Subgroups — #18069276

Order 4864.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561699	C₂	1	1	yes	maximal, characteristic
2	#14561552	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1367	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
5	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₉×C₄⋊C₁₆	—	2	1	no	—
8	C₈²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	—	4	1	no	—
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	—	2	1	no	—
14	C₂×C₁₉⋊C₁₆	—	4	1	no	—
15	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
16	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
17	C₂×C₈×C₁₉	—	2	1	no	—
18	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
22	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	—	8	1	no	—
24	C₁₉⋊C₁₆	—	2	2	no	—
25	C₁₉⋊C₁₆	—	2	1	no	—
26	C₁₉⋊C₁₆	—	8	1	no	—
27	C₁₉⋊C₁₆	C₁₆	1	2	yes	complemented
28	#7099	—	19	1	no	maximal, Sylow
29	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
31	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
32	C₈×C₁₉	—	2	1	no	—
33	C₈×C₁₉	—	2	1	no	—
34	C₈×C₁₉	—	2	1	no	—
35	C₈×C₁₉	—	4	1	no	—
36	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
37	C₈×C₁₉	M₃₂	1	1	yes	characteristic
38	#1367	—	19	1	no	—
39	#1367	D₁₉	1	1	yes	characteristic
40	#1311	—	19	1	no	—
41	C₂²×C₁₉	#334	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
44	C₄×C₁₉	#364	1	1	yes	characteristic
45	C₄×C₁₉	#365	1	1	yes	characteristic
46	C₄×C₁₉	#365	1	1	yes	characteristic
47	C₄⋊C₁₆	—	2	1	no	—
48	C₄⋊C₁₆	—	38	1	no	—
49	C₄×C₁₆	—	19	1	no	—
50	C₄×C₁₆	—	19	1	no	—
51	C₈²	C₂×D₁₉	1	1	yes	characteristic
52	C₂×C₁₉	#1367	1	1	yes	characteristic
53	C₂×C₁₉	#1368	1	1	yes	characteristic
54	C₂×C₁₉	#1369	1	1	yes	characteristic
55	C₂×C₁₆	—	4	1	no	—
56	C₂×C₁₆	—	19	1	no	—
57	C₂×C₁₆	—	19	1	no	—
58	C₂×C₁₆	—	38	1	no	—
59	C₂×C₁₆	—	76	1	no	—
60	C₄×C₈	Dic₃₈	1	1	yes	characteristic
61	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
62	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₁₉	#7099	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
66	C₂×C₈	#64515	1	1	yes	characteristic
67	C₂×C₈	#64526	1	1	yes	characteristic
68	C₂×C₈	#64527	1	1	yes	characteristic
69	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
70	C₁₆	—	8	1	no	—
71	C₁₆	—	19	2	no	—
72	C₁₆	—	38	2	no	—
73	C₁₆	—	38	1	no	—
74	C₁₆	—	152	1	no	—
75	C₂×C₄	#10597265	1	1	yes	characteristic
76	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
77	C₂×C₄	#10597279	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	2	1	no	—
80	C₈	—	2	1	no	—
81	C₈	—	4	1	no	—
82	C₈	C₁₆×D₁₉	1	1	yes	characteristic
83	C₈	#10597255	1	1	yes	characteristic
84	C₂²	#11926294	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	Dic₁₉⋊C₁₆	1	1	yes	characteristic
87	C₄	#11926364	1	1	yes	characteristic
88	C₄	#11926366	1	1	yes	characteristic
89	C₄	#11926368	1	1	yes	characteristic
90	C₂	#14561698	1	1	yes	characteristic
91	C₂	#14561700	1	1	yes	characteristic
92	C₂	#14561702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597265
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1367	C₂
socle, prime radical	C₂²×C₁₉	#334
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1367	D₁₉
hypocenter	C₁₉	#7099
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1367

Complements

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

N	H ≅ G/N	type
27. C₁₉⋊C₁₆	C₁₆	semidirect
63. C₁₉	#7099	semidirect

Maximal subgroups

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

subgroup	index
#14561699	2
#14561552	2
C₁₉×#1367	2
#7099	19