Subgroups — C₁₉×#13014 #18018973

Order 4864.

554 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	C₂²×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	—	2	1	no	—
11	C₂×C₁₉×SD₃₂	—	2	2	no	—
12	C₂×C₁₉×SD₃₂	—	2	2	no	—
13	C₂×C₁₉×SD₃₂	C₄	1	4	yes	complemented
14	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₁₉	—	2	2	no	—
17	C₄×D₈×C₁₉	—	2	2	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#102	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#358	—	2	2	no	—
25	C₁₉×#357	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	4	1	no	—
29	C₂×Q₁₆×C₁₉	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	—	2	1	no	—
31	C₂×Q₁₆×C₁₉	—	2	1	no	—
32	C₂×Q₁₆×C₁₉	—	2	1	no	—
33	C₂×Q₁₆×C₁₉	—	2	1	no	—
34	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
35	C₂×D₈×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₂×D₈×C₁₉	—	2	1	no	—
38	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×D₈×C₁₉	D₄	1	2	yes	—
40	C₂×D₈×C₁₉	D₄	1	2	yes	—
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₁₉	—	2	4	no	—
44	C₄×D₄×C₁₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₁₉×SD₃₂	—	2	8	no	—
50	C₂×C₁₆×C₁₉	—	2	1	no	—
51	C₂×C₁₆×C₁₉	—	2	1	no	—
52	C₂×C₁₆×C₁₉	—	2	1	no	—
53	C₂×C₁₆×C₁₉	—	2	1	no	—
54	C₂×C₁₆×C₁₉	—	2	1	no	—
55	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
56	C₁₉×#107	—	2	1	no	—
57	C₁₉×#107	—	2	1	no	—
58	C₁₉×#107	—	2	1	no	—
59	C₁₉×#107	D₄	1	2	yes	—
60	C₁₉×#103	—	4	2	no	—
61	C₁₉×#102	—	2	4	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₁₉×#95	—	4	1	no	—
65	C₁₉×#95	—	4	1	no	—
66	C₂⁴×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	4	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	8	2	no	—
84	C₂²×C₄×C₁₉	—	8	2	no	—
85	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	Q₁₆×C₁₉	—	2	2	no	—
89	Q₁₆×C₁₉	—	2	2	no	—
90	Q₁₆×C₁₉	—	4	1	no	—
91	Q₁₆×C₁₉	—	4	1	no	—
92	D₈×C₁₉	—	2	2	no	—
93	D₈×C₁₉	—	2	2	no	—
94	D₈×C₁₉	—	2	2	no	—
95	D₈×C₁₉	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₉	—	2	1	no	—
97	C₂×C₈×C₁₉	—	2	1	no	—
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
104	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₂²⋊C₄×C₁₉	—	4	4	no	—
110	C₄²×C₁₉	—	2	1	no	—
111	C₄²×C₁₉	—	2	1	no	—
112	C₁₆×C₁₉	—	2	2	no	—
113	C₁₆×C₁₉	—	4	1	no	—
114	#13014	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	—	4	2	no	—
116	C₂³×C₁₉	—	4	2	no	—
117	C₂³×C₁₉	—	4	2	no	—
118	C₂³×C₁₉	—	8	1	no	—
119	C₂³×C₁₉	—	8	1	no	—
120	C₂³×C₁₉	—	8	1	no	—
121	C₂³×C₁₉	—	8	1	no	—
122	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
123	Q₈×C₁₉	—	4	2	no	—
124	Q₈×C₁₉	—	4	2	no	—
125	Q₈×C₁₉	—	8	1	no	—
126	Q₈×C₁₉	—	8	1	no	—
127	D₄×C₁₉	—	2	4	no	—
128	D₄×C₁₉	—	4	2	no	—
129	D₄×C₁₉	—	4	2	no	—
130	D₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	8	8	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	—	8	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	SD₃₂	1	2	yes	complemented
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₈×C₁₉	—	4	1	no	—
154	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
156	C₈×C₁₉	#121	1	1	yes	characteristic
157	C₈×C₁₉	#123	1	1	yes	characteristic
158	C₂²×SD₃₂	C₂×C₁₉	1	1	yes	characteristic
