Subgroups — C₂×Dic₅×C₅⋊D₅ #14522876

Order 2000.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#92553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₅×C₅⋊D₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅³	C₂²	1	1	yes	characteristic
6	C₂×C₅×C₅⋊D₅	C₄	1	4	yes	complemented
7	C₂×C₅×C₅⋊D₅	C₂²	1	2	yes	—
8	#92553	C₂²	1	2	yes	complemented
9	C₅²×Dic₅	C₂²	1	2	yes	complemented
10	C₂×C₄×C₅⋊D₅	—	5	1	no	maximal
11	C₂×D₅×Dic₅	—	5	6	no	maximal
12	C₂×C₅³	C₂×C₄	1	2	yes	complemented
13	C₂×C₅³	C₂³	1	1	yes	characteristic
14	C₅×C₅⋊D₅	C₂×C₄	1	4	yes	complemented
15	C₂²×C₅⋊D₅	D₅	1	1	yes	characteristic
16	C₂²×C₅×D₅	—	5	6	no	—
17	C₂×C₄×C₅²	—	5	1	no	—
18	C₂×#1039	—	5	1	no	—
19	C₂×#1039	—	5	6	no	—
20	C₂×#1039	—	10	12	no	—
21	C₄×C₅⋊D₅	—	5	4	no	—
22	C₂×C₅×Dic₅	D₅	1	6	yes	complemented
23	D₅×Dic₅	—	5	24	no	—
24	C₅³	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₅²	—	2	12	no	—
26	C₂²×C₅²	C₂×D₅	1	6	yes	—
27	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
28	C₂×C₅⋊D₅	Dic₅	1	4	yes	direct product factor
29	C₂×C₅⋊D₅	C₂×D₅	1	2	yes	—
30	C₂×C₅×D₅	—	5	24	no	—
31	C₂×C₅×D₅	—	5	12	no	—
32	C₄×C₅²	—	5	2	no	—
33	#1039	—	5	2	no	—
34	#1039	—	5	12	no	—
35	#1039	—	10	24	no	—
36	C₅×Dic₅	C₂×D₅	1	12	yes	complemented
37	C₂²×Dic₅	—	25	1	no	—
38	C₂×C₄×D₅	—	25	6	no	—
39	C₂×C₅²	—	2	24	no	—
40	C₂×C₅²	—	2	12	no	—
41	C₂×C₅²	C₄×D₅	1	12	yes	complemented
42	C₂×C₅²	C₂×Dic₅	1	2	yes	complemented
43	C₂×C₅²	C₂²×D₅	1	6	yes	—
44	C₂×C₅²	C₂²×D₅	1	1	yes	characteristic
45	C₅⋊D₅	C₂×Dic₅	1	4	yes	direct product factor
46	C₅×D₅	—	5	24	no	—
47	C₂³×C₅	—	25	1	no	—
48	C₂²×D₅	—	5	6	no	—
49	C₂×C₄×C₅	—	5	6	no	—
50	C₂×Dic₅	—	25	6	no	—
51	C₂×Dic₅	—	25	1	no	—
52	C₂×Dic₅	—	25	4	no	—
53	C₂×Dic₅	—	50	12	no	—
54	C₂×Dic₅	C₅⋊D₅	1	1	yes	characteristic, direct product factor
55	C₄×D₅	—	25	24	no	—
56	C₅²	—	2	12	no	—
57	C₅²	C₂×C₄×D₅	1	6	yes	complemented
58	C₅²	C₂²×Dic₅	1	1	yes	characteristic, complemented
59	C₂²×C₅	—	2	12	no	—
60	C₂²×C₅	—	25	4	no	—
61	C₂²×C₅	—	25	2	no	—
62	C₂²×C₅	D₅²	1	6	yes	—
63	C₂²×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
64	C₂×D₅	—	5	24	no	—
65	C₂×D₅	—	5	12	no	—
66	C₄×C₅	—	5	12	no	—
67	Dic₅	—	25	12	no	—
68	Dic₅	—	25	2	no	—
69	Dic₅	—	50	24	no	—
70	Dic₅	C₂×C₅⋊D₅	1	2	yes	direct product factor
71	C₂²×C₄	—	125	1	no	Sylow
72	C₂×C₅	—	2	24	no	—
73	C₂×C₅	—	2	12	no	—
74	C₂×C₅	—	25	4	no	—
75	C₂×C₅	D₅×Dic₅	1	12	yes	complemented
76	C₂×C₅	C₄×C₅⋊D₅	1	2	yes	complemented
77	C₂×C₅	C₂×D₅²	1	6	yes	—
78	C₂×C₅	C₂²×C₅⋊D₅	1	1	yes	characteristic
79	D₅	—	5	24	no	—
80	C₂³	—	25	1	no	—
81	C₂×C₄	—	5	1	no	—
82	C₂×C₄	—	125	4	no	—
83	C₂×C₄	—	125	1	no	—
84	C₅	—	2	12	no	—
85	C₅	C₂×D₅×Dic₅	1	6	yes	complemented
86	C₅	C₂×C₄×C₅⋊D₅	1	1	yes	characteristic, complemented
87	C₂²	—	25	4	no	—
88	C₂²	—	25	2	no	—
89	C₂²	D₅×C₅⋊D₅	1	1	yes	characteristic
90	C₄	—	5	2	no	—
91	C₄	—	125	2	no	—
92	C₂	—	25	4	no	—
93	C₂	Dic₅×C₅⋊D₅	1	2	yes	direct product factor
94	C₂	C₂×D₅×C₅⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#92553	C₂	semidirect
3. C₂×C₅²×Dic₅	C₂	semidirect
4. Dic₅×C₅⋊D₅	C₂	direct (N × H)
6. C₂×C₅×C₅⋊D₅	C₄	semidirect
8. #92553	C₂²	semidirect
9. C₅²×Dic₅	C₂²	semidirect
12. C₂×C₅³	C₂×C₄	semidirect
14. C₅×C₅⋊D₅	C₂×C₄	semidirect
22. C₂×C₅×Dic₅	D₅	semidirect
24. C₅³	C₂²×C₄	semidirect
28. C₂×C₅⋊D₅	Dic₅	direct (N × H)
36. C₅×Dic₅	C₂×D₅	semidirect
41. C₂×C₅²	C₄×D₅	semidirect
42. C₂×C₅²	C₂×Dic₅	semidirect
45. C₅⋊D₅	C₂×Dic₅	direct (N × H)
54. C₂×Dic₅	C₅⋊D₅	direct (N × H)
57. C₅²	C₂×C₄×D₅	semidirect
58. C₅²	C₂²×Dic₅	semidirect
70. Dic₅	C₂×C₅⋊D₅	direct (N × H)
75. C₂×C₅	D₅×Dic₅	semidirect
76. C₂×C₅	C₄×C₅⋊D₅	semidirect
85. C₅	C₂×D₅×Dic₅	semidirect
86. C₅	C₂×C₄×C₅⋊D₅	semidirect
93. C₂	Dic₅×C₅⋊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
C₂²×C₅×C₅⋊D₅	2
C₂×#92553	2
C₂×C₅²×Dic₅	2
Dic₅×C₅⋊D₅	2
C₂×C₄×C₅⋊D₅	5
C₂×D₅×Dic₅	5

Subgroups — C2×Dic5×C5⋊D5 #14522876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₅×C₅⋊D₅ #14522876