Subgroups — C₃⋊D₃×AGL(1,𝔽₅) #67197

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×AGL(1,𝔽₅)	—	3	4	no	maximal
5	C₃⋊D₁₅	C₄	1	1	yes	characteristic, complemented
6	C₅×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
7	C₃²×D₅	C₂²	1	1	yes	characteristic
8	C₄×C₃⋊D₃	—	5	1	no	maximal, Hall
9	D₃×D₅	—	3	4	no	—
10	ΓL(1,𝔽₁₆)	—	3	4	no	—
11	C₃×AGL(1,𝔽₅)	D₃	1	4	yes	complemented
12	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×AGL(1,𝔽₅)	—	9	1	no	Hall
14	C₂×C₃⋊D₃	—	5	1	no	—
15	C₃²×C₄	—	5	1	no	—
16	C₃⋊Dic₃	—	5	1	no	—
17	D₁₅	—	3	4	no	—
18	C₃×D₅	C₂×D₃	1	4	yes	—
19	C₅×D₃	—	3	4	no	—
20	C₄×D₃	—	15	4	no	—
21	C₂×D₅	—	9	1	no	—
22	AGL(1,𝔽₅)	—	9	1	no	—
23	AGL(1,𝔽₅)	C₃⋊D₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃²	—	5	1	no	—
25	C₃⋊D₃	—	5	1	no	—
26	C₃⋊D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
27	C₃×C₅	C₄×D₃	1	4	yes	complemented
28	C₂×D₃	—	15	4	no	—
29	C₃×C₄	—	5	4	no	—
30	Dic₃	—	15	4	no	—
31	C₂×C₅	—	9	1	no	—
32	D₅	—	9	1	no	—
33	D₅	C₂×C₃⋊D₃	1	1	yes	characteristic
34	C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₄	—	45	1	no	Sylow
36	C₂×C₃	—	5	4	no	—
37	D₃	—	3	4	no	—
38	D₃	—	15	4	no	—
39	C₅	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	45	1	no	—
41	C₄	—	5	1	no	—
42	C₄	—	45	1	no	—
43	C₃	D₃×AGL(1,𝔽₅)	1	4	yes	complemented
44	C₂	—	5	1	no	—
45	C₂	—	9	1	no	—
46	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₂×C₄
prime radical	D₅×C₃⋊D₃	C₂
cosocle	C₃²×D₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊ΓL(1,𝔽₁₆)	C₂	semidirect
3. C₃²×AGL(1,𝔽₅)	C₂	semidirect
5. C₃⋊D₁₅	C₄	semidirect
6. C₅×C₃⋊D₃	C₄	semidirect
11. C₃×AGL(1,𝔽₅)	D₃	semidirect
12. C₃²×C₅	C₂×C₄	semidirect
23. AGL(1,𝔽₅)	C₃⋊D₃	direct (N × H)
26. C₃⋊D₃	AGL(1,𝔽₅)	direct (N × H)
27. C₃×C₅	C₄×D₃	semidirect
34. C₃²	C₂×AGL(1,𝔽₅)	semidirect
39. C₅	C₄×C₃⋊D₃	semidirect
43. C₃	D₃×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃⋊D₃	2
C₃⋊ΓL(1,𝔽₁₆)	2
C₃²×AGL(1,𝔽₅)	2
D₃×AGL(1,𝔽₅)	3
C₄×C₃⋊D₃	5

Subgroups — C3⋊D3×AGL(1,𝔽5) #67197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×AGL(1,𝔽₅) #67197