159	C₂×C₄×D₈	C₂×C₁₉	1	1	yes	characteristic
160	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
161	C₂×#357	C₂×C₁₉	1	1	yes	characteristic
162	#1969	C₂×C₁₉	1	1	yes	characteristic, complemented
163	#1380	C₂×C₁₉	1	1	yes	characteristic, complemented
164	#1374	C₂×C₁₉	1	1	yes	characteristic, complemented
165	C₂²×C₁₉	—	4	4	no	—
166	C₂²×C₁₉	—	8	2	no	—
167	C₂²×C₁₉	—	8	2	no	—
168	C₂²×C₁₉	—	8	2	no	—
169	C₂²×C₁₉	—	8	2	no	—
170	C₂²×C₁₉	—	8	2	no	—
171	C₂²×C₁₉	—	8	2	no	—
172	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
173	C₂²×C₁₉	#447	1	1	yes	characteristic
174	C₂²×C₁₉	#459	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
176	C₂²×C₁₉	#508	1	1	yes	characteristic
177	C₂²×C₁₉	#509	1	1	yes	characteristic
178	C₂²×C₁₉	#510	1	1	yes	characteristic
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	4	1	no	—
181	C₄×C₁₉	—	8	2	no	—
182	C₄×C₁₉	—	8	2	no	—
183	C₄×C₁₉	—	16	1	no	—
184	C₄×C₁₉	#386	1	1	yes	characteristic
185	C₄×C₁₉	#442	1	1	yes	characteristic
186	C₄×C₁₉	#449	1	1	yes	characteristic
187	C₄×C₁₉	#463	1	1	yes	characteristic
188	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
189	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
190	C₂×C₄×D₄	—	2	1	no	—
191	C₂×SD₃₂	—	2	2	no	—
192	C₂×SD₃₂	—	2	2	no	—
193	C₂×SD₃₂	C₄×C₁₉	1	4	yes	complemented
194	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
195	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
196	C₄×D₈	—	2	2	no	—
197	C₄×D₈	—	2	2	no	—
198	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×#103	—	2	1	no	—
201	C₂×#102	—	2	1	no	—
202	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
203	#391	—	2	1	no	—
204	#358	—	2	2	no	—
205	#357	—	2	2	no	—
206	C₂×C₁₉	—	8	4	no	—
207	C₂×C₁₉	#1879	1	1	yes	characteristic
208	C₂×C₁₉	C₄×SD₃₂	1	1	yes	characteristic
209	C₂×C₁₉	#2175	1	1	yes	characteristic
210	C₂×C₁₉	#2187	1	1	yes	characteristic
211	C₂×C₁₉	#2189	1	1	yes	characteristic
212	C₂×C₁₉	#2208	1	1	yes	characteristic
213	C₂×C₁₉	#2210	1	1	yes	characteristic
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂³×C₄	—	4	1	no	—
217	C₂×Q₁₆	—	2	1	no	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	complemented
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	—	2	1	no	—
225	C₂×D₈	—	2	1	no	—
226	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
227	C₂×D₈	D₄×C₁₉	1	2	yes	—
228	C₂×D₈	D₄×C₁₉	1	2	yes	—
229	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
231	C₄×D₄	—	2	4	no	—
232	C₄×D₄	—	4	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	4	1	no	—
236	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
237	SD₃₂	—	2	8	no	—
238	C₂×C₁₆	—	2	1	no	—
239	C₂×C₁₆	—	2	1	no	—
240	C₂×C₁₆	—	2	1	no	—
241	C₂×C₁₆	—	2	1	no	—
242	C₂×C₁₆	—	2	1	no	—
243	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	complemented
244	#107	—	2	1	no	—
245	#107	—	2	1	no	—
246	#107	—	2	1	no	—
247	#107	D₄×C₁₉	1	2	yes	—
248	#103	—	4	2	no	—
249	#102	—	2	4	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	#95	—	4	1	no	—
253	#95	—	4	1	no	—
254	C₁₉	#13014	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	4	1	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	8	2	no	—
273	C₂²×C₄	—	8	2	no	—
