	—
238	C₂×C₄×C₃₁	—	4	2	no	—
239	C₂×C₄×C₃₁	—	4	2	no	—
240	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
254	#3560	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₃₁	—	2	1	no	—
256	C₂²×C₃₁	—	2	1	no	—
257	C₂²×C₃₁	—	2	2	no	—
258	C₂²×C₃₁	—	2	2	no	—
259	C₂²×C₃₁	—	2	2	no	—
260	C₂²×C₃₁	—	2	2	no	—
261	C₂²×C₃₁	—	2	2	no	—
262	C₂²×C₃₁	—	2	2	no	—
263	C₂²×C₃₁	—	2	2	no	—
264	C₂²×C₃₁	—	2	2	no	—
265	C₂²×C₃₁	—	2	2	no	—
266	C₂²×C₃₁	—	2	2	no	—
267	C₂²×C₃₁	—	2	2	no	—
268	C₂²×C₃₁	—	2	2	no	—
269	C₂²×C₃₁	—	8	2	no	—
270	C₂²×C₃₁	—	8	4	no	—
271	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
273	C₄×C₃₁	—	2	1	no	—
274	C₄×C₃₁	—	2	2	no	—
275	C₄×C₃₁	—	2	1	no	—
276	C₄×C₃₁	—	2	2	no	—
277	C₄×C₃₁	—	2	2	no	—
278	C₄×C₃₁	—	2	2	no	—
279	C₄×C₃₁	—	2	1	no	—
280	C₄×C₃₁	—	2	2	no	—
281	C₄×C₃₁	—	2	2	no	—
282	C₄×C₃₁	—	2	2	no	—
283	C₄×C₃₁	—	2	1	no	—
284	C₄×C₃₁	—	2	1	no	—
285	C₄×C₃₁	—	2	2	no	—
286	C₄×C₃₁	—	2	1	no	—
287	#563	C₂×C₃₁	1	2	yes	complemented
288	#560	C₂×C₃₁	1	2	yes	complemented
289	#553	C₂×C₃₁	1	2	yes	complemented
290	#553	C₂×C₃₁	1	2	yes	complemented
291	#551	C₂×C₃₁	1	2	yes	complemented
292	#547	C₂×C₃₁	1	2	yes	complemented
293	#546	C₂×C₃₁	1	2	yes	complemented
294	#546	C₂×C₃₁	1	2	yes	complemented
295	#542	C₂×C₃₁	1	2	yes	complemented
296	#539	C₂×C₃₁	1	2	yes	complemented
297	#539	C₂×C₃₁	1	1	yes	characteristic, complemented
298	#538	C₂×C₃₁	1	1	yes	characteristic, complemented
299	#538	C₂×C₃₁	1	2	yes	complemented
300	#538	C₂×C₃₁	1	2	yes	complemented
301	#537	C₂×C₃₁	1	1	yes	characteristic, complemented
302	#534	C₂×C₃₁	1	1	yes	characteristic, complemented
303	#532	C₂×C₃₁	1	1	yes	characteristic, complemented
304	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
305	C₂×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
306	C₂×C₃₁	—	2	2	no	—
307	C₂×C₃₁	—	4	2	no	—
308	C₂×C₃₁	—	4	2	no	—
309	C₂×C₃₁	—	4	2	no	—
310	C₂×C₃₁	—	4	2	no	—
311	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₃₁	#585	1	1	yes	characteristic
313	C₂×C₃₁	#585	1	1	yes	characteristic
314	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
315	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
316	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
317	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
318	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
319	#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
320	#126	C₂²×C₃₁	1	2	yes	complemented
321	#126	C₂²×C₃₁	1	2	yes	complemented
322	#126	C₂²×C₃₁	1	2	yes	complemented
323	#126	C₂²×C₃₁	1	2	yes	complemented
324	#126	C₂²×C₃₁	1	2	yes	complemented
325	#126	C₂²×C₃₁	1	2	yes	complemented
326	#126	C₂²×C₃₁	1	2	yes	complemented
327	#126	C₂²×C₃₁	1	2	yes	complemented
328	#126	C₂²×C₃₁	1	2	yes	complemented
329	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
330	#125	C₂²×C₃₁	1	2	yes	complemented
331	#125	C₂²×C₃₁	1	2	yes	complemented
332	#124	C₂²×C₃₁	1	2	yes	—
333	#124	C₂²×C₃₁	1	2	yes	—
334	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
335	#124	C₂²×C₃₁	1	2	yes	complemented
336	#124	C₂²×C₃₁	1	2	yes	complemented
337	#123	C₂²×C₃₁	1	2	yes	—
338	#123	C₂²×C₃₁	1	2	yes	—
339	#123	C₂²×C₃₁	1	2	yes	—
340	#123	C₂²×C₃₁	1	2	yes	—
341	#123	C₂²×C₃₁	1	2	yes	complemented
342	#123	C₂²×C₃₁	1	2	yes	complemented
343	#123	C₂²×C₃₁	1	2	yes	complemented
344	#123	C₂²×C₃₁	1	2	yes	complemented
345	#123	C₂²×C₃₁	1	2	yes	complemented
346	#123	C₂²×C₃₁	1	2	yes	complemented
347	#123	C₂²×C₃₁	1	2	yes	complemented
348	#123	C₂²×C₃₁	1	2	yes	complemented
349	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
350	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
351	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
352	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
353	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
354	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
355	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
356	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
