Subgroups — C₂×C₁₃×C₂²⋊A₄ #11929343

Order 1248.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂⁵×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×A₄×C₁₃	—	4	5	no	maximal
4	C₂⁴×C₁₃	—	3	5	no	—
5	C₂⁴×C₁₃	—	3	5	no	—
6	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	A₄×C₁₃	—	4	5	no	—
8	C₂³×C₁₃	—	3	30	no	—
9	C₂³×C₁₃	—	3	10	no	—
10	C₂³×C₁₃	—	3	5	no	—
11	C₂³×C₁₃	—	3	5	no	—
12	C₂³×C₁₃	A₄	1	5	yes	complemented
13	C₂×C₂²⋊A₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₁₃	—	16	1	no	—
15	C₂²×C₁₃	—	3	5	no	—
16	C₂²×C₁₃	—	3	30	no	—
17	C₂²×C₁₃	—	3	10	no	—
18	C₂²×C₁₃	—	3	5	no	—
19	C₂²×C₁₃	C₂×A₄	1	5	yes	complemented
20	C₂²⋊A₄	C₂×C₁₃	1	1	yes	characteristic, direct product factor
21	C₃×C₁₃	—	16	1	no	Hall
22	C₂⁵	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₃	—	3	5	no	—
24	C₂×C₁₃	—	3	5	no	—
25	C₂×C₁₃	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
26	C₂×A₄	—	4	5	no	—
27	C₂⁴	—	3	5	no	—
28	C₂⁴	—	3	5	no	—
29	C₂⁴	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₁₃	C₂×C₂²⋊A₄	1	1	yes	characteristic, direct product factor, Sylow
31	A₄	—	4	5	no	—
32	C₂³	—	3	30	no	—
33	C₂³	—	3	10	no	—
34	C₂³	—	3	5	no	—
35	C₂³	—	3	5	no	—
36	C₂³	A₄×C₁₃	1	5	yes	complemented
37	C₂×C₃	—	16	1	no	—
38	C₂²	—	3	5	no	—
39	C₂²	—	3	10	no	—
40	C₂²	—	3	30	no	—
41	C₂²	—	3	5	no	—
42	C₂²	C₂×A₄×C₁₃	1	5	yes	complemented
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	5	no	—
45	C₂	—	3	5	no	—
46	C₂	C₁₃×C₂²⋊A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂²⋊A₄	C₂	direct (N × H)
2. C₂⁵×C₁₃	C₃	semidirect
6. C₂⁴×C₁₃	C₂×C₃	semidirect
12. C₂³×C₁₃	A₄	semidirect
13. C₂×C₂²⋊A₄	C₁₃	direct (N × H)
19. C₂²×C₁₃	C₂×A₄	semidirect
20. C₂²⋊A₄	C₂×C₁₃	direct (N × H)
22. C₂⁵	C₃×C₁₃	semidirect
25. C₂×C₁₃	C₂²⋊A₄	direct (N × H)
29. C₂⁴	C₂×C₃×C₁₃	semidirect
30. C₁₃	C₂×C₂²⋊A₄	direct (N × H)
36. C₂³	A₄×C₁₃	semidirect
42. C₂²	C₂×A₄×C₁₃	semidirect
46. C₂	C₁₃×C₂²⋊A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₂²⋊A₄	2
C₂⁵×C₁₃	3
C₂×A₄×C₁₃	4
C₂×C₂²⋊A₄	13

Subgroups — C2×C13×C22⋊A4 #11929343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₂²⋊A₄ #11929343