Subgroups — C₄×D₅⋊M₃₂ #13043099

Order 1280.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#10604702	C₂	1	2	yes	maximal, complemented
4	C₄×#3998	C₂	1	2	yes	maximal, complemented
5	#10603825	C₂	1	2	yes	maximal, complemented
6	C₄×#3990	C₂	1	2	yes	maximal, complemented
7	#10603823	C₂	1	2	yes	maximal, complemented
8	C₄×D₅⋊C₁₆	C₂	1	2	yes	maximal, complemented
9	C₂²×C₈×D₅	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₅	C₄	1	1	yes	characteristic
12	C₂×#3998	C₂²	1	4	yes	—
13	D₅⋊M₃₂	C₄	1	16	yes	direct product factor
14	C₂×#3990	C₂²	1	4	yes	—
15	C₂×D₅⋊C₁₆	C₂²	1	4	yes	—
16	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₄×#168	C₂²	1	1	yes	characteristic
20	C₄×C₈×D₅	C₄	1	1	yes	characteristic
21	C₄×C₈×D₅	C₄	1	1	yes	characteristic
22	C₄×C₈×D₅	C₄	1	1	yes	characteristic
23	C₄×C₈×D₅	C₄	1	1	yes	characteristic
24	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
28	#64886	C₂²	1	4	yes	complemented
29	#64885	C₂²	1	4	yes	complemented
30	#64859	C₂²	1	4	yes	complemented
31	C₄×#674	C₂²	1	4	yes	complemented
32	C₂×C₄×M₃₂	—	5	1	no	maximal, Sylow
33	C₂²×C₄×D₅	C₈	1	2	yes	—
34	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₅	C₈	1	2	yes	—
39	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×#168	C₂×C₄	1	1	yes	characteristic
41	C₂²×#168	C₂³	1	1	yes	characteristic
42	C₂×C₈×D₅	C₈	1	8	yes	—
43	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅	C₂×C₄	1	8	yes	—
46	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
52	C₄²×D₅	C₈	1	2	yes	—
53	C₄²×D₅	C₈	1	2	yes	—
54	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
58	#3998	C₂×C₄	1	16	yes	complemented
59	C₂×#674	C₂³	1	8	yes	—
60	#3990	C₂×C₄	1	16	yes	complemented
61	D₅⋊C₁₆	C₂×C₄	1	16	yes	complemented
62	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
64	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₅	C₂³	1	1	yes	characteristic
73	C₈×Dic₅	C₂³	1	1	yes	characteristic
74	C₄×#168	C₂×C₄	1	1	yes	characteristic
75	C₄×#168	C₂×C₄	1	1	yes	characteristic
76	C₄×#168	C₂³	1	1	yes	characteristic
77	C₄×#168	C₂³	1	1	yes	characteristic
78	C₂²×M₃₂	—	5	2	no	—
79	C₂²×C₄×C₈	—	5	1	no	—
80	C₄×M₃₂	—	5	2	no	—
81	C₄×M₃₂	—	5	2	no	—
82	C₄×M₃₂	—	5	2	no	—
83	C₄×M₃₂	—	5	2	no	—
84	C₂×#346	—	5	2	no	—
85	C₂×C₄×C₁₆	—	5	2	no	—
86	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₅	C₂×C₈	1	2	yes	—
90	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₅	—	2	8	no	—
92	C₂×C₄×D₅	C₄²	1	4	yes	—
93	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
94	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₅	C₂×C₈	1	4	yes	—
99	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
100	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₅×C₈	C₄²	1	4	yes	—
