Subgroups — C₅×D₄×M₃₂ #11956157

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#2169	C₂	1	2	yes	maximal, complemented
4	C₅×#2168	C₂	1	4	yes	maximal, complemented
5	C₅×D₄×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₅×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2112	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂×C₅×M₃₂	—	2	8	no	—
12	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₅×M₃₂	C₂²	1	2	yes	—
14	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
16	C₂²×C₅×C₁₆	C₂²	1	4	yes	complemented
17	C₅×C₈×D₄	C₄	1	2	yes	—
18	C₅×C₈×D₄	C₄	1	1	yes	characteristic
19	C₅×C₈×D₄	C₄	1	1	yes	characteristic
20	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	2	yes	—
22	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
27	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
28	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
30	C₅×#346	C₂²	1	2	yes	complemented
31	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
32	D₄×M₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₅×C₈	—	2	4	no	—
36	C₂²×C₅×C₈	—	2	4	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₄×C₅×D₄	C₈	1	2	yes	—
45	C₄×C₅×D₄	C₈	1	1	yes	characteristic
46	C₄×C₅×D₄	C₈	1	1	yes	characteristic
47	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
48	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₄	C₈	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₅×M₃₂	—	2	4	no	—
54	C₅×M₃₂	—	2	2	no	—
55	C₅×M₃₂	—	2	8	no	—
56	C₅×M₃₂	D₄	1	4	yes	direct product factor
57	C₂×C₅×C₁₆	—	2	8	no	—
58	C₂×C₅×C₁₆	C₂³	1	2	yes	—
59	C₂×C₅×C₁₆	C₂³	1	4	yes	—
60	C₂×C₅×C₁₆	C₂³	1	2	yes	—
61	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
68	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×M₃₂	C₂×C₅	1	2	yes	complemented
73	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
74	#2169	C₂×C₅	1	2	yes	complemented
75	#2168	C₂×C₅	1	4	yes	complemented
76	D₄×C₁₆	C₂×C₅	1	2	yes	complemented
77	#2150	C₂×C₅	1	1	yes	characteristic, complemented
78	#2112	C₂×C₅	1	2	yes	complemented
79	C₄×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂⁴×C₅	C₂×C₈	1	2	yes	—
81	C₂×C₅×D₄	—	2	4	no	—
82	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
83	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
84	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	—	2	4	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
89	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
90	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
91	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₅×C₈	—	2	4	no	—
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
109	C₂×C₅×C₈	#41	1	2	yes	—
110	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
112	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
113	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
114	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
115	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
116	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
117	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
118	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
119	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₅×C₁₆	—	2	4	no	—
123	C₅×C₁₆	—	2	2	no	—
124	C₅×C₁₆	C₂×D₄	1	4	yes	complemented
125	C₂³×C₈	C₂²×C₅	1	2	yes	—
126	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
127	C₂×M₃₂	—	2	8	no	—
128	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
129	C₂×M₃₂	C₂²×C₅	1	2	yes	—
130	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
131	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
132	C₂²×C₁₆	C₂²×C₅	1	4	yes	complemented
133	C₈×D₄	C₄×C₅	1	2	yes	—
134	C₈×D₄	C₄×C₅	1	1	yes	characteristic
135	C₈×D₄	C₄×C₅	1	1	yes	characteristic
136	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₈×D₄	C₂²×C₅	1	2	yes	—
138	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
140	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
141	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
142	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
143	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
144	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	complemented
145	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	complemented
146	#346	C₂²×C₅	1	2	yes	complemented
147	C₄×C₁₆	C₂²×C₅	1	2	yes	complemented
148	C₂³×C₅	—	2	4	no	—
149	C₂³×C₅	—	2	4	no	—
150	C₂³×C₅	—	4	2	no	—
151	C₂³×C₅	C₂²×C₈	1	2	yes	—
152	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
153	C₂³×C₅	C₂²×C₈	1	2	yes	—
154	C₅×D₄	—	2	4	no	—
155	C₅×D₄	—	2	2	no	—
156	C₅×D₄	M₃₂	1	4	yes	direct product factor
157	C₂×C₄×C₅	—	2	4	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	2	4	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	4	1	no	—
166	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
172	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₅	#131	1	2	yes	—
175	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₅×C₈	—	2	2	no	—
177	C₅×C₈	—	2	2	no	—
178	C₅×C₈	—	2	1	no	—
179	C₅×C₈	—	2	1	no	—
180	C₅×C₈	C₄×D₄	1	2	yes	—
181	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
182	C₅×C₈	C₂×#41	1	1	yes	characteristic
183	C₂²×D₄	C₅×C₈	1	1	yes	characteristic
184	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
185	C₂²×C₈	—	2	4	no	—
186	C₂²×C₈	—	2	4	no	—
187	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
188	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
189	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
190	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₅	1	2	yes	—
192	C₂²×C₈	C₂³×C₅	1	2	yes	—
193	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
194	C₄×D₄	C₅×C₈	1	2	yes	—
