Subgroups — C₁₉×#23129 #18029088

Order 4864.

866 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2362	C₂	1	2	yes	maximal
3	C₁₉×#1933	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1918	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1878	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1873	C₂	1	2	yes	maximal
7	C₄×C₁₉×#103	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#117	C₂²	1	2	yes	—
15	C₁₉×#467	C₄	1	8	yes	complemented
16	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#391	C₂²	1	2	yes	—
23	C₁₉×#389	C₂²	1	2	yes	—
24	C₁₉×#388	—	2	2	no	—
25	C₁₉×#388	—	2	2	no	—
26	C₁₉×#387	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₁₉	—	4	2	no	—
39	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₉	—	4	2	no	—
41	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₁₉×C₂²⋊Q₈	—	2	4	no	—
46	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
47	C₄×Q₈×C₁₉	—	2	4	no	—
48	C₄×Q₈×C₁₉	—	4	2	no	—
49	C₁₉×#117	—	2	4	no	—
50	C₁₉×#117	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₄²×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	—	2	2	no	—
62	C₂×C₄²×C₁₉	—	2	2	no	—
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#107	C₂×C₄	1	4	yes	—
65	C₁₉×#103	—	2	4	no	—
66	C₁₉×#103	—	4	2	no	—
67	C₁₉×#103	C₂×C₄	1	8	yes	—
68	C₁₉×C₂²⋊C₈	—	2	2	no	—
69	C₄×C₈×C₁₉	—	4	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	2	no	—
72	C₁₉×#95	—	2	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	D₄	1	1	yes	characteristic
75	C₁₉×#95	D₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	#41	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
95	Q₁₆×C₁₉	—	4	4	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	4	4	no	—
102	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
104	C₄⋊C₄×C₁₉	—	2	8	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	4	4	no	—
110	C₄⋊C₄×C₁₉	—	4	4	no	—
111	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
112	C₄⋊C₄×C₁₉	#41	1	4	yes	—
113	C₂²⋊C₄×C₁₉	—	2	8	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	4	4	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	4	4	no	—
119	C₄²×C₁₉	—	4	4	no	—
120	C₄²×C₁₉	—	4	4	no	—
121	#23129	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	C₄×D₄	1	2	yes	—
127	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₁₉	—	2	4	no	—
129	Q₈×C₁₉	—	2	4	no	—
130	Q₈×C₁₉	—	4	2	no	—
131	Q₈×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	4	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	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₉	#135	1	4	yes	—
155	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
157	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
159	C₈×C₁₉	—	2	2	no	—
160	C₈×C₁₉	—	2	2	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₂×#467	C₂×C₁₉	1	1	yes	characteristic
163	#2362	C₂×C₁₉	1	2	yes	—
164	#1933	C₂×C₁₉	1	2	yes	complemented
165	#1918	C₂×C₁₉	1	2	yes	complemented
166	#1878	C₂×C₁₉	1	2	yes	complemented
167	#1873	C₂×C₁₉	1	2	yes	—
168	C₄×#103	C₂×C₁₉	1	2	yes	complemented
169	C₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
170	#1735	C₂×C₁₉	1	1	yes	characteristic
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂²×C₁₉	#546	1	2	yes	—
178	C₂²×C₁₉	C₂×#135	1	2	yes	—
179	C₂²×C₁₉	#578	1	1	yes	characteristic
180	C₂²×C₁₉	#578	1	1	yes	characteristic
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	4	no	—
183	C₄×C₁₉	—	4	4	no	—
184	C₄×C₁₉	—	4	4	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	4	4	no	—
187	C₄×C₁₉	—	8	2	no	—
188	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
189	C₄×C₁₉	#518	1	1	yes	characteristic
190	C₄×C₁₉	#553	1	2	yes	—
191	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
195	C₂×#117	C₂²×C₁₉	1	2	yes	—