103	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₅	C₂×C₈	1	2	yes	—
109	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₅	C₂×C₈	1	2	yes	—
112	C₄×Dic₅	C₂×C₈	1	2	yes	—
113	C₄×Dic₅	C₂×C₈	1	2	yes	—
114	C₄×Dic₅	C₂×C₈	1	2	yes	—
115	C₄×Dic₅	C₂×C₈	1	2	yes	—
116	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×#168	C₂×C₈	1	4	yes	—
119	C₂×#168	C₂²×C₄	1	1	yes	characteristic
120	C₂×#168	C₂²×C₄	1	4	yes	—
121	C₂×#168	C₂²×C₄	1	1	yes	characteristic
122	C₂×#168	C₂²×C₄	1	1	yes	characteristic
123	C₂×#168	C₂⁴	1	1	yes	characteristic
124	C₈×D₅	C₄²	1	4	yes	—
125	C₈×D₅	C₄²	1	4	yes	—
126	C₈×D₅	C₂×C₈	1	4	yes	—
127	C₈×D₅	C₂×C₈	1	4	yes	—
128	C₈×D₅	C₂×C₈	1	4	yes	—
129	C₈×D₅	C₂×C₈	1	4	yes	—
130	C₈×D₅	C₂²×C₄	1	4	yes	—
131	C₈×D₅	C₂²×C₄	1	4	yes	—
132	#674	C₂²×C₄	1	16	yes	complemented
133	C₂³×C₈	—	5	1	no	—
134	C₂³×C₈	—	5	1	no	—
135	C₂²×C₄²	—	5	1	no	—
136	C₂×M₃₂	—	5	4	no	—
137	C₂×M₃₂	—	5	4	no	—
138	C₂×M₃₂	—	5	16	no	—
139	C₂²×C₁₆	—	5	4	no	—
140	C₂×C₄×C₈	—	5	1	no	—
141	C₂×C₄×C₈	—	5	1	no	—
142	C₂×C₄×C₈	—	5	1	no	—
143	C₂×C₄×C₈	—	5	1	no	—
144	C₂×C₄×C₈	—	5	1	no	—
145	C₂×C₄×C₈	—	5	1	no	—
146	C₂×C₄×C₈	—	5	1	no	—
147	C₂×C₄×C₈	—	5	1	no	—
148	C₂×C₄×C₈	—	5	1	no	—
149	C₂×C₄×C₈	—	5	1	no	—
150	C₂×C₄×C₈	—	5	1	no	—
151	C₂×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
152	#346	—	5	4	no	—
153	#346	—	5	4	no	—
154	C₄×C₁₆	—	5	4	no	—
155	C₄×C₁₆	—	5	4	no	—
156	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₅	—	2	4	no	—
158	C₂²×D₅	C₄×C₈	1	4	yes	—
159	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₅	—	2	4	no	—
162	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
165	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
168	C₂×Dic₅	—	2	4	no	—
169	C₂×Dic₅	C₄×C₈	1	4	yes	—
170	C₂×Dic₅	C₂²×C₈	1	2	yes	—
171	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₅	C₂²×C₈	1	2	yes	—
174	C₄×D₅	—	2	4	no	—
175	C₄×D₅	—	2	4	no	—
176	C₄×D₅	—	2	4	no	—
177	C₄×D₅	C₄×C₈	1	4	yes	—
178	C₄×D₅	C₄×C₈	1	4	yes	—
179	C₄×D₅	M₃₂	1	8	yes	complemented
180	C₄×D₅	C₂×C₄²	1	2	yes	—
181	C₄×D₅	C₂×C₄²	1	2	yes	—
182	C₄×D₅	C₂²×C₈	1	2	yes	—
183	C₄×D₅	C₂²×C₈	1	2	yes	—
184	C₅×C₈	C₂×C₄²	1	2	yes	—
185	C₅×C₈	C₂×C₄²	1	2	yes	—
186	C₅×C₈	C₂²×C₈	1	2	yes	—
187	C₅×C₈	C₂²×C₈	1	2	yes	—
188	#168	C₂×C₄²	1	2	yes	—
189	#168	C₂²×C₈	1	2	yes	—
190	#168	C₂²×C₈	1	2	yes	—
191	#168	C₂³×C₄	1	2	yes	—
192	C₂³×C₄	—	5	1	no	—
193	C₂³×C₄	—	5	2	no	—
194	C₂²×C₈	—	5	1	no	—
195	C₂²×C₈	—	5	1	no	—
196	C₂²×C₈	—	5	8	no	—
197	C₂²×C₈	—	5	8	no	—
198	C₂²×C₈	—	5	1	no	—
199	C₂²×C₈	—	5	1	no	—
200	C₂²×C₈	—	5	1	no	—
201	C₂²×C₈	—	5	1	no	—
202	C₂²×C₈	—	5	1	no	—
203	C₂²×C₈	—	5	1	no	—
204	C₂²×C₈	—	5	1	no	—
205	C₂²×C₈	—	5	1	no	—
