Subgroups — C₃×C₅⋊D₅×C₁₄₉ #36375321

Order 22350.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊D₅×C₁₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₁₄₉	—	5	6	no	maximal
4	C₅²×C₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₄₉	D₅	1	6	yes	complemented
6	D₅×C₁₄₉	—	5	6	no	—
7	C₂×C₃×C₁₄₉	—	25	1	no	Hall
8	C₅×C₁₄₉	C₃×D₅	1	6	yes	complemented
9	C₃×C₁₄₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₄₉	—	25	1	no	Hall
11	C₃×C₅⋊D₅	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₄₉	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₅²	C₂×C₁₄₉	1	1	yes	characteristic, complemented, Hall
14	C₅⋊D₅	C₃×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×D₅	—	5	6	no	—
16	C₅²	C₂×C₃×C₁₄₉	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	D₅×C₁₄₉	1	6	yes	complemented
18	D₅	—	5	6	no	—
19	C₂×C₃	—	25	1	no	Hall
20	C₅	C₃×D₅×C₁₄₉	1	6	yes	complemented
21	C₃	C₅⋊D₅×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₄₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₄₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₄₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₄₉

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

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