Subgroups — #18070426

Order 4864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561846	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2262	C₂	1	1	yes	maximal, characteristic
4	#11926370	—	2	1	no	—
5	C₁₉⋊C₆₄	—	2	1	no	—
6	C₁₉×#508	—	2	1	no	—
7	C₁₉×Q₆₄	C₄	1	1	yes	characteristic, complemented
8	C₁₉×SD₆₄	—	2	1	no	—
9	C₁₉×D₃₂	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₉×#135	—	4	1	no	—
12	C₁₉×Q₃₂	—	2	1	no	—
13	C₁₉×SD₃₂	—	4	1	no	—
14	C₁₉×D₁₆	—	2	1	no	—
15	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
16	#10597275	—	4	1	no	—
17	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₉×C₃₂	D₄	1	1	yes	characteristic
19	#41×C₁₉	—	8	1	no	—
20	Q₁₆×C₁₉	—	4	1	no	—
21	SD₁₆×C₁₉	—	8	1	no	—
22	D₈×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
24	C₄⋊Dic₁₉	—	8	1	no	—
25	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
27	#7540	—	19	1	no	maximal, Sylow
28	Q₈×C₁₉	—	8	1	no	—
29	D₄×C₁₉	—	8	1	no	—
30	D₄×C₁₉	—	16	1	no	—
31	C₂×C₄×C₁₉	—	16	1	no	—
32	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
33	C₂×Dic₁₉	—	16	1	no	—
34	C₈×C₁₉	#102	1	1	yes	characteristic
35	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
36	#2262	D₁₉	1	1	yes	characteristic
37	M₁₂₈	—	19	1	no	—
38	#1424	—	19	1	no	—
39	C₂²×C₁₉	—	16	1	no	—
40	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
41	C₄×C₁₉	—	16	1	no	—
42	C₄×C₁₉	#357	1	1	yes	characteristic
43	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
44	Dic₁₉	—	32	1	no	—
45	#508	—	2	1	no	—
46	Q₆₄	Dic₁₉	1	1	yes	characteristic, complemented
47	SD₆₄	—	2	1	no	—
48	D₃₂	Dic₁₉	1	1	yes	characteristic, complemented
49	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
50	#366	—	38	1	no	—
51	C₆₄	—	38	1	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	32	1	no	—
54	C₂×C₁₉	#1415	1	1	yes	characteristic
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
60	#107	—	76	1	no	—
61	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₁₉	#7540	1	1	yes	characteristic, complemented, Sylow
64	#41	—	8	1	no	—
65	Q₁₆	—	4	1	no	—
66	SD₁₆	—	8	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	#64525	1	1	yes	characteristic
69	C₄⋊C₄	—	152	1	no	—
70	C₁₆	#64526	1	1	yes	characteristic
71	C₁₆	C₂²⋊Dic₁₉	1	1	yes	characteristic
72	Q₈	—	8	1	no	—
73	D₄	—	8	1	no	—
74	D₄	—	16	1	no	—
75	C₂×C₄	—	16	1	no	—
76	C₂×C₄	—	304	1	no	—
77	C₂×C₄	#10597283	1	1	yes	characteristic
78	C₈	#10597284	1	1	yes	characteristic
79	C₈	#10597289	1	1	yes	characteristic
80	C₂²	—	16	1	no	—
81	C₂²	#11926379	1	1	yes	characteristic
82	C₄	—	16	1	no	—
83	C₄	—	608	1	no	—
84	C₄	#11926345	1	1	yes	characteristic
85	C₄	#11926382	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	32	1	no	—
88	C₂	#14561813	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561813
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting, prime radical	C₁₉×#2262	C₂
socle	C₂×C₁₉	#1415
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#2262	D₁₉
hypocenter	C₁₉	#7540
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. #14561846	C₂	semidirect
2. #14561837	C₂	semidirect
7. C₁₉×Q₆₄	C₄	semidirect
9. C₁₉×D₃₂	C₄	semidirect
46. Q₆₄	Dic₁₉	semidirect
48. D₃₂	Dic₁₉	semidirect
63. C₁₉	#7540	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×#2262	2
#7540	19