Subgroups — C₃₁×#10836 #21467595

Order 7936.

850 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×H(3,ℤ/4)	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
6	C₂×C₃₁×#117	C₂²	1	2	yes	—
7	C₂×C₃₁×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#423	—	2	2	no	—
10	C₃₁×#423	—	2	1	no	—
11	C₃₁×#423	—	2	1	no	—
12	C₂×C₃₁×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₃₁×#384	—	2	1	no	—
14	C₃₁×#382	—	2	1	no	—
15	C₃₁×#380	—	2	2	no	—
16	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
17	C₄×C₄⋊C₄×C₃₁	C₄	1	4	yes	complemented
18	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
19	C₃₁×#376	C₄	1	2	yes	complemented
20	C₄³×C₃₁	C₄	1	2	yes	complemented
21	C₃₁×H(3,ℤ/4)	—	2	8	no	—
22	C₂³×C₄×C₃₁	D₄	1	2	yes	—
23	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₃₁	—	2	2	no	—
25	C₂×M₁₆×C₃₁	—	2	2	no	—
26	C₂×M₁₆×C₃₁	—	2	4	no	—
27	C₂×M₁₆×C₃₁	—	2	4	no	—
28	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
29	C₃₁×#117	—	2	2	no	—
30	C₃₁×#117	—	2	2	no	—
31	C₃₁×#117	—	2	4	no	—
32	C₃₁×#117	—	2	4	no	—
33	C₃₁×#117	D₄	1	4	yes	—
34	C₃₁×#117	Q₈	1	4	yes	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₄²×C₃₁	—	2	4	no	—
41	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₃₁	D₄	1	2	yes	—
48	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
52	C₃₁×C₄⋊C₈	—	2	4	no	—
53	C₃₁×C₄⋊C₈	—	2	4	no	—
54	C₃₁×#95	—	2	4	no	—
55	C₃₁×#95	—	2	4	no	—
56	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₃₁	—	2	4	no	—
58	C₂²×C₄×C₃₁	—	2	4	no	—
59	C₂²×C₄×C₃₁	—	4	4	no	—
60	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
74	C₂²×C₄×C₃₁	#41	1	2	yes	—
75	C₂²×C₄×C₃₁	#41	1	2	yes	—
76	M₁₆×C₃₁	—	4	4	no	—
77	M₁₆×C₃₁	—	4	2	no	—
78	M₁₆×C₃₁	—	4	2	no	—
79	C₂×C₈×C₃₁	—	2	4	no	—
80	C₂×C₈×C₃₁	—	2	8	no	—
81	C₄⋊C₄×C₃₁	—	2	4	no	—
82	C₄⋊C₄×C₃₁	—	2	4	no	—
83	C₄⋊C₄×C₃₁	—	4	8	no	—
84	C₄⋊C₄×C₃₁	—	4	2	no	—
85	C₄⋊C₄×C₃₁	—	4	2	no	—
86	C₂²⋊C₄×C₃₁	—	2	4	no	—
87	C₂²⋊C₄×C₃₁	—	2	4	no	—
88	C₂²⋊C₄×C₃₁	—	4	4	no	—
89	C₄²×C₃₁	—	2	4	no	—
90	C₄²×C₃₁	—	2	8	no	—
91	C₄²×C₃₁	—	4	8	no	—
92	C₄²×C₃₁	C₄²	1	2	yes	—
93	C₄²×C₃₁	C₄²	1	2	yes	—
94	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
100	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
101	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₃₁	C₄⋊C₄	1	8	yes	complemented
103	#10836	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂³×C₃₁	—	4	2	no	—
105	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂³×C₃₁	#121	1	2	yes	—
109	C₂³×C₃₁	C₂²⋊Q₈	1	2	yes	—
110	C₂×C₄×C₃₁	—	2	4	no	—
111	C₂×C₄×C₃₁	—	2	4	no	—
112	C₂×C₄×C₃₁	—	2	4	no	—
113	C₂×C₄×C₃₁	—	2	8	no	—
114	C₂×C₄×C₃₁	—	4	2	no	—
115	C₂×C₄×C₃₁	—	4	2	no	—
116	C₂×C₄×C₃₁	—	4	2	no	—
117	C₂×C₄×C₃₁	—	4	8	no	—
118	C₂×C₄×C₃₁	—	4	8	no	—
119	C₂×C₄×C₃₁	—	4	4	no	—
120	C₂×C₄×C₃₁	#95	1	2	yes	—
121	C₂×C₄×C₃₁	#95	1	2	yes	—
122	C₂×C₄×C₃₁	#95	1	2	yes	—
123	C₂×C₄×C₃₁	#95	1	2	yes	—
124	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
125	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₃₁	#117	1	2	yes	—
130	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₃₁	#121	1	2	yes	—
135	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
137	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
138	C₂×C₄×C₃₁	#125	1	2	yes	—
139	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
142	C₈×C₃₁	—	4	4	no	—
143	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
