Subgroups — C₁₉×#9564 #18015523

Order 4864.

466 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#106	—	2	1	no	—
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#102	—	2	1	no	—
14	C₂×C₁₉×#102	—	2	1	no	—
15	C₂×C₁₉×#102	—	2	1	no	—
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	—	2	1	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#340	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#331	C₄	1	4	yes	complemented
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₁₉×#127	—	2	1	no	—
33	C₁₉×#127	—	2	1	no	—
34	C₁₉×#127	—	2	1	no	—
35	C₁₉×#127	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₁₉×#106	—	4	2	no	—
44	C₁₉×C₄⋊C₈	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
49	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
50	C₁₉×#102	—	4	2	no	—
51	C₁₉×#102	—	4	2	no	—
52	C₁₉×#102	—	4	2	no	—
53	C₁₉×#102	—	4	2	no	—
54	C₄×C₈×C₁₉	—	2	1	no	—
55	C₄×C₈×C₁₉	—	2	1	no	—
56	C₄×C₈×C₁₉	—	4	2	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₂⁴×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	—	2	2	no	—
61	C₂×D₄×C₁₉	—	2	2	no	—
62	C₂×D₄×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	—	4	1	no	—
64	C₂×D₄×C₁₉	—	4	1	no	—
65	C₂×D₄×C₁₉	—	4	1	no	—
66	C₂×D₄×C₁₉	—	4	1	no	—
67	C₂×D₄×C₁₉	—	4	1	no	—
68	C₂×D₄×C₁₉	—	4	1	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	4	1	no	—
71	C₂×D₄×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	8	1	no	—
74	C₂×D₄×C₁₉	—	8	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂×C₈×C₁₉	—	2	1	no	—
82	C₂×C₈×C₁₉	—	2	1	no	—
83	C₂×C₈×C₁₉	—	2	2	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	1	no	—
86	C₂×C₈×C₁₉	—	2	1	no	—
87	C₂×C₈×C₁₉	—	2	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	8	1	no	—
103	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
104	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	#9564	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₉	—	4	2	no	—
113	C₂³×C₁₉	—	8	1	no	—
114	C₂³×C₁₉	—	8	1	no	—
115	C₂³×C₁₉	—	8	1	no	—
116	C₂³×C₁₉	—	8	1	no	—
117	C₂³×C₁₉	—	8	1	no	—
118	C₂³×C₁₉	—	8	1	no	—
119	C₂³×C₁₉	#121	1	1	yes	characteristic
120	D₄×C₁₉	—	4	2	no	—
121	D₄×C₁₉	—	4	2	no	—
122	D₄×C₁₉	—	4	2	no	—
123	D₄×C₁₉	—	4	2	no	—
124	D₄×C₁₉	—	8	2	no	—
125	D₄×C₁₉	—	8	2	no	—
126	D₄×C₁₉	—	8	1	no	—
127	D₄×C₁₉	—	8	1	no	—
128	D₄×C₁₉	—	8	1	no	—
129	D₄×C₁₉	—	8	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	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	1	no	—
141	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₈×C₁₉	—	2	2	no	—
156	C₈×C₁₉	—	4	2	no	—
157	C₈×C₁₉	—	4	2	no	—
158	C₈×C₁₉	—	4	1	no	—
159	C₈×C₁₉	—	8	1	no	—
160	#1982	C₂×C₁₉	1	1	yes	characteristic
161	#1957	C₂×C₁₉	1	1	yes	characteristic
162	#1948	C₂×C₁₉	1	1	yes	characteristic, complemented
163	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
164	C₂×#331	C₂×C₁₉	1	1	yes	characteristic
165	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#1277	C₂×C₁₉	1	1	yes	characteristic, complemented
167	C₂²×C₁₉	—	8	2	no	—
168	C₂²×C₁₉	—	8	2	no	—
169	C₂²×C₁₉	—	8	2	no	—
170	C₂²×C₁₉	—	16	1	no	—
171	C₂²×C₁₉	—	16	1	no	—
172	C₂²×C₁₉	—	16	1	no	—
173	C₂²×C₁₉	—	16	1	no	—
174	C₂²×C₁₉	#388	1	1	yes	characteristic
175	C₂²×C₁₉	#460	1	1	yes	characteristic
176	C₂²×C₁₉	#463	1	1	yes	characteristic
177	C₂²×C₁₉	#465	1	1	yes	characteristic
178	C₂²×C₁₉	#466	1	1	yes	characteristic
179	C₂²×C₁₉	#471	1	1	yes	characteristic
180	C₂²×C₁₉	#472	1	1	yes	characteristic
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	4	2	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	16	1	no	—
186	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
187	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
188	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
189	C₄×C₁₉	#442	1	1	yes	characteristic
190	C₄×C₁₉	#481	1	1	yes	characteristic
191	C₄×C₁₉	#482	1	1	yes	characteristic
192	C₄×C₁₉	#486	1	1	yes	characteristic
193	C₄×C₁₉	#488	1	1	yes	characteristic
194	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×#106	—	2	1	no	—
196	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#102	—	2	1	no	—
200	C₂×#102	—	2	1	no	—
201	C₂×#102	—	2	1	no	—
202	C₂×#102	—	2	1	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
205	#384	C₂²×C₁₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
207	#340	—	2	1	no	—
208	#336	—	2	1	no	—
209	#331	C₄×C₁₉	1	4	yes	complemented
210	C₂×C₁₉	—	16	2	no	—
211	C₂×C₁₉	#1666	1	1	yes	characteristic
