Subgroups — C₅×C₂²⋊#1043 #14522794

Order 2000.

332 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×C₅×#1043	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅³	C₄	1	1	yes	characteristic, complemented
4	C₂×C₅×C₅⋊D₅	—	2	2	no	—
5	C₂×C₅×C₅⋊D₅	C₄	1	1	yes	characteristic, complemented
6	C₂×C₅×C₅⋊D₅	C₂²	1	1	yes	characteristic
7	C₅×#1043	—	2	2	no	—
8	C₂²⋊#1043	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₅×C₂²⋊AGL(1,𝔽₅)	—	5	6	no	maximal
10	C₂×C₅³	—	2	1	no	—
11	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
12	C₅×C₅⋊D₅	—	2	1	no	—
13	C₅×C₅⋊D₅	D₄	1	2	yes	—
14	C₂²×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
15	C₂²×C₅×D₅	—	5	6	no	—
16	C₂×#1043	C₂×C₅	1	2	yes	complemented
17	C₂×C₅×AGL(1,𝔽₅)	—	5	12	no	—
18	C₅³	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	—	4	6	no	—
20	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic, complemented
21	C₂²×C₅²	AGL(1,𝔽₅)	1	6	yes	complemented
22	C₂×C₅⋊D₅	—	2	2	no	—
23	C₂×C₅⋊D₅	C₄×C₅	1	1	yes	characteristic, complemented
24	C₂×C₅⋊D₅	C₂²×C₅	1	1	yes	characteristic
25	C₂×C₅×D₅	—	5	6	no	—
26	C₂×C₅×D₅	—	5	6	no	—
27	C₂×C₅×D₅	—	10	12	no	—
28	#1043	—	2	2	no	—
29	C₅×AGL(1,𝔽₅)	—	10	12	no	—
30	C₂²⋊AGL(1,𝔽₅)	—	5	6	no	—
31	C₅×C₂²⋊C₄	—	25	1	no	—
32	C₂×C₅²	—	2	1	no	—
33	C₂×C₅²	—	2	6	no	—
34	C₂×C₅²	—	4	12	no	—
35	C₂×C₅²	—	4	6	no	—
36	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
37	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	6	yes	—
38	C₅⋊D₅	—	2	1	no	—
39	C₅⋊D₅	C₅×D₄	1	2	yes	—
40	C₅×D₅	—	5	12	no	—
41	C₅×D₅	—	10	6	no	—
42	C₂³×C₅	—	25	1	no	—
43	C₂²×D₅	—	5	6	no	—
44	C₂×AGL(1,𝔽₅)	—	5	12	no	—
45	C₂×C₄×C₅	—	25	2	no	—
46	C₅²	—	4	6	no	—
47	C₅²	C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
48	C₅²	C₂²⋊AGL(1,𝔽₅)	1	6	yes	complemented
49	C₂²×C₅	—	4	6	no	—
50	C₂²×C₅	—	25	1	no	—
51	C₂²×C₅	—	25	1	no	—
52	C₂²×C₅	—	50	2	no	—
53	C₂²×C₅	C₅×AGL(1,𝔽₅)	1	6	yes	complemented
54	C₂²×C₅	#1043	1	1	yes	characteristic, complemented
55	C₂×D₅	—	5	6	no	—
56	C₂×D₅	—	5	6	no	—
57	C₂×D₅	—	10	12	no	—
58	AGL(1,𝔽₅)	—	10	12	no	—
59	C₄×C₅	—	50	2	no	—
60	C₂²⋊C₄	—	25	1	no	Sylow
61	C₂×C₅	—	2	6	no	—
62	C₂×C₅	—	2	1	no	—
63	C₂×C₅	—	4	12	no	—
64	C₂×C₅	—	4	6	no	—
65	C₂×C₅	—	25	2	no	—
66	C₂×C₅	—	50	1	no	—
67	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	6	yes	—
68	C₂×C₅	C₂×#1043	1	1	yes	characteristic
69	D₅	—	5	12	no	—
70	D₅	—	10	6	no	—
71	C₂³	—	25	1	no	—
72	C₂×C₄	—	25	2	no	—
73	C₅	—	4	6	no	—
74	C₅	C₅×C₂²⋊AGL(1,𝔽₅)	1	6	yes	complemented
75	C₅	C₂²⋊#1043	1	1	yes	characteristic, direct product factor
76	C₂²	—	25	1	no	—
77	C₂²	—	25	1	no	—
78	C₂²	—	50	2	no	—
79	C₂²	C₅×#1043	1	1	yes	characteristic, complemented
80	C₄	—	50	2	no	—
81	C₂	—	2	1	no	—
82	C₂	—	25	2	no	—
83	C₂	—	50	1	no	—
84	C₂	C₂×C₅×#1043	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#1043
commutator	C₂×C₅²	C₂×C₄×C₅
Frattini	C₂	C₂×C₅×#1043
Fitting	C₂²×C₅³	C₄
socle	C₂×C₅³	C₂×C₄
prime radical	C₂²×C₅×C₅⋊D₅	C₂
cosocle	C₂×C₅⋊D₅	C₂²×C₅
hypercenter	C₂²×C₅	#1043
hypocenter	C₅²	C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#1043	C₂	semidirect
3. C₂²×C₅³	C₄	semidirect
5. C₂×C₅×C₅⋊D₅	C₄	semidirect
8. C₂²⋊#1043	C₅	direct (N × H)
16. C₂×#1043	C₂×C₅	semidirect
18. C₅³	C₂²⋊C₄	semidirect
20. C₂²×C₅²	C₄×C₅	semidirect
21. C₂²×C₅²	AGL(1,𝔽₅)	semidirect
23. C₂×C₅⋊D₅	C₄×C₅	semidirect
47. C₅²	C₅×C₂²⋊C₄	semidirect
48. C₅²	C₂²⋊AGL(1,𝔽₅)	semidirect
53. C₂²×C₅	C₅×AGL(1,𝔽₅)	semidirect
54. C₂²×C₅	#1043	semidirect
74. C₅	C₅×C₂²⋊AGL(1,𝔽₅)	semidirect
75. C₅	C₂²⋊#1043	direct (N × H)
79. C₂²	C₅×#1043	semidirect

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×C₅×#1043	2
C₂²⋊#1043	5
C₅×C₂²⋊AGL(1,𝔽₅)	5

Subgroups — C5×C22⋊#1043 #14522794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊#1043 #14522794