Subgroups — #18070446

Order 4864.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561846	C₂	1	1	yes	maximal, characteristic
2	#14561837	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1425	C₂	1	1	yes	maximal, characteristic
4	#11926370	—	2	1	no	—
5	C₁₉⋊C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₉×#368	—	2	1	no	—
8	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
9	C₁₉×#108	—	4	1	no	—
10	#10597275	—	4	1	no	—
11	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₉×C₃₂	Q₈	1	1	yes	characteristic
13	M₁₆×C₁₉	—	8	1	no	—
14	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
15	C₄⋊Dic₁₉	—	8	1	no	—
16	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
18	#7548	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
20	C₂×Dic₁₉	—	16	1	no	—
21	C₈×C₁₉	—	16	1	no	—
22	C₈×C₁₉	#107	1	1	yes	characteristic
23	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
24	M₁₂₈	—	19	1	no	—
25	#1425	D₁₉	1	1	yes	characteristic
26	#1424	—	19	1	no	—
27	C₂²×C₁₉	SD₆₄	1	1	yes	characteristic
28	C₄×C₁₉	#366	1	1	yes	characteristic
29	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
30	Dic₁₉	—	32	1	no	—
31	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
32	#368	—	2	1	no	—
33	#366	—	38	1	no	—
34	C₆₄	—	19	2	no	—
35	C₂×C₁₉	—	2	1	no	—
36	C₂×C₁₉	#1424	1	1	yes	characteristic
37	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#107	—	76	1	no	—
40	C₃₂	Dic₃₈	1	1	yes	characteristic
41	C₃₂	C₄×D₁₉	1	1	yes	characteristic
42	C₁₉	#7548	1	1	yes	characteristic, complemented, Sylow
43	M₁₆	—	8	1	no	—
44	C₂×C₈	#64525	1	1	yes	characteristic
45	C₄⋊C₄	—	152	1	no	—
46	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
47	C₁₆	#64528	1	1	yes	characteristic
48	C₂×C₄	—	304	1	no	—
49	C₂×C₄	#10597283	1	1	yes	characteristic
50	C₈	—	16	1	no	—
51	C₈	#10597264	1	1	yes	characteristic
52	C₈	#10597286	1	1	yes	characteristic
53	C₂²	#11926381	1	1	yes	characteristic
54	C₄	—	608	1	no	—
55	C₄	#11926369	1	1	yes	characteristic
56	C₄	#11926382	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#14561836	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561836
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1425	C₂
socle	C₂×C₁₉	#1424
prime radical	C₂²×C₁₉	SD₆₄
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1425	D₁₉
hypocenter	C₁₉	#7548
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
5. C₁₉⋊C₆₄	C₄	semidirect
42. C₁₉	#7548	semidirect

Maximal subgroups

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

subgroup	index
#14561846	2
#14561837	2
C₁₉×#1425	2
#7548	19