Subgroups — C₂×C₃²×D₂₉₉ #24924591

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₂₉₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₂₉₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	4	yes	complemented
6	C₃×D₂₉₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×D₂₉₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	4	yes	complemented
9	C₂×C₃²×D₂₃	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
11	D₂₉₉	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×D₁₃	—	23	1	no	maximal, Hall
13	C₂×C₃²×C₂₃	D₁₃	1	1	yes	characteristic, complemented
14	C₃²×D₂₃	—	13	2	no	—
15	C₁₃×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×D₂₃	—	13	4	no	—
17	C₂×C₃²×C₁₃	D₂₃	1	1	yes	characteristic, complemented
18	C₃²×D₁₃	—	23	2	no	—
19	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×D₁₃	—	23	4	no	—
21	C₂×C₃×C₂₃	C₃×D₁₃	1	4	yes	complemented
22	C₃×D₂₃	—	13	8	no	—
23	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₂₃	—	13	1	no	Hall
25	C₂×C₃×C₁₃	C₃×D₂₃	1	4	yes	complemented
26	C₃×D₁₃	—	23	8	no	—
27	C₃×C₂₃	C₂×C₃×D₁₃	1	4	yes	complemented
28	C₂×D₁₃	—	23	1	no	Hall
29	C₂×C₂₃	C₃²×D₁₃	1	1	yes	characteristic, complemented
30	D₂₃	—	13	2	no	—
31	C₃×C₁₃	C₂×C₃×D₂₃	1	4	yes	complemented
32	C₂²×C₃²	—	299	1	no	Hall
33	C₂×C₁₃	C₃²×D₂₃	1	1	yes	characteristic, complemented
34	D₁₃	—	23	2	no	—
35	C₂₃	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	299	2	no	—
37	C₂×C₃²	D₂₉₉	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂×C₃²×D₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	299	4	no	—
40	C₃²	C₂×D₂₉₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	299	8	no	—
42	C₂×C₃	C₃×D₂₉₉	1	4	yes	direct product factor
43	C₂²	—	299	1	no	Sylow
44	C₃	C₂×C₃×D₂₉₉	1	4	yes	direct product factor
45	C₂	—	299	2	no	—
46	C₂	C₃²×D₂₉₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₂₉₉
commutator, cosocle, hypocenter	C₁₃×C₂₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₂₉₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
3. C₂×C₃×D₂₉₉	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
6. C₃×D₂₉₉	C₂×C₃	direct (N × H)
7. C₂×D₂₉₉	C₃²	direct (N × H)
8. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
10. C₂×C₁₃×C₂₃	C₂×C₃²	semidirect
11. D₂₉₉	C₂×C₃²	direct (N × H)
13. C₂×C₃²×C₂₃	D₁₃	semidirect
15. C₁₃×C₂₃	C₂²×C₃²	semidirect
17. C₂×C₃²×C₁₃	D₂₃	semidirect
19. C₃²×C₂₃	C₂×D₁₃	semidirect
21. C₂×C₃×C₂₃	C₃×D₁₃	semidirect
23. C₃²×C₁₃	C₂×D₂₃	semidirect
25. C₂×C₃×C₁₃	C₃×D₂₃	semidirect
27. C₃×C₂₃	C₂×C₃×D₁₃	semidirect
29. C₂×C₂₃	C₃²×D₁₃	semidirect
31. C₃×C₁₃	C₂×C₃×D₂₃	semidirect
33. C₂×C₁₃	C₃²×D₂₃	semidirect
35. C₂₃	C₂×C₃²×D₁₃	semidirect
37. C₂×C₃²	D₂₉₉	direct (N × H)
38. C₁₃	C₂×C₃²×D₂₃	semidirect
40. C₃²	C₂×D₂₉₉	direct (N × H)
42. C₂×C₃	C₃×D₂₉₉	direct (N × H)
44. C₃	C₂×C₃×D₂₉₉	direct (N × H)
46. C₂	C₃²×D₂₉₉	direct (N × H)

Subgroups — C2×C32×D299 #24924591

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₂₉₉ #24924591