Subgroups — C₁₉×#953 #14269705

Order 1824.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#67	C₂	1	3	yes	maximal, complemented
3	C₁₉×#217	C₂	1	3	yes	maximal, complemented
4	C₁₉×#120	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₉	—	2	6	no	—
6	C₂³×C₃×C₁₉	C₂²	1	3	yes	—
7	C₂²×D₃×C₁₉	C₂²	1	1	yes	characteristic, complemented
8	C₁₉×#67	—	2	6	no	—
9	C₂×Dic₃×C₁₉	C₂²	1	3	yes	complemented
10	C₂⁴×C₁₉	D₃	1	1	yes	characteristic, complemented
11	C₂×D₄×C₁₉	—	3	3	no	—
12	C₂²⋊C₄×C₁₉	—	3	3	no	—
13	C₂²×C₃×C₁₉	—	2	8	no	—
14	C₂²×C₃×C₁₉	—	2	6	no	—
15	C₂²×C₃×C₁₉	D₄	1	6	yes	complemented
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₉	—	2	3	no	—
18	Dic₃×C₁₉	—	2	3	no	—
19	C₂³×C₁₉	—	2	6	no	—
20	C₂³×C₁₉	—	3	1	no	—
21	C₂³×C₁₉	C₂×D₃	1	3	yes	—
22	D₄×C₁₉	—	6	6	no	—
23	C₂×C₄×C₁₉	—	3	3	no	—
24	C₂×C₃×C₁₉	—	2	6	no	—
25	C₂×C₃×C₁₉	C₂×D₄	1	3	yes	—
26	D₃×C₁₉	—	4	1	no	—
27	#953	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₁₉	—	2	8	no	—
29	C₂²×C₁₉	—	2	6	no	—
30	C₂²×C₁₉	—	6	3	no	—
31	C₂²×C₁₉	#67	1	6	yes	complemented
32	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₉	—	6	3	no	—
34	C₃×C₁₉	#120	1	1	yes	characteristic, complemented, Hall
35	C₂⁴×C₃	C₂×C₁₉	1	1	yes	characteristic, complemented
36	C₂×#67	C₂×C₁₉	1	3	yes	complemented
37	#217	C₂×C₁₉	1	3	yes	complemented
38	C₂×C₁₉	—	2	6	no	—
39	C₂×C₁₉	—	12	1	no	—
40	C₂×C₁₉	C₂×#67	1	3	yes	—
41	#120	—	3	1	no	Sylow
42	C₂³×C₃	—	2	6	no	—
43	C₂³×C₃	C₂²×C₁₉	1	3	yes	—
44	C₂²×D₃	C₂²×C₁₉	1	1	yes	characteristic, complemented
45	#67	—	2	6	no	—
46	C₂×Dic₃	C₂²×C₁₉	1	3	yes	complemented
47	C₁₉	#953	1	1	yes	characteristic, direct product factor, Sylow
48	C₂⁴	D₃×C₁₉	1	1	yes	characteristic, complemented
49	C₂×D₄	—	3	3	no	—
50	C₂²⋊C₄	—	3	3	no	—
51	C₂²×C₃	—	2	8	no	—
52	C₂²×C₃	—	2	6	no	—
53	C₂²×C₃	D₄×C₁₉	1	6	yes	complemented
54	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
55	C₂×D₃	—	2	3	no	—
56	Dic₃	—	2	3	no	—
57	C₂³	—	2	6	no	—
58	C₂³	—	3	1	no	—
59	C₂³	C₂×D₃×C₁₉	1	3	yes	—
60	D₄	—	6	6	no	—
61	C₂×C₄	—	3	3	no	—
62	C₂×C₃	—	2	6	no	—
63	C₂×C₃	C₂×D₄×C₁₉	1	3	yes	—
64	D₃	—	4	1	no	—
65	C₂²	—	2	8	no	—
66	C₂²	—	2	6	no	—
67	C₂²	—	6	3	no	—
68	C₂²	C₁₉×#67	1	6	yes	complemented
69	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
70	C₄	—	6	3	no	—
71	C₃	C₁₉×#120	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	2	6	no	—
73	C₂	—	12	1	no	—
74	C₂	C₂×C₁₉×#67	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂⁴×C₃×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
hypercenter	C₂⁴×C₁₉	D₃
hypocenter	C₃	C₁₉×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₉	C₂	semidirect
2. C₂×C₁₉×#67	C₂	semidirect
3. C₁₉×#217	C₂	semidirect
7. C₂²×D₃×C₁₉	C₂²	semidirect
9. C₂×Dic₃×C₁₉	C₂²	semidirect
10. C₂⁴×C₁₉	D₃	semidirect
15. C₂²×C₃×C₁₉	D₄	semidirect
27. #953	C₁₉	direct (N × H)
31. C₂²×C₁₉	#67	semidirect
34. C₃×C₁₉	#120	semidirect
35. C₂⁴×C₃	C₂×C₁₉	semidirect
36. C₂×#67	C₂×C₁₉	semidirect
37. #217	C₂×C₁₉	semidirect
44. C₂²×D₃	C₂²×C₁₉	semidirect
46. C₂×Dic₃	C₂²×C₁₉	semidirect
47. C₁₉	#953	direct (N × H)
48. C₂⁴	D₃×C₁₉	semidirect
53. C₂²×C₃	D₄×C₁₉	semidirect
68. C₂²	C₁₉×#67	semidirect
71. C₃	C₁₉×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₉	2
C₂×C₁₉×#67	2
C₁₉×#217	2
C₁₉×#120	3
#953	19

Subgroups — C19×#953 #14269705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#953 #14269705