Subgroups — C₇×C₅⋊D₅×C₇₃ #38784381

Order 25550.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₇₃	—	5	6	no	maximal
3	C₅⋊D₅×C₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₇₃	D₅	1	6	yes	complemented
5	C₅²×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₇₃	—	25	1	no	Hall
7	D₅×C₇₃	—	5	6	no	—
8	C₇×C₇₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇₃	C₇×D₅	1	6	yes	complemented
10	C₇×C₅⋊D₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅²×C₇	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇₃	—	25	1	no	Hall
13	C₇₃	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₇×D₅	—	5	6	no	—
15	C₅⋊D₅	C₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇	D₅×C₇₃	1	6	yes	complemented
17	C₅²	C₂×C₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	25	1	no	Hall
19	D₅	—	5	6	no	—
20	C₇	C₅⋊D₅×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×D₅×C₇₃	1	6	yes	complemented
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₇₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇×C₇₃
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₇₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₇×C₇₃

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.