Subgroups — C₃₁×#3543 #16843476

Order 3968.

1260 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#560	C₂	1	4	yes	maximal, complemented
2	C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#550	C₂	1	2	yes	maximal, complemented
4	C₃₁×#546	C₂	1	4	yes	maximal, complemented
5	D₄²×C₃₁	C₂	1	4	yes	maximal, complemented
6	D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#540	C₂	1	4	yes	maximal, complemented
8	C₃₁×#535	C₂	1	4	yes	maximal, complemented
9	C₃₁×#534	C₂	1	4	yes	maximal, complemented
10	C₂×C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#529	C₂	1	2	yes	maximal, complemented
12	C₂×#41×C₃₁	C₂²	1	4	yes	complemented
13	C₂²×D₄×C₃₁	C₂²	1	2	yes	complemented
14	C₂²×D₄×C₃₁	C₂²	1	4	yes	complemented
15	C₂²×D₄×C₃₁	C₂²	1	4	yes	complemented
16	C₂²×D₄×C₃₁	C₂²	1	4	yes	complemented
17	C₃₁×#127	C₂²	1	1	yes	characteristic
18	C₃₁×#127	C₂²	1	4	yes	complemented
19	C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#127	C₂²	1	2	yes	complemented
21	C₃₁×#127	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	2	yes	complemented
25	C₃₁×#124	C₂²	1	4	yes	complemented
26	C₃₁×#123	C₂²	1	4	yes	complemented
27	C₃₁×#123	C₂²	1	4	yes	complemented
28	C₃₁×#123	C₂²	1	4	yes	complemented
29	C₃₁×#123	C₂²	1	8	yes	complemented
30	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
31	C₃₁×#121	C₂²	1	2	yes	—
32	C₃₁×#121	C₂²	1	8	yes	complemented
33	C₃₁×#121	C₂²	1	8	yes	complemented
34	C₃₁×#121	C₂²	1	8	yes	complemented
35	C₃₁×#121	C₂²	1	4	yes	complemented
36	C₃₁×#121	C₂²	1	4	yes	complemented
37	C₃₁×#121	C₂²	1	8	yes	complemented
38	C₃₁×#120	C₂²	1	4	yes	complemented
39	C₃₁×#120	C₂²	1	8	yes	complemented
40	C₃₁×#120	C₂²	1	4	yes	complemented
41	C₃₁×#120	C₂²	1	8	yes	complemented
42	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
43	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
44	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
45	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
46	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
47	C₃₁×#117	C₂²	1	4	yes	complemented
48	C₂×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
49	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×C₃₁	C₂³	1	4	yes	—
51	C₂⁴×C₃₁	C₂³	1	4	yes	—
52	#41×C₃₁	—	4	8	no	—
53	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
54	C₂×D₄×C₃₁	—	4	8	no	—
55	C₂×D₄×C₃₁	—	4	8	no	—
56	C₂×D₄×C₃₁	—	4	4	no	—
57	C₂×D₄×C₃₁	—	4	8	no	—
58	C₂×D₄×C₃₁	C₂³	1	4	yes	—
59	C₂×D₄×C₃₁	C₂³	1	2	yes	—
60	C₂×D₄×C₃₁	C₂³	1	4	yes	—
61	C₂×D₄×C₃₁	C₂³	1	4	yes	—
62	C₂×D₄×C₃₁	C₂³	1	8	yes	—
63	C₂×D₄×C₃₁	C₂³	1	8	yes	—
64	C₂×D₄×C₃₁	C₂³	1	2	yes	—
65	C₂×D₄×C₃₁	C₂³	1	8	yes	—
66	C₂×D₄×C₃₁	C₂³	1	4	yes	—
67	C₂×D₄×C₃₁	C₂³	1	8	yes	—
68	C₂×D₄×C₃₁	C₂³	1	2	yes	—
69	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
70	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
72	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
73	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
74	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
75	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
76	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
77	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
78	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
79	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
80	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
81	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
82	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
83	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
84	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
85	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
