Subgroups — C₂³×C₂²⋊(C₁₃⋊C₃) #11929342

Order 1248.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊(C₁₃⋊C₃)	C₂	1	7	yes	maximal, direct product factor
2	C₂⁵×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₂²⋊(C₁₃⋊C₃)	C₂²	1	7	yes	direct product factor
4	C₂³×C₁₃⋊C₃	—	4	1	no	maximal
5	C₂⁴×C₁₃	—	3	7	no	—
6	C₂⁴×C₁₃	—	3	1	no	—
7	C₂⁴×C₁₃	C₂×C₃	1	7	yes	complemented
8	C₂²⋊(C₁₃⋊C₃)	C₂³	1	1	yes	characteristic, direct product factor
9	C₂²×C₁₃⋊C₃	—	4	7	no	—
10	C₂³×C₁₃	—	3	14	no	—
11	C₂³×C₁₃	—	3	7	no	—
12	C₂³×C₁₃	—	3	7	no	—
13	C₂³×C₁₃	—	3	21	no	—
14	C₂³×C₁₃	A₄	1	1	yes	characteristic, complemented
15	C₂³×C₁₃	C₂²×C₃	1	7	yes	complemented
16	C₂³×A₄	—	13	1	no	maximal, Hall
17	C₂×C₁₃⋊C₃	—	4	7	no	—
18	C₂²×C₁₃	—	3	7	no	—
19	C₂²×C₁₃	—	3	14	no	—
20	C₂²×C₁₃	—	3	21	no	—
21	C₂²×C₁₃	—	3	7	no	—
22	C₂²×C₁₃	C₂×A₄	1	7	yes	complemented
23	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic, complemented
24	C₂²×A₄	—	13	7	no	—
25	C₁₃⋊C₃	—	4	1	no	Hall
26	C₂⁵	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	3	7	no	—
28	C₂×C₁₃	—	3	1	no	—
29	C₂×C₁₃	C₂²×A₄	1	7	yes	complemented
30	C₂³×C₃	—	52	1	no	—
31	C₂×A₄	—	13	7	no	—
32	C₂⁴	—	3	7	no	—
33	C₂⁴	—	3	1	no	—
34	C₂⁴	C₂×C₁₃⋊C₃	1	7	yes	complemented
35	C₁₃	C₂³×A₄	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	—	52	7	no	—
37	A₄	—	13	1	no	—
38	C₂³	—	3	21	no	—
39	C₂³	—	3	14	no	—
40	C₂³	—	3	7	no	—
41	C₂³	—	3	7	no	—
42	C₂³	C₂²×C₁₃⋊C₃	1	7	yes	complemented
43	C₂³	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
44	C₂×C₃	—	52	7	no	—
45	C₂²	—	3	7	no	—
46	C₂²	—	3	14	no	—
47	C₂²	—	3	21	no	—
48	C₂²	—	3	7	no	—
49	C₂²	C₂³×C₁₃⋊C₃	1	1	yes	characteristic, complemented
50	C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	1	7	yes	direct product factor
51	C₃	—	52	1	no	Sylow
52	C₂	—	3	1	no	—
53	C₂	—	3	7	no	—
54	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊(C₁₃⋊C₃)	C₂	direct (N × H)
2. C₂⁵×C₁₃	C₃	semidirect
3. C₂×C₂²⋊(C₁₃⋊C₃)	C₂²	direct (N × H)
7. C₂⁴×C₁₃	C₂×C₃	semidirect
8. C₂²⋊(C₁₃⋊C₃)	C₂³	direct (N × H)
14. C₂³×C₁₃	A₄	semidirect
15. C₂³×C₁₃	C₂²×C₃	semidirect
22. C₂²×C₁₃	C₂×A₄	semidirect
23. C₂²×C₁₃	C₂³×C₃	semidirect
26. C₂⁵	C₁₃⋊C₃	semidirect
29. C₂×C₁₃	C₂²×A₄	semidirect
34. C₂⁴	C₂×C₁₃⋊C₃	semidirect
35. C₁₃	C₂³×A₄	semidirect
42. C₂³	C₂²×C₁₃⋊C₃	semidirect
43. C₂³	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
49. C₂²	C₂³×C₁₃⋊C₃	semidirect
50. C₂²	C₂×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
54. C₂	C₂²×C₂²⋊(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×C₂²⋊(C₁₃⋊C₃)	2
C₂⁵×C₁₃	3
C₂³×C₁₃⋊C₃	4
C₂³×A₄	13

Subgroups — C23×C22⋊(C13⋊C3) #11929342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂²⋊(C₁₃⋊C₃) #11929342