Subgroups — C₃₁×#2414 #16842347

Order 3968.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#394	C₂	1	2	yes	maximal, complemented
6	C₃₁×#392	C₂	1	2	yes	maximal, complemented
7	C₃₁×#390	C₂	1	2	yes	maximal, complemented
8	C₃₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#388	C₂	1	2	yes	maximal, complemented
11	C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
16	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#121	—	2	4	no	—
19	C₃₁×#121	—	2	4	no	—
20	C₄×D₄×C₃₁	—	2	4	no	—
21	C₃₁×#117	—	2	4	no	—
22	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
36	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#95	C₂²	1	2	yes	—
38	C₃₁×#95	C₂²	1	2	yes	—
39	C₂⁴×C₃₁	C₂³	1	2	yes	—
40	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
41	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
42	C₂×D₄×C₃₁	—	2	2	no	—
43	C₂×D₄×C₃₁	—	2	2	no	—
44	C₂×D₄×C₃₁	—	2	4	no	—
45	C₂×D₄×C₃₁	—	2	4	no	—
46	C₂×D₄×C₃₁	—	2	4	no	—
47	C₂×D₄×C₃₁	—	2	2	no	—
48	C₂×D₄×C₃₁	—	2	2	no	—
49	C₂×D₄×C₃₁	—	2	2	no	—
50	C₂×D₄×C₃₁	—	2	2	no	—
51	C₂×D₄×C₃₁	—	4	2	no	—
52	C₂×D₄×C₃₁	—	4	2	no	—
53	C₂×D₄×C₃₁	—	4	2	no	—
54	C₂²×C₄×C₃₁	—	2	2	no	—
55	C₂²×C₄×C₃₁	—	2	2	no	—
56	C₂²×C₄×C₃₁	—	2	2	no	—
57	C₂²×C₄×C₃₁	—	2	2	no	—
58	C₂²×C₄×C₃₁	—	2	2	no	—
59	C₂²×C₄×C₃₁	D₄	1	4	yes	complemented
60	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
62	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
63	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
65	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₃₁	—	2	2	no	—
69	C₄⋊C₄×C₃₁	—	2	2	no	—
70	C₄⋊C₄×C₃₁	—	2	2	no	—
71	C₄⋊C₄×C₃₁	—	4	2	no	—
72	C₄⋊C₄×C₃₁	D₄	1	4	yes	complemented
73	C₂²⋊C₄×C₃₁	—	2	2	no	—
74	C₂²⋊C₄×C₃₁	—	2	4	no	—
75	C₂²⋊C₄×C₃₁	—	2	2	no	—
76	C₂²⋊C₄×C₃₁	—	2	4	no	—
77	C₂²⋊C₄×C₃₁	—	2	4	no	—
78	C₂²⋊C₄×C₃₁	—	2	4	no	—
79	C₂²⋊C₄×C₃₁	—	4	2	no	—
80	C₂²⋊C₄×C₃₁	—	4	2	no	—
81	C₄²×C₃₁	—	2	4	no	—
82	C₄²×C₃₁	—	2	2	no	—
83	C₂³×C₃₁	—	2	1	no	—
84	C₂³×C₃₁	—	2	1	no	—
85	C₂³×C₃₁	—	2	1	no	—
86	C₂³×C₃₁	—	2	1	no	—
87	C₂³×C₃₁	—	2	1	no	—
88	C₂³×C₃₁	—	2	1	no	—
89	C₂³×C₃₁	—	2	1	no	—
90	C₂³×C₃₁	—	2	1	no	—
91	C₂³×C₃₁	—	2	1	no	—
92	C₂³×C₃₁	—	2	1	no	—
93	C₂³×C₃₁	—	2	1	no	—
94	C₂³×C₃₁	—	2	1	no	—
95	C₂³×C₃₁	—	2	2	no	—
96	C₂³×C₃₁	—	2	2	no	—
97	C₂³×C₃₁	—	2	2	no	—
98	C₂³×C₃₁	—	2	2	no	—
99	C₂³×C₃₁	—	2	2	no	—
100	C₂³×C₃₁	—	2	2	no	—
101	C₂³×C₃₁	—	2	2	no	—
102	C₂³×C₃₁	C₂×D₄	1	2	yes	—
103	C₂³×C₃₁	#41	1	2	yes	—
104	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
105	D₄×C₃₁	—	2	8	no	—
106	D₄×C₃₁	—	4	8	no	—
107	D₄×C₃₁	—	4	8	no	—
108	D₄×C₃₁	—	4	4	no	—
109	C₂×C₄×C₃₁	—	2	1	no	—
110	C₂×C₄×C₃₁	—	2	1	no	—
111	C₂×C₄×C₃₁	—	2	1	no	—
112	C₂×C₄×C₃₁	—	2	1	no	—
113	C₂×C₄×C₃₁	—	2	2	no	—
114	C₂×C₄×C₃₁	—	2	2	no	—
115	C₂×C₄×C₃₁	—	2	8	no	—
116	C₂×C₄×C₃₁	—	2	1	no	—
117	C₂×C₄×C₃₁	—	2	2	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	1	no	—
123	C₂×C₄×C₃₁	—	2	1	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	4	4	no	—
