Subgroups — C₃₁×#19907 #21476666

Order 7936.

602 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1699	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1652	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1651	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1589	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#556	C₂²	1	2	yes	—
13	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#500	—	2	1	no	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#498	C₂²	1	2	yes	—
17	C₃₁×#495	—	2	1	no	—
18	C₃₁×#494	C₂²	1	1	yes	characteristic
19	C₃₁×#487	C₂²	1	2	yes	—
20	C₃₁×#485	—	2	2	no	—
21	C₃₁×#475	C₂²	1	2	yes	—
22	C₃₁×#474	—	2	2	no	—
23	C₃₁×#474	C₂²	1	2	yes	—
24	C₃₁×#470	—	2	2	no	—
25	C₃₁×#464	—	2	2	no	—
26	C₃₁×#462	C₂²	1	2	yes	—
27	C₃₁×#461	C₂²	1	2	yes	—
28	C₃₁×#451	—	2	2	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₃₁	—	2	1	no	—
32	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₃₁	—	2	1	no	—
34	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#436	C₂²	1	2	yes	—
36	C₃₁×#419	—	2	2	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	1	yes	characteristic
39	C₃₁×#332	C₂²	1	2	yes	—
40	C₃₁×#332	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₃₁	—	2	2	no	—
51	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
52	C₂×M₁₆×C₃₁	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	—	2	2	no	—
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₃₁×#126	—	4	2	no	—
57	C₃₁×#124	—	2	2	no	—
58	C₃₁×C₂²⋊Q₈	—	2	2	no	—
59	C₃₁×C₂²⋊Q₈	—	2	2	no	—
60	C₃₁×C₂²⋊Q₈	—	4	2	no	—
61	C₄×Q₈×C₃₁	—	2	2	no	—
62	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₃₁	—	2	2	no	—
65	C₄×D₄×C₃₁	C₂³	1	2	yes	—
66	C₃₁×#117	—	2	2	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	D₄	1	1	yes	characteristic
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	4	2	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	—	2	1	no	—
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	D₄	1	1	yes	characteristic
85	C₃₁×#103	D₄	1	1	yes	characteristic
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	D₄	1	2	yes	—
88	C₃₁×C₂²⋊C₈	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	4	2	no	—
97	C₂×Q₈×C₃₁	—	4	4	no	—
98	C₂×Q₈×C₃₁	—	8	2	no	—
99	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
104	Q₁₆×C₃₁	—	2	2	no	—
105	Q₁₆×C₃₁	—	4	2	no	—
106	Q₁₆×C₃₁	—	8	1	no	—
107	Q₁₆×C₃₁	—	8	2	no	—
108	SD₁₆×C₃₁	—	8	2	no	—
109	D₈×C₃₁	—	2	2	no	—
110	M₁₆×C₃₁	—	8	2	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₃₁	—	2	1	no	—
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₃₁	—	2	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	—	2	1	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	4	2	no	—
137	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
138	#19907	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	2	1	no	—
142	Q₈×C₃₁	—	2	1	no	—
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	8	4	no	—
148	Q₈×C₃₁	#135	1	2	yes	—
149	D₄×C₃₁	—	2	2	no	—
150	D₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	8	4	no	—
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₃₁	—	2	2	no	—
165	C₈×C₃₁	—	2	1	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	1	no	—
170	C₈×C₃₁	—	4	1	no	—
171	C₈×C₃₁	#137	1	2	yes	—
172	#3393	C₂×C₃₁	1	1	yes	characteristic
173	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic
174	#3328	C₂×C₃₁	1	2	yes	complemented
175	#1707	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1699	C₂×C₃₁	1	2	yes	complemented
177	#1674	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#1670	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1652	C₂×C₃₁	1	2	yes	complemented
180	#1651	C₂×C₃₁	1	2	yes	complemented
181	#1589	C₂×C₃₁	1	1	yes	characteristic
182	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	4	2	no	—
184	C₂²×C₃₁	—	4	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	D₄²	1	1	yes	characteristic
187	C₄×C₃₁	—	2	2	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
