Subgroups — C₃×D₅₃₄₃ #44545406

Order 32058.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₃₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₇₈₁	—	3	1	no	maximal
4	C₃×C₁₃×C₁₃₇	—	2	1	no	—
5	C₃×C₁₃×C₁₃₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₇₈₁	—	3	1	no	Hall
8	C₃×D₄₁₁	—	13	1	no	maximal, Hall
9	C₁₃×C₁₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
11	D₄₁₁	—	13	1	no	—
12	C₃×D₁₃₇	—	39	1	no	—
13	C₃×C₁₃₇	—	2	1	no	—
14	C₃×C₁₃₇	C₃×D₁₃	1	1	yes	characteristic, complemented
15	C₃×C₁₃₇	D₃₉	1	1	yes	characteristic, complemented
16	D₁₃₇	—	39	1	no	Hall
17	C₃×D₃₉	—	137	1	no	maximal, Hall
18	C₁₃₇	C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₁₃	D₁₃₇	1	1	yes	characteristic, complemented, Hall
20	D₃₉	—	137	1	no	—
21	C₃×D₁₃	—	411	1	no	—
22	C₃×C₁₃	—	2	1	no	—
23	C₃×C₁₃	C₃×D₁₃₇	1	1	yes	characteristic, complemented
24	C₃×C₁₃	D₄₁₁	1	1	yes	characteristic, complemented
25	D₁₃	—	411	1	no	Hall
26	C₃×D₃	—	1781	1	no	Hall
27	C₁₃	C₃×D₄₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₁₇₈₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	5343	1	no	—
30	D₃	—	1781	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₇₈₁	1	1	yes	characteristic, complemented
33	C₃	D₅₃₄₃	1	1	yes	characteristic, direct product factor
34	C₂	—	5343	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₃₄₃
commutator, cosocle, hypocenter	C₃×C₁₃×C₁₃₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₃₇	C₂
LCS	G ▷ C₃×C₁₃×C₁₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₁₃₇	C₂	semidirect
2. D₅₃₄₃	C₃	direct (N × H)
5. C₃×C₁₃×C₁₃₇	D₃	semidirect
6. C₃×C₁₃×C₁₃₇	C₂×C₃	semidirect
9. C₁₃×C₁₃₇	C₃×D₃	semidirect
10. C₃²×C₁₃₇	D₁₃	semidirect
14. C₃×C₁₃₇	C₃×D₁₃	semidirect
15. C₃×C₁₃₇	D₃₉	semidirect
18. C₁₃₇	C₃×D₃₉	semidirect
19. C₃²×C₁₃	D₁₃₇	semidirect
23. C₃×C₁₃	C₃×D₁₃₇	semidirect
24. C₃×C₁₃	D₄₁₁	semidirect
27. C₁₃	C₃×D₄₁₁	semidirect
28. C₃²	D₁₇₈₁	semidirect
32. C₃	C₃×D₁₇₈₁	semidirect
33. C₃	D₅₃₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₁₃₇	2
D₅₃₄₃	3
C₃×D₁₇₈₁	3
C₃×D₄₁₁	13
C₃×D₃₉	137

Subgroups — C3×D5343 #44545406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₃₄₃ #44545406