Subgroups — #18072661

Order 4864.

788 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597372	C₂	1	2	yes	maximal
2	#14561520	C₂	1	4	yes	maximal
3	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597372	—	2	2	no	—
5	C₄×C₄⋊Dic₁₉	—	2	2	no	—
6	C₄×C₄⋊Dic₁₉	C₄	1	4	yes	complemented
7	C₄×C₂²⋊Dic₁₉	—	2	2	no	—
8	C₄×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
9	#11926390	C₄	1	4	yes	complemented
10	C₄²×Dic₁₉	—	2	2	no	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#432	—	2	2	no	—
13	C₁₉×#431	—	2	2	no	—
14	C₁₉×#423	C₄	1	2	yes	complemented
15	C₁₉×#407	C₂²	1	2	yes	—
16	C₄×M₁₆×C₁₉	C₄	1	2	yes	complemented
17	C₂³×C₄×C₁₉	D₄	1	2	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
27	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
28	#10597372	—	2	16	no	—
29	C₂×C₄⋊Dic₁₉	—	2	4	no	—
30	C₂×C₄×Dic₁₉	—	2	4	no	—
31	C₂×C₄×Dic₁₉	—	2	4	no	—
32	C₂×C₄×Dic₁₉	—	2	4	no	—
33	C₁₉×C₄⋊C₈	—	2	4	no	—
34	C₁₉×C₂²⋊C₈	—	2	4	no	—
35	C₁₉×#97	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	C₁₉⋊#95	—	2	4	no	—
38	C₁₉⋊#95	C₂×C₄	1	8	yes	—
39	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	—	2	8	no	—
41	C₂²×C₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×Dic₁₉	—	2	8	no	—
53	M₁₆×C₁₉	—	4	4	no	—
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₄²×C₁₉	C₄²	1	1	yes	characteristic
56	C₄²×C₁₉	C₄²	1	2	yes	—
57	C₄²×C₁₉	C₄²	1	1	yes	characteristic
58	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
62	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
63	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
64	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
65	C₂²⋊Dic₁₉	—	2	16	no	—
66	C₄⋊Dic₁₉	—	2	16	no	—
67	C₄×Dic₁₉	—	2	16	no	—
68	C₄×Dic₁₉	—	4	8	no	—
69	C₄×Dic₁₉	—	4	8	no	—
70	#8048	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	—	2	4	no	—
72	C₂³×C₁₉	—	4	1	no	—
73	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
74	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	4	no	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	4	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	#95	1	2	yes	—
85	C₂×C₄×C₁₉	#95	1	2	yes	—
86	C₂×C₄×C₁₉	#95	1	2	yes	—
87	C₂×C₄×C₁₉	#95	1	2	yes	—
88	C₂×C₄×C₁₉	#104	1	8	yes	—
89	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
92	C₂×Dic₁₉	—	2	16	no	—
93	C₂×Dic₁₉	—	4	8	no	—
94	C₂×Dic₁₉	—	4	8	no	—
95	C₈×C₁₉	—	4	4	no	—
96	#2920	D₁₉	1	1	yes	characteristic
97	C₄×#117	—	19	2	no	—
98	#1297	—	19	4	no	—
99	C₂²×C₁₉	—	2	2	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	—	2	2	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	—	4	4	no	—
104	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×#104	1	4	yes	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	#339	1	4	yes	—
111	C₄×C₁₉	#339	1	4	yes	—
112	C₄×C₁₉	#410	1	2	yes	—
113	Dic₁₉	—	4	16	no	—
114	C₂×#117	—	38	2	no	—
115	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
116	#432	—	2	2	no	—
117	#431	—	2	2	no	—
118	#423	Dic₁₉	1	2	yes	complemented
119	#407	C₂×D₁₉	1	2	yes	—
120	C₄×M₁₆	Dic₁₉	1	2	yes	complemented
121	C₄×C₄⋊C₄	—	19	4	no	—
122	C₄×C₄⋊C₄	—	38	2	no	—
123	C₄×C₂²⋊C₄	—	19	4	no	—
124	C₄×C₂²⋊C₄	—	38	2	no	—
125	#376	—	19	4	no	—
126	C₄³	—	38	2	no	—
127	C₂×C₁₉	—	2	4	no	—
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	C₂×#339	1	2	yes	—
130	C₂×C₁₉	#1740	1	1	yes	characteristic
131	C₂³×C₄	D₇₆	1	2	yes	—
