Subgroups — C₂²×Q₈×D₂₅ #13099689

Order 1600.

1275 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈×D₂₅	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₄×D₂₅	C₂	1	3	yes	maximal
4	C₂²×Dic₅₀	C₂	1	3	yes	maximal, complemented
5	C₂³×D₂₅	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₂₅	C₂²	1	12	yes	complemented
7	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
8	C₂²×Dic₂₅	C₂²	1	3	yes	—
9	Q₈×D₂₅	C₂²	1	64	yes	direct product factor
10	C₂×C₄×D₂₅	C₂²	1	36	yes	—
11	C₂×Dic₅₀	C₂²	1	36	yes	complemented
12	C₂²×Q₈×D₅	—	5	1	no	maximal
13	C₂³×C₂₅	C₂³	1	1	yes	characteristic
14	C₂²×D₂₅	Q₈	1	8	yes	direct product factor
15	C₂²×D₂₅	C₂³	1	6	yes	—
16	Q₈×C₂₅	C₂³	1	16	yes	complemented
17	C₂×C₄×C₂₅	C₂³	1	18	yes	—
18	C₂×Dic₂₅	C₂³	1	18	yes	—
19	C₄×D₂₅	C₂³	1	48	yes	—
20	Dic₅₀	C₂³	1	48	yes	complemented
21	C₂²×C₅×Q₈	D₅	1	1	yes	characteristic
22	C₂×Q₈×D₅	—	5	24	no	—
23	C₂²×C₄×D₅	—	5	3	no	—
24	C₂²×Dic₁₀	—	5	3	no	—
25	C₂²×C₂₅	C₂×Q₈	1	4	yes	complemented
26	C₂²×C₂₅	C₂⁴	1	3	yes	—
27	C₂×D₂₅	C₂×Q₈	1	24	yes	direct product factor
28	C₂×D₂₅	C₂⁴	1	4	yes	—
29	C₄×C₂₅	C₂⁴	1	12	yes	—
30	Dic₂₅	C₂⁴	1	12	yes	—
31	C₂³×D₅	—	5	1	no	—
32	C₂×C₅×Q₈	C₂×D₅	1	12	yes	—
33	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
34	C₂²×Dic₅	—	5	3	no	—
35	Q₈×D₅	—	5	64	no	—
36	C₂×C₄×D₅	—	5	36	no	—
37	C₂×Dic₁₀	—	5	36	no	—
38	C₂³×Q₈	—	25	1	no	Sylow
39	C₂×C₂₅	C₂²×Q₈	1	6	yes	complemented
40	C₂×C₂₅	C₂⁵	1	1	yes	characteristic
41	D₂₅	C₂²×Q₈	1	8	yes	direct product factor
42	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
43	C₂²×D₅	—	5	8	no	—
44	C₂²×D₅	—	5	6	no	—
45	C₅×Q₈	C₂²×D₅	1	16	yes	—
46	C₂×C₄×C₅	C₂²×D₅	1	18	yes	—
47	C₂×Dic₅	—	5	18	no	—
48	C₄×D₅	—	5	48	no	—
49	Dic₁₀	—	5	48	no	—
50	C₂²×Q₈	—	25	24	no	—
51	C₂²×Q₈	—	25	3	no	—
52	C₂²×Q₈	D₂₅	1	1	yes	characteristic, direct product factor
53	C₂³×C₄	—	25	3	no	—
54	C₂₅	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	Q₈×D₅	1	4	yes	—
56	C₂²×C₅	C₂³×D₅	1	3	yes	—
57	C₂×D₅	—	5	24	no	—
58	C₂×D₅	—	5	4	no	—
59	C₄×C₅	C₂³×D₅	1	12	yes	—
60	Dic₅	—	5	12	no	—
61	C₂⁴	—	25	1	no	—
62	C₂×Q₈	—	25	64	no	—
63	C₂×Q₈	—	25	36	no	—
64	C₂×Q₈	C₂×D₂₅	1	12	yes	direct product factor
65	C₂²×C₄	—	25	3	no	—
66	C₂²×C₄	—	25	36	no	—
67	C₂²×C₄	C₂×D₂₅	1	3	yes	—
68	C₂×C₅	C₂×Q₈×D₅	1	6	yes	—
69	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
70	D₅	—	5	8	no	—
71	C₂³	—	25	8	no	—
72	C₂³	—	25	6	no	—
73	C₂³	C₂²×D₂₅	1	1	yes	characteristic
74	Q₈	—	25	48	no	—
75	Q₈	C₂²×D₂₅	1	16	yes	direct product factor
76	C₂×C₄	—	25	18	no	—
77	C₂×C₄	—	25	48	no	—
78	C₂×C₄	C₂²×D₂₅	1	18	yes	—
79	C₅	C₂²×Q₈×D₅	1	1	yes	characteristic
80	C₂²	—	25	4	no	—
81	C₂²	—	25	24	no	—
82	C₂²	Q₈×D₂₅	1	4	yes	direct product factor
83	C₂²	C₂³×D₂₅	1	3	yes	—
84	C₄	—	25	12	no	—
85	C₄	C₂³×D₂₅	1	12	yes	—
86	C₂	—	25	8	no	—
87	C₂	C₂×Q₈×D₂₅	1	6	yes	direct product factor
88	C₂	C₂⁴×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂×C₂₅	C₂⁵
Frattini	C₂×C₅	C₂⁴×D₅
Fitting	C₂²×Q₈×C₂₅	C₂
socle	C₂³×C₅	C₂²×D₅
prime radical	C₂³×D₂₅	C₂²
hypercenter	C₂²×Q₈	D₂₅
hypocenter	C₂₅	C₂³×Q₈
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₂₅	C₂	semidirect
2. C₂×Q₈×D₂₅	C₂	direct (N × H)
4. C₂²×Dic₅₀	C₂	semidirect
6. C₂×Q₈×C₂₅	C₂²	semidirect
9. Q₈×D₂₅	C₂²	direct (N × H)
11. C₂×Dic₅₀	C₂²	semidirect
14. C₂²×D₂₅	Q₈	direct (N × H)
16. Q₈×C₂₅	C₂³	semidirect
20. Dic₅₀	C₂³	semidirect
25. C₂²×C₂₅	C₂×Q₈	semidirect
27. C₂×D₂₅	C₂×Q₈	direct (N × H)
39. C₂×C₂₅	C₂²×Q₈	semidirect
41. D₂₅	C₂²×Q₈	direct (N × H)
52. C₂²×Q₈	D₂₅	direct (N × H)
54. C₂₅	C₂³×Q₈	semidirect
64. C₂×Q₈	C₂×D₂₅	direct (N × H)
75. Q₈	C₂²×D₂₅	direct (N × H)
82. C₂²	Q₈×D₂₅	direct (N × H)
87. C₂	C₂×Q₈×D₂₅	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×Q₈×C₂₅	2
C₂×Q₈×D₂₅	2
C₂²×C₄×D₂₅	2
C₂²×Dic₅₀	2
C₂²×Q₈×D₅	5

Subgroups — C22×Q8×D25 #13099689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×D₂₅ #13099689