Subgroups — C₁₉×#9055 #18015014

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#131	—	2	1	no	—
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₂²	1	1	yes	characteristic
11	C₁₉×#498	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#492	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#487	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#465	—	2	2	no	—
16	C₄×SD₁₆×C₁₉	—	2	2	no	—
17	C₁₉×#436	—	2	1	no	—
18	C₁₉×#435	—	2	2	no	—
19	C₈×D₄×C₁₉	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×#408	—	2	1	no	—
23	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#339	—	2	1	no	—
27	C₁₉×#339	—	2	1	no	—
28	C₁₉×#327	—	2	2	no	—
29	C₁₉×Q₈⋊C₈	—	2	1	no	—
30	C₁₉×Q₈⋊C₈	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×SD₁₆×C₁₉	—	2	2	no	—
33	C₁₉×#131	—	4	2	no	—
34	C₁₉×#131	—	4	2	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
43	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
45	C₁₉×#125	—	2	1	no	—
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	D₄	1	2	yes	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	D₄	1	2	yes	—
55	C₁₉×#117	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#106	—	2	2	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
64	C₁₉×#103	—	2	2	no	—
65	C₁₉×#102	—	2	2	no	—
66	C₁₉×C₂²⋊C₈	—	2	2	no	—
67	C₁₉×C₂²⋊C₈	—	2	2	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×#97	—	2	1	no	—
70	C₄×C₈×C₁₉	—	2	1	no	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₄×C₈×C₁₉	—	2	1	no	—
73	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₁₉×#95	—	2	1	no	—
76	#41×C₁₉	—	4	1	no	—
77	#41×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	SD₁₆×C₁₉	—	4	4	no	—
93	M₁₆×C₁₉	—	2	1	no	—
94	M₁₆×C₁₉	—	2	1	no	—
95	M₁₆×C₁₉	—	2	1	no	—
96	M₁₆×C₁₉	—	4	4	no	—
97	M₁₆×C₁₉	SD₁₆	1	2	yes	complemented
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	—	2	1	no	—
100	C₂×C₈×C₁₉	—	2	1	no	—
101	C₂×C₈×C₁₉	—	2	1	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	4	2	no	—
105	C₂×C₈×C₁₉	—	4	4	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₂²⋊C₄×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	#41	1	1	yes	characteristic
129	#9055	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	#121	1	1	yes	characteristic
132	Q₈×C₁₉	—	4	2	no	—
133	Q₈×C₁₉	—	4	1	no	—
134	Q₈×C₁₉	—	4	1	no	—
135	Q₈×C₁₉	—	4	1	no	—
136	Q₈×C₁₉	—	4	1	no	—
137	D₄×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	4	2	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	1	no	—
141	D₄×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	1	no	—
143	D₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	8	1	no	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
165	C₈×C₁₉	—	2	2	no	—
166	C₈×C₁₉	—	2	2	no	—
167	C₈×C₁₉	—	4	1	no	—
168	C₈×C₁₉	—	4	1	no	—
169	C₈×C₁₉	—	4	1	no	—
170	C₈×C₁₉	—	4	1	no	—
171	C₈×C₁₉	—	8	1	no	—
172	#3167	C₂×C₁₉	1	1	yes	characteristic
173	#2935	C₂×C₁₉	1	1	yes	characteristic
174	#1986	C₂×C₁₉	1	1	yes	characteristic, complemented
175	#1502	C₂×C₁₉	1	1	yes	characteristic
176	#1481	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#1279	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#1278	C₂×C₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	2	no	—
184	C₂²×C₁₉	#386	1	1	yes	characteristic
185	C₂²×C₁₉	#461	1	1	yes	characteristic
186	C₂²×C₁₉	#463	1	1	yes	characteristic
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	8	2	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	—	8	1	no	—
194	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
195	C₄×C₁₉	#440	1	1	yes	characteristic
196	C₄×C₁₉	#443	1	1	yes	characteristic
197	C₄×C₁₉	#444	1	1	yes	characteristic
198	C₄×C₁₉	#450	1	1	yes	characteristic
199	C₄×C₁₉	#452	1	1	yes	characteristic
200	C₂×#131	—	2	1	no	—
201	#533	C₂²×C₁₉	1	1	yes	characteristic
202	#532	C₂²×C₁₉	1	1	yes	characteristic
203	#498	C₄×C₁₉	1	1	yes	characteristic, complemented
204	#492	C₄×C₁₉	1	1	yes	characteristic, complemented
