Subgroups — C₃×C₅₃×#3874 #37558711

Order 23850.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₅×C₅₃	—	3	1	no	maximal
3	C₅₃×#3874	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₅₃×C₅²⋊C₃	—	2	1	no	—
5	C₅₃×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₅₃	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₅₃	—	3	1	no	Hall
8	C₂×C₃×C₅×C₅₃	—	15	1	no	—
9	C₃×D₅×C₅₃	—	3	1	no	—
10	C₅²×C₅₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃×C₅₃	—	25	1	no	maximal, Hall
12	C₃×C₅×C₅₃	—	3	1	no	—
13	C₃×C₅×C₅₃	—	3	1	no	—
14	C₂×C₅×C₅₃	—	15	1	no	—
15	D₅×C₅₃	—	3	1	no	—
16	C₃²×C₅₃	—	25	1	no	Hall
17	C₃×#3874	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₅₃	—	15	1	no	—
19	D₃×C₅₃	—	25	1	no	—
20	C₅×C₅₃	—	3	1	no	—
21	C₅×C₅₃	—	3	1	no	—
22	C₃×C₅²⋊C₃	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅₃	—	25	1	no	—
24	C₃×C₅₃	—	50	1	no	—
25	C₃×C₅₃	#3874	1	1	yes	characteristic, direct product factor
26	C₃×C₅×D₅	—	3	1	no	—
27	#3874	C₃×C₅₃	1	1	yes	characteristic, direct product factor
28	C₂×C₅₃	—	15	1	no	Hall
29	C₃×C₅²	D₃×C₅₃	1	1	yes	characteristic, complemented
30	C₅²⋊C₃	—	2	1	no	—
31	C₅²⋊C₃	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented
32	C₅₃	C₃×#3874	1	1	yes	characteristic, direct product factor, Sylow
33	C₅×D₅	—	3	1	no	Hall
34	C₂×C₃×C₅	—	15	1	no	—
35	C₃×D₅	—	3	1	no	—
36	C₅²	C₃×D₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
37	C₃×D₃	—	25	1	no	Hall
38	C₃×C₅	—	3	1	no	—
39	C₃×C₅	—	3	1	no	—
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	C₃²	—	25	1	no	Sylow
43	C₂×C₃	—	15	1	no	—
44	D₃	—	25	1	no	—
45	C₅	—	3	1	no	—
46	C₅	—	3	1	no	—
47	C₃	—	25	1	no	—
48	C₃	—	50	1	no	—
49	C₃	C₅₃×#3874	1	1	yes	characteristic, direct product factor
50	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅₃	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₅₃	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₃×C₅²⋊C₃	C₂	semidirect
3. C₅₃×#3874	C₃	direct (N × H)
5. C₅₃×C₅²⋊C₃	C₂×C₃	semidirect
6. C₃×C₅²×C₅₃	D₃	semidirect
10. C₅²×C₅₃	C₃×D₃	semidirect
17. C₃×#3874	C₅₃	direct (N × H)
22. C₃×C₅²⋊C₃	C₂×C₅₃	semidirect
25. C₃×C₅₃	#3874	direct (N × H)
27. #3874	C₃×C₅₃	direct (N × H)
29. C₃×C₅²	D₃×C₅₃	semidirect
31. C₅²⋊C₃	C₂×C₃×C₅₃	semidirect
32. C₅₃	C₃×#3874	direct (N × H)
36. C₅²	C₃×D₃×C₅₃	semidirect
49. C₃	C₅₃×#3874	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅₃×C₅²⋊C₃	2
C₃×C₅×D₅×C₅₃	3
C₅₃×#3874	3
C₃×D₃×C₅₃	25
C₃×#3874	53

Subgroups — C3×C53×#3874 #37558711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₃×#3874 #37558711