Subgroups — C₂×AGL(1,𝔽₅)×M₃₂ #13043097

Order 1280.

918 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic
4	AGL(1,𝔽₅)×M₃₂	C₂	1	8	yes	maximal, direct product factor
5	C₂×#64844	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₆×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×AGL(1,𝔽₅)	C₄	1	1	yes	characteristic
8	C₂²×D₅⋊C₈	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
10	C₂×#3998	C₄	1	2	yes	complemented
11	C₂×C₈×AGL(1,𝔽₅)	C₄	1	1	yes	characteristic
12	C₂×C₈×AGL(1,𝔽₅)	C₄	1	1	yes	characteristic
13	C₂×C₈×AGL(1,𝔽₅)	C₄	1	4	yes	—
14	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
16	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	4	yes	—
17	D₅⋊M₃₂	C₄	1	4	yes	complemented
18	D₅⋊M₃₂	C₂²	1	4	yes	—
19	C₂×#3990	C₄	1	2	yes	complemented
20	C₂×D₅⋊C₁₆	C₂²	1	2	yes	—
21	C₂×C₅×M₃₂	C₄	1	1	yes	characteristic, complemented
22	C₂×#3944	C₄	1	1	yes	characteristic, complemented
23	D₅×M₃₂	C₄	1	4	yes	complemented
24	D₅×M₃₂	C₂²	1	4	yes	—
25	C₂×#3930	C₄	1	2	yes	complemented
26	C₂×D₅×C₁₆	C₂²	1	2	yes	—
27	#64844	C₂²	1	8	yes	complemented
28	C₁₆×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
29	C₂×C₄×M₃₂	—	5	1	no	maximal, Sylow
30	C₂³×AGL(1,𝔽₅)	C₈	1	2	yes	—
31	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×#170	C₈	1	2	yes	—
33	C₂×C₄×AGL(1,𝔽₅)	C₈	1	4	yes	—
34	C₂×C₄×AGL(1,𝔽₅)	C₈	1	2	yes	—
35	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
37	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	1	yes	characteristic
38	C₂×D₅⋊C₈	C₈	1	2	yes	—
39	C₂×D₅⋊C₈	C₈	1	4	yes	—
40	C₂×D₅⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×D₅⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×D₅⋊C₈	C₂×C₄	1	4	yes	—
43	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×#168	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅	C₂×C₄	1	2	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	2	yes	—
49	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
51	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₅	C₂³	1	2	yes	—
53	#3998	C₂×C₄	1	8	yes	complemented
54	C₂×#674	C₂×C₄	1	4	yes	complemented
55	C₈×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
56	C₈×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
57	C₈×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
58	C₈×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
59	C₈×AGL(1,𝔽₅)	C₂³	1	2	yes	—
60	C₈×AGL(1,𝔽₅)	C₂³	1	2	yes	—
61	#3990	C₂×C₄	1	8	yes	complemented
62	D₅⋊C₁₆	C₂×C₄	1	4	yes	complemented
63	D₅⋊C₁₆	C₂³	1	4	yes	—
64	C₅×M₃₂	C₂×C₄	1	4	yes	complemented
