Subgroups — (C₅⋊D₅)⋊D₇ #10622011

Order 700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₇	—	5	2	no	maximal
5	D₅²	—	7	1	no	maximal, Hall
6	D₃₅	D₅	1	2	yes	complemented
7	C₅×D₇	—	5	2	no	—
8	C₇×D₅	—	5	2	no	—
9	C₇×D₅	—	10	2	no	—
10	C₅⋊D₅	D₇	1	1	yes	characteristic, complemented
11	C₅×D₅	—	7	2	no	—
12	C₅×C₇	—	2	2	no	—
13	C₅×C₇	C₂×D₅	1	2	yes	complemented
14	C₂×D₇	—	25	1	no	Hall
15	C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅	—	35	2	no	—
17	C₂×C₇	—	25	1	no	—
18	D₇	—	5	2	no	—
19	C₂×C₅	—	35	2	no	—
20	D₅	—	5	2	no	—
21	D₅	—	7	2	no	—
22	D₅	—	10	2	no	—
23	C₇	D₅²	1	1	yes	characteristic, complemented, Sylow
24	C₅	—	2	2	no	—
25	C₅	D₅×D₇	1	2	yes	complemented
26	C₂²	—	175	1	no	Sylow
27	C₂	—	25	1	no	—
28	C₂	—	35	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇	C₂²
LCS	G ▷ C₅²×C₇
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.