206	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
207	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₂×C₄²	—	5	2	no	—
209	C₂×C₄²	—	5	1	no	—
210	C₂×C₄²	—	5	2	no	—
211	C₂×C₄²	—	5	2	no	—
212	C₂×C₄²	—	5	1	no	—
213	C₂×C₄²	—	5	1	no	—
214	C₂×C₄²	—	5	1	no	—
215	C₂×C₄²	—	5	1	no	—
216	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
217	M₃₂	—	5	16	no	—
218	M₃₂	—	5	16	no	—
219	C₂×C₁₆	—	5	8	no	—
220	C₂×C₁₆	—	5	16	no	—
221	C₄×C₈	—	5	1	no	—
222	C₄×C₈	—	5	1	no	—
223	C₄×C₈	—	5	1	no	—
224	C₄×C₈	—	5	1	no	—
225	C₄×C₈	—	5	1	no	—
226	C₄×C₈	—	5	1	no	—
227	C₄×C₈	—	5	1	no	—
228	C₄×C₈	—	5	1	no	—
229	C₄×C₈	—	5	1	no	—
230	C₄×C₈	—	5	1	no	—
231	C₄×C₈	—	5	1	no	—
232	C₄×C₈	—	5	1	no	—
233	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
234	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
235	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
236	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	C₂×C₄×C₈	1	2	yes	—
239	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
240	C₂×D₅	—	2	2	no	—
241	C₂×D₅	—	2	8	no	—
242	C₂×D₅	C₂×C₄×C₈	1	2	yes	—
243	C₂×D₅	C₂×C₄×C₈	1	2	yes	—
244	C₂×D₅	C₂×M₃₂	1	4	yes	—
245	C₄×C₅	—	2	2	no	—
246	C₄×C₅	C₂×C₄×C₈	1	2	yes	—
247	C₄×C₅	C₂×M₃₂	1	4	yes	complemented
248	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
249	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
250	Dic₅	—	2	2	no	—
251	Dic₅	C₂×C₄×C₈	1	2	yes	—
252	Dic₅	C₂×C₄×C₈	1	2	yes	—
253	Dic₅	C₂×M₃₂	1	4	yes	complemented
254	C₂⁴	—	5	1	no	—
255	C₂²×C₄	—	5	1	no	—
256	C₂²×C₄	—	5	1	no	—
257	C₂²×C₄	—	5	1	no	—
258	C₂²×C₄	—	5	2	no	—
259	C₂²×C₄	—	5	4	no	—
260	C₂²×C₄	—	5	4	no	—
261	C₂²×C₄	—	5	1	no	—
262	C₂²×C₄	—	5	1	no	—
263	C₂²×C₄	—	5	2	no	—
264	C₂²×C₄	—	5	2	no	—
265	C₂²×C₄	—	5	2	no	—
266	C₂²×C₄	—	5	2	no	—
267	C₂²×C₄	—	10	8	no	—
268	C₂²×C₄	D₅⋊C₈	1	2	yes	—
269	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
270	C₂×C₈	—	5	4	no	—
271	C₂×C₈	—	5	4	no	—
272	C₂×C₈	—	5	1	no	—
273	C₂×C₈	—	5	1	no	—
274	C₂×C₈	—	5	1	no	—
275	C₂×C₈	—	5	1	no	—
276	C₂×C₈	—	5	4	no	—
277	C₂×C₈	—	5	4	no	—
278	C₂×C₈	—	5	4	no	—
279	C₂×C₈	—	5	4	no	—
280	C₂×C₈	—	5	4	no	—
281	C₂×C₈	—	5	4	no	—
282	C₂×C₈	—	5	4	no	—
283	C₂×C₈	—	5	4	no	—
284	C₂×C₈	D₅⋊C₈	1	4	yes	—
285	C₂×C₈	C₄×AGL(1,𝔽₅)	1	4	yes	—
286	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₄²	—	5	2	no	—
291	C₄²	—	5	2	no	—
292	C₄²	—	5	2	no	—
293	C₄²	—	5	2	no	—
294	C₄²	—	5	2	no	—
295	C₄²	—	5	1	no	—
296	C₄²	—	5	1	no	—
297	C₄²	D₅⋊C₈	1	2	yes	—
298	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
299	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₁₆	—	5	16	no	—
301	C₂×C₅	—	2	2	no	—
302	C₂×C₅	C₂²×C₄×C₈	1	1	yes	characteristic
303	C₂×C₅	C₂²×M₃₂	1	2	yes	—
304	D₅	—	2	2	no	—