86	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
87	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
88	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
89	C₄²×C₃₁	C₂³	1	2	yes	—
90	C₄²×C₃₁	C₂³	1	1	yes	characteristic
91	C₄²×C₃₁	C₂³	1	1	yes	characteristic
92	C₄²×C₃₁	C₂³	1	4	yes	—
93	C₂³×C₃₁	—	2	8	no	—
94	C₂³×C₃₁	—	4	8	no	—
95	C₂³×C₃₁	—	4	8	no	—
96	C₂³×C₃₁	—	4	4	no	—
97	C₂³×C₃₁	C₂⁴	1	4	yes	—
98	C₂³×C₃₁	C₂⁴	1	4	yes	—
99	C₂³×C₃₁	C₂⁴	1	4	yes	—
100	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
101	Q₈×C₃₁	—	2	4	no	—
102	D₄×C₃₁	—	2	8	no	—
103	D₄×C₃₁	—	2	4	no	—
104	D₄×C₃₁	—	2	8	no	—
105	D₄×C₃₁	—	2	8	no	—
106	D₄×C₃₁	—	4	8	no	—
107	D₄×C₃₁	—	4	8	no	—
108	D₄×C₃₁	—	4	2	no	—
109	D₄×C₃₁	—	4	4	no	—
110	D₄×C₃₁	—	4	2	no	—
111	D₄×C₃₁	—	4	8	no	—
112	D₄×C₃₁	—	4	8	no	—
113	C₂×C₄×C₃₁	—	2	2	no	—
114	C₂×C₄×C₃₁	—	2	4	no	—
115	C₂×C₄×C₃₁	—	2	8	no	—
116	C₂×C₄×C₃₁	—	4	4	no	—
117	C₂×C₄×C₃₁	—	4	8	no	—
118	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
119	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
120	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
121	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
123	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
124	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
125	#3543	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₃₁	—	2	2	no	—
127	C₂²×C₃₁	—	2	4	no	—
128	C₂²×C₃₁	—	2	8	no	—
129	C₂²×C₃₁	—	2	4	no	—
130	C₂²×C₃₁	—	2	4	no	—
131	C₂²×C₃₁	—	2	4	no	—
132	C₂²×C₃₁	—	2	8	no	—
133	C₂²×C₃₁	—	2	4	no	—
134	C₂²×C₃₁	—	8	8	no	—
135	C₂²×C₃₁	—	8	8	no	—
136	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
137	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
138	C₄×C₃₁	—	2	4	no	—
139	C₄×C₃₁	—	2	1	no	—
140	C₄×C₃₁	—	2	1	no	—
141	C₄×C₃₁	—	2	2	no	—
142	C₄×C₃₁	—	2	4	no	—
143	C₄×C₃₁	—	2	4	no	—
144	C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
145	#560	C₂×C₃₁	1	4	yes	complemented
146	#559	C₂×C₃₁	1	1	yes	characteristic, complemented
147	#550	C₂×C₃₁	1	2	yes	complemented
148	#546	C₂×C₃₁	1	4	yes	complemented
149	D₄²	C₂×C₃₁	1	4	yes	complemented
150	D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
151	#540	C₂×C₃₁	1	4	yes	complemented
152	#535	C₂×C₃₁	1	4	yes	complemented
153	#534	C₂×C₃₁	1	4	yes	complemented
154	C₂×#127	C₂×C₃₁	1	1	yes	characteristic, complemented
155	#529	C₂×C₃₁	1	2	yes	complemented
156	C₂×C₃₁	—	2	2	no	—
157	C₂×C₃₁	—	4	4	no	—
158	C₂×C₃₁	—	4	4	no	—
159	C₂×C₃₁	—	4	4	no	—
160	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
162	C₂×#41	C₂²×C₃₁	1	4	yes	complemented
163	C₂²×D₄	C₂²×C₃₁	1	2	yes	complemented
164	C₂²×D₄	C₂²×C₃₁	1	4	yes	complemented
165	C₂²×D₄	C₂²×C₃₁	1	4	yes	complemented
166	C₂²×D₄	C₂²×C₃₁	1	4	yes	complemented
167	#127	C₂²×C₃₁	1	1	yes	characteristic
168	#127	C₂²×C₃₁	1	4	yes	complemented
169	#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
170	#127	C₂²×C₃₁	1	2	yes	complemented
171	#127	C₂²×C₃₁	1	4	yes	complemented
172	#126	C₂²×C₃₁	1	4	yes	complemented
173	#125	C₂²×C₃₁	1	2	yes	complemented
174	#124	C₂²×C₃₁	1	2	yes	complemented
175	#124	C₂²×C₃₁	1	4	yes	complemented
176	#123	C₂²×C₃₁	1	4	yes	complemented
177	#123	C₂²×C₃₁	1	4	yes	complemented
178	#123	C₂²×C₃₁	1	4	yes	complemented
179	#123	C₂²×C₃₁	1	8	yes	complemented
180	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
181	#121	C₂²×C₃₁	1	2	yes	—
182	#121	C₂²×C₃₁	1	8	yes	complemented
183	#121	C₂²×C₃₁	1	8	yes	complemented
184	#121	C₂²×C₃₁	1	8	yes	complemented
185	#121	C₂²×C₃₁	1	4	yes	complemented
186	#121	C₂²×C₃₁	1	4	yes	complemented
187	#121	C₂²×C₃₁	1	8	yes	complemented
188	#120	C₂²×C₃₁	1	4	yes	complemented
