Subgroups — C₃₁×#33789 #21490548

Order 7936.

562 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2211	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2209	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2189	C₂	1	2	yes	maximal
10	C₃₁×#2188	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#137	—	2	1	no	—
13	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#541	—	2	1	no	—
16	C₃₁×#536	—	2	1	no	—
17	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
21	C₃₁×#499	C₂²	1	1	yes	characteristic
22	C₃₁×#497	—	2	1	no	—
23	C₃₁×#497	—	2	1	no	—
24	C₃₁×#495	C₂²	1	1	yes	characteristic
25	C₃₁×#495	C₂²	1	1	yes	characteristic
26	C₃₁×#494	C₂²	1	1	yes	characteristic
27	C₃₁×#494	C₂²	1	1	yes	characteristic
28	C₃₁×#494	C₂²	1	1	yes	characteristic
29	C₃₁×#491	—	2	1	no	—
30	C₃₁×#470	—	2	1	no	—
31	C₃₁×#467	C₂²	1	2	yes	—
32	C₃₁×#441	—	2	1	no	—
33	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#405	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#358	C₂²	1	2	yes	—
38	C₃₁×#358	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	—
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₃₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂²×Q₈×C₃₁	—	2	1	no	—
45	C₃₁×#137	—	4	4	no	—
46	C₃₁×#135	—	4	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	—	2	1	no	—
50	C₂×Q₁₆×C₃₁	—	2	1	no	—
51	C₂×Q₁₆×C₃₁	—	4	2	no	—
52	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₃₁	—	2	1	no	—
57	C₂×SD₁₆×C₃₁	—	2	1	no	—
58	C₂×SD₁₆×C₃₁	—	2	1	no	—
59	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×C₄⋊Q₈	—	2	1	no	—
63	C₃₁×C₄⋊Q₈	—	2	1	no	—
64	C₃₁×C₄⋊Q₈	—	2	1	no	—
65	C₃₁×#126	—	4	2	no	—
66	C₃₁×#125	—	2	1	no	—
67	C₃₁×#125	—	4	2	no	—
68	C₃₁×#124	—	2	1	no	—
69	C₃₁×#124	—	2	1	no	—
70	C₃₁×#123	—	4	2	no	—
71	C₃₁×C₂²⋊Q₈	—	2	2	no	—
72	C₃₁×C₂²⋊Q₈	—	4	2	no	—
73	C₄×Q₈×C₃₁	—	2	2	no	—
74	C₃₁×#117	D₄	1	1	yes	characteristic
75	C₃₁×Q₃₂	—	4	2	no	—
76	C₃₁×Q₃₂	—	4	2	no	—
77	C₃₁×Q₃₂	—	4	2	no	—
78	C₃₁×SD₃₂	—	4	2	no	—
79	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
81	C₃₁×#107	C₂³	1	2	yes	—
82	C₃₁×#106	—	2	1	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#97	D₄	1	1	yes	characteristic
86	C₃₁×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	#41×C₃₁	—	4	2	no	—
90	#41×C₃₁	—	4	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×Q₈×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	2	1	no	—
95	C₂×Q₈×C₃₁	—	4	2	no	—
96	C₂×Q₈×C₃₁	—	4	2	no	—
97	C₂×Q₈×C₃₁	—	4	1	no	—
98	C₂×D₄×C₃₁	—	2	1	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₃₁	—	2	2	no	—
104	Q₁₆×C₃₁	—	2	2	no	—
105	Q₁₆×C₃₁	—	2	2	no	—
106	Q₁₆×C₃₁	—	2	2	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	4	2	no	—
109	Q₁₆×C₃₁	—	4	2	no	—
110	Q₁₆×C₃₁	—	4	2	no	—
111	Q₁₆×C₃₁	—	4	2	no	—
112	SD₁₆×C₃₁	—	4	2	no	—
113	SD₁₆×C₃₁	—	4	2	no	—
114	SD₁₆×C₃₁	—	4	2	no	—
115	D₈×C₃₁	—	2	2	no	—
116	M₁₆×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	4	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₁	—	2	2	no	—
138	C₁₆×C₃₁	—	2	2	no	—
139	#33789	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	1	no	—
141	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
142	Q₈×C₃₁	—	4	1	no	—
143	Q₈×C₃₁	—	4	1	no	—
144	Q₈×C₃₁	—	4	1	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	1	no	—
147	Q₈×C₃₁	—	4	1	no	—
148	Q₈×C₃₁	—	4	1	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	8	2	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	1	no	—
153	D₄×C₃₁	—	8	2	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	1	no	—
159	C₂×C₄×C₃₁	—	4	1	no	—
160	C₂×C₄×C₃₁	—	4	1	no	—
161	C₂×C₄×C₃₁	—	8	2	no	—
162	C₂×C₄×C₃₁	—	8	2	no	—
163	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	2	1	no	—
169	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
170	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
171	#3177	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#3156	C₂×C₃₁	1	1	yes	characteristic
173	#2251	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#2247	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#2245	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2242	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2211	C₂×C₃₁	1	2	yes	complemented
178	#2209	C₂×C₃₁	1	2	yes	complemented
179	#2189	C₂×C₃₁	1	2	yes	—
180	#2188	C₂×C₃₁	1	2	yes	complemented
181	#2164	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	1	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	1	no	—
186	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₃₁	—	2	2	no	—
188	C₄×C₃₁	—	2	2	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	8	2	no	—
191	C₄×C₃₁	—	8	1	no	—
