Subgroups — C₂×C₂₃×C₃⋊(D₁₃⋊C₃) #24924541

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×C₃⋊(D₁₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂₃×D₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×D₁₃⋊C₃	—	3	1	no	maximal
5	C₃×C₂₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂₃×D₃₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₃×C₁₃⋊C₃	—	2	1	no	—
9	C₂×C₂₃×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
10	C₂₃×D₁₃⋊C₃	—	3	2	no	—
11	C₂×C₂₃×D₁₃	—	3	1	no	Hall
12	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₂₃×C₁₃⋊C₃	—	2	1	no	—
14	C₂₃×C₁₃⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₃×C₂₃	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₂₃	C₃×D₃	1	1	yes	characteristic, complemented
17	C₂₃×D₁₃	—	3	2	no	—
18	C₂×C₃⋊(D₁₃⋊C₃)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃²×C₂₃	—	13	1	no	—
20	C₃×D₃×C₂₃	—	13	2	no	—
21	C₁₃×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃×C₂₃	—	39	1	no	—
23	C₂×D₃×C₂₃	—	13	1	no	—
24	C₂×C₃×C₁₃⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₃⋊(D₁₃⋊C₃)	C₂×C₂₃	1	2	yes	direct product factor
26	C₃²×C₂₃	—	13	1	no	Hall
27	C₂×D₃₉	C₃×C₂₃	1	1	yes	characteristic, complemented
28	C₂×D₁₃⋊C₃	—	3	1	no	—
29	C₂×C₃×C₂₃	—	13	1	no	—
30	C₂×C₃×C₂₃	—	26	1	no	—
31	C₂×C₃×C₂₃	—	39	2	no	—
32	C₂×C₃×C₂₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
33	D₃×C₂₃	—	13	2	no	—
34	C₃×C₁₃⋊C₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₂₃	—	39	1	no	Hall
36	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
37	D₃₉	C₂×C₃×C₂₃	1	2	yes	complemented
38	C₂×C₁₃⋊C₃	—	2	1	no	—
39	C₂×C₁₃⋊C₃	D₃×C₂₃	1	1	yes	characteristic, complemented
40	D₁₃⋊C₃	—	3	2	no	—
41	C₃×C₂₃	—	13	1	no	—
42	C₃×C₂₃	—	26	1	no	—
43	C₃×C₂₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
44	C₂×D₁₃	—	3	1	no	Hall
45	C₂×C₂₃	—	39	2	no	—
46	C₂×C₂₃	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
47	C₃×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
48	C₁₃⋊C₃	—	2	1	no	—
49	C₁₃⋊C₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
50	C₂×C₃×D₃	—	13	1	no	Hall
51	C₂×C₁₃	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented
52	D₁₃	—	3	2	no	—
53	C₂₃	C₂×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃²	—	13	1	no	—
55	C₃×D₃	—	13	2	no	—
56	C₁₃	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	39	1	no	—
58	C₂×D₃	—	13	1	no	—
59	C₃²	—	13	1	no	Sylow
60	C₂×C₃	—	13	1	no	—
61	C₂×C₃	—	26	1	no	—
62	C₂×C₃	—	39	2	no	—
63	C₂×C₃	C₂₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
64	D₃	—	13	2	no	—
65	C₂²	—	39	1	no	Sylow
66	C₃	—	13	1	no	—
67	C₃	—	26	1	no	—
68	C₃	C₂×C₂₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	39	2	no	—
70	C₂	C₂₃×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	C₃⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₃×C₁₃⋊C₃	C₂	semidirect
2. C₂₃×C₃⋊(D₁₃⋊C₃)	C₂	direct (N × H)
3. C₂×C₂₃×D₃₉	C₃	semidirect
5. C₃×C₂₃×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
7. C₂₃×D₃₉	C₂×C₃	semidirect
9. C₂×C₂₃×C₁₃⋊C₃	D₃	semidirect
12. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
14. C₂₃×C₁₃⋊C₃	C₂×D₃	semidirect
16. C₂×C₁₃×C₂₃	C₃×D₃	semidirect
18. C₂×C₃⋊(D₁₃⋊C₃)	C₂₃	direct (N × H)
21. C₁₃×C₂₃	C₂×C₃×D₃	semidirect
24. C₂×C₃×C₁₃⋊C₃	C₂×C₂₃	semidirect
25. C₃⋊(D₁₃⋊C₃)	C₂×C₂₃	direct (N × H)
27. C₂×D₃₉	C₃×C₂₃	semidirect
32. C₂×C₃×C₂₃	D₁₃⋊C₃	semidirect
34. C₃×C₁₃⋊C₃	C₂²×C₂₃	semidirect
36. C₂×C₃×C₁₃	C₂×C₃×C₂₃	semidirect
37. D₃₉	C₂×C₃×C₂₃	semidirect
39. C₂×C₁₃⋊C₃	D₃×C₂₃	semidirect
43. C₃×C₂₃	C₂×D₁₃⋊C₃	semidirect
46. C₂×C₂₃	C₃⋊(D₁₃⋊C₃)	direct (N × H)
47. C₃×C₁₃	C₂²×C₃×C₂₃	semidirect
49. C₁₃⋊C₃	C₂×D₃×C₂₃	semidirect
51. C₂×C₁₃	C₃×D₃×C₂₃	semidirect
53. C₂₃	C₂×C₃⋊(D₁₃⋊C₃)	direct (N × H)
56. C₁₃	C₂×C₃×D₃×C₂₃	semidirect
63. C₂×C₃	C₂₃×D₁₃⋊C₃	semidirect
68. C₃	C₂×C₂₃×D₁₃⋊C₃	semidirect
70. C₂	C₂₃×C₃⋊(D₁₃⋊C₃)	direct (N × H)

Subgroups — C2×C23×C3⋊(D13⋊C3) #24924541

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₃×C₃⋊(D₁₃⋊C₃) #24924541