Subgroups — #14269025

Order 1824.

152 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	C₂²×Dic₅₇	C₂	1	2	yes	maximal
3	C₁₉⋊#95	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₉	—	2	2	no	—
6	C₂×C₃×C₄×C₁₉	C₄	1	2	yes	complemented
7	C₂×Dic₅₇	—	2	2	no	—
8	C₂×Dic₅₇	—	2	2	no	—
9	C₂×Dic₅₇	C₄	1	4	yes	complemented
10	C₂²×C₄×C₁₉	D₃	1	1	yes	characteristic
11	C₂²×Dic₁₉	—	3	2	no	—
12	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₃×C₁₉	D₄	1	2	yes	—
16	C₂²×C₃×C₁₉	Q₈	1	1	yes	characteristic
17	C₃×C₄×C₁₉	—	2	2	no	—
18	Dic₅₇	—	2	4	no	—
19	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
20	C₂×C₄×C₁₉	—	2	2	no	—
21	C₂×C₄×C₁₉	Dic₃	1	2	yes	complemented
22	C₂×Dic₁₉	—	3	4	no	—
23	C₂×Dic₁₉	—	6	2	no	—
24	C₂×Dic₁₉	—	6	2	no	—
25	C₂×C₃×C₁₉	C₄²	1	1	yes	characteristic
26	C₂×C₃×C₁₉	C₂²⋊C₄	1	2	yes	—
27	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₃×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₃⋊#95	—	19	1	no	maximal, Hall
31	C₂²×C₁₉	Dic₆	1	1	yes	characteristic
32	C₂²×C₁₉	C₄×D₃	1	2	yes	—
33	C₂²×C₁₉	D₁₂	1	1	yes	characteristic
34	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
35	C₂²×C₁₉	#67	1	2	yes	—
36	C₄×C₁₉	—	2	2	no	—
37	Dic₁₉	—	6	4	no	—
38	C₃×C₁₉	#95	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃×C₄	D₁₉	1	1	yes	characteristic
40	C₂²×Dic₃	—	19	2	no	—
41	C₂×C₁₉	C₄×Dic₃	1	1	yes	characteristic
42	C₂×C₁₉	Dic₃⋊C₄	1	2	yes	—
43	C₂×C₁₉	C₄⋊Dic₃	1	1	yes	characteristic
44	C₂×C₁₉	(C₂×D₃)⋊C₄	1	2	yes	—
45	C₂×C₁₉	#217	1	1	yes	characteristic
46	#95	—	57	1	no	Sylow
47	C₂³×C₃	C₂×D₁₉	1	1	yes	characteristic
48	C₂×C₃×C₄	—	2	2	no	—
49	C₂×C₃×C₄	Dic₁₉	1	2	yes	complemented
50	C₂×Dic₃	—	19	4	no	—
51	C₂×Dic₃	—	38	2	no	—
52	C₂×Dic₃	—	38	2	no	—
53	C₁₉	C₃⋊#95	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	—	57	2	no	—
55	C₂²×C₄	D₅₇	1	1	yes	characteristic
56	C₂²×C₃	Dic₃₈	1	1	yes	characteristic
57	C₂²×C₃	C₄×D₁₉	1	2	yes	—
58	C₂²×C₃	D₇₆	1	1	yes	characteristic
59	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
60	C₂²×C₃	C₂²⋊D₁₉	1	2	yes	—
61	C₃×C₄	—	2	2	no	—
62	Dic₃	—	38	4	no	—
63	C₂³	C₂×D₅₇	1	1	yes	characteristic
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	57	4	no	—
66	C₂×C₄	—	114	2	no	—
67	C₂×C₄	—	114	2	no	—
68	C₂×C₄	Dic₅₇	1	2	yes	complemented
69	C₂×C₃	C₄×Dic₁₉	1	1	yes	characteristic
70	C₂×C₃	Dic₁₉⋊C₄	1	2	yes	—
71	C₂×C₃	C₄⋊Dic₁₉	1	1	yes	characteristic
72	C₂×C₃	(C₂×D₁₉)⋊C₄	1	2	yes	—
73	C₂×C₃	C₂²⋊Dic₁₉	1	1	yes	characteristic
74	C₂²	Dic₁₁₄	1	1	yes	characteristic
75	C₂²	C₄×D₅₇	1	2	yes	—
76	C₂²	D₂₂₈	1	1	yes	characteristic
77	C₂²	C₂×Dic₅₇	1	1	yes	characteristic
78	C₂²	#90718	1	2	yes	—
79	C₄	—	2	2	no	—
80	C₄	—	114	4	no	—
81	C₃	C₁₉⋊#95	1	1	yes	characteristic, complemented, Sylow
82	C₂	C₄×Dic₅₇	1	1	yes	characteristic
83	C₂	#11744887	1	2	yes	—
84	C₂	C₄⋊Dic₅₇	1	1	yes	characteristic
85	C₂	#11744889	1	2	yes	—
86	C₂	#11744894	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×D₅₇
commutator	C₂×C₃×C₁₉	C₄²
Fitting	C₂²×C₃×C₄×C₁₉	C₂
socle, prime radical, cosocle	C₂³×C₃×C₁₉	C₂²
hypercenter	C₂²×C₄	D₅₇
hypocenter	C₃×C₁₉	#95
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
6. C₂×C₃×C₄×C₁₉	C₄	semidirect
9. C₂×Dic₅₇	C₄	semidirect
21. C₂×C₄×C₁₉	Dic₃	semidirect
38. C₃×C₁₉	#95	semidirect
49. C₂×C₃×C₄	Dic₁₉	semidirect
53. C₁₉	C₃⋊#95	semidirect
68. C₂×C₄	Dic₅₇	semidirect
81. C₃	C₁₉⋊#95	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
C₂²×Dic₅₇	2
C₁₉⋊#95	3
C₃⋊#95	19