Subgroups — C₂×#6029⋊C₅ #14522183

Order 2000.

109 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	#6029⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₂²×H(3,𝔽₅)	C₄	1	1	yes	characteristic
4	C₄×H(3,𝔽₅)	C₄	1	1	yes	characteristic
5	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
6	C₂×#6029	C₅	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#168	—	5	1	no	maximal
8	C₂×H(3,𝔽₅)	C₈	1	2	yes	complemented
9	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅²	—	2	2	no	—
11	C₂×C₄×C₅²	D₅	1	1	yes	characteristic
12	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic
13	#6029	C₂×C₅	1	2	yes	complemented
14	C₅×#168	—	5	2	no	—
15	H(3,𝔽₅)	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅²	—	2	2	no	—
17	C₂²×C₅²	Dic₅	1	1	yes	characteristic
18	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic
19	C₄×C₅²	—	2	2	no	—
20	C₄×C₅²	—	2	2	no	—
21	C₄×C₅²	Dic₅	1	1	yes	characteristic
22	C₄×C₅²	C₄×C₅	1	1	yes	characteristic
23	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
25	C₂×C₅×C₈	—	25	1	no	—
26	C₂×#168	—	5	1	no	—
27	C₂×#168	—	25	1	no	—
28	C₂×C₅²	—	2	4	no	—
29	C₂×C₅²	—	2	2	no	—
30	C₂×C₅²	#168	1	2	yes	complemented
31	C₂×C₅²	C₅×C₈	1	2	yes	complemented
32	C₂×C₅²	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
34	C₂×C₄×C₅	—	5	1	no	—
35	C₂×C₄×C₅	—	5	1	no	—
36	C₂×C₄×C₅	—	10	2	no	—
37	C₂×C₄×C₅	C₅×D₅	1	1	yes	characteristic
38	C₅×C₈	—	25	2	no	—
39	#168	—	5	2	no	—
40	#168	—	25	2	no	—
41	C₅²	—	2	2	no	—
42	C₅²	C₂×#168	1	1	yes	characteristic, complemented
43	C₅²	C₂×C₅×C₈	1	1	yes	characteristic, complemented
44	C₂²×C₅	—	5	1	no	—
45	C₂²×C₅	—	5	1	no	—
46	C₂²×C₅	—	10	2	no	—
47	C₂²×C₅	C₅×Dic₅	1	1	yes	characteristic
48	C₄×C₅	—	5	1	no	—
49	C₄×C₅	—	5	1	no	—
50	C₄×C₅	—	5	1	no	—
51	C₄×C₅	—	5	1	no	—
52	C₄×C₅	—	10	2	no	—
53	C₄×C₅	—	10	2	no	—
54	C₄×C₅	C₅×Dic₅	1	1	yes	characteristic
55	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
56	C₂×C₈	—	25	1	no	Sylow
57	C₂×C₅	—	5	2	no	—
58	C₂×C₅	—	5	2	no	—
59	C₂×C₅	—	5	1	no	—
60	C₂×C₅	—	5	1	no	—
61	C₂×C₅	—	10	4	no	—
62	C₂×C₅	—	10	2	no	—
63	C₂×C₅	C₅×#168	1	2	yes	—
64	C₂×C₅	C₂×C₅×Dic₅	1	1	yes	characteristic
65	C₂×C₄	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
66	C₈	—	25	2	no	—
67	C₅	—	5	1	no	—
68	C₅	—	5	1	no	—
69	C₅	—	10	2	no	—
70	C₅	C₂×C₅×#168	1	1	yes	characteristic
71	C₂²	#1039⋊C₅	1	1	yes	characteristic
72	C₄	#1039⋊C₅	1	1	yes	characteristic
73	C₄	C₂×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
74	C₂	#6029⋊C₅	1	2	yes	direct product factor
75	C₂	C₂×#1039⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	(C₅⋊D₅)⋊C₅
commutator, hypocenter	C₅²	C₂×C₅×C₈
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₂×C₄×H(3,𝔽₅)	C₂
socle	C₂²×C₅	C₅×Dic₅
prime radical	C₂²×H(3,𝔽₅)	C₄
cosocle	C₄×C₅²	C₂²×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #6029⋊C₅	C₂	direct (N × H)
6. C₂×#6029	C₅	semidirect
8. C₂×H(3,𝔽₅)	C₈	semidirect
13. #6029	C₂×C₅	semidirect
15. H(3,𝔽₅)	C₂×C₈	semidirect
30. C₂×C₅²	#168	semidirect
31. C₂×C₅²	C₅×C₈	semidirect
42. C₅²	C₂×#168	semidirect
43. C₅²	C₂×C₅×C₈	semidirect
74. C₂	#6029⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×H(3,𝔽₅)	2
#6029⋊C₅	2
C₂×#6029	5
C₂×C₅×#168	5

Subgroups — C2×#6029⋊C5 #14522183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6029⋊C₅ #14522183