196	#467	C₄×C₁₉	1	8	yes	complemented
197	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×#103	C₂²×C₁₉	1	2	yes	—
199	C₂×#103	C₂²×C₁₉	1	2	yes	—
200	C₂×#103	C₂²×C₁₉	1	2	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
203	#391	C₂²×C₁₉	1	2	yes	—
204	#389	C₂²×C₁₉	1	2	yes	—
205	#388	—	2	2	no	—
206	#388	—	2	2	no	—
207	#387	—	2	2	no	—
208	C₄×C₄⋊C₄	—	2	2	no	—
209	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
210	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
211	#340	C₂²×C₁₉	1	2	yes	—
212	#340	C₂²×C₁₉	1	2	yes	—
213	#340	C₂²×C₁₉	1	2	yes	—
214	#340	C₂²×C₁₉	1	1	yes	characteristic
215	#340	C₂²×C₁₉	1	1	yes	characteristic
216	#336	C₂²×C₁₉	1	2	yes	—
217	C₂×C₁₉	—	4	2	no	—
218	C₂×C₁₉	#2364	1	1	yes	characteristic
219	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
220	C₂×C₁₉	#2950	1	1	yes	characteristic
221	C₂×C₁₉	#3300	1	2	yes	—
222	C₂×C₁₉	#3302	1	2	yes	—
223	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
225	C₂×Q₁₆	—	4	2	no	—
226	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
227	C₂²×C₈	—	4	2	no	—
228	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
229	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
232	C₂²⋊Q₈	—	2	4	no	—
233	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	4	2	no	—
236	#117	—	2	4	no	—
237	#117	—	4	2	no	—
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×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
251	#107	C₂×C₄×C₁₉	1	4	yes	—
252	#103	—	2	4	no	—
253	#103	—	4	2	no	—
254	#103	C₂×C₄×C₁₉	1	8	yes	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₄×C₈	—	4	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	D₄×C₁₉	1	1	yes	characteristic
262	#95	D₄×C₁₉	1	1	yes	characteristic
263	C₁₉	#23129	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
281	C₂²×C₄	#41×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
283	Q₁₆	—	4	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
291	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
300	C₄⋊C₄	#41×C₁₉	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	4	no	—
307	C₄²	—	4	4	no	—
308	C₄²	—	4	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	C₄×D₄×C₁₉	1	2	yes	—
314	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	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	C₄×D₄×C₁₉	1	2	yes	—
341	C₂×C₄	C₁₉×#135	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
344	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
345	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
355	C₂²	C₁₉×#546	1	2	yes	—
356	C₂²	C₂×C₁₉×#135	1	2	yes	—
357	C₂²	C₁₉×#578	1	1	yes	characteristic
358	C₂²	C₁₉×#578	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	4	no	—
365	C₄	—	8	2	no	—
366	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
367	C₄	C₁₉×#518	1	1	yes	characteristic
368	C₄	C₁₉×#553	1	2	yes	—
369	C₂	—	4	2	no	—
370	C₂	C₁₉×#2364	1	1	yes	characteristic
371	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
372	C₂	C₁₉×#2950	1	1	yes	characteristic
373	C₂	C₁₉×#3300	1	2	yes	—
374	C₂	C₁₉×#3302	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1933	C₂	semidirect
4. C₁₉×#1918	C₂	semidirect
5. C₁₉×#1878	C₂	semidirect
7. C₄×C₁₉×#103	C₂	semidirect
15. C₁₉×#467	C₄	semidirect
121. #23129	C₁₉	direct (N × H)
164. #1933	C₂×C₁₉	semidirect
165. #1918	C₂×C₁₉	semidirect
166. #1878	C₂×C₁₉	semidirect
168. C₄×#103	C₂×C₁₉	semidirect
196. #467	C₄×C₁₉	semidirect
263. C₁₉	#23129	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×#467	2
C₁₉×#2362	2
C₁₉×#1933	2
C₁₉×#1918	2
C₁₉×#1878	2
C₁₉×#1873	2
C₄×C₁₉×#103	2
C₈×C₂²⋊C₄×C₁₉	2
C₁₉×#1735	2
#23129	19

Subgroups — C19×#23129 #18029088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23129 #18029088