Subgroups — #14564801

Order 2432.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926405	C₂	1	3	yes	maximal
2	#11926311	C₂	1	3	yes	maximal
3	C₁₉×#543	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×C₂²⋊Q₈	—	2	6	no	—
6	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
8	C₁₉⋊#95	—	2	6	no	—
9	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
10	C₂×Q₈×C₁₉	—	2	2	no	—
11	C₂²×C₄×C₁₉	D₄	1	6	yes	—
12	C₂²×Dic₁₉	—	2	3	no	—
13	C₂²×Dic₁₉	—	2	3	no	—
14	C₂²×Dic₁₉	—	2	3	no	—
15	C₂²×Dic₁₉	Q₈	1	2	yes	complemented
16	C₄⋊C₄×C₁₉	—	2	6	no	—
17	C₂²⋊C₄×C₁₉	—	2	6	no	—
18	C₂²⋊Dic₁₉	—	2	6	no	—
19	C₂³×C₁₉	—	4	2	no	—
20	C₂³×C₁₉	C₂×D₄	1	3	yes	—
21	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
22	C₂³×C₁₉	#41	1	3	yes	—
23	Q₈×C₁₉	—	8	2	no	—
24	C₂×C₄×C₁₉	—	2	6	no	—
25	C₂×C₄×C₁₉	—	4	6	no	—
26	C₂×Dic₁₉	—	2	6	no	—
27	C₂×Dic₁₉	—	4	1	no	—
28	C₂×Dic₁₉	—	4	3	no	—
29	C₂×Dic₁₉	—	4	6	no	—
30	C₂×Dic₁₉	—	4	3	no	—
31	#2030	—	19	1	no	maximal, Sylow
32	C₂²×C₁₉	—	2	6	no	—
33	C₂²×C₁₉	—	4	1	no	—
34	C₂²×C₁₉	—	4	3	no	—
35	C₂²×C₁₉	#120	1	1	yes	characteristic
36	C₂²×C₁₉	C₂²⋊Q₈	1	3	yes	—
37	C₂²×C₁₉	#124	1	3	yes	—
38	C₄×C₁₉	—	4	6	no	—
39	Dic₁₉	—	4	2	no	—
40	Dic₁₉	—	8	3	no	—
41	#543	D₁₉	1	1	yes	characteristic
42	#381	—	19	3	no	—
43	#342	—	19	3	no	—
44	C₂×C₁₉	—	2	3	no	—
45	C₂×C₁₉	—	2	3	no	—
46	C₂×C₁₉	#393	1	1	yes	characteristic
47	C₂×C₁₉	#458	1	2	yes	—
48	C₂³×C₄	—	19	1	no	—
49	C₂²⋊Q₈	—	2	6	no	—
50	C₂×C₂²⋊C₄	—	19	3	no	—
51	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
52	#95	—	38	6	no	—
53	C₁₉	#2030	1	1	yes	characteristic, complemented, Sylow
54	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
55	C₂×Q₈	—	2	2	no	—
56	C₂²×C₄	—	19	2	no	—
57	C₂²×C₄	—	38	3	no	—
58	C₂²×C₄	—	38	3	no	—
59	C₂²×C₄	—	38	3	no	—
60	C₂²×C₄	C₂²⋊D₁₉	1	6	yes	—
61	C₄⋊C₄	—	2	6	no	—
62	C₂²⋊C₄	—	2	6	no	—
63	C₂²⋊C₄	—	38	6	no	—
64	C₂³	—	4	2	no	—
65	C₂³	Q₈×D₁₉	1	1	yes	characteristic
66	C₂³	#64545	1	3	yes	—
67	C₂³	C₂×C₂²⋊D₁₉	1	3	yes	—
68	Q₈	—	8	2	no	—
69	C₂×C₄	—	2	6	no	—
70	C₂×C₄	—	4	6	no	—
71	C₂×C₄	—	38	6	no	—
72	C₂×C₄	—	76	3	no	—
73	C₂×C₄	—	76	1	no	—
74	C₂×C₄	—	76	6	no	—
75	C₂×C₄	—	76	3	no	—
76	C₂²	—	2	6	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	3	no	—
79	C₂²	#10597392	1	3	yes	—
80	C₂²	#10597393	1	3	yes	—
81	C₂²	#10597399	1	1	yes	characteristic
82	C₄	—	4	6	no	—
83	C₄	—	76	2	no	—
84	C₄	—	152	3	no	—
85	C₂	—	2	3	no	—
86	C₂	—	2	3	no	—
87	C₂	#11926455	1	1	yes	characteristic
88	C₂	#11926734	1	2	yes	—

	subgroup	G/H
center	C₂²	#10597399
commutator, prime radical, cosocle	C₂⁴×C₁₉	C₂³
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#543	C₂
socle	C₂²×C₁₉	#120
hypercenter	#543	D₁₉
hypocenter	C₁₉	#2030
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

Complements

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

N	H ≅ G/N	type
15. C₂²×Dic₁₉	Q₈	semidirect
53. C₁₉	#2030	semidirect

Maximal subgroups

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

subgroup	index
#11926405	2
#11926311	2
C₁₉×#543	2
#2030	19