Subgroups — C₃×C₁₃⋊C₃×D₁₃₇ #44545394

Order 32058.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊C₃×D₁₃₇
commutator, cosocle, hypocenter	C₁₃×C₁₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₃₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₁₃₇	C₂	semidirect
2. C₁₃⋊C₃×D₁₃₇	C₃	direct (N × H)
3. C₃×C₁₃×D₁₃₇	C₃	semidirect
4. C₃×C₁₃×C₁₃₇	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₁₃₇	C₂×C₃	semidirect
6. C₁₃×D₁₃₇	C₃²	semidirect
8. C₁₃×C₁₃₇	C₂×C₃²	semidirect
11. C₃×D₁₃₇	C₁₃⋊C₃	direct (N × H)
13. C₃×C₁₃₇	C₂×C₁₃⋊C₃	semidirect
14. D₁₃₇	C₃×C₁₃⋊C₃	direct (N × H)
16. C₁₃₇	C₂×C₃×C₁₃⋊C₃	semidirect
17. C₃×C₁₃⋊C₃	D₁₃₇	direct (N × H)
20. C₃×C₁₃	C₃×D₁₃₇	semidirect
21. C₁₃⋊C₃	C₃×D₁₃₇	direct (N × H)
24. C₁₃	C₃²×D₁₃₇	semidirect
29. C₃	C₁₃⋊C₃×D₁₃₇	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×C₁₃⋊C₃×C₁₃₇	2
C₁₃⋊C₃×D₁₃₇	3
C₃×C₁₃×D₁₃₇	3
C₃²×D₁₃₇	13
C₂×C₃×C₁₃⋊C₃	137

Subgroups — C3×C13⋊C3×D137 #44545394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃⋊C₃×D₁₃₇ #44545394