Subgroups — C₂₃×(C₃⋊D₃)⋊D₁₉ #30628639

Order 15732.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃×D₅₇	C₂	1	2	yes	maximal, complemented
3	D₃×C₂₃×D₁₉	—	3	2	no	maximal
4	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₃×D₅₇	D₃	1	2	yes	complemented
6	D₃×C₁₉×C₂₃	—	3	2	no	—
7	D₃×C₁₉×C₂₃	—	6	1	no	—
8	C₃×C₂₃×D₁₉	—	3	2	no	—
9	C₂×C₂₃×D₁₉	—	9	1	no	Hall
10	C₃×C₁₉×C₂₃	—	2	1	no	—
11	C₃×C₁₉×C₂₃	C₂×D₃	1	2	yes	complemented
12	C₂×C₁₉×C₂₃	—	9	1	no	—
13	C₂₃×D₁₉	—	3	2	no	—
14	D₃²×C₂₃	—	19	1	no	maximal, Hall
15	(C₃⋊D₃)⋊D₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₉×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
17	C₃⋊D₃×C₂₃	D₁₉	1	1	yes	characteristic, complemented
18	C₃×D₃×C₂₃	—	19	2	no	—
19	C₃⋊D₃×C₁₉	C₂×C₂₃	1	1	yes	characteristic, complemented
20	C₃×D₅₇	C₂×C₂₃	1	2	yes	complemented
21	C₂×D₃×C₂₃	—	57	2	no	—
22	D₃×D₁₉	—	3	2	no	—
23	C₃²×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₁₉	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₂₃	—	57	2	no	—
26	D₃×C₂₃	—	3	2	no	—
27	D₃×C₂₃	—	6	1	no	—
28	D₃×C₂₃	—	19	2	no	—
29	D₅₇	D₃×C₂₃	1	2	yes	complemented
30	C₃×D₁₉	—	3	2	no	—
31	D₃×C₁₉	—	3	2	no	—
32	D₃×C₁₉	—	6	1	no	—
33	C₂²×C₂₃	—	171	1	no	Hall
34	C₂×D₁₉	—	9	1	no	Hall
35	C₃×C₂₃	—	2	1	no	—
36	C₃×C₂₃	D₃×D₁₉	1	2	yes	complemented
37	C₃×C₁₉	—	2	1	no	—
38	C₃×C₁₉	C₂×D₃×C₂₃	1	2	yes	complemented
39	C₂×C₂₃	—	9	1	no	—
40	C₂×C₂₃	—	57	2	no	—
41	C₂×C₁₉	—	9	1	no	—
42	D₁₉	—	3	2	no	—
43	D₃²	—	19	1	no	Hall
44	C₂₃	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₁₉	D₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
46	C₃⋊D₃	C₂₃×D₁₉	1	1	yes	characteristic, complemented
47	C₃×D₃	—	19	2	no	—
48	C₂×D₃	—	57	2	no	—
49	C₃²	C₂×C₂₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	57	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	19	2	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₂₃×D₁₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	57	2	no	—

	subgroup	G/H
center, hypercenter	C₂₃	(C₃⋊D₃)⋊D₁₉
commutator, cosocle, hypocenter	C₃²×C₁₉	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉×C₂₃	C₂²
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₉×C₂₃	C₂	semidirect
2. C₃×C₂₃×D₅₇	C₂	semidirect
4. C₃²×C₁₉×C₂₃	C₂²	semidirect
5. C₂₃×D₅₇	D₃	semidirect
11. C₃×C₁₉×C₂₃	C₂×D₃	semidirect
15. (C₃⋊D₃)⋊D₁₉	C₂₃	direct (N × H)
16. C₁₉×C₂₃	D₃²	semidirect
17. C₃⋊D₃×C₂₃	D₁₉	semidirect
19. C₃⋊D₃×C₁₉	C₂×C₂₃	semidirect
20. C₃×D₅₇	C₂×C₂₃	semidirect
23. C₃²×C₂₃	C₂×D₁₉	semidirect
24. C₃²×C₁₉	C₂²×C₂₃	semidirect
29. D₅₇	D₃×C₂₃	semidirect
36. C₃×C₂₃	D₃×D₁₉	semidirect
38. C₃×C₁₉	C₂×D₃×C₂₃	semidirect
44. C₂₃	(C₃⋊D₃)⋊D₁₉	direct (N × H)
45. C₁₉	D₃²×C₂₃	semidirect
46. C₃⋊D₃	C₂₃×D₁₉	semidirect
49. C₃²	C₂×C₂₃×D₁₉	semidirect
56. C₃	D₃×C₂₃×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₉×C₂₃	2
C₃×C₂₃×D₅₇	2
D₃×C₂₃×D₁₉	3
D₃²×C₂₃	19
(C₃⋊D₃)⋊D₁₉	23

Subgroups — C23×(C3⋊D3)⋊D19 #30628639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×(C₃⋊D₃)⋊D₁₉ #30628639