Subgroups — #26043859

Order 11700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#14556847	—	5	6	no	maximal
4	C₅²×D₃×C₁₃	—	6	2	no	—
5	#13049918	—	9	1	no	maximal, Hall
6	C₅×C₁₃×C₃⋊D₃	D₅	1	6	yes	—
7	C₃×C₅²×C₁₃	—	2	2	no	—
8	#11744710	—	13	1	no	maximal, Hall
9	C₂×C₅²×C₁₃	—	9	1	no	—
10	C₃²×C₅×C₁₃	Dic₅	1	6	yes	complemented
11	#90865	—	25	1	no	Hall
12	C₅²×C₃⋊D₃	D₁₃	1	1	yes	characteristic
13	C₅×D₃×C₁₃	—	6	12	no	—
14	C₅²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
15	Dic₆₅	—	45	6	no	—
16	C₁₃×C₃⋊D₃	C₅⋊D₅	1	1	yes	characteristic
17	C₃²×C₅²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₁₃	—	2	12	no	—
19	#4379	—	65	6	no	—
20	C₅²×D₃	—	6	2	no	—
21	C₂×C₅×C₁₃	—	9	6	no	—
22	C₃²×C₁₃	#1039	1	1	yes	characteristic, complemented, Hall
23	#1039	—	117	1	no	Hall
24	C₅×C₃⋊D₃	D₆₅	1	6	yes	—
25	D₃×C₁₃	—	6	2	no	—
26	C₃×C₅²	—	2	2	no	—
27	C₅×C₁₃	#4379	1	6	yes	complemented
28	Dic₁₃	—	225	1	no	Hall
29	C₂×C₅²	—	9	1	no	—
30	C₃²×C₅	Dic₆₅	1	6	yes	complemented
31	C₃×C₁₃	—	2	2	no	—
32	#157	—	325	1	no	Hall
33	C₅×D₃	—	6	12	no	—
34	C₂×C₁₃	—	9	1	no	—
35	C₅²	#90865	1	1	yes	characteristic, complemented, Sylow
36	Dic₅	—	585	6	no	—
37	C₃⋊D₃	C₅⋊D₆₅	1	1	yes	characteristic
38	C₃×C₅	—	2	12	no	—
39	C₁₃	#11744710	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	9	6	no	—
41	C₃²	#13049918	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	#14556847	1	6	yes	complemented
44	C₄	—	2925	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₃	C₄
prime radical, cosocle	C₅²×C₁₃×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₅²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₃	C₄	semidirect
10. C₃²×C₅×C₁₃	Dic₅	semidirect
14. C₅²×C₁₃	#157	semidirect
17. C₃²×C₅²	Dic₁₃	semidirect
22. C₃²×C₁₃	#1039	semidirect
27. C₅×C₁₃	#4379	semidirect
30. C₃²×C₅	Dic₆₅	semidirect
35. C₅²	#90865	semidirect
39. C₁₃	#11744710	semidirect
41. C₃²	#13049918	semidirect
43. C₅	#14556847	semidirect

Maximal subgroups

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

subgroup	index
C₅²×C₁₃×C₃⋊D₃	2
#14556847	5
#13049918	9
#11744710	13