65	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	complemented
66	#3944	C₂×C₄	1	4	yes	complemented
67	C₂×#672	C₂×C₄	1	2	yes	complemented
68	#3930	C₂×C₄	1	8	yes	complemented
69	D₅×C₁₆	C₂×C₄	1	4	yes	complemented
70	D₅×C₁₆	C₂³	1	4	yes	—
71	C₂²×M₃₂	—	5	1	no	—
72	C₂²×M₃₂	—	5	1	no	—
73	C₂²×C₄×C₈	—	5	1	no	—
74	C₄×M₃₂	—	5	8	no	—
75	C₂×#346	—	5	2	no	—
76	C₂×C₄×C₁₆	—	5	2	no	—
77	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
78	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
79	C₂²×AGL(1,𝔽₅)	C₂×C₈	1	2	yes	—
80	C₂²×AGL(1,𝔽₅)	C₂×C₈	1	8	yes	—
81	C₂²×AGL(1,𝔽₅)	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
83	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
84	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
85	C₂×C₄×D₅	C₄²	1	2	yes	—
86	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
90	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
91	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×#170	C₂×C₈	1	8	yes	—
93	C₂×#170	C₂×C₈	1	2	yes	—
94	C₂×#170	C₂×C₈	1	2	yes	—
95	C₄×AGL(1,𝔽₅)	C₂×C₈	1	2	yes	—
96	C₄×AGL(1,𝔽₅)	C₂×C₈	1	8	yes	—
97	C₄×AGL(1,𝔽₅)	C₂×C₈	1	2	yes	—
98	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
99	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
100	D₅⋊C₈	C₂×C₈	1	8	yes	—
101	D₅⋊C₈	C₂×C₈	1	2	yes	—
102	D₅⋊C₈	C₂×C₈	1	2	yes	—
103	D₅⋊C₈	C₂²×C₄	1	2	yes	—
104	D₅⋊C₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
106	C₂×C₅×C₈	C₄²	1	2	yes	—
107	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×#168	C₄²	1	1	yes	characteristic
110	C₂×#168	C₄²	1	2	yes	—
111	C₂×#168	C₂²×C₄	1	1	yes	characteristic
112	C₂×#168	C₂²×C₄	1	2	yes	—
113	C₈×D₅	C₄²	1	2	yes	—
114	C₈×D₅	C₄²	1	2	yes	—
115	C₈×D₅	C₄²	1	2	yes	—
116	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₈×D₅	C₂²×C₄	1	2	yes	—
118	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
119	C₈×D₅	C₂²×C₄	1	2	yes	—
120	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₅	C₂²×C₄	1	2	yes	—
122	C₈×D₅	C₂⁴	1	1	yes	characteristic
123	#674	C₂²×C₄	1	8	yes	complemented
124	C₅×C₁₆	C₂²×C₄	1	4	yes	complemented
125	#672	C₂²×C₄	1	4	yes	complemented
126	C₂³×C₈	—	5	1	no	—
127	C₂³×C₈	—	5	1	no	—
128	C₂²×C₄²	—	5	1	no	—
129	C₂×M₃₂	—	5	4	no	—
130	C₂×M₃₂	—	5	2	no	—
131	C₂×M₃₂	—	5	4	no	—
132	C₂×M₃₂	—	5	2	no	—
133	C₂×M₃₂	—	5	1	no	—
134	C₂×M₃₂	—	5	4	no	—
135	C₂×M₃₂	—	5	4	no	—
136	C₂×M₃₂	—	5	2	no	—
137	C₂×M₃₂	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
138	C₂²×C₁₆	—	5	2	no	—
139	C₂²×C₁₆	—	5	2	no	—
140	C₂×C₄×C₈	—	5	1	no	—
141	C₂×C₄×C₈	—	5	1	no	—
142	C₂×C₄×C₈	—	5	4	no	—
