Subgroups — C₂×C₃×C₂₃⋊(D₁₉⋊C₃) #30628613

Order 15732.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₃⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₄₃₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃⋊(D₁₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
6	C₃×C₂₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂₃⋊(D₁₉⋊C₃)	C₂×C₃	1	3	yes	direct product factor
8	C₂₃⋊(D₁₉⋊C₃)	C₂×C₃	1	3	yes	direct product factor
9	C₃×D₄₃₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₄₃₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₂₃×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
12	C₂×C₃×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×D₄₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂₃×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
16	C₂×C₁₉×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₄₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
18	D₄₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₂×C₃²×D₂₃	—	19	1	no	maximal, Hall
20	C₂×C₃×D₁₉⋊C₃	—	23	1	no	maximal, Hall
21	C₁₉×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₂₃	—	19	1	no	—
23	C₃²×D₂₃	—	19	1	no	—
24	C₃²×D₂₃	—	19	1	no	—
25	C₂×C₃×C₁₉⋊C₃	D₂₃	1	1	yes	characteristic, complemented
26	C₃×D₁₉⋊C₃	—	23	1	no	—
27	C₃×D₁₉⋊C₃	—	23	1	no	—
28	C₂×C₃×D₂₃	—	19	3	no	—
29	C₂×C₃×D₂₃	—	57	1	no	—
30	C₂×C₃×D₁₉	—	23	1	no	—
31	C₂×D₁₉⋊C₃	—	23	3	no	—
32	C₃²×C₂₃	—	19	1	no	Hall
33	C₃×C₁₉⋊C₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₃	—	19	3	no	—
35	C₂×C₃×C₂₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
36	C₃×D₂₃	—	19	1	no	—
37	C₃×D₂₃	—	19	3	no	—
38	C₃×D₂₃	—	19	3	no	—
39	C₃×D₂₃	—	57	1	no	—
40	C₂×C₃×C₁₉	C₃×D₂₃	1	1	yes	characteristic, complemented
41	C₃×D₁₉	—	23	1	no	—
42	C₃×D₁₉	—	23	1	no	—
43	C₂×C₁₉⋊C₃	C₃×D₂₃	1	3	yes	complemented
44	D₁₉⋊C₃	—	23	3	no	—
45	D₁₉⋊C₃	—	23	3	no	—
46	C₂×D₂₃	—	57	1	no	Hall
47	C₂×D₁₉	—	23	1	no	Hall
48	C₃×C₂₃	—	19	3	no	—
49	C₃×C₂₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
50	C₃×C₁₉	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented
51	C₁₉⋊C₃	C₂×C₃×D₂₃	1	3	yes	complemented
52	C₂×C₂₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
53	D₂₃	—	19	1	no	—
54	D₂₃	—	57	1	no	—
55	C₂×C₁₉	C₃²×D₂₃	1	1	yes	characteristic, complemented
56	D₁₉	—	23	1	no	—
57	D₁₉	—	23	1	no	—
58	C₂²×C₃²	—	437	1	no	Hall
59	C₂₃	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₁₉	C₂×C₃²×D₂₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃²	—	19	1	no	—
62	C₂×C₃²	—	437	1	no	—
63	C₂×C₃²	—	437	1	no	—
64	C₂²×C₃	—	1311	1	no	—
65	C₂²×C₃	—	437	3	no	—
66	C₃²	—	19	1	no	Sylow
67	C₂×C₃	—	19	3	no	—
68	C₂×C₃	—	1311	1	no	—
69	C₂×C₃	—	1311	1	no	—
70	C₂×C₃	—	437	3	no	—
71	C₂×C₃	—	437	3	no	—
72	C₂×C₃	C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
73	C₂²	—	1311	1	no	Sylow
74	C₃	—	19	3	no	—
75	C₃	C₂×C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
76	C₂	—	1311	1	no	—
77	C₂	—	1311	1	no	—
78	C₂	C₃×C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂₃⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₁₉×C₂₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₁₉×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₃×C₁₉⋊C₃	C₂	semidirect
2. C₃×C₂₃⋊(D₁₉⋊C₃)	C₂	direct (N × H)
3. C₃×C₂₃⋊(D₁₉⋊C₃)	C₂	direct (N × H)
4. C₂×C₃×D₄₃₇	C₃	semidirect
5. C₂×C₂₃⋊(D₁₉⋊C₃)	C₃	direct (N × H)
6. C₃×C₂₃×C₁₉⋊C₃	C₂²	semidirect
7. C₂₃⋊(D₁₉⋊C₃)	C₂×C₃	direct (N × H)
8. C₂₃⋊(D₁₉⋊C₃)	C₂×C₃	direct (N × H)
9. C₃×D₄₃₇	C₂×C₃	semidirect
10. C₃×D₄₃₇	C₂×C₃	semidirect
11. C₂×C₂₃×C₁₉⋊C₃	C₂×C₃	semidirect
12. C₂×C₃×C₁₉×C₂₃	C₂×C₃	semidirect
13. C₂×D₄₃₇	C₃²	semidirect
14. C₃×C₁₉×C₂₃	C₂²×C₃	semidirect
15. C₂₃×C₁₉⋊C₃	C₂²×C₃	semidirect
16. C₂×C₁₉×C₂₃	C₂×C₃²	semidirect
17. D₄₃₇	C₂×C₃²	semidirect
18. D₄₃₇	C₂×C₃²	semidirect
21. C₁₉×C₂₃	C₂²×C₃²	semidirect
25. C₂×C₃×C₁₉⋊C₃	D₂₃	semidirect
33. C₃×C₁₉⋊C₃	C₂×D₂₃	semidirect
35. C₂×C₃×C₂₃	D₁₉⋊C₃	semidirect
40. C₂×C₃×C₁₉	C₃×D₂₃	semidirect
43. C₂×C₁₉⋊C₃	C₃×D₂₃	semidirect
49. C₃×C₂₃	C₂×D₁₉⋊C₃	semidirect
50. C₃×C₁₉	C₂×C₃×D₂₃	semidirect
51. C₁₉⋊C₃	C₂×C₃×D₂₃	semidirect
52. C₂×C₂₃	C₃×D₁₉⋊C₃	semidirect
55. C₂×C₁₉	C₃²×D₂₃	semidirect
59. C₂₃	C₂×C₃×D₁₉⋊C₃	semidirect
60. C₁₉	C₂×C₃²×D₂₃	semidirect
72. C₂×C₃	C₂₃⋊(D₁₉⋊C₃)	direct (N × H)
75. C₃	C₂×C₂₃⋊(D₁₉⋊C₃)	direct (N × H)
78. C₂	C₃×C₂₃⋊(D₁₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂₃×C₁₉⋊C₃	2
C₃×C₂₃⋊(D₁₉⋊C₃)	2
C₂×C₃×D₄₃₇	3
C₂×C₂₃⋊(D₁₉⋊C₃)	3
C₂×C₃²×D₂₃	19
C₂×C₃×D₁₉⋊C₃	23

Subgroups — C2×C3×C23⋊(D19⋊C3) #30628613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₃⋊(D₁₉⋊C₃) #30628613