Subgroups — #14565864

Order 2432.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926924	C₂	1	1	yes	maximal, characteristic
2	#11926347	C₂	1	4	yes	maximal
3	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊Q₈	—	2	1	no	—
6	C₂×Dic₇₆	—	2	1	no	—
7	C₂×Dic₇₆	C₂²	1	2	yes	—
8	#10597315	—	2	1	no	—
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	C₂²	1	2	yes	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₉	—	4	1	no	—
14	C₂×Dic₃₈	—	2	2	no	—
15	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₉	—	4	1	no	—
21	C₄⋊Dic₁₉	—	4	1	no	—
22	Dic₇₆	—	2	4	no	—
23	Dic₇₆	—	4	2	no	—
24	C₁₉⋊C₁₆	—	2	2	no	—
25	Q₈×C₁₉	—	8	2	no	—
26	C₂×C₄×C₁₉	—	4	2	no	—
27	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₉	—	4	2	no	—
31	Dic₃₈	—	4	2	no	—
32	Dic₃₈	—	4	2	no	—
33	C₈×C₁₉	SD₁₆	1	2	yes	—
34	C₈×C₁₉	#41	1	2	yes	—
35	#2241	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₉	—	8	2	no	—
38	C₄×C₁₉	SD₃₂	1	2	yes	—
39	C₄×C₁₉	Q₃₂	1	2	yes	—
40	C₄×C₁₉	#124	1	1	yes	characteristic
41	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
42	Dic₁₉	—	8	2	no	—
43	#500	D₁₉	1	1	yes	characteristic
44	#494	—	19	1	no	—
45	#358	—	19	4	no	—
46	C₄×C₁₆	—	19	1	no	—
47	C₂×C₁₉	#486	1	1	yes	characteristic
48	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
49	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×Q₁₆	—	19	2	no	—
51	C₂×Q₁₆	—	38	1	no	—
52	C₄⋊Q₈	—	2	1	no	—
53	C₄⋊Q₈	—	38	1	no	—
54	C₂×C₁₆	—	19	2	no	—
55	#107	—	2	1	no	—
56	#107	C₂×D₁₉	1	2	yes	—
57	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
58	C₁₉	#2241	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	38	2	no	—
61	Q₁₆	—	38	4	no	—
62	Q₁₆	—	76	2	no	—
63	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	76	1	no	—
68	C₄⋊C₄	—	76	1	no	—
69	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₁₆	—	38	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	76	2	no	—
73	Q₈	—	76	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	76	2	no	—
76	C₂×C₄	#64525	1	1	yes	characteristic
77	C₂×C₄	#64525	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
79	C₈	#64527	1	2	yes	—
80	C₈	#64545	1	2	yes	—
81	C₂²	C₂×#64525	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	152	2	no	—
84	C₄	#10597284	1	2	yes	—
85	C₄	#10597286	1	2	yes	—
86	C₄	C₂×#64527	1	1	yes	characteristic
87	C₄	#10597393	1	1	yes	characteristic
88	C₂	#11926892	1	1	yes	characteristic
89	C₂	C₂×#10597284	1	1	yes	characteristic
90	C₂	C₂×#10597286	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#500	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	#500	D₁₉
hypocenter	C₁₉	#2241
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
58. C₁₉	#2241	semidirect

Maximal subgroups

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

subgroup	index
#11926924	2
#11926347	2
C₄×C₁₉⋊C₁₆	2
C₁₉×#500	2
#2241	19