Subgroups — C₂×#41×Dic₁₉ #14576817

Order 2432.

1728 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×Dic₁₉	C₂	1	16	yes	maximal, direct product factor
2	C₂×Q₈×Dic₁₉	C₂	1	2	yes	maximal, complemented
3	C₂×D₄×Dic₁₉	C₂	1	6	yes	maximal, complemented
4	C₂×#10597372	C₂	1	3	yes	maximal, complemented
5	C₂²×C₄×Dic₁₉	C₂	1	3	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₂×#41×C₁₉	C₄	1	16	yes	complemented
8	C₂×#41×C₁₉	C₂²	1	8	yes	—
9	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×D₄×C₁₉	C₂²	1	3	yes	—
11	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
12	C₂³×Dic₁₉	C₂²	1	6	yes	—
13	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
14	Q₈×Dic₁₉	C₂²	1	16	yes	complemented
15	D₄×Dic₁₉	C₂²	1	48	yes	complemented
16	#10597372	C₂²	1	24	yes	complemented
17	C₂×C₄⋊Dic₁₉	C₂²	1	6	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
20	C₂×C₄×Dic₁₉	C₂²	1	6	yes	—
21	C₂×C₄×Dic₁₉	C₂²	1	24	yes	complemented
22	C₂⁴×C₁₉	C₂³	1	3	yes	—
23	#41×C₁₉	C₂×C₄	1	64	yes	complemented
24	C₂×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
25	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
26	C₂×D₄×C₁₉	C₂×C₄	1	24	yes	complemented
27	C₂×D₄×C₁₉	C₂³	1	12	yes	—
28	C₂²×C₄×C₁₉	C₂×C₄	1	24	yes	complemented
29	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	12	yes	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	24	no	—
33	C₂²×Dic₁₉	C₂³	1	24	yes	—
34	C₂²×Dic₁₉	C₂³	1	6	yes	—
35	C₂²×Dic₁₉	C₂³	1	2	yes	—
36	C₂²⋊Dic₁₉	C₂³	1	24	yes	—
37	C₄⋊Dic₁₉	C₂³	1	24	yes	—
38	C₄×Dic₁₉	C₂³	1	24	yes	—
39	C₄×Dic₁₉	C₂³	1	4	yes	—
40	C₄×Dic₁₉	C₂³	1	12	yes	—
41	C₂³×C₁₉	—	2	12	no	—
42	C₂³×C₁₉	C₂²×C₄	1	12	yes	—
43	C₂³×C₁₉	C₂⁴	1	6	yes	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	Q₈×C₁₉	C₂²×C₄	1	16	yes	complemented
46	D₄×C₁₉	C₂²×C₄	1	48	yes	complemented
47	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	48	yes	complemented
50	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
52	C₂×Dic₁₉	—	2	12	no	—
53	C₂×Dic₁₉	—	2	48	no	—
54	C₂×Dic₁₉	#41	1	8	yes	direct product factor
55	C₂×Dic₁₉	C₂⁴	1	12	yes	—
56	C₂×Dic₁₉	C₂⁴	1	4	yes	—
57	C₂×C₄×#41	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	24	no	—
59	C₂²×C₁₉	—	2	12	no	—
60	C₂²×C₁₉	C₂³×C₄	1	12	yes	—
61	C₂²×C₁₉	C₂³×C₄	1	2	yes	—
62	C₂²×C₁₉	C₂×#41	1	4	yes	—
63	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
64	C₄×C₁₉	C₂³×C₄	1	4	yes	—
65	C₄×C₁₉	C₂³×C₄	1	12	yes	—
66	Dic₁₉	—	2	12	no	—
67	Dic₁₉	C₂×#41	1	8	yes	direct product factor
68	C₂²×#41	D₁₉	1	1	yes	characteristic
69	C₄×#41	—	19	16	no	—
70	C₂×C₄×Q₈	—	19	2	no	—
71	C₂×C₄×D₄	—	19	6	no	—
72	C₂×#117	—	19	3	no	—
73	C₂²×C₄²	—	19	3	no	—
74	C₂×C₁₉	—	2	12	no	—
75	C₂×C₁₉	C₄×#41	1	4	yes	complemented
76	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
77	C₂×C₁₉	C₂²×#41	1	2	yes	—
78	C₂×#41	Dic₁₉	1	16	yes	direct product factor
79	C₂×#41	C₂×D₁₉	1	8	yes	—
80	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×D₄	C₂×D₁₉	1	3	yes	—
82	C₂³×C₄	—	19	6	no	—
83	C₂³×C₄	C₂×D₁₉	1	3	yes	—
84	C₄×Q₈	—	19	16	no	—
85	C₄×D₄	—	19	48	no	—
86	#117	—	19	24	no	—
87	C₂×C₄⋊C₄	—	19	6	no	—
88	C₂×C₂²⋊C₄	—	19	6	no	—
89	C₂×C₄²	—	19	6	no	—
