Subgroups — #18070417

Order 4864.

98 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, complemented
2	#14561835	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₃₂	C₂	1	1	yes	maximal, characteristic
4	#11926370	—	2	1	no	—
5	C₁₉⋊C₆₄	—	2	1	no	—
6	C₂×C₁₉×D₁₆	—	2	1	no	—
7	C₁₉×D₃₂	—	2	1	no	—
8	C₁₉×D₃₂	C₄	1	2	yes	complemented
9	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₁₉	—	4	1	no	—
11	C₁₉×D₁₆	—	2	2	no	—
12	C₁₉×D₁₆	—	4	1	no	—
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	#10597275	—	4	1	no	—
15	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₄×C₁₉	—	8	1	no	—
18	D₈×C₁₉	—	4	2	no	—
19	D₈×C₁₉	—	8	1	no	—
20	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	8	1	no	—
22	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	#7537	—	19	1	no	maximal, Sylow
25	C₂³×C₁₉	—	16	1	no	—
26	D₄×C₁₉	—	8	2	no	—
27	D₄×C₁₉	—	16	1	no	—
28	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
29	C₂×Dic₁₉	—	16	1	no	—
30	C₈×C₁₉	#102	1	1	yes	characteristic
31	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
32	C₂×D₃₂	D₁₉	1	1	yes	characteristic
33	C₂×C₆₄	—	19	1	no	—
34	#1423	—	19	1	no	—
35	C₂²×C₁₉	—	16	2	no	—
36	C₂²×C₁₉	—	32	1	no	—
37	C₂²×C₁₉	—	32	1	no	—
38	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
39	C₄×C₁₉	#357	1	1	yes	characteristic
40	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
41	Dic₁₉	—	32	1	no	—
42	C₂×D₁₆	—	2	1	no	—
43	D₃₂	—	2	1	no	—
44	D₃₂	Dic₁₉	1	2	yes	complemented
45	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
46	#366	—	38	1	no	—
47	C₆₄	—	38	1	no	—
48	C₂×C₁₉	—	32	2	no	—
49	C₂×C₁₉	#1415	1	1	yes	characteristic
50	C₂×C₁₉	D₆₄	1	1	yes	characteristic
51	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
52	C₂×D₈	—	4	1	no	—
53	D₁₆	—	2	2	no	—
54	D₁₆	—	4	1	no	—
55	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
56	#107	—	76	1	no	—
57	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
58	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
59	C₁₉	#7537	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₄	—	8	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	8	1	no	—
63	C₂×C₈	#64525	1	1	yes	characteristic
64	C₄⋊C₄	—	152	1	no	—
65	C₁₆	#64526	1	1	yes	characteristic
66	C₁₆	C₂²⋊Dic₁₉	1	1	yes	characteristic
67	C₂³	—	16	1	no	—
68	D₄	—	8	2	no	—
69	D₄	—	16	1	no	—
70	C₂×C₄	—	304	1	no	—
71	C₂×C₄	#10597283	1	1	yes	characteristic
72	C₈	#10597284	1	1	yes	characteristic
73	C₈	#10597289	1	1	yes	characteristic
74	C₂²	—	16	2	no	—
75	C₂²	—	32	1	no	—
76	C₂²	—	32	1	no	—
77	C₂²	#11926379	1	1	yes	characteristic
78	C₄	—	608	1	no	—
79	C₄	#11926345	1	1	yes	characteristic
80	C₄	#11926382	1	1	yes	characteristic
81	C₂	—	32	2	no	—
82	C₂	#14561813	1	1	yes	characteristic
83	C₂	#14561847	1	1	yes	characteristic
84	C₂	#14561850	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting, prime radical	C₂×C₁₉×D₃₂	C₂
socle	C₂²×C₁₉	D₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	C₂×D₃₂	D₁₉
hypocenter	C₁₉	#7537
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×D₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉⋊C₆₄	C₂	semidirect
2. #14561835	C₂	semidirect
8. C₁₉×D₃₂	C₄	semidirect
44. D₃₂	Dic₁₉	semidirect
59. C₁₉	#7537	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
C₂×C₁₉×D₃₂	2
#7537	19