Subgroups — C₃₁×#33189 #21489948

Order 7936.

1030 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#471	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic
5	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1977	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#137	C₂²	1	2	yes	—
11	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	—
13	C₂×C₃₁×#131	C₂²	1	2	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
16	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#492	—	2	1	no	—
18	C₃₁×#492	—	2	1	no	—
19	C₃₁×#492	—	2	2	no	—
20	C₃₁×#471	—	2	16	no	—
21	C₃₁×#462	—	2	2	no	—
22	C₃₁×#461	—	2	2	no	—
23	C₃₁×#460	—	2	2	no	—
24	C₃₁×#459	—	2	2	no	—
25	C₂×C₃₁×#108	C₂²	1	4	yes	—
26	C₃₁×#423	C₂²	1	1	yes	characteristic
27	C₃₁×#423	C₂²	1	1	yes	characteristic
28	C₃₁×#419	C₂²	1	2	yes	—
29	C₃₁×#418	C₂²	1	2	yes	—
30	C₂×C₃₁×#101	C₂²	1	4	yes	—
31	C₂×C₃₁×#100	C₂²	1	4	yes	—
32	C₃₁×#405	—	2	2	no	—
33	C₃₁×#405	C₂²	1	2	yes	—
34	C₄×M₁₆×C₃₁	—	2	1	no	—
35	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₃₁	—	2	1	no	—
37	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₃₁	—	2	2	no	—
41	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
42	C₃₁×#137	—	2	8	no	—
43	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×SD₁₆×C₃₁	—	2	2	no	—
46	C₂×SD₁₆×C₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₃₁	—	2	8	no	—
48	C₂×SD₁₆×C₃₁	—	2	4	no	—
49	C₂×SD₁₆×C₃₁	—	2	4	no	—
50	C₂×SD₁₆×C₃₁	—	2	8	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₃₁×#131	—	2	4	no	—
53	C₃₁×#131	D₄	1	8	yes	complemented
54	C₂×M₁₆×C₃₁	—	2	2	no	—
55	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
56	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₃₁	—	2	2	no	—
59	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
60	C₃₁×C₄⋊Q₈	—	2	2	no	—
61	C₃₁×C₄⋊Q₈	—	2	1	no	—
62	C₃₁×C₄⋊Q₈	—	2	1	no	—
63	C₃₁×#127	—	2	2	no	—
64	C₃₁×#127	—	2	1	no	—
65	C₃₁×#127	—	2	1	no	—
66	C₄×Q₈×C₃₁	D₄	1	2	yes	—
67	C₄×D₄×C₃₁	—	2	2	no	—
68	C₄×D₄×C₃₁	D₄	1	2	yes	—
69	C₃₁×#117	—	2	1	no	—
70	C₃₁×#117	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₄²×C₃₁	—	2	1	no	—
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×#108	—	2	8	no	—
75	C₃₁×C₄⋊C₈	—	2	2	no	—
76	C₃₁×C₄⋊C₈	—	2	2	no	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×#101	—	2	8	no	—
80	C₃₁×#100	—	2	8	no	—
81	C₃₁×#97	—	2	2	no	—
82	C₃₁×#97	—	2	1	no	—
83	C₄×C₈×C₃₁	—	2	2	no	—
84	C₄×C₈×C₃₁	—	2	1	no	—
85	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	D₄	1	2	yes	—
88	C₂⁴×C₃₁	—	2	2	no	—
89	#41×C₃₁	—	2	2	no	—
90	#41×C₃₁	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₃₁	—	2	4	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	4	no	—
95	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	2	4	no	—
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	4	no	—
101	C₂×D₄×C₃₁	—	4	2	no	—
102	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂×D₄×C₃₁	—	8	4	no	—
104	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	#41	1	2	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₃₁	—	4	4	no	—
111	SD₁₆×C₃₁	—	4	4	no	—
112	SD₁₆×C₃₁	—	4	4	no	—
113	SD₁₆×C₃₁	—	4	8	no	—
114	SD₁₆×C₃₁	—	4	8	no	—
115	D₈×C₃₁	—	4	4	no	—
116	M₁₆×C₃₁	—	2	2	no	—
117	M₁₆×C₃₁	—	2	8	no	—
118	M₁₆×C₃₁	—	2	4	no	—
119	M₁₆×C₃₁	—	2	4	no	—
120	M₁₆×C₃₁	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₃₁	—	2	2	no	—
122	C₂×C₈×C₃₁	—	2	8	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
