Subgroups — C₇⋊#19104097 #49112674

Order 35980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₅₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#11759967	—	5	1	no	maximal, Hall
4	#19104097	—	7	1	no	maximal, Hall
5	C₇×D₂₅₇	D₅	1	1	yes	characteristic
6	C₅×D₂₅₇	D₇	1	1	yes	characteristic
7	C₇×C₂₅₇	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₅₇	Dic₇	1	1	yes	characteristic, complemented, Hall
9	#11759967	—	35	1	no	Hall
10	D₂₅₇	D₃₅	1	1	yes	characteristic
11	C₂₅₇	Dic₃₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₃₅	—	257	1	no	maximal, Hall
13	C₂×C₅×C₇	—	257	1	no	—
14	C₅×C₇	#11759967	1	1	yes	characteristic, complemented, Hall
15	Dic₇	—	1285	1	no	Hall
16	Dic₅	—	1799	1	no	Hall
17	C₂×C₇	—	257	1	no	—
18	C₂×C₅	—	257	1	no	—
19	C₇	#19104097	1	1	yes	characteristic, complemented, Sylow
20	C₅	C₇⋊#11759967	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8995	1	no	Sylow
22	C₂	—	257	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₂₅₇	C₄
prime radical, cosocle	C₅×C₇×D₂₅₇	C₂
LCS	G ▷ C₅×C₇×C₂₅₇
UCS	C₁

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.