357	#121	C₂²×C₃₁	1	1	yes	characteristic
358	#121	C₂²×C₃₁	1	1	yes	characteristic
359	#121	C₂²×C₃₁	1	2	yes	—
360	#121	C₂²×C₃₁	1	2	yes	—
361	#121	C₂²×C₃₁	1	2	yes	—
362	#121	C₂²×C₃₁	1	2	yes	—
363	#121	C₂²×C₃₁	1	2	yes	—
364	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
365	#121	C₂²×C₃₁	1	2	yes	complemented
366	#121	C₂²×C₃₁	1	2	yes	complemented
367	#121	C₂²×C₃₁	1	2	yes	complemented
368	#121	C₂²×C₃₁	1	2	yes	complemented
369	#121	C₂²×C₃₁	1	2	yes	complemented
370	#121	C₂²×C₃₁	1	2	yes	complemented
371	#121	C₂²×C₃₁	1	2	yes	complemented
372	#120	C₂²×C₃₁	1	2	yes	—
373	#120	C₂²×C₃₁	1	2	yes	—
374	#120	C₂²×C₃₁	1	2	yes	—
375	#120	C₂²×C₃₁	1	2	yes	complemented
376	#120	C₂²×C₃₁	1	2	yes	complemented
377	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
378	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
379	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
380	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
381	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
382	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
383	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
384	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
385	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
386	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
387	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
388	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
389	#117	C₂²×C₃₁	1	2	yes	complemented
390	#117	C₂²×C₃₁	1	2	yes	complemented
391	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
392	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
394	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
395	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
399	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
400	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
401	C₃₁	#3560	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
403	C₂⁴	C₂³×C₃₁	1	2	yes	—
404	#41	—	4	4	no	—
405	#41	—	4	4	no	—
406	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
407	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
408	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	C₂³×C₃₁	1	2	yes	—
411	C₂×D₄	C₂³×C₃₁	1	2	yes	—
412	C₂×D₄	C₂³×C₃₁	1	2	yes	—
413	C₂×D₄	C₂³×C₃₁	1	2	yes	—
414	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
415	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
416	C₂×D₄	C₂³×C₃₁	1	2	yes	—
417	C₂×D₄	C₂³×C₃₁	1	2	yes	—
418	C₂×D₄	C₂³×C₃₁	1	2	yes	—
419	C₂×D₄	C₂³×C₃₁	1	2	yes	—
420	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
421	C₂×D₄	C₂³×C₃₁	1	2	yes	—
422	C₂×D₄	C₂³×C₃₁	1	2	yes	—
423	C₂×D₄	C₂³×C₃₁	1	2	yes	—
424	C₂×D₄	C₂³×C₃₁	1	2	yes	—
425	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
426	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
430	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
431	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
432	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
433	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
434	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
435	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
436	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
437	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
438	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
439	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
440	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
441	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
442	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
443	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
444	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
445	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
446	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
447	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
448	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