143	C₂×C₄×C₈	—	5	4	no	—
144	C₂×C₄×C₈	—	5	1	no	—
145	C₂×C₄×C₈	—	5	1	no	—
146	#346	—	5	8	no	—
147	C₄×C₁₆	—	5	8	no	—
148	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
149	C₂²×D₅	—	2	4	no	—
150	C₂²×D₅	C₄×C₈	1	1	yes	characteristic
151	C₂²×D₅	C₄×C₈	1	2	yes	—
152	C₂²×D₅	C₂²×C₈	1	2	yes	—
153	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
154	C₂×AGL(1,𝔽₅)	—	2	4	no	—
155	C₂×AGL(1,𝔽₅)	—	2	16	no	—
156	C₂×AGL(1,𝔽₅)	M₃₂	1	8	yes	direct product factor
157	C₂×AGL(1,𝔽₅)	C₂²×C₈	1	4	yes	—
158	C₂×AGL(1,𝔽₅)	C₂²×C₈	1	4	yes	—
159	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
160	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
162	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₅	C₄×C₈	1	2	yes	—
164	C₂×Dic₅	C₄×C₈	1	1	yes	characteristic
165	C₂×Dic₅	C₂²×C₈	1	2	yes	—
166	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
167	C₄×D₅	C₄×C₈	1	2	yes	—
168	C₄×D₅	C₄×C₈	1	2	yes	—
169	C₄×D₅	C₄×C₈	1	2	yes	—
170	C₄×D₅	C₂×C₄²	1	2	yes	—
171	C₄×D₅	C₂×C₄²	1	1	yes	characteristic
172	C₄×D₅	C₂²×C₈	1	2	yes	—
173	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
174	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
175	C₄×D₅	C₂²×C₈	1	2	yes	—
176	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
177	#170	C₂²×C₈	1	4	yes	—
178	#170	C₂²×C₈	1	4	yes	—
179	C₅×C₈	C₂×C₄²	1	2	yes	—
180	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
181	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
182	#168	C₂×C₄²	1	1	yes	characteristic
183	#168	C₂×C₄²	1	2	yes	—
184	#168	C₂³×C₄	1	1	yes	characteristic
185	C₂³×C₄	—	5	1	no	—
186	C₂³×C₄	—	5	2	no	—
187	C₂²×C₈	—	5	4	no	—
188	C₂²×C₈	—	5	2	no	—
189	C₂²×C₈	—	5	1	no	—
190	C₂²×C₈	—	5	1	no	—
191	C₂²×C₈	—	5	4	no	—
192	C₂²×C₈	—	5	2	no	—
193	C₂²×C₈	—	5	1	no	—
194	C₂²×C₈	—	5	2	no	—
195	C₂²×C₈	—	5	1	no	—
196	C₂²×C₈	—	5	1	no	—
197	C₂²×C₈	—	5	2	no	—
198	C₂²×C₈	—	5	2	no	—
199	C₂²×C₈	—	5	2	no	—
200	C₂²×C₈	—	5	1	no	—
201	C₂²×C₈	—	5	1	no	—
202	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
203	C₂×C₄²	—	5	2	no	—
204	C₂×C₄²	—	5	4	no	—
205	C₂×C₄²	—	5	1	no	—
206	C₂×C₄²	—	5	1	no	—
207	C₂×C₄²	—	5	4	no	—
208	M₃₂	—	5	8	no	—
209	M₃₂	—	5	8	no	—
210	M₃₂	—	5	4	no	—
211	M₃₂	—	5	8	no	—
212	M₃₂	C₂×AGL(1,𝔽₅)	1	4	yes	direct product factor
213	C₂×C₁₆	—	5	4	no	—
214	C₂×C₁₆	—	5	4	no	—
215	C₂×C₁₆	—	5	4	no	—
216	C₂×C₁₆	—	5	2	no	—
217	C₂×C₁₆	—	5	4	no	—
218	C₂×C₁₆	—	5	4	no	—
219	C₂×C₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
220	C₄×C₈	—	5	2	no	—
221	C₄×C₈	—	5	2	no	—
222	C₄×C₈	—	5	2	no	—
223	C₄×C₈	—	5	2	no	—
224	C₄×C₈	—	5	4	no	—
