Subgroups — C₂×C₃₁×#2180 #21490225

Order 7936.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#510	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#444	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2180	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#360	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃₁×#347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#131	—	2	1	no	—
12	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
13	C₃₁×#510	C₄	1	4	yes	complemented
14	C₃₁×#510	C₂²	1	4	yes	—
15	C₂×C₃₁×Q₃₂	C₄	1	2	yes	complemented
16	C₂×C₃₁×SD₃₂	C₄	1	2	yes	complemented
17	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
19	C₃₁×#444	—	2	2	no	—
20	C₃₁×#444	C₂²	1	4	yes	—
21	C₃₁×#441	—	2	2	no	—
22	C₃₁×#441	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#104	—	2	1	no	—
26	C₂×C₃₁×#103	—	2	1	no	—
27	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
28	C₃₁×#365	C₂²	1	4	yes	complemented
29	C₃₁×#362	C₂²	1	4	yes	complemented
30	C₃₁×#360	C₂²	1	4	yes	—
31	C₃₁×#347	C₂²	1	4	yes	complemented
32	C₂×#41×C₃₁	—	2	1	no	—
33	C₂²×Q₈×C₃₁	—	2	1	no	—
34	C₃₁×#135	—	2	1	no	—
35	C₃₁×#135	—	2	1	no	—
36	C₃₁×#135	C₂×C₄	1	2	yes	—
37	C₃₁×#135	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₃₁	—	2	1	no	—
39	C₂×Q₁₆×C₃₁	—	2	1	no	—
40	C₂×Q₁₆×C₃₁	—	2	1	no	—
41	C₂×Q₁₆×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×Q₁₆×C₃₁	C₂×C₄	1	2	yes	—
44	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
45	C₂×SD₁₆×C₃₁	—	2	1	no	—
46	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
47	C₃₁×#131	—	2	4	no	—
48	C₃₁×#131	—	4	2	no	—
49	C₂×M₁₆×C₃₁	—	2	1	no	—
50	C₂×M₁₆×C₃₁	—	4	1	no	—
51	C₂²×C₈×C₃₁	—	4	1	no	—
52	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₄×Q₈×C₃₁	—	4	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	—	4	1	no	—
58	C₂×C₄²×C₃₁	—	4	1	no	—
59	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
60	C₃₁×Q₃₂	C₂×C₄	1	8	yes	complemented
61	C₃₁×SD₃₂	C₂×C₄	1	8	yes	complemented
62	C₃₁×M₃₂	—	2	1	no	—
63	C₃₁×M₃₂	C₂×C₄	1	2	yes	—
64	C₃₁×M₃₂	C₂³	1	2	yes	—
65	C₃₁×M₃₂	C₂³	1	2	yes	—
66	C₂×C₁₆×C₃₁	—	2	1	no	—
67	C₂×C₁₆×C₃₁	C₂×C₄	1	2	yes	—
68	C₃₁×#108	—	2	1	no	—
69	C₃₁×#108	C₂³	1	2	yes	—
70	C₃₁×#106	—	2	1	no	—
71	C₃₁×#106	C₂³	1	2	yes	—
72	C₃₁×#104	—	2	4	no	—
73	C₃₁×#103	—	2	4	no	—
74	C₃₁×#97	D₄	1	2	yes	—
75	C₃₁×#97	C₂³	1	2	yes	—
76	#41×C₃₁	—	2	2	no	—
77	#41×C₃₁	—	2	2	no	—
78	#41×C₃₁	—	4	1	no	—
79	#41×C₃₁	—	4	1	no	—
80	C₂×Q₈×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×Q₈×C₃₁	—	2	2	no	—
84	C₂×Q₈×C₃₁	—	4	1	no	—
85	C₂×Q₈×C₃₁	—	4	1	no	—
86	C₂×Q₈×C₃₁	—	4	1	no	—
87	C₂×D₄×C₃₁	—	2	1	no	—
88	C₂×D₄×C₃₁	—	4	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	4	1	no	—
91	C₂²×C₄×C₃₁	—	4	1	no	—
92	C₂²×C₄×C₃₁	—	4	1	no	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	Q₁₆×C₃₁	—	2	2	no	—
95	Q₁₆×C₃₁	—	2	2	no	—
96	Q₁₆×C₃₁	—	2	1	no	—
97	Q₁₆×C₃₁	—	2	2	no	—
98	Q₁₆×C₃₁	C₂²×C₄	1	4	yes	—
99	Q₁₆×C₃₁	C₂²×C₄	1	2	yes	—
100	SD₁₆×C₃₁	—	2	2	no	—
101	SD₁₆×C₃₁	—	2	2	no	—
102	D₈×C₃₁	—	2	1	no	—
103	D₈×C₃₁	C₂²×C₄	1	2	yes	—
104	M₁₆×C₃₁	—	2	2	no	—
105	M₁₆×C₃₁	—	4	4	no	—
106	M₁₆×C₃₁	—	4	1	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	4	4	no	—
110	C₂×C₈×C₃₁	—	4	1	no	—
111	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
116	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	4	4	no	—
120	C₄⋊C₄×C₃₁	—	4	1	no	—
