Subgroups — C₁₉×C₄⋊Dic₅ #13095073

Order 1520.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×Dic₅	C₂	1	2	yes	maximal
3	C₂²×C₅×C₁₉	C₂²	1	1	yes	characteristic
4	C₄×C₅×C₁₉	C₄	1	2	yes	complemented
5	C₁₉×Dic₅	—	2	2	no	—
6	C₄⋊C₄×C₁₉	—	5	1	no	maximal, Hall
7	C₂×C₅×C₁₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₅×C₁₉	D₄	1	1	yes	characteristic
9	C₂×C₅×C₁₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₉	—	5	2	no	—
11	C₂×C₄×C₁₉	D₅	1	1	yes	characteristic
12	C₅×C₁₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
13	C₄⋊Dic₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₁₉	C₂×D₅	1	1	yes	characteristic
15	C₄×C₁₉	—	10	2	no	—
16	C₄×C₁₉	Dic₅	1	2	yes	complemented
17	C₂×C₄×C₅	C₂×C₁₉	1	1	yes	characteristic
18	C₂×Dic₅	C₂×C₁₉	1	2	yes	—
19	C₂×C₁₉	Dic₁₀	1	1	yes	characteristic
20	C₂×C₁₉	D₂₀	1	1	yes	characteristic
21	C₂×C₁₉	C₂×Dic₅	1	1	yes	characteristic
22	C₂²×C₅	C₂²×C₁₉	1	1	yes	characteristic
23	C₄×C₅	C₄×C₁₉	1	2	yes	complemented
24	Dic₅	—	2	2	no	—
25	C₁₉	C₄⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₄⋊C₄	—	5	1	no	Sylow
27	C₂×C₅	C₂×C₄×C₁₉	1	1	yes	characteristic
28	C₂×C₅	D₄×C₁₉	1	1	yes	characteristic
29	C₂×C₅	Q₈×C₁₉	1	1	yes	characteristic
30	C₂×C₄	—	5	2	no	—
31	C₂×C₄	D₅×C₁₉	1	1	yes	characteristic
32	C₅	C₄⋊C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₂²	C₂×D₅×C₁₉	1	1	yes	characteristic
34	C₄	—	10	2	no	—
35	C₄	C₁₉×Dic₅	1	2	yes	complemented
36	C₂	C₁₉×Dic₁₀	1	1	yes	characteristic
37	C₂	C₁₉×D₂₀	1	1	yes	characteristic
38	C₂	C₂×C₁₉×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₁₉
Frattini	C₂²	C₂×D₅×C₁₉
Fitting	C₂×C₄×C₅×C₁₉	C₂
socle, prime radical	C₂²×C₅×C₁₉	C₂²
cosocle	C₂²×C₅	C₂²×C₁₉
hypercenter	C₂×C₄×C₁₉	D₅
hypocenter	C₅	C₄⋊C₄×C₁₉
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉

Complements

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

N	H ≅ G/N	type
4. C₄×C₅×C₁₉	C₄	semidirect
12. C₅×C₁₉	C₄⋊C₄	semidirect
13. C₄⋊Dic₅	C₁₉	direct (N × H)
16. C₄×C₁₉	Dic₅	semidirect
23. C₄×C₅	C₄×C₁₉	semidirect
25. C₁₉	C₄⋊Dic₅	direct (N × H)
32. C₅	C₄⋊C₄×C₁₉	semidirect
35. C₄	C₁₉×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₉	2
C₂×C₁₉×Dic₅	2
C₄⋊C₄×C₁₉	5
C₄⋊Dic₅	19

Subgroups — C19×C4⋊Dic5 #13095073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₄⋊Dic₅ #13095073