Subgroups — D₁₃×D₄₃⋊C₇ #30627770

Order 15652.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊(D₄₃⋊C₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₄₃⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₄₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×D₄₃⋊C₇	—	13	1	no	maximal, Hall
7	D₅₅₉	C₂×C₇	1	1	yes	characteristic, complemented
8	C₁₃×D₄₃	C₂×C₇	1	1	yes	characteristic, complemented
9	D₁₃×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
10	C₂×C₄₃⋊C₇	—	13	1	no	—
11	D₄₃⋊C₇	—	13	1	no	—
12	D₄₃⋊C₇	D₁₃	1	1	yes	characteristic, direct product factor
13	C₁₃×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×D₁₃	—	43	1	no	maximal, Hall
15	C₄₃⋊C₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₁₃	—	43	1	no	—
17	C₇×D₁₃	—	43	1	no	—
18	C₇×D₁₃	—	43	1	no	—
19	C₂×D₄₃	—	13	1	no	Hall
20	C₇×C₁₃	—	43	1	no	Hall
21	C₂×C₄₃	—	13	1	no	—
22	D₄₃	—	13	1	no	—
23	D₄₃	C₇×D₁₃	1	1	yes	characteristic, complemented
24	C₂×D₁₃	—	301	1	no	Hall
25	C₄₃	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂²×C₇	—	559	1	no	Hall
27	C₂×C₁₃	—	301	1	no	—
28	D₁₃	—	301	1	no	—
29	D₁₃	D₄₃⋊C₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇	—	43	1	no	—
31	C₂×C₇	—	559	1	no	—
32	C₂×C₇	—	559	1	no	—
33	C₁₃	C₂×D₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
34	C₇	—	43	1	no	Sylow
35	C₂²	—	3913	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	301	1	no	—
38	C₂	—	3913	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₄₃	C₂²×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⋊(D₄₃⋊C₇)	C₂	semidirect
2. D₁₃×C₄₃⋊C₇	C₂	semidirect
3. C₁₃×D₄₃⋊C₇	C₂	semidirect
4. C₁₃×C₄₃⋊C₇	C₂²	semidirect
5. D₁₃×D₄₃	C₇	semidirect
7. D₅₅₉	C₂×C₇	semidirect
8. C₁₃×D₄₃	C₂×C₇	semidirect
9. D₁₃×C₄₃	C₂×C₇	semidirect
12. D₄₃⋊C₇	D₁₃	direct (N × H)
13. C₁₃×C₄₃	C₂²×C₇	semidirect
15. C₄₃⋊C₇	C₂×D₁₃	semidirect
23. D₄₃	C₇×D₁₃	semidirect
25. C₄₃	C₂×C₇×D₁₃	semidirect
29. D₁₃	D₄₃⋊C₇	direct (N × H)
33. C₁₃	C₂×D₄₃⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊(D₄₃⋊C₇)	2
D₁₃×C₄₃⋊C₇	2
C₁₃×D₄₃⋊C₇	2
D₁₃×D₄₃	7
C₂×D₄₃⋊C₇	13
C₂×C₇×D₁₃	43

Subgroups — D13×D43⋊C7 #30627770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₄₃⋊C₇ #30627770