Subgroups — #18076090

Order 4864.

530 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563623	C₂	1	1	yes	maximal, characteristic
2	#14561953	C₂	1	1	yes	maximal, characteristic
3	#14561514	C₂	1	2	yes	maximal, complemented
4	#14561502	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2349	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597291	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	#11926404	C₂²	1	2	yes	—
9	#11926311	—	2	1	no	—
10	#11926270	—	2	1	no	—
11	#11926268	—	2	1	no	—
12	C₂×C₄×D₄×C₁₉	—	2	1	no	—
13	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#385	—	2	1	no	—
16	C₁₉×#385	—	2	1	no	—
17	C₁₉×#382	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#380	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#380	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#95	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₄×D₄×C₁₉	—	4	4	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	2	no	—
45	C₁₉×#95	—	2	1	no	—
46	C₁₉×#95	—	2	1	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
52	#10597291	—	4	2	no	—
53	C₁₉⋊#95	—	2	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
61	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	8	1	no	—
73	C₂²×C₄×C₁₉	—	8	1	no	—
74	C₂²×C₄×C₁₉	—	8	1	no	—
75	C₂²×C₄×C₁₉	—	8	1	no	—
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	2	yes	—
82	C₂²×C₄×C₁₉	#41	1	2	yes	—
83	C₂²×Dic₁₉	—	4	2	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	4	2	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	8	1	no	—
88	C₄⋊C₄×C₁₉	—	8	1	no	—
89	C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂²⋊C₄×C₁₉	—	4	2	no	—
92	C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₄²×C₁₉	—	2	1	no	—
94	C₄²×C₁₉	—	2	1	no	—
95	C₄²×C₁₉	—	4	2	no	—
96	C₂²⋊Dic₁₉	—	4	2	no	—
97	C₂²⋊Dic₁₉	—	4	2	no	—
98	C₄⋊Dic₁₉	—	8	2	no	—
99	C₂×C₁₉⋊C₈	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	8	2	no	—
101	#8761	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	4	1	no	—
105	C₂³×C₁₉	—	4	1	no	—
106	C₂³×C₁₉	—	4	1	no	—
107	C₂³×C₁₉	—	4	1	no	—
108	C₂³×C₁₉	#103	1	2	yes	—
109	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×C₁₉	#123	1	2	yes	—
111	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
112	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
113	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
114	D₄×C₁₉	—	2	4	no	—
115	D₄×C₁₉	—	2	4	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	4	no	—
141	C₂×C₄×C₁₉	—	8	4	no	—
142	C₂×C₄×C₁₉	#103	1	2	yes	—
143	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#123	1	2	yes	—
146	C₂×Dic₁₉	—	8	2	no	—
147	C₂×Dic₁₉	—	8	2	no	—
148	C₂×Dic₁₉	—	8	2	no	—
149	C₁₉⋊C₈	—	8	2	no	—
150	#2349	D₁₉	1	1	yes	characteristic
151	#1799	—	19	1	no	—
152	#1459	—	19	1	no	—
153	#1294	—	19	2	no	—
154	#1289	—	19	2	no	—
155	C₂²×C₁₉	—	2	2	no	—
156	C₂²×C₁₉	—	2	1	no	—
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	2	1	no	—
159	C₂²×C₁₉	—	2	2	no	—
160	C₂²×C₁₉	—	4	2	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	1	no	—
163	C₂²×C₁₉	—	4	2	no	—
164	C₂²×C₁₉	—	4	2	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	—	4	1	no	—
167	C₂²×C₁₉	#381	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
169	C₂²×C₁₉	#418	1	1	yes	characteristic
170	C₂²×C₁₉	#481	1	2	yes	—
171	C₂²×C₁₉	#484	1	2	yes	—
172	C₄×C₁₉	—	2	2	no	—
173	C₄×C₁₉	—	2	2	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	4	2	no	—
177	C₄×C₁₉	—	4	1	no	—
178	C₄×C₁₉	—	4	1	no	—
179	C₄×C₁₉	—	8	1	no	—
180	C₄×C₁₉	—	8	1	no	—
181	C₄×C₁₉	—	8	1	no	—
182	Dic₁₉	—	16	2	no	—
183	C₂×C₄×D₄	—	2	1	no	—
184	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
185	C₂×#99	—	38	1	no	—
186	C₂×C₂²⋊C₈	—	19	2	no	—
187	#389	—	2	1	no	—
188	#385	—	2	1	no	—
189	#385	—	2	1	no	—
190	#382	Dic₁₉	1	1	yes	characteristic, complemented
191	#380	—	19	2	no	—
192	#380	Dic₁₉	1	1	yes	characteristic, complemented
193	#380	C₂×D₁₉	1	1	yes	characteristic
194	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic, complemented
195	C₂×#95	Dic₁₉	1	1	yes	characteristic, complemented
196	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
197	#342	—	38	1	no	—
198	#324	—	38	1	no	—
199	#323	—	38	1	no	—
200	C₂×C₁₉	—	2	2	no	—
201	C₂×C₁₉	—	2	1	no	—
