Subgroups — C₅×C₃⋊#14546128 #45658338

Order 32700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅×#14546128	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14546128	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₃₂₇	—	5	1	no	maximal
6	C₅×D₅×C₁₀₉	D₃	1	1	yes	characteristic
7	C₃×D₅×C₁₀₉	C₂×C₅	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₀₉	—	5	1	no	—
9	C₅²×C₁₀₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	#14546128	—	3	1	no	—
11	C₅×Dic₁₀₉	—	15	1	no	—
12	C₃×C₅×C₁₀₉	—	4	1	no	—
13	C₃×C₅×C₁₀₉	C₄×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₀₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	Dic₃₂₇	—	5	1	no	Hall
16	C₂×C₅×C₁₀₉	—	5	1	no	—
17	D₅×C₁₀₉	C₅×D₃	1	1	yes	characteristic
18	C₂×C₃×C₁₀₉	—	5	1	no	—
19	C₅×C₁₀₉	—	4	1	no	—
20	C₅×C₁₀₉	C₅×Dic₃	1	1	yes	characteristic, complemented
21	C₅×C₁₀₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
22	Dic₁₀₉	—	15	1	no	Hall
23	C₃×C₁₀₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
24	C₅×ΓL(1,𝔽₁₆)	—	109	1	no	maximal, Hall
25	C₂×C₁₀₉	—	5	1	no	—
26	C₃×C₅×D₅	D₁₀₉	1	1	yes	characteristic
27	C₁₀₉	C₅×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
28	C₅×AGL(1,𝔽₅)	—	327	1	no	Hall
29	C₃×C₅²	Dic₁₀₉	1	1	yes	characteristic, complemented, Hall
30	ΓL(1,𝔽₁₆)	—	109	1	no	—
31	C₅×Dic₃	—	545	1	no	—
32	C₅×D₅	D₃₂₇	1	1	yes	characteristic
33	C₂×C₃×C₅	—	5	1	no	—
34	C₃×D₅	C₅×D₁₀₉	1	1	yes	characteristic
35	C₅²	Dic₃₂₇	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	327	1	no	—
37	C₄×C₅	—	1635	1	no	—
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	C₅×Dic₁₀₉	1	1	yes	characteristic, complemented
40	C₃×C₅	#14546128	1	1	yes	characteristic, complemented
41	Dic₃	—	545	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₅×D₃₂₇	1	1	yes	characteristic
44	C₂×C₃	—	5	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₅×Dic₃₂₇	1	1	yes	characteristic, complemented
47	C₅	C₃⋊#14546128	1	1	yes	characteristic, direct product factor
48	C₄	—	1635	1	no	Sylow
49	C₃	C₅×#14546128	1	1	yes	characteristic, complemented, Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#14546128
commutator, hypocenter	C₃×C₅×C₁₀₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₀₉	C₄
prime radical	C₃×C₅×D₅×C₁₀₉	C₂
cosocle	C₃×D₅×C₁₀₉	C₂×C₅
LCS	G ▷ C₃×C₅×C₁₀₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₀₉	C₄	semidirect
4. C₃⋊#14546128	C₅	direct (N × H)
9. C₅²×C₁₀₉	Dic₃	semidirect
13. C₃×C₅×C₁₀₉	C₄×C₅	semidirect
14. C₃×C₅×C₁₀₉	AGL(1,𝔽₅)	semidirect
20. C₅×C₁₀₉	C₅×Dic₃	semidirect
21. C₅×C₁₀₉	ΓL(1,𝔽₁₆)	semidirect
23. C₃×C₁₀₉	C₅×AGL(1,𝔽₅)	semidirect
27. C₁₀₉	C₅×ΓL(1,𝔽₁₆)	semidirect
29. C₃×C₅²	Dic₁₀₉	semidirect
35. C₅²	Dic₃₂₇	semidirect
39. C₃×C₅	C₅×Dic₁₀₉	semidirect
40. C₃×C₅	#14546128	semidirect
46. C₅	C₅×Dic₃₂₇	semidirect
47. C₅	C₃⋊#14546128	direct (N × H)
49. C₃	C₅×#14546128	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₅×C₁₀₉	2
C₅×#14546128	3
C₃⋊#14546128	5
C₅×Dic₃₂₇	5
C₅×ΓL(1,𝔽₁₆)	109

Subgroups — C5×C3⋊#14546128 #45658338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#14546128 #45658338