Subgroups — C₂×D₂₅×C₂₃₉ #37560721

Order 23900.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₅×C₂₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₅×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×C₂₃₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₂₃₉	—	5	1	no	maximal
5	C₂×C₅×C₂₃₉	D₅	1	1	yes	characteristic
6	D₅×C₂₃₉	—	5	2	no	—
7	C₅×C₂₃₉	C₂×D₅	1	1	yes	characteristic
8	C₂²×C₂₃₉	—	25	1	no	Hall
9	C₂×C₂₃₉	—	25	2	no	—
10	C₂×C₂₃₉	D₂₅	1	1	yes	characteristic, direct product factor
11	C₂₃₉	C₂×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×D₂₅	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₂₅	C₂×C₂₃₉	1	1	yes	characteristic, complemented
14	D₂₅	C₂×C₂₃₉	1	2	yes	direct product factor
15	C₂₅	C₂²×C₂₃₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅	—	5	1	no	—
17	C₂×C₅	D₅×C₂₃₉	1	1	yes	characteristic
18	D₅	—	5	2	no	—
19	C₅	C₂×D₅×C₂₃₉	1	1	yes	characteristic
20	C₂²	—	25	1	no	Sylow
21	C₂	—	25	2	no	—
22	C₂	D₂₅×C₂₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃₉	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₂₃₉
Frattini	C₅	C₂×D₅×C₂₃₉
Fitting	C₂×C₂₅×C₂₃₉	C₂
socle	C₂×C₅×C₂₃₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₂₃₉

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.