202	C₂×C₁₉	—	2	1	no	—
203	C₂×C₁₉	—	2	2	no	—
204	C₂×C₁₉	—	4	2	no	—
205	C₂×C₁₉	#1824	1	1	yes	characteristic
206	C₂×C₁₉	#1827	1	1	yes	characteristic
207	C₂×C₁₉	#1828	1	1	yes	characteristic
208	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
209	C₂³×C₄	—	2	1	no	—
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
212	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
213	C₂²×C₈	—	38	2	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	4	4	no	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	—	2	1	no	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	38	2	no	—
222	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₂²⋊C₄	—	38	2	no	—
226	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
228	C₂×C₄²	—	2	1	no	—
229	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
230	#99	—	76	2	no	—
231	C₂²⋊C₈	—	38	2	no	—
232	C₂²⋊C₈	—	38	2	no	—
233	#95	—	2	1	no	—
234	#95	—	2	1	no	—
235	#95	—	2	1	no	—
236	#95	—	38	2	no	—
237	#95	C₂×Dic₁₉	1	1	yes	characteristic
238	#95	C₂×Dic₁₉	1	1	yes	characteristic
239	#95	C₂×Dic₁₉	1	1	yes	characteristic
240	#95	C₂×Dic₁₉	1	1	yes	characteristic
241	C₁₉	#8761	1	1	yes	characteristic, complemented, Sylow
242	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
243	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	#64527	1	2	yes	—
247	C₂×D₄	#64528	1	2	yes	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	8	1	no	—
259	C₂²×C₄	—	8	1	no	—
260	C₂²×C₄	—	8	1	no	—
261	C₂²×C₄	—	8	1	no	—
262	C₂²×C₄	—	76	2	no	—
263	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
266	C₂²×C₄	#64541	1	2	yes	—
267	C₂²×C₄	#64541	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
270	C₂×C₈	—	76	2	no	—
271	C₂×C₈	—	152	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₄⋊C₄	—	4	2	no	—
275	C₄⋊C₄	—	8	1	no	—
276	C₄⋊C₄	—	8	1	no	—
277	C₄⋊C₄	—	152	2	no	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	4	2	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	76	2	no	—
283	C₂²⋊C₄	—	76	2	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	4	2	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	4	1	no	—
290	C₂³	—	4	1	no	—
291	C₂³	—	4	1	no	—
292	C₂³	—	4	1	no	—
293	C₂³	#10597292	1	2	yes	—
294	C₂³	#10597375	1	2	yes	—
295	C₂³	#10597378	1	2	yes	—
296	C₂³	C₂×#64527	1	1	yes	characteristic
297	C₂³	C₂×#64528	1	1	yes	characteristic
298	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
299	D₄	—	2	4	no	—
300	D₄	—	2	4	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	8	1	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	—	8	4	no	—
326	C₂×C₄	—	8	4	no	—
327	C₂×C₄	—	152	2	no	—
328	C₂×C₄	—	152	2	no	—
329	C₂×C₄	—	152	2	no	—
330	C₂×C₄	#10597292	1	2	yes	—
331	C₂×C₄	#10597372	1	1	yes	characteristic
332	C₂×C₄	#10597372	1	1	yes	characteristic
333	C₂×C₄	#10597375	1	2	yes	—
334	C₈	—	152	2	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	#11926407	1	1	yes	characteristic
348	C₂²	C₂×#10597292	1	1	yes	characteristic
349	C₂²	#11926549	1	1	yes	characteristic
350	C₂²	#11926862	1	2	yes	—
351	C₂²	#11926879	1	2	yes	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	8	1	no	—
360	C₄	—	8	1	no	—
361	C₄	—	8	1	no	—
362	C₄	—	304	2	no	—
363	C₂	—	2	1	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	2	no	—
367	C₂	—	4	2	no	—
368	C₂	#14563725	1	1	yes	characteristic
369	C₂	#14563739	1	1	yes	characteristic
370	C₂	#14563743	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926407
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2349	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2349	D₁₉
hypocenter	C₁₉	#8761
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2349

Complements

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

N	H ≅ G/N	type
3. #14561514	C₂	semidirect
4. #14561502	C₂	semidirect
17. C₁₉×#382	C₄	semidirect
18. C₁₉×#380	C₄	semidirect
20. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
21. C₂×C₁₉×#95	C₄	semidirect
190. #382	Dic₁₉	semidirect
192. #380	Dic₁₉	semidirect
194. C₄×C₄⋊C₄	Dic₁₉	semidirect
195. C₂×#95	Dic₁₉	semidirect
241. C₁₉	#8761	semidirect

Maximal subgroups

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

subgroup	index
#14563623	2
#14561953	2
#14561514	2
#14561502	2
C₁₉×#2349	2
#8761	19