Subgroups — C₃₁×#3536 #16843469

Order 3968.

1134 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#562	C₂	1	4	yes	maximal, complemented
2	C₃₁×#554	C₂	1	2	yes	maximal, complemented
3	C₃₁×#548	C₂	1	2	yes	maximal, complemented
4	C₃₁×#547	C₂	1	2	yes	maximal, complemented
5	C₃₁×#546	C₂	1	4	yes	maximal, complemented
6	C₃₁×#546	C₂	1	2	yes	maximal, complemented
7	C₃₁×#543	C₂	1	2	yes	maximal, complemented
8	C₃₁×#542	C₂	1	2	yes	maximal, complemented
9	C₃₁×#539	C₂	1	2	yes	maximal, complemented
10	C₃₁×#538	C₂	1	2	yes	maximal, complemented
11	C₃₁×#537	C₂	1	2	yes	maximal, complemented
12	C₃₁×#537	C₂	1	2	yes	maximal, complemented
13	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×#41×C₃₁	C₂²	1	4	yes	complemented
18	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
19	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
22	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃₁×#126	C₂²	1	4	yes	complemented
25	C₃₁×#125	C₂²	1	4	yes	complemented
26	C₃₁×#124	C₂²	1	4	yes	complemented
27	C₃₁×#124	C₂²	1	2	yes	complemented
28	C₃₁×#124	C₂²	1	4	yes	complemented
29	C₃₁×#123	C₂²	1	2	yes	complemented
30	C₃₁×#123	C₂²	1	4	yes	complemented
31	C₃₁×#123	C₂²	1	4	yes	complemented
32	C₃₁×#123	C₂²	1	4	yes	complemented
33	C₃₁×#123	C₂²	1	4	yes	complemented
34	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
38	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₃₁×#121	C₂²	1	2	yes	—
48	C₃₁×#121	C₂²	1	2	yes	—
49	C₃₁×#121	C₂²	1	2	yes	—
50	C₃₁×#121	C₂²	1	2	yes	—
51	C₃₁×#121	C₂²	1	1	yes	characteristic
52	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#121	C₂²	1	4	yes	complemented
54	C₃₁×#121	C₂²	1	2	yes	complemented
55	C₃₁×#121	C₂²	1	4	yes	complemented
56	C₃₁×#121	C₂²	1	4	yes	complemented
57	C₃₁×#121	C₂²	1	4	yes	complemented
58	C₃₁×#121	C₂²	1	4	yes	complemented
59	C₃₁×#120	C₂²	1	2	yes	—
60	C₃₁×#120	C₂²	1	4	yes	—
61	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
62	C₄×D₄×C₃₁	C₂²	1	2	yes	—
63	C₄×D₄×C₃₁	C₂²	1	4	yes	—
64	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
65	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
66	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
67	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
70	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
73	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
74	C₂×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
75	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
76	C₂⁴×C₃₁	C₂³	1	2	yes	—
77	#41×C₃₁	—	4	2	no	—
78	#41×C₃₁	—	4	8	no	—
79	#41×C₃₁	—	4	4	no	—
80	C₂×Q₈×C₃₁	—	4	2	no	—
81	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
82	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
84	C₂×Q₈×C₃₁	C₂³	1	4	yes	—
85	C₂×D₄×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	4	4	no	—
87	C₂×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂×D₄×C₃₁	C₂³	1	4	yes	—
90	C₂×D₄×C₃₁	C₂³	1	2	yes	—
91	C₂×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂×D₄×C₃₁	C₂³	1	4	yes	—
93	C₂×D₄×C₃₁	C₂³	1	4	yes	—
94	C₂×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂×D₄×C₃₁	C₂³	1	4	yes	—
96	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	—	4	2	no	—
98	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
107	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
108	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
110	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
114	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
117	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
131	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₄²×C₃₁	C₂³	1	2	yes	—
140	C₄²×C₃₁	C₂³	1	4	yes	—
141	C₂³×C₃₁	—	2	2	no	—
142	C₂³×C₃₁	—	2	2	no	—
143	C₂³×C₃₁	—	2	4	no	—
144	C₂³×C₃₁	—	4	1	no	—
145	C₂³×C₃₁	—	4	2	no	—
146	C₂³×C₃₁	—	4	2	no	—
147	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
148	C₂³×C₃₁	C₂⁴	1	4	yes	—
149	C₂³×C₃₁	C₂⁴	1	2	yes	—
150	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
151	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
152	Q₈×C₃₁	—	2	4	no	—
153	Q₈×C₃₁	—	4	2	no	—
154	Q₈×C₃₁	—	4	1	no	—
155	Q₈×C₃₁	—	4	4	no	—
156	D₄×C₃₁	—	2	8	no	—
157	D₄×C₃₁	—	2	4	no	—
158	D₄×C₃₁	—	2	4	no	—
159	D₄×C₃₁	—	2	4	no	—
