Subgroups — C₃₁×#33857 #21490616

Order 7936.

646 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	C₃₁×#3416	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3290	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2223	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2212	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2195	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2192	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2178	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#578	C₂²	1	2	yes	—
11	C₃₁×#577	—	2	2	no	—
12	C₃₁×#576	C₂²	1	2	yes	complemented
13	C₃₁×#510	—	2	2	no	—
14	C₃₁×#510	C₂²	1	2	yes	complemented
15	C₃₁×#509	—	2	2	no	—
16	C₃₁×#509	C₂²	1	2	yes	—
17	C₃₁×#508	—	2	2	no	—
18	C₃₁×#508	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×Q₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃₁×SD₃₂	—	2	2	no	—
21	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
22	C₂×C₃₁×D₁₆	C₂²	1	1	yes	characteristic
23	C₃₁×#504	C₂²	1	2	yes	complemented
24	C₃₁×#495	C₂²	1	2	yes	complemented
25	C₃₁×#473	C₂²	1	2	yes	complemented
26	C₃₁×#472	C₂²	1	2	yes	—
27	C₃₁×#471	—	2	2	no	—
28	C₃₁×#455	—	2	2	no	—
29	C₃₁×#454	—	2	2	no	—
30	C₃₁×#443	C₂²	1	1	yes	characteristic
31	C₃₁×#443	C₂²	1	2	yes	complemented
32	C₃₁×#368	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#364	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#362	C₂²	1	2	yes	complemented
35	C₃₁×#361	C₂²	1	2	yes	complemented
36	C₃₁×#359	C₂²	1	2	yes	complemented
37	C₃₁×#350	C₂²	1	2	yes	complemented
38	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×2₋¹⁺⁴	—	2	2	no	—
40	C₃₁×H(5,𝔽₂)	—	2	2	no	—
41	C₃₁×#137	—	2	2	no	—
42	C₃₁×#137	—	2	2	no	—
43	C₃₁×#137	—	4	2	no	—
44	C₃₁×#137	—	4	2	no	—
45	C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
46	C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
47	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
48	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
49	C₃₁×#135	—	2	2	no	—
50	C₃₁×#135	—	2	2	no	—
51	C₃₁×#135	—	4	2	no	—
52	C₃₁×#135	D₄	1	1	yes	characteristic
53	C₃₁×#135	C₂³	1	2	yes	—
54	C₂×Q₁₆×C₃₁	—	2	2	no	—
55	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
56	C₂×SD₁₆×C₃₁	—	2	2	no	—
57	C₂×SD₁₆×C₃₁	—	4	2	no	—
58	C₂×D₈×C₃₁	—	2	2	no	—
59	C₂×D₈×C₃₁	C₂³	1	2	yes	—
60	C₃₁×#131	—	2	2	no	—
61	C₃₁×#131	C₂³	1	2	yes	—
62	C₃₁×#124	—	2	2	no	—
63	C₃₁×Q₃₂	—	2	2	no	—
64	C₃₁×Q₃₂	—	4	1	no	—
65	C₃₁×Q₃₂	D₄	1	1	yes	characteristic
66	C₃₁×SD₃₂	—	2	2	no	—
67	C₃₁×SD₃₂	—	2	2	no	—
68	C₃₁×SD₃₂	—	2	2	no	—
69	C₃₁×SD₃₂	—	2	2	no	—
70	C₃₁×SD₃₂	D₄	1	2	yes	—
71	C₃₁×D₁₆	—	2	2	no	—
72	C₃₁×D₁₆	—	4	1	no	—
73	C₃₁×D₁₆	D₄	1	1	yes	characteristic
74	C₃₁×M₃₂	—	2	2	no	—
75	C₃₁×M₃₂	C₂³	1	2	yes	—
76	C₂×C₁₆×C₃₁	—	2	2	no	—
77	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
79	C₃₁×#108	D₄	1	1	yes	characteristic
80	C₃₁×#108	C₂³	1	2	yes	—
81	C₃₁×#104	—	2	2	no	—
