Subgroups — D₁₃⋊C₃×C₄₃⋊C₇ #37553549

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₄₃⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₄₃⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₄₃⋊C₇	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃⋊C₇	—	13	1	no	Hall
9	C₂×C₄₃⋊C₇	—	13	1	no	Hall
10	C₁₃×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₁₃⋊C₃	—	43	1	no	maximal, Hall
12	C₄₃⋊C₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₃⋊C₃	—	43	1	no	Hall
14	C₂×C₃×C₄₃	—	13	1	no	Hall
15	C₇×D₁₃	—	43	1	no	Hall
16	C₃×C₄₃	—	13	1	no	Hall
17	C₇×C₁₃	—	43	1	no	Hall
18	C₂×C₄₃	—	13	1	no	Hall
19	D₁₃⋊C₃	C₄₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₄₃	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₇	—	559	1	no	Hall
22	C₁₃⋊C₃	C₂×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Hall
23	D₁₃	C₃×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇	—	559	1	no	Hall
25	C₂×C₇	—	559	1	no	Hall
26	C₁₃	C₂×C₃×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	—	43	1	no	Sylow
28	C₂×C₃	—	13	1	no	Hall
29	C₃	—	13	1	no	Sylow
30	C₂	—	13	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×C₄₃⋊C₇	C₂	semidirect
2. D₁₃×C₄₃⋊C₇	C₃	semidirect
3. C₁₃×C₄₃⋊C₇	C₂×C₃	semidirect
4. C₄₃×D₁₃⋊C₃	C₇	semidirect
6. C₁₃⋊C₃×C₄₃	C₂×C₇	semidirect
7. D₁₃×C₄₃	C₃×C₇	semidirect
10. C₁₃×C₄₃	C₂×C₃×C₇	semidirect
12. C₄₃⋊C₇	D₁₃⋊C₃	direct (N × H)
19. D₁₃⋊C₃	C₄₃⋊C₇	direct (N × H)
20. C₄₃	C₇×D₁₃⋊C₃	semidirect
22. C₁₃⋊C₃	C₂×C₄₃⋊C₇	semidirect
23. D₁₃	C₃×C₄₃⋊C₇	semidirect
26. C₁₃	C₂×C₃×C₄₃⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×C₄₃⋊C₇	2
D₁₃×C₄₃⋊C₇	3
C₄₃×D₁₃⋊C₃	7
C₂×C₃×C₄₃⋊C₇	13
C₇×D₁₃⋊C₃	43

Subgroups — D13⋊C3×C43⋊C7 #37553549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊C₃×C₄₃⋊C₇ #37553549