Subgroups — C₃×D₃×D₆₅₃ #37555100

Order 23508.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₆₅₃	—	3	1	no	maximal
5	D₃×D₆₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₆₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₆₅₃	—	3	1	no	—
8	D₁₉₅₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₆₅₃	—	2	1	no	—
10	C₃×D₆₅₃	—	3	1	no	—
11	C₃×D₆₅₃	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₆₅₃	C₂×C₃	1	1	yes	characteristic, complemented
13	D₃×C₆₅₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₆₅₃	—	3	1	no	Hall
15	C₃×C₆₅₃	—	2	1	no	—
16	C₃×C₆₅₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₆₅₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₆₅₃	—	3	1	no	—
19	D₆₅₃	—	3	1	no	—
20	D₆₅₃	C₃×D₃	1	1	yes	characteristic, direct product factor
21	C₆₅₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×D₃	—	653	1	no	maximal, Hall
23	C₂×C₃²	—	653	1	no	—
24	C₃×D₃	—	653	1	no	—
25	C₃×D₃	D₆₅₃	1	1	yes	characteristic, direct product factor
26	C₂²×C₃	—	1959	1	no	—
27	C₂×D₃	—	653	1	no	—
28	C₃²	C₂×D₆₅₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	1306	1	no	—
31	C₂×C₃	—	653	1	no	—
32	C₂×C₃	—	653	1	no	—
33	C₂×C₃	—	1959	1	no	—
34	D₃	—	653	1	no	—
35	D₃	C₃×D₆₅₃	1	1	yes	characteristic, direct product factor
36	C₂²	—	1959	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₆₅₃	1	1	yes	characteristic, direct product factor
39	C₃	C₂×C₃×D₆₅₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	653	1	no	—
42	C₂	—	1959	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×D₆₅₃
commutator, cosocle, hypocenter	C₃×C₆₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₆₅₃	C₂²
LCS	G ▷ C₃×C₆₅₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₅₃	C₂	semidirect
2. C₃×D₃×C₆₅₃	C₂	semidirect
3. C₃×D₁₉₅₉	C₂	semidirect
5. D₃×D₆₅₃	C₃	direct (N × H)
6. C₃²×C₆₅₃	C₂²	semidirect
8. D₁₉₅₉	C₂×C₃	semidirect
11. C₃×D₆₅₃	D₃	direct (N × H)
12. C₃×D₆₅₃	C₂×C₃	semidirect
13. D₃×C₆₅₃	C₂×C₃	semidirect
16. C₃×C₆₅₃	C₂×D₃	semidirect
17. C₃×C₆₅₃	C₂²×C₃	semidirect
20. D₆₅₃	C₃×D₃	direct (N × H)
21. C₆₅₃	C₂×C₃×D₃	semidirect
25. C₃×D₃	D₆₅₃	direct (N × H)
28. C₃²	C₂×D₆₅₃	semidirect
35. D₃	C₃×D₆₅₃	direct (N × H)
38. C₃	D₃×D₆₅₃	direct (N × H)
39. C₃	C₂×C₃×D₆₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₆₅₃	2
C₃×D₃×C₆₅₃	2
C₃×D₁₉₅₉	2
C₂×C₃×D₆₅₃	3
D₃×D₆₅₃	3
C₂×C₃×D₃	653

Subgroups — C3×D3×D653 #37555100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₆₅₃ #37555100