Subgroups — C₁₃×(C₄₃⋊C₃)⋊D₇ #37553505

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₄₃⋊C₃	—	7	1	no	maximal, Hall
5	(C₄₃⋊C₃)⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₃⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₄₃	—	7	1	no	Hall
8	C₇×C₄₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	D₃₀₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×D₇	—	43	1	no	maximal, Hall
12	C₇×C₄₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₃	—	43	1	no	Hall
14	D₄₃⋊C₃	—	7	1	no	Hall
15	C₁₃×D₇	—	43	1	no	Hall
16	C₄₃⋊C₃	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	D₄₃	—	7	1	no	Hall
19	C₂×C₃×C₁₃	—	301	1	no	Hall
20	C₄₃	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₇	—	43	1	no	Hall
22	C₃×C₁₃	—	43	1	no	Hall
23	C₂×C₁₃	—	301	1	no	Hall
24	C₃×C₇	—	43	1	no	Hall
25	D₇	—	43	1	no	Hall
26	C₁₃	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₃×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	301	1	no	Hall
29	C₃	—	43	1	no	Sylow
30	C₂	—	301	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	(C₄₃⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₄₃	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₄₃⋊C₃	C₂	semidirect
2. C₁₃×D₃₀₁	C₃	semidirect
3. C₇×C₁₃×C₄₃	C₂×C₃	semidirect
5. (C₄₃⋊C₃)⋊D₇	C₁₃	direct (N × H)
6. C₁₃×C₄₃⋊C₃	D₇	semidirect
8. C₇×C₄₃⋊C₃	C₂×C₁₃	semidirect
9. D₃₀₁	C₃×C₁₃	semidirect
10. C₁₃×C₄₃	C₃×D₇	semidirect
12. C₇×C₄₃	C₂×C₃×C₁₃	semidirect
16. C₄₃⋊C₃	C₁₃×D₇	semidirect
17. C₇×C₁₃	D₄₃⋊C₃	semidirect
20. C₄₃	C₃×C₁₃×D₇	semidirect
26. C₁₃	(C₄₃⋊C₃)⋊D₇	direct (N × H)
27. C₇	C₁₃×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₄₃⋊C₃	2
C₁₃×D₃₀₁	3
C₁₃×D₄₃⋊C₃	7
(C₄₃⋊C₃)⋊D₇	13
C₃×C₁₃×D₇	43

Subgroups — C13×(C43⋊C3)⋊D7 #37553505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₄₃⋊C₃)⋊D₇ #37553505