Subgroups — C₅×C₇₃×C₇⋊D₇ #49088708

Order 35770.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₇×C₇₃	—	7	8	no	maximal
4	C₇²×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₇₃	D₇	1	8	yes	complemented
6	D₇×C₇₃	—	7	8	no	—
7	C₂×C₅×C₇₃	—	49	1	no	Hall
8	C₇×C₇₃	C₅×D₇	1	8	yes	complemented
9	C₅×C₇⋊D₇	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₇₃	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₇²	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇₃	—	49	1	no	Hall
13	C₇⋊D₇	C₅×C₇₃	1	1	yes	characteristic, direct product factor, Hall
14	C₇₃	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₅×D₇	—	7	8	no	—
16	C₇²	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₇	D₇×C₇₃	1	8	yes	complemented
18	D₇	—	7	8	no	—
19	C₂×C₅	—	49	1	no	Hall
20	C₇	C₅×D₇×C₇₃	1	8	yes	complemented
21	C₅	C₇₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇₃	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₅×C₇₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₇₃	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×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.