197	C₄×C₃₁	#576	1	1	yes	characteristic
198	C₄×C₃₁	#577	1	1	yes	characteristic
199	#556	C₂²×C₃₁	1	2	yes	—
200	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
201	#500	—	2	1	no	—
202	#500	C₂²×C₃₁	1	1	yes	characteristic
203	#498	C₂²×C₃₁	1	2	yes	—
204	#495	—	2	1	no	—
205	#494	C₂²×C₃₁	1	1	yes	characteristic
206	#487	C₂²×C₃₁	1	2	yes	—
207	#485	—	2	2	no	—
208	#475	C₂²×C₃₁	1	2	yes	—
209	#474	—	2	2	no	—
210	#474	C₂²×C₃₁	1	2	yes	—
211	#470	—	2	2	no	—
212	#464	—	2	2	no	—
213	#462	C₂²×C₃₁	1	2	yes	—
214	#461	C₂²×C₃₁	1	2	yes	—
215	#451	—	2	2	no	—
216	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
220	C₄×D₈	—	2	1	no	—
221	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
222	#436	C₂²×C₃₁	1	2	yes	—
223	#419	—	2	2	no	—
224	#335	C₂²×C₃₁	1	1	yes	characteristic
225	#335	C₂²×C₃₁	1	1	yes	characteristic
226	#332	C₂²×C₃₁	1	2	yes	—
227	#332	C₂²×C₃₁	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
229	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
230	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
231	C₈²	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₃₁	—	8	2	no	—
233	C₂×C₃₁	#3278	1	1	yes	characteristic
234	C₂×C₃₁	#3280	1	1	yes	characteristic
235	C₂×C₃₁	#3293	1	1	yes	characteristic
236	C₂²×Q₈	—	2	2	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
247	#126	—	4	2	no	—
248	#124	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	4	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	C₂³×C₃₁	1	2	yes	—
257	#117	—	2	2	no	—
258	#107	—	2	1	no	—
259	#107	—	2	1	no	—
260	#107	—	2	2	no	—
261	#107	D₄×C₃₁	1	1	yes	characteristic
262	#107	D₄×C₃₁	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	#106	—	4	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	D₄×C₃₁	1	1	yes	characteristic
276	#103	D₄×C₃₁	1	1	yes	characteristic
277	#102	—	2	2	no	—
278	#102	D₄×C₃₁	1	2	yes	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₃₁	#19907	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	4	2	no	—
298	Q₁₆	—	8	1	no	—
299	Q₁₆	—	8	2	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	2	2	no	—
302	M₁₆	—	8	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
320	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
330	C₂³	—	2	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	8	4	no	—
339	Q₈	C₃₁×#135	1	2	yes	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	4	no	—
352	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
354	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
355	C₈	—	2	2	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	1	no	—
361	C₈	—	4	1	no	—
362	C₈	C₃₁×#137	1	2	yes	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	D₄²×C₃₁	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
376	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
377	C₄	C₃₁×#576	1	1	yes	characteristic
378	C₄	C₃₁×#577	1	1	yes	characteristic
379	C₂	—	8	2	no	—
380	C₂	C₃₁×#3278	1	1	yes	characteristic
381	C₂	C₃₁×#3280	1	1	yes	characteristic
382	C₂	C₃₁×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×D₈×C₃₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#3328	C₂	semidirect
4. C₃₁×#1707	C₂	semidirect
5. C₃₁×#1699	C₂	semidirect
6. C₃₁×#1674	C₂	semidirect
7. C₃₁×#1670	C₂	semidirect
8. C₃₁×#1652	C₂	semidirect
9. C₃₁×#1651	C₂	semidirect
11. C₈×Q₁₆×C₃₁	C₂	semidirect
138. #19907	C₃₁	direct (N × H)
174. #3328	C₂×C₃₁	semidirect
175. #1707	C₂×C₃₁	semidirect
176. #1699	C₂×C₃₁	semidirect
177. #1674	C₂×C₃₁	semidirect
178. #1670	C₂×C₃₁	semidirect
179. #1652	C₂×C₃₁	semidirect
180. #1651	C₂×C₃₁	semidirect
182. C₈×Q₁₆	C₂×C₃₁	semidirect
285. C₃₁	#19907	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×#3393	2
Q₈×D₈×C₃₁	2
C₃₁×#3328	2
C₃₁×#1707	2
C₃₁×#1699	2
C₃₁×#1674	2
C₃₁×#1670	2
C₃₁×#1652	2
C₃₁×#1651	2
C₃₁×#1589	2
C₈×Q₁₆×C₃₁	2
#19907	31

Subgroups — C31×#19907 #21476666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19907 #21476666