Subgroups — Dic₂₅×C₂₈₉ #43274607

Order 28900.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₂₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₂₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₅×C₂₈₉	—	5	1	no	maximal
4	C₂×C₅×C₂₈₉	D₅	1	1	yes	characteristic
5	C₁₇×Dic₂₅	C₁₇	1	1	yes	maximal, characteristic
6	C₅×C₂₈₉	Dic₅	1	1	yes	characteristic
7	C₄×C₂₈₉	—	25	1	no	Hall
8	C₂×C₁₇×C₂₅	C₂×C₁₇	1	1	yes	characteristic
9	C₂×C₂₈₉	D₂₅	1	1	yes	characteristic
10	C₁₇×C₂₅	C₄×C₁₇	1	1	yes	characteristic
11	C₁₇×Dic₅	—	5	1	no	—
12	C₂₈₉	Dic₂₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₅×C₁₇	D₅×C₁₇	1	1	yes	characteristic
14	Dic₂₅	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₇	C₁₇×Dic₅	1	1	yes	characteristic
16	C₄×C₁₇	—	25	1	no	—
17	C₂×C₂₅	C₂×C₂₈₉	1	1	yes	characteristic
18	C₂×C₁₇	C₁₇×D₂₅	1	1	yes	characteristic
19	C₂₅	C₄×C₂₈₉	1	1	yes	characteristic, complemented, Sylow
20	Dic₅	—	5	1	no	—
21	C₁₇	C₁₇×Dic₂₅	1	1	yes	characteristic
22	C₂×C₅	D₅×C₂₈₉	1	1	yes	characteristic
23	C₅	Dic₅×C₂₈₉	1	1	yes	characteristic
24	C₄	—	25	1	no	Sylow
25	C₂	D₂₅×C₂₈₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₈₉	D₂₅
commutator, hypocenter	C₂₅	C₄×C₂₈₉
Frattini, socle, prime radical	C₂×C₅×C₁₇	D₅×C₁₇
Fitting	C₂×C₂₅×C₂₈₉	C₂
cosocle	C₂×C₁₇×C₂₅	C₂×C₁₇
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₂₈₉

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.