128	C₂×C₈×C₃₁	#41	1	4	yes	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	4	2	no	—
131	C₄⋊C₄×C₃₁	—	4	2	no	—
132	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₃₁	—	2	1	no	—
134	C₂²⋊C₄×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	2	2	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₃₁	C₂×D₄	1	2	yes	—
140	#33189	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	2	1	no	—
142	C₂³×C₃₁	—	4	2	no	—
143	C₂³×C₃₁	—	4	4	no	—
144	C₂³×C₃₁	—	8	4	no	—
145	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
146	Q₈×C₃₁	—	2	1	no	—
147	Q₈×C₃₁	—	4	4	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	#127	1	2	yes	—
151	D₄×C₃₁	—	2	4	no	—
152	D₄×C₃₁	—	2	1	no	—
153	D₄×C₃₁	—	4	4	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	8	4	no	—
157	D₄×C₃₁	—	8	4	no	—
158	D₄×C₃₁	#127	1	2	yes	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	2	4	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	4	4	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	4	no	—
166	C₂×C₄×C₃₁	#121	1	2	yes	—
167	C₂×C₄×C₃₁	#121	1	2	yes	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
172	C₈×C₃₁	—	2	4	no	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₈×C₃₁	#121	1	4	yes	—
176	C₈×C₃₁	#121	1	4	yes	—
177	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂×#471	C₂×C₃₁	1	4	yes	complemented
179	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#3038	C₂×C₃₁	1	1	yes	characteristic
181	C₄×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#1977	C₂×C₃₁	1	4	yes	complemented
183	#1966	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#1965	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#1848	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	4	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	4	no	—
191	C₂²×C₃₁	—	16	4	no	—
192	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃₁	#532	1	2	yes	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	2	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	#471	1	4	yes	complemented
199	C₄×C₃₁	C₂×#121	1	2	yes	—
200	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
201	C₄×C₃₁	#532	1	1	yes	characteristic
202	C₂×#137	C₂²×C₃₁	1	2	yes	—
203	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
204	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	—
205	C₂×#131	C₂²×C₃₁	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
208	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
209	#492	—	2	1	no	—
210	#492	—	2	1	no	—
211	#492	—	2	2	no	—
212	#471	—	2	16	no	—
213	#462	—	2	2	no	—
214	#461	—	2	2	no	—
215	#460	—	2	2	no	—
216	#459	—	2	2	no	—
217	C₂×#108	C₂²×C₃₁	1	4	yes	—
218	#423	C₂²×C₃₁	1	1	yes	characteristic
219	#423	C₂²×C₃₁	1	1	yes	characteristic
220	#419	C₂²×C₃₁	1	2	yes	—
221	#418	C₂²×C₃₁	1	2	yes	—
222	C₂×#101	C₂²×C₃₁	1	4	yes	—
223	C₂×#100	C₂²×C₃₁	1	4	yes	—
224	#405	—	2	2	no	—
225	#405	C₂²×C₃₁	1	2	yes	—
226	C₄×M₁₆	—	2	1	no	—
227	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₄×C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₃₁	—	2	2	no	—
231	C₂×C₃₁	—	4	2	no	—
232	C₂×C₃₁	—	16	2	no	—
233	C₂×C₃₁	#2856	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#471	1	2	yes	—
235	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
237	C₂²×D₄	—	2	2	no	—
238	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
239	#137	—	2	8	no	—
240	AGL(1,ℤ/8)	—	2	8	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	—	2	8	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	8	no	—
248	C₂×D₈	—	2	2	no	—
