Subgroups — D₁₉×D₄₂₃ #44565262

Order 32148.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₀₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₄₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₄₁	—	3	1	no	maximal
5	C₉×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₇₉	—	3	1	no	—
7	C₁₉×D₁₄₁	—	3	1	no	—
8	C₃×D₁₉×C₄₇	D₃	1	1	yes	characteristic
9	D₁₉×D₄₇	—	9	1	no	Hall
10	C₃×C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic
11	D₈₉₃	—	9	1	no	—
12	C₁₉×D₄₇	—	9	1	no	—
13	D₁₉×C₄₇	D₉	1	1	yes	characteristic, complemented
14	C₂×D₄₂₃	—	19	1	no	maximal, Hall
15	C₁₉×C₄₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₉×C₄₇	—	19	1	no	—
17	D₄₂₃	—	19	1	no	—
18	D₄₂₃	D₁₉	1	1	yes	characteristic, direct product factor
19	D₉×D₁₉	—	47	1	no	maximal, Hall
20	C₂×D₁₄₁	—	57	1	no	—
21	C₉×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
22	D₁₇₁	—	47	1	no	—
23	C₉×D₁₉	D₄₇	1	1	yes	characteristic, complemented
24	D₉×C₁₉	—	47	1	no	—
25	C₂×C₃×C₄₇	—	19	1	no	—
26	D₁₄₁	—	3	1	no	—
27	D₁₄₁	—	57	1	no	—
28	D₃×D₁₉	—	141	1	no	—
29	C₂×D₄₇	—	171	1	no	Hall
30	C₉×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₇	D₃×D₁₉	1	1	yes	characteristic
32	D₅₇	—	141	1	no	—
33	C₃×D₁₉	D₁₄₁	1	1	yes	characteristic
34	D₃×C₁₉	—	141	1	no	—
35	C₂×C₄₇	—	19	1	no	—
36	D₄₇	—	9	1	no	—
37	D₄₇	—	171	1	no	—
38	C₂×D₁₉	—	423	1	no	Hall
39	C₃×C₁₉	C₂×D₁₄₁	1	1	yes	characteristic
40	C₄₇	D₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₉	—	423	1	no	—
42	D₁₉	—	423	1	no	—
43	D₁₉	D₄₂₃	1	1	yes	characteristic, direct product factor
44	C₂×D₉	—	893	1	no	Hall
45	C₁₉	C₂×D₄₂₃	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	19	1	no	—
47	D₉	—	47	1	no	—
48	D₉	—	893	1	no	—
49	C₂×D₃	—	2679	1	no	—
50	C₉	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	1	no	—
52	D₃	—	2679	1	no	—
53	D₃	—	141	1	no	—
54	C₂²	—	8037	1	no	Sylow
55	C₃	D₁₉×D₁₄₁	1	1	yes	characteristic
56	C₂	—	19	1	no	—
57	C₂	—	8037	1	no	—
58	C₂	—	423	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₄₇	C₂²
Frattini	C₃	D₁₉×D₁₄₁
socle	C₃×C₁₉×C₄₇	C₂×D₃
LCS	G ▷ C₉×C₁₉×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₀₃₇	C₂	semidirect
2. C₁₉×D₄₂₃	C₂	semidirect
3. C₉×D₁₉×C₄₇	C₂	semidirect
5. C₉×C₁₉×C₄₇	C₂²	semidirect
13. D₁₉×C₄₇	D₉	semidirect
15. C₁₉×C₄₇	C₂×D₉	semidirect
18. D₄₂₃	D₁₉	direct (N × H)
21. C₉×C₄₇	C₂×D₁₉	semidirect
23. C₉×D₁₉	D₄₇	semidirect
30. C₉×C₁₉	C₂×D₄₇	semidirect
40. C₄₇	D₉×D₁₉	semidirect
43. D₁₉	D₄₂₃	direct (N × H)
45. C₁₉	C₂×D₄₂₃	semidirect
50. C₉	D₁₉×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₈₀₃₇	2
C₁₉×D₄₂₃	2
C₉×D₁₉×C₄₇	2
D₁₉×D₁₄₁	3
C₂×D₄₂₃	19
D₉×D₁₉	47

Subgroups — D19×D423 #44565262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₄₂₃ #44565262