305	D₅	C₄×M₃₂	1	4	yes	complemented
306	C₂³	—	5	1	no	—
307	C₂³	—	5	4	no	—
308	C₂³	—	5	1	no	—
309	C₂³	—	10	4	no	—
310	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	5	4	no	—
313	C₂×C₄	—	5	2	no	—
314	C₂×C₄	—	5	1	no	—
315	C₂×C₄	—	5	1	no	—
316	C₂×C₄	—	5	4	no	—
317	C₂×C₄	—	5	4	no	—
318	C₂×C₄	—	5	8	no	—
319	C₂×C₄	—	5	2	no	—
320	C₂×C₄	—	5	2	no	—
321	C₂×C₄	—	5	2	no	—
322	C₂×C₄	—	5	2	no	—
323	C₂×C₄	—	5	2	no	—
324	C₂×C₄	—	10	4	no	—
325	C₂×C₄	—	10	4	no	—
326	C₂×C₄	—	10	4	no	—
327	C₂×C₄	—	10	4	no	—
328	C₂×C₄	C₂×D₅⋊C₈	1	2	yes	—
329	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
330	C₂×C₄	C₂×D₅⋊C₈	1	2	yes	—
331	C₂×C₄	C₂×D₅⋊C₈	1	2	yes	—
332	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
333	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₈	—	5	2	no	—
335	C₈	—	5	2	no	—
336	C₈	—	5	2	no	—
337	C₈	—	5	2	no	—
338	C₈	C₂×D₅⋊C₈	1	2	yes	—
339	C₈	C₂×D₅⋊C₈	1	2	yes	—
340	C₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
341	C₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
342	C₅	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	2	2	no	—
344	C₂²	—	5	4	no	—
345	C₂²	—	5	2	no	—
346	C₂²	—	5	2	no	—
347	C₂²	—	10	8	no	—
348	C₂²	—	10	2	no	—
349	C₂²	C₄×D₅⋊C₈	1	2	yes	—
350	C₂²	C₂²×D₅⋊C₈	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	5	4	no	—
353	C₄	—	5	2	no	—
354	C₄	—	5	2	no	—
355	C₄	—	10	2	no	—
356	C₄	C₄×D₅⋊C₈	1	2	yes	—
357	C₄	D₅⋊M₃₂	1	4	yes	direct product factor
358	C₄	C₂²×D₅⋊C₈	1	1	yes	characteristic
359	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	5	4	no	—
362	C₂	—	10	2	no	—
363	C₂	C₂×C₄×D₅⋊C₈	1	1	yes	characteristic
364	C₂	C₂×D₅⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₈	C₄
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂³×D₅	C₂×C₈
cosocle	C₂×#168	C₂⁴
hypercenter	C₂×C₄×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #10604702	C₂	semidirect
4. C₄×#3998	C₂	semidirect
5. #10603825	C₂	semidirect
6. C₄×#3990	C₂	semidirect
7. #10603823	C₂	semidirect
8. C₄×D₅⋊C₁₆	C₂	semidirect
13. D₅⋊M₃₂	C₄	direct (N × H)
28. #64886	C₂²	semidirect
29. #64885	C₂²	semidirect
30. #64859	C₂²	semidirect
31. C₄×#674	C₂²	semidirect
58. #3998	C₂×C₄	semidirect
60. #3990	C₂×C₄	semidirect
61. D₅⋊C₁₆	C₂×C₄	semidirect
132. #674	C₂²×C₄	semidirect
179. C₄×D₅	M₃₂	semidirect
247. C₄×C₅	C₂×M₃₂	semidirect
253. Dic₅	C₂×M₃₂	semidirect
305. D₅	C₄×M₃₂	semidirect
342. C₅	C₂×C₄×M₃₂	semidirect
357. C₄	D₅⋊M₃₂	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×D₅⋊M₃₂	2
C₂×C₄×C₈×D₅	2
#10604702	2
C₄×#3998	2
#10603825	2
C₄×#3990	2
#10603823	2
C₄×D₅⋊C₁₆	2
C₂×C₄×M₃₂	5

Subgroups — C4×D5⋊M32 #13043099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅⋊M₃₂ #13043099