144	#2285	C₂×C₃₁	1	1	yes	characteristic
145	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
146	C₂×H(3,ℤ/4)	C₂×C₃₁	1	4	yes	—
147	C₂²×C₃₁	—	2	2	no	—
148	C₂²×C₃₁	—	2	2	no	—
149	C₂²×C₃₁	—	2	2	no	—
150	C₂²×C₃₁	—	4	2	no	—
151	C₂²×C₃₁	—	4	2	no	—
152	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
153	C₂²×C₃₁	#380	1	2	yes	—
154	C₂²×C₃₁	#389	1	2	yes	—
155	C₂²×C₃₁	#390	1	1	yes	characteristic
156	C₂²×C₃₁	#391	1	1	yes	characteristic
157	C₄×C₃₁	—	2	2	no	—
158	C₄×C₃₁	—	2	2	no	—
159	C₄×C₃₁	—	2	2	no	—
160	C₄×C₃₁	—	4	8	no	—
161	C₄×C₃₁	—	8	4	no	—
162	C₄×C₃₁	H(3,ℤ/4)	1	4	yes	complemented
163	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
164	C₄×C₃₁	#382	1	1	yes	characteristic
165	C₄×C₃₁	#384	1	1	yes	characteristic
166	C₄×C₃₁	#389	1	2	yes	—
167	C₄×C₃₁	#390	1	1	yes	characteristic
168	C₄×C₃₁	#391	1	1	yes	characteristic
169	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
170	C₂×#117	C₂²×C₃₁	1	2	yes	—
171	C₂×#117	C₂²×C₃₁	1	2	yes	—
172	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
173	#423	—	2	2	no	—
174	#423	—	2	1	no	—
175	#423	—	2	1	no	—
176	C₂×C₄⋊C₈	C₄×C₃₁	1	4	yes	complemented
177	#384	—	2	1	no	—
178	#382	—	2	1	no	—
179	#380	—	2	2	no	—
180	C₄×C₄⋊C₄	—	2	2	no	—
181	C₄×C₄⋊C₄	C₄×C₃₁	1	4	yes	complemented
182	C₄×C₂²⋊C₄	—	2	2	no	—
183	#376	C₄×C₃₁	1	2	yes	complemented
184	C₄³	C₄×C₃₁	1	2	yes	complemented
185	H(3,ℤ/4)	—	2	8	no	—
186	C₂×C₃₁	—	2	2	no	—
187	C₂×C₃₁	—	2	1	no	—
188	C₂×C₃₁	—	2	2	no	—
189	C₂×C₃₁	—	2	1	no	—
190	C₂×C₃₁	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₃₁	C₂×H(3,ℤ/4)	1	2	yes	—
192	C₂³×C₄	D₄×C₃₁	1	2	yes	—
193	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
194	C₂×M₁₆	—	2	4	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	4	no	—
198	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
199	#117	—	2	2	no	—
200	#117	—	2	2	no	—
201	#117	—	2	4	no	—
202	#117	—	2	4	no	—
203	#117	D₄×C₃₁	1	4	yes	—
204	#117	Q₈×C₃₁	1	4	yes	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²	—	2	4	no	—
211	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
212	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
213	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
214	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
217	C₂×C₄²	D₄×C₃₁	1	2	yes	—
218	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
219	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
220	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
221	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
222	C₄⋊C₈	—	2	4	no	—
223	C₄⋊C₈	—	2	4	no	—
224	#95	—	2	4	no	—
225	#95	—	2	4	no	—
226	C₃₁	#10836	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
232	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
234	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
235	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
236	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
243	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
244	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
245	C₂²×C₄	#41×C₃₁	1	2	yes	—
246	C₂²×C₄	#41×C₃₁	1	2	yes	—
247	M₁₆	—	4	4	no	—
248	M₁₆	—	4	2	no	—
249	M₁₆	—	4	2	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	8	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	4	8	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	2	4	no	—
259	C₂²⋊C₄	—	4	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	8	no	—
