Subgroups — #20301201

Order 7350.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊D₂₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#11760384	—	7	1	no	maximal
5	C₇×C₅²⋊C₃	D₇	1	1	yes	characteristic
6	D₂₄₅	—	15	2	no	—
7	C₅⋊D₃₅	—	7	1	no	—
8	C₃×D₄₉	—	25	1	no	maximal, Hall
9	C₅×C₄₉	—	3	2	no	—
10	C₅²×C₇	C₃×D₇	1	1	yes	characteristic
11	(C₅⋊D₅)⋊C₃	—	49	1	no	Hall
12	C₃×C₄₉	—	25	1	no	Hall
13	D₄₉	—	25	1	no	Hall
14	C₅²⋊C₃	D₄₉	1	1	yes	characteristic, complemented, Hall
15	D₃₅	—	105	2	no	—
16	C₅⋊D₅	—	49	1	no	Hall
17	C₄₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₇	—	175	1	no	—
19	C₅×C₇	—	3	2	no	—
20	C₅²	C₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₇	—	25	1	no	—
22	D₇	—	175	1	no	—
23	D₅	—	735	2	no	—
24	C₇	#11760384	1	1	yes	characteristic
25	C₂×C₃	—	1225	1	no	Hall
26	C₅	—	3	2	no	—
27	C₃	—	25	1	no	Sylow
28	C₂	—	1225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₄₉	C₂×C₃
Frattini	C₇	#11760384
socle	C₅²×C₇	C₃×D₇
LCS	G ▷ C₅²×C₄₉
UCS	C₁

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