Subgroups — C₁₉×#3338 #14561195

Order 2432.

356 conjugacy classes of subgroups.

The subgroup lattice has 168 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
2	C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#484	C₂	1	4	yes	maximal, complemented
4	C₁₉×#477	C₂	1	2	yes	maximal, complemented
5	C₁₉×#467	C₂	1	2	yes	maximal, complemented
6	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#107	C₂	1	2	yes	maximal, complemented
9	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
11	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₉×#125	—	2	2	no	—
13	C₁₉×C₂²⋊Q₈	—	2	4	no	—
14	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₄×D₄×C₁₉	—	2	2	no	—
17	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
19	C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₁₉×#107	C₂²	1	2	yes	—
21	C₁₉×#107	C₂²	1	4	yes	—
22	C₁₉×#107	C₂²	1	2	yes	—
23	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#103	C₂²	1	2	yes	—
25	C₁₉×#103	C₂²	1	4	yes	—
26	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×C₁₉	—	2	2	no	—
29	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
30	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	—	2	4	no	—
32	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
33	Q₁₆×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	—	2	4	no	—
35	C₂×C₈×C₁₉	C₂³	1	2	yes	—
36	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₁₉	—	2	4	no	—
39	C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
44	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
45	C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₁₉	C₂×D₄	1	2	yes	—
50	Q₈×C₁₉	—	2	2	no	—
51	Q₈×C₁₉	—	2	2	no	—
52	Q₈×C₁₉	—	8	2	no	—
53	D₄×C₁₉	Q₁₆	1	4	yes	complemented
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	4	no	—
59	C₂×C₄×C₁₉	—	8	4	no	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
64	C₈×C₁₉	—	2	2	no	—
65	C₈×C₁₉	—	2	1	no	—
66	C₈×C₁₉	#41	1	2	yes	—
67	#3338	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	2	2	no	—
70	C₂²×C₁₉	C₂×Q₁₆	1	4	yes	—
71	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	4	2	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	—	4	4	no	—
77	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
78	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
79	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
80	#554	C₂×C₁₉	1	2	yes	—
81	#500	C₂×C₁₉	1	1	yes	characteristic, complemented
82	#484	C₂×C₁₉	1	4	yes	complemented
83	#477	C₂×C₁₉	1	2	yes	complemented
84	#467	C₂×C₁₉	1	2	yes	complemented
85	C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
86	C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
87	C₂×#107	C₂×C₁₉	1	2	yes	complemented
88	C₂×C₁₉	—	2	4	no	—
89	C₂×C₁₉	#547	1	1	yes	characteristic
90	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
91	C₂×C₁₉	#576	1	1	yes	characteristic
92	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
93	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
94	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
95	#125	—	2	2	no	—
96	C₂²⋊Q₈	—	2	4	no	—
97	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
98	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
99	C₄×D₄	—	2	2	no	—
100	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
101	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
102	#107	C₂²×C₁₉	1	1	yes	characteristic
103	#107	C₂²×C₁₉	1	2	yes	—
104	#107	C₂²×C₁₉	1	4	yes	—
105	#107	C₂²×C₁₉	1	2	yes	—
106	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
107	#103	C₂²×C₁₉	1	2	yes	—
108	#103	C₂²×C₁₉	1	4	yes	—
109	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
110	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
111	C₁₉	#3338	1	1	yes	characteristic, direct product factor, Sylow
112	C₂×Q₈	—	2	2	no	—
113	C₂×Q₈	C₂³×C₁₉	1	2	yes	—
114	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
115	C₂²×C₄	—	2	4	no	—
116	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
117	Q₁₆	—	2	2	no	—
118	C₂×C₈	—	2	4	no	—
119	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
120	C₂×C₈	C₂³×C₁₉	1	2	yes	—
121	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	—	2	2	no	—
125	C₄⋊C₄	—	2	4	no	—
126	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
127	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
128	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
129	C₂²⋊C₄	—	2	4	no	—
130	C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
131	C₄²	—	2	2	no	—
132	C₄²	C₂³×C₁₉	1	1	yes	characteristic
133	C₂³	C₂×D₄×C₁₉	1	2	yes	—
134	Q₈	—	2	2	no	—
135	Q₈	—	2	2	no	—
136	Q₈	—	8	2	no	—
137	D₄	Q₁₆×C₁₉	1	4	yes	complemented
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	8	4	no	—
144	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
145	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
146	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
147	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
148	C₈	—	2	2	no	—
149	C₈	—	2	1	no	—
150	C₈	#41×C₁₉	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	—	2	2	no	—
153	C₂²	C₂×Q₁₆×C₁₉	1	4	yes	—
154	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
155	C₄	—	2	2	no	—
156	C₄	—	2	1	no	—
157	C₄	—	4	2	no	—
158	C₄	—	4	2	no	—
159	C₄	—	4	4	no	—
160	C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
161	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
162	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
163	C₂	—	2	4	no	—
164	C₂	C₁₉×#547	1	1	yes	characteristic
165	C₂	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
166	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×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#500	C₂	semidirect
3. C₁₉×#484	C₂	semidirect
4. C₁₉×#477	C₂	semidirect
5. C₁₉×#467	C₂	semidirect
6. C₄×Q₁₆×C₁₉	C₂	semidirect
8. C₂×C₁₉×#107	C₂	semidirect
53. D₄×C₁₉	Q₁₆	semidirect
67. #3338	C₁₉	direct (N × H)
81. #500	C₂×C₁₉	semidirect
82. #484	C₂×C₁₉	semidirect
83. #477	C₂×C₁₉	semidirect
84. #467	C₂×C₁₉	semidirect
85. C₄×Q₁₆	C₂×C₁₉	semidirect
87. C₂×#107	C₂×C₁₉	semidirect
111. C₁₉	#3338	direct (N × H)
137. D₄	Q₁₆×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×#484	2
C₁₉×#477	2
C₁₉×#467	2
C₄×Q₁₆×C₁₉	2
C₈×D₄×C₁₉	2
C₂×C₁₉×#107	2
#3338	19

Subgroups — C19×#3338 #14561195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3338 #14561195