Subgroups — #14565918

Order 2432.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926946	C₂	1	1	yes	maximal, characteristic
2	#11926371	C₂	1	2	yes	maximal
3	#11926369	C₂	1	2	yes	maximal
4	#11926320	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	—	2	1	no	—
7	#10597316	—	2	1	no	—
8	C₁₉×#107	—	2	1	no	—
9	C₁₉×#107	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597275	C₂²	1	1	yes	characteristic
12	#10597275	C₂²	1	1	yes	characteristic
13	#10597274	—	2	1	no	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	4	1	no	—
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₄⋊C₄×C₁₉	—	4	1	no	—
20	C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	2	1	no	—
22	C₄⋊Dic₁₉	—	2	1	no	—
23	Dic₁₉⋊C₄	—	4	1	no	—
24	Dic₁₉⋊C₄	—	4	1	no	—
25	C₁₉⋊C₁₆	Q₈	1	4	yes	complemented
26	Q₈×C₁₉	—	8	2	no	—
27	C₂×C₄×C₁₉	—	4	2	no	—
28	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₁₉	—	4	1	no	—
32	C₂×Dic₁₉	—	4	1	no	—
33	C₈×C₁₉	Q₁₆	1	2	yes	—
34	C₈×C₁₉	C₂×Q₈	1	2	yes	—
35	#2255	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₉	—	2	1	no	—
38	C₄×C₁₉	—	2	1	no	—
39	C₄×C₁₉	—	8	2	no	—
40	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
41	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₁₉	—	8	1	no	—
43	Dic₁₉	—	8	1	no	—
44	#500	D₁₉	1	1	yes	characteristic
45	#499	—	19	1	no	—
46	#367	—	19	2	no	—
47	#366	—	19	2	no	—
48	#346	—	19	1	no	—
49	C₂×C₁₉	#500	1	1	yes	characteristic
50	C₂×C₁₉	#509	1	1	yes	characteristic
51	C₂×C₁₉	#510	1	1	yes	characteristic
52	C₄⋊Q₈	—	2	1	no	—
53	#125	—	38	1	no	—
54	C₂×C₁₆	—	19	2	no	—
55	#107	—	2	1	no	—
56	#107	—	19	1	no	—
57	#107	—	19	1	no	—
58	#107	C₂×D₁₉	1	2	yes	—
59	#106	—	38	1	no	—
60	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₁₉	#2255	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	4	1	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	—	38	1	no	—
68	C₄⋊C₄	—	38	1	no	—
69	C₄⋊C₄	—	76	1	no	—
70	C₄⋊C₄	—	76	1	no	—
71	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
72	C₁₆	—	19	4	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	76	1	no	—
76	C₂×C₄	—	76	1	no	—
77	C₂×C₄	#64525	1	1	yes	characteristic
78	C₂×C₄	#64525	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
80	C₈	#64528	1	2	yes	—
81	C₈	Q₈×D₁₉	1	2	yes	—
82	C₂²	C₂×#64525	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	152	1	no	—
87	C₄	—	152	1	no	—
88	C₄	C₂×#64528	1	1	yes	characteristic
89	C₄	#10597390	1	1	yes	characteristic
90	C₂	#11926947	1	1	yes	characteristic
91	C₂	#11926980	1	1	yes	characteristic
92	C₂	#11926985	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	#2255
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
25. C₁₉⋊C₁₆	Q₈	semidirect
61. C₁₉	#2255	semidirect

Maximal subgroups

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

subgroup	index
#11926946	2
#11926371	2
#11926369	2
#11926320	2
C₁₉×#500	2
#2255	19