225	C₄×C₈	—	5	4	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	C₂×C₄×C₈	1	2	yes	—
228	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
229	C₂×D₅	—	2	2	no	—
230	C₂×D₅	—	2	4	no	—
231	C₂×D₅	—	2	4	no	—
232	C₂×D₅	C₂×C₄×C₈	1	2	yes	—
233	C₂×D₅	C₂×C₄×C₈	1	1	yes	characteristic
234	C₂×D₅	C₂×M₃₂	1	4	yes	—
235	C₂×D₅	C₂³×C₈	1	1	yes	characteristic
236	AGL(1,𝔽₅)	—	2	4	no	—
237	AGL(1,𝔽₅)	C₂×M₃₂	1	8	yes	direct product factor
238	C₄×C₅	C₂×C₄×C₈	1	2	yes	—
239	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
240	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
241	Dic₅	C₂×C₄×C₈	1	1	yes	characteristic
242	Dic₅	C₂×C₄×C₈	1	2	yes	—
243	Dic₅	C₂³×C₈	1	1	yes	characteristic
244	C₂⁴	—	5	1	no	—
245	C₂²×C₄	—	5	2	no	—
246	C₂²×C₄	—	5	1	no	—
247	C₂²×C₄	—	5	2	no	—
248	C₂²×C₄	—	5	1	no	—
249	C₂²×C₄	—	5	2	no	—
250	C₂²×C₄	—	5	1	no	—
251	C₂²×C₄	—	5	1	no	—
252	C₂²×C₄	—	5	2	no	—
253	C₂²×C₄	—	5	2	no	—
254	C₂²×C₄	—	5	1	no	—
255	C₂²×C₄	—	5	8	no	—
256	C₂²×C₄	—	5	2	no	—
257	C₂²×C₄	—	10	8	no	—
258	C₂²×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₂×C₈	—	5	2	no	—
260	C₂×C₈	—	5	2	no	—
261	C₂×C₈	—	5	2	no	—
262	C₂×C₈	—	5	2	no	—
263	C₂×C₈	—	5	8	no	—
264	C₂×C₈	—	5	8	no	—
265	C₂×C₈	—	5	2	no	—
266	C₂×C₈	—	5	2	no	—
267	C₂×C₈	—	5	1	no	—
268	C₂×C₈	—	5	2	no	—
269	C₂×C₈	—	5	2	no	—
270	C₂×C₈	—	5	1	no	—
271	C₂×C₈	—	5	2	no	—
272	C₂×C₈	—	5	1	no	—
273	C₂×C₈	—	5	1	no	—
274	C₂×C₈	—	5	2	no	—
275	C₂×C₈	—	5	2	no	—
276	C₂×C₈	—	5	2	no	—
277	C₂×C₈	—	5	2	no	—
278	C₂×C₈	—	5	1	no	—
279	C₂×C₈	—	5	1	no	—
280	C₂×C₈	—	5	2	no	—
281	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
282	C₂×C₈	C₄×AGL(1,𝔽₅)	1	2	yes	—
283	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
284	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₄²	—	5	2	no	—
286	C₄²	—	5	2	no	—
287	C₄²	—	5	2	no	—
288	C₄²	—	5	8	no	—
289	C₄²	—	5	2	no	—
290	C₁₆	—	5	8	no	—
291	C₁₆	—	5	4	no	—
292	C₁₆	C₂²×AGL(1,𝔽₅)	1	4	yes	complemented
293	C₂×C₅	—	2	2	no	—
294	C₂×C₅	C₄×M₃₂	1	2	yes	complemented
295	C₂×C₅	C₂²×C₄×C₈	1	1	yes	characteristic
296	D₅	—	2	2	no	—
297	D₅	C₄×M₃₂	1	2	yes	complemented
298	D₅	C₂²×M₃₂	1	2	yes	—
299	C₂³	—	5	1	no	—
300	C₂³	—	5	2	no	—
301	C₂³	—	5	2	no	—
302	C₂³	—	5	1	no	—
303	C₂³	—	10	4	no	—
304	C₂³	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
305	C₂×C₄	—	5	4	no	—
306	C₂×C₄	—	5	8	no	—
307	C₂×C₄	—	5	2	no	—
308	C₂×C₄	—	5	1	no	—
309	C₂×C₄	—	5	2	no	—
310	C₂×C₄	—	5	1	no	—
311	C₂×C₄	—	5	2	no	—
312	C₂×C₄	—	5	1	no	—
313	C₂×C₄	—	5	1	no	—
314	C₂×C₄	—	5	2	no	—
315	C₂×C₄	—	5	2	no	—
316	C₂×C₄	—	5	2	no	—
317	C₂×C₄	—	5	2	no	—
