Subgroups — C₃₁×#3545 #16843478

Order 3968.

1060 conjugacy classes of subgroups.

The subgroup lattice has 380 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	1	yes	maximal, characteristic, complemented
2	C₃₁×#562	C₂	1	2	yes	maximal, complemented
3	C₃₁×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#555	C₂	1	2	yes	maximal, complemented
5	C₃₁×#551	C₂	1	2	yes	maximal, complemented
6	C₃₁×#551	C₂	1	4	yes	maximal, complemented
7	C₃₁×#546	C₂	1	4	yes	maximal, complemented
8	C₃₁×#542	C₂	1	4	yes	maximal, complemented
9	C₃₁×#538	C₂	1	4	yes	maximal, complemented
10	C₃₁×#536	C₂	1	2	yes	maximal, complemented
11	C₃₁×#534	C₂	1	2	yes	maximal, complemented
12	C₃₁×#529	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₃₁	C₂²	1	2	yes	—
15	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₃₁	C₂²	1	2	yes	complemented
18	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃₁×#126	C₂²	1	4	yes	complemented
21	C₃₁×#126	C₂²	1	4	yes	complemented
22	C₃₁×#126	C₂²	1	4	yes	complemented
23	C₃₁×#125	C₂²	1	2	yes	complemented
24	C₃₁×#124	C₂²	1	1	yes	characteristic
25	C₃₁×#124	C₂²	1	1	yes	characteristic
26	C₃₁×#124	C₂²	1	4	yes	complemented
27	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#124	C₂²	1	2	yes	complemented
30	C₃₁×#124	C₂²	1	2	yes	complemented
31	C₃₁×#124	C₂²	1	2	yes	complemented
32	C₃₁×#124	C₂²	1	4	yes	complemented
33	C₃₁×#124	C₂²	1	4	yes	complemented
34	C₃₁×#123	C₂²	1	2	yes	—
35	C₃₁×#123	C₂²	1	4	yes	complemented
36	C₃₁×#123	C₂²	1	2	yes	complemented
37	C₃₁×#123	C₂²	1	4	yes	complemented
38	C₃₁×#123	C₂²	1	4	yes	complemented
39	C₃₁×#123	C₂²	1	4	yes	complemented
40	C₃₁×#123	C₂²	1	4	yes	complemented
41	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
44	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃₁×#121	C₂²	1	2	yes	—
47	C₃₁×#121	C₂²	1	4	yes	—
48	C₃₁×#121	C₂²	1	4	yes	complemented
49	C₃₁×#121	C₂²	1	4	yes	complemented
50	C₃₁×#121	C₂²	1	4	yes	complemented
51	C₃₁×#120	C₂²	1	4	yes	—
52	C₃₁×#120	C₂²	1	2	yes	—
53	C₃₁×#120	C₂²	1	2	yes	complemented
54	C₃₁×#120	C₂²	1	4	yes	complemented
55	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
56	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
57	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
58	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
59	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
60	C₃₁×#117	C₂²	1	4	yes	complemented
61	C₃₁×#117	C₂²	1	2	yes	complemented
62	C₃₁×#117	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
64	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
66	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₂⁴×C₃₁	C₂³	1	2	yes	—
68	C₂⁴×C₃₁	C₂³	1	2	yes	—
69	#41×C₃₁	—	4	4	no	—
70	C₂×Q₈×C₃₁	—	4	2	no	—
71	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
72	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
74	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
75	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₃₁	—	4	2	no	—
77	C₂×D₄×C₃₁	—	4	4	no	—
78	C₂×D₄×C₃₁	C₂³	1	4	yes	—
79	C₂×D₄×C₃₁	C₂³	1	4	yes	—
80	C₂×D₄×C₃₁	C₂³	1	4	yes	—
81	C₂×D₄×C₃₁	C₂³	1	2	yes	—
82	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₃₁	C₂³	1	2	yes	—
84	C₂×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂×D₄×C₃₁	C₂³	1	4	yes	—
86	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
91	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
92	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
93	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
94	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
95	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
96	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
97	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
98	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
99	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
100	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
101	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
102	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
103	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
