Subgroups — #45685969

Order 33300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₅⋊D₅)⋊#66524	C₂	1	1	yes	maximal, characteristic
2	C₃×#16814879	C₃	1	1	yes	maximal, characteristic
3	C₅²⋊#66524	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	#16814879	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic
7	C₃×#10625193	—	15	2	no	—
8	C₃₇×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
9	#13050607	—	25	1	no	maximal, Hall
10	C₃×D₅×C₃₇	—	15	2	no	—
11	C₅²×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	#1043⋊C₉	—	37	1	no	maximal, Hall
13	#10625193	—	15	2	no	—
14	C₂×#66524	—	25	1	no	—
15	C₃×C₅×C₃₇	—	3	2	no	—
16	(C₅⋊D₅)⋊C₉	—	37	1	no	—
17	C₃×Dic₃₇	—	25	1	no	—
18	D₅×C₃₇	—	15	2	no	—
19	#66524	—	25	1	no	Hall
20	C₃×#1043	—	37	1	no	—
21	C₅²⋊C₉	—	37	1	no	Hall
22	C₂×C₃×C₃₇	—	25	1	no	—
23	C₅×C₃₇	—	3	2	no	—
24	C₃×C₅⋊D₅	D₃₇⋊C₃	1	1	yes	characteristic
25	Dic₃₇	—	25	1	no	Hall
26	C₃×C₃₇	#1043⋊C₃	1	1	yes	characteristic
27	#1043	—	37	1	no	Hall
28	C₃×C₅²	Dic₃₇⋊C₃	1	1	yes	characteristic
29	C₂×C₃₇	—	25	1	no	—
30	C₃×AGL(1,𝔽₅)	—	555	2	no	—
31	C₅⋊D₅	#66524⋊C₂	1	1	yes	characteristic
32	C₃₇	#1043⋊C₉	1	1	yes	characteristic, complemented, Sylow
33	C₄×C₉	—	925	1	no	Hall
34	C₃×D₅	—	15	2	no	—
35	C₅²	#13050607	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	555	2	no	—
37	C₂×C₉	—	925	1	no	—
38	C₃×C₅	—	3	2	no	—
39	C₃×C₄	—	925	1	no	—
40	D₅	—	15	2	no	—
41	C₉	—	925	1	no	Sylow
42	C₂×C₃	—	25	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	925	1	no	Sylow
45	C₃	#26012840	1	1	yes	characteristic
46	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#26012840
commutator, hypocenter	C₅²×C₃₇	C₄×C₉
Fitting, socle	C₃×C₅²×C₃₇	C₃×C₄
prime radical, cosocle	C₃×C₃₇×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅²⋊#66524	C₄	semidirect
5. #16814879	C₉	semidirect
11. C₅²×C₃₇	C₄×C₉	semidirect
32. C₃₇	#1043⋊C₉	semidirect
35. C₅²	#13050607	semidirect

Maximal subgroups

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

subgroup	index
(C₅⋊D₅)⋊#66524	2
C₃×#16814879	3
#13050607	25
#1043⋊C₉	37