Subgroups — C₁₇×C₁₉×D₂₅ #30633367

Order 16150.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₇×C₁₉	—	5	1	no	maximal
3	C₅×C₁₇×C₁₉	D₅	1	1	yes	characteristic
4	C₁₉×D₂₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇×D₂₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₇×C₁₉	—	25	1	no	Hall
7	C₁₉×C₂₅	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₂₅	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₁₉	D₂₅	1	1	yes	characteristic, direct product factor, Hall
10	D₅×C₁₉	—	5	1	no	—
11	D₅×C₁₇	—	5	1	no	—
12	C₅×C₁₉	D₅×C₁₇	1	1	yes	characteristic
13	C₅×C₁₇	D₅×C₁₉	1	1	yes	characteristic
14	D₂₅	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₉	—	25	1	no	Hall
16	C₂×C₁₇	—	25	1	no	Hall
17	C₂₅	C₂×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
18	C₁₉	C₁₇×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₁₉×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
20	D₅	—	5	1	no	—
21	C₅	D₅×C₁₇×C₁₉	1	1	yes	characteristic
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₁₇×C₁₉
Frattini	C₅	D₅×C₁₇×C₁₉
Fitting	C₁₇×C₁₉×C₂₅	C₂
socle	C₅×C₁₇×C₁₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₁₇×C₁₉

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.