132	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
133	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
134	#117	—	38	16	no	—
135	C₂×C₄⋊C₄	—	38	4	no	—
136	C₂×C₂²⋊C₄	—	38	4	no	—
137	C₂×C₄²	—	38	4	no	—
138	C₂×C₄²	—	38	4	no	—
139	C₂×C₄²	—	38	4	no	—
140	C₂×C₄²	Dic₃₈	1	2	yes	—
141	C₂×C₄²	C₄×D₁₉	1	2	yes	—
142	C₂×C₄²	C₄×D₁₉	1	2	yes	—
143	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
144	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
146	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
147	C₄⋊C₈	—	2	4	no	—
148	C₂²⋊C₈	—	2	4	no	—
149	#97	—	2	2	no	—
150	C₄×C₈	—	2	2	no	—
151	#95	—	19	8	no	—
152	#95	—	38	4	no	—
153	C₁₉	#8048	1	1	yes	characteristic, complemented, Sylow
154	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
155	C₂²×C₄	—	2	8	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	—	38	8	no	—
158	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
159	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
160	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
161	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
162	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
163	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
164	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
166	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
168	M₁₆	—	4	4	no	—
169	C₂×C₈	—	2	4	no	—
170	C₄⋊C₄	—	38	16	no	—
171	C₂²⋊C₄	—	38	16	no	—
172	C₄²	—	38	16	no	—
173	C₄²	—	76	8	no	—
174	C₄²	—	76	8	no	—
175	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
176	C₄²	C₄×Dic₁₉	1	2	yes	—
177	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
178	C₄²	Dic₁₉⋊C₄	1	2	yes	—
179	C₄²	Dic₁₉⋊C₄	1	2	yes	—
180	C₄²	Dic₁₉⋊C₄	1	2	yes	—
181	C₄²	Dic₁₉⋊C₄	1	2	yes	—
182	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
183	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
184	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
185	C₂³	—	2	4	no	—
186	C₂³	—	4	1	no	—
187	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
188	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	38	16	no	—
199	C₂×C₄	—	76	8	no	—
200	C₂×C₄	—	76	8	no	—
201	C₂×C₄	#10597282	1	8	yes	—
202	C₂×C₄	C₁₉⋊#95	1	2	yes	—
203	C₂×C₄	C₁₉⋊#95	1	2	yes	—
204	C₂×C₄	C₁₉⋊#95	1	2	yes	—
205	C₂×C₄	C₁₉⋊#95	1	2	yes	—
206	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
207	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
208	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₈	—	4	4	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	4	4	no	—
215	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
216	C₂²	C₂×#10597282	1	4	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	76	16	no	—
222	C₄	#11926305	1	4	yes	—
223	C₄	#11926305	1	4	yes	—
224	C₄	#11926518	1	2	yes	—
225	C₂	—	2	4	no	—
226	C₂	—	4	1	no	—
227	C₂	C₂×#11926305	1	2	yes	—
228	C₂	#14563368	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2920	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2920	D₁₉
hypocenter	C₁₉	#8048
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
6. C₄×C₄⋊Dic₁₉	C₄	semidirect
9. #11926390	C₄	semidirect
14. C₁₉×#423	C₄	semidirect
16. C₄×M₁₆×C₁₉	C₄	semidirect
118. #423	Dic₁₉	semidirect
120. C₄×M₁₆	Dic₁₉	semidirect
153. C₁₉	#8048	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597372	2
#14561520	2
C₁₉×#2920	2
#8048	19