121	C₄²×C₃₁	—	2	1	no	—
122	C₄²×C₃₁	—	4	4	no	—
123	C₄²×C₃₁	C₂×D₄	1	2	yes	—
124	C₁₆×C₃₁	—	2	2	no	—
125	C₁₆×C₃₁	C₂²×C₄	1	4	yes	—
126	C₂×#2180	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
129	Q₈×C₃₁	—	2	2	no	—
130	Q₈×C₃₁	—	2	4	no	—
131	Q₈×C₃₁	—	4	2	no	—
132	Q₈×C₃₁	—	4	2	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	—	4	1	no	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	4	1	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	4	2	no	—
141	C₂×C₄×C₃₁	—	4	2	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	1	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	8	2	no	—
149	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₃₁	—	2	2	no	—
156	C₈×C₃₁	—	4	2	no	—
157	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
158	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
159	C₈×C₃₁	C₂³×C₄	1	1	yes	characteristic
160	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₂×#510	C₂×C₃₁	1	1	yes	characteristic
162	C₂×#444	C₂×C₃₁	1	1	yes	characteristic
163	C₂×#441	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#2180	C₂×C₃₁	1	8	yes	direct product factor
165	C₂×#365	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂×#362	C₂×C₃₁	1	1	yes	characteristic, complemented
167	C₂×#360	C₂×C₃₁	1	1	yes	characteristic
168	C₂×#347	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	4	2	no	—
171	C₂²×C₃₁	—	8	2	no	—
172	C₂²×C₃₁	#442	1	1	yes	characteristic
173	C₂²×C₃₁	#442	1	1	yes	characteristic
174	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₄×C₃₁	—	4	2	no	—
176	C₄×C₃₁	—	4	2	no	—
177	C₄×C₃₁	—	4	4	no	—
178	C₄×C₃₁	—	8	2	no	—
179	C₄×C₃₁	#442	1	1	yes	characteristic
180	C₄×C₃₁	#442	1	1	yes	characteristic
181	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
182	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
184	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×#131	—	2	1	no	—
186	C₂×C₄×Q₈	—	2	1	no	—
187	#510	C₄×C₃₁	1	4	yes	complemented
188	#510	C₂²×C₃₁	1	4	yes	—
189	C₂×Q₃₂	C₄×C₃₁	1	2	yes	complemented
190	C₂×SD₃₂	C₄×C₃₁	1	2	yes	complemented
191	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
193	#444	—	2	2	no	—
194	#444	C₂²×C₃₁	1	4	yes	—
195	#441	—	2	2	no	—
196	#441	C₂²×C₃₁	1	4	yes	complemented
197	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×#104	—	2	1	no	—
200	C₂×#103	—	2	1	no	—
201	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
202	#365	C₂²×C₃₁	1	4	yes	complemented
203	#362	C₂²×C₃₁	1	4	yes	complemented
204	#360	C₂²×C₃₁	1	4	yes	—
205	#347	C₂²×C₃₁	1	4	yes	complemented
206	C₂×C₃₁	—	2	1	no	—
207	C₂×C₃₁	—	2	1	no	—
208	C₂×C₃₁	—	8	2	no	—
209	C₂×C₃₁	#2180	1	2	yes	direct product factor
210	C₂×C₃₁	C₂×#442	1	1	yes	characteristic
211	C₂×#41	—	2	1	no	—
212	C₂²×Q₈	—	2	1	no	—
213	#135	—	2	1	no	—
214	#135	—	2	1	no	—
215	#135	C₂×C₄×C₃₁	1	2	yes	—
216	#135	C₂³×C₃₁	1	2	yes	—
217	C₂×Q₁₆	—	2	1	no	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×Q₁₆	C₂×C₄×C₃₁	1	2	yes	—
222	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
226	#131	—	2	4	no	—
227	#131	—	4	2	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	—	4	1	no	—
230	C₂²×C₈	—	4	1	no	—
231	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
233	C₄×Q₈	—	2	4	no	—
234	C₄×Q₈	—	4	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
239	Q₃₂	C₂×C₄×C₃₁	1	8	yes	complemented
240	SD₃₂	C₂×C₄×C₃₁	1	8	yes	complemented
241	M₃₂	—	2	1	no	—
