Subgroups — C₃×D₃×D₂₉₉ #24924554

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₈₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₂₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₂₉₉	—	3	1	no	maximal
5	D₃×D₂₉₉	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
8	D₈₉₇	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₂₉₉	—	2	1	no	—
11	C₃×D₂₉₉	—	3	1	no	—
12	C₃×D₂₉₉	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₂₉₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₂₉₉	—	3	1	no	Hall
15	C₃×C₁₃×C₂₃	—	2	1	no	—
16	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₂₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₂₃	—	3	1	no	—
20	D₂₉₉	—	3	1	no	—
21	D₂₉₉	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₃×D₁₃	—	23	1	no	maximal, Hall
23	C₃×D₆₉	—	13	1	no	—
24	C₃×D₃×C₂₃	D₁₃	1	1	yes	characteristic, complemented
25	C₃²×D₂₃	—	13	1	no	—
26	C₁₃×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₂₃	—	39	1	no	—
28	D₃×D₂₃	—	13	1	no	—
29	C₃×D₃₉	—	23	1	no	—
30	C₃×D₃×C₁₃	D₂₃	1	1	yes	characteristic, complemented
31	C₃²×D₁₃	—	23	1	no	—
32	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₃	—	69	1	no	—
34	D₃×D₁₃	—	23	1	no	—
35	C₂×C₃×C₂₃	—	3	1	no	—
36	D₆₉	—	13	1	no	—
37	C₃×D₂₃	—	13	1	no	—
38	C₃×D₂₃	—	13	1	no	—
39	C₃×D₂₃	—	26	1	no	—
40	C₃×D₂₃	—	39	1	no	—
41	D₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic, complemented
42	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂×D₂₃	—	39	1	no	Hall
44	C₂×C₃×C₁₃	—	3	1	no	—
45	D₃₉	—	23	1	no	—
46	C₃×D₁₃	—	23	1	no	—
47	C₃×D₁₃	—	23	1	no	—
48	C₃×D₁₃	—	46	1	no	—
49	C₃×D₁₃	—	69	1	no	—
50	D₃×C₁₃	C₃×D₂₃	1	1	yes	characteristic, complemented
51	C₃×C₂₃	—	2	1	no	—
52	C₃×C₂₃	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₂₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	69	1	no	Hall
55	C₂×C₂₃	—	3	1	no	—
56	D₂₃	—	13	1	no	—
57	D₂₃	—	39	1	no	—
58	C₃×C₁₃	—	2	1	no	—
59	C₃×C₁₃	D₃×D₂₃	1	1	yes	characteristic, complemented
60	C₃×C₁₃	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃	—	299	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	23	1	no	—
64	D₁₃	—	69	1	no	—
65	C₂₃	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	299	1	no	—
67	C₃×D₃	—	299	1	no	—
68	C₃×D₃	D₂₉₉	1	1	yes	characteristic, direct product factor
69	C₁₃	C₃×D₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	897	1	no	—
71	C₂×D₃	—	299	1	no	—
72	C₃²	C₂×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	299	1	no	—
75	C₂×C₃	—	299	1	no	—
76	C₂×C₃	—	598	1	no	—
77	C₂×C₃	—	897	1	no	—
78	D₃	—	299	1	no	—
79	D₃	C₃×D₂₉₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	897	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₂₉₉	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₂₉₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	299	1	no	—
86	C₂	—	897	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×D₂₉₉
commutator, cosocle, hypocenter	C₃×C₁₃×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₁₃×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₈₉₇	C₂	semidirect
2. C₃×D₃×C₁₃×C₂₃	C₂	semidirect
3. C₃²×D₂₉₉	C₂	semidirect
5. D₃×D₂₉₉	C₃	direct (N × H)
6. C₃²×C₁₃×C₂₃	C₂²	semidirect
8. D₈₉₇	C₂×C₃	semidirect
9. D₃×C₁₃×C₂₃	C₂×C₃	semidirect
12. C₃×D₂₉₉	D₃	direct (N × H)
13. C₃×D₂₉₉	C₂×C₃	semidirect
16. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
21. D₂₉₉	C₃×D₃	direct (N × H)
24. C₃×D₃×C₂₃	D₁₃	semidirect
26. C₁₃×C₂₃	C₂×C₃×D₃	semidirect
30. C₃×D₃×C₁₃	D₂₃	semidirect
32. C₃²×C₂₃	C₂×D₁₃	semidirect
41. D₃×C₂₃	C₃×D₁₃	semidirect
42. C₃²×C₁₃	C₂×D₂₃	semidirect
50. D₃×C₁₃	C₃×D₂₃	semidirect
52. C₃×C₂₃	D₃×D₁₃	semidirect
53. C₃×C₂₃	C₂×C₃×D₁₃	semidirect
59. C₃×C₁₃	D₃×D₂₃	semidirect
60. C₃×C₁₃	C₂×C₃×D₂₃	semidirect
65. C₂₃	C₃×D₃×D₁₃	semidirect
68. C₃×D₃	D₂₉₉	direct (N × H)
69. C₁₃	C₃×D₃×D₂₃	semidirect
72. C₃²	C₂×D₂₉₉	semidirect
79. D₃	C₃×D₂₉₉	direct (N × H)
82. C₃	D₃×D₂₉₉	direct (N × H)
83. C₃	C₂×C₃×D₂₉₉	semidirect

Subgroups — C3×D3×D299 #24924554

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×D₂₉₉ #24924554