Subgroups — D₅⋊(C₃⋊(C₃⋊C₁₆)) #13086291

Order 1440.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#674)	C₂	1	2	yes	maximal, complemented
3	D₅⋊(C₃⋊C₁₆)	—	3	4	no	maximal
4	C₃²×C₄×D₅	C₄	1	1	yes	characteristic
5	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃²×#168	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊(C₃⋊C₁₆)	—	5	1	no	maximal, Hall
8	C₃×C₈×D₅	D₃	1	4	yes	—
9	C₃⋊#674	—	3	8	no	—
10	C₂×C₃²×D₅	C₈	1	1	yes	characteristic
11	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃²×Dic₅	C₈	1	1	yes	characteristic
13	D₅⋊C₁₆	—	9	1	no	Hall
14	C₂×C₃²×C₈	—	5	1	no	—
15	C₃⋊(C₃⋊C₁₆)	—	5	2	no	—
16	C₃×C₄×D₅	Dic₃	1	4	yes	—
17	C₃×C₅×C₈	Dic₃	1	4	yes	—
18	C₃×#168	C₂×D₃	1	4	yes	—
19	C₂×C₃⋊C₁₆	—	15	4	no	—
20	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
21	C₃²×D₅	C₁₆	1	2	yes	complemented
22	C₈×D₅	C₃⋊D₃	1	1	yes	characteristic
23	#674	—	9	2	no	—
24	C₂×C₃²×C₄	—	5	1	no	—
25	C₃²×C₈	—	5	1	no	—
26	C₃²×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₂×C₃×D₅	C₃⋊C₈	1	4	yes	—
28	C₃×C₄×C₅	C₂×Dic₃	1	4	yes	—
29	C₃×Dic₅	C₃⋊C₈	1	4	yes	—
30	C₂×C₃×C₈	—	5	4	no	—
31	C₃⋊C₁₆	—	15	8	no	—
32	C₃²×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
33	C₄×D₅	C₃⋊Dic₃	1	1	yes	characteristic
34	C₅×C₈	C₃⋊Dic₃	1	1	yes	characteristic
35	#168	C₂×C₃⋊D₃	1	1	yes	characteristic
36	C₂²×C₃²	—	5	1	no	—
37	C₃²×C₄	—	5	1	no	—
38	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₂×C₁₆	—	45	1	no	Sylow
40	C₂×C₃×C₅	C₂×C₃⋊C₈	1	4	yes	—
41	C₃×D₅	C₃⋊C₁₆	1	8	yes	complemented
42	C₂×C₃×C₄	—	5	4	no	—
43	C₃×C₈	—	5	4	no	—
44	C₃×C₈	ΓL(1,𝔽₁₆)	1	4	yes	—
45	C₂×D₅	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
46	C₄×C₅	C₂×C₃⋊Dic₃	1	1	yes	characteristic
47	Dic₅	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
48	C₂×C₃²	—	5	2	no	—
49	C₂×C₃²	D₅⋊C₈	1	1	yes	characteristic
50	C₂×C₈	—	5	1	no	—
51	C₁₆	—	45	2	no	—
52	C₃×C₅	C₂×C₃⋊C₁₆	1	4	yes	complemented
53	C₂²×C₃	—	5	4	no	—
54	C₃×C₄	—	5	4	no	—
55	C₃×C₄	C₂×ΓL(1,𝔽₁₆)	1	4	yes	—
56	C₂×C₅	C₂×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
57	D₅	C₃⋊(C₃⋊C₁₆)	1	2	yes	complemented
58	C₃²	D₅⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄	—	5	1	no	—
60	C₈	—	5	1	no	—
61	C₈	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
62	C₂×C₃	—	5	8	no	—
63	C₂×C₃	D₅⋊(C₃⋊C₈)	1	4	yes	—
64	C₅	C₂×C₃⋊(C₃⋊C₁₆)	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	5	1	no	—
66	C₄	—	5	1	no	—
67	C₄	C₂×C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
68	C₃	D₅⋊(C₃⋊C₁₆)	1	4	yes	complemented
69	C₂	—	5	2	no	—
70	C₂	D₅⋊(C₃⋊(C₃⋊C₈))	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	C₃⋊ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃²×C₅	C₂×C₁₆
Frattini	C₄	C₂×C₃⋊ΓL(1,𝔽₁₆)
Fitting	C₃²×C₅×C₈	C₄
socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₃²×D₅	C₈
cosocle	C₃²×#168	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊#674)	C₂	semidirect
21. C₃²×D₅	C₁₆	semidirect
32. C₃²×C₅	C₂×C₁₆	semidirect
41. C₃×D₅	C₃⋊C₁₆	semidirect
52. C₃×C₅	C₂×C₃⋊C₁₆	semidirect
57. D₅	C₃⋊(C₃⋊C₁₆)	semidirect
58. C₃²	D₅⋊C₁₆	semidirect
64. C₅	C₂×C₃⋊(C₃⋊C₁₆)	semidirect
68. C₃	D₅⋊(C₃⋊C₁₆)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₈×D₅	2
C₃⋊(C₃⋊#674)	2
D₅⋊(C₃⋊C₁₆)	3
C₂×C₃⋊(C₃⋊C₁₆)	5

Subgroups — D5⋊(C3⋊(C3⋊C16)) #13086291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊(C₃⋊(C₃⋊C₁₆)) #13086291