Subgroups — C₂²×D₅×C₂²⋊D₅ #13107852

Order 1600.

2960 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅×C₂²⋊D₅	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#6038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6037	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₅²	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₅⋊D₅	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₅×D₅	—	2	8	no	—
12	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic
13	C₂³×C₅×D₅	C₂²	1	12	yes	complemented
14	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₅²	—	2	8	no	—
17	C₂²×D₅²	C₂²	1	12	yes	complemented
18	C₂×C₂²⋊(C₅⋊D₅)	C₂²	1	12	yes	complemented
19	C₂²×#1039	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×C₂²⋊D₅	C₂²	1	12	yes	complemented
21	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
22	D₅×C₂²⋊D₅	C₂²	1	64	yes	direct product factor
23	C₂×#6038	C₂²	1	12	yes	complemented
24	C₂×#6037	C₂²	1	12	yes	complemented
25	C₂×D₅×Dic₅	C₂²	1	12	yes	complemented
26	C₂³×C₂²⋊D₅	—	5	1	no	maximal
27	C₂²×D₄×D₅	—	5	1	no	maximal
28	C₂³×C₅²	—	2	4	no	—
29	C₂³×C₅²	C₂³	1	1	yes	characteristic
30	C₂³×C₅²	C₂³	1	6	yes	complemented
31	C₂²×C₅⋊D₅	—	2	4	no	—
32	C₂²×C₅⋊D₅	C₂³	1	6	yes	complemented
33	C₂²×C₅×D₅	—	2	4	no	—
34	C₂²×C₅×D₅	—	2	4	no	—
35	C₂²×C₅×D₅	—	2	48	no	—
36	C₂²×C₅×D₅	D₄	1	8	yes	complemented
37	C₂²×C₅×D₅	C₂³	1	6	yes	—
38	C₂²×C₅×D₅	C₂³	1	16	yes	complemented
39	C₂²×C₅×D₅	C₂³	1	6	yes	complemented
40	C₂²×C₅×D₅	C₂³	1	6	yes	complemented
41	C₂×D₅²	—	2	48	no	—
42	C₂×D₅²	C₂³	1	16	yes	complemented
43	C₂²⋊(C₅⋊D₅)	C₂³	1	16	yes	complemented
44	C₂×#1039	C₂³	1	6	yes	complemented
45	C₅×C₂²⋊D₅	C₂³	1	16	yes	complemented
46	C₂×C₅×Dic₅	C₂³	1	6	yes	complemented
47	#6038	C₂³	1	16	yes	complemented
48	#6037	C₂³	1	16	yes	complemented
49	D₅×Dic₅	C₂³	1	16	yes	complemented
50	C₂⁵×C₅	—	5	1	no	—
51	C₂⁴×D₅	—	5	1	no	—
52	C₂⁴×D₅	—	5	1	no	—
53	C₂⁴×D₅	D₅	1	1	yes	characteristic, complemented
54	C₂²×C₅×D₄	—	5	1	no	—
55	C₂²×C₂²⋊D₅	—	5	1	no	—
56	C₂²×C₂²⋊D₅	—	5	1	no	—
57	C₂²×C₂²⋊D₅	—	5	1	no	—
58	C₂²×C₂²⋊D₅	—	5	1	no	—
59	C₂²×C₂²⋊D₅	—	5	24	no	—
60	C₂²×C₂²⋊D₅	—	5	1	no	—
61	C₂²×C₂²⋊D₅	—	10	2	no	—
62	C₂²×C₂²⋊D₅	D₅	1	1	yes	characteristic, direct product factor
63	C₂³×Dic₅	—	5	1	no	—
64	C₂×D₄×D₅	—	5	24	no	—
65	C₂²×D₂₀	—	5	1	no	—
66	C₂²×C₄×D₅	—	5	1	no	—
67	C₂²×C₅²	—	2	12	no	—
68	C₂²×C₅²	C₂×D₄	1	4	yes	complemented
69	C₂²×C₅²	C₂⁴	1	3	yes	—