189	#120	C₂²×C₃₁	1	8	yes	complemented
190	#120	C₂²×C₃₁	1	4	yes	complemented
191	#120	C₂²×C₃₁	1	8	yes	complemented
192	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
193	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
194	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
195	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
196	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
197	#117	C₂²×C₃₁	1	4	yes	complemented
198	C₂×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
199	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
200	C₃₁	#3543	1	1	yes	characteristic, direct product factor, Sylow
201	C₂⁴	C₂³×C₃₁	1	4	yes	—
202	C₂⁴	C₂³×C₃₁	1	4	yes	—
203	#41	—	4	8	no	—
204	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
205	C₂×D₄	—	4	8	no	—
206	C₂×D₄	—	4	8	no	—
207	C₂×D₄	—	4	4	no	—
208	C₂×D₄	—	4	8	no	—
209	C₂×D₄	C₂³×C₃₁	1	4	yes	—
210	C₂×D₄	C₂³×C₃₁	1	2	yes	—
211	C₂×D₄	C₂³×C₃₁	1	4	yes	—
212	C₂×D₄	C₂³×C₃₁	1	4	yes	—
213	C₂×D₄	C₂³×C₃₁	1	8	yes	—
214	C₂×D₄	C₂³×C₃₁	1	8	yes	—
215	C₂×D₄	C₂³×C₃₁	1	2	yes	—
216	C₂×D₄	C₂³×C₃₁	1	8	yes	—
217	C₂×D₄	C₂³×C₃₁	1	4	yes	—
218	C₂×D₄	C₂³×C₃₁	1	8	yes	—
219	C₂×D₄	C₂³×C₃₁	1	2	yes	—
220	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
221	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
222	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
223	C₂²×C₄	C₂³×C₃₁	1	8	yes	—
224	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
225	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
226	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
227	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
228	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
229	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
230	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
231	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
232	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
233	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
234	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
235	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
236	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
237	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
238	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
239	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
240	C₄²	C₂³×C₃₁	1	2	yes	—
241	C₄²	C₂³×C₃₁	1	1	yes	characteristic
242	C₄²	C₂³×C₃₁	1	1	yes	characteristic
243	C₄²	C₂³×C₃₁	1	4	yes	—
244	C₂³	—	2	8	no	—
245	C₂³	—	4	8	no	—
246	C₂³	—	4	8	no	—
247	C₂³	—	4	4	no	—
248	C₂³	C₂⁴×C₃₁	1	4	yes	—
249	C₂³	C₂⁴×C₃₁	1	4	yes	—
250	C₂³	C₂⁴×C₃₁	1	4	yes	—
251	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
252	Q₈	—	2	4	no	—
253	D₄	—	2	8	no	—
254	D₄	—	2	4	no	—
255	D₄	—	2	8	no	—
256	D₄	—	2	8	no	—
257	D₄	—	4	8	no	—
258	D₄	—	4	8	no	—
259	D₄	—	4	2	no	—
260	D₄	—	4	4	no	—
261	D₄	—	4	2	no	—
262	D₄	—	4	8	no	—
263	D₄	—	4	8	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	8	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	8	no	—
269	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
270	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
271	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
272	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
273	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
274	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
275	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
276	C₂²	—	2	2	no	—
277	C₂²	—	2	4	no	—
278	C₂²	—	2	8	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	4	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	2	4	no	—
284	C₂²	—	8	8	no	—
