Subgroups — #18073071

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561949	C₂	1	2	yes	maximal
2	#14561927	C₂	1	2	yes	maximal, complemented
3	#14561480	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926270	C₄	1	4	yes	—
7	#11926268	C₄	1	4	yes	—
8	#11926266	—	2	4	no	—
9	C₂²×M₁₆×C₁₉	C₄	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₁₉×#405	—	2	4	no	—
13	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
14	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	—	2	2	no	—
19	C₂×M₁₆×C₁₉	—	2	2	no	—
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₉×#117	—	2	2	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×#97	—	2	2	no	—
35	C₁₉×#97	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	C₄×C₈×C₁₉	D₄	1	4	yes	—
38	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
39	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
40	C₄×C₁₉⋊C₈	—	2	4	no	—
41	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
49	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	M₁₆×C₁₉	—	2	8	no	—
53	C₂×C₈×C₁₉	—	2	8	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	—	2	1	no	—
56	C₂×C₈×C₁₉	—	2	1	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	—	2	1	no	—
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
65	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	#41	1	2	yes	—
72	C₂×C₁₉⋊C₈	—	2	8	no	—
73	#8157	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	—	2	1	no	—
75	C₂³×C₁₉	—	2	1	no	—
76	C₂³×C₁₉	—	4	2	no	—
77	C₂³×C₁₉	#97	1	2	yes	—
78	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	#97	1	2	yes	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
92	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
96	C₈×C₁₉	—	2	2	no	—
97	C₈×C₁₉	—	2	2	no	—
98	C₈×C₁₉	—	2	2	no	—
99	C₈×C₁₉	—	2	2	no	—
100	C₁₉⋊C₈	—	4	8	no	—
101	C₂×#405	D₁₉	1	1	yes	characteristic
102	#1458	—	19	2	no	—
103	#1452	—	19	2	no	—
104	#1281	—	19	2	no	—
105	C₂²×C₁₉	—	2	2	no	—
106	C₂²×C₁₉	—	2	2	no	—
107	C₂²×C₁₉	—	4	2	no	—
108	C₂²×C₁₉	—	4	2	no	—
109	C₂²×C₁₉	—	4	2	no	—
110	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
112	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	4	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	#407	1	1	yes	characteristic
117	C₄×C₁₉	#407	1	1	yes	characteristic
118	C₄×C₁₉	#432	1	1	yes	characteristic
119	C₄×C₁₉	#432	1	1	yes	characteristic
120	C₂²×M₁₆	Dic₁₉	1	1	yes	characteristic
121	C₂³×C₈	Dic₁₉	1	1	yes	characteristic
122	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
123	#431	—	19	4	no	—
124	#405	—	2	4	no	—
125	C₂×#97	Dic₁₉	1	1	yes	characteristic
126	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
127	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
129	#324	—	19	4	no	—
130	#323	—	19	4	no	—
131	#322	—	38	4	no	—
132	C₂×C₁₉	—	2	1	no	—
133	C₂×C₁₉	—	2	1	no	—
134	C₂×C₁₉	—	4	2	no	—
135	C₂×C₁₉	#1749	1	1	yes	characteristic
136	C₂×C₁₉	#1757	1	2	yes	—
137	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
138	C₂×M₁₆	—	2	2	no	—
139	C₂×M₁₆	—	2	2	no	—
140	C₂×M₁₆	—	2	2	no	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
146	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
147	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
148	#117	—	2	2	no	—
149	#117	—	2	2	no	—
150	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
151	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
152	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	38	4	no	—
155	C₂²⋊C₈	—	19	8	no	—
156	#97	—	2	2	no	—
157	#97	—	2	2	no	—
158	C₄×C₈	—	2	2	no	—
159	C₄×C₈	—	38	4	no	—
160	C₄×C₈	C₂²⋊D₁₉	1	4	yes	—
161	C₁₉	#8157	1	1	yes	characteristic, complemented, Sylow
162	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	2	1	no	—
167	C₂²×C₄	#64520	1	2	yes	—
168	C₂²×C₄	#64520	1	2	yes	—
169	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
170	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
171	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
172	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
173	M₁₆	—	2	8	no	—
174	C₂×C₈	—	2	8	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	—	38	8	no	—
184	C₂×C₈	#64520	1	2	yes	—
185	C₂×C₈	#64520	1	2	yes	—
186	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
188	C₄⋊C₄	—	2	4	no	—
189	C₂²⋊C₄	—	2	4	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	1	no	—
192	C₄²	#64541	1	2	yes	—
193	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	2	1	no	—
196	C₂³	—	4	2	no	—
197	C₂³	#10597260	1	2	yes	—
198	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	#10597260	1	2	yes	—
209	C₂×C₄	C₂×#64520	1	1	yes	characteristic
210	C₂×C₄	C₂×#64520	1	1	yes	characteristic
211	C₂×C₄	C₂×#64520	1	1	yes	characteristic
212	C₂×C₄	C₂×#64520	1	1	yes	characteristic
213	C₂×C₄	#10597372	1	1	yes	characteristic
214	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
215	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
216	C₈	—	2	2	no	—
217	C₈	—	2	2	no	—
218	C₈	—	2	2	no	—
219	C₈	—	2	2	no	—
220	C₈	—	76	8	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	2	no	—
226	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
227	C₂²	C₂×#10597260	1	1	yes	characteristic
228	C₂²	C₄×#64520	1	1	yes	characteristic
229	C₄	—	2	2	no	—
230	C₄	—	2	4	no	—
231	C₄	—	4	2	no	—
232	C₄	#11926508	1	1	yes	characteristic
233	C₄	#11926508	1	1	yes	characteristic
234	C₄	#11926601	1	1	yes	characteristic
235	C₄	#11926601	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	—	4	2	no	—
239	C₂	#14563397	1	1	yes	characteristic
240	C₂	#14563435	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#405	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#405	D₁₉
hypocenter	C₁₉	#8157
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #14561927	C₂	semidirect
3. #14561480	C₂	semidirect
161. C₁₉	#8157	semidirect

Maximal subgroups

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

subgroup	index
#14561949	2
#14561927	2
#14561480	2
C₂×C₁₉×#405	2
#8157	19