90	C₂×C₄²	—	19	24	no	—
91	C₂×C₄²	—	19	3	no	—
92	C₂×C₄²	—	19	1	no	—
93	C₁₉	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
94	C₂⁴	C₂²×D₁₉	1	3	yes	—
95	#41	C₂×Dic₁₉	1	64	yes	direct product factor
96	C₂×Q₈	C₂×Dic₁₉	1	8	yes	complemented
97	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
98	C₂×D₄	C₂×Dic₁₉	1	24	yes	complemented
99	C₂×D₄	C₂²×D₁₉	1	12	yes	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	—	19	6	no	—
102	C₂²×C₄	—	19	24	no	—
103	C₂²×C₄	—	38	24	no	—
104	C₂²×C₄	C₂×Dic₁₉	1	24	yes	complemented
105	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
106	C₂²×C₄	C₂²×D₁₉	1	12	yes	—
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	C₄⋊C₄	—	19	24	no	—
109	C₂²⋊C₄	—	19	24	no	—
110	C₄²	—	19	4	no	—
111	C₄²	—	19	12	no	—
112	C₄²	—	19	24	no	—
113	C₂³	—	2	12	no	—
114	C₂³	C₂²×Dic₁₉	1	12	yes	—
115	C₂³	C₂³×D₁₉	1	6	yes	—
116	C₂³	C₂³×D₁₉	1	1	yes	characteristic
117	Q₈	C₂²×Dic₁₉	1	16	yes	complemented
118	D₄	C₂²×Dic₁₉	1	48	yes	complemented
119	C₂×C₄	—	19	8	no	—
120	C₂×C₄	—	19	4	no	—
121	C₂×C₄	—	19	12	no	—
122	C₂×C₄	—	38	48	no	—
123	C₂×C₄	—	38	12	no	—
124	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
125	C₂×C₄	C₂²×Dic₁₉	1	12	yes	—
126	C₂×C₄	C₂²×Dic₁₉	1	48	yes	complemented
127	C₂×C₄	C₂³×D₁₉	1	2	yes	—
128	C₂×C₄	C₂³×D₁₉	1	6	yes	—
129	C₂²	—	2	12	no	—
130	C₂²	—	2	24	no	—
131	C₂²	#41×D₁₉	1	4	yes	—
132	C₂²	C₂³×Dic₁₉	1	12	yes	—
133	C₂²	C₂³×Dic₁₉	1	2	yes	—
134	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
135	C₄	—	19	8	no	—
136	C₄	—	38	12	no	—
137	C₄	C₂³×Dic₁₉	1	4	yes	—
138	C₄	C₂³×Dic₁₉	1	12	yes	—
139	C₂	—	2	12	no	—
140	C₂	#41×Dic₁₉	1	4	yes	direct product factor
141	C₂	C₂⁴×Dic₁₉	1	1	yes	characteristic
142	C₂	C₂×#41×D₁₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₉
Fitting, prime radical	C₂²×#41×C₁₉	C₂
socle	C₂³×C₁₉	C₂⁴
cosocle	C₂²×C₁₉	C₂⁵
hypercenter	C₂²×#41	D₁₉
hypocenter	C₁₉	C₂×C₄×#41
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. #41×Dic₁₉	C₂	direct (N × H)
2. C₂×Q₈×Dic₁₉	C₂	semidirect
3. C₂×D₄×Dic₁₉	C₂	semidirect
4. C₂×#10597372	C₂	semidirect
5. C₂²×C₄×Dic₁₉	C₂	semidirect
7. C₂×#41×C₁₉	C₄	semidirect
14. Q₈×Dic₁₉	C₂²	semidirect
15. D₄×Dic₁₉	C₂²	semidirect
16. #10597372	C₂²	semidirect
21. C₂×C₄×Dic₁₉	C₂²	semidirect
23. #41×C₁₉	C₂×C₄	semidirect
24. C₂×Q₈×C₁₉	C₂×C₄	semidirect
26. C₂×D₄×C₁₉	C₂×C₄	semidirect
28. C₂²×C₄×C₁₉	C₂×C₄	semidirect
45. Q₈×C₁₉	C₂²×C₄	semidirect
46. D₄×C₁₉	C₂²×C₄	semidirect
49. C₂×C₄×C₁₉	C₂²×C₄	semidirect
54. C₂×Dic₁₉	#41	direct (N × H)
67. Dic₁₉	C₂×#41	direct (N × H)
75. C₂×C₁₉	C₄×#41	semidirect
78. C₂×#41	Dic₁₉	direct (N × H)
93. C₁₉	C₂×C₄×#41	semidirect
95. #41	C₂×Dic₁₉	direct (N × H)
96. C₂×Q₈	C₂×Dic₁₉	semidirect
98. C₂×D₄	C₂×Dic₁₉	semidirect
104. C₂²×C₄	C₂×Dic₁₉	semidirect
117. Q₈	C₂²×Dic₁₉	semidirect
118. D₄	C₂²×Dic₁₉	semidirect
126. C₂×C₄	C₂²×Dic₁₉	semidirect
140. C₂	#41×Dic₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
#41×Dic₁₉	2
C₂×Q₈×Dic₁₉	2
C₂×D₄×Dic₁₉	2
C₂×#10597372	2
C₂²×C₄×Dic₁₉	2
C₂²×#41×C₁₉	2
C₂×C₄×#41	19

Subgroups — C2×#41×Dic19 #14576817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×Dic₁₉ #14576817