274	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
275	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	2	2	no	—
279	Q₁₆	—	4	1	no	—
280	Q₁₆	—	4	1	no	—
281	D₈	—	2	2	no	—
282	D₈	—	2	2	no	—
283	D₈	—	2	2	no	—
284	D₈	C₂²⋊C₄×C₁₉	1	4	yes	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
293	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₁₆	—	2	2	no	—
302	C₁₆	—	4	1	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	8	1	no	—
307	C₂³	—	8	1	no	—
308	C₂³	—	8	1	no	—
309	C₂³	—	8	1	no	—
310	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
311	Q₈	—	4	2	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	8	1	no	—
314	Q₈	—	8	1	no	—
315	D₄	—	2	4	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	8	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	—	8	1	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	C₁₉×SD₃₂	1	2	yes	complemented
335	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
336	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
337	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
338	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
339	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₈	—	4	1	no	—
342	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
343	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
344	C₈	C₁₉×#121	1	1	yes	characteristic
345	C₈	C₁₉×#123	1	1	yes	characteristic
346	C₂²	—	4	4	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
354	C₂²	C₁₉×#447	1	1	yes	characteristic
355	C₂²	C₁₉×#459	1	1	yes	characteristic
356	C₂²	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
357	C₂²	C₁₉×#508	1	1	yes	characteristic
358	C₂²	C₁₉×#509	1	1	yes	characteristic
359	C₂²	C₁₉×#510	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	4	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	—	16	1	no	—
365	C₄	C₁₉×#386	1	1	yes	characteristic
366	C₄	C₁₉×#442	1	1	yes	characteristic
367	C₄	C₁₉×#449	1	1	yes	characteristic
368	C₄	C₁₉×#463	1	1	yes	characteristic
369	C₂	—	8	4	no	—
370	C₂	C₁₉×#1879	1	1	yes	characteristic
371	C₂	C₄×C₁₉×SD₃₂	1	1	yes	characteristic
372	C₂	C₁₉×#2175	1	1	yes	characteristic
373	C₂	C₁₉×#2187	1	1	yes	characteristic
374	C₂	C₁₉×#2189	1	1	yes	characteristic
375	C₂	C₁₉×#2208	1	1	yes	characteristic
376	C₂	C₁₉×#2210	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#358	C₂	semidirect
5. C₁₉×#1969	C₂	semidirect
6. C₁₉×#1380	C₂	semidirect
7. C₁₉×#1374	C₂	semidirect
13. C₂×C₁₉×SD₃₂	C₄	semidirect
34. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
55. C₂×C₁₆×C₁₉	C₂×C₄	semidirect
114. #13014	C₁₉	direct (N × H)
146. C₂×C₄×C₁₉	SD₃₂	semidirect
160. C₂×#358	C₂×C₁₉	semidirect
162. #1969	C₂×C₁₉	semidirect
163. #1380	C₂×C₁₉	semidirect
164. #1374	C₂×C₁₉	semidirect
193. C₂×SD₃₂	C₄×C₁₉	semidirect
222. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
243. C₂×C₁₆	C₂×C₄×C₁₉	semidirect
254. C₁₉	#13014	direct (N × H)
334. C₂×C₄	C₁₉×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×SD₃₂	2
C₂×C₄×D₈×C₁₉	2
C₂×C₁₉×#358	2
C₂×C₁₉×#357	2
C₁₉×#1969	2
C₁₉×#1380	2
C₁₉×#1374	2
#13014	19

Subgroups — C19×#13014 #18018973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13014 #18018973