Subgroups — #49146760

Order 36900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#20301657	—	5	1	no	maximal
4	C₂₅×D₁₂₃	—	6	2	no	—
5	#16861483	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₁₂₃	D₅	1	1	yes	characteristic
7	C₃×C₂₅×C₄₁	—	2	2	no	—
8	C₂₅×D₄₁	—	9	1	no	—
9	C₃²×C₅×C₄₁	Dic₅	1	1	yes	characteristic
10	#13093287	—	25	1	no	Hall
11	C₅×D₁₂₃	—	6	2	no	—
12	C₂₅×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
13	#11744620	—	41	1	no	maximal, Hall
14	#11717964	—	45	1	no	—
15	C₃⋊D₁₂₃	D₂₅	1	1	yes	characteristic
16	C₃×C₅×C₄₁	—	2	2	no	—
17	C₃⋊D₃×C₂₅	—	41	1	no	—
18	C₅×D₄₁	—	9	1	no	—
19	C₃²×C₄₁	Dic₂₅	1	1	yes	characteristic, complemented, Hall
20	D₁₂₃	—	6	2	no	—
21	C₃²×C₂₅	#4223	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₁	#4379	1	1	yes	characteristic
23	#4379	—	205	1	no	—
24	#4223	—	225	1	no	Hall
25	D₃×C₂₅	—	246	2	no	—
26	C₃×C₄₁	—	2	2	no	—
27	Dic₂₅	—	369	1	no	Hall
28	C₅×C₃⋊D₃	—	41	1	no	—
29	D₄₁	—	9	1	no	—
30	C₃×C₂₅	—	2	2	no	—
31	C₂×C₂₅	—	369	1	no	—
32	C₃²×C₅	#11717964	1	1	yes	characteristic
33	C₄₁	#11744620	1	1	yes	characteristic, complemented, Sylow
34	#157	—	1025	1	no	Hall
35	C₅×D₃	—	246	2	no	—
36	C₂₅	#13093287	1	1	yes	characteristic, complemented, Sylow
37	Dic₅	—	1845	1	no	—
38	C₃⋊D₃	—	41	1	no	—
39	C₃×C₅	—	2	2	no	—
40	C₂×C₅	—	369	1	no	—
41	C₃²	#16861483	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	246	2	no	—
43	C₅	#20301657	1	1	yes	characteristic
44	C₄	—	9225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	369	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₅×C₄₁	C₄
Frattini	C₅	#20301657
socle	C₃²×C₅×C₄₁	Dic₅
prime radical	C₅×C₃⋊D₁₂₃	D₅
cosocle	C₂₅×C₃⋊D₁₂₃	C₂
LCS	G ▷ C₃²×C₂₅×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₄₁	C₄	semidirect
12. C₂₅×C₄₁	#157	semidirect
19. C₃²×C₄₁	Dic₂₅	semidirect
21. C₃²×C₂₅	#4223	semidirect
33. C₄₁	#11744620	semidirect
36. C₂₅	#13093287	semidirect
41. C₃²	#16861483	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×C₃⋊D₁₂₃	2
#20301657	5
#16861483	9
#11744620	41