Subgroups — C₁₉×#21810 #18027769

Order 4864.

1990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1982	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1961	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1786	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₉	—	2	1	no	—
8	C₂³×D₄×C₁₉	—	2	1	no	—
9	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#127	—	2	1	no	—
11	C₂×C₁₉×#127	—	2	1	no	—
12	C₂×C₁₉×#127	—	2	4	no	—
13	C₂×C₁₉×#127	C₄	1	8	yes	complemented
14	C₂×C₁₉×#127	C₂²	1	2	yes	—
15	C₂×C₁₉×#127	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#432	—	2	4	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#102	C₂²	1	16	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#97	C₂²	1	2	yes	complemented
22	C₁₉×#383	—	2	1	no	—
23	C₁₉×#382	C₂²	1	2	yes	complemented
24	C₁₉×#381	—	2	1	no	—
25	C₁₉×#380	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
27	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₁₉×#376	—	2	1	no	—
29	C₂⁵×C₁₉	—	2	2	no	—
30	C₂²×D₄×C₁₉	—	2	8	no	—
31	C₂²×D₄×C₁₉	—	2	8	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	4	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	4	8	no	—
39	C₂²×D₄×C₁₉	—	4	8	no	—
40	C₂²×D₄×C₁₉	—	4	8	no	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
42	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
47	C₁₉×#127	—	2	8	no	—
48	C₁₉×#127	—	2	8	no	—
49	C₁₉×#127	—	2	4	no	—
50	C₁₉×#127	—	2	4	no	—
51	C₁₉×#127	C₂×C₄	1	8	yes	—
52	C₁₉×#127	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	D₄	1	4	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊C₈	—	2	4	no	—
63	C₁₉×#102	—	4	16	no	—
64	C₁₉×C₂²⋊C₈	—	2	4	no	—
65	C₁₉×#97	—	2	4	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₁₉×#95	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	8	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	4	8	no	—
73	C₂⁴×C₁₉	—	4	8	no	—
74	C₂⁴×C₁₉	—	4	8	no	—
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₁₉	—	2	8	no	—
77	C₂×D₄×C₁₉	—	2	8	no	—
78	C₂×D₄×C₁₉	—	2	8	no	—
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	2	8	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	16	no	—
83	C₂×D₄×C₁₉	—	4	16	no	—
84	C₂×D₄×C₁₉	—	4	8	no	—
85	C₂×D₄×C₁₉	—	4	8	no	—
86	C₂×D₄×C₁₉	—	4	8	no	—
87	C₂×D₄×C₁₉	—	4	8	no	—
88	C₂×D₄×C₁₉	—	4	32	no	—
89	C₂×D₄×C₁₉	—	4	16	no	—
90	C₂×D₄×C₁₉	—	4	32	no	—
91	C₂×D₄×C₁₉	—	4	8	no	—
92	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₉	—	2	4	no	—
108	C₂×C₈×C₁₉	—	2	8	no	—
109	C₄⋊C₄×C₁₉	—	2	8	no	—
110	C₂²⋊C₄×C₁₉	—	4	4	no	—
111	C₄²×C₁₉	—	4	4	no	—
112	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
113	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₉	C₂×D₄	1	2	yes	—
117	C₄²×C₁₉	C₂×D₄	1	2	yes	—
118	#21810	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	8	no	—
122	C₂³×C₁₉	—	4	16	no	—
123	C₂³×C₁₉	—	4	16	no	—
124	C₂³×C₁₉	—	4	8	no	—
125	C₂³×C₁₉	—	4	8	no	—
126	C₂³×C₁₉	—	4	8	no	—
127	C₂³×C₁₉	—	4	16	no	—
128	C₂³×C₁₉	—	8	32	no	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
131	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₁₉	—	2	16	no	—
133	D₄×C₁₉	—	4	16	no	—
134	D₄×C₁₉	—	4	16	no	—
135	D₄×C₁₉	—	4	16	no	—
136	D₄×C₁₉	—	4	16	no	—
137	D₄×C₁₉	—	4	8	no	—
138	D₄×C₁₉	—	4	16	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	8	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
156	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
159	C₈×C₁₉	—	4	4	no	—
160	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic
161	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
162	#2283	C₂×C₁₉	1	1	yes	characteristic, complemented
163	#1982	C₂×C₁₉	1	4	yes	complemented
164	#1961	C₂×C₁₉	1	4	yes	complemented
165	#1786	C₂×C₁₉	1	4	yes	complemented
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	8	no	—
169	C₂²×C₁₉	—	4	8	no	—
170	C₂²×C₁₉	—	4	8	no	—
171	C₂²×C₁₉	—	4	8	no	—
172	C₂²×C₁₉	—	8	32	no	—
173	C₂²×C₁₉	—	8	16	no	—
174	C₂²×C₁₉	#418	1	4	yes	—
175	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₉	#535	1	2	yes	—
177	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
178	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	8	4	no	—
184	C₄×C₁₉	#418	1	4	yes	—
185	C₄×C₁₉	#518	1	2	yes	—
186	C₄×C₁₉	#535	1	2	yes	—
187	C₂³×D₄	—	2	1	no	—
188	C₂³×D₄	—	2	1	no	—
189	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
190	C₂×#127	—	2	1	no	—
191	C₂×#127	—	2	1	no	—
192	C₂×#127	—	2	4	no	—
193	C₂×#127	C₄×C₁₉	1	8	yes	complemented
194	C₂×#127	C₂²×C₁₉	1	2	yes	—
195	C₂×#127	C₂²×C₁₉	1	2	yes	—
196	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
