Subgroups — C₁₉×#21287 #18027246

Order 4864.

798 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2295	C₂	1	2	yes	maximal
3	C₁₉×#1971	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1944	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1935	C₂	1	2	yes	maximal
8	C₁₉×#1933	C₂	1	2	yes	maximal
9	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1763	C₂	1	2	yes	maximal
11	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#441	C₄	1	8	yes	complemented
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#391	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#387	—	2	2	no	—
32	C₁₉×#387	—	2	2	no	—
33	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#376	—	2	2	no	—
36	C₄³×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₁₉	—	2	2	no	—
42	C₂×Q₁₆×C₁₉	—	2	2	no	—
43	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₄×Q₈×C₁₉	—	2	4	no	—
49	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	2	2	no	—
58	C₂×C₄²×C₁₉	D₄	1	2	yes	—
59	C₂×C₄²×C₁₉	D₄	1	2	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#107	—	2	2	no	—
64	C₁₉×#106	—	2	2	no	—
65	C₁₉×#106	C₂×C₄	1	4	yes	—
66	C₁₉×#103	—	2	4	no	—
67	C₁₉×#103	—	2	4	no	—
68	C₁₉×#103	C₂×C₄	1	8	yes	—
69	C₁₉×#97	—	2	2	no	—
70	C₁₉×#97	—	2	2	no	—
71	C₁₉×#97	—	2	2	no	—
72	C₁₉×#97	C₂×C₄	1	4	yes	—
73	C₄×C₈×C₁₉	—	2	2	no	—
74	C₄×C₈×C₁₉	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
97	Q₁₆×C₁₉	—	2	8	no	—
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	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₉	#41	1	2	yes	—
107	C₂×C₈×C₁₉	#41	1	2	yes	—
108	C₂×C₈×C₁₉	#41	1	2	yes	—
109	C₂×C₈×C₁₉	#41	1	2	yes	—
110	C₄⋊C₄×C₁₉	—	2	8	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	4	4	no	—
118	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
119	C₄²×C₁₉	—	2	8	no	—
120	C₄²×C₁₉	—	2	4	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	2	1	no	—
125	C₄²×C₁₉	—	4	2	no	—
126	C₄²×C₁₉	—	4	4	no	—
127	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₉	#41	1	2	yes	—
129	#21287	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₁₉	—	2	4	no	—
132	Q₈×C₁₉	—	2	4	no	—
133	Q₈×C₁₉	—	4	2	no	—
134	Q₈×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	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	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
156	C₂×C₄×C₁₉	#137	1	4	yes	—
157	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
163	C₈×C₁₉	—	2	2	no	—
164	C₈×C₁₉	—	2	2	no	—
165	C₈×C₁₉	—	2	2	no	—
166	C₈×C₁₉	#117	1	4	yes	—
167	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
168	#2295	C₂×C₁₉	1	2	yes	—
169	#1971	C₂×C₁₉	1	1	yes	characteristic
170	#1969	C₂×C₁₉	1	1	yes	characteristic
171	#1944	C₂×C₁₉	1	1	yes	characteristic
172	#1941	C₂×C₁₉	1	1	yes	characteristic
173	#1935	C₂×C₁₉	1	2	yes	—
174	#1933	C₂×C₁₉	1	2	yes	—
175	#1776	C₂×C₁₉	1	1	yes	characteristic
176	#1763	C₂×C₁₉	1	2	yes	—
177	C₄×#97	C₂×C₁₉	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₁₉	#532	1	1	yes	characteristic
180	C₂²×C₁₉	#532	1	1	yes	characteristic
181	C₂²×C₁₉	C₂×#137	1	2	yes	—
182	C₂²×C₁₉	#575	1	2	yes	—
183	C₄×C₁₉	—	2	4	no	—
184	C₄×C₁₉	—	2	4	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	4	no	—
188	C₄×C₁₉	—	4	4	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	—	8	2	no	—
191	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
192	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
193	C₄×C₁₉	#529	1	1	yes	characteristic
194	C₄×C₁₉	#529	1	1	yes	characteristic