70	C₂²×C₅²	C₂⁴	1	4	yes	complemented
71	C₂×C₅⋊D₅	—	2	12	no	—
72	C₂×C₅⋊D₅	C₂⁴	1	4	yes	complemented
73	C₂×C₅×D₅	—	2	32	no	—
74	C₂×C₅×D₅	—	2	12	no	—
75	C₂×C₅×D₅	—	2	12	no	—
76	C₂×C₅×D₅	C₂×D₄	1	24	yes	complemented
77	C₂×C₅×D₅	C₂⁴	1	4	yes	—
78	C₂×C₅×D₅	C₂⁴	1	4	yes	complemented
79	C₂×C₅×D₅	C₂⁴	1	4	yes	complemented
80	D₅²	—	2	32	no	—
81	#1039	C₂⁴	1	4	yes	complemented
82	C₅×Dic₅	C₂⁴	1	4	yes	complemented
83	C₂⁴×C₅	—	2	2	no	—
84	C₂⁴×C₅	—	5	1	no	—
85	C₂⁴×C₅	—	5	1	no	—
86	C₂⁴×C₅	—	5	1	no	—
87	C₂⁴×C₅	—	5	12	no	—
88	C₂⁴×C₅	—	10	8	no	—
89	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic, complemented
91	C₂³×D₅	—	2	8	no	—
92	C₂³×D₅	—	5	1	no	—
93	C₂³×D₅	—	5	1	no	—
94	C₂³×D₅	—	5	12	no	—
95	C₂³×D₅	—	5	12	no	—
96	C₂³×D₅	—	10	2	no	—
97	C₂³×D₅	—	10	8	no	—
98	C₂³×D₅	—	10	8	no	—
99	C₂³×D₅	C₂×D₅	1	1	yes	characteristic
100	C₂³×D₅	C₂×D₅	1	12	yes	complemented
101	C₂³×D₅	C₂×D₅	1	1	yes	characteristic, complemented
102	C₂³×D₅	C₂×D₅	1	1	yes	characteristic, complemented
103	C₂×C₅×D₄	—	5	12	no	—
104	C₂²×C₄×C₅	—	5	1	no	—
105	C₂×C₂²⋊D₅	—	5	12	no	—
106	C₂×C₂²⋊D₅	—	5	12	no	—
107	C₂×C₂²⋊D₅	—	5	12	no	—
108	C₂×C₂²⋊D₅	—	5	12	no	—
109	C₂×C₂²⋊D₅	—	5	64	no	—
110	C₂×C₂²⋊D₅	—	5	12	no	—
111	C₂×C₂²⋊D₅	—	10	24	no	—
112	C₂×C₂²⋊D₅	C₂×D₅	1	12	yes	direct product factor
113	C₂²×Dic₅	—	5	1	no	—
114	C₂²×Dic₅	—	5	1	no	—
115	C₂²×Dic₅	—	5	12	no	—
116	C₂²×Dic₅	—	10	2	no	—
117	C₂²×Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
118	D₄×D₅	—	5	64	no	—
119	C₂×D₂₀	—	5	12	no	—
120	C₂×C₄×D₅	—	5	12	no	—
121	C₂³×D₄	—	25	1	no	Sylow
122	C₂×C₅²	—	2	4	no	—
123	C₂×C₅²	C₂²×D₄	1	6	yes	complemented
124	C₂×C₅²	C₂⁵	1	1	yes	characteristic
125	C₅⋊D₅	—	2	4	no	—
126	C₅×D₅	—	2	4	no	—
127	C₅×D₅	—	2	4	no	—
128	C₅×D₅	C₂²×D₄	1	8	yes	complemented
129	C₂³×C₅	—	2	4	no	—
130	C₂³×C₅	—	2	4	no	—
131	C₂³×C₅	—	2	2	no	—
132	C₂³×C₅	—	2	12	no	—
133	C₂³×C₅	—	4	8	no	—
134	C₂³×C₅	—	5	8	no	—
135	C₂³×C₅	—	5	6	no	—
136	C₂³×C₅	—	5	6	no	—
137	C₂³×C₅	—	5	6	no	—
138	C₂³×C₅	—	5	16	no	—
139	C₂³×C₅	—	10	48	no	—
140	C₂³×C₅	—	10	4	no	—
141	C₂³×C₅	—	10	4	no	—
142	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
143	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
144	C₂³×C₅	C₂²×D₅	1	6	yes	complemented
145	C₂³×C₅	C₂²×D₅	1	6	yes	complemented
146	C₂²×D₅	—	2	4	no	—
147	C₂²×D₅	—	2	4	no	—
148	C₂²×D₅	—	2	48	no	—
149	C₂²×D₅	—	5	6	no	—
150	C₂²×D₅	—	5	6	no	—
151	C₂²×D₅	—	5	16	no	—
152	C₂²×D₅	—	5	16	no	—
