Subgroups — #18072003

Order 4864.

758 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926566	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561469	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64515	—	2	2	no	—
7	C₂²×C₈×D₁₉	C₄	1	2	yes	—
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	#11926566	—	2	4	no	—
10	#11926566	C₄	1	8	yes	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×Dic₁₉⋊C₈	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
15	C₄×C₈×D₁₉	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
29	C₂×#64515	—	2	8	no	—
30	C₂×#64515	—	4	4	no	—
31	C₂×#64515	—	4	4	no	—
32	C₂×C₈×D₁₉	—	2	4	no	—
33	C₂×C₈×D₁₉	—	2	4	no	—
34	C₂×C₈×D₁₉	—	2	4	no	—
35	C₄²×D₁₉	C₂×C₄	1	4	yes	—
36	C₄²×D₁₉	D₄	1	4	yes	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	Dic₁₉⋊C₈	—	2	8	no	—
41	C₈×Dic₁₉	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
44	C₄×C₁₉⋊C₈	—	2	2	no	—
45	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₄×D₁₉	—	2	2	no	—
53	C₂×C₄×D₁₉	—	2	2	no	—
54	C₂×C₄×D₁₉	—	2	4	no	—
55	C₂×C₄×D₁₉	C₄²	1	2	yes	—
56	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂×C₄×D₁₉	C₂²⋊C₄	1	4	yes	—
58	C₂×C₄×D₁₉	C₄⋊C₄	1	4	yes	—
59	C₂×C₄×D₁₉	D₈	1	2	yes	—
60	C₂×C₄×D₁₉	SD₁₆	1	4	yes	—
61	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	4	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	M₁₆	1	4	yes	complemented
68	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄×Dic₁₉	C₄²	1	2	yes	—
71	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
72	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
73	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	complemented
80	#64515	—	4	16	no	—
81	C₈×D₁₉	—	2	16	no	—
82	#7874	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂²×D₁₉	—	2	2	no	—
85	C₂²×D₁₉	—	2	2	no	—
86	C₂²×D₁₉	#95	1	2	yes	—
87	C₂²×D₁₉	#106	1	2	yes	—
88	C₂²×D₁₉	#107	1	2	yes	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
93	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
94	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
95	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
96	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	#95	1	2	yes	—
101	C₂×Dic₁₉	#95	1	2	yes	—
102	C₂×Dic₁₉	#95	1	2	yes	—
103	C₂×Dic₁₉	#106	1	2	yes	—
104	C₂×Dic₁₉	#107	1	2	yes	—
105	C₂×Dic₁₉	#108	1	4	yes	—
106	C₄×D₁₉	—	2	2	no	—
107	C₄×D₁₉	—	2	2	no	—
108	C₄×D₁₉	—	2	4	no	—
109	C₄×D₁₉	—	2	8	no	—
110	C₄×D₁₉	#102	1	8	yes	—
111	C₄×D₁₉	#103	1	8	yes	—
112	C₈×C₁₉	—	2	4	no	—
113	C₈×C₁₉	—	4	4	no	—
114	C₁₉⋊C₈	—	2	4	no	—
115	C₁₉⋊C₈	—	4	4	no	—
116	C₂×#423	—	19	2	no	—
117	C₂²×C₄×C₈	—	19	1	no	—
118	#1277	—	19	2	no	—
119	#1277	—	19	1	no	—
120	#1277	D₁₉	1	1	yes	characteristic, complemented
121	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
122	C₂²×C₁₉	#423	1	2	yes	—
123	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
124	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
125	C₂²×C₁₉	C₂×#108	1	2	yes	—
126	C₂×D₁₉	—	2	4	no	—
127	C₂×D₁₉	—	2	4	no	—
128	C₂×D₁₉	—	2	2	no	—
129	C₂×D₁₉	—	2	2	no	—
130	C₂×D₁₉	#340	1	4	yes	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
133	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
134	C₄×C₁₉	#407	1	2	yes	—
135	C₄×C₁₉	C₂×#102	1	2	yes	—
136	C₄×C₁₉	C₂×#103	1	2	yes	—
137	Dic₁₉	—	2	2	no	—
138	Dic₁₉	#340	1	4	yes	—
139	Dic₁₉	#341	1	4	yes	—
140	C₂²×M₁₆	—	38	2	no	—
141	C₂³×C₈	—	19	2	no	—
142	C₂²×C₄²	—	19	1	no	—
143	#423	—	19	8	no	—
144	#423	—	38	4	no	—
145	C₂×C₄⋊C₈	—	19	2	no	—
146	C₂×C₄⋊C₈	—	38	2	no	—
147	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
148	C₂×C₄×C₈	—	19	2	no	—
149	C₂×C₄×C₈	—	19	1	no	—
150	C₂×C₄×C₈	—	38	4	no	—
151	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
152	C₂×C₁₉	#1566	1	2	yes	—
153	C₂×C₁₉	#1567	1	2	yes	—
154	C₂×C₁₉	#1728	1	1	yes	characteristic
155	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
156	C₂×C₁₉	C₂×#341	1	1	yes	characteristic
157	D₁₉	—	2	4	no	—
