Subgroups — C₅₃×C₅⋊(C₇⋊D₇) #39906901

Order 25970.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₃×C₇⋊D₇	—	5	1	no	maximal, Hall
3	C₅₃×D₃₅	—	7	8	no	maximal
4	C₇²×C₅₃	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₅₃	D₇	1	8	yes	complemented
6	D₇×C₅₃	—	35	8	no	—
7	D₅×C₅₃	—	49	1	no	Hall
8	C₅⋊(C₇⋊D₇)	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₅₃	D₃₅	1	8	yes	complemented
10	C₅×C₅₃	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇²	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅₃	—	245	1	no	Hall
13	C₇⋊D₇	—	5	1	no	Hall
14	D₃₅	—	7	8	no	—
15	C₅₃	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
16	C₇²	D₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₇	D₇×C₅₃	1	8	yes	complemented
18	D₇	—	35	8	no	—
19	D₅	—	49	1	no	Hall
20	C₇	C₅₃×D₃₅	1	8	yes	complemented
21	C₅	C₅₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	C₅⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₅×C₇²	C₂×C₅₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₅₃	C₂
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₅₃

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.