Subgroups — #26043377

Order 11700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19154330	C₂	1	1	yes	maximal, characteristic
2	C₃×#13049928	C₃	1	1	yes	maximal, characteristic
3	C₁₃⋊(C₅²⋊C₉)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅⋊D₆₅	C₂×C₃	1	1	yes	characteristic
5	#13049928	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₁₃	C₃×C₄	1	1	yes	characteristic
7	#1043⋊C₉	—	13	1	no	maximal, Hall
8	C₃×#63122	—	15	2	no	—
9	C₅⋊D₆₅	C₂×C₉	1	1	yes	characteristic
10	#261⋊C₉	—	25	1	no	maximal, Hall
11	(C₅⋊D₅)⋊C₉	—	13	1	no	—
12	C₃×D₆₅	—	15	2	no	—
13	C₅²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃×#1043	—	13	1	no	—
15	#63122	—	15	2	no	—
16	D₁₃⋊C₉	—	25	1	no	—
17	C₅²⋊C₉	—	13	1	no	Hall
18	C₃×C₅×C₁₃	—	3	2	no	—
19	C₃×#261	—	25	1	no	—
20	C₃×C₅⋊D₅	—	13	1	no	—
21	D₆₅	—	15	2	no	—
22	C₁₃⋊C₉	—	25	1	no	Hall
23	#1043	—	13	1	no	Hall
24	C₃×D₁₃	—	25	1	no	—
25	C₃×C₅²	AGL(1,𝔽₁₃)	1	1	yes	characteristic
26	C₅×C₁₃	—	3	2	no	—
27	C₃×AGL(1,𝔽₅)	—	195	2	no	—
28	#261	—	25	1	no	Hall
29	C₅⋊D₅	—	13	1	no	—
30	C₃×C₁₃	#1043⋊C₃	1	1	yes	characteristic
31	C₄×C₉	—	325	1	no	Hall
32	C₃×D₅	—	195	2	no	—
33	D₁₃	—	25	1	no	—
34	C₅²	#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
35	AGL(1,𝔽₅)	—	195	2	no	—
36	C₂×C₉	—	325	1	no	—
37	C₃×C₅	—	3	2	no	—
38	C₁₃	#1043⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₄	—	325	1	no	—
40	D₅	—	195	2	no	—
41	C₉	—	325	1	no	Sylow
42	C₂×C₃	—	325	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	325	1	no	Sylow
45	C₃	#16839103	1	1	yes	characteristic
46	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#16839103
commutator, hypocenter	C₅²×C₁₃	C₄×C₉
Fitting, socle	C₃×C₅²×C₁₃	C₃×C₄
prime radical, cosocle	C₃×C₅⋊D₆₅	C₂×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₁₃⋊(C₅²⋊C₉)	C₄	semidirect
5. #13049928	C₉	semidirect
13. C₅²×C₁₃	C₄×C₉	semidirect
34. C₅²	#261⋊C₉	semidirect
38. C₁₃	#1043⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#19154330	2
C₃×#13049928	3
#1043⋊C₉	13
#261⋊C₉	25