158	C₂³×C₄	—	19	1	no	—
159	C₂³×C₄	—	19	1	no	—
160	C₂³×C₄	—	19	1	no	—
161	C₂×M₁₆	—	38	8	no	—
162	C₂×M₁₆	—	76	4	no	—
163	C₂×M₁₆	—	76	4	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	19	2	no	—
166	C₂²×C₈	—	38	4	no	—
167	C₂²×C₈	—	38	4	no	—
168	C₂²×C₈	—	38	4	no	—
169	C₂²×C₈	—	38	2	no	—
170	C₂²×C₈	C₄×D₁₉	1	2	yes	—
171	C₂×C₄²	—	19	1	no	—
172	C₂×C₄²	—	19	1	no	—
173	C₂×C₄²	—	19	1	no	—
174	C₂×C₄²	—	19	4	no	—
175	C₂×C₄²	—	19	4	no	—
176	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	19	4	no	—
179	C₄⋊C₈	—	38	8	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₄⋊C₈	C₄×D₁₉	1	4	yes	—
182	C₄×C₈	—	2	2	no	—
183	C₄×C₈	—	38	4	no	—
184	C₄×C₈	—	38	2	no	—
185	C₁₉	#7874	1	1	yes	characteristic, complemented, Sylow
186	C₂⁴	—	19	1	no	—
187	C₂²×C₄	—	19	1	no	—
188	C₂²×C₄	—	19	1	no	—
189	C₂²×C₄	—	19	4	no	—
190	C₂²×C₄	—	19	2	no	—
191	C₂²×C₄	—	19	4	no	—
192	C₂²×C₄	—	19	2	no	—
193	C₂²×C₄	—	19	1	no	—
194	C₂²×C₄	—	19	2	no	—
195	C₂²×C₄	—	19	2	no	—
196	C₂²×C₄	—	19	4	no	—
197	C₂²×C₄	—	38	4	no	—
198	C₂²×C₄	—	38	2	no	—
199	C₂²×C₄	—	38	2	no	—
200	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
201	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
202	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
203	M₁₆	—	76	16	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	4	no	—
207	C₂×C₈	—	4	2	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	19	4	no	—
210	C₂×C₈	—	38	16	no	—
211	C₂×C₈	—	38	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	—	38	4	no	—
214	C₂×C₈	—	76	2	no	—
215	C₂×C₈	—	76	2	no	—
216	C₂×C₈	#64515	1	4	yes	complemented
217	C₄²	—	19	2	no	—
218	C₄²	—	19	2	no	—
219	C₄²	—	19	4	no	—
220	C₄²	—	19	4	no	—
221	C₄²	C₂×C₄×D₁₉	1	2	yes	—
222	C₄²	D₄×D₁₉	1	2	yes	—
223	C₂³	—	19	2	no	—
224	C₂³	—	19	2	no	—
225	C₂³	—	19	2	no	—
226	C₂³	—	38	2	no	—
227	C₂³	—	38	2	no	—
228	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	19	2	no	—
231	C₂×C₄	—	19	2	no	—
232	C₂×C₄	—	19	4	no	—
233	C₂×C₄	—	19	2	no	—
234	C₂×C₄	—	19	2	no	—
235	C₂×C₄	—	19	8	no	—
236	C₂×C₄	—	19	8	no	—
237	C₂×C₄	—	19	2	no	—
238	C₂×C₄	—	38	8	no	—
239	C₂×C₄	—	38	2	no	—
240	C₂×C₄	—	38	2	no	—
241	C₂×C₄	—	38	2	no	—
242	C₂×C₄	—	38	4	no	—
243	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
244	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
245	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
246	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
247	C₂×C₄	C₂×#64515	1	2	yes	—
248	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
249	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
250	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
251	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
252	C₈	—	2	4	no	—
253	C₈	—	4	4	no	—
254	C₈	—	38	4	no	—
255	C₈	—	76	4	no	—
256	C₂²	—	19	4	no	—
257	C₂²	—	38	2	no	—
258	C₂²	—	38	4	no	—
259	C₂²	—	38	4	no	—
260	C₂²	—	38	2	no	—
261	C₂²	#95×D₁₉	1	1	yes	characteristic
262	C₂²	#11926566	1	2	yes	—
263	C₂²	#106×D₁₉	1	1	yes	characteristic
264	C₂²	#107×D₁₉	1	1	yes	characteristic
265	C₂²	#108×D₁₉	1	2	yes	—
266	C₄	—	2	2	no	—
267	C₄	—	19	4	no	—
268	C₄	—	19	4	no	—
269	C₄	—	38	2	no	—
270	C₄	C₄×#64515	1	1	yes	characteristic
271	C₄	#11926496	1	1	yes	characteristic
272	C₄	#11926506	1	2	yes	—
273	C₄	#102×D₁₉	1	2	yes	—
274	C₄	#103×D₁₉	1	2	yes	—
275	C₂	—	38	4	no	—
276	C₂	#14562389	1	2	yes	—
277	C₂	#14562392	1	2	yes	—
278	C₂	#14563327	1	1	yes	characteristic
279	C₂	D₁₉×#340	1	1	yes	characteristic
280	C₂	D₁₉×#341	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#7874
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. #14561470	C₂	semidirect
4. #14561469	C₂	semidirect
5. C₁₉×#1277	C₂	semidirect
67. C₂×C₈×C₁₉	M₁₆	semidirect
79. C₂×C₁₉⋊C₈	M₁₆	semidirect
120. #1277	D₁₉	semidirect
185. C₁₉	#7874	semidirect
216. C₂×C₈	#64515	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926566	2
C₂×C₄×C₈×D₁₉	2
#14561470	2
#14561469	2
C₁₉×#1277	2
#7874	19