Subgroups — C₂×C₄²×C₁₃⋊C₃ #11928719

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₃⋊C₃	C₂	1	3	yes	maximal
2	C₄²×C₁₃⋊C₃	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₃⋊C₃	C₄	1	12	yes	direct product factor
6	C₂×C₄×C₁₃⋊C₃	C₂²	1	6	yes	—
7	C₂²×C₄×C₁₃	C₂×C₃	1	3	yes	—
8	C₄²×C₁₃	C₂×C₃	1	4	yes	complemented
9	C₂²×C₁₃⋊C₃	C₂×C₄	1	6	yes	—
10	C₂²×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
11	C₄×C₁₃⋊C₃	C₂×C₄	1	12	yes	direct product factor
12	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₄×C₁₃	C₃×C₄	1	12	yes	complemented
14	C₂×C₄×C₁₃	C₂²×C₃	1	6	yes	—
15	C₂×C₃×C₄²	—	13	1	no	maximal, Hall
16	C₂×C₁₃⋊C₃	C₄²	1	4	yes	direct product factor
17	C₂×C₁₃⋊C₃	C₂²×C₄	1	3	yes	—
18	C₂²×C₁₃	C₂×C₃×C₄	1	6	yes	—
19	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
20	C₄×C₁₃	C₂×C₃×C₄	1	12	yes	complemented
21	C₂²×C₃×C₄	—	13	3	no	—
22	C₃×C₄²	—	13	4	no	—
23	C₁₃⋊C₃	C₂×C₄²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₄²	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₃	C₃×C₄²	1	4	yes	complemented
26	C₂×C₁₃	C₂²×C₃×C₄	1	3	yes	—
27	C₂³×C₃	—	13	1	no	—
28	C₂×C₃×C₄	—	13	12	no	—
29	C₂×C₃×C₄	—	13	6	no	—
30	C₂²×C₄	C₂×C₁₃⋊C₃	1	3	yes	—
31	C₄²	C₂×C₁₃⋊C₃	1	4	yes	direct product factor
32	C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	—	13	6	no	—
34	C₂²×C₃	—	13	1	no	—
35	C₃×C₄	—	13	12	no	—
36	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
37	C₂×C₄	C₄×C₁₃⋊C₃	1	12	yes	direct product factor
38	C₂×C₄	C₂²×C₁₃⋊C₃	1	6	yes	—
39	C₂×C₃	—	13	3	no	—
40	C₂×C₃	—	13	4	no	—
41	C₂²	C₂×C₄×C₁₃⋊C₃	1	6	yes	—
42	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic
43	C₄	C₂×C₄×C₁₃⋊C₃	1	12	yes	direct product factor
44	C₃	—	13	1	no	Sylow
45	C₂	C₄²×C₁₃⋊C₃	1	4	yes	direct product factor
46	C₂	C₂²×C₄×C₁₃⋊C₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₃×C₄²
Frattini	C₂²	C₂³×C₁₃⋊C₃
Fitting	C₂×C₄²×C₁₃	C₃
socle	C₂³×C₁₃	C₂²×C₃
prime radical	C₂³×C₁₃⋊C₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂×C₄²×C₁₃	C₃	semidirect
5. C₂×C₄×C₁₃⋊C₃	C₄	direct (N × H)
8. C₄²×C₁₃	C₂×C₃	semidirect
11. C₄×C₁₃⋊C₃	C₂×C₄	direct (N × H)
13. C₂×C₄×C₁₃	C₃×C₄	semidirect
16. C₂×C₁₃⋊C₃	C₄²	direct (N × H)
20. C₄×C₁₃	C₂×C₃×C₄	semidirect
23. C₁₃⋊C₃	C₂×C₄²	direct (N × H)
24. C₂×C₄²	C₁₃⋊C₃	direct (N × H)
25. C₂×C₁₃	C₃×C₄²	semidirect
31. C₄²	C₂×C₁₃⋊C₃	direct (N × H)
32. C₁₃	C₂×C₃×C₄²	semidirect
37. C₂×C₄	C₄×C₁₃⋊C₃	direct (N × H)
43. C₄	C₂×C₄×C₁₃⋊C₃	direct (N × H)
45. C₂	C₄²×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
C₂²×C₄×C₁₃⋊C₃	2
C₄²×C₁₃⋊C₃	2
C₂×C₄²×C₁₃	3
C₂×C₃×C₄²	13

Subgroups — C2×C42×C13⋊C3 #11928719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×C₁₃⋊C₃ #11928719