Subgroups — #18070442

Order 4864.

60 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	#14561839	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1425	C₂	1	1	yes	maximal, characteristic
4	#11926374	—	2	1	no	—
5	C₁₉⋊C₆₄	C₄	1	2	yes	—
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	#10597276	—	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	#64520	—	8	1	no	—
16	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
18	#7547	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
20	C₈×C₁₉	—	16	1	no	—
21	C₈×C₁₉	#107	1	1	yes	characteristic
22	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
23	C₁₉⋊C₈	—	16	1	no	—
24	C₂×C₆₄	—	19	1	no	—
25	#1425	—	19	1	no	—
26	#1425	D₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	Q₆₄	1	1	yes	characteristic
28	C₄×C₁₉	#366	1	1	yes	characteristic
29	C₄×C₁₉	D₃₂	1	1	yes	characteristic
30	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
31	#368	—	2	1	no	—
32	#368	—	38	1	no	—
33	C₆₄	—	19	2	no	—
34	C₂×C₁₉	—	2	1	no	—
35	C₂×C₁₉	#1423	1	1	yes	characteristic
36	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
37	#108	—	4	1	no	—
38	#108	—	76	1	no	—
39	C₃₂	Dic₃₈	1	1	yes	characteristic
40	C₃₂	C₄×D₁₉	1	1	yes	characteristic
41	C₁₉	#7547	1	1	yes	characteristic, complemented, Sylow
42	M₁₆	—	8	1	no	—
43	M₁₆	—	152	1	no	—
44	C₂×C₈	#64525	1	1	yes	characteristic
45	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
46	C₁₆	#64528	1	1	yes	characteristic
47	C₂×C₄	#10597283	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	304	1	no	—
50	C₈	#10597264	1	1	yes	characteristic
51	C₈	#10597286	1	1	yes	characteristic
52	C₂²	#11926384	1	1	yes	characteristic
53	C₄	#11926369	1	1	yes	characteristic
54	C₄	#11926379	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#14561834	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1425	C₂
socle	C₂×C₁₉	#1423
prime radical	C₂²×C₁₉	Q₆₄
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1425	D₁₉
hypocenter	C₁₉	#7547
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ 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
41. C₁₉	#7547	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
#14561839	2
C₁₉×#1425	2
#7547	19