82	C₃₁×#104	D₄	1	2	yes	—
83	C₃₁×#101	—	2	2	no	—
84	C₃₁×#100	—	2	2	no	—
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	#41×C₃₁	—	2	2	no	—
87	#41×C₃₁	—	4	2	no	—
88	#41×C₃₁	—	4	2	no	—
89	#41×C₃₁	—	4	2	no	—
90	#41×C₃₁	—	4	2	no	—
91	#41×C₃₁	—	8	2	no	—
92	#41×C₃₁	C₂×D₄	1	2	yes	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	4	2	no	—
95	C₂×Q₈×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	8	2	no	—
100	Q₁₆×C₃₁	—	2	2	no	—
101	Q₁₆×C₃₁	—	2	2	no	—
102	Q₁₆×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	4	2	no	—
104	Q₁₆×C₃₁	D₈	1	1	yes	characteristic
105	Q₁₆×C₃₁	C₂×D₄	1	2	yes	—
106	SD₁₆×C₃₁	—	2	2	no	—
107	SD₁₆×C₃₁	—	4	2	no	—
108	SD₁₆×C₃₁	—	4	2	no	—
109	SD₁₆×C₃₁	—	4	2	no	—
110	SD₁₆×C₃₁	—	4	2	no	—
111	SD₁₆×C₃₁	—	4	2	no	—
112	SD₁₆×C₃₁	—	4	2	no	—
113	SD₁₆×C₃₁	D₈	1	2	yes	—
114	D₈×C₃₁	—	2	2	no	—
115	D₈×C₃₁	—	2	2	no	—
116	D₈×C₃₁	—	4	2	no	—
117	D₈×C₃₁	—	4	2	no	—
118	D₈×C₃₁	D₈	1	1	yes	characteristic
119	D₈×C₃₁	C₂×D₄	1	2	yes	—
120	M₁₆×C₃₁	—	2	2	no	—
121	M₁₆×C₃₁	—	2	2	no	—
122	M₁₆×C₃₁	—	4	2	no	—
123	M₁₆×C₃₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	—	4	2	no	—
126	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
128	C₂²⋊C₄×C₃₁	—	8	2	no	—
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₁₆×C₃₁	—	2	2	no	—
131	C₁₆×C₃₁	—	2	1	no	—
132	C₁₆×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₁₆×C₃₁	C₂×D₄	1	1	yes	characteristic
134	#33857	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	—	8	2	no	—
137	Q₈×C₃₁	—	2	2	no	—
138	Q₈×C₃₁	—	4	2	no	—
139	Q₈×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	8	2	no	—
141	Q₈×C₃₁	C₂×D₈	1	2	yes	—
142	D₄×C₃₁	—	2	2	no	—
143	D₄×C₃₁	—	2	2	no	—
144	D₄×C₃₁	—	4	2	no	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	8	2	no	—
148	D₄×C₃₁	—	8	2	no	—
149	D₄×C₃₁	—	8	2	no	—
150	D₄×C₃₁	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	8	2	no	—
156	C₂×C₄×C₃₁	—	8	2	no	—
157	C₂×C₄×C₃₁	—	8	2	no	—
158	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	4	2	no	—
161	C₈×C₃₁	C₂×D₈	1	1	yes	characteristic
162	C₈×C₃₁	C₂×D₈	1	1	yes	characteristic
163	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	#3416	C₂×C₃₁	1	2	yes	complemented
166	#3290	C₂×C₃₁	1	2	yes	complemented
167	#2249	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#2223	C₂×C₃₁	1	2	yes	complemented
169	#2212	C₂×C₃₁	1	2	yes	complemented
170	#2195	C₂×C₃₁	1	2	yes	complemented
171	#2192	C₂×C₃₁	1	2	yes	complemented
172	#2178	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#2170	C₂×C₃₁	1	1	yes	characteristic, complemented
174	C₂²×C₃₁	—	2	2	no	—
175	C₂²×C₃₁	—	4	2	no	—
176	C₂²×C₃₁	—	8	2	no	—
177	C₂²×C₃₁	—	16	2	no	—
178	C₂²×C₃₁	—	32	2	no	—
179	C₂²×C₃₁	#576	1	1	yes	characteristic
180	C₄×C₃₁	—	2	2	no	—
181	C₄×C₃₁	—	4	1	no	—
182	C₄×C₃₁	—	4	2	no	—
183	C₄×C₃₁	—	8	2	no	—
184	C₄×C₃₁	D₄²	1	1	yes	characteristic
185	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
