Subgroups — #18070221

Order 4864.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561769	C₂	1	1	yes	maximal, characteristic
2	#14561709	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
6	#11926297	—	2	1	no	—
7	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#335	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
11	C₁₉×C₄⋊C₈	—	4	1	no	—
12	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
14	C₁₉⋊C₃₂	—	2	1	no	—
15	C₁₉⋊C₃₂	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₉	—	8	1	no	—
17	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
19	C₄²×C₁₉	D₈	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	—	8	1	no	—
21	C₁₆×C₁₉	—	2	1	no	—
22	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
24	#7463	—	19	1	no	maximal, Sylow
25	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
26	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
27	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
28	C₈×C₁₉	—	2	1	no	—
29	C₈×C₁₉	—	16	1	no	—
30	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
31	C₈×C₁₉	#108	1	1	yes	characteristic
32	C₁₉⋊C₈	—	16	1	no	—
33	#1397	—	19	1	no	—
34	#1372	—	19	1	no	—
35	#1372	D₁₉	1	1	yes	characteristic
36	C₂²×C₁₉	#367	1	1	yes	characteristic
37	C₄×C₁₉	—	2	1	no	—
38	C₄×C₁₉	—	2	1	no	—
39	C₄×C₁₉	#335	1	1	yes	characteristic
40	C₄×C₁₉	#368	1	1	yes	characteristic
41	C₂×C₃₂	—	19	1	no	—
42	C₂×C₃₂	—	19	1	no	—
43	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
44	#335	—	2	1	no	—
45	#335	—	38	1	no	—
46	C₂×C₁₉	#1372	1	1	yes	characteristic
47	C₂×C₁₉	#1426	1	1	yes	characteristic
48	C₂×C₁₉	#1426	1	1	yes	characteristic
49	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
50	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
51	C₄⋊C₈	—	4	1	no	—
52	C₄⋊C₈	—	76	1	no	—
53	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
54	C₃₂	—	19	2	no	—
55	C₃₂	—	38	1	no	—
56	C₁₉	#7463	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₈	—	8	1	no	—
58	C₂×C₈	—	152	1	no	—
59	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
60	C₂×C₈	#64528	1	1	yes	characteristic
61	C₄²	#64525	1	1	yes	characteristic
62	C₁₆	—	2	1	no	—
63	C₁₆	C₈×D₁₉	1	1	yes	characteristic
64	C₁₆	#64515	1	1	yes	characteristic
65	C₂×C₄	#10597264	1	1	yes	characteristic
66	C₂×C₄	#10597284	1	1	yes	characteristic
67	C₂×C₄	#10597285	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	16	1	no	—
70	C₈	—	304	1	no	—
71	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
72	C₈	#10597279	1	1	yes	characteristic
73	C₂²	#11926371	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	#11926296	1	1	yes	characteristic
77	C₄	#11926373	1	1	yes	characteristic
78	C₂	#14561708	1	1	yes	characteristic
79	C₂	#14561840	1	1	yes	characteristic
80	C₂	#14561842	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926371
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1372	C₂
socle, prime radical	C₂²×C₁₉	#367
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1372	D₁₉
hypocenter	C₁₉	#7463
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

Complements

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

N	H ≅ G/N	type
15. C₁₉⋊C₃₂	C₈	semidirect
56. C₁₉	#7463	semidirect

Maximal subgroups

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

subgroup	index
#14561769	2
#14561709	2
C₁₉×#1372	2
#7463	19