Subgroups — D₁₃⋊C₃×D₁₉₉ #44526820

Order 31044.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₃)⋊D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃⋊C₃×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃⋊C₃×D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₉₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃⋊C₃×C₁₉₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₅₈₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₉₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₃×C₁₉₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃×C₁₉₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₁₉₉	—	13	1	no	maximal, Hall
11	C₂×C₃×C₁₉₉	—	13	1	no	—
12	C₃×D₁₉₉	—	13	1	no	—
13	C₃×D₁₉₉	—	13	1	no	—
14	C₂×D₁₉₉	—	13	1	no	Hall
15	C₃×C₁₉₉	—	13	1	no	Hall
16	C₂×C₁₉₉	—	13	1	no	—
17	D₁₉₉	—	13	1	no	—
18	D₁₉₉	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
19	C₁₉₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₃⋊C₃	—	199	1	no	maximal, Hall
21	C₂×C₁₃⋊C₃	—	199	1	no	—
22	D₁₃⋊C₃	—	199	1	no	—
23	D₁₃⋊C₃	D₁₉₉	1	1	yes	characteristic, direct product factor
24	C₂×D₁₃	—	199	1	no	Hall
25	C₁₃⋊C₃	C₂×D₁₉₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	199	1	no	—
27	D₁₃	—	199	1	no	—
28	D₁₃	C₃×D₁₉₉	1	1	yes	characteristic, complemented
29	C₁₃	C₂×C₃×D₁₉₉	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2587	1	no	Hall
31	C₂×C₃	—	13	1	no	—
32	C₂×C₃	—	2587	1	no	—
33	C₂×C₃	—	2587	1	no	—
34	C₂²	—	2587	1	no	Sylow
35	C₃	—	13	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	2587	1	no	—
38	C₂	—	199	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₉₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₁₃⋊C₃)⋊D₁₉₉	C₂	semidirect
2. D₁₃⋊C₃×C₁₉₉	C₂	semidirect
3. C₁₃⋊C₃×D₁₉₉	C₂	semidirect
4. D₁₃×D₁₉₉	C₃	semidirect
5. C₁₃⋊C₃×C₁₉₉	C₂²	semidirect
6. D₂₅₈₇	C₂×C₃	semidirect
7. C₁₃×D₁₉₉	C₂×C₃	semidirect
8. D₁₃×C₁₉₉	C₂×C₃	semidirect
9. C₁₃×C₁₉₉	C₂²×C₃	semidirect
18. D₁₉₉	D₁₃⋊C₃	direct (N × H)
19. C₁₉₉	C₂×D₁₃⋊C₃	semidirect
23. D₁₃⋊C₃	D₁₉₉	direct (N × H)
25. C₁₃⋊C₃	C₂×D₁₉₉	semidirect
28. D₁₃	C₃×D₁₉₉	semidirect
29. C₁₃	C₂×C₃×D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
(C₁₃⋊C₃)⋊D₁₉₉	2
D₁₃⋊C₃×C₁₉₉	2
C₁₃⋊C₃×D₁₉₉	2
D₁₃×D₁₉₉	3
C₂×C₃×D₁₉₉	13
C₂×D₁₃⋊C₃	199

Subgroups — D13⋊C3×D199 #44526820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊C₃×D₁₉₉ #44526820