Subgroups — C₁₉×#9885 #18015844

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1294	C₂	1	4	yes	maximal
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
6	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	—	2	1	no	—
11	C₁₉×#391	—	2	1	no	—
12	C₁₉×#389	—	2	1	no	—
13	C₁₉×#389	C₄	1	2	yes	complemented
14	C₁₉×#384	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#380	—	2	1	no	—
16	C₁₉×#380	C₂²	1	2	yes	—
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	C₂²	1	2	yes	—
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	4	2	no	—
27	C₁₉×C₂²⋊Q₈	—	4	2	no	—
28	C₁₉×C₂²⋊Q₈	—	4	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄²×C₁₉	—	4	2	no	—
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×C₂²⋊C₈	—	2	2	no	—
45	C₁₉×C₂²⋊C₈	Q₈	1	4	yes	complemented
46	C₄×C₈×C₁₉	—	4	2	no	—
47	C₁₉×#95	—	2	2	no	—
48	C₁₉×#95	—	2	2	no	—
49	C₁₉×#95	—	2	4	no	—
50	C₁₉×#95	—	4	2	no	—
51	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	4	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	4	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	D₈	1	2	yes	—
75	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₉	#41	1	2	yes	—
82	C₂×C₈×C₁₉	—	2	4	no	—
83	C₂×C₈×C₁₉	—	4	2	no	—
84	C₂×C₈×C₁₉	—	4	2	no	—
85	C₄⋊C₄×C₁₉	—	4	2	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	4	2	no	—
88	C₄⋊C₄×C₁₉	—	4	8	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄⋊C₄×C₁₉	—	4	4	no	—
92	C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₂²⋊C₄×C₁₉	—	4	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	—	4	1	no	—
97	C₄²×C₁₉	—	4	1	no	—
98	#9885	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	—	2	1	no	—
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₁₉	#124	1	1	yes	characteristic
105	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
106	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
107	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
110	Q₈×C₁₉	—	8	4	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
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	4	no	—
122	C₂×C₄×C₁₉	—	2	4	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	4	no	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	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	—	8	2	no	—
137	C₂×C₄×C₁₉	—	8	2	no	—
138	C₂×C₄×C₁₉	—	8	2	no	—
139	C₂×C₄×C₁₉	—	8	2	no	—
140	C₂×C₄×C₁₉	#99	1	2	yes	—
141	C₂×C₄×C₁₉	#102	1	2	yes	—
142	C₂×C₄×C₁₉	#102	1	2	yes	—
143	C₂×C₄×C₁₉	#103	1	2	yes	—
144	C₂×C₄×C₁₉	#103	1	2	yes	—
145	C₂×C₄×C₁₉	#104	1	2	yes	—
146	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
147	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
148	C₈×C₁₉	—	4	4	no	—
149	#2857	C₂×C₁₉	1	1	yes	characteristic
150	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
151	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
152	#1294	C₂×C₁₉	1	4	yes	—
153	C₂²×C₁₉	—	2	1	no	—
154	C₂²×C₁₉	—	2	1	no	—
155	C₂²×C₁₉	—	2	1	no	—
156	C₂²×C₁₉	—	2	1	no	—
157	C₂²×C₁₉	—	2	1	no	—
158	C₂²×C₁₉	—	2	1	no	—
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	#391	1	1	yes	characteristic
166	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
167	C₂²×C₁₉	#410	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
169	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
170	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
171	C₂²×C₁₉	#421	1	1	yes	characteristic
172	C₂²×C₁₉	#486	1	1	yes	characteristic
173	C₂²×C₁₉	#487	1	1	yes	characteristic
174	C₂²×C₁₉	#498	1	1	yes	characteristic
175	C₂²×C₁₉	#500	1	1	yes	characteristic
176	C₄×C₁₉	—	2	2	no	—
177	C₄×C₁₉	—	2	2	no	—
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	8	4	no	—
182	C₄×C₁₉	—	8	2	no	—
183	C₄×C₁₉	—	8	2	no	—
184	C₄×C₁₉	#327	1	4	yes	—
185	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊Q₈	—	2	1	no	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
189	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
190	C₂×C₄×C₈	—	2	1	no	—
191	#391	—	2	1	no	—
192	#389	—	2	1	no	—
193	#389	C₄×C₁₉	1	2	yes	complemented
194	#384	C₄×C₁₉	1	1	yes	characteristic, complemented
