Subgroups — C₃×C₅×#14524190 #44570073

Order 32445.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14524190	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₅×C₇×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#14524190	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₀₃⋊C₃	—	7	1	no	maximal, Hall
5	C₅×C₇×C₁₀₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₁₀₃	C₃×C₅	1	1	yes	characteristic, complemented
7	#14524190	C₃×C₅	1	3	yes	direct product factor
8	C₃×C₅×C₁₀₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
9	C₅×C₁₀₃⋊C₃	—	7	3	no	—
10	C₃×C₁₀₃⋊C₃	—	7	1	no	Hall
11	C₇×C₁₀₃	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₀₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×ΓL(1,𝔽₈)	—	103	1	no	maximal, Hall
14	C₃×C₁₀₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₁₀₃⋊C₃	—	7	3	no	—
16	C₃×C₅×C₇	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
17	C₅×ΓL(1,𝔽₈)	—	103	3	no	—
18	C₁₀₃	C₃×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
19	C₃×ΓL(1,𝔽₈)	—	103	1	no	Hall
20	C₃²×C₅	—	721	1	no	Hall
21	C₅×C₇	C₃×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	C₅×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented
23	ΓL(1,𝔽₈)	—	103	3	no	—
24	C₃×C₅	—	721	3	no	—
25	C₃×C₅	#14524190	1	1	yes	characteristic, direct product factor
26	C₃²	—	721	1	no	Sylow
27	C₇	C₃×C₅×C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₅	C₃×#14524190	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	721	3	no	—
30	C₃	C₅×#14524190	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₅	#14524190
commutator, cosocle, hypocenter	C₇×C₁₀₃	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₀₃	C₃
LCS	G ▷ C₇×C₁₀₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14524190	C₃	direct (N × H)
2. C₃×C₅×C₇×C₁₀₃	C₃	semidirect
3. C₃×#14524190	C₅	direct (N × H)
5. C₅×C₇×C₁₀₃	C₃²	semidirect
6. C₃×C₇×C₁₀₃	C₃×C₅	semidirect
7. #14524190	C₃×C₅	direct (N × H)
8. C₃×C₅×C₁₀₃	ΓL(1,𝔽₈)	semidirect
11. C₇×C₁₀₃	C₃²×C₅	semidirect
12. C₅×C₁₀₃	C₃×ΓL(1,𝔽₈)	semidirect
14. C₃×C₁₀₃	C₅×ΓL(1,𝔽₈)	semidirect
16. C₃×C₅×C₇	C₁₀₃⋊C₃	semidirect
18. C₁₀₃	C₃×C₅×ΓL(1,𝔽₈)	semidirect
21. C₅×C₇	C₃×C₁₀₃⋊C₃	semidirect
22. C₃×C₇	C₅×C₁₀₃⋊C₃	semidirect
25. C₃×C₅	#14524190	direct (N × H)
27. C₇	C₃×C₅×C₁₀₃⋊C₃	semidirect
28. C₅	C₃×#14524190	direct (N × H)
30. C₃	C₅×#14524190	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×#14524190	3
C₃×C₅×C₇×C₁₀₃	3
C₃×#14524190	5
C₃×C₅×C₁₀₃⋊C₃	7
C₃×C₅×ΓL(1,𝔽₈)	103

Subgroups — C3×C5×#14524190 #44570073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14524190 #44570073