Subgroups — #49137613

Order 36300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×(C₁₁⋊D₁₁)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#27130990	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#14559102⋊C₃	—	5	6	no	maximal
5	C₅²×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
6	C₅×(C₁₁⋊D₁₁)⋊C₃	D₅	1	6	yes	—
7	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#14559102	—	5	6	no	—
9	C₅×C₁₁²⋊C₃	Dic₅	1	6	yes	complemented
10	#92150⋊C₃	—	25	1	no	Hall
11	C₅×C₁₁⋊D₁₁	C₃×D₅	1	6	yes	—
12	(C₁₁⋊D₁₁)⋊C₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅×C₁₁²	C₃×Dic₅	1	6	yes	complemented
14	C₅²×D₁₁	—	66	2	no	—
15	#92150	—	25	1	no	Hall
16	C₁₁²⋊C₃	#1039	1	1	yes	characteristic, complemented, Hall
17	C₃×#1039	—	121	1	no	maximal, Hall
18	C₅²×C₁₁	—	6	2	no	—
19	C₁₁⋊D₁₁	C₃×C₅⋊D₅	1	1	yes	characteristic
20	C₂×C₃×C₅²	—	121	1	no	—
21	C₁₁²	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
22	C₅×D₁₁	—	66	12	no	—
23	#1039	—	121	1	no	Hall
24	C₃×C₅²	—	484	1	no	Hall
25	C₃×Dic₅	—	605	6	no	—
26	C₅×C₁₁	—	6	12	no	—
27	C₂×C₅²	—	121	1	no	—
28	C₂×C₃×C₅	—	121	6	no	—
29	C₅²	#92150⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	D₁₁	—	66	2	no	—
31	Dic₅	—	605	6	no	—
32	C₃×C₅	—	484	6	no	—
33	C₃×C₄	—	3025	1	no	Hall
34	C₁₁	—	6	2	no	—
35	C₂×C₅	—	121	6	no	—
36	C₂×C₃	—	121	1	no	—
37	C₅	#14559102⋊C₃	1	6	yes	complemented
38	C₄	—	3025	1	no	Sylow
39	C₃	—	484	1	no	Sylow
40	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁²	C₃×C₄
prime radical	C₅²×(C₁₁⋊D₁₁)⋊C₃	C₂
cosocle	C₅²×C₁₁⋊D₁₁	C₂×C₃
LCS	G ▷ C₅²×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #27130990	C₃	semidirect
3. C₅²×C₁₁²⋊C₃	C₄	semidirect
7. C₅²×C₁₁²	C₃×C₄	semidirect
9. C₅×C₁₁²⋊C₃	Dic₅	semidirect
13. C₅×C₁₁²	C₃×Dic₅	semidirect
16. C₁₁²⋊C₃	#1039	semidirect
21. C₁₁²	C₃×#1039	semidirect
29. C₅²	#92150⋊C₃	semidirect
37. C₅	#14559102⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅²×(C₁₁⋊D₁₁)⋊C₃	2
#27130990	3
#14559102⋊C₃	5
C₃×#1039	121