Subgroups — D₅⋊#5997 #14520022

Order 1960.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	#11758266	C₂	1	2	yes	maximal, complemented
3	C₅⋊(C₇⋊D₇)	C₂²	1	1	yes	characteristic
4	C₇²×D₅	C₄	1	1	yes	characteristic, complemented
5	C₅×C₇⋊D₇	C₄	1	1	yes	characteristic, complemented
6	C₂×#5997	—	5	1	no	maximal, Hall
7	C₅×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇⋊D₇	—	5	1	no	—
9	#5997	—	5	2	no	—
10	D₅×D₇	—	14	4	no	—
11	C₂×C₇²	—	5	1	no	—
12	C₇⋊D₇	—	5	1	no	—
13	C₇⋊D₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
14	D₃₅	—	14	4	no	—
15	C₅×D₇	—	14	4	no	—
16	C₇×D₅	—	2	4	no	—
17	C₇²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₂×AGL(1,𝔽₅)	—	49	1	no	maximal, Hall
19	C₅×C₇	—	2	4	no	—
20	C₂×D₇	—	70	4	no	—
21	C₂×D₅	—	49	1	no	—
22	AGL(1,𝔽₅)	—	49	2	no	—
23	C₂×C₇	—	10	4	no	—
24	D₇	—	14	4	no	—
25	D₇	—	70	4	no	—
26	C₂×C₅	—	49	1	no	—
27	D₅	—	49	1	no	—
28	D₅	#5997	1	1	yes	characteristic, complemented
29	C₂×C₄	—	245	1	no	Sylow
30	C₇	—	2	4	no	—
31	C₅	C₂×#5997	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	245	1	no	—
33	C₄	—	245	2	no	—
34	C₂	—	5	1	no	—
35	C₂	—	49	1	no	—
36	C₂	—	245	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²	C₂×C₄
prime radical	D₅×C₇⋊D₇	C₂
cosocle	C₅⋊(C₇⋊D₇)	C₂²
LCS	G ▷ C₅×C₇²
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.