Subgroups — C₇×C₄₁×D₂₅ #28385124

Order 14350.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₄₁	—	5	1	no	maximal
3	C₄₁×D₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₄₁	D₅	1	1	yes	characteristic
5	C₂₅×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₄₁	—	25	1	no	Hall
7	D₅×C₄₁	—	5	1	no	—
8	C₇×D₂₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₄₁	D₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₄₁	C₇×D₅	1	1	yes	characteristic
11	C₇×C₂₅	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₄₁	—	25	1	no	Hall
13	C₇×D₅	—	5	1	no	—
14	D₂₅	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
15	C₄₁	C₇×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₇	D₅×C₄₁	1	1	yes	characteristic
17	C₂₅	C₂×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	25	1	no	Hall
19	D₅	—	5	1	no	—
20	C₇	C₄₁×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×D₅×C₄₁	1	1	yes	characteristic
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₁	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₇×C₄₁
Frattini	C₅	C₇×D₅×C₄₁
Fitting	C₇×C₂₅×C₄₁	C₂
socle	C₅×C₇×C₄₁	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₇×C₄₁

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.