Subgroups — C₂×C₁₃×D₉×C₅₃ #37613629

Order 24804.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₉×C₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₃×C₅₃	—	3	1	no	maximal
4	C₉×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₃×C₅₃	—	3	2	no	—
6	C₂×C₃×C₁₃×C₅₃	D₃	1	1	yes	characteristic
7	C₂²×C₁₃×C₅₃	—	9	1	no	Hall
8	C₃×C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic
9	C₂×D₉×C₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₅₃	—	9	2	no	—
11	C₂×C₁₃×C₅₃	D₉	1	1	yes	characteristic, direct product factor
12	C₂×C₉×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented
13	D₉×C₅₃	C₂×C₁₃	1	2	yes	direct product factor
14	C₁₃×C₅₃	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×D₃×C₅₃	—	3	1	no	—
16	C₉×C₅₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×D₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₅₃	D₃×C₁₃	1	1	yes	characteristic
19	D₃×C₅₃	—	3	2	no	—
20	C₂×C₉×C₁₃	C₂×C₅₃	1	1	yes	characteristic, complemented
21	C₁₃×D₉	C₂×C₅₃	1	2	yes	direct product factor
22	C₂²×C₅₃	—	9	1	no	Hall
23	C₃×C₅₃	C₂×D₃×C₁₃	1	1	yes	characteristic
24	C₂×D₃×C₁₃	—	3	1	no	—
25	C₉×C₁₃	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₃	—	9	2	no	—
27	C₂×C₅₃	C₁₃×D₉	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₁₃	D₃×C₅₃	1	1	yes	characteristic
29	D₃×C₁₃	—	3	2	no	—
30	C₅₃	C₂×C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₁₃	—	9	1	no	Hall
32	C₃×C₁₃	C₂×D₃×C₅₃	1	1	yes	characteristic
33	C₂×D₉	C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₃	—	9	2	no	—
35	C₂×C₁₃	D₉×C₅₃	1	1	yes	characteristic, direct product factor
36	C₂×C₉	C₂×C₁₃×C₅₃	1	1	yes	characteristic, complemented
37	D₉	C₂×C₁₃×C₅₃	1	2	yes	direct product factor
38	C₁₃	C₂×D₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	3	1	no	—
40	C₉	C₂²×C₁₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₃×C₅₃	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₃×C₅₃	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₁₃×D₉×C₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₅₃	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₃×C₅₃
Frattini	C₃	C₂×D₃×C₁₃×C₅₃
Fitting	C₂×C₉×C₁₃×C₅₃	C₂
socle	C₂×C₃×C₁₃×C₅₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₉×C₅₃	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₅₃	C₂	semidirect
4. C₉×C₁₃×C₅₃	C₂²	semidirect
9. C₂×D₉×C₅₃	C₁₃	direct (N × H)
11. C₂×C₁₃×C₅₃	D₉	direct (N × H)
12. C₂×C₉×C₅₃	C₂×C₁₃	semidirect
13. D₉×C₅₃	C₂×C₁₃	direct (N × H)
14. C₁₃×C₅₃	C₂×D₉	direct (N × H)
16. C₉×C₅₃	C₂²×C₁₃	semidirect
17. C₂×C₁₃×D₉	C₅₃	direct (N × H)
20. C₂×C₉×C₁₃	C₂×C₅₃	semidirect
21. C₁₃×D₉	C₂×C₅₃	direct (N × H)
25. C₉×C₁₃	C₂²×C₅₃	semidirect
27. C₂×C₅₃	C₁₃×D₉	direct (N × H)
30. C₅₃	C₂×C₁₃×D₉	direct (N × H)
33. C₂×D₉	C₁₃×C₅₃	direct (N × H)
35. C₂×C₁₃	D₉×C₅₃	direct (N × H)
36. C₂×C₉	C₂×C₁₃×C₅₃	semidirect
37. D₉	C₂×C₁₃×C₅₃	direct (N × H)
38. C₁₃	C₂×D₉×C₅₃	direct (N × H)
40. C₉	C₂²×C₁₃×C₅₃	semidirect
46. C₂	C₁₃×D₉×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₉×C₅₃	2
C₂×C₉×C₁₃×C₅₃	2
C₂×D₃×C₁₃×C₅₃	3
C₂×D₉×C₅₃	13
C₂×C₁₃×D₉	53

Subgroups — C2×C13×D9×C53 #37613629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₉×C₅₃ #37613629