Subgroups — C₁₃×C₂₉×D₂₅ #34038121

Order 18850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₃×C₂₉	—	5	1	no	maximal
3	C₅×C₁₃×C₂₉	D₅	1	1	yes	characteristic
4	C₂₉×D₂₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₂₉	—	25	1	no	Hall
6	C₂₅×C₂₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₂₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×C₂₉	D₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₁₃×C₂₅	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
10	D₅×C₂₉	—	5	1	no	—
11	C₅×C₂₉	D₅×C₁₃	1	1	yes	characteristic
12	D₅×C₁₃	—	5	1	no	—
13	C₅×C₁₃	D₅×C₂₉	1	1	yes	characteristic
14	C₂×C₂₉	—	25	1	no	Hall
15	D₂₅	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂₉	C₁₃×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₃	—	25	1	no	Hall
18	C₂₅	C₂×C₁₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	C₂₉×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
20	D₅	—	5	1	no	—
21	C₅	D₅×C₁₃×C₂₉	1	1	yes	characteristic
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₂₉	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₁₃×C₂₉
Frattini	C₅	D₅×C₁₃×C₂₉
Fitting	C₁₃×C₂₅×C₂₉	C₂
socle	C₅×C₁₃×C₂₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₁₃×C₂₉

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.