160	D₄×C₃₁	—	4	2	no	—
161	D₄×C₃₁	—	4	4	no	—
162	D₄×C₃₁	—	4	2	no	—
163	D₄×C₃₁	—	4	1	no	—
164	D₄×C₃₁	—	4	4	no	—
165	D₄×C₃₁	—	4	4	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	4	1	no	—
172	C₂×C₄×C₃₁	—	4	1	no	—
173	C₂×C₄×C₃₁	—	4	1	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	4	no	—
177	C₂×C₄×C₃₁	—	4	4	no	—
178	C₂×C₄×C₃₁	—	4	4	no	—
179	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
180	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
181	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
182	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
183	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
185	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	#3536	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₃₁	—	2	1	no	—
191	C₂²×C₃₁	—	2	1	no	—
192	C₂²×C₃₁	—	2	1	no	—
193	C₂²×C₃₁	—	2	1	no	—
194	C₂²×C₃₁	—	2	1	no	—
195	C₂²×C₃₁	—	2	2	no	—
196	C₂²×C₃₁	—	2	2	no	—
197	C₂²×C₃₁	—	2	4	no	—
198	C₂²×C₃₁	—	2	4	no	—
199	C₂²×C₃₁	—	2	1	no	—
200	C₂²×C₃₁	—	2	2	no	—
201	C₂²×C₃₁	—	2	1	no	—
202	C₂²×C₃₁	—	2	4	no	—
203	C₂²×C₃₁	—	4	4	no	—
204	C₂²×C₃₁	—	8	4	no	—
205	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
206	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
207	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
208	C₄×C₃₁	—	2	1	no	—
209	C₄×C₃₁	—	2	4	no	—
210	C₄×C₃₁	—	2	1	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	2	1	no	—
213	C₄×C₃₁	—	2	4	no	—
214	C₄×C₃₁	—	2	2	no	—
215	C₄×C₃₁	—	2	4	no	—
216	C₄×C₃₁	—	2	2	no	—
217	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
218	#562	C₂×C₃₁	1	4	yes	complemented
219	#554	C₂×C₃₁	1	2	yes	complemented
220	#548	C₂×C₃₁	1	2	yes	complemented
221	#547	C₂×C₃₁	1	2	yes	complemented
222	#546	C₂×C₃₁	1	4	yes	complemented
223	#546	C₂×C₃₁	1	2	yes	complemented
224	#543	C₂×C₃₁	1	2	yes	complemented
225	#542	C₂×C₃₁	1	2	yes	complemented
226	#539	C₂×C₃₁	1	2	yes	complemented
227	#538	C₂×C₃₁	1	2	yes	complemented
228	#537	C₂×C₃₁	1	2	yes	complemented
229	#537	C₂×C₃₁	1	2	yes	complemented
230	#525	C₂×C₃₁	1	1	yes	characteristic, complemented
231	C₂×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
232	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
233	C₂×C₃₁	—	2	2	no	—
234	C₂×C₃₁	—	2	2	no	—
235	C₂×C₃₁	—	4	2	no	—
236	C₂×C₃₁	—	4	1	no	—
237	C₂×C₃₁	—	4	4	no	—
238	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
241	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
242	C₂×#41	C₂²×C₃₁	1	4	yes	complemented
243	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
244	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
245	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
246	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
247	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
248	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
249	#126	C₂²×C₃₁	1	4	yes	complemented
250	#125	C₂²×C₃₁	1	4	yes	complemented
251	#124	C₂²×C₃₁	1	4	yes	complemented
252	#124	C₂²×C₃₁	1	2	yes	complemented
253	#124	C₂²×C₃₁	1	4	yes	complemented
254	#123	C₂²×C₃₁	1	2	yes	complemented
255	#123	C₂²×C₃₁	1	4	yes	complemented
256	#123	C₂²×C₃₁	1	4	yes	complemented
257	#123	C₂²×C₃₁	1	4	yes	complemented
258	#123	C₂²×C₃₁	1	4	yes	complemented
259	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
260	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
261	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
262	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
263	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
264	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
265	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
266	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
267	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
268	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
269	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
270	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
271	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
272	#121	C₂²×C₃₁	1	2	yes	—
273	#121	C₂²×C₃₁	1	2	yes	—
274	#121	C₂²×C₃₁	1	2	yes	—
275	#121	C₂²×C₃₁	1	2	yes	—
276	#121	C₂²×C₃₁	1	1	yes	characteristic
277	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