153	C₂²×D₅	—	10	12	no	—
154	C₂²×D₅	—	10	48	no	—
155	C₂²×D₅	—	10	4	no	—
156	C₂²×D₅	—	10	4	no	—
157	C₂²×D₅	—	10	48	no	—
158	C₂²×D₅	—	20	8	no	—
159	C₂²×D₅	C₂²⋊D₅	1	8	yes	direct product factor
160	C₂²×D₅	C₂²×D₅	1	6	yes	—
161	C₂²×D₅	C₂²×D₅	1	16	yes	complemented
162	C₂²×D₅	C₂²×D₅	1	6	yes	complemented
163	C₂²×D₅	C₂²×D₅	1	6	yes	complemented
164	C₅×D₄	—	5	16	no	—
165	C₂×C₄×C₅	—	5	6	no	—
166	C₂²⋊D₅	—	5	16	no	—
167	C₂²⋊D₅	—	5	16	no	—
168	C₂²⋊D₅	—	5	16	no	—
169	C₂²⋊D₅	—	5	16	no	—
170	C₂²⋊D₅	—	5	16	no	—
171	C₂²⋊D₅	—	10	32	no	—
172	C₂²⋊D₅	C₂²×D₅	1	16	yes	direct product factor
173	C₂×Dic₅	—	5	6	no	—
174	C₂×Dic₅	—	5	6	no	—
175	C₂×Dic₅	—	5	16	no	—
176	C₂×Dic₅	—	10	12	no	—
177	C₂×Dic₅	C₂²×D₅	1	6	yes	complemented
178	D₂₀	—	5	16	no	—
179	C₄×D₅	—	5	16	no	—
180	C₂⁵	—	5	1	no	—
181	C₂⁵	—	25	1	no	—
182	C₂²×D₄	—	5	1	no	—
183	C₂²×D₄	—	25	1	no	—
184	C₂²×D₄	—	25	24	no	—
185	C₂²×D₄	—	25	1	no	—
186	C₂²×D₄	—	25	1	no	—
187	C₂³×C₄	—	25	1	no	—
188	C₅²	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
189	C₂²×C₅	—	2	12	no	—
190	C₂²×C₅	—	2	12	no	—
191	C₂²×C₅	—	2	8	no	—
192	C₂²×C₅	—	2	6	no	—
193	C₂²×C₅	—	2	8	no	—
194	C₂²×C₅	—	4	24	no	—
195	C₂²×C₅	—	5	24	no	—
196	C₂²×C₅	—	5	4	no	—
197	C₂²×C₅	—	5	4	no	—
198	C₂²×C₅	—	5	4	no	—
199	C₂²×C₅	—	10	32	no	—
200	C₂²×C₅	—	10	12	no	—
201	C₂²×C₅	—	10	12	no	—
202	C₂²×C₅	D₄×D₅	1	4	yes	complemented
203	C₂²×C₅	C₂×C₂²⋊D₅	1	4	yes	complemented
204	C₂²×C₅	C₂³×D₅	1	3	yes	—
205	C₂²×C₅	C₂³×D₅	1	3	yes	—
206	C₂²×C₅	C₂³×D₅	1	4	yes	complemented
207	C₂²×C₅	C₂³×D₅	1	4	yes	complemented
208	C₂×D₅	—	2	12	no	—
209	C₂×D₅	—	2	12	no	—
210	C₂×D₅	—	2	32	no	—
211	C₂×D₅	—	5	4	no	—
212	C₂×D₅	—	5	4	no	—
213	C₂×D₅	—	10	8	no	—
214	C₂×D₅	—	10	32	no	—
215	C₂×D₅	—	10	12	no	—
216	C₂×D₅	—	10	12	no	—
217	C₂×D₅	—	10	32	no	—
218	C₂×D₅	—	20	24	no	—
219	C₂×D₅	C₂×C₂²⋊D₅	1	24	yes	direct product factor
220	C₂×D₅	C₂³×D₅	1	4	yes	—
221	C₂×D₅	C₂³×D₅	1	4	yes	complemented
222	C₂×D₅	C₂³×D₅	1	4	yes	complemented
223	C₄×C₅	—	5	4	no	—
224	Dic₅	—	5	4	no	—
225	Dic₅	—	5	4	no	—
226	Dic₅	—	10	8	no	—
227	Dic₅	C₂³×D₅	1	4	yes	complemented
228	C₂⁴	—	5	1	no	—
229	C₂⁴	—	5	1	no	—
230	C₂⁴	—	5	1	no	—
231	C₂⁴	—	5	12	no	—
232	C₂⁴	—	10	8	no	—
233	C₂⁴	—	25	12	no	—
234	C₂⁴	—	25	1	no	—
235	C₂⁴	—	50	8	no	—
236	C₂⁴	D₅²	1	1	yes	characteristic, complemented
237	C₂×D₄	—	5	12	no	—
238	C₂×D₄	—	25	12	no	—
239	C₂×D₄	—	25	64	no	—
240	C₂×D₄	—	25	12	no	—
241	C₂×D₄	—	25	12	no	—
242	C₂²×C₄	—	5	1	no	—