192	C₄×C₃₁	—	8	1	no	—
193	C₄×C₃₁	—	8	1	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	#535	1	1	yes	characteristic
196	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×#137	—	2	1	no	—
198	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
199	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
200	#541	—	2	1	no	—
201	#536	—	2	1	no	—
202	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
203	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
204	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
205	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
206	#499	C₂²×C₃₁	1	1	yes	characteristic
207	#497	—	2	1	no	—
208	#497	—	2	1	no	—
209	#495	C₂²×C₃₁	1	1	yes	characteristic
210	#495	C₂²×C₃₁	1	1	yes	characteristic
211	#494	C₂²×C₃₁	1	1	yes	characteristic
212	#494	C₂²×C₃₁	1	1	yes	characteristic
213	#494	C₂²×C₃₁	1	1	yes	characteristic
214	#491	—	2	1	no	—
215	#470	—	2	1	no	—
216	#467	C₂²×C₃₁	1	2	yes	—
217	#441	—	2	1	no	—
218	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
219	#405	C₂²×C₃₁	1	1	yes	characteristic
220	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	—
221	#358	C₂²×C₃₁	1	2	yes	—
222	#358	C₂²×C₃₁	1	2	yes	—
223	#358	C₂²×C₃₁	1	2	yes	—
224	#357	C₂²×C₃₁	1	2	yes	—
225	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
226	#346	C₂²×C₃₁	1	1	yes	characteristic
227	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₃₁	—	4	1	no	—
229	C₂×C₃₁	—	16	1	no	—
230	C₂×C₃₁	#3205	1	1	yes	characteristic
231	C₂×C₃₁	#3417	1	2	yes	—
232	C₂×#41	—	2	1	no	—
233	C₂²×Q₈	—	2	1	no	—
234	#137	—	4	4	no	—
235	#135	—	4	2	no	—
236	C₂×Q₁₆	—	2	1	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	4	2	no	—
241	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
244	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
249	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	#126	—	4	2	no	—
255	#125	—	2	1	no	—
256	#125	—	4	2	no	—
257	#124	—	2	1	no	—
258	#124	—	2	1	no	—
259	#123	—	4	2	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₂²⋊Q₈	—	4	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	#117	D₄×C₃₁	1	1	yes	characteristic
264	Q₃₂	—	4	2	no	—
265	Q₃₂	—	4	2	no	—
266	Q₃₂	—	4	2	no	—
267	SD₃₂	—	4	2	no	—
268	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
269	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
270	#107	C₂³×C₃₁	1	2	yes	—
271	#106	—	2	1	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#97	D₄×C₃₁	1	1	yes	characteristic
275	#97	D₄×C₃₁	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₃₁	#33789	1	1	yes	characteristic, direct product factor, Sylow
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	4	2	no	—
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	Q₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	SD₁₆	—	4	2	no	—
304	SD₁₆	—	4	2	no	—
305	D₈	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
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	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	D₈×C₃₁	1	2	yes	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₁₆	—	2	2	no	—
328	C₁₆	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	1	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
353	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
354	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
359	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	1	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	2	no	—
373	C₄	C₃₁×#535	1	1	yes	characteristic
374	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₂	—	4	1	no	—
376	C₂	—	16	1	no	—
377	C₂	C₃₁×#3205	1	1	yes	characteristic
378	C₂	C₃₁×#3417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#117 ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3177	C₂	semidirect
3. C₃₁×#2251	C₂	semidirect
4. C₃₁×#2247	C₂	semidirect
5. C₃₁×#2245	C₂	semidirect
6. C₃₁×#2242	C₂	semidirect
7. C₃₁×#2211	C₂	semidirect
8. C₃₁×#2209	C₂	semidirect
10. C₃₁×#2188	C₂	semidirect
11. C₃₁×#2164	C₂	semidirect
139. #33789	C₃₁	direct (N × H)
171. #3177	C₂×C₃₁	semidirect
173. #2251	C₂×C₃₁	semidirect
174. #2247	C₂×C₃₁	semidirect
175. #2245	C₂×C₃₁	semidirect
176. #2242	C₂×C₃₁	semidirect
177. #2211	C₂×C₃₁	semidirect
178. #2209	C₂×C₃₁	semidirect
180. #2188	C₂×C₃₁	semidirect
181. #2164	C₂×C₃₁	semidirect
278. C₃₁	#33789	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×#3177	2
C₃₁×#3156	2
C₃₁×#2251	2
C₃₁×#2247	2
C₃₁×#2245	2
C₃₁×#2242	2
C₃₁×#2211	2
C₃₁×#2209	2
C₃₁×#2189	2
C₃₁×#2188	2
C₃₁×#2164	2
#33789	31

Subgroups — C31×#33789 #21490548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33789 #21490548