249	#131	—	2	4	no	—
250	#131	D₄×C₃₁	1	8	yes	complemented
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
253	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
254	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	#127	—	2	2	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	C₄×Q₈	D₄×C₃₁	1	2	yes	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	D₄×C₃₁	1	2	yes	—
266	#117	—	2	1	no	—
267	#117	C₂³×C₃₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
271	#108	—	2	8	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	#103	—	2	4	no	—
275	#102	—	2	4	no	—
276	#101	—	2	8	no	—
277	#100	—	2	8	no	—
278	#97	—	2	2	no	—
279	#97	—	2	1	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
283	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
284	C₄×C₈	D₄×C₃₁	1	2	yes	—
285	C₃₁	#33189	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	—	2	2	no	—
287	#41	—	2	2	no	—
288	#41	C₂×D₄×C₃₁	1	4	yes	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	#41×C₃₁	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
308	Q₁₆	—	4	4	no	—
309	SD₁₆	—	4	4	no	—
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	4	8	no	—
312	SD₁₆	—	4	8	no	—
313	D₈	—	4	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	8	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	2	4	no	—
318	M₁₆	C₂×D₄×C₃₁	1	4	yes	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
324	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
326	C₂×C₈	#41×C₃₁	1	4	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₃₁	1	2	yes	—
338	C₂³	—	2	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	8	4	no	—
342	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
343	Q₈	—	2	1	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	C₃₁×#127	1	2	yes	—
348	D₄	—	2	4	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	8	4	no	—
354	D₄	—	8	4	no	—
355	D₄	C₃₁×#127	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	C₃₁×#121	1	2	yes	—
364	C₂×C₄	C₃₁×#121	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	C₃₁×#121	1	4	yes	—
373	C₈	C₃₁×#121	1	4	yes	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
381	C₂²	C₃₁×#532	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₃₁×#471	1	4	yes	complemented
387	C₄	C₂×C₃₁×#121	1	2	yes	—
388	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
389	C₄	C₃₁×#532	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	4	2	no	—
392	C₂	—	16	2	no	—
393	C₂	C₃₁×#2856	1	1	yes	characteristic
394	C₂	C₂×C₃₁×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#492	C₂	semidirect
2. C₂×C₃₁×#471	C₂	semidirect
3. C₃₁×#3039	C₂	semidirect
5. C₄×C₃₁×#131	C₂	semidirect
6. C₃₁×#1977	C₂	semidirect
7. C₃₁×#1966	C₂	semidirect
8. C₃₁×#1965	C₂	semidirect
9. C₃₁×#1848	C₂	semidirect
53. C₃₁×#131	D₄	semidirect
140. #33189	C₃₁	direct (N × H)
177. C₂×#492	C₂×C₃₁	semidirect
178. C₂×#471	C₂×C₃₁	semidirect
179. #3039	C₂×C₃₁	semidirect
181. C₄×#131	C₂×C₃₁	semidirect
182. #1977	C₂×C₃₁	semidirect
183. #1966	C₂×C₃₁	semidirect
184. #1965	C₂×C₃₁	semidirect
185. #1848	C₂×C₃₁	semidirect
198. C₄×C₃₁	#471	semidirect
250. #131	D₄×C₃₁	semidirect
285. C₃₁	#33189	direct (N × H)
386. C₄	C₃₁×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#492	2
C₂×C₃₁×#471	2
C₃₁×#3039	2
C₃₁×#3038	2
C₄×C₃₁×#131	2
C₃₁×#1977	2
C₃₁×#1966	2
C₃₁×#1965	2
C₃₁×#1848	2
#33189	31

Subgroups — C31×#33189 #21489948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33189 #21489948