197	#432	—	2	4	no	—
198	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
199	C₂×#102	C₂²×C₁₉	1	16	yes	complemented
200	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
201	C₂×#97	C₂²×C₁₉	1	2	yes	complemented
202	#383	—	2	1	no	—
203	#382	C₂²×C₁₉	1	2	yes	complemented
204	#381	—	2	1	no	—
205	#380	C₂²×C₁₉	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
207	C₄×C₂²⋊C₄	—	2	1	no	—
208	#376	—	2	1	no	—
209	C₂×C₁₉	—	2	4	no	—
210	C₂×C₁₉	—	8	8	no	—
211	C₂×C₁₉	#2309	1	1	yes	characteristic
212	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
213	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
214	C₂×C₁₉	#3217	1	4	yes	—
215	C₂⁵	—	2	2	no	—
216	C₂²×D₄	—	2	8	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	2	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	4	8	no	—
225	C₂²×D₄	—	4	8	no	—
226	C₂²×D₄	—	4	8	no	—
227	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
228	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
229	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
233	#127	—	2	8	no	—
234	#127	—	2	8	no	—
235	#127	—	2	4	no	—
236	#127	—	2	4	no	—
237	#127	C₂×C₄×C₁₉	1	8	yes	—
238	#127	C₂×C₄×C₁₉	1	8	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
243	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₁₉	1	4	yes	—
246	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
248	C₄⋊C₈	—	2	4	no	—
249	#102	—	4	16	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	#97	—	2	4	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	C₁₉	#21810	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	4	8	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	—	4	8	no	—
262	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	4	16	no	—
271	C₂×D₄	—	4	32	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	—	4	32	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	8	no	—
279	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	8	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₄²	—	4	4	no	—
299	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
300	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
301	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
302	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
303	C₄²	C₂×D₄×C₁₉	1	2	yes	—
304	C₄²	C₂×D₄×C₁₉	1	2	yes	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	8	32	no	—
315	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
316	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
317	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
318	D₄	—	2	16	no	—
319	D₄	—	4	16	no	—
320	D₄	—	4	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	16	no	—
323	D₄	—	4	16	no	—
324	D₄	—	4	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
341	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
345	C₈	—	4	4	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₉×#418	1	4	yes	—
355	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂²	C₁₉×#535	1	2	yes	—
357	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
358	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	8	4	no	—
364	C₄	C₁₉×#418	1	4	yes	—
365	C₄	C₁₉×#518	1	2	yes	—
366	C₄	C₁₉×#535	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₁₉×#2309	1	1	yes	characteristic
370	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
371	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
372	C₂	C₁₉×#3217	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#432	C₂	semidirect
3. C₁₉×#2283	C₂	semidirect
4. C₁₉×#1982	C₂	semidirect
5. C₁₉×#1961	C₂	semidirect
6. C₁₉×#1786	C₂	semidirect
13. C₂×C₁₉×#127	C₄	semidirect
18. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
19. C₂×C₁₉×#102	C₂²	semidirect
21. C₂×C₁₉×#97	C₂²	semidirect
23. C₁₉×#382	C₂²	semidirect
26. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
118. #21810	C₁₉	direct (N × H)
161. C₂×#432	C₂×C₁₉	semidirect
162. #2283	C₂×C₁₉	semidirect
163. #1982	C₂×C₁₉	semidirect
164. #1961	C₂×C₁₉	semidirect
165. #1786	C₂×C₁₉	semidirect
193. C₂×#127	C₄×C₁₉	semidirect
198. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
199. C₂×#102	C₂²×C₁₉	semidirect
201. C₂×#97	C₂²×C₁₉	semidirect
203. #382	C₂²×C₁₉	semidirect
206. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
256. C₁₉	#21810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#127	2
C₂×C₁₉×#432	2
C₁₉×#2283	2
C₁₉×#1982	2
C₁₉×#1961	2
C₁₉×#1786	2
#21810	19

Subgroups — C19×#21810 #18027769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21810 #18027769