Subgroups — #18070403

Order 4864.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561804	C₂	1	2	yes	maximal
2	C₁₉×#1713	C₂	1	1	yes	maximal, characteristic
3	#11926343	—	2	2	no	—
4	C₁₉×#500	—	2	2	no	—
5	C₁₉×#494	C₄	1	1	yes	characteristic
6	C₁₉×#494	C₂²	1	1	yes	characteristic
7	C₈²×C₁₉	C₄	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₉	—	4	1	no	—
9	C₂×Q₁₆×C₁₉	—	4	1	no	—
10	C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
12	C₁₉×#107	—	4	4	no	—
13	C₄×C₈×C₁₉	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	#10597293	—	4	2	no	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	4	1	no	—
18	Q₁₆×C₁₉	—	8	2	no	—
19	Q₁₆×C₁₉	—	8	2	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	4	2	no	—
23	C₄⋊C₄×C₁₉	—	4	2	no	—
24	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	#64520	—	8	2	no	—
26	#7532	—	19	1	no	maximal, Sylow
27	Q₈×C₁₉	—	8	2	no	—
28	Q₈×C₁₉	—	8	2	no	—
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	4	2	no	—
31	C₂×C₄×C₁₉	—	8	1	no	—
32	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
33	C₈×C₁₉	—	2	4	no	—
34	C₈×C₁₉	—	2	2	no	—
35	C₁₉⋊C₈	—	16	2	no	—
36	#1713	D₁₉	1	1	yes	characteristic
37	#1411	—	19	2	no	—
38	C₂²×C₁₉	#353	1	1	yes	characteristic
39	C₄×C₁₉	—	2	2	no	—
40	C₄×C₁₉	—	2	1	no	—
41	C₄×C₁₉	—	8	2	no	—
42	C₄×C₁₉	—	16	1	no	—
43	#500	—	2	2	no	—
44	#494	Dic₁₉	1	1	yes	characteristic
45	#494	C₂×D₁₉	1	1	yes	characteristic
46	#356	—	38	2	no	—
47	C₈²	Dic₁₉	1	1	yes	characteristic
48	C₂×C₁₉	—	2	1	no	—
49	C₂×C₁₉	#1408	1	1	yes	characteristic
50	C₂×Q₁₆	—	4	1	no	—
51	C₂×Q₁₆	—	4	1	no	—
52	C₄⋊Q₈	—	2	1	no	—
53	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
54	#107	—	4	4	no	—
55	#101	—	76	2	no	—
56	C₄×C₈	—	2	1	no	—
57	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
58	C₁₉	#7532	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	4	1	no	—
61	Q₁₆	—	8	2	no	—
62	Q₁₆	—	8	2	no	—
63	M₁₆	—	152	2	no	—
64	C₂×C₈	—	2	2	no	—
65	C₂×C₈	—	2	1	no	—
66	C₄⋊C₄	—	4	2	no	—
67	C₄⋊C₄	—	4	2	no	—
68	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	8	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	—	8	1	no	—
74	C₂×C₄	#10597291	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	2	4	no	—
77	C₈	—	304	2	no	—
78	C₂²	#11926337	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	2	1	no	—
81	C₄	—	8	2	no	—
82	C₄	—	16	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#14561798	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561798
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#494	C₂×D₁₉
Fitting	C₁₉×#1713	C₂
socle	C₂×C₁₉	#1408
prime radical	C₂²×C₁₉	#353
cosocle	C₁₉×#494	C₂²
hypercenter	#1713	D₁₉
hypocenter	C₁₉	#7532
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1713

Complements

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

N	H ≅ G/N	type
58. C₁₉	#7532	semidirect

Maximal subgroups

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

subgroup	index
#14561804	2
C₁₉×#1713	2
#7532	19