Subgroups — C₂⁴×C₃×D₁₃ #11929345

Order 1248.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₁₃	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₁₃	C₂²	1	15	yes	complemented
5	C₂²×C₃×D₁₃	C₂²	1	140	yes	direct product factor
6	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂³×D₁₃	C₂×C₃	1	30	yes	direct product factor
8	C₂²×C₃×C₁₃	C₂³	1	35	yes	complemented
9	C₂×C₃×D₁₃	C₂³	1	120	yes	direct product factor
10	C₂³×C₁₃	C₂²×C₃	1	15	yes	complemented
11	C₂²×D₁₃	C₂²×C₃	1	140	yes	direct product factor
12	C₂⁵×C₃	—	13	1	no	maximal, Hall
13	C₂×C₃×C₁₃	C₂⁴	1	15	yes	complemented
14	C₃×D₁₃	C₂⁴	1	16	yes	direct product factor
15	C₂²×C₁₃	C₂³×C₃	1	35	yes	complemented
16	C₂×D₁₃	C₂³×C₃	1	120	yes	direct product factor
17	C₂⁴×C₃	—	13	30	no	—
18	C₂⁴×C₃	D₁₃	1	1	yes	characteristic, direct product factor
19	C₃×C₁₃	C₂⁵	1	1	yes	characteristic, complemented, Hall
20	C₂⁵	—	13	1	no	Sylow
21	C₂×C₁₃	C₂⁴×C₃	1	15	yes	complemented
22	D₁₃	C₂⁴×C₃	1	16	yes	direct product factor
23	C₂³×C₃	—	13	140	no	—
24	C₂³×C₃	C₂×D₁₃	1	15	yes	direct product factor
25	C₂⁴	—	13	30	no	—
26	C₂⁴	C₃×D₁₃	1	1	yes	characteristic, direct product factor
27	C₁₃	C₂⁵×C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₃	—	13	120	no	—
29	C₂²×C₃	C₂²×D₁₃	1	35	yes	direct product factor
30	C₂³	—	13	140	no	—
31	C₂³	C₂×C₃×D₁₃	1	15	yes	direct product factor
32	C₂×C₃	—	13	16	no	—
33	C₂×C₃	C₂³×D₁₃	1	15	yes	direct product factor
34	C₂²	—	13	120	no	—
35	C₂²	C₂²×C₃×D₁₃	1	35	yes	direct product factor
36	C₃	C₂⁴×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	13	16	no	—
38	C₂	C₂³×C₃×D₁₃	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴×C₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₃	C₂	semidirect
2. C₂³×C₃×D₁₃	C₂	direct (N × H)
3. C₂⁴×D₁₃	C₃	direct (N × H)
4. C₂³×C₃×C₁₃	C₂²	semidirect
5. C₂²×C₃×D₁₃	C₂²	direct (N × H)
6. C₂⁴×C₁₃	C₂×C₃	semidirect
7. C₂³×D₁₃	C₂×C₃	direct (N × H)
8. C₂²×C₃×C₁₃	C₂³	semidirect
9. C₂×C₃×D₁₃	C₂³	direct (N × H)
10. C₂³×C₁₃	C₂²×C₃	semidirect
11. C₂²×D₁₃	C₂²×C₃	direct (N × H)
13. C₂×C₃×C₁₃	C₂⁴	semidirect
14. C₃×D₁₃	C₂⁴	direct (N × H)
15. C₂²×C₁₃	C₂³×C₃	semidirect
16. C₂×D₁₃	C₂³×C₃	direct (N × H)
18. C₂⁴×C₃	D₁₃	direct (N × H)
19. C₃×C₁₃	C₂⁵	semidirect
21. C₂×C₁₃	C₂⁴×C₃	semidirect
22. D₁₃	C₂⁴×C₃	direct (N × H)
24. C₂³×C₃	C₂×D₁₃	direct (N × H)
26. C₂⁴	C₃×D₁₃	direct (N × H)
27. C₁₃	C₂⁵×C₃	semidirect
29. C₂²×C₃	C₂²×D₁₃	direct (N × H)
31. C₂³	C₂×C₃×D₁₃	direct (N × H)
33. C₂×C₃	C₂³×D₁₃	direct (N × H)
35. C₂²	C₂²×C₃×D₁₃	direct (N × H)
36. C₃	C₂⁴×D₁₃	direct (N × H)
38. C₂	C₂³×C₃×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₃	2
C₂³×C₃×D₁₃	2
C₂⁴×D₁₃	3
C₂⁵×C₃	13

Subgroups — C24×C3×D13 #11929345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃×D₁₃ #11929345