Subgroups — D₅⋊(C₃⋊C₁₆) #91218

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#674	C₂	1	2	yes	maximal, complemented
3	D₅⋊C₁₆	—	3	1	no	maximal, Hall
4	C₃×C₄×D₅	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃×#168	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₁₆	—	5	1	no	maximal, Hall
8	C₈×D₅	D₃	1	1	yes	characteristic
9	#674	—	3	2	no	—
10	C₂×C₃×D₅	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×Dic₅	C₈	1	1	yes	characteristic
13	C₂×C₃×C₈	—	5	1	no	—
14	C₃⋊C₁₆	—	5	2	no	—
15	C₄×D₅	Dic₃	1	1	yes	characteristic
16	C₅×C₈	Dic₃	1	1	yes	characteristic
17	#168	C₂×D₃	1	1	yes	characteristic
18	C₂×C₁₆	—	15	1	no	Sylow
19	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
20	C₃×D₅	C₁₆	1	2	yes	complemented
21	C₂×C₃×C₄	—	5	1	no	—
22	C₃×C₈	—	5	1	no	—
23	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₂×D₅	C₃⋊C₈	1	1	yes	characteristic
25	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
26	Dic₅	C₃⋊C₈	1	1	yes	characteristic
27	C₂×C₈	—	5	1	no	—
28	C₁₆	—	15	2	no	—
29	C₃×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	—	5	1	no	—
31	C₃×C₄	—	5	1	no	—
32	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₂×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
34	D₅	C₃⋊C₁₆	1	2	yes	complemented
35	C₂×C₄	—	5	1	no	—
36	C₈	—	5	1	no	—
37	C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
38	C₂×C₃	—	5	2	no	—
39	C₂×C₃	D₅⋊C₈	1	1	yes	characteristic
40	C₅	C₂×C₃⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	5	1	no	—
42	C₄	—	5	1	no	—
43	C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
44	C₃	D₅⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	5	2	no	—
46	C₂	D₅⋊(C₃⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₂×C₁₆
Frattini	C₄	C₂×ΓL(1,𝔽₁₆)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×C₃×D₅	C₈
cosocle	C₃×#168	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊#674	C₂	semidirect
20. C₃×D₅	C₁₆	semidirect
29. C₃×C₅	C₂×C₁₆	semidirect
34. D₅	C₃⋊C₁₆	semidirect
40. C₅	C₂×C₃⋊C₁₆	semidirect
44. C₃	D₅⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₈×D₅	2
C₃⋊#674	2
D₅⋊C₁₆	3
C₂×C₃⋊C₁₆	5

Subgroups — D5⋊(C3⋊C16) #91218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊(C₃⋊C₁₆) #91218