Subgroups — #36347607

Order 22050.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₂₄₅	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅²×C₄₉	C₂×C₃	1	1	yes	characteristic
4	#15691245	—	7	1	no	maximal
5	C₅⋊D₂₄₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×C₅²⋊C₉	D₇	1	1	yes	characteristic
7	C₃×D₂₄₅	—	15	2	no	—
8	C₅²×C₄₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅⋊D₃₅	—	7	1	no	—
10	C₉×D₄₉	—	25	1	no	maximal, Hall
11	C₃×C₅×C₄₉	—	3	2	no	—
12	C₃×C₅²×C₇	C₃×D₇	1	1	yes	characteristic
13	D₂₄₅	—	15	2	no	—
14	(C₅⋊D₅)⋊C₉	—	49	1	no	Hall
15	C₉×C₄₉	—	25	1	no	Hall
16	C₅⋊D₃₅	—	7	1	no	—
17	C₃×D₄₉	—	75	1	no	—
18	C₅×C₄₉	—	3	2	no	—
19	C₅²⋊C₉	D₄₉	1	1	yes	characteristic, complemented, Hall
20	C₃×D₃₅	—	105	2	no	—
21	C₅²×C₇	C₉×D₇	1	1	yes	characteristic
22	C₃×C₅⋊D₅	—	49	1	no	—
23	C₃×C₄₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
24	C₉×D₇	—	175	1	no	—
25	C₃×C₅×C₇	—	3	2	no	—
26	D₄₉	—	75	1	no	Hall
27	C₃×C₅²	C₃×D₄₉	1	1	yes	characteristic
28	D₃₅	—	105	2	no	—
29	C₇×C₉	—	25	1	no	—
30	C₅⋊D₅	—	49	1	no	Hall
31	C₄₉	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	525	1	no	—
33	C₅×C₇	—	3	2	no	—
34	C₃×D₅	—	735	2	no	—
35	C₅²	C₉×D₄₉	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	#11760384	1	1	yes	characteristic
37	C₂×C₉	—	1225	1	no	Hall
38	C₃×C₅	—	3	2	no	—
39	D₇	—	525	1	no	—
40	D₅	—	735	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₇	#15691245	1	1	yes	characteristic
43	C₂×C₃	—	3675	1	no	—
44	C₅	—	3	2	no	—
45	C₃	#20301201	1	1	yes	characteristic
46	C₂	—	3675	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#20301201
commutator, hypocenter	C₅²×C₄₉	C₂×C₉
Frattini	C₃×C₇	#11760384
Fitting, cosocle	C₃×C₅²×C₄₉	C₂×C₃
socle	C₃×C₅²×C₇	C₃×D₇
prime radical	C₃×C₅⋊D₂₄₅	C₃
LCS	G ▷ C₅²×C₄₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₄₉×C₅²⋊C₉	C₂	semidirect
5. C₅⋊D₂₄₅	C₉	semidirect
8. C₅²×C₄₉	C₂×C₉	semidirect
19. C₅²⋊C₉	D₄₉	semidirect
31. C₄₉	(C₅⋊D₅)⋊C₉	semidirect
35. C₅²	C₉×D₄₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₉×C₅²⋊C₉	2
C₃×C₅⋊D₂₄₅	3
#15691245	7
C₉×D₄₉	25