186	#578	C₂²×C₃₁	1	2	yes	—
187	#577	—	2	2	no	—
188	#576	C₂²×C₃₁	1	2	yes	complemented
189	#510	—	2	2	no	—
190	#510	C₂²×C₃₁	1	2	yes	complemented
191	#509	—	2	2	no	—
192	#509	C₂²×C₃₁	1	2	yes	—
193	#508	—	2	2	no	—
194	#508	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×Q₃₂	C₂²×C₃₁	1	1	yes	characteristic, complemented
196	C₂×SD₃₂	—	2	2	no	—
197	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
198	C₂×D₁₆	C₂²×C₃₁	1	1	yes	characteristic
199	#504	C₂²×C₃₁	1	2	yes	complemented
200	#495	C₂²×C₃₁	1	2	yes	complemented
201	#473	C₂²×C₃₁	1	2	yes	complemented
202	#472	C₂²×C₃₁	1	2	yes	—
203	#471	—	2	2	no	—
204	#455	—	2	2	no	—
205	#454	—	2	2	no	—
206	#443	C₂²×C₃₁	1	1	yes	characteristic
207	#443	C₂²×C₃₁	1	2	yes	complemented
208	#368	C₂²×C₃₁	1	1	yes	characteristic, complemented
209	#364	C₂²×C₃₁	1	1	yes	characteristic, complemented
210	#362	C₂²×C₃₁	1	2	yes	complemented
211	#361	C₂²×C₃₁	1	2	yes	complemented
212	#359	C₂²×C₃₁	1	2	yes	complemented
213	#350	C₂²×C₃₁	1	2	yes	complemented
214	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
215	C₂×C₃₁	—	2	1	no	—
216	C₂×C₃₁	—	4	2	no	—
217	C₂×C₃₁	—	8	2	no	—
218	C₂×C₃₁	—	16	2	no	—
219	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
220	2₋¹⁺⁴	—	2	2	no	—
221	H(5,𝔽₂)	—	2	2	no	—
222	#137	—	2	2	no	—
223	#137	—	2	2	no	—
224	#137	—	4	2	no	—
225	#137	—	4	2	no	—
226	AGL(1,ℤ/8)	—	2	2	no	—
227	AGL(1,ℤ/8)	—	2	2	no	—
228	AGL(1,ℤ/8)	—	4	2	no	—
229	AGL(1,ℤ/8)	—	4	2	no	—
230	#135	—	2	2	no	—
231	#135	—	2	2	no	—
232	#135	—	4	2	no	—
233	#135	D₄×C₃₁	1	1	yes	characteristic
234	#135	C₂³×C₃₁	1	2	yes	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	C₂³×C₃₁	1	2	yes	—
241	#131	—	2	2	no	—
242	#131	C₂³×C₃₁	1	2	yes	—
243	#124	—	2	2	no	—
244	Q₃₂	—	2	2	no	—
245	Q₃₂	—	4	1	no	—
246	Q₃₂	D₄×C₃₁	1	1	yes	characteristic
247	SD₃₂	—	2	2	no	—
248	SD₃₂	—	2	2	no	—
249	SD₃₂	—	2	2	no	—
250	SD₃₂	—	2	2	no	—
251	SD₃₂	D₄×C₃₁	1	2	yes	—
252	D₁₆	—	2	2	no	—
253	D₁₆	—	4	1	no	—
254	D₁₆	D₄×C₃₁	1	1	yes	characteristic
255	M₃₂	—	2	2	no	—
256	M₃₂	C₂³×C₃₁	1	2	yes	—
257	C₂×C₁₆	—	2	2	no	—
258	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
260	#108	D₄×C₃₁	1	1	yes	characteristic
261	#108	C₂³×C₃₁	1	2	yes	—
262	#104	—	2	2	no	—
263	#104	D₄×C₃₁	1	2	yes	—
264	#101	—	2	2	no	—
265	#100	—	2	2	no	—
266	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₃₁	#33857	1	1	yes	characteristic, direct product factor, Sylow
268	#41	—	2	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	#41	—	8	2	no	—
274	#41	C₂×D₄×C₃₁	1	2	yes	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	8	2	no	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	4	2	no	—
285	Q₁₆	—	4	2	no	—
286	Q₁₆	D₈×C₃₁	1	1	yes	characteristic
287	Q₁₆	C₂×D₄×C₃₁	1	2	yes	—
288	SD₁₆	—	2	2	no	—
289	SD₁₆	—	4	2	no	—
290	SD₁₆	—	4	2	no	—
291	SD₁₆	—	4	2	no	—
292	SD₁₆	—	4	2	no	—
293	SD₁₆	—	4	2	no	—
294	SD₁₆	—	4	2	no	—
