Subgroups — D₃×C₁₃×D₁₉₉ #44526839

Order 31044.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₅₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₁₉₉	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₉₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₉₉	—	3	1	no	—
7	C₁₃×D₁₉₉	—	3	1	no	—
8	C₁₃×D₁₉₉	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₁₉₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₉₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₅₉₇	C₂×C₁₃	1	1	yes	characteristic, complemented
12	C₃×D₁₉₉	C₂×C₁₃	1	1	yes	characteristic, complemented
13	D₃×C₁₉₉	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₂×D₁₉₉	—	3	1	no	Hall
15	C₃×C₁₉₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉₉	—	3	1	no	—
17	D₁₉₉	—	3	1	no	—
18	D₁₉₉	D₃×C₁₃	1	1	yes	characteristic, direct product factor
19	C₁₉₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃×C₁₃	—	199	1	no	maximal, Hall
21	C₂×C₃×C₁₃	—	199	1	no	—
22	D₃×C₁₃	—	199	1	no	—
23	D₃×C₁₃	D₁₉₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₃	—	597	1	no	Hall
25	C₃×C₁₃	C₂×D₁₉₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	C₂×C₁₃	—	597	1	no	—
28	C₂×C₁₃	—	199	1	no	—
29	C₁₃	D₃×D₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₃	—	199	1	no	Hall
31	C₂×C₃	—	199	1	no	—
32	D₃	—	199	1	no	—
33	D₃	C₁₃×D₁₉₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	597	1	no	Sylow
35	C₃	C₂×C₁₃×D₁₉₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	597	1	no	—
38	C₂	—	199	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₁₉₉
commutator, cosocle, hypocenter	C₃×C₁₉₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉₉	C₂²
LCS	G ▷ C₃×C₁₉₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₅₉₇	C₂	semidirect
2. D₃×C₁₃×C₁₉₉	C₂	semidirect
3. C₃×C₁₃×D₁₉₉	C₂	semidirect
5. C₃×C₁₃×C₁₉₉	C₂²	semidirect
8. C₁₃×D₁₉₉	D₃	direct (N × H)
9. C₁₃×C₁₉₉	C₂×D₃	semidirect
10. D₃×D₁₉₉	C₁₃	direct (N × H)
11. D₅₉₇	C₂×C₁₃	semidirect
12. C₃×D₁₉₉	C₂×C₁₃	semidirect
13. D₃×C₁₉₉	C₂×C₁₃	semidirect
15. C₃×C₁₉₉	C₂²×C₁₃	semidirect
18. D₁₉₉	D₃×C₁₃	direct (N × H)
19. C₁₉₉	C₂×D₃×C₁₃	semidirect
23. D₃×C₁₃	D₁₉₉	direct (N × H)
25. C₃×C₁₃	C₂×D₁₉₉	semidirect
29. C₁₃	D₃×D₁₉₉	direct (N × H)
33. D₃	C₁₃×D₁₉₉	direct (N × H)
35. C₃	C₂×C₁₃×D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₅₉₇	2
D₃×C₁₃×C₁₉₉	2
C₃×C₁₃×D₁₉₉	2
C₂×C₁₃×D₁₉₉	3
D₃×D₁₉₉	13
C₂×D₃×C₁₃	199

Subgroups — D3×C13×D199 #44526839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×D₁₉₉ #44526839