262	C₄²	—	4	8	no	—
263	C₄²	C₄²×C₃₁	1	2	yes	—
264	C₄²	C₄²×C₃₁	1	2	yes	—
265	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
266	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
267	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
268	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
269	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
270	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
271	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
272	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
273	C₄²	C₄⋊C₄×C₃₁	1	8	yes	complemented
274	C₂³	—	4	2	no	—
275	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
276	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
277	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
278	C₂³	C₃₁×#121	1	2	yes	—
279	C₂³	C₃₁×C₂²⋊Q₈	1	2	yes	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	8	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	C₃₁×#95	1	2	yes	—
291	C₂×C₄	C₃₁×#95	1	2	yes	—
292	C₂×C₄	C₃₁×#95	1	2	yes	—
293	C₂×C₄	C₃₁×#95	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
295	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
296	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
297	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
299	C₂×C₄	C₃₁×#117	1	2	yes	—
300	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
301	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
302	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
304	C₂×C₄	C₃₁×#121	1	2	yes	—
305	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
306	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
307	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
308	C₂×C₄	C₃₁×#125	1	2	yes	—
309	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
310	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
311	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
312	C₈	—	4	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
319	C₂²	C₃₁×#380	1	2	yes	—
320	C₂²	C₃₁×#389	1	2	yes	—
321	C₂²	C₃₁×#390	1	1	yes	characteristic
322	C₂²	C₃₁×#391	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	8	no	—
327	C₄	—	8	4	no	—
328	C₄	C₃₁×H(3,ℤ/4)	1	4	yes	complemented
329	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
330	C₄	C₃₁×#382	1	1	yes	characteristic
331	C₄	C₃₁×#384	1	1	yes	characteristic
332	C₄	C₃₁×#389	1	2	yes	—
333	C₄	C₃₁×#390	1	1	yes	characteristic
334	C₄	C₃₁×#391	1	1	yes	characteristic
335	C₂	—	2	2	no	—
336	C₂	—	2	1	no	—
337	C₂	—	2	2	no	—
338	C₂	—	2	1	no	—
339	C₂	C₃₁×C₄⋊#95	1	1	yes	characteristic
340	C₂	C₂×C₃₁×H(3,ℤ/4)	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×#95
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
17. C₄×C₄⋊C₄×C₃₁	C₄	semidirect
19. C₃₁×#376	C₄	semidirect
20. C₄³×C₃₁	C₄	semidirect
102. C₄²×C₃₁	C₄⋊C₄	semidirect
103. #10836	C₃₁	direct (N × H)
162. C₄×C₃₁	H(3,ℤ/4)	semidirect
176. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
181. C₄×C₄⋊C₄	C₄×C₃₁	semidirect
183. #376	C₄×C₃₁	semidirect
184. C₄³	C₄×C₃₁	semidirect
226. C₃₁	#10836	direct (N × H)
273. C₄²	C₄⋊C₄×C₃₁	semidirect
328. C₄	C₃₁×H(3,ℤ/4)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#423	2
C₃₁×#2285	2
C₄×C₃₁×#117	2
C₂×C₃₁×H(3,ℤ/4)	2
#10836	31

Subgroups — C31×#10836 #21467595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10836 #21467595