295	SD₁₆	D₈×C₃₁	1	2	yes	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	4	2	no	—
299	D₈	—	4	2	no	—
300	D₈	D₈×C₃₁	1	1	yes	characteristic
301	D₈	C₂×D₄×C₃₁	1	2	yes	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	4	2	no	—
305	M₁₆	C₂×D₄×C₃₁	1	2	yes	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
310	C₂²⋊C₄	—	8	2	no	—
311	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₁₆	—	2	2	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₁₆	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂³	—	4	2	no	—
317	C₂³	—	8	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	C₂×D₈×C₃₁	1	2	yes	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	C₂×D₈×C₃₁	1	2	yes	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	4	2	no	—
342	C₈	C₂×D₈×C₃₁	1	1	yes	characteristic
343	C₈	C₂×D₈×C₃₁	1	1	yes	characteristic
344	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	16	2	no	—
350	C₂²	—	32	2	no	—
351	C₂²	C₃₁×#576	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	D₄²×C₃₁	1	1	yes	characteristic
357	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	4	2	no	—
360	C₂	—	8	2	no	—
361	C₂	—	16	2	no	—
362	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3416	C₂	semidirect
2. C₃₁×#3290	C₂	semidirect
3. C₃₁×#2249	C₂	semidirect
4. C₃₁×#2223	C₂	semidirect
5. C₃₁×#2212	C₂	semidirect
6. C₃₁×#2195	C₂	semidirect
7. C₃₁×#2192	C₂	semidirect
8. C₃₁×#2178	C₂	semidirect
9. C₃₁×#2170	C₂	semidirect
12. C₃₁×#576	C₂²	semidirect
14. C₃₁×#510	C₂²	semidirect
19. C₂×C₃₁×Q₃₂	C₂²	semidirect
21. C₂×C₃₁×SD₃₂	C₂²	semidirect
23. C₃₁×#504	C₂²	semidirect
24. C₃₁×#495	C₂²	semidirect
25. C₃₁×#473	C₂²	semidirect
31. C₃₁×#443	C₂²	semidirect
32. C₃₁×#368	C₂²	semidirect
33. C₃₁×#364	C₂²	semidirect
34. C₃₁×#362	C₂²	semidirect
35. C₃₁×#361	C₂²	semidirect
36. C₃₁×#359	C₂²	semidirect
37. C₃₁×#350	C₂²	semidirect
38. C₄×C₁₆×C₃₁	C₂²	semidirect
134. #33857	C₃₁	direct (N × H)
165. #3416	C₂×C₃₁	semidirect
166. #3290	C₂×C₃₁	semidirect
167. #2249	C₂×C₃₁	semidirect
168. #2223	C₂×C₃₁	semidirect
169. #2212	C₂×C₃₁	semidirect
170. #2195	C₂×C₃₁	semidirect
171. #2192	C₂×C₃₁	semidirect
172. #2178	C₂×C₃₁	semidirect
173. #2170	C₂×C₃₁	semidirect
188. #576	C₂²×C₃₁	semidirect
190. #510	C₂²×C₃₁	semidirect
195. C₂×Q₃₂	C₂²×C₃₁	semidirect
197. C₂×SD₃₂	C₂²×C₃₁	semidirect
199. #504	C₂²×C₃₁	semidirect
200. #495	C₂²×C₃₁	semidirect
201. #473	C₂²×C₃₁	semidirect
207. #443	C₂²×C₃₁	semidirect
208. #368	C₂²×C₃₁	semidirect
209. #364	C₂²×C₃₁	semidirect
210. #362	C₂²×C₃₁	semidirect
211. #361	C₂²×C₃₁	semidirect
212. #359	C₂²×C₃₁	semidirect
213. #350	C₂²×C₃₁	semidirect
214. C₄×C₁₆	C₂²×C₃₁	semidirect
267. C₃₁	#33857	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×#3416	2
C₃₁×#3290	2
C₃₁×#2249	2
C₃₁×#2223	2
C₃₁×#2212	2
C₃₁×#2195	2
C₃₁×#2192	2
C₃₁×#2178	2
C₃₁×#2170	2
#33857	31

Subgroups — C31×#33857 #21490616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33857 #21490616