Subgroups — C₅×#14546126⋊C₃ #45658271

Order 32700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₅⋊(D₁₀₉⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₅×#14546126	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#14546126⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×#89137⋊C₃	—	5	1	no	maximal
6	C₅×D₅₄₅	C₂×C₃	1	1	yes	characteristic
7	C₅⋊(D₁₀₉⋊C₃)	C₂×C₅	1	1	yes	characteristic
8	C₅×D₁₀₉⋊C₃	—	5	1	no	—
9	C₅²×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	#14546126	C₃×C₅	1	1	yes	characteristic, complemented
11	C₅×#89137	—	5	1	no	—
12	C₅×C₁₀₉⋊C₃	—	4	1	no	—
13	C₅×C₁₀₉⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented
14	C₅×C₁₀₉⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	#89137⋊C₃	—	5	1	no	Hall
16	D₅₄₅	C₂×C₃×C₅	1	1	yes	characteristic
17	C₅×D₁₀₉	—	5	1	no	—
18	D₁₀₉⋊C₃	—	5	1	no	—
19	C₅×C₁₀₉	—	4	1	no	—
20	C₅×C₁₀₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented
21	C₅×C₁₀₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
22	#89137	—	5	1	no	Hall
23	C₁₀₉⋊C₃	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×AGL(1,𝔽₅)	—	109	1	no	maximal, Hall
25	D₁₀₉	—	5	1	no	—
26	C₃×C₅×D₅	—	109	1	no	—
27	C₁₀₉	C₃×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
28	C₅×AGL(1,𝔽₅)	—	109	1	no	Hall
29	C₃×C₅²	—	109	1	no	Hall
30	C₃×AGL(1,𝔽₅)	—	109	1	no	—
31	C₃×C₄×C₅	—	545	1	no	—
32	C₅×D₅	—	109	1	no	—
33	C₂×C₃×C₅	—	545	1	no	—
34	C₃×D₅	—	109	1	no	—
35	C₅²	#89137⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	109	1	no	—
37	C₄×C₅	—	545	1	no	—
38	C₃×C₅	—	109	1	no	—
39	C₃×C₅	—	109	1	no	—
40	C₃×C₅	—	436	1	no	—
41	C₃×C₄	—	545	1	no	Hall
42	C₂×C₅	—	545	1	no	—
43	D₅	—	109	1	no	—
44	C₂×C₃	—	545	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₅×#89137⋊C₃	1	1	yes	characteristic, complemented
47	C₅	#14546126⋊C₃	1	1	yes	characteristic, direct product factor
48	C₄	—	545	1	no	Sylow
49	C₃	—	109	1	no	Sylow
50	C₂	—	545	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#14546126⋊C₃
commutator, hypocenter	C₅×C₁₀₉	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₁₀₉	C₃×C₄
prime radical	C₅×C₅⋊(D₁₀₉⋊C₃)	C₂
cosocle	D₅₄₅	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₀₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14546126	C₃	semidirect
3. C₅²×C₁₀₉⋊C₃	C₄	semidirect
4. #14546126⋊C₃	C₅	direct (N × H)
9. C₅²×C₁₀₉	C₃×C₄	semidirect
10. #14546126	C₃×C₅	semidirect
13. C₅×C₁₀₉⋊C₃	C₄×C₅	semidirect
14. C₅×C₁₀₉⋊C₃	AGL(1,𝔽₅)	semidirect
20. C₅×C₁₀₉	C₃×C₄×C₅	semidirect
21. C₅×C₁₀₉	C₃×AGL(1,𝔽₅)	semidirect
23. C₁₀₉⋊C₃	C₅×AGL(1,𝔽₅)	semidirect
27. C₁₀₉	C₃×C₅×AGL(1,𝔽₅)	semidirect
35. C₅²	#89137⋊C₃	semidirect
46. C₅	C₅×#89137⋊C₃	semidirect
47. C₅	#14546126⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₅⋊(D₁₀₉⋊C₃)	2
C₅×#14546126	3
#14546126⋊C₃	5
C₅×#89137⋊C₃	5
C₃×C₅×AGL(1,𝔽₅)	109

Subgroups — C5×#14546126⋊C3 #45658271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#14546126⋊C₃ #45658271