Subgroups — A₄×C₁₃×C₂₉⋊C₇ #44539796

Order 31668.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×C₂₉⋊C₇	—	4	1	no	maximal, Hall
3	C₂×C₁₃×C₂₉⋊C₇	—	3	1	no	—
4	A₄×C₁₃×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃×C₂₉⋊C₇	A₄	1	1	yes	characteristic, direct product factor, Hall
6	A₄×C₂₉⋊C₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₁₃×C₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₂₉	—	4	1	no	Hall
9	C₇×A₄×C₁₃	—	29	1	no	maximal, Hall
10	C₂²×C₂₉⋊C₇	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₃×C₂₉	—	3	1	no	—
12	C₃×C₂₉⋊C₇	—	4	1	no	Hall
13	C₂×C₂₉⋊C₇	—	3	1	no	—
14	C₁₃×C₂₉	C₇×A₄	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₇×C₁₃	—	29	1	no	Hall
16	A₄×C₂₉	C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₃	—	116	1	no	Hall
18	C₂₉⋊C₇	A₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₁₃	—	87	1	no	—
20	A₄×C₁₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₂₉	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₇×C₁₃	—	29	1	no	Hall
23	C₃×C₂₉	—	4	1	no	Hall
24	C₇×A₄	—	29	1	no	Hall
25	C₂×C₂₉	—	3	1	no	—
26	C₂²×C₁₃	C₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
27	C₃×C₁₃	—	4	1	no	Hall
28	C₂₉	C₇×A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₇	—	29	1	no	Hall
30	C₂×C₁₃	—	3	1	no	—
31	C₃×C₇	—	116	1	no	Hall
32	C₂×C₇	—	87	1	no	—
33	C₁₃	A₄×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
34	A₄	C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
35	C₇	—	29	1	no	Sylow
36	C₂²	C₃×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	4	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	A₄×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂²×C₂₉	C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₂₉	C₃×C₇
LCS	G ▷ C₂²×C₂₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂₉⋊C₇	C₃	semidirect
4. A₄×C₁₃×C₂₉	C₇	semidirect
5. C₁₃×C₂₉⋊C₇	A₄	direct (N × H)
6. A₄×C₂₉⋊C₇	C₁₃	direct (N × H)
7. C₂²×C₁₃×C₂₉	C₃×C₇	semidirect
10. C₂²×C₂₉⋊C₇	C₃×C₁₃	semidirect
14. C₁₃×C₂₉	C₇×A₄	semidirect
16. A₄×C₂₉	C₇×C₁₃	semidirect
18. C₂₉⋊C₇	A₄×C₁₃	direct (N × H)
20. A₄×C₁₃	C₂₉⋊C₇	direct (N × H)
21. C₂²×C₂₉	C₃×C₇×C₁₃	semidirect
26. C₂²×C₁₃	C₃×C₂₉⋊C₇	semidirect
28. C₂₉	C₇×A₄×C₁₃	semidirect
33. C₁₃	A₄×C₂₉⋊C₇	direct (N × H)
34. A₄	C₁₃×C₂₉⋊C₇	direct (N × H)
36. C₂²	C₃×C₁₃×C₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂₉⋊C₇	3
C₃×C₁₃×C₂₉⋊C₇	4
A₄×C₁₃×C₂₉	7
A₄×C₂₉⋊C₇	13
C₇×A₄×C₁₃	29

Subgroups — A4×C13×C29⋊C7 #44539796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×C₁₃×C₂₉⋊C₇ #44539796