449	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
451	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
453	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
455	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
456	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
459	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
461	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
462	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
468	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
469	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₄²	C₂³×C₃₁	1	1	yes	characteristic
486	C₄²	C₂³×C₃₁	1	1	yes	characteristic
487	C₄²	C₂³×C₃₁	1	1	yes	characteristic
488	C₄²	C₂³×C₃₁	1	1	yes	characteristic
489	C₄²	C₂³×C₃₁	1	2	yes	—
490	C₄²	C₂³×C₃₁	1	2	yes	—
491	C₄²	C₂³×C₃₁	1	2	yes	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	C₂⁴×C₃₁	1	2	yes	—
499	C₂³	C₂⁴×C₃₁	1	2	yes	—
500	C₂³	C₂⁴×C₃₁	1	2	yes	—
501	C₂³	C₂⁴×C₃₁	1	2	yes	—
502	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	4	no	—
508	D₄	—	2	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
536	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
537	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
538	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
539	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
540	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
541	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
542	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
543	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
544	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
545	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
546	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
547	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	4	no	—
565	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
566	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂	C₃₁×#585	1	1	yes	characteristic
588	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×#563	C₂	semidirect
2. C₃₁×#560	C₂	semidirect
3. C₃₁×#553	C₂	semidirect
4. C₃₁×#553	C₂	semidirect
5. C₃₁×#551	C₂	semidirect
6. C₃₁×#547	C₂	semidirect
7. C₃₁×#546	C₂	semidirect
8. C₃₁×#546	C₂	semidirect
9. C₃₁×#542	C₂	semidirect
10. C₃₁×#539	C₂	semidirect
11. C₃₁×#539	C₂	semidirect
12. C₃₁×#538	C₂	semidirect
13. C₃₁×#538	C₂	semidirect
14. C₃₁×#538	C₂	semidirect
15. C₃₁×#537	C₂	semidirect
16. C₃₁×#534	C₂	semidirect
17. C₃₁×#532	C₂	semidirect
18. C₃₁×#529	C₂	semidirect
19. C₂×C₃₁×#126	C₂	semidirect
20. C₂×#41×C₃₁	C₂²	semidirect
21. C₂×#41×C₃₁	C₂²	semidirect
23. C₃₁×C₄⋊Q₈	C₂²	semidirect
24. C₃₁×C₄⋊Q₈	C₂²	semidirect
25. C₃₁×#127	C₂²	semidirect
26. C₃₁×#126	C₂²	semidirect
27. C₃₁×#126	C₂²	semidirect
28. C₃₁×#126	C₂²	semidirect
29. C₃₁×#126	C₂²	semidirect
30. C₃₁×#126	C₂²	semidirect
31. C₃₁×#126	C₂²	semidirect
32. C₃₁×#126	C₂²	semidirect
33. C₃₁×#126	C₂²	semidirect
34. C₃₁×#126	C₂²	semidirect
35. C₃₁×#125	C₂²	semidirect
36. C₃₁×#125	C₂²	semidirect
37. C₃₁×#125	C₂²	semidirect
40. C₃₁×#124	C₂²	semidirect
41. C₃₁×#124	C₂²	semidirect
42. C₃₁×#124	C₂²	semidirect
47. C₃₁×#123	C₂²	semidirect
48. C₃₁×#123	C₂²	semidirect
49. C₃₁×#123	C₂²	semidirect
50. C₃₁×#123	C₂²	semidirect
51. C₃₁×#123	C₂²	semidirect
52. C₃₁×#123	C₂²	semidirect
53. C₃₁×#123	C₂²	semidirect
54. C₃₁×#123	C₂²	semidirect
55. C₃₁×C₂²⋊Q₈	C₂²	semidirect
56. C₃₁×C₂²⋊Q₈	C₂²	semidirect
57. C₃₁×C₂²⋊Q₈	C₂²	semidirect
58. C₃₁×C₂²⋊Q₈	C₂²	semidirect
59. C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₃₁×C₂²⋊Q₈	C₂²	semidirect
61. C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₃₁×C₂²⋊Q₈	C₂²	semidirect
70. C₃₁×#121	C₂²	semidirect
71. C₃₁×#121	C₂²	semidirect
72. C₃₁×#121	C₂²	semidirect
73. C₃₁×#121	C₂²	semidirect
74. C₃₁×#121	C₂²	semidirect
75. C₃₁×#121	C₂²	semidirect
76. C₃₁×#121	C₂²	semidirect
77. C₃₁×#121	C₂²	semidirect
