Subgroups — #14561629

Order 2432.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926326	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#470	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×C₂²⋊Q₈	—	2	1	no	—
7	C₂×#64520	—	2	1	no	—
8	C₁₉×#106	C₄	1	1	yes	characteristic
9	C₁₉×#103	—	2	1	no	—
10	#10597269	—	2	1	no	—
11	C₂×Q₈×C₁₉	—	2	1	no	—
12	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
13	Q₁₆×C₁₉	—	4	1	no	—
14	M₁₆×C₁₉	—	4	1	no	—
15	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₂²⋊C₄×C₁₉	—	4	1	no	—
20	#64520	—	4	1	no	—
21	#64520	—	4	1	no	—
22	C₂×C₁₉⋊C₈	—	2	2	no	—
23	C₁₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
25	Q₈×C₁₉	—	4	1	no	—
26	Q₈×C₁₉	—	4	1	no	—
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	—	2	1	no	—
29	C₂×C₄×C₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₈×C₁₉	—	2	1	no	—
34	C₈×C₁₉	—	2	1	no	—
35	C₁₉⋊C₈	—	4	2	no	—
36	#1342	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	2	1	no	—
38	C₂²×C₁₉	—	4	1	no	—
39	C₂²×C₁₉	#102	1	1	yes	characteristic
40	C₄×C₁₉	—	2	1	no	—
41	C₄×C₁₉	—	8	1	no	—
42	C₄×C₁₉	—	8	1	no	—
43	C₄×C₁₉	#99	1	1	yes	characteristic
44	C₄×C₁₉	#104	1	1	yes	characteristic
45	#470	D₁₉	1	1	yes	characteristic
46	#349	—	19	1	no	—
47	#338	—	19	1	no	—
48	C₂×C₁₉	—	2	1	no	—
49	C₂×C₁₉	—	4	1	no	—
50	C₂×C₁₉	#327	1	1	yes	characteristic
51	C₂×Q₁₆	Dic₁₉	1	1	yes	characteristic
52	C₂×M₁₆	—	38	1	no	—
53	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
54	C₂²⋊Q₈	—	2	1	no	—
55	M₃₂	—	38	1	no	—
56	#106	Dic₁₉	1	1	yes	characteristic
57	#103	—	2	1	no	—
58	C₁₉	#1342	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	76	1	no	—
64	M₁₆	—	76	1	no	—
65	C₂×C₈	—	38	2	no	—
66	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₁₆	—	76	1	no	—
72	C₂³	#64526	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	#64525	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	76	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#10597289	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	—	8	1	no	—
90	C₄	#10597291	1	1	yes	characteristic
91	C₄	#10597294	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#11926278	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926278
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₉
Fitting	C₁₉×#470	C₂
socle	C₂×C₁₉	#327
prime radical	C₂³×C₁₉	SD₁₆
cosocle	C₂×M₁₆×C₁₉	C₂²
hypercenter	#470	D₁₉
hypocenter	C₁₉	#1342
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
58. C₁₉	#1342	semidirect

Maximal subgroups

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

subgroup	index
#11926326	2
C₁₉⋊#338	2
C₁₉×#470	2
#1342	19