Subgroups — D₁₃×D₄₃₇ #36384352

Order 22724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆₈₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₄₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₃₇	—	13	1	no	maximal, Hall
6	D₁₃×D₂₃	—	19	1	no	maximal, Hall
7	D₁₃×D₁₉	—	23	1	no	maximal, Hall
8	C₂×C₁₉×C₂₃	—	13	1	no	—
9	D₄₃₇	—	13	1	no	—
10	D₄₃₇	D₁₃	1	1	yes	characteristic, direct product factor
11	D₂₉₉	—	19	1	no	—
12	C₁₃×D₂₃	—	19	1	no	—
13	C₂₃×D₁₃	D₁₉	1	1	yes	characteristic, complemented
14	D₂₄₇	—	23	1	no	—
15	C₁₃×D₁₉	—	23	1	no	—
16	C₁₉×D₁₃	D₂₃	1	1	yes	characteristic, complemented
17	C₁₉×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
18	C₁₃×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₁₉	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₂₃	—	247	1	no	Hall
21	C₂×D₁₉	—	299	1	no	Hall
22	C₂×D₁₃	—	437	1	no	Hall
23	C₂×C₂₃	—	13	1	no	—
24	D₂₃	—	19	1	no	—
25	D₂₃	—	247	1	no	—
26	C₂×C₁₉	—	13	1	no	—
27	D₁₉	—	23	1	no	—
28	D₁₉	—	299	1	no	—
29	C₂×C₁₃	—	437	1	no	—
30	D₁₃	—	437	1	no	—
31	D₁₃	D₄₃₇	1	1	yes	characteristic, direct product factor
32	C₂₃	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₁₉	D₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₃	C₂×D₄₃₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5681	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	5681	1	no	—
38	C₂	—	437	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₉×C₂₃	C₂²
LCS	G ▷ C₁₃×C₁₉×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₆₈₁	C₂	semidirect
2. C₁₉×C₂₃×D₁₃	C₂	semidirect
3. C₁₃×D₄₃₇	C₂	semidirect
4. C₁₃×C₁₉×C₂₃	C₂²	semidirect
10. D₄₃₇	D₁₃	direct (N × H)
13. C₂₃×D₁₃	D₁₉	semidirect
16. C₁₉×D₁₃	D₂₃	semidirect
17. C₁₉×C₂₃	C₂×D₁₃	semidirect
18. C₁₃×C₂₃	C₂×D₁₉	semidirect
19. C₁₃×C₁₉	C₂×D₂₃	semidirect
31. D₁₃	D₄₃₇	direct (N × H)
32. C₂₃	D₁₃×D₁₉	semidirect
33. C₁₉	D₁₃×D₂₃	semidirect
34. C₁₃	C₂×D₄₃₇	semidirect

Maximal subgroups

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

subgroup	index
D₅₆₈₁	2
C₁₉×C₂₃×D₁₃	2
C₁₃×D₄₃₇	2
C₂×D₄₃₇	13
D₁₃×D₂₃	19
D₁₃×D₁₉	23

Subgroups — D13×D437 #36384352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₄₃₇ #36384352