278	#121	C₂²×C₃₁	1	4	yes	complemented
279	#121	C₂²×C₃₁	1	2	yes	complemented
280	#121	C₂²×C₃₁	1	4	yes	complemented
281	#121	C₂²×C₃₁	1	4	yes	complemented
282	#121	C₂²×C₃₁	1	4	yes	complemented
283	#121	C₂²×C₃₁	1	4	yes	complemented
284	#120	C₂²×C₃₁	1	2	yes	—
285	#120	C₂²×C₃₁	1	4	yes	—
286	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
287	C₄×D₄	C₂²×C₃₁	1	2	yes	—
288	C₄×D₄	C₂²×C₃₁	1	4	yes	—
289	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
290	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
291	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
292	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
293	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
295	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
296	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
297	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
300	C₃₁	#3536	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
302	C₂⁴	C₂³×C₃₁	1	2	yes	—
303	#41	—	4	2	no	—
304	#41	—	4	8	no	—
305	#41	—	4	4	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
308	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
309	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
310	C₂×Q₈	C₂³×C₃₁	1	4	yes	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	C₂³×C₃₁	1	2	yes	—
314	C₂×D₄	C₂³×C₃₁	1	2	yes	—
315	C₂×D₄	C₂³×C₃₁	1	4	yes	—
316	C₂×D₄	C₂³×C₃₁	1	2	yes	—
317	C₂×D₄	C₂³×C₃₁	1	2	yes	—
318	C₂×D₄	C₂³×C₃₁	1	4	yes	—
319	C₂×D₄	C₂³×C₃₁	1	4	yes	—
320	C₂×D₄	C₂³×C₃₁	1	2	yes	—
321	C₂×D₄	C₂³×C₃₁	1	4	yes	—
322	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
325	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
327	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
331	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
332	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
333	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
334	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
336	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
338	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
339	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
340	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
341	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
342	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
343	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
344	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
345	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
346	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
347	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
348	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
349	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
350	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
351	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
352	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
353	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
354	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
355	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
356	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
357	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
358	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
359	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
360	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
361	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
362	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
363	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
364	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
365	C₄²	C₂³×C₃₁	1	2	yes	—
366	C₄²	C₂³×C₃₁	1	4	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
374	C₂³	C₂⁴×C₃₁	1	4	yes	—
375	C₂³	C₂⁴×C₃₁	1	2	yes	—
376	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
377	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	4	no	—
382	D₄	—	2	8	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
406	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
407	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
408	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
409	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