104	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
113	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
117	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₄²×C₃₁	C₂³	1	1	yes	characteristic
119	C₄²×C₃₁	C₂³	1	2	yes	—
120	C₄²×C₃₁	C₂³	1	1	yes	characteristic
121	C₄²×C₃₁	C₂³	1	2	yes	—
122	C₄²×C₃₁	C₂³	1	4	yes	—
123	C₄²×C₃₁	C₂³	1	2	yes	—
124	C₂³×C₃₁	—	2	4	no	—
125	C₂³×C₃₁	—	4	2	no	—
126	C₂³×C₃₁	—	4	4	no	—
127	C₂³×C₃₁	—	4	4	no	—
128	C₂³×C₃₁	C₂⁴	1	2	yes	—
129	C₂³×C₃₁	C₂⁴	1	4	yes	—
130	C₂³×C₃₁	C₂⁴	1	2	yes	—
131	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
132	Q₈×C₃₁	—	4	1	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	—	4	1	no	—
135	Q₈×C₃₁	—	4	2	no	—
136	Q₈×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	2	8	no	—
138	D₄×C₃₁	—	4	1	no	—
139	D₄×C₃₁	—	4	2	no	—
140	D₄×C₃₁	—	4	1	no	—
141	D₄×C₃₁	—	4	4	no	—
142	D₄×C₃₁	—	4	4	no	—
143	D₄×C₃₁	—	4	4	no	—
144	D₄×C₃₁	—	4	2	no	—
145	D₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	4	4	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
154	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
155	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
156	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
157	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
160	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
161	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
162	#3545	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	2	4	no	—
165	C₂²×C₃₁	—	2	2	no	—
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	2	4	no	—
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	2	4	no	—
170	C₂²×C₃₁	—	2	4	no	—
171	C₂²×C₃₁	—	8	4	no	—
172	C₂²×C₃₁	—	8	4	no	—
173	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
174	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
175	C₄×C₃₁	—	2	2	no	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	2	4	no	—
180	C₄×C₃₁	—	2	2	no	—
181	C₄×C₃₁	—	2	4	no	—
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	2	4	no	—
184	#563	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#562	C₂×C₃₁	1	2	yes	complemented
186	H(3,𝔽₄)	C₂×C₃₁	1	1	yes	characteristic, complemented
187	#555	C₂×C₃₁	1	2	yes	complemented
188	#551	C₂×C₃₁	1	2	yes	complemented
189	#551	C₂×C₃₁	1	4	yes	complemented
190	#546	C₂×C₃₁	1	4	yes	complemented
191	#542	C₂×C₃₁	1	4	yes	complemented
192	#538	C₂×C₃₁	1	4	yes	complemented
193	#536	C₂×C₃₁	1	2	yes	complemented
194	#534	C₂×C₃₁	1	2	yes	complemented
195	#529	C₂×C₃₁	1	2	yes	complemented
196	C₂×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
197	C₂×C₃₁	—	2	2	no	—
198	C₂×C₃₁	—	4	4	no	—
199	C₂×C₃₁	—	4	2	no	—
200	C₂×C₃₁	—	4	2	no	—
201	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₃₁	#585	1	2	yes	—
203	C₂×#41	C₂²×C₃₁	1	2	yes	—
204	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
205	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
206	C₂²×D₄	C₂²×C₃₁	1	2	yes	complemented
207	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
208	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
209	#126	C₂²×C₃₁	1	4	yes	complemented
210	#126	C₂²×C₃₁	1	4	yes	complemented
211	#126	C₂²×C₃₁	1	4	yes	complemented
212	#125	C₂²×C₃₁	1	2	yes	complemented
213	#124	C₂²×C₃₁	1	1	yes	characteristic
214	#124	C₂²×C₃₁	1	1	yes	characteristic
215	#124	C₂²×C₃₁	1	4	yes	complemented
216	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
217	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
218	#124	C₂²×C₃₁	1	2	yes	complemented
219	#124	C₂²×C₃₁	1	2	yes	complemented
220	#124	C₂²×C₃₁	1	2	yes	complemented
221	#124	C₂²×C₃₁	1	4	yes	complemented
222	#124	C₂²×C₃₁	1	4	yes	complemented
223	#123	C₂²×C₃₁	1	2	yes	—
224	#123	C₂²×C₃₁	1	4	yes	complemented
225	#123	C₂²×C₃₁	1	2	yes	complemented
226	#123	C₂²×C₃₁	1	4	yes	complemented
227	#123	C₂²×C₃₁	1	4	yes	complemented
228	#123	C₂²×C₃₁	1	4	yes	complemented
229	#123	C₂²×C₃₁	1	4	yes	complemented
230	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
231	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
232	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
