Subgroups — C₄×C₂₅×C₁₀₉⋊C₃ #45658166

Order 32700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₅×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₅×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₅×C₁₀₉⋊C₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₅×C₁₀₉⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₂₅×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₅×C₁₀₉	C₃×C₅	1	1	yes	characteristic
9	C₅×C₁₀₉⋊C₃	C₄×C₅	1	1	yes	characteristic
10	C₄×C₁₀₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₀₉	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₁₀₉⋊C₃	C₂×C₂₅	1	1	yes	characteristic
13	C₅×C₁₀₉	C₃×C₄×C₅	1	1	yes	characteristic
14	C₄×C₁₀₉	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₁₀₉⋊C₃	C₄×C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄×C₂₅	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	C₂×C₃×C₂₅	1	1	yes	characteristic
18	C₂×C₃×C₂₅	—	109	1	no	—
19	C₁₀₉	C₃×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₄×C₂₅	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₂₅	—	109	1	no	Hall
22	C₃×C₄×C₅	—	109	1	no	—
23	C₂×C₂₅	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic
24	C₂×C₃×C₅	—	109	1	no	—
25	C₂₅	C₄×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	C₅×C₁₀₉⋊C₃	1	1	yes	characteristic
27	C₃×C₅	—	109	1	no	—
28	C₃×C₄	—	109	1	no	Hall
29	C₂×C₅	C₂×C₅×C₁₀₉⋊C₃	1	1	yes	characteristic
30	C₂×C₃	—	109	1	no	—
31	C₅	C₄×C₅×C₁₀₉⋊C₃	1	1	yes	characteristic
32	C₄	C₂₅×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	109	1	no	Sylow
34	C₂	C₂×C₂₅×C₁₀₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₂₅	C₁₀₉⋊C₃
commutator, hypocenter	C₁₀₉	C₃×C₄×C₂₅
Frattini	C₂×C₅	C₂×C₅×C₁₀₉⋊C₃
Fitting	C₄×C₂₅×C₁₀₉	C₃
socle, cosocle	C₂×C₅×C₁₀₉	C₂×C₃×C₅
prime radical	C₂×C₅×C₁₀₉⋊C₃	C₂×C₅
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₄×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₅×C₁₀₉	C₃	semidirect
3. C₂₅×C₁₀₉⋊C₃	C₄	direct (N × H)
7. C₂₅×C₁₀₉	C₃×C₄	semidirect
10. C₄×C₁₀₉⋊C₃	C₂₅	direct (N × H)
14. C₄×C₁₀₉	C₃×C₂₅	semidirect
15. C₁₀₉⋊C₃	C₄×C₂₅	direct (N × H)
19. C₁₀₉	C₃×C₄×C₂₅	semidirect
20. C₄×C₂₅	C₁₀₉⋊C₃	direct (N × H)
25. C₂₅	C₄×C₁₀₉⋊C₃	direct (N × H)
32. C₄	C₂₅×C₁₀₉⋊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
C₂×C₂₅×C₁₀₉⋊C₃	2
C₄×C₂₅×C₁₀₉	3
C₄×C₅×C₁₀₉⋊C₃	5
C₃×C₄×C₂₅	109

Subgroups — C4×C25×C109⋊C3 #45658166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₅×C₁₀₉⋊C₃ #45658166