243	C₂²×C₄	—	25	12	no	—
244	C₂²×C₄	—	25	1	no	—
245	C₂×C₅	—	2	4	no	—
246	C₂×C₅	—	2	4	no	—
247	C₂×C₅	—	2	12	no	—
248	C₂×C₅	—	2	2	no	—
249	C₂×C₅	—	4	8	no	—
250	C₂×C₅	—	5	8	no	—
251	C₂×C₅	—	10	4	no	—
252	C₂×C₅	—	10	4	no	—
253	C₂×C₅	C₂×D₄×D₅	1	6	yes	complemented
254	C₂×C₅	C₂²×C₂²⋊D₅	1	6	yes	complemented
255	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
256	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
257	D₅	—	2	4	no	—
258	D₅	—	2	4	no	—
259	D₅	—	10	4	no	—
260	D₅	—	10	4	no	—
261	D₅	—	20	8	no	—
262	D₅	C₂²×C₂²⋊D₅	1	8	yes	direct product factor
263	C₂³	—	2	4	no	—
264	C₂³	—	5	8	no	—
265	C₂³	—	5	6	no	—
266	C₂³	—	5	6	no	—
267	C₂³	—	5	6	no	—
268	C₂³	—	5	16	no	—
269	C₂³	—	10	48	no	—
270	C₂³	—	10	4	no	—
271	C₂³	—	10	4	no	—
272	C₂³	—	25	16	no	—
273	C₂³	—	25	6	no	—
274	C₂³	—	50	48	no	—
275	C₂³	—	50	4	no	—
276	C₂³	C₂×D₅²	1	1	yes	characteristic
277	C₂³	C₂×D₅²	1	6	yes	complemented
278	D₄	—	5	16	no	—
279	D₄	—	25	16	no	—
280	D₄	—	25	16	no	—
281	D₄	—	25	16	no	—
282	C₂×C₄	—	5	6	no	—
283	C₂×C₄	—	25	16	no	—
284	C₂×C₄	—	25	6	no	—
285	C₅	—	2	2	no	—
286	C₅	C₂²×D₄×D₅	1	1	yes	characteristic, complemented
287	C₅	C₂³×C₂²⋊D₅	1	1	yes	characteristic, complemented
288	C₂²	—	2	12	no	—
289	C₂²	—	5	24	no	—
290	C₂²	—	5	4	no	—
291	C₂²	—	5	4	no	—
292	C₂²	—	5	4	no	—
293	C₂²	—	10	32	no	—
294	C₂²	—	10	12	no	—
295	C₂²	—	10	12	no	—
296	C₂²	—	25	4	no	—
297	C₂²	—	50	32	no	—
298	C₂²	—	50	12	no	—
299	C₂²	D₅×C₂²⋊D₅	1	4	yes	direct product factor
300	C₂²	C₂²×D₅²	1	3	yes	—
301	C₂²	C₂²×D₅²	1	4	yes	complemented
302	C₄	—	5	4	no	—
303	C₄	—	25	4	no	—
304	C₂	—	2	4	no	—
305	C₂	—	5	8	no	—
306	C₂	—	10	4	no	—
307	C₂	—	10	4	no	—
308	C₂	—	50	4	no	—
309	C₂	C₂×D₅×C₂²⋊D₅	1	6	yes	direct product factor
310	C₂	C₂³×D₅²	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₅²
commutator, cosocle	C₂×C₅²	C₂⁵
Frattini	C₂	C₂³×D₅²
Fitting	C₂⁴×C₅²	C₂²
socle	C₂³×C₅²	C₂³
hypercenter	C₂⁴	D₅²
hypocenter	C₅²	C₂³×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×D₅	C₂	semidirect
2. C₂³×D₅²	C₂	semidirect
3. C₂²×C₂²⋊(C₅⋊D₅)	C₂	semidirect
4. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
5. C₂×D₅×C₂²⋊D₅	C₂	direct (N × H)
6. C₂²×#6038	C₂	semidirect
7. C₂²×#6037	C₂	semidirect
8. C₂²×D₅×Dic₅	C₂	semidirect
9. C₂⁴×C₅²	C₂²	semidirect
10. C₂³×C₅⋊D₅	C₂²	semidirect
13. C₂³×C₅×D₅	C₂²	semidirect
14. C₂³×C₅×D₅	C₂²	semidirect
15. C₂³×C₅×D₅	C₂²	semidirect
17. C₂²×D₅²	C₂²	semidirect