129	C₂×C₄×C₃₁	C₂×D₄	1	4	yes	—
130	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
131	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
132	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₃₁	#41	1	2	yes	—
134	C₂×C₄×C₃₁	#41	1	2	yes	—
135	#2414	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂²×C₃₁	—	2	2	no	—
137	C₂²×C₃₁	—	2	2	no	—
138	C₂²×C₃₁	—	2	2	no	—
139	C₂²×C₃₁	—	2	2	no	—
140	C₂²×C₃₁	—	2	2	no	—
141	C₂²×C₃₁	—	2	2	no	—
142	C₂²×C₃₁	—	4	1	no	—
143	C₂²×C₃₁	—	4	1	no	—
144	C₂²×C₃₁	—	4	1	no	—
145	C₂²×C₃₁	—	4	1	no	—
146	C₂²×C₃₁	—	4	1	no	—
147	C₂²×C₃₁	—	4	1	no	—
148	C₂²×C₃₁	—	4	1	no	—
149	C₂²×C₃₁	—	4	1	no	—
150	C₂²×C₃₁	—	4	2	no	—
151	C₂²×C₃₁	—	4	2	no	—
152	C₂²×C₃₁	—	4	2	no	—
153	C₂²×C₃₁	—	4	2	no	—
154	C₂²×C₃₁	—	4	2	no	—
155	C₂²×C₃₁	—	4	2	no	—
156	C₂²×C₃₁	—	4	2	no	—
157	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
160	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
162	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	4	no	—
167	C₄×C₃₁	—	4	1	no	—
168	C₄×C₃₁	—	4	1	no	—
169	C₄×C₃₁	—	4	2	no	—
170	C₄×C₃₁	—	4	2	no	—
171	C₄×C₃₁	#121	1	4	yes	—
172	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
174	C₂×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#394	C₂×C₃₁	1	2	yes	complemented
177	#392	C₂×C₃₁	1	2	yes	complemented
178	#390	C₂×C₃₁	1	2	yes	complemented
179	#390	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#389	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#388	C₂×C₃₁	1	2	yes	complemented
182	#380	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂×C₃₁	—	4	2	no	—
184	C₂×C₃₁	—	4	2	no	—
185	C₂×C₃₁	—	8	2	no	—
186	C₂×C₃₁	C₂×#121	1	1	yes	characteristic
187	C₂×C₃₁	#525	1	1	yes	characteristic
188	C₂×C₃₁	#535	1	1	yes	characteristic
189	C₂×C₃₁	#546	1	1	yes	characteristic
190	C₂×C₃₁	#550	1	1	yes	characteristic
191	C₂×C₃₁	#553	1	1	yes	characteristic
192	C₂×C₃₁	#555	1	1	yes	characteristic
193	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
194	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
195	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
196	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
197	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
199	#121	—	2	4	no	—
200	#121	—	2	4	no	—
201	C₄×D₄	—	2	4	no	—
202	#117	—	2	4	no	—
203	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
216	C₂×C₄²	C₂²×C₃₁	1	2	yes	—
217	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
218	#95	C₂²×C₃₁	1	2	yes	—
219	#95	C₂²×C₃₁	1	2	yes	—
220	C₃₁	#2414	1	1	yes	characteristic, direct product factor, Sylow
221	C₂⁴	C₂³×C₃₁	1	2	yes	—
222	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
223	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	4	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	2	2	no	—
233	C₂×D₄	—	4	2	no	—
234	C₂×D₄	—	4	2	no	—
235	C₂×D₄	—	4	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	D₄×C₃₁	1	4	yes	complemented