411	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
412	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
413	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
414	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
431	C₂²	C₃₁×2₋¹⁺⁴	1	2	yes	—
432	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	4	1	no	—
446	C₂	—	4	4	no	—
447	C₂	—	4	2	no	—
448	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂	C₂×C₃₁×2₋¹⁺⁴	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×#562	C₂	semidirect
2. C₃₁×#554	C₂	semidirect
3. C₃₁×#548	C₂	semidirect
4. C₃₁×#547	C₂	semidirect
5. C₃₁×#546	C₂	semidirect
6. C₃₁×#546	C₂	semidirect
7. C₃₁×#543	C₂	semidirect
8. C₃₁×#542	C₂	semidirect
9. C₃₁×#539	C₂	semidirect
10. C₃₁×#538	C₂	semidirect
11. C₃₁×#537	C₂	semidirect
12. C₃₁×#537	C₂	semidirect
13. C₃₁×#525	C₂	semidirect
14. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
15. C₂×C₃₁×#121	C₂	semidirect
16. C₂×#41×C₃₁	C₂²	semidirect
17. C₂×#41×C₃₁	C₂²	semidirect
18. C₂×#41×C₃₁	C₂²	semidirect
19. C₂²×Q₈×C₃₁	C₂²	semidirect
23. C₃₁×C₄⋊Q₈	C₂²	semidirect
24. C₃₁×#126	C₂²	semidirect
25. C₃₁×#125	C₂²	semidirect
26. C₃₁×#124	C₂²	semidirect
27. C₃₁×#124	C₂²	semidirect
28. C₃₁×#124	C₂²	semidirect
29. C₃₁×#123	C₂²	semidirect
30. C₃₁×#123	C₂²	semidirect
31. C₃₁×#123	C₂²	semidirect
32. C₃₁×#123	C₂²	semidirect
33. C₃₁×#123	C₂²	semidirect
38. C₃₁×C₂²⋊Q₈	C₂²	semidirect
39. C₃₁×C₂²⋊Q₈	C₂²	semidirect
40. C₃₁×C₂²⋊Q₈	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
46. C₃₁×C₂²⋊Q₈	C₂²	semidirect
52. C₃₁×#121	C₂²	semidirect
53. C₃₁×#121	C₂²	semidirect
54. C₃₁×#121	C₂²	semidirect
55. C₃₁×#121	C₂²	semidirect
56. C₃₁×#121	C₂²	semidirect
57. C₃₁×#121	C₂²	semidirect
58. C₃₁×#121	C₂²	semidirect
61. C₄×Q₈×C₃₁	C₂²	semidirect
64. C₄×D₄×C₃₁	C₂²	semidirect
65. C₄×D₄×C₃₁	C₂²	semidirect
66. C₄×D₄×C₃₁	C₂²	semidirect
67. C₃₁×#117	C₂²	semidirect
69. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
70. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
71. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
189. #3536	C₃₁	direct (N × H)
218. #562	C₂×C₃₁	semidirect
219. #554	C₂×C₃₁	semidirect
220. #548	C₂×C₃₁	semidirect
221. #547	C₂×C₃₁	semidirect
222. #546	C₂×C₃₁	semidirect
223. #546	C₂×C₃₁	semidirect
224. #543	C₂×C₃₁	semidirect
225. #542	C₂×C₃₁	semidirect
226. #539	C₂×C₃₁	semidirect
227. #538	C₂×C₃₁	semidirect
228. #537	C₂×C₃₁	semidirect
229. #537	C₂×C₃₁	semidirect
230. #525	C₂×C₃₁	semidirect
231. C₂×C₂²⋊Q₈	C₂×C₃₁	semidirect
232. C₂×#121	C₂×C₃₁	semidirect
241. C₂×#41	C₂²×C₃₁	semidirect
242. C₂×#41	C₂²×C₃₁	semidirect
243. C₂×#41	C₂²×C₃₁	semidirect
244. C₂²×Q₈	C₂²×C₃₁	semidirect
248. C₄⋊Q₈	C₂²×C₃₁	semidirect
249. #126	C₂²×C₃₁	semidirect
250. #125	C₂²×C₃₁	semidirect
251. #124	C₂²×C₃₁	semidirect
252. #124	C₂²×C₃₁	semidirect
253. #124	C₂²×C₃₁	semidirect
254. #123	C₂²×C₃₁	semidirect
255. #123	C₂²×C₃₁	semidirect
256. #123	C₂²×C₃₁	semidirect
257. #123	C₂²×C₃₁	semidirect
258. #123	C₂²×C₃₁	semidirect
263. C₂²⋊Q₈	C₂²×C₃₁	semidirect
264. C₂²⋊Q₈	C₂²×C₃₁	semidirect
265. C₂²⋊Q₈	C₂²×C₃₁	semidirect
266. C₂²⋊Q₈	C₂²×C₃₁	semidirect
267. C₂²⋊Q₈	C₂²×C₃₁	semidirect
268. C₂²⋊Q₈	C₂²×C₃₁	semidirect
269. C₂²⋊Q₈	C₂²×C₃₁	semidirect
270. C₂²⋊Q₈	C₂²×C₃₁	semidirect
271. C₂²⋊Q₈	C₂²×C₃₁	semidirect
277. #121	C₂²×C₃₁	semidirect
278. #121	C₂²×C₃₁	semidirect
279. #121	C₂²×C₃₁	semidirect
280. #121	C₂²×C₃₁	semidirect
281. #121	C₂²×C₃₁	semidirect
282. #121	C₂²×C₃₁	semidirect
283. #121	C₂²×C₃₁	semidirect
286. C₄×Q₈	C₂²×C₃₁	semidirect
289. C₄×D₄	C₂²×C₃₁	semidirect
290. C₄×D₄	C₂²×C₃₁	semidirect
291. C₄×D₄	C₂²×C₃₁	semidirect
292. #117	C₂²×C₃₁	semidirect
294. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
295. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
296. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
300. C₃₁	#3536	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×#562	2
C₃₁×#554	2
C₃₁×#548	2
C₃₁×#547	2
C₃₁×#546	2
C₃₁×#543	2
C₃₁×#542	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#537	2
C₃₁×#525	2
C₂×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#121	2
#3536	31

Subgroups — C31×#3536 #16843469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3536 #16843469