18. C₂×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
19. C₂²×#1039	C₂²	semidirect
20. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₂²×C₅×Dic₅	C₂²	semidirect
22. D₅×C₂²⋊D₅	C₂²	direct (N × H)
23. C₂×#6038	C₂²	semidirect
24. C₂×#6037	C₂²	semidirect
25. C₂×D₅×Dic₅	C₂²	semidirect
30. C₂³×C₅²	C₂³	semidirect
32. C₂²×C₅⋊D₅	C₂³	semidirect
36. C₂²×C₅×D₅	D₄	semidirect
38. C₂²×C₅×D₅	C₂³	semidirect
39. C₂²×C₅×D₅	C₂³	semidirect
40. C₂²×C₅×D₅	C₂³	semidirect
42. C₂×D₅²	C₂³	semidirect
43. C₂²⋊(C₅⋊D₅)	C₂³	semidirect
44. C₂×#1039	C₂³	semidirect
45. C₅×C₂²⋊D₅	C₂³	semidirect
46. C₂×C₅×Dic₅	C₂³	semidirect
47. #6038	C₂³	semidirect
48. #6037	C₂³	semidirect
49. D₅×Dic₅	C₂³	semidirect
53. C₂⁴×D₅	D₅	semidirect
62. C₂²×C₂²⋊D₅	D₅	direct (N × H)
68. C₂²×C₅²	C₂×D₄	semidirect
70. C₂²×C₅²	C₂⁴	semidirect
72. C₂×C₅⋊D₅	C₂⁴	semidirect
76. C₂×C₅×D₅	C₂×D₄	semidirect
78. C₂×C₅×D₅	C₂⁴	semidirect
79. C₂×C₅×D₅	C₂⁴	semidirect
81. #1039	C₂⁴	semidirect
82. C₅×Dic₅	C₂⁴	semidirect
89. C₂⁴×C₅	C₂×D₅	semidirect
90. C₂⁴×C₅	C₂×D₅	semidirect
100. C₂³×D₅	C₂×D₅	semidirect
101. C₂³×D₅	C₂×D₅	semidirect
102. C₂³×D₅	C₂×D₅	semidirect
112. C₂×C₂²⋊D₅	C₂×D₅	direct (N × H)
117. C₂²×Dic₅	C₂×D₅	semidirect
123. C₂×C₅²	C₂²×D₄	semidirect
128. C₅×D₅	C₂²×D₄	semidirect
144. C₂³×C₅	C₂²×D₅	semidirect
145. C₂³×C₅	C₂²×D₅	semidirect
159. C₂²×D₅	C₂²⋊D₅	direct (N × H)
161. C₂²×D₅	C₂²×D₅	semidirect
162. C₂²×D₅	C₂²×D₅	semidirect
163. C₂²×D₅	C₂²×D₅	semidirect
172. C₂²⋊D₅	C₂²×D₅	direct (N × H)
177. C₂×Dic₅	C₂²×D₅	semidirect
188. C₅²	C₂³×D₄	semidirect
202. C₂²×C₅	D₄×D₅	semidirect
203. C₂²×C₅	C₂×C₂²⋊D₅	semidirect
206. C₂²×C₅	C₂³×D₅	semidirect
207. C₂²×C₅	C₂³×D₅	semidirect
219. C₂×D₅	C₂×C₂²⋊D₅	direct (N × H)
221. C₂×D₅	C₂³×D₅	semidirect
222. C₂×D₅	C₂³×D₅	semidirect
227. Dic₅	C₂³×D₅	semidirect
236. C₂⁴	D₅²	semidirect
253. C₂×C₅	C₂×D₄×D₅	semidirect
254. C₂×C₅	C₂²×C₂²⋊D₅	semidirect
262. D₅	C₂²×C₂²⋊D₅	direct (N × H)
277. C₂³	C₂×D₅²	semidirect
286. C₅	C₂²×D₄×D₅	semidirect
287. C₅	C₂³×C₂²⋊D₅	semidirect
299. C₂²	D₅×C₂²⋊D₅	direct (N × H)
301. C₂²	C₂²×D₅²	semidirect
309. C₂	C₂×D₅×C₂²⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×D₅	2
C₂³×D₅²	2
C₂²×C₂²⋊(C₅⋊D₅)	2
C₂²×C₅×C₂²⋊D₅	2
C₂×D₅×C₂²⋊D₅	2
C₂²×#6038	2
C₂²×#6037	2
C₂²×D₅×Dic₅	2
C₂³×C₂²⋊D₅	5
C₂²×D₄×D₅	5

Subgroups — C22×D5×C22⋊D5 #13107852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₅×C₂²⋊D₅ #13107852