242	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
244	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
245	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
247	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	2	no	—
254	C₄⋊C₄	D₄×C₃₁	1	4	yes	complemented
255	C₂²⋊C₄	—	2	2	no	—
256	C₂²⋊C₄	—	2	4	no	—
257	C₂²⋊C₄	—	2	2	no	—
258	C₂²⋊C₄	—	2	4	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₂²⋊C₄	—	4	2	no	—
262	C₂²⋊C₄	—	4	2	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	2	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	1	no	—
268	C₂³	—	2	1	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	C₂×D₄×C₃₁	1	2	yes	—
285	C₂³	#41×C₃₁	1	2	yes	—
286	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
287	D₄	—	2	8	no	—
288	D₄	—	4	8	no	—
289	D₄	—	4	8	no	—
290	D₄	—	4	4	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	C₂×D₄×C₃₁	1	4	yes	—
312	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
313	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
314	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₂×C₄	#41×C₃₁	1	2	yes	—
316	C₂×C₄	#41×C₃₁	1	2	yes	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
339	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
341	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
342	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
343	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	2	no	—
352	C₄	C₃₁×#121	1	4	yes	—
353	C₂	—	4	2	no	—
354	C₂	—	4	2	no	—
355	C₂	—	8	2	no	—
356	C₂	C₂×C₃₁×#121	1	1	yes	characteristic
357	C₂	C₃₁×#525	1	1	yes	characteristic
358	C₂	C₃₁×#535	1	1	yes	characteristic
359	C₂	C₃₁×#546	1	1	yes	characteristic
360	C₂	C₃₁×#550	1	1	yes	characteristic
361	C₂	C₃₁×#553	1	1	yes	characteristic
362	C₂	C₃₁×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#121	C₂	semidirect
2. C₂×C₃₁×#121	C₂	semidirect
3. C₂×C₄×D₄×C₃₁	C₂	semidirect
4. C₂×C₃₁×#117	C₂	semidirect
5. C₃₁×#394	C₂	semidirect
6. C₃₁×#392	C₂	semidirect
7. C₃₁×#390	C₂	semidirect
8. C₃₁×#390	C₂	semidirect
9. C₃₁×#389	C₂	semidirect
10. C₃₁×#388	C₂	semidirect
11. C₃₁×#380	C₂	semidirect
59. C₂²×C₄×C₃₁	D₄	semidirect
72. C₄⋊C₄×C₃₁	D₄	semidirect
135. #2414	C₃₁	direct (N × H)
172. C₂×#121	C₂×C₃₁	semidirect
173. C₂×#121	C₂×C₃₁	semidirect
174. C₂×C₄×D₄	C₂×C₃₁	semidirect
175. C₂×#117	C₂×C₃₁	semidirect
176. #394	C₂×C₃₁	semidirect
177. #392	C₂×C₃₁	semidirect
178. #390	C₂×C₃₁	semidirect
179. #390	C₂×C₃₁	semidirect
180. #389	C₂×C₃₁	semidirect
181. #388	C₂×C₃₁	semidirect
182. #380	C₂×C₃₁	semidirect
220. C₃₁	#2414	direct (N × H)
241. C₂²×C₄	D₄×C₃₁	semidirect
254. C₄⋊C₄	D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#121	2
C₂×C₄×D₄×C₃₁	2
C₂×C₃₁×#117	2
C₃₁×#394	2
C₃₁×#392	2
C₃₁×#390	2
C₃₁×#389	2
C₃₁×#388	2
C₃₁×#380	2
#2414	31

Subgroups — C31×#2414 #16842347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2414 #16842347