Subgroups — #18070440

Order 4864.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#14561835	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1423	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×#366	—	2	1	no	—
8	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
9	C₁₉×#107	—	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	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
14	C₄⋊C₄×C₁₉	—	8	1	no	—
15	C₄⋊Dic₁₉	—	8	1	no	—
16	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
18	#7546	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	—	16	1	no	—
20	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
21	C₂×Dic₁₉	—	16	1	no	—
22	C₈×C₁₉	#107	1	1	yes	characteristic
23	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
24	C₂×C₆₄	—	19	1	no	—
25	#1423	—	19	1	no	—
26	#1423	D₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
28	C₄×C₁₉	—	32	1	no	—
29	C₄×C₁₉	#366	1	1	yes	characteristic
30	C₄×C₁₉	Q₆₄	1	1	yes	characteristic
31	Dic₁₉	—	32	1	no	—
32	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
33	#366	—	2	1	no	—
34	#366	—	38	1	no	—
35	C₆₄	—	19	2	no	—
36	C₂×C₁₉	#1423	1	1	yes	characteristic
37	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
38	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
39	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
40	#107	—	4	1	no	—
41	#107	—	76	1	no	—
42	C₃₂	Dic₃₈	1	1	yes	characteristic
43	C₃₂	C₄×D₁₉	1	1	yes	characteristic
44	C₁₉	#7546	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₈	#64525	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	152	1	no	—
48	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
49	C₁₆	#64528	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	304	1	no	—
52	C₂×C₄	#10597283	1	1	yes	characteristic
53	C₈	#10597264	1	1	yes	characteristic
54	C₈	#10597286	1	1	yes	characteristic
55	C₂²	#11926379	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	608	1	no	—
58	C₄	#11926369	1	1	yes	characteristic
59	C₄	#11926384	1	1	yes	characteristic
60	C₂	#14561834	1	1	yes	characteristic
61	C₂	#14561849	1	1	yes	characteristic
62	C₂	#14561850	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1423	C₂
socle, prime radical	C₂²×C₁₉	D₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1423	D₁₉
hypocenter	C₁₉	#7546
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. C₁₉⋊C₆₄	C₄	semidirect
44. C₁₉	#7546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉⋊C₆₄	2
#14561835	2
C₁₉×#1423	2
#7546	19