Subgroups — #18070222

Order 4864.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561709	C₂	1	2	yes	maximal
2	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
3	#11926297	—	2	2	no	—
4	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
9	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
10	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
11	C₁₉×C₃₂	—	2	1	no	—
12	C₁₉×C₃₂	C₈	1	2	yes	complemented
13	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
15	C₄²×C₁₉	D₈	1	1	yes	characteristic
16	C₂×C₁₉⋊C₈	—	8	2	no	—
17	C₁₆×C₁₉	—	2	1	no	—
18	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
20	#7463	—	19	1	no	maximal, Sylow
21	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
22	C₂×C₄×C₁₉	SD₃₂	1	2	yes	—
23	C₈×C₁₉	—	2	1	no	—
24	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₉	#108	1	1	yes	characteristic
26	C₁₉⋊C₈	—	16	2	no	—
27	#1397	D₁₉	1	1	yes	characteristic
28	#1372	—	19	2	no	—
29	C₂²×C₁₉	#367	1	1	yes	characteristic
30	C₄×C₁₉	—	2	2	no	—
31	C₄×C₁₉	#335	1	1	yes	characteristic
32	C₄×C₁₉	#368	1	1	yes	characteristic
33	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
34	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
35	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
36	#335	—	38	2	no	—
37	C₂×C₁₉	#1372	1	1	yes	characteristic
38	C₂×C₁₉	#1426	1	2	yes	—
39	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
40	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
41	C₄⋊C₈	—	76	2	no	—
42	C₄×C₈	D₇₆	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	C₁₉⋊C₈	1	2	yes	complemented
45	C₁₉	#7463	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₈	—	152	2	no	—
47	C₂×C₈	Dic₇₆	1	1	yes	characteristic
48	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
49	C₄²	D₁₅₂	1	1	yes	characteristic
50	C₁₆	—	2	1	no	—
51	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
52	C₁₆	#64520	1	1	yes	characteristic
53	C₂×C₄	#10597257	1	2	yes	—
54	C₂×C₄	#10597275	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	—	304	2	no	—
57	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
58	C₈	#10597276	1	1	yes	characteristic
59	C₂²	#11926372	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	#11926297	1	1	yes	characteristic
62	C₄	#11926374	1	1	yes	characteristic
63	C₂	#14561709	1	1	yes	characteristic
64	C₂	#14561841	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926372
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1397	C₂
socle, prime radical	C₂²×C₁₉	#367
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1397	D₁₉
hypocenter	C₁₉	#7463
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
12. C₁₉×C₃₂	C₈	semidirect
44. C₃₂	C₁₉⋊C₈	semidirect
45. C₁₉	#7463	semidirect

Maximal subgroups

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

subgroup	index
#14561709	2
C₁₉×#1397	2
#7463	19