Subgroups — #18082588

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14561478	C₂	1	2	yes	maximal
4	#14561478	C₂	1	2	yes	maximal
5	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926299	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#387	—	2	1	no	—
16	C₁₉×#387	—	2	1	no	—
17	C₁₉×#387	—	2	1	no	—
18	C₁₉×#387	—	2	1	no	—
19	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
20	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
21	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
36	C₂×C₄⋊C₄×C₁₉	C₈	1	4	yes	complemented
37	C₂×C₄²×C₁₉	—	4	2	no	—
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	—	2	2	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₁₉×#95	—	2	1	no	—
45	C₁₉×#95	—	2	1	no	—
46	C₁₉×#95	—	2	1	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
54	C₂²⋊(C₁₉⋊C₈)	Q₈	1	4	yes	—
55	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
56	C₄×C₁₉⋊C₈	—	4	2	no	—
57	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
88	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₉	#41	1	2	yes	—
93	C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₄⋊C₄×C₁₉	—	2	4	no	—
95	C₄⋊C₄×C₁₉	—	4	2	no	—
96	C₄⋊C₄×C₁₉	—	4	2	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₂×C₁₉⋊C₈	—	2	4	no	—
102	C₂×C₁₉⋊C₈	—	4	2	no	—
103	C₂×C₁₉⋊C₈	—	4	2	no	—
104	C₂×C₁₉⋊C₈	—	4	2	no	—
105	C₂×C₁₉⋊C₈	—	4	2	no	—
106	C₂×C₁₉⋊C₈	—	4	2	no	—
107	#9880	—	19	1	no	maximal, Sylow
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
113	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
114	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
115	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
116	C₂³×C₁₉	#131	1	2	yes	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	8	2	no	—
152	C₂×C₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
155	C₂×C₄×C₁₉	#99	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
159	C₁₉⋊C₈	—	4	4	no	—
160	C₁₉⋊C₈	—	8	2	no	—
161	C₂×#387	D₁₉	1	1	yes	characteristic
162	#1797	—	19	1	no	—
163	C₄×C₂²⋊C₈	—	19	1	no	—
164	#1280	—	19	2	no	—
165	#1280	—	19	2	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	#391	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
176	C₂²×C₁₉	#408	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
178	C₂²×C₁₉	#410	1	1	yes	characteristic
179	C₂²×C₁₉	#413	1	1	yes	characteristic
180	C₂²×C₁₉	#413	1	1	yes	characteristic
181	C₂²×C₁₉	C₈×Q₈	1	2	yes	—
182	C₂²×C₁₉	#446	1	2	yes	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	—	8	1	no	—
194	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
195	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
196	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₈	—	38	1	no	—
198	C₂×C₂²⋊C₈	—	19	2	no	—
199	C₂×C₂²⋊C₈	—	19	2	no	—
200	C₂×C₄×C₈	—	38	1	no	—
201	#387	—	2	1	no	—
202	#387	—	2	1	no	—
203	#387	—	2	1	no	—
204	#387	—	2	1	no	—
205	C₂×#95	Dic₁₉	1	1	yes	characteristic
206	C₂×#95	Dic₁₉	1	1	yes	characteristic
207	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
208	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
209	#336	—	38	1	no	—
210	#336	—	38	1	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	#1458	1	1	yes	characteristic
214	C₂×C₁₉	#1459	1	1	yes	characteristic
215	C₂×C₁₉	#1468	1	1	yes	characteristic
216	C₂×C₁₉	#1473	1	1	yes	characteristic
217	C₂×C₁₉	#1984	1	1	yes	characteristic
218	C₂×C₁₉	#1996	1	1	yes	characteristic
219	C₂×C₁₉	#1998	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
222	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
223	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
225	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
227	C₂²×C₈	—	38	2	no	—
228	C₂²×C₈	—	38	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	4	2	no	—
235	C₂×C₄⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
236	C₂×C₄²	—	4	2	no	—
237	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
241	C₄⋊C₈	—	76	2	no	—
242	C₂²⋊C₈	—	19	4	no	—
243	C₂²⋊C₈	—	38	2	no	—
244	C₂²⋊C₈	—	38	4	no	—
245	C₄×C₈	—	76	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	C₁₉	#9880	1	1	yes	characteristic, complemented, Sylow
255	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
280	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
281	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
282	C₂²×C₄	#64520	1	2	yes	—
283	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
287	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
288	C₂²×C₄	#64545	1	2	yes	—
289	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
291	C₂×C₈	—	38	4	no	—
292	C₂×C₈	—	76	2	no	—
293	C₂×C₈	—	76	2	no	—
294	C₂×C₈	—	76	2	no	—
295	C₂×C₈	—	76	2	no	—
296	C₂×C₈	—	76	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	1	no	—
304	C₄²	—	4	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
310	C₂³	C₂×#64520	1	1	yes	characteristic
311	C₂³	Q₈×Dic₁₉	1	2	yes	—
312	C₂³	#10597394	1	2	yes	—
313	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
351	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
352	C₂×C₄	#10597291	1	2	yes	—
353	C₂×C₄	#10597390	1	1	yes	characteristic
354	C₂×C₄	#10597392	1	2	yes	—
355	C₂×C₄	#10597393	1	1	yes	characteristic
356	C₈	—	76	4	no	—
357	C₈	—	152	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	#11926451	1	1	yes	characteristic
367	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
368	C₂²	#11926511	1	1	yes	characteristic
369	C₂²	C₂×#10597291	1	1	yes	characteristic
370	C₂²	#11926518	1	1	yes	characteristic
371	C₂²	#11926528	1	1	yes	characteristic
372	C₂²	#11926528	1	1	yes	characteristic
373	C₂²	Q₈×C₁₉⋊C₈	1	2	yes	—
374	C₂²	#11926675	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	1	no	—
386	C₂	—	2	2	no	—
387	C₂	—	2	2	no	—
388	C₂	#14561949	1	1	yes	characteristic
389	C₂	#14561953	1	1	yes	characteristic
390	C₂	#14561983	1	1	yes	characteristic
391	C₂	#14562004	1	1	yes	characteristic
392	C₂	#14564572	1	1	yes	characteristic
393	C₂	#14564621	1	1	yes	characteristic
394	C₂	#14564629	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#387	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#387	D₁₉
hypocenter	C₁₉	#9880
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#387

Complements

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

N	H ≅ G/N	type
36. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
235. C₂×C₄⋊C₄	C₁₉⋊C₈	semidirect
254. C₁₉	#9880	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₄×C₂²⋊(C₁₉⋊C₈)	2
#14561478	2
C₂×C₁₉×#387	2
#9880	19