Subgroups — C₂³×C₄×C₁₃⋊C₃ #11929246

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂³×C₄×C₁₃	C₃	semidirect
4. C₂³×C₁₃⋊C₃	C₄	direct (N × H)
6. C₂×C₄×C₁₃⋊C₃	C₂²	direct (N × H)
8. C₂²×C₄×C₁₃	C₂×C₃	semidirect
9. C₂²×C₁₃⋊C₃	C₂×C₄	direct (N × H)
11. C₄×C₁₃⋊C₃	C₂³	direct (N × H)
12. C₂³×C₁₃	C₃×C₄	semidirect
14. C₂×C₄×C₁₃	C₂²×C₃	semidirect
16. C₂×C₁₃⋊C₃	C₂²×C₄	direct (N × H)
18. C₂²×C₁₃	C₂×C₃×C₄	semidirect
20. C₄×C₁₃	C₂³×C₃	semidirect
23. C₁₃⋊C₃	C₂³×C₄	direct (N × H)
24. C₂³×C₄	C₁₃⋊C₃	direct (N × H)
25. C₂×C₁₃	C₂²×C₃×C₄	semidirect
31. C₂²×C₄	C₂×C₁₃⋊C₃	direct (N × H)
32. C₁₃	C₂³×C₃×C₄	semidirect
36. C₂³	C₄×C₁₃⋊C₃	direct (N × H)
38. C₂×C₄	C₂²×C₁₃⋊C₃	direct (N × H)
41. C₂²	C₂×C₄×C₁₃⋊C₃	direct (N × H)
43. C₄	C₂³×C₁₃⋊C₃	direct (N × H)
45. C₂	C₂²×C₄×C₁₃⋊C₃	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×C₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂³×C₄×C₁₃	3
C₂³×C₃×C₄	13

Subgroups — C23×C4×C13⋊C3 #11929246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₁₃⋊C₃ #11929246