195	C₄×D₄	C₅×C₈	1	1	yes	characteristic
196	C₄×D₄	C₅×C₈	1	1	yes	characteristic
197	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
198	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₅×C₈	1	2	yes	—
202	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
203	M₃₂	—	2	4	no	—
204	M₃₂	—	2	2	no	—
205	M₃₂	—	2	8	no	—
206	M₃₂	C₅×D₄	1	4	yes	direct product factor
207	C₂×C₁₆	—	2	8	no	—
208	C₂×C₁₆	C₂³×C₅	1	2	yes	—
209	C₂×C₁₆	C₂³×C₅	1	4	yes	—
210	C₂×C₁₆	C₂³×C₅	1	2	yes	—
211	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
212	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
213	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
215	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
216	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
217	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
218	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
219	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
220	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	2	no	—
229	C₂²×C₅	—	4	8	no	—
230	C₂²×C₅	C₈×D₄	1	2	yes	—
231	C₂²×C₅	C₂×M₃₂	1	4	yes	complemented
232	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
233	C₄×C₅	—	2	1	no	—
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	2	no	—
238	C₄×C₅	C₈×D₄	1	2	yes	—
239	C₄×C₅	C₂×M₃₂	1	2	yes	complemented
240	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₅	C₂×#131	1	1	yes	characteristic
242	C₂⁴	C₂×C₅×C₈	1	2	yes	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
245	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
246	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
251	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
252	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
253	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
268	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
271	C₂×C₈	C₅×#41	1	2	yes	—
272	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
273	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
274	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
275	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
276	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
277	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
278	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
279	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
280	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
281	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₁₆	—	2	4	no	—
285	C₁₆	—	2	2	no	—
286	C₁₆	C₂×C₅×D₄	1	4	yes	complemented
287	C₂×C₅	—	2	2	no	—
288	C₂×C₅	—	2	4	no	—
289	C₂×C₅	—	4	2	no	—
290	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
291	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
292	C₂×C₅	#3407	1	1	yes	characteristic
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	4	2	no	—
296	C₂³	C₂²×C₅×C₈	1	2	yes	—
297	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
298	C₂³	C₂²×C₅×C₈	1	2	yes	—
299	D₄	—	2	4	no	—
300	D₄	—	2	2	no	—
301	D₄	C₅×M₃₂	1	4	yes	direct product factor
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
312	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
316	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
317	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
318	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
319	C₂×C₄	C₅×#131	1	2	yes	—
320	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
321	C₈	—	2	2	no	—
322	C₈	—	2	2	no	—
323	C₈	—	2	1	no	—
324	C₈	—	2	1	no	—
325	C₈	C₄×C₅×D₄	1	2	yes	—
326	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
327	C₈	C₂×C₅×#41	1	1	yes	characteristic
328	C₅	D₄×M₃₂	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	C₅×C₈×D₄	1	2	yes	—
338	C₂²	C₂×C₅×M₃₂	1	4	yes	complemented
339	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	C₅×C₈×D₄	1	2	yes	—
346	C₄	C₂×C₅×M₃₂	1	2	yes	complemented
347	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
348	C₄	C₂×C₅×#131	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
353	C₂	C₂²×C₅×M₃₂	1	1	yes	characteristic
354	C₂	C₅×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂²×C₅×D₄	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×M₃₂	C₂	semidirect
3. C₅×#2169	C₂	semidirect
4. C₅×#2168	C₂	semidirect
5. C₅×D₄×C₁₆	C₂	semidirect
6. C₅×#2150	C₂	semidirect
7. C₅×#2112	C₂	semidirect
8. C₄×C₅×M₃₂	C₂	semidirect
15. C₂×C₅×M₃₂	C₂²	semidirect
16. C₂²×C₅×C₁₆	C₂²	semidirect
26. C₅×C₄⋊C₁₆	C₂²	semidirect
27. C₅×C₄⋊C₁₆	C₂²	semidirect
28. C₅×C₂²⋊C₁₆	C₂²	semidirect
29. C₅×C₂²⋊C₁₆	C₂²	semidirect
30. C₅×#346	C₂²	semidirect
31. C₄×C₅×C₁₆	C₂²	semidirect
32. D₄×M₃₂	C₅	direct (N × H)
56. C₅×M₃₂	D₄	direct (N × H)
72. C₂²×M₃₂	C₂×C₅	semidirect
74. #2169	C₂×C₅	semidirect
75. #2168	C₂×C₅	semidirect
76. D₄×C₁₆	C₂×C₅	semidirect
77. #2150	C₂×C₅	semidirect
78. #2112	C₂×C₅	semidirect
79. C₄×M₃₂	C₂×C₅	semidirect
124. C₅×C₁₆	C₂×D₄	semidirect
131. C₂×M₃₂	C₂²×C₅	semidirect
132. C₂²×C₁₆	C₂²×C₅	semidirect
142. C₄⋊C₁₆	C₂²×C₅	semidirect
143. C₄⋊C₁₆	C₂²×C₅	semidirect
144. C₂²⋊C₁₆	C₂²×C₅	semidirect
145. C₂²⋊C₁₆	C₂²×C₅	semidirect
146. #346	C₂²×C₅	semidirect
147. C₄×C₁₆	C₂²×C₅	semidirect
156. C₅×D₄	M₃₂	direct (N × H)
206. M₃₂	C₅×D₄	direct (N × H)
231. C₂²×C₅	C₂×M₃₂	semidirect
239. C₄×C₅	C₂×M₃₂	semidirect
286. C₁₆	C₂×C₅×D₄	semidirect
301. D₄	C₅×M₃₂	direct (N × H)
328. C₅	D₄×M₃₂	direct (N × H)
338. C₂²	C₂×C₅×M₃₂	semidirect
346. C₄	C₂×C₅×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×M₃₂	2
C₂×C₅×C₈×D₄	2
C₅×#2169	2
C₅×#2168	2
C₅×D₄×C₁₆	2
C₅×#2150	2
C₅×#2112	2
C₄×C₅×M₃₂	2
D₄×M₃₂	5

Subgroups — C5×D4×M32 #11956157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×M₃₂ #11956157