195	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
197	#441	C₄×C₁₉	1	8	yes	complemented
198	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
201	C₂×#103	C₂²×C₁₉	1	2	yes	—
202	C₂×#103	C₂²×C₁₉	1	2	yes	—
203	C₂×#103	C₂²×C₁₉	1	2	yes	—
204	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
210	#391	C₂²×C₁₉	1	2	yes	—
211	#391	C₂²×C₁₉	1	2	yes	—
212	#389	C₂²×C₁₉	1	2	yes	—
213	#389	C₂²×C₁₉	1	2	yes	—
214	#387	—	2	2	no	—
215	#387	—	2	2	no	—
216	C₄×C₄⋊C₄	—	2	2	no	—
217	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
218	#376	—	2	2	no	—
219	C₄³	C₂²×C₁₉	1	1	yes	characteristic
220	#340	C₂²×C₁₉	1	2	yes	—
221	#340	C₂²×C₁₉	1	2	yes	—
222	#340	C₂²×C₁₉	1	2	yes	—
223	C₂×C₁₉	#2293	1	1	yes	characteristic
224	C₂×C₁₉	C₄×#137	1	2	yes	—
225	C₂×C₁₉	#3181	1	2	yes	—
226	C₂×C₁₉	#3183	1	1	yes	characteristic
227	C₂×C₁₉	#3185	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
229	C₂×Q₁₆	—	2	2	no	—
230	C₂×Q₁₆	—	2	2	no	—
231	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
232	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	D₄×C₁₉	1	2	yes	—
247	C₂×C₄²	D₄×C₁₉	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
251	#107	—	2	2	no	—
252	#106	—	2	2	no	—
253	#106	C₂×C₄×C₁₉	1	4	yes	—
254	#103	—	2	4	no	—
255	#103	—	2	4	no	—
256	#103	C₂×C₄×C₁₉	1	8	yes	—
257	#97	—	2	2	no	—
258	#97	—	2	2	no	—
259	#97	—	2	2	no	—
260	#97	C₂×C₄×C₁₉	1	4	yes	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₁₉	#21287	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
286	Q₁₆	—	2	8	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
295	C₂×C₈	#41×C₁₉	1	2	yes	—
296	C₂×C₈	#41×C₁₉	1	2	yes	—
297	C₂×C₈	#41×C₁₉	1	2	yes	—
298	C₂×C₈	#41×C₁₉	1	2	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
308	C₄²	—	2	8	no	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	4	4	no	—
316	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
317	C₄²	#41×C₁₉	1	2	yes	—
318	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
319	Q₈	—	2	4	no	—
320	Q₈	—	2	4	no	—
321	Q₈	—	4	2	no	—
322	Q₈	—	4	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
344	C₂×C₄	C₁₉×#137	1	4	yes	—
345	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	2	2	no	—
353	C₈	—	2	2	no	—
354	C₈	C₁₉×#117	1	4	yes	—
355	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
356	C₂²	C₁₉×#532	1	1	yes	characteristic
357	C₂²	C₁₉×#532	1	1	yes	characteristic
358	C₂²	C₂×C₁₉×#137	1	2	yes	—
359	C₂²	C₁₉×#575	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	2	4	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	4	no	—
365	C₄	—	4	4	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	2	no	—
368	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
369	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
370	C₄	C₁₉×#529	1	1	yes	characteristic
371	C₄	C₁₉×#529	1	1	yes	characteristic
372	C₂	C₁₉×#2293	1	1	yes	characteristic
373	C₂	C₄×C₁₉×#137	1	2	yes	—
374	C₂	C₁₉×#3181	1	2	yes	—
375	C₂	C₁₉×#3183	1	1	yes	characteristic
376	C₂	C₁₉×#3185	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₉×#441	C₄	semidirect
129. #21287	C₁₉	direct (N × H)
197. #441	C₄×C₁₉	semidirect
270. C₁₉	#21287	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#441	2
C₁₉×#2295	2
C₁₉×#1971	2
C₁₉×#1969	2
C₁₉×#1944	2
C₁₉×#1941	2
C₁₉×#1935	2
C₁₉×#1933	2
C₁₉×#1776	2
C₁₉×#1763	2
C₄×C₁₉×#97	2
#21287	19

Subgroups — C19×#21287 #18027246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21287 #18027246