Subgroups — C₄⋊Dic₉₅ #13095089

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×Dic₉₅	C₂	1	2	yes	maximal
3	C₂²×C₅×C₁₉	C₂²	1	1	yes	characteristic
4	C₄×C₅×C₁₉	C₄	1	2	yes	complemented
5	Dic₉₅	—	2	2	no	—
6	C₄⋊Dic₁₉	—	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	D₅	1	1	yes	characteristic
11	C₂×Dic₁₉	—	5	2	no	—
12	C₅×C₁₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
13	C₄⋊Dic₅	—	19	1	no	maximal, Hall
14	C₂²×C₁₉	C₂×D₅	1	1	yes	characteristic
15	C₄×C₁₉	Dic₅	1	2	yes	complemented
16	Dic₁₉	—	10	2	no	—
17	C₂×C₄×C₅	D₁₉	1	1	yes	characteristic
18	C₂×Dic₅	—	19	2	no	—
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	C₂×D₁₉	1	1	yes	characteristic
23	C₄×C₅	Dic₁₉	1	2	yes	complemented
24	Dic₅	—	38	2	no	—
25	C₁₉	C₄⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
26	C₄⋊C₄	—	95	1	no	Sylow
27	C₂×C₅	Dic₃₈	1	1	yes	characteristic
28	C₂×C₅	D₇₆	1	1	yes	characteristic
29	C₂×C₅	C₂×Dic₁₉	1	1	yes	characteristic
30	C₂×C₄	—	95	2	no	—
31	C₂×C₄	D₉₅	1	1	yes	characteristic
32	C₅	C₄⋊Dic₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₂²	C₂×D₉₅	1	1	yes	characteristic
34	C₄	—	190	2	no	—
35	C₄	Dic₉₅	1	2	yes	complemented
36	C₂	Dic₁₉₀	1	1	yes	characteristic
37	C₂	D₃₈₀	1	1	yes	characteristic
38	C₂	C₂×Dic₉₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₉₅
commutator	C₂×C₅×C₁₉	C₂×C₄
Fitting	C₂×C₄×C₅×C₁₉	C₂
socle, prime radical, cosocle	C₂²×C₅×C₁₉	C₂²
hypercenter	C₂×C₄	D₉₅
hypocenter	C₅×C₁₉	C₄⋊C₄
LCS	G ▷ C₂×C₅×C₁₉ ▷ C₅×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

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
15. C₄×C₁₉	Dic₅	semidirect
23. C₄×C₅	Dic₁₉	semidirect
25. C₁₉	C₄⋊Dic₅	semidirect
32. C₅	C₄⋊Dic₁₉	semidirect
35. C₄	Dic₉₅	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×Dic₉₅	2
C₄⋊Dic₁₉	5
C₄⋊Dic₅	19

Subgroups — C4⋊Dic95 #13095089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊Dic₉₅ #13095089