242	M₃₂	C₂×C₄×C₃₁	1	2	yes	—
243	M₃₂	C₂³×C₃₁	1	2	yes	—
244	M₃₂	C₂³×C₃₁	1	2	yes	—
245	C₂×C₁₆	—	2	1	no	—
246	C₂×C₁₆	C₂×C₄×C₃₁	1	2	yes	—
247	#108	—	2	1	no	—
248	#108	C₂³×C₃₁	1	2	yes	—
249	#106	—	2	1	no	—
250	#106	C₂³×C₃₁	1	2	yes	—
251	#104	—	2	4	no	—
252	#103	—	2	4	no	—
253	#97	D₄×C₃₁	1	2	yes	—
254	#97	C₂³×C₃₁	1	2	yes	—
255	C₃₁	C₂×#2180	1	1	yes	characteristic, direct product factor, Sylow
256	#41	—	2	2	no	—
257	#41	—	2	2	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
274	Q₁₆	—	2	2	no	—
275	Q₁₆	—	2	2	no	—
276	Q₁₆	—	2	1	no	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	C₂²×C₄×C₃₁	1	4	yes	—
279	Q₁₆	C₂²×C₄×C₃₁	1	2	yes	—
280	SD₁₆	—	2	2	no	—
281	SD₁₆	—	2	2	no	—
282	D₈	—	2	1	no	—
283	D₈	C₂²×C₄×C₃₁	1	2	yes	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	4	4	no	—
286	M₁₆	—	4	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
294	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
296	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
297	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	4	4	no	—
303	C₄²	C₂×D₄×C₃₁	1	2	yes	—
304	C₁₆	—	2	2	no	—
305	C₁₆	C₂²×C₄×C₃₁	1	4	yes	—
306	C₂³	—	4	1	no	—
307	C₂³	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
330	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
337	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
338	C₈	C₂³×C₄×C₃₁	1	1	yes	characteristic
339	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	C₃₁×#442	1	1	yes	characteristic
344	C₂²	C₃₁×#442	1	1	yes	characteristic
345	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₄	—	4	2	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	2	no	—
350	C₄	C₃₁×#442	1	1	yes	characteristic
351	C₄	C₃₁×#442	1	1	yes	characteristic
352	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
353	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	8	2	no	—
357	C₂	C₃₁×#2180	1	2	yes	direct product factor
358	C₂	C₂×C₃₁×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	#442
commutator	C₈	C₂³×C₄×C₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ C₂×C₃₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃₁×#441	C₂	semidirect
4. C₃₁×#2180	C₂	direct (N × H)
5. C₂×C₃₁×#365	C₂	semidirect
6. C₂×C₃₁×#362	C₂	semidirect
8. C₂×C₃₁×#347	C₂	semidirect
13. C₃₁×#510	C₄	semidirect
15. C₂×C₃₁×Q₃₂	C₄	semidirect
16. C₂×C₃₁×SD₃₂	C₄	semidirect
22. C₃₁×#441	C₂²	semidirect
28. C₃₁×#365	C₂²	semidirect
29. C₃₁×#362	C₂²	semidirect
31. C₃₁×#347	C₂²	semidirect
60. C₃₁×Q₃₂	C₂×C₄	semidirect
61. C₃₁×SD₃₂	C₂×C₄	semidirect
126. C₂×#2180	C₃₁	direct (N × H)
163. C₂×#441	C₂×C₃₁	semidirect
164. #2180	C₂×C₃₁	direct (N × H)
165. C₂×#365	C₂×C₃₁	semidirect
166. C₂×#362	C₂×C₃₁	semidirect
168. C₂×#347	C₂×C₃₁	semidirect
187. #510	C₄×C₃₁	semidirect
189. C₂×Q₃₂	C₄×C₃₁	semidirect
190. C₂×SD₃₂	C₄×C₃₁	semidirect
196. #441	C₂²×C₃₁	semidirect
202. #365	C₂²×C₃₁	semidirect
203. #362	C₂²×C₃₁	semidirect
205. #347	C₂²×C₃₁	semidirect
209. C₂×C₃₁	#2180	direct (N × H)
239. Q₃₂	C₂×C₄×C₃₁	semidirect
240. SD₃₂	C₂×C₄×C₃₁	semidirect
255. C₃₁	C₂×#2180	direct (N × H)
357. C₂	C₃₁×#2180	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#510	2
C₂×C₃₁×#444	2
C₂×C₃₁×#441	2
C₃₁×#2180	2
C₂×C₃₁×#365	2
C₂×C₃₁×#362	2
C₂×C₃₁×#360	2
C₂×C₃₁×#347	2
C₂×#2180	31

Subgroups — C2×C31×#2180 #21490225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2180 #21490225