Subgroups — C₃×D₁₃×D₁₇₃ #41008773

Order 26988.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₂₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₂₄₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₃×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃×C₁₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₁₇₃	—	13	1	no	maximal, Hall
11	C₂×C₃×C₁₇₃	—	13	1	no	—
12	C₃×D₁₇₃	—	13	1	no	—
13	C₃×D₁₇₃	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×D₁₇₃	—	13	1	no	Hall
15	C₃×C₁₇₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇₃	—	13	1	no	—
17	D₁₇₃	—	13	1	no	—
18	D₁₇₃	C₃×D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₇₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×D₁₃	—	173	1	no	maximal, Hall
21	C₂×C₃×C₁₃	—	173	1	no	—
22	C₃×D₁₃	—	173	1	no	—
23	C₃×D₁₃	D₁₇₃	1	1	yes	characteristic, direct product factor
24	C₂×D₁₃	—	173	1	no	Hall
25	C₃×C₁₃	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	173	1	no	—
27	D₁₃	—	173	1	no	—
28	D₁₃	C₃×D₁₇₃	1	1	yes	characteristic, direct product factor
29	C₁₃	C₂×C₃×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2249	1	no	Hall
31	C₂×C₃	—	13	1	no	—
32	C₂×C₃	—	173	1	no	—
33	C₂×C₃	—	2249	1	no	—
34	C₂²	—	2249	1	no	Sylow
35	C₃	D₁₃×D₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	13	1	no	—
37	C₂	—	173	1	no	—
38	C₂	—	2249	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₁₇₃
commutator, cosocle, hypocenter	C₁₃×C₁₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₇₃	C₂²
LCS	G ▷ C₁₃×C₁₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₂₄₉	C₂	semidirect
2. C₃×D₁₃×C₁₇₃	C₂	semidirect
3. C₃×C₁₃×D₁₇₃	C₂	semidirect
4. D₁₃×D₁₇₃	C₃	direct (N × H)
5. C₃×C₁₃×C₁₇₃	C₂²	semidirect
6. D₂₂₄₉	C₂×C₃	semidirect
7. C₁₃×D₁₇₃	C₂×C₃	semidirect
8. D₁₃×C₁₇₃	C₂×C₃	semidirect
9. C₁₃×C₁₇₃	C₂²×C₃	semidirect
13. C₃×D₁₇₃	D₁₃	direct (N × H)
15. C₃×C₁₇₃	C₂×D₁₃	semidirect
18. D₁₇₃	C₃×D₁₃	direct (N × H)
19. C₁₇₃	C₂×C₃×D₁₃	semidirect
23. C₃×D₁₃	D₁₇₃	direct (N × H)
25. C₃×C₁₃	C₂×D₁₇₃	semidirect
28. D₁₃	C₃×D₁₇₃	direct (N × H)
29. C₁₃	C₂×C₃×D₁₇₃	semidirect
35. C₃	D₁₃×D₁₇₃	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×D₂₂₄₉	2
C₃×D₁₃×C₁₇₃	2
C₃×C₁₃×D₁₇₃	2
D₁₃×D₁₇₃	3
C₂×C₃×D₁₇₃	13
C₂×C₃×D₁₃	173

Subgroups — C3×D13×D173 #41008773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₁₇₃ #41008773