Subgroups — C₁₉×#10500 #18016459

Order 4864.

508 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₁₉×#493	—	2	1	no	—
11	C₁₉×#486	—	2	1	no	—
12	C₁₉×#459	—	2	1	no	—
13	C₁₉×#459	—	2	1	no	—
14	C₁₉×#447	—	2	2	no	—
15	C₁₉×#431	C₂²	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#104	—	2	1	no	—
19	C₂×C₁₉×#104	—	2	1	no	—
20	C₂×C₁₉×#102	—	2	2	no	—
21	C₂×C₁₉×#100	—	2	1	no	—
22	C₂×C₁₉×#100	—	2	1	no	—
23	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#335	—	2	1	no	—
26	C₁₉×#334	—	2	1	no	—
27	C₁₉×#332	—	2	1	no	—
28	C₁₉×#331	—	2	1	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	2	yes	—
33	C₂×D₈×C₁₉	—	2	2	no	—
34	C₂×D₈×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	D₄	1	1	yes	characteristic
45	C₁₉×#124	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₁₉×#121	—	2	1	no	—
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
59	C₁₉×#104	—	4	2	no	—
60	C₁₉×#104	—	4	2	no	—
61	C₁₉×#102	—	2	2	no	—
62	C₁₉×#102	—	2	2	no	—
63	C₁₉×#102	—	4	4	no	—
64	C₁₉×#100	—	4	2	no	—
65	C₁₉×#100	—	4	2	no	—
66	C₁₉×C₂²⋊C₈	—	2	1	no	—
67	C₁₉×#97	—	2	1	no	—
68	C₄×C₈×C₁₉	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	C₁₉×#95	—	2	1	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	#41×C₁₉	—	4	1	no	—
73	#41×C₁₉	—	4	1	no	—
74	#41×C₁₉	—	4	1	no	—
75	#41×C₁₉	—	4	1	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	8	2	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	D₈×C₁₉	—	8	2	no	—
100	D₈×C₁₉	—	8	2	no	—
101	M₁₆×C₁₉	—	2	1	no	—
102	M₁₆×C₁₉	—	2	1	no	—
103	M₁₆×C₁₉	—	2	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	D₈	1	2	yes	complemented
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	#41	1	1	yes	characteristic
125	C₄²×C₁₉	#41	1	1	yes	characteristic
126	#10500	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	8	2	no	—
132	C₂³×C₁₉	—	8	2	no	—
133	C₂³×C₁₉	#121	1	1	yes	characteristic
134	Q₈×C₁₉	—	4	1	no	—
135	Q₈×C₁₉	—	4	1	no	—
136	D₄×C₁₉	—	4	4	no	—
137	D₄×C₁₉	—	4	1	no	—
138	D₄×C₁₉	—	4	2	no	—
139	D₄×C₁₉	—	4	1	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	1	no	—
143	D₄×C₁₉	—	8	1	no	—
144	D₄×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	8	2	no	—
146	D₄×C₁₉	—	8	1	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	—	8	1	no	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	4	1	no	—
173	C₈×C₁₉	—	4	1	no	—
174	C₈×C₁₉	—	4	1	no	—
175	C₈×C₁₉	—	8	1	no	—
176	C₈×C₁₉	—	8	1	no	—
177	#3205	C₂×C₁₉	1	1	yes	characteristic
178	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#1980	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#1965	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1565	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1303	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	8	2	no	—
187	C₂²×C₁₉	—	8	1	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	16	2	no	—
193	C₂²×C₁₉	—	16	2	no	—
194	C₂²×C₁₉	#394	1	1	yes	characteristic
195	C₂²×C₁₉	#459	1	1	yes	characteristic
196	C₂²×C₁₉	#463	1	1	yes	characteristic
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	#453	1	1	yes	characteristic
203	C₄×C₁₉	#455	1	1	yes	characteristic
204	C₄×C₁₉	#459	1	1	yes	characteristic
205	C₄×C₁₉	#463	1	1	yes	characteristic
206	C₄×C₁₉	#466	1	1	yes	characteristic
207	C₄×C₁₉	#469	1	1	yes	characteristic
208	#532	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
210	#493	—	2	1	no	—
211	#486	—	2	1	no	—
212	#459	—	2	1	no	—
213	#459	—	2	1	no	—
214	#447	—	2	2	no	—
215	#431	C₂²×C₁₉	1	1	yes	characteristic
216	#423	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×#104	—	2	1	no	—
219	C₂×#104	—	2	1	no	—
220	C₂×#102	—	2	2	no	—
221	C₂×#100	—	2	1	no	—
222	C₂×#100	—	2	1	no	—
223	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	#335	—	2	1	no	—