195	#380	—	2	1	no	—
196	#380	C₂²×C₁₉	1	2	yes	—
197	C₂×#95	—	2	1	no	—
198	C₂×#95	C₂²×C₁₉	1	2	yes	—
199	#336	—	2	1	no	—
200	C₂×C₁₉	—	2	1	no	—
201	C₂×C₁₉	—	2	1	no	—
202	C₂×C₁₉	—	2	1	no	—
203	C₂×C₁₉	—	2	1	no	—
204	C₂×C₁₉	C₂×#327	1	1	yes	characteristic
205	C₂×C₁₉	#1503	1	1	yes	characteristic
206	C₂×C₁₉	#1517	1	1	yes	characteristic
207	C₂×C₁₉	#1520	1	1	yes	characteristic
208	C₂×C₁₉	#1986	1	1	yes	characteristic
209	C₂×C₁₉	#1990	1	1	yes	characteristic
210	C₂×C₁₉	#1996	1	1	yes	characteristic
211	C₂²×Q₈	—	2	1	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₄⋊Q₈	—	4	2	no	—
218	C₂²⋊Q₈	—	4	2	no	—
219	C₂²⋊Q₈	—	4	2	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	4	2	no	—
226	C₂×C₄⋊C₄	—	4	2	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₄²	—	4	2	no	—
231	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	Q₈×C₁₉	1	4	yes	complemented
237	C₄×C₈	—	4	2	no	—
238	#95	—	2	2	no	—
239	#95	—	2	2	no	—
240	#95	—	2	4	no	—
241	#95	—	4	2	no	—
242	C₁₉	#9885	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
244	C₂×Q₈	—	4	2	no	—
245	C₂×Q₈	—	4	2	no	—
246	C₂×Q₈	—	4	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	—	4	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	D₈×C₁₉	1	2	yes	—
267	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
268	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
269	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
273	C₂²×C₄	#41×C₁₉	1	2	yes	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	4	2	no	—
276	C₂×C₈	—	4	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	8	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₂²⋊C₄	—	4	2	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	4	1	no	—
289	C₄²	—	4	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
295	C₂³	C₁₉×#124	1	1	yes	characteristic
296	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
297	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
298	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
299	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
300	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
301	Q₈	—	8	4	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₁₉×#99	1	2	yes	—
332	C₂×C₄	C₁₉×#102	1	2	yes	—
333	C₂×C₄	C₁₉×#102	1	2	yes	—
334	C₂×C₄	C₁₉×#103	1	2	yes	—
335	C₂×C₄	C₁₉×#103	1	2	yes	—
336	C₂×C₄	C₁₉×#104	1	2	yes	—
337	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
338	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
339	C₈	—	4	4	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	C₁₉×#391	1	1	yes	characteristic
353	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
354	C₂²	C₁₉×#410	1	1	yes	characteristic
355	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
356	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
357	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
358	C₂²	C₁₉×#421	1	1	yes	characteristic
359	C₂²	C₁₉×#486	1	1	yes	characteristic
360	C₂²	C₁₉×#487	1	1	yes	characteristic
361	C₂²	C₁₉×#498	1	1	yes	characteristic
362	C₂²	C₁₉×#500	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	8	4	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	C₁₉×#327	1	4	yes	—
372	C₂	—	2	1	no	—
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	C₂×C₁₉×#327	1	1	yes	characteristic
377	C₂	C₁₉×#1503	1	1	yes	characteristic
378	C₂	C₁₉×#1517	1	1	yes	characteristic
379	C₂	C₁₉×#1520	1	1	yes	characteristic
380	C₂	C₁₉×#1986	1	1	yes	characteristic
381	C₂	C₁₉×#1990	1	1	yes	characteristic
382	C₂	C₁₉×#1996	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
13. C₁₉×#389	C₄	semidirect
14. C₁₉×#384	C₄	semidirect
45. C₁₉×C₂²⋊C₈	Q₈	semidirect
98. #9885	C₁₉	direct (N × H)
185. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
193. #389	C₄×C₁₉	semidirect
194. #384	C₄×C₁₉	semidirect
236. C₂²⋊C₈	Q₈×C₁₉	semidirect
242. C₁₉	#9885	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2857	2
C₄×C₁₉×C₂²⋊C₈	2
C₁₉×C₄⋊#95	2
C₁₉×#1294	2
#9885	19

Subgroups — C19×#9885 #18015844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9885 #18015844