Subgroups — C₂³×Dic₃×C₁₃ #11929298

Order 1248.

472 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
2	C₂²×Dic₃×C₁₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₄×C₁₃	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	8	yes	complemented
5	C₂³×C₃×C₁₃	C₂²	1	7	yes	—
6	C₂×Dic₃×C₁₃	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₁₃	D₃	1	1	yes	characteristic
8	C₂²×C₄×C₁₃	—	3	14	no	—
9	C₂²×C₃×C₁₃	C₂×C₄	1	28	yes	complemented
10	C₂²×C₃×C₁₃	C₂³	1	7	yes	—
11	Dic₃×C₁₃	C₂³	1	8	yes	direct product factor
12	C₂³×C₁₃	Dic₃	1	8	yes	direct product factor
13	C₂³×C₁₃	C₂×D₃	1	7	yes	—
14	C₂×C₄×C₁₃	—	3	28	no	—
15	C₂³×Dic₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₁₃	C₂²×C₄	1	14	yes	complemented
17	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
18	C₂²×C₁₃	C₂×Dic₃	1	28	yes	direct product factor
19	C₂²×C₁₃	C₂²×D₃	1	7	yes	—
20	C₄×C₁₃	—	3	8	no	—
21	C₂⁴×C₃	C₂×C₁₃	1	1	yes	characteristic
22	C₂²×Dic₃	C₂×C₁₃	1	14	yes	direct product factor
23	C₃×C₁₃	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂³×C₄	—	3	1	no	Sylow
25	C₂×C₁₃	C₂²×Dic₃	1	14	yes	direct product factor
26	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
27	C₂³×C₃	C₄×C₁₃	1	8	yes	complemented
28	C₂³×C₃	C₂²×C₁₃	1	7	yes	—
29	C₂×Dic₃	C₂²×C₁₃	1	28	yes	direct product factor
30	C₂⁴	D₃×C₁₃	1	1	yes	characteristic
31	C₂²×C₄	—	3	14	no	—
32	C₁₃	C₂³×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²×C₃	C₂×C₄×C₁₃	1	28	yes	complemented
34	C₂²×C₃	C₂³×C₁₃	1	7	yes	—
35	Dic₃	C₂³×C₁₃	1	8	yes	direct product factor
36	C₂³	Dic₃×C₁₃	1	8	yes	direct product factor
37	C₂³	C₂×D₃×C₁₃	1	7	yes	—
38	C₂×C₄	—	3	28	no	—
39	C₂×C₃	C₂²×C₄×C₁₃	1	14	yes	complemented
40	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
41	C₂²	C₂×Dic₃×C₁₃	1	28	yes	direct product factor
42	C₂²	C₂²×D₃×C₁₃	1	7	yes	—
43	C₄	—	3	8	no	—
44	C₃	C₂³×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂	C₂²×Dic₃×C₁₃	1	14	yes	direct product factor
46	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₁₃	D₃
commutator, hypocenter	C₃	C₂³×C₄×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting, socle, prime radical	C₂⁴×C₃×C₁₃	C₂
cosocle	C₂×C₃	C₂⁴×C₁₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃×C₁₃	C₂	direct (N × H)
4. C₂³×C₃×C₁₃	C₄	semidirect
6. C₂×Dic₃×C₁₃	C₂²	direct (N × H)
9. C₂²×C₃×C₁₃	C₂×C₄	semidirect
11. Dic₃×C₁₃	C₂³	direct (N × H)
12. C₂³×C₁₃	Dic₃	direct (N × H)
15. C₂³×Dic₃	C₁₃	direct (N × H)
16. C₂×C₃×C₁₃	C₂²×C₄	semidirect
18. C₂²×C₁₃	C₂×Dic₃	direct (N × H)
22. C₂²×Dic₃	C₂×C₁₃	direct (N × H)
23. C₃×C₁₃	C₂³×C₄	semidirect
25. C₂×C₁₃	C₂²×Dic₃	direct (N × H)
27. C₂³×C₃	C₄×C₁₃	semidirect
29. C₂×Dic₃	C₂²×C₁₃	direct (N × H)
32. C₁₃	C₂³×Dic₃	direct (N × H)
33. C₂²×C₃	C₂×C₄×C₁₃	semidirect
35. Dic₃	C₂³×C₁₃	direct (N × H)
36. C₂³	Dic₃×C₁₃	direct (N × H)
39. C₂×C₃	C₂²×C₄×C₁₃	semidirect
41. C₂²	C₂×Dic₃×C₁₃	direct (N × H)
44. C₃	C₂³×C₄×C₁₃	semidirect
45. C₂	C₂²×Dic₃×C₁₃	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
C₂²×Dic₃×C₁₃	2
C₂³×C₄×C₁₃	3
C₂³×Dic₃	13

Subgroups — C23×Dic3×C13 #11929298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₃×C₁₃ #11929298