Subgroups — C₇×D₇₇₅ #24925744

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₅₅	—	5	1	no	maximal
3	D₇₇₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₁	D₅	1	1	yes	characteristic
5	C₂₅×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₃₁	—	25	1	no	Hall
7	C₇×D₂₅	—	31	1	no	maximal, Hall
8	D₁₅₅	—	5	1	no	—
9	C₇×C₃₁	D₂₅	1	1	yes	characteristic, complemented, Hall
10	C₇×C₂₅	D₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	C₇×D₅	1	1	yes	characteristic
12	C₇×D₅	—	155	1	no	—
13	D₃₁	—	25	1	no	Hall
14	D₂₅	—	31	1	no	Hall
15	C₅×C₇	D₁₅₅	1	1	yes	characteristic
16	C₃₁	C₇×D₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	C₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	775	1	no	Hall
19	D₅	—	155	1	no	—
20	C₇	D₇₇₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×D₁₅₅	1	1	yes	characteristic
22	C₂	—	775	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₇₇₅
commutator, cosocle, hypocenter	C₂₅×C₃₁	C₂×C₇
Frattini	C₅	C₇×D₁₅₅
Fitting	C₇×C₂₅×C₃₁	C₂
socle	C₅×C₇×C₃₁	D₅
LCS	G ▷ C₂₅×C₃₁
UCS	C₁ ◁ C₇

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.