233	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
234	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
235	#121	C₂²×C₃₁	1	2	yes	—
236	#121	C₂²×C₃₁	1	4	yes	—
237	#121	C₂²×C₃₁	1	4	yes	complemented
238	#121	C₂²×C₃₁	1	4	yes	complemented
239	#121	C₂²×C₃₁	1	4	yes	complemented
240	#120	C₂²×C₃₁	1	4	yes	—
241	#120	C₂²×C₃₁	1	2	yes	—
242	#120	C₂²×C₃₁	1	2	yes	complemented
243	#120	C₂²×C₃₁	1	4	yes	complemented
244	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
245	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
246	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
247	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
248	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
249	#117	C₂²×C₃₁	1	4	yes	complemented
250	#117	C₂²×C₃₁	1	2	yes	complemented
251	#117	C₂²×C₃₁	1	4	yes	complemented
252	C₂×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
253	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
254	C₂×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
255	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
256	C₃₁	#3545	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁴	C₂³×C₃₁	1	2	yes	—
258	C₂⁴	C₂³×C₃₁	1	2	yes	—
259	#41	—	4	4	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
262	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
263	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
264	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
265	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	C₂³×C₃₁	1	4	yes	—
269	C₂×D₄	C₂³×C₃₁	1	4	yes	—
270	C₂×D₄	C₂³×C₃₁	1	4	yes	—
271	C₂×D₄	C₂³×C₃₁	1	2	yes	—
272	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
273	C₂×D₄	C₂³×C₃₁	1	2	yes	—
274	C₂×D₄	C₂³×C₃₁	1	2	yes	—
275	C₂×D₄	C₂³×C₃₁	1	4	yes	—
276	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
280	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
281	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
282	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
283	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
284	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
285	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
286	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
287	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
288	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
289	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
290	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
291	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
292	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
293	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
294	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
295	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
296	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
297	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
298	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
299	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
300	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
301	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
303	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
304	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
307	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
308	C₄²	C₂³×C₃₁	1	1	yes	characteristic
309	C₄²	C₂³×C₃₁	1	2	yes	—
310	C₄²	C₂³×C₃₁	1	1	yes	characteristic
311	C₄²	C₂³×C₃₁	1	2	yes	—
312	C₄²	C₂³×C₃₁	1	4	yes	—
313	C₄²	C₂³×C₃₁	1	2	yes	—
314	C₂³	—	2	4	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	C₂⁴×C₃₁	1	2	yes	—
319	C₂³	C₂⁴×C₃₁	1	4	yes	—
320	C₂³	C₂⁴×C₃₁	1	2	yes	—
321	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	D₄	—	2	8	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
344	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
345	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
346	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
347	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
350	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
351	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
