Subgroups — C₂×D₃×C₁₃×C₁₇₃ #41008792

Order 26988.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₃×C₁₇₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₁₇₃	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₇₃	—	3	2	no	—
6	C₂×C₁₃×C₁₇₃	D₃	1	1	yes	characteristic, direct product factor
7	C₁₃×C₁₇₃	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₃×C₁₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₇₃	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₃×C₁₇₃	C₂×C₁₃	1	2	yes	direct product factor
11	C₂²×C₁₇₃	—	3	1	no	Hall
12	C₃×C₁₇₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₇₃	—	3	2	no	—
14	C₂×C₁₇₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
15	C₁₇₃	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₃×C₁₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₁₃	C₂×C₁₇₃	1	1	yes	characteristic, complemented
18	D₃×C₁₃	C₂×C₁₇₃	1	2	yes	direct product factor
19	C₂²×C₁₃	—	3	1	no	Hall
20	C₃×C₁₃	C₂²×C₁₇₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	—	3	2	no	—
22	C₂×C₁₃	D₃×C₁₇₃	1	1	yes	characteristic, direct product factor
23	C₁₃	C₂×D₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	C₁₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃	C₂×C₁₃×C₁₇₃	1	1	yes	characteristic, complemented
26	D₃	C₂×C₁₃×C₁₇₃	1	2	yes	direct product factor
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₁₃×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₃×C₁₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₇₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₁₃×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₇₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₃×C₁₇₃

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₃×C₁₇₃	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₇₃	C₂	semidirect
4. C₃×C₁₃×C₁₇₃	C₂²	semidirect
6. C₂×C₁₃×C₁₇₃	D₃	direct (N × H)
7. C₁₃×C₁₇₃	C₂×D₃	direct (N × H)
8. C₂×D₃×C₁₇₃	C₁₃	direct (N × H)
9. C₂×C₃×C₁₇₃	C₂×C₁₃	semidirect
10. D₃×C₁₇₃	C₂×C₁₃	direct (N × H)
12. C₃×C₁₇₃	C₂²×C₁₃	semidirect
14. C₂×C₁₇₃	D₃×C₁₃	direct (N × H)
15. C₁₇₃	C₂×D₃×C₁₃	direct (N × H)
16. C₂×D₃×C₁₃	C₁₇₃	direct (N × H)
17. C₂×C₃×C₁₃	C₂×C₁₇₃	semidirect
18. D₃×C₁₃	C₂×C₁₇₃	direct (N × H)
20. C₃×C₁₃	C₂²×C₁₇₃	semidirect
22. C₂×C₁₃	D₃×C₁₇₃	direct (N × H)
23. C₁₃	C₂×D₃×C₁₇₃	direct (N × H)
24. C₂×D₃	C₁₃×C₁₇₃	direct (N × H)
25. C₂×C₃	C₂×C₁₃×C₁₇₃	semidirect
26. D₃	C₂×C₁₃×C₁₇₃	direct (N × H)
28. C₃	C₂²×C₁₃×C₁₇₃	semidirect
30. C₂	D₃×C₁₃×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃×C₁₃×C₁₇₃	2
C₂×C₃×C₁₃×C₁₇₃	2
C₂²×C₁₃×C₁₇₃	3
C₂×D₃×C₁₇₃	13
C₂×D₃×C₁₃	173

Subgroups — C2×D3×C13×C173 #41008792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₃×C₁₇₃ #41008792