318	C₂×C₄	—	5	1	no	—
319	C₂×C₄	—	5	1	no	—
320	C₂×C₄	—	5	2	no	—
321	C₂×C₄	—	5	4	no	—
322	C₂×C₄	—	10	16	no	—
323	C₂×C₄	—	10	4	no	—
324	C₂×C₄	C₈×AGL(1,𝔽₅)	1	2	yes	—
325	C₂×C₄	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
327	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₈	—	5	4	no	—
329	C₈	—	5	4	no	—
330	C₈	—	5	1	no	—
331	C₈	—	5	1	no	—
332	C₈	—	5	2	no	—
333	C₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
334	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₈	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₅	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
337	C₂²	—	2	2	no	—
338	C₂²	—	5	1	no	—
339	C₂²	—	5	1	no	—
340	C₂²	—	5	4	no	—
341	C₂²	—	5	2	no	—
342	C₂²	—	10	4	no	—
343	C₂²	—	10	4	no	—
344	C₂²	—	10	2	no	—
345	C₂²	C₂×C₈×AGL(1,𝔽₅)	1	2	yes	—
346	C₂²	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
347	C₄	—	5	8	no	—
348	C₄	—	5	1	no	—
349	C₄	—	5	2	no	—
350	C₄	—	5	1	no	—
351	C₄	—	10	4	no	—
352	C₄	C₂×C₈×AGL(1,𝔽₅)	1	2	yes	—
353	C₄	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	5	2	no	—
357	C₂	—	5	2	no	—
358	C₂	—	10	2	no	—
359	C₂	AGL(1,𝔽₅)×M₃₂	1	2	yes	direct product factor
360	C₂	C₂²×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. AGL(1,𝔽₅)×M₃₂	C₂	direct (N × H)
5. C₂×#64844	C₂	semidirect
6. C₂×C₁₆×AGL(1,𝔽₅)	C₂	semidirect
10. C₂×#3998	C₄	semidirect
17. D₅⋊M₃₂	C₄	semidirect
19. C₂×#3990	C₄	semidirect
21. C₂×C₅×M₃₂	C₄	semidirect
22. C₂×#3944	C₄	semidirect
23. D₅×M₃₂	C₄	semidirect
25. C₂×#3930	C₄	semidirect
27. #64844	C₂²	semidirect
28. C₁₆×AGL(1,𝔽₅)	C₂²	semidirect
53. #3998	C₂×C₄	semidirect
54. C₂×#674	C₂×C₄	semidirect
61. #3990	C₂×C₄	semidirect
62. D₅⋊C₁₆	C₂×C₄	semidirect
64. C₅×M₃₂	C₂×C₄	semidirect
65. C₂×C₅×C₁₆	C₂×C₄	semidirect
66. #3944	C₂×C₄	semidirect
67. C₂×#672	C₂×C₄	semidirect
68. #3930	C₂×C₄	semidirect
69. D₅×C₁₆	C₂×C₄	semidirect
123. #674	C₂²×C₄	semidirect
124. C₅×C₁₆	C₂²×C₄	semidirect
125. #672	C₂²×C₄	semidirect
137. C₂×M₃₂	AGL(1,𝔽₅)	direct (N × H)
156. C₂×AGL(1,𝔽₅)	M₃₂	direct (N × H)
212. M₃₂	C₂×AGL(1,𝔽₅)	direct (N × H)
219. C₂×C₁₆	C₂×AGL(1,𝔽₅)	semidirect
237. AGL(1,𝔽₅)	C₂×M₃₂	direct (N × H)
292. C₁₆	C₂²×AGL(1,𝔽₅)	semidirect
294. C₂×C₅	C₄×M₃₂	semidirect
297. D₅	C₄×M₃₂	semidirect
336. C₅	C₂×C₄×M₃₂	semidirect
359. C₂	AGL(1,𝔽₅)×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
C₂²×C₈×AGL(1,𝔽₅)	2
C₂×D₅⋊M₃₂	2
C₂×D₅×M₃₂	2
AGL(1,𝔽₅)×M₃₂	2
C₂×#64844	2
C₂×C₁₆×AGL(1,𝔽₅)	2
C₂×C₄×M₃₂	5

Subgroups — C2×AGL(1,𝔽5)×M32 #13043097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×AGL(1,𝔽₅)×M₃₂ #13043097