285	C₂²	—	8	8	no	—
286	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
287	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
288	C₄	—	2	4	no	—
289	C₄	—	2	1	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	4	no	—
293	C₄	—	2	4	no	—
294	C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
295	C₂	—	2	2	no	—
296	C₂	—	4	4	no	—
297	C₂	—	4	4	no	—
298	C₂	—	4	4	no	—
299	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
300	C₂	C₂×C₃₁×H(5,𝔽₂)	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×#560	C₂	semidirect
2. C₃₁×#559	C₂	semidirect
3. C₃₁×#550	C₂	semidirect
4. C₃₁×#546	C₂	semidirect
5. D₄²×C₃₁	C₂	semidirect
6. D₄²×C₃₁	C₂	semidirect
7. C₃₁×#540	C₂	semidirect
8. C₃₁×#535	C₂	semidirect
9. C₃₁×#534	C₂	semidirect
10. C₂×C₃₁×#127	C₂	semidirect
11. C₃₁×#529	C₂	semidirect
12. C₂×#41×C₃₁	C₂²	semidirect
13. C₂²×D₄×C₃₁	C₂²	semidirect
14. C₂²×D₄×C₃₁	C₂²	semidirect
15. C₂²×D₄×C₃₁	C₂²	semidirect
16. C₂²×D₄×C₃₁	C₂²	semidirect
18. C₃₁×#127	C₂²	semidirect
19. C₃₁×#127	C₂²	semidirect
20. C₃₁×#127	C₂²	semidirect
21. C₃₁×#127	C₂²	semidirect
22. C₃₁×#126	C₂²	semidirect
23. C₃₁×#125	C₂²	semidirect
24. C₃₁×#124	C₂²	semidirect
25. C₃₁×#124	C₂²	semidirect
26. C₃₁×#123	C₂²	semidirect
27. C₃₁×#123	C₂²	semidirect
28. C₃₁×#123	C₂²	semidirect
29. C₃₁×#123	C₂²	semidirect
30. C₃₁×C₂²⋊Q₈	C₂²	semidirect
32. C₃₁×#121	C₂²	semidirect
33. C₃₁×#121	C₂²	semidirect
34. C₃₁×#121	C₂²	semidirect
35. C₃₁×#121	C₂²	semidirect
36. C₃₁×#121	C₂²	semidirect
37. C₃₁×#121	C₂²	semidirect
38. C₃₁×#120	C₂²	semidirect
39. C₃₁×#120	C₂²	semidirect
40. C₃₁×#120	C₂²	semidirect
41. C₃₁×#120	C₂²	semidirect
42. C₄×Q₈×C₃₁	C₂²	semidirect
43. C₄×D₄×C₃₁	C₂²	semidirect
44. C₄×D₄×C₃₁	C₂²	semidirect
45. C₄×D₄×C₃₁	C₂²	semidirect
46. C₄×D₄×C₃₁	C₂²	semidirect
47. C₃₁×#117	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
49. C₂×C₄²×C₃₁	C₂²	semidirect
125. #3543	C₃₁	direct (N × H)
145. #560	C₂×C₃₁	semidirect
146. #559	C₂×C₃₁	semidirect
147. #550	C₂×C₃₁	semidirect
148. #546	C₂×C₃₁	semidirect
149. D₄²	C₂×C₃₁	semidirect
150. D₄²	C₂×C₃₁	semidirect
151. #540	C₂×C₃₁	semidirect
152. #535	C₂×C₃₁	semidirect
153. #534	C₂×C₃₁	semidirect
154. C₂×#127	C₂×C₃₁	semidirect
155. #529	C₂×C₃₁	semidirect
162. C₂×#41	C₂²×C₃₁	semidirect
163. C₂²×D₄	C₂²×C₃₁	semidirect
164. C₂²×D₄	C₂²×C₃₁	semidirect
165. C₂²×D₄	C₂²×C₃₁	semidirect
166. C₂²×D₄	C₂²×C₃₁	semidirect
168. #127	C₂²×C₃₁	semidirect
169. #127	C₂²×C₃₁	semidirect
170. #127	C₂²×C₃₁	semidirect
171. #127	C₂²×C₃₁	semidirect
172. #126	C₂²×C₃₁	semidirect
173. #125	C₂²×C₃₁	semidirect
174. #124	C₂²×C₃₁	semidirect
175. #124	C₂²×C₃₁	semidirect
176. #123	C₂²×C₃₁	semidirect
177. #123	C₂²×C₃₁	semidirect
178. #123	C₂²×C₃₁	semidirect
179. #123	C₂²×C₃₁	semidirect
180. C₂²⋊Q₈	C₂²×C₃₁	semidirect
182. #121	C₂²×C₃₁	semidirect
183. #121	C₂²×C₃₁	semidirect
184. #121	C₂²×C₃₁	semidirect
185. #121	C₂²×C₃₁	semidirect
186. #121	C₂²×C₃₁	semidirect
187. #121	C₂²×C₃₁	semidirect
188. #120	C₂²×C₃₁	semidirect
189. #120	C₂²×C₃₁	semidirect
190. #120	C₂²×C₃₁	semidirect
191. #120	C₂²×C₃₁	semidirect
192. C₄×Q₈	C₂²×C₃₁	semidirect
193. C₄×D₄	C₂²×C₃₁	semidirect
194. C₄×D₄	C₂²×C₃₁	semidirect
195. C₄×D₄	C₂²×C₃₁	semidirect
196. C₄×D₄	C₂²×C₃₁	semidirect
197. #117	C₂²×C₃₁	semidirect
198. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
199. C₂×C₄²	C₂²×C₃₁	semidirect
200. C₃₁	#3543	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×#560	2
C₃₁×#559	2
C₃₁×#550	2
C₃₁×#546	2
D₄²×C₃₁	2
C₃₁×#540	2
C₃₁×#535	2
C₃₁×#534	2
C₂×C₃₁×#127	2
C₃₁×#529	2
#3543	31

Subgroups — C31×#3543 #16843476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3543 #16843476