363	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	4	no	—
373	C₂	—	2	2	no	—
374	C₂	—	4	2	no	—
375	C₂	—	4	4	no	—
376	C₂	—	4	2	no	—
377	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂	C₃₁×#585	1	2	yes	—

	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×#562	C₂	semidirect
3. C₃₁×H(3,𝔽₄)	C₂	semidirect
4. C₃₁×#555	C₂	semidirect
5. C₃₁×#551	C₂	semidirect
6. C₃₁×#551	C₂	semidirect
7. C₃₁×#546	C₂	semidirect
8. C₃₁×#542	C₂	semidirect
9. C₃₁×#538	C₂	semidirect
10. C₃₁×#536	C₂	semidirect
11. C₃₁×#534	C₂	semidirect
12. C₃₁×#529	C₂	semidirect
13. C₂×C₃₁×#124	C₂	semidirect
15. C₂²×Q₈×C₃₁	C₂²	semidirect
17. C₂²×D₄×C₃₁	C₂²	semidirect
18. C₃₁×C₄⋊Q₈	C₂²	semidirect
19. C₃₁×C₄⋊Q₈	C₂²	semidirect
20. C₃₁×#126	C₂²	semidirect
21. C₃₁×#126	C₂²	semidirect
22. C₃₁×#126	C₂²	semidirect
23. C₃₁×#125	C₂²	semidirect
26. C₃₁×#124	C₂²	semidirect
27. C₃₁×#124	C₂²	semidirect
28. C₃₁×#124	C₂²	semidirect
29. C₃₁×#124	C₂²	semidirect
30. C₃₁×#124	C₂²	semidirect
31. C₃₁×#124	C₂²	semidirect
32. C₃₁×#124	C₂²	semidirect
33. C₃₁×#124	C₂²	semidirect
35. C₃₁×#123	C₂²	semidirect
36. C₃₁×#123	C₂²	semidirect
37. C₃₁×#123	C₂²	semidirect
38. C₃₁×#123	C₂²	semidirect
39. C₃₁×#123	C₂²	semidirect
40. C₃₁×#123	C₂²	semidirect
41. C₃₁×C₂²⋊Q₈	C₂²	semidirect
42. C₃₁×C₂²⋊Q₈	C₂²	semidirect
43. C₃₁×C₂²⋊Q₈	C₂²	semidirect
44. C₃₁×C₂²⋊Q₈	C₂²	semidirect
45. C₃₁×C₂²⋊Q₈	C₂²	semidirect
48. C₃₁×#121	C₂²	semidirect
49. C₃₁×#121	C₂²	semidirect
50. C₃₁×#121	C₂²	semidirect
53. C₃₁×#120	C₂²	semidirect
54. C₃₁×#120	C₂²	semidirect
55. C₄×Q₈×C₃₁	C₂²	semidirect
56. C₄×D₄×C₃₁	C₂²	semidirect
57. C₄×D₄×C₃₁	C₂²	semidirect
58. C₄×D₄×C₃₁	C₂²	semidirect
59. C₄×D₄×C₃₁	C₂²	semidirect
60. C₃₁×#117	C₂²	semidirect
61. C₃₁×#117	C₂²	semidirect
62. C₃₁×#117	C₂²	semidirect
63. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
64. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
66. C₂×C₄²×C₃₁	C₂²	semidirect
162. #3545	C₃₁	direct (N × H)
184. #563	C₂×C₃₁	semidirect
185. #562	C₂×C₃₁	semidirect
186. H(3,𝔽₄)	C₂×C₃₁	semidirect
187. #555	C₂×C₃₁	semidirect
188. #551	C₂×C₃₁	semidirect
189. #551	C₂×C₃₁	semidirect
190. #546	C₂×C₃₁	semidirect
191. #542	C₂×C₃₁	semidirect
192. #538	C₂×C₃₁	semidirect
193. #536	C₂×C₃₁	semidirect
194. #534	C₂×C₃₁	semidirect
195. #529	C₂×C₃₁	semidirect
196. C₂×#124	C₂×C₃₁	semidirect
204. C₂²×Q₈	C₂²×C₃₁	semidirect
206. C₂²×D₄	C₂²×C₃₁	semidirect
207. C₄⋊Q₈	C₂²×C₃₁	semidirect
208. C₄⋊Q₈	C₂²×C₃₁	semidirect
209. #126	C₂²×C₃₁	semidirect
210. #126	C₂²×C₃₁	semidirect
211. #126	C₂²×C₃₁	semidirect
212. #125	C₂²×C₃₁	semidirect
215. #124	C₂²×C₃₁	semidirect
216. #124	C₂²×C₃₁	semidirect
217. #124	C₂²×C₃₁	semidirect
218. #124	C₂²×C₃₁	semidirect
219. #124	C₂²×C₃₁	semidirect
220. #124	C₂²×C₃₁	semidirect
221. #124	C₂²×C₃₁	semidirect
222. #124	C₂²×C₃₁	semidirect
224. #123	C₂²×C₃₁	semidirect
225. #123	C₂²×C₃₁	semidirect
226. #123	C₂²×C₃₁	semidirect
227. #123	C₂²×C₃₁	semidirect
228. #123	C₂²×C₃₁	semidirect
229. #123	C₂²×C₃₁	semidirect
230. C₂²⋊Q₈	C₂²×C₃₁	semidirect
231. C₂²⋊Q₈	C₂²×C₃₁	semidirect
232. C₂²⋊Q₈	C₂²×C₃₁	semidirect
233. C₂²⋊Q₈	C₂²×C₃₁	semidirect
234. C₂²⋊Q₈	C₂²×C₃₁	semidirect
237. #121	C₂²×C₃₁	semidirect
238. #121	C₂²×C₃₁	semidirect
239. #121	C₂²×C₃₁	semidirect
242. #120	C₂²×C₃₁	semidirect
243. #120	C₂²×C₃₁	semidirect
244. C₄×Q₈	C₂²×C₃₁	semidirect
245. C₄×D₄	C₂²×C₃₁	semidirect
246. C₄×D₄	C₂²×C₃₁	semidirect
247. C₄×D₄	C₂²×C₃₁	semidirect
248. C₄×D₄	C₂²×C₃₁	semidirect
249. #117	C₂²×C₃₁	semidirect
250. #117	C₂²×C₃₁	semidirect
251. #117	C₂²×C₃₁	semidirect
252. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
253. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
254. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
255. C₂×C₄²	C₂²×C₃₁	semidirect
256. C₃₁	#3545	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×#562	2
C₃₁×H(3,𝔽₄)	2
C₃₁×#555	2
C₃₁×#551	2
C₃₁×#546	2
C₃₁×#542	2
C₃₁×#538	2
C₃₁×#536	2
C₃₁×#534	2
C₃₁×#529	2
C₂×C₃₁×#124	2
#3545	31

Subgroups — C31×#3545 #16843478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3545 #16843478