Subgroups — #14269024

Order 1824.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
3	C₂²⋊(C₁₉⋊C₈)	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₉	—	2	2	no	—
6	C₂×C₃×C₄×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₃⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂²×C₄×C₁₉	D₃	1	1	yes	characteristic
10	C₂×C₁₉⋊C₈	—	3	2	no	—
11	C₂²×C₃×C₁₉	—	2	1	no	—
12	C₂²×C₃×C₁₉	—	2	1	no	—
13	C₂²×C₃×C₁₉	C₈	1	2	yes	complemented
14	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₁₉	—	2	1	no	—
16	C₃×C₄×C₁₉	D₄	1	2	yes	—
17	C₂³×C₁₉	Dic₃	1	1	yes	characteristic
18	C₂×C₄×C₁₉	—	2	2	no	—
19	C₂×C₄×C₁₉	Dic₃	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
21	C₁₉⋊C₈	—	6	2	no	—
22	C₂×C₃×C₁₉	—	2	2	no	—
23	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₃×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃×C₁₉	M₁₆	1	1	yes	characteristic
26	#830	—	19	1	no	maximal, Hall
27	C₂²×C₁₉	—	2	1	no	—
28	C₂²×C₁₉	—	2	1	no	—
29	C₂²×C₁₉	C₃⋊C₈	1	2	yes	complemented
30	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
31	C₄×C₁₉	—	2	1	no	—
32	C₄×C₁₉	#67	1	2	yes	—
33	C₃×C₁₉	C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₃×C₄	D₁₉	1	1	yes	characteristic
35	C₂×C₃⋊C₈	—	19	2	no	—
36	C₂×C₁₉	—	2	2	no	—
37	C₂×C₁₉	C₂×C₃⋊C₈	1	1	yes	characteristic
38	C₂×C₁₉	#208	1	1	yes	characteristic
39	C₂×C₁₉	#217	1	1	yes	characteristic
40	C₂²⋊C₈	—	57	1	no	Sylow
41	C₂³×C₃	Dic₁₉	1	1	yes	characteristic
42	C₂×C₃×C₄	—	2	2	no	—
43	C₂×C₃×C₄	Dic₁₉	1	1	yes	characteristic
44	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
45	C₃⋊C₈	—	38	2	no	—
46	C₁₉	#830	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	D₅₇	1	1	yes	characteristic
48	C₂×C₈	—	57	2	no	—
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	C₁₉⋊C₈	1	2	yes	complemented
52	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	C₂²⋊D₁₉	1	2	yes	—
55	C₂³	Dic₅₇	1	1	yes	characteristic
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	Dic₅₇	1	1	yes	characteristic
58	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
59	C₈	—	114	2	no	—
60	C₂×C₃	—	2	2	no	—
61	C₂×C₃	C₂×C₁₉⋊C₈	1	1	yes	characteristic
62	C₂×C₃	#64520	1	1	yes	characteristic
63	C₂×C₃	C₂²⋊Dic₁₉	1	1	yes	characteristic
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	C₃⋊(C₁₉⋊C₈)	1	2	yes	complemented
67	C₂²	C₂×Dic₅₇	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	#90718	1	2	yes	—
70	C₃	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	2	2	no	—
72	C₂	C₂×C₃⋊(C₁₉⋊C₈)	1	1	yes	characteristic
73	C₂	#11744885	1	1	yes	characteristic
74	C₂	#11744894	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₅₇
commutator	C₂×C₃×C₁₉	C₂×C₈
Fitting	C₂²×C₃×C₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂×C₄
prime radical	C₂³×C₃×C₁₉	C₄
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂²×C₄	D₅₇
hypocenter	C₃×C₁₉	C₂²⋊C₈
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊(C₁₉⋊C₈)	C₂	semidirect
13. C₂²×C₃×C₁₉	C₈	semidirect
29. C₂²×C₁₉	C₃⋊C₈	semidirect
33. C₃×C₁₉	C₂²⋊C₈	semidirect
46. C₁₉	#830	semidirect
51. C₂²×C₃	C₁₉⋊C₈	semidirect
66. C₂²	C₃⋊(C₁₉⋊C₈)	semidirect
70. C₃	C₂²⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₉	2
C₂×C₃⋊(C₁₉⋊C₈)	2
C₂²⋊(C₁₉⋊C₈)	3
#830	19