Subgroups — C₁₉×#2552 #14560409

Order 2432.

452 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#125	C₂	1	2	yes	maximal
2	C₁₉×#398	C₂	1	4	yes	maximal
3	C₁₉×#389	C₂	1	2	yes	maximal
4	C₁₉×#389	C₂	1	2	yes	maximal
5	C₁₉×#384	C₂	1	2	yes	maximal
6	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#125	—	2	8	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₁₉×#95	C₂²	1	2	yes	—
25	C₁₉×#95	C₂²	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₁₉	—	2	8	no	—
35	C₄⋊C₄×C₁₉	—	2	8	no	—
36	C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₄⋊C₄×C₁₉	—	4	4	no	—
41	C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₄⋊C₄×C₁₉	D₄	1	4	yes	—
43	C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
44	C₄²×C₁₉	—	2	4	no	—
45	C₄²×C₁₉	—	2	4	no	—
46	C₄²×C₁₉	Q₈	1	4	yes	—
47	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	4	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	4	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
64	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
67	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
70	C₂×C₄×C₁₉	#41	1	2	yes	—
71	C₂×C₄×C₁₉	#41	1	2	yes	—
72	#2552	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
74	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
75	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
76	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
78	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
79	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	4	no	—
82	C₄×C₁₉	—	2	4	no	—
83	C₄×C₁₉	—	4	2	no	—
84	C₄×C₁₉	—	4	2	no	—
85	C₄×C₁₉	—	4	4	no	—
86	C₄×C₁₉	#125	1	4	yes	complemented
87	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
88	C₂×#125	C₂×C₁₉	1	2	yes	—
89	#398	C₂×C₁₉	1	4	yes	—
90	#389	C₂×C₁₉	1	2	yes	—
91	#389	C₂×C₁₉	1	2	yes	—
92	#384	C₂×C₁₉	1	2	yes	—
93	#384	C₂×C₁₉	1	1	yes	characteristic
94	C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
95	C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
96	C₂×C₁₉	C₂×#125	1	1	yes	characteristic
97	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
98	C₂×C₁₉	#544	1	1	yes	characteristic
99	C₂×C₁₉	#547	1	1	yes	characteristic
100	C₂×C₁₉	#550	1	1	yes	characteristic
101	C₂×C₁₉	#554	1	1	yes	characteristic
102	C₂×C₁₉	#557	1	1	yes	characteristic
103	#125	—	2	8	no	—
104	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
105	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
106	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
107	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
108	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
109	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
110	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
111	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
112	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
113	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
114	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
115	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
116	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
117	#95	C₂²×C₁₉	1	2	yes	—
118	#95	C₂²×C₁₉	1	2	yes	—
119	#95	C₂²×C₁₉	1	4	yes	—
120	C₁₉	#2552	1	1	yes	characteristic, direct product factor, Sylow
121	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
122	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
123	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
124	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
125	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
126	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
127	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
128	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
129	C₄⋊C₄	—	2	8	no	—
130	C₄⋊C₄	—	2	8	no	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	—	2	4	no	—
135	C₄⋊C₄	—	4	4	no	—
136	C₄⋊C₄	—	4	2	no	—
137	C₄⋊C₄	D₄×C₁₉	1	4	yes	—
138	C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
139	C₄²	—	2	4	no	—
140	C₄²	—	2	4	no	—
141	C₄²	Q₈×C₁₉	1	4	yes	—
142	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	C₂×D₄×C₁₉	1	4	yes	—
159	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
160	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
161	C₂×C₄	C₂×Q₈×C₁₉	1	4	yes	—
162	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
163	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
164	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
165	C₂×C₄	#41×C₁₉	1	2	yes	—
166	C₂×C₄	#41×C₁₉	1	2	yes	—
167	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
168	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
169	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
170	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
171	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
172	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
173	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	2	4	no	—
176	C₄	—	2	4	no	—
177	C₄	—	4	2	no	—
178	C₄	—	4	2	no	—
179	C₄	—	4	4	no	—
180	C₄	C₁₉×#125	1	4	yes	complemented
181	C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
182	C₂	C₂×C₁₉×#125	1	1	yes	characteristic
183	C₂	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
184	C₂	C₁₉×#544	1	1	yes	characteristic
185	C₂	C₁₉×#547	1	1	yes	characteristic
186	C₂	C₁₉×#550	1	1	yes	characteristic
187	C₂	C₁₉×#554	1	1	yes	characteristic
188	C₂	C₁₉×#557	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
72. #2552	C₁₉	direct (N × H)
86. C₄×C₁₉	#125	semidirect
120. C₁₉	#2552	direct (N × H)
180. C₄	C₁₉×#125	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#125	2
C₁₉×#398	2
C₁₉×#389	2
C₁₉×#384	2
C₄×C₄⋊C₄×C₁₉	2
#2552	19

Subgroups — C19×#2552 #14560409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2552 #14560409