205	#487	C₄×C₁₉	1	1	yes	characteristic, complemented
206	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
207	#465	—	2	2	no	—
208	C₄×SD₁₆	—	2	2	no	—
209	#436	—	2	1	no	—
210	#435	—	2	2	no	—
211	C₈×D₄	—	2	1	no	—
212	#431	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
214	#408	—	2	1	no	—
215	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	#339	—	2	1	no	—
219	#339	—	2	1	no	—
220	#327	—	2	2	no	—
221	Q₈⋊C₈	—	2	1	no	—
222	Q₈⋊C₈	—	2	1	no	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	8	2	no	—
226	C₂×C₁₉	#1876	1	1	yes	characteristic
227	C₂×C₁₉	#1877	1	1	yes	characteristic
228	C₂×C₁₉	#1884	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	#131	—	4	2	no	—
232	#131	—	4	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
235	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
240	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
242	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
243	#125	—	2	1	no	—
244	#124	—	2	1	no	—
245	C₂²⋊Q₈	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	#121	—	2	1	no	—
248	#121	D₄×C₁₉	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	D₄×C₁₉	1	2	yes	—
253	#117	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
257	#106	—	2	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
261	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
262	#103	—	2	2	no	—
263	#102	—	2	2	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	#97	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
273	#95	—	2	1	no	—
274	C₁₉	#9055	1	1	yes	characteristic, direct product factor, Sylow
275	#41	—	4	1	no	—
276	#41	—	4	1	no	—
277	#41	—	4	1	no	—
278	#41	—	4	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
291	SD₁₆	—	4	4	no	—
292	M₁₆	—	2	1	no	—
293	M₁₆	—	2	1	no	—
294	M₁₆	—	2	1	no	—
295	M₁₆	—	4	4	no	—
296	M₁₆	SD₁₆×C₁₉	1	2	yes	complemented
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₄²	#41×C₁₉	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₁₉×#121	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	Q₈	—	4	1	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
357	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
358	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
359	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
360	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
361	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	8	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	C₁₉×#386	1	1	yes	characteristic
376	C₂²	C₁₉×#461	1	1	yes	characteristic
377	C₂²	C₁₉×#463	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	1	no	—
384	C₄	—	8	1	no	—
385	C₄	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
386	C₄	C₁₉×#440	1	1	yes	characteristic
387	C₄	C₁₉×#443	1	1	yes	characteristic
388	C₄	C₁₉×#444	1	1	yes	characteristic
389	C₄	C₁₉×#450	1	1	yes	characteristic
390	C₄	C₁₉×#452	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	8	2	no	—
394	C₂	C₁₉×#1876	1	1	yes	characteristic
395	C₂	C₁₉×#1877	1	1	yes	characteristic
396	C₂	C₁₉×#1884	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1986	C₂	semidirect
5. C₁₉×#1481	C₂	semidirect
6. C₁₉×#1279	C₂	semidirect
7. C₁₉×#1278	C₂	semidirect
11. C₁₉×#498	C₄	semidirect
12. C₁₉×#492	C₄	semidirect
13. C₁₉×#487	C₄	semidirect
14. C₁₉×#486	C₄	semidirect
97. M₁₆×C₁₉	SD₁₆	semidirect
129. #9055	C₁₉	direct (N × H)
174. #1986	C₂×C₁₉	semidirect
176. #1481	C₂×C₁₉	semidirect
177. #1279	C₂×C₁₉	semidirect
178. #1278	C₂×C₁₉	semidirect
203. #498	C₄×C₁₉	semidirect
204. #492	C₄×C₁₉	semidirect
205. #487	C₄×C₁₉	semidirect
206. #486	C₄×C₁₉	semidirect
274. C₁₉	#9055	direct (N × H)
296. M₁₆	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3167	2
C₁₉×#2935	2
C₁₉×#1986	2
C₁₉×#1502	2
C₁₉×#1481	2
C₁₉×#1279	2
C₁₉×#1278	2
#9055	19

Subgroups — C19×#9055 #18015014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9055 #18015014