81. C₃₁×#120	C₂²	semidirect
82. C₃₁×#120	C₂²	semidirect
83. C₄×Q₈×C₃₁	C₂²	semidirect
84. C₄×D₄×C₃₁	C₂²	semidirect
85. C₄×D₄×C₃₁	C₂²	semidirect
86. C₄×D₄×C₃₁	C₂²	semidirect
87. C₄×D₄×C₃₁	C₂²	semidirect
88. C₄×D₄×C₃₁	C₂²	semidirect
89. C₄×D₄×C₃₁	C₂²	semidirect
90. C₄×D₄×C₃₁	C₂²	semidirect
91. C₄×D₄×C₃₁	C₂²	semidirect
92. C₄×D₄×C₃₁	C₂²	semidirect
93. C₄×D₄×C₃₁	C₂²	semidirect
94. C₄×D₄×C₃₁	C₂²	semidirect
95. C₃₁×#117	C₂²	semidirect
96. C₃₁×#117	C₂²	semidirect
97. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
98. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
99. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
100. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
104. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₂×C₄²×C₃₁	C₂²	semidirect
254. #3560	C₃₁	direct (N × H)
287. #563	C₂×C₃₁	semidirect
288. #560	C₂×C₃₁	semidirect
289. #553	C₂×C₃₁	semidirect
290. #553	C₂×C₃₁	semidirect
291. #551	C₂×C₃₁	semidirect
292. #547	C₂×C₃₁	semidirect
293. #546	C₂×C₃₁	semidirect
294. #546	C₂×C₃₁	semidirect
295. #542	C₂×C₃₁	semidirect
296. #539	C₂×C₃₁	semidirect
297. #539	C₂×C₃₁	semidirect
298. #538	C₂×C₃₁	semidirect
299. #538	C₂×C₃₁	semidirect
300. #538	C₂×C₃₁	semidirect
301. #537	C₂×C₃₁	semidirect
302. #534	C₂×C₃₁	semidirect
303. #532	C₂×C₃₁	semidirect
304. #529	C₂×C₃₁	semidirect
305. C₂×#126	C₂×C₃₁	semidirect
314. C₂×#41	C₂²×C₃₁	semidirect
315. C₂×#41	C₂²×C₃₁	semidirect
317. C₄⋊Q₈	C₂²×C₃₁	semidirect
318. C₄⋊Q₈	C₂²×C₃₁	semidirect
319. #127	C₂²×C₃₁	semidirect
320. #126	C₂²×C₃₁	semidirect
321. #126	C₂²×C₃₁	semidirect
322. #126	C₂²×C₃₁	semidirect
323. #126	C₂²×C₃₁	semidirect
324. #126	C₂²×C₃₁	semidirect
325. #126	C₂²×C₃₁	semidirect
326. #126	C₂²×C₃₁	semidirect
327. #126	C₂²×C₃₁	semidirect
328. #126	C₂²×C₃₁	semidirect
329. #125	C₂²×C₃₁	semidirect
330. #125	C₂²×C₃₁	semidirect
331. #125	C₂²×C₃₁	semidirect
334. #124	C₂²×C₃₁	semidirect
335. #124	C₂²×C₃₁	semidirect
336. #124	C₂²×C₃₁	semidirect
341. #123	C₂²×C₃₁	semidirect
342. #123	C₂²×C₃₁	semidirect
343. #123	C₂²×C₃₁	semidirect
344. #123	C₂²×C₃₁	semidirect
345. #123	C₂²×C₃₁	semidirect
346. #123	C₂²×C₃₁	semidirect
347. #123	C₂²×C₃₁	semidirect
348. #123	C₂²×C₃₁	semidirect
349. C₂²⋊Q₈	C₂²×C₃₁	semidirect
350. C₂²⋊Q₈	C₂²×C₃₁	semidirect
351. C₂²⋊Q₈	C₂²×C₃₁	semidirect
352. C₂²⋊Q₈	C₂²×C₃₁	semidirect
353. C₂²⋊Q₈	C₂²×C₃₁	semidirect
354. C₂²⋊Q₈	C₂²×C₃₁	semidirect
355. C₂²⋊Q₈	C₂²×C₃₁	semidirect
356. C₂²⋊Q₈	C₂²×C₃₁	semidirect
364. #121	C₂²×C₃₁	semidirect
365. #121	C₂²×C₃₁	semidirect
366. #121	C₂²×C₃₁	semidirect
367. #121	C₂²×C₃₁	semidirect
368. #121	C₂²×C₃₁	semidirect
369. #121	C₂²×C₃₁	semidirect
370. #121	C₂²×C₃₁	semidirect
371. #121	C₂²×C₃₁	semidirect
375. #120	C₂²×C₃₁	semidirect
376. #120	C₂²×C₃₁	semidirect
377. C₄×Q₈	C₂²×C₃₁	semidirect
378. C₄×D₄	C₂²×C₃₁	semidirect
379. C₄×D₄	C₂²×C₃₁	semidirect
380. C₄×D₄	C₂²×C₃₁	semidirect
381. C₄×D₄	C₂²×C₃₁	semidirect
382. C₄×D₄	C₂²×C₃₁	semidirect
383. C₄×D₄	C₂²×C₃₁	semidirect
384. C₄×D₄	C₂²×C₃₁	semidirect
385. C₄×D₄	C₂²×C₃₁	semidirect
386. C₄×D₄	C₂²×C₃₁	semidirect
387. C₄×D₄	C₂²×C₃₁	semidirect
388. C₄×D₄	C₂²×C₃₁	semidirect
389. #117	C₂²×C₃₁	semidirect
390. #117	C₂²×C₃₁	semidirect
391. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
392. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
393. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
394. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
398. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
399. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
400. C₂×C₄²	C₂²×C₃₁	semidirect
401. C₃₁	#3560	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×#563	2
C₃₁×#560	2
C₃₁×#553	2
C₃₁×#551	2
C₃₁×#547	2
C₃₁×#546	2
C₃₁×#542	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#537	2
C₃₁×#534	2
C₃₁×#532	2
C₃₁×#529	2
C₂×C₃₁×#126	2
#3560	31

Subgroups — C31×#3560 #16843493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3560 #16843493