Subgroups — C₁₉×#3380 #14561237

Order 2432.

352 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#554	C₂	1	2	yes	maximal, complemented
2	C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#499	C₂	1	2	yes	maximal, complemented
4	C₁₉×#478	C₂	1	4	yes	maximal, complemented
5	C₁₉×#476	C₂	1	2	yes	maximal, complemented
6	C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₄×D₈×C₁₉	C₂	1	2	yes	maximal
9	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₁₉×#125	C₂²	1	4	yes	—
12	C₁₉×C₂²⋊Q₈	—	2	2	no	—
13	C₁₉×C₂²⋊Q₈	—	2	4	no	—
14	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₄×D₄×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₁₉×#107	C₂²	1	2	yes	—
20	C₁₉×#107	C₂²	1	2	yes	—
21	C₁₉×#106	C₂²	1	4	yes	—
22	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#102	C₂²	1	4	yes	—
25	C₁₉×#102	C₂²	1	2	yes	—
26	C₄×C₈×C₁₉	C₂²	1	2	yes	—
27	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×C₁₉	—	2	2	no	—
29	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂×D₄×C₁₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	D₈×C₁₉	Q₈	1	4	yes	complemented
34	C₂×C₈×C₁₉	C₂³	1	2	yes	—
35	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₁₉	—	2	4	no	—
38	C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
42	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
43	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
44	C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₄²×C₁₉	C₂³	1	2	yes	—
47	C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₁₉	—	2	2	no	—
49	Q₈×C₁₉	—	2	2	no	—
50	Q₈×C₁₉	—	8	2	no	—
51	D₄×C₁₉	—	2	2	no	—
52	D₄×C₁₉	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	8	4	no	—
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
62	C₈×C₁₉	—	2	2	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	C₂×Q₈	1	2	yes	—
65	#3380	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂²×C₁₉	—	2	4	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	4	2	no	—
74	C₄×C₁₉	—	4	4	no	—
75	C₄×C₁₉	#135	1	2	yes	—
76	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
77	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
78	#554	C₂×C₁₉	1	2	yes	complemented
79	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
80	#499	C₂×C₁₉	1	2	yes	complemented
81	#478	C₂×C₁₉	1	4	yes	complemented
82	#476	C₂×C₁₉	1	2	yes	complemented
83	C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
84	C₄×D₈	C₂×C₁₉	1	2	yes	—
85	C₄×D₈	C₂×C₁₉	1	1	yes	characteristic
86	C₂×C₁₉	—	4	4	no	—
87	C₂×C₁₉	D₄×Q₈	1	1	yes	characteristic
88	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
89	C₂×C₁₉	#576	1	1	yes	characteristic
90	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
91	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
92	#125	C₂²×C₁₉	1	4	yes	—
93	C₂²⋊Q₈	—	2	2	no	—
94	C₂²⋊Q₈	—	2	4	no	—
95	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
96	C₄×D₄	C₂²×C₁₉	1	2	yes	—
97	C₄×D₄	C₂²×C₁₉	1	4	yes	—
98	C₂×C₄⋊C₄	—	2	2	no	—
99	#107	C₂²×C₁₉	1	1	yes	characteristic
100	#107	C₂²×C₁₉	1	2	yes	—
101	#107	C₂²×C₁₉	1	2	yes	—
102	#106	C₂²×C₁₉	1	4	yes	—
103	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
104	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
105	#102	C₂²×C₁₉	1	4	yes	—
106	#102	C₂²×C₁₉	1	2	yes	—
107	C₄×C₈	C₂²×C₁₉	1	2	yes	—
108	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
109	C₁₉	#3380	1	1	yes	characteristic, direct product factor, Sylow
110	C₂×Q₈	—	2	2	no	—
111	C₂×Q₈	D₄×C₁₉	1	1	yes	characteristic
112	C₂×D₄	C₂³×C₁₉	1	2	yes	—
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	—	2	4	no	—
115	D₈	Q₈×C₁₉	1	4	yes	complemented
116	C₂×C₈	C₂³×C₁₉	1	2	yes	—
117	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
118	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
119	C₄⋊C₄	—	2	4	no	—
120	C₄⋊C₄	—	2	2	no	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
123	C₄⋊C₄	D₄×C₁₉	1	2	yes	—
124	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
125	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
126	C₂²⋊C₄	—	2	2	no	—
127	C₂²⋊C₄	—	2	4	no	—
128	C₄²	C₂³×C₁₉	1	2	yes	—
129	C₄²	C₂³×C₁₉	1	1	yes	characteristic
130	C₂³	—	2	2	no	—
131	Q₈	—	2	2	no	—
132	Q₈	—	8	2	no	—
133	D₄	—	2	2	no	—
134	D₄	C₂×Q₈×C₁₉	1	4	yes	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	4	4	no	—
138	C₂×C₄	—	8	4	no	—
139	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
140	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
141	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
142	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	2	1	no	—
146	C₈	C₂×Q₈×C₁₉	1	2	yes	—
147	C₂²	—	2	4	no	—
148	C₂²	—	4	2	no	—
149	C₂²	—	4	2	no	—
150	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	2	1	no	—
154	C₄	—	4	2	no	—
155	C₄	—	4	4	no	—
156	C₄	C₁₉×#135	1	2	yes	—
157	C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
158	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
159	C₂	—	4	4	no	—
160	C₂	D₄×Q₈×C₁₉	1	1	yes	characteristic
161	C₂	C₂×C₁₉×#135	1	1	yes	characteristic
162	C₂	C₁₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×D₈×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#554	C₂	semidirect
2. C₁₉×#500	C₂	semidirect
3. C₁₉×#499	C₂	semidirect
4. C₁₉×#478	C₂	semidirect
5. C₁₉×#476	C₂	semidirect
6. C₈×Q₈×C₁₉	C₂	semidirect
33. D₈×C₁₉	Q₈	semidirect
65. #3380	C₁₉	direct (N × H)
78. #554	C₂×C₁₉	semidirect
79. #500	C₂×C₁₉	semidirect
80. #499	C₂×C₁₉	semidirect
81. #478	C₂×C₁₉	semidirect
82. #476	C₂×C₁₉	semidirect
83. C₈×Q₈	C₂×C₁₉	semidirect
109. C₁₉	#3380	direct (N × H)
115. D₈	Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#554	2
C₁₉×#500	2
C₁₉×#499	2
C₁₉×#478	2
C₁₉×#476	2
C₈×Q₈×C₁₉	2
C₄×D₈×C₁₉	2
#3380	19

Subgroups — C19×#3380 #14561237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3380 #14561237