Subgroups — C₁₉×#19280 #18025239

Order 4864.

766 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×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3036	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1701	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1693	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1687	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
10	C₂²×M₁₆×C₁₉	—	2	1	no	—
11	C₁₉×#532	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
14	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#486	C₂²	1	2	yes	complemented
16	C₁₉×#466	—	2	1	no	—
17	C₁₉×#466	—	2	1	no	—
18	C₁₉×#463	—	2	4	no	—
19	C₁₉×#461	C₂²	1	4	yes	—
20	C₁₉×#459	C₂²	1	4	yes	—
21	C₄×D₈×C₁₉	—	2	1	no	—
22	C₄×D₈×C₁₉	—	2	1	no	—
23	C₁₉×#436	—	2	1	no	—
24	C₁₉×#436	—	2	1	no	—
25	C₁₉×#436	C₂²	1	2	yes	—
26	C₁₉×#436	C₂²	1	2	yes	—
27	C₁₉×#423	C₂²	1	2	yes	—
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#417	—	2	2	no	—
30	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#334	C₂²	1	2	yes	complemented
33	C₁₉×#334	C₂²	1	2	yes	complemented
34	C₁₉×#332	C₂²	1	4	yes	complemented
35	C₁₉×#331	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
40	C₂×SD₁₆×C₁₉	—	2	4	no	—
41	C₂×D₈×C₁₉	—	2	4	no	—
42	C₂×D₈×C₁₉	—	2	1	no	—
43	C₂×D₈×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	4	4	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
51	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
52	C₁₉×#127	C₂³	1	2	yes	—
53	C₁₉×#124	—	2	2	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	2	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	D₄	1	2	yes	—
61	C₄×D₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#107	—	2	1	no	—
66	C₁₉×#107	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	2	no	—
69	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
71	C₁₉×#103	—	2	4	no	—
72	C₁₉×#102	—	2	2	no	—
73	C₁₉×#102	—	2	2	no	—
74	C₁₉×#102	—	2	4	no	—
75	C₁₉×C₂²⋊C₈	—	2	2	no	—
76	C₁₉×C₂²⋊C₈	—	2	2	no	—
77	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂⁴×C₁₉	—	2	1	no	—
82	#41×C₁₉	—	4	4	no	—
83	#41×C₁₉	—	4	4	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	SD₁₆×C₁₉	—	4	8	no	—
102	D₈×C₁₉	—	4	2	no	—
103	D₈×C₁₉	—	4	8	no	—
104	D₈×C₁₉	—	4	2	no	—
105	M₁₆×C₁₉	—	4	4	no	—
106	M₁₆×C₁₉	—	4	4	no	—
107	M₁₆×C₁₉	—	4	4	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	4	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	2	no	—
113	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	#41	1	1	yes	characteristic
128	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
129	#19280	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	#121	1	1	yes	characteristic
136	Q₈×C₁₉	—	4	2	no	—
137	Q₈×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	2	4	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	8	4	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	4	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	—	8	4	no	—
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
160	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
163	C₈×C₁₉	—	2	1	no	—
164	C₈×C₁₉	—	2	1	no	—
165	C₈×C₁₉	—	2	1	no	—
166	C₈×C₁₉	—	4	2	no	—
167	C₈×C₁₉	—	4	4	no	—
168	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
169	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#3036	C₂×C₁₉	1	2	yes	complemented
171	C₂×#436	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#1701	C₂×C₁₉	1	4	yes	complemented
173	#1693	C₂×C₁₉	1	2	yes	complemented
174	#1687	C₂×C₁₉	1	2	yes	complemented
175	#1566	C₂×C₁₉	1	1	yes	characteristic, complemented
176	#1547	C₂×C₁₉	1	2	yes	complemented
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	4	2	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	—	8	4	no	—
183	C₂²×C₁₉	—	8	2	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	#469	1	2	yes	—
187	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	8	2	no	—
193	C₄×C₁₉	#469	1	2	yes	—
194	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
196	C₄×C₁₉	#575	1	1	yes	characteristic
197	C₂×AGL(1,ℤ/8)	—	2	2	no	—
198	C₂²×M₁₆	—	2	1	no	—
199	#532	C₂²×C₁₉	1	2	yes	—
200	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
201	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