226	#334	—	2	1	no	—
227	#332	—	2	1	no	—
228	#331	—	2	1	no	—
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	16	1	no	—
232	C₂×C₁₉	—	16	2	no	—
233	C₂×C₁₉	#2037	1	1	yes	characteristic
234	C₂×C₁₉	#2048	1	1	yes	characteristic
235	C₂×C₁₉	#2054	1	1	yes	characteristic
236	C₂×#41	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	D₄×C₁₉	1	2	yes	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
244	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
245	C₂²×C₈	—	2	1	no	—
246	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	—	2	1	no	—
250	#127	—	2	1	no	—
251	#127	D₄×C₁₉	1	1	yes	characteristic
252	#124	—	2	1	no	—
253	#121	—	2	1	no	—
254	#121	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
265	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
266	#104	—	4	2	no	—
267	#104	—	4	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	4	4	no	—
271	#100	—	4	2	no	—
272	#100	—	4	2	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	#97	—	2	1	no	—
275	C₄×C₈	—	2	1	no	—
276	C₄×C₈	—	2	1	no	—
277	#95	—	2	1	no	—
278	C₁₉	#10500	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	#41	—	4	1	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	8	2	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
307	D₈	—	8	2	no	—
308	D₈	—	8	2	no	—
309	M₁₆	—	2	1	no	—
310	M₁₆	—	2	1	no	—
311	M₁₆	—	2	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	D₈×C₁₉	1	2	yes	complemented
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₄²	#41×C₁₉	1	1	yes	characteristic
333	C₄²	#41×C₁₉	1	1	yes	characteristic
334	C₂³	—	4	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	C₁₉×#121	1	1	yes	characteristic
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	1	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	8	1	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	1	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
369	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
370	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
371	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
372	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
373	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
374	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
376	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	16	2	no	—
393	C₂²	—	16	2	no	—
394	C₂²	C₁₉×#394	1	1	yes	characteristic
395	C₂²	C₁₉×#459	1	1	yes	characteristic
396	C₂²	C₁₉×#463	1	1	yes	characteristic
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	C₁₉×#453	1	1	yes	characteristic
403	C₄	C₁₉×#455	1	1	yes	characteristic
404	C₄	C₁₉×#459	1	1	yes	characteristic
405	C₄	C₁₉×#463	1	1	yes	characteristic
406	C₄	C₁₉×#466	1	1	yes	characteristic
407	C₄	C₁₉×#469	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	16	2	no	—
411	C₂	—	16	1	no	—
412	C₂	C₁₉×#2037	1	1	yes	characteristic
413	C₂	C₁₉×#2048	1	1	yes	characteristic
414	C₂	C₁₉×#2054	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3205	C₂
LCS	G ▷ C₂×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
2. C₁₉×#1982	C₂	semidirect
3. C₁₉×#1980	C₂	semidirect
4. C₁₉×#1965	C₂	semidirect
5. C₁₉×#1565	C₂	semidirect
6. C₁₉×#1547	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
106. M₁₆×C₁₉	D₈	semidirect
126. #10500	C₁₉	direct (N × H)
178. #1982	C₂×C₁₉	semidirect
179. #1980	C₂×C₁₉	semidirect
180. #1965	C₂×C₁₉	semidirect
181. #1565	C₂×C₁₉	semidirect
182. #1547	C₂×C₁₉	semidirect
183. #1303	C₂×C₁₉	semidirect
278. C₁₉	#10500	direct (N × H)
314. M₁₆	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3205	2
C₁₉×#1982	2
C₁₉×#1980	2
C₁₉×#1965	2
C₁₉×#1565	2
C₁₉×#1547	2
C₁₉×#1303	2
#10500	19

Subgroups — C19×#10500 #18016459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10500 #18016459