Subgroups — (C₅⋊D₅)⋊#3861 #20301296

Order 7350.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	—	7	8	no	maximal
5	C₇⋊(C₅²⋊C₃)	—	7	8	no	—
6	C₇²×D₅	—	15	2	no	—
7	C₇×C₅⋊D₅	ΓL(1,𝔽₈)	1	8	yes	complemented
8	C₂×#3861	—	25	1	no	maximal, Hall
9	C₅×C₇²	—	3	2	no	—
10	C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
11	(C₅⋊D₅)⋊C₃	—	49	1	no	Hall
12	#3861	—	25	1	no	Hall
13	C₂×C₇²	—	25	1	no	Hall
14	C₅²⋊C₃	—	49	1	no	Hall
15	C₇×D₅	—	15	16	no	—
16	C₅⋊D₅	#3861	1	1	yes	characteristic, complemented, Hall
17	C₇²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×ΓL(1,𝔽₈)	—	175	8	no	—
19	C₅×C₇	—	3	16	no	—
20	C₅²	C₂×#3861	1	1	yes	characteristic, complemented, Sylow
21	ΓL(1,𝔽₈)	—	175	8	no	—
22	C₂×C₇	—	25	8	no	—
23	D₅	—	15	2	no	—
24	C₇	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	1	8	yes	complemented
25	C₂×C₃	—	1225	1	no	Hall
26	C₅	—	3	2	no	—
27	C₃	—	1225	1	no	Sylow
28	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.