Subgroups — C₅²×C₂²⋊Dic₅ #14522621

Order 2000.

656 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅²×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅³	—	2	2	no	—
4	C₂²×C₅³	C₄	1	2	yes	complemented
5	C₂²×C₅³	C₂²	1	1	yes	characteristic
6	C₅²×Dic₅	—	2	2	no	—
7	C₅²×C₂²⋊C₄	—	5	1	no	maximal
8	C₅×C₂²⋊Dic₅	C₅	1	6	yes	maximal, direct product factor
9	C₂×C₅³	—	2	2	no	—
10	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅³	D₄	1	2	yes	—
12	C₂³×C₅²	—	2	12	no	—
13	C₂³×C₅²	D₅	1	1	yes	characteristic
14	C₂³×C₅²	C₂×C₅	1	6	yes	—
15	C₂×C₄×C₅²	—	5	2	no	—
16	C₂×C₅×Dic₅	C₂×C₅	1	12	yes	complemented
17	C₅³	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅²	—	2	48	no	—
19	C₂²×C₅²	—	2	24	no	—
20	C₂²×C₅²	—	2	12	no	—
21	C₂²×C₅²	—	2	2	no	—
22	C₂²×C₅²	—	2	12	no	—
23	C₂²×C₅²	Dic₅	1	2	yes	complemented
24	C₂²×C₅²	C₄×C₅	1	12	yes	complemented
25	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
26	C₂²×C₅²	C₂²×C₅	1	6	yes	—
27	C₄×C₅²	—	10	2	no	—
28	C₅×Dic₅	—	2	12	no	—
29	C₅×C₂²⋊C₄	—	5	6	no	—
30	C₂²⋊Dic₅	C₅²	1	1	yes	characteristic, direct product factor
31	C₂×C₅²	—	2	48	no	—
32	C₂×C₅²	—	2	2	no	—
33	C₂×C₅²	—	2	12	no	—
34	C₂×C₅²	—	2	12	no	—
35	C₂×C₅²	—	2	24	no	—
36	C₂×C₅²	C₂×Dic₅	1	1	yes	characteristic
37	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
38	C₂×C₅²	C₂×C₄×C₅	1	6	yes	—
39	C₂×C₅²	C₅×D₄	1	12	yes	—
40	C₂³×C₅	—	2	12	no	—
41	C₂³×C₅	C₅×D₅	1	6	yes	—
42	C₂³×C₅	C₂×C₅²	1	1	yes	characteristic
43	C₂×C₄×C₅	—	5	12	no	—
44	C₂×Dic₅	C₂×C₅²	1	2	yes	complemented
45	C₅²	—	2	12	no	—
46	C₅²	C₂²⋊Dic₅	1	1	yes	characteristic, direct product factor
47	C₅²	C₅×C₂²⋊C₄	1	6	yes	complemented
48	C₂²×C₅	—	2	48	no	—
49	C₂²×C₅	—	2	12	no	—
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	—	2	24	no	—
52	C₂²×C₅	—	2	12	no	—
53	C₂²×C₅	C₅×Dic₅	1	12	yes	complemented
54	C₂²×C₅	C₄×C₅²	1	2	yes	complemented
55	C₂²×C₅	C₂×C₅×D₅	1	6	yes	—
56	C₂²×C₅	C₂²×C₅²	1	1	yes	characteristic
57	C₄×C₅	—	10	12	no	—
58	Dic₅	—	2	2	no	—
59	C₂²⋊C₄	—	5	1	no	Sylow
60	C₂×C₅	—	2	48	no	—
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	—	2	12	no	—
63	C₂×C₅	—	2	12	no	—
64	C₂×C₅	—	2	24	no	—
65	C₂×C₅	C₂×C₅×Dic₅	1	6	yes	—
66	C₂×C₅	C₅×C₂²⋊D₅	1	12	yes	—
67	C₂×C₅	C₂×C₄×C₅²	1	1	yes	characteristic
68	C₂×C₅	C₅²×D₄	1	2	yes	—
69	C₂³	C₅²×D₅	1	1	yes	characteristic
70	C₂×C₄	—	5	2	no	—
71	C₅	—	2	12	no	—
72	C₅	C₅×C₂²⋊Dic₅	1	6	yes	direct product factor
73	C₅	C₅²×C₂²⋊C₄	1	1	yes	characteristic, complemented
74	C₂²	—	2	2	no	—
75	C₂²	C₅²×Dic₅	1	2	yes	complemented
76	C₂²	C₂×C₅²×D₅	1	1	yes	characteristic
77	C₄	—	10	2	no	—
78	C₂	—	2	2	no	—
79	C₂	C₂×C₅²×Dic₅	1	1	yes	characteristic
80	C₂	C₅²×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅²	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₅²
Frattini	C₂²	C₂×C₅²×D₅
Fitting, prime radical	C₂³×C₅³	C₂
socle	C₂²×C₅³	C₂²
cosocle	C₂²×C₅	C₂²×C₅²
hypercenter	C₂³×C₅²	D₅
hypocenter	C₅	C₅²×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅² ◁ C₂³×C₅²

Complements

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

N	H ≅ G/N	type
2. C₂×C₅²×Dic₅	C₂	semidirect
4. C₂²×C₅³	C₄	semidirect
8. C₅×C₂²⋊Dic₅	C₅	direct (N × H)
16. C₂×C₅×Dic₅	C₂×C₅	semidirect
17. C₅³	C₂²⋊C₄	semidirect
23. C₂²×C₅²	Dic₅	semidirect
24. C₂²×C₅²	C₄×C₅	semidirect
30. C₂²⋊Dic₅	C₅²	direct (N × H)
44. C₂×Dic₅	C₂×C₅²	semidirect
46. C₅²	C₂²⋊Dic₅	direct (N × H)
47. C₅²	C₅×C₂²⋊C₄	semidirect
53. C₂²×C₅	C₅×Dic₅	semidirect
54. C₂²×C₅	C₄×C₅²	semidirect
72. C₅	C₅×C₂²⋊Dic₅	direct (N × H)
73. C₅	C₅²×C₂²⋊C₄	semidirect
75. C₂²	C₅²×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅³	2
C₂×C₅²×Dic₅	2
C₅²×C₂²⋊C₄	5
C₅×C₂²⋊Dic₅	5

Subgroups — C52×C22⋊Dic5 #14522621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₂²⋊Dic₅ #14522621