202	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
203	#486	C₂²×C₁₉	1	2	yes	complemented
204	#466	—	2	1	no	—
205	#466	—	2	1	no	—
206	#463	—	2	4	no	—
207	#461	C₂²×C₁₉	1	4	yes	—
208	#459	C₂²×C₁₉	1	4	yes	—
209	C₄×D₈	—	2	1	no	—
210	C₄×D₈	—	2	1	no	—
211	#436	—	2	1	no	—
212	#436	—	2	1	no	—
213	#436	C₂²×C₁₉	1	2	yes	—
214	#436	C₂²×C₁₉	1	2	yes	—
215	#423	C₂²×C₁₉	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
217	#417	—	2	2	no	—
218	C₂×C₂²⋊C₈	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
220	#334	C₂²×C₁₉	1	2	yes	complemented
221	#334	C₂²×C₁₉	1	2	yes	complemented
222	#332	C₂²×C₁₉	1	4	yes	complemented
223	#331	C₂²×C₁₉	1	4	yes	complemented
224	C₂×C₁₉	—	2	2	no	—
225	C₂×C₁₉	—	8	2	no	—
226	C₂×C₁₉	—	16	2	no	—
227	C₂×C₁₉	#3036	1	1	yes	characteristic
228	C₂×C₁₉	C₂×#469	1	1	yes	characteristic
229	C₂×C₁₉	#3067	1	1	yes	characteristic
230	C₂×#41	—	2	2	no	—
231	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	AGL(1,ℤ/8)	—	4	8	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×D₈	—	2	4	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	4	4	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
244	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
246	#127	C₂³×C₁₉	1	2	yes	—
247	#124	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	D₄×C₁₉	1	2	yes	—
255	C₄×D₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
264	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
265	#103	—	2	4	no	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	—	2	4	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
272	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₁₉	#19280	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	2	1	no	—
277	#41	—	4	4	no	—
278	#41	—	4	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
296	SD₁₆	—	4	8	no	—
297	D₈	—	4	2	no	—
298	D₈	—	4	8	no	—
299	D₈	—	4	2	no	—
300	M₁₆	—	4	4	no	—
301	M₁₆	—	4	4	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₄²	#41×C₁₉	1	1	yes	characteristic
323	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	C₁₉×#121	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	D₄	—	2	4	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	8	2	no	—
339	D₄	—	8	4	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
351	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
352	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
353	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
354	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	4	no	—
362	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	complemented
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	C₁₉×#469	1	2	yes	—
373	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₁₉×#469	1	2	yes	—
380	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
382	C₄	C₁₉×#575	1	1	yes	characteristic
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₁₉×#3036	1	1	yes	characteristic
387	C₂	C₂×C₁₉×#469	1	1	yes	characteristic
388	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3169	C₂	semidirect
2. C₁₉×#3036	C₂	semidirect
3. C₂×C₁₉×#436	C₂	semidirect
4. C₁₉×#1701	C₂	semidirect
5. C₁₉×#1693	C₂	semidirect
6. C₁₉×#1687	C₂	semidirect
7. C₁₉×#1566	C₂	semidirect
8. C₁₉×#1547	C₂	semidirect
13. C₁₉×#500	C₂²	semidirect
14. C₁₉×#493	C₂²	semidirect
15. C₁₉×#486	C₂²	semidirect
32. C₁₉×#334	C₂²	semidirect
33. C₁₉×#334	C₂²	semidirect
34. C₁₉×#332	C₂²	semidirect
35. C₁₉×#331	C₂²	semidirect
129. #19280	C₁₉	direct (N × H)
168. C₈×C₁₉	AGL(1,ℤ/8)	semidirect
169. #3169	C₂×C₁₉	semidirect
170. #3036	C₂×C₁₉	semidirect
171. C₂×#436	C₂×C₁₉	semidirect
172. #1701	C₂×C₁₉	semidirect
173. #1693	C₂×C₁₉	semidirect
174. #1687	C₂×C₁₉	semidirect
175. #1566	C₂×C₁₉	semidirect
176. #1547	C₂×C₁₉	semidirect
201. #500	C₂²×C₁₉	semidirect
202. #493	C₂²×C₁₉	semidirect
203. #486	C₂²×C₁₉	semidirect
220. #334	C₂²×C₁₉	semidirect
221. #334	C₂²×C₁₉	semidirect
222. #332	C₂²×C₁₉	semidirect
223. #331	C₂²×C₁₉	semidirect
275. C₁₉	#19280	direct (N × H)
362. C₈	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3169	2
C₁₉×#3036	2
C₂×C₁₉×#436	2
C₁₉×#1701	2
C₁₉×#1693	2
C₁₉×#1687	2
C₁₉×#1566	2
C₁₉×#1547	2
#19280	19

Subgroups — C19×#19280 #18025239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19280 #18025239