Subgroups — C₂³×C₃×Dic₁₃ #11929283

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×C₃×Dic₁₃	C₂	1	14	yes	maximal, direct product factor
3	C₂³×Dic₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₁₃	C₄	1	8	yes	complemented
5	C₂³×C₃×C₁₃	C₂²	1	7	yes	—
6	C₂×C₃×Dic₁₃	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₂²×Dic₁₃	C₂×C₃	1	14	yes	direct product factor
9	C₂²×C₃×C₁₃	C₂×C₄	1	28	yes	complemented
10	C₂²×C₃×C₁₃	C₂³	1	7	yes	—
11	C₃×Dic₁₃	C₂³	1	8	yes	direct product factor
12	C₂³×C₁₃	C₃×C₄	1	8	yes	complemented
13	C₂³×C₁₃	C₂²×C₃	1	7	yes	—
14	C₂×Dic₁₃	C₂²×C₃	1	28	yes	direct product factor
15	C₂³×C₃×C₄	—	13	1	no	maximal, Hall
16	C₂×C₃×C₁₃	C₂²×C₄	1	14	yes	complemented
17	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
18	C₂²×C₁₃	C₂×C₃×C₄	1	28	yes	complemented
19	C₂²×C₁₃	C₂³×C₃	1	7	yes	—
20	Dic₁₃	C₂³×C₃	1	8	yes	direct product factor
21	C₂⁴×C₃	D₁₃	1	1	yes	characteristic
22	C₂²×C₃×C₄	—	13	14	no	—
23	C₃×C₁₃	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂³×C₄	—	13	1	no	Sylow
25	C₂×C₁₃	C₂²×C₃×C₄	1	14	yes	complemented
26	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
27	C₂³×C₃	Dic₁₃	1	8	yes	direct product factor
28	C₂³×C₃	C₂×D₁₃	1	7	yes	—
29	C₂×C₃×C₄	—	13	28	no	—
30	C₂⁴	C₃×D₁₃	1	1	yes	characteristic
31	C₂²×C₄	—	13	14	no	—
32	C₁₃	C₂³×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	C₂×Dic₁₃	1	28	yes	direct product factor
34	C₂²×C₃	C₂²×D₁₃	1	7	yes	—
35	C₃×C₄	—	13	8	no	—
36	C₂³	C₃×Dic₁₃	1	8	yes	direct product factor
37	C₂³	C₂×C₃×D₁₃	1	7	yes	—
38	C₂×C₄	—	13	28	no	—
39	C₂×C₃	C₂²×Dic₁₃	1	14	yes	direct product factor
40	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
41	C₂²	C₂×C₃×Dic₁₃	1	28	yes	direct product factor
42	C₂²	C₂²×C₃×D₁₃	1	7	yes	—
43	C₄	—	13	8	no	—
44	C₃	C₂³×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₂²×C₃×Dic₁₃	1	14	yes	direct product factor
46	C₂	C₂³×C₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₃	D₁₃
commutator, hypocenter	C₁₃	C₂³×C₃×C₄
Frattini	C₂	C₂³×C₃×D₁₃
Fitting, socle, prime radical	C₂⁴×C₃×C₁₃	C₂
cosocle	C₂×C₁₃	C₂⁴×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₁₃	C₂	direct (N × H)
3. C₂³×Dic₁₃	C₃	direct (N × H)
4. C₂³×C₃×C₁₃	C₄	semidirect
6. C₂×C₃×Dic₁₃	C₂²	direct (N × H)
8. C₂²×Dic₁₃	C₂×C₃	direct (N × H)
9. C₂²×C₃×C₁₃	C₂×C₄	semidirect
11. C₃×Dic₁₃	C₂³	direct (N × H)
12. C₂³×C₁₃	C₃×C₄	semidirect
14. C₂×Dic₁₃	C₂²×C₃	direct (N × H)
16. C₂×C₃×C₁₃	C₂²×C₄	semidirect
18. C₂²×C₁₃	C₂×C₃×C₄	semidirect
20. Dic₁₃	C₂³×C₃	direct (N × H)
23. C₃×C₁₃	C₂³×C₄	semidirect
25. C₂×C₁₃	C₂²×C₃×C₄	semidirect
27. C₂³×C₃	Dic₁₃	direct (N × H)
32. C₁₃	C₂³×C₃×C₄	semidirect
33. C₂²×C₃	C₂×Dic₁₃	direct (N × H)
36. C₂³	C₃×Dic₁₃	direct (N × H)
39. C₂×C₃	C₂²×Dic₁₃	direct (N × H)
41. C₂²	C₂×C₃×Dic₁₃	direct (N × H)
44. C₃	C₂³×Dic₁₃	direct (N × H)
45. C₂	C₂²×C₃×Dic₁₃	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×C₃×Dic₁₃	2
C₂³×Dic₁₃	3
C₂³×C₃×C₄	13

Subgroups — C23×C3×Dic13 #11929283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×Dic₁₃ #11929283