212	C₂×C₁₉	#1668	1	1	yes	characteristic
213	C₂×C₁₉	#1677	1	1	yes	characteristic
214	C₂×C₁₉	#1681	1	1	yes	characteristic
215	C₂×C₁₉	#1926	1	1	yes	characteristic
216	C₂×C₁₉	#1931	1	1	yes	characteristic
217	C₂×C₁₉	#1934	1	1	yes	characteristic
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
225	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
226	#127	—	2	1	no	—
227	#127	—	2	1	no	—
228	#127	—	2	1	no	—
229	#127	C₂×C₄×C₁₉	1	2	yes	—
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	D₄×C₁₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
237	#106	—	4	2	no	—
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
243	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
244	#102	—	4	2	no	—
245	#102	—	4	2	no	—
246	#102	—	4	2	no	—
247	#102	—	4	2	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	4	2	no	—
251	#95	—	2	1	no	—
252	C₁₉	#9564	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	4	1	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	4	1	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	—	4	1	no	—
260	C₂×D₄	—	4	1	no	—
261	C₂×D₄	—	4	1	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	8	1	no	—
269	C₂×D₄	—	8	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
275	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	8	1	no	—
298	C₄⋊C₄	D₈×C₁₉	1	2	yes	—
299	C₄⋊C₄	SD₁₆×C₁₉	1	2	yes	—
300	C₄²	—	4	1	no	—
301	C₄²	—	4	1	no	—
302	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
303	C₄²	#41×C₁₉	1	1	yes	characteristic
304	C₄²	#41×C₁₉	1	1	yes	characteristic
305	C₄²	#41×C₁₉	1	1	yes	characteristic
306	C₂³	—	4	2	no	—
307	C₂³	—	8	1	no	—
308	C₂³	—	8	1	no	—
309	C₂³	—	8	1	no	—
310	C₂³	—	8	1	no	—
311	C₂³	—	8	1	no	—
312	C₂³	—	8	1	no	—
313	C₂³	C₁₉×#121	1	1	yes	characteristic
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	8	2	no	—
319	D₄	—	8	2	no	—
320	D₄	—	8	1	no	—
321	D₄	—	8	1	no	—
322	D₄	—	8	1	no	—
323	D₄	—	8	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
336	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
337	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
339	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
340	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
341	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
342	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
344	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
345	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
346	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
347	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	1	no	—
353	C₈	—	8	1	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	16	1	no	—
358	C₂²	—	16	1	no	—
359	C₂²	—	16	1	no	—
360	C₂²	—	16	1	no	—
361	C₂²	C₁₉×#388	1	1	yes	characteristic
362	C₂²	C₁₉×#460	1	1	yes	characteristic
363	C₂²	C₁₉×#463	1	1	yes	characteristic
364	C₂²	C₁₉×#465	1	1	yes	characteristic
365	C₂²	C₁₉×#466	1	1	yes	characteristic
366	C₂²	C₁₉×#471	1	1	yes	characteristic
367	C₂²	C₁₉×#472	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	16	1	no	—
373	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
374	C₄	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
375	C₄	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
376	C₄	C₁₉×#442	1	1	yes	characteristic
377	C₄	C₁₉×#481	1	1	yes	characteristic
378	C₄	C₁₉×#482	1	1	yes	characteristic
379	C₄	C₁₉×#486	1	1	yes	characteristic
380	C₄	C₁₉×#488	1	1	yes	characteristic
381	C₂	—	16	2	no	—
382	C₂	C₁₉×#1666	1	1	yes	characteristic
383	C₂	C₁₉×#1668	1	1	yes	characteristic
384	C₂	C₁₉×#1677	1	1	yes	characteristic
385	C₂	C₁₉×#1681	1	1	yes	characteristic
386	C₂	C₁₉×#1926	1	1	yes	characteristic
387	C₂	C₁₉×#1931	1	1	yes	characteristic
388	C₂	C₁₉×#1934	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1948	C₂	semidirect
4. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
6. C₁₉×#1296	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
23. C₁₉×#331	C₄	semidirect
111. #9564	C₁₉	direct (N × H)
162. #1948	C₂×C₁₉	semidirect
163. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
165. #1296	C₂×C₁₉	semidirect
166. #1277	C₂×C₁₉	semidirect
209. #331	C₄×C₁₉	semidirect
252. C₁₉	#9564	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×#1982	2
C₁₉×#1957	2
C₁₉×#1948	2
C₈×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#331	2
C₁₉×#1296	2
C₁₉×#1277	2
#9564	19

Subgroups — C19×#9564 #18015523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9564 #18015523