Subgroups — C₁₉×#18684 #18024643

Order 4864.

1006 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1624	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1623	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1622	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×SD₁₆×C₁₉	—	2	2	no	—
10	C₁₉×#563	—	2	2	no	—
11	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
13	C₁₉×#554	C₂²	1	2	yes	complemented
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#544	—	2	2	no	—
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#536	—	2	2	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#496	—	2	2	no	—
23	C₁₉×#492	—	2	2	no	—
24	C₁₉×#492	C₂²	1	2	yes	—
25	C₁₉×#492	C₂²	1	2	yes	—
26	C₁₉×#490	—	2	2	no	—
27	C₁₉×#460	C₂²	1	4	yes	—
28	C₁₉×#459	C₂²	1	4	yes	—
29	C₁₉×#450	—	2	2	no	—
30	C₁₉×#447	—	2	2	no	—
31	C₁₉×#432	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#333	C₂²	1	2	yes	complemented
34	C₁₉×#333	C₂²	1	2	yes	complemented
35	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂×SD₁₆×C₁₉	—	2	4	no	—
42	C₂×SD₁₆×C₁₉	—	2	4	no	—
43	C₂×SD₁₆×C₁₉	—	2	4	no	—
44	C₂×SD₁₆×C₁₉	—	4	8	no	—
45	C₂×D₈×C₁₉	—	2	4	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
52	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#127	—	2	1	no	—
56	C₁₉×#127	C₂³	1	2	yes	—
57	C₁₉×#126	—	2	4	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	D₄	1	2	yes	—
62	C₁₉×#124	—	2	2	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	D₄	1	2	yes	—
65	C₁₉×#123	—	2	4	no	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	4	no	—
69	C₁₉×C₂²⋊Q₈	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	D₄	1	2	yes	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×#97	—	2	2	no	—
91	C₄×C₈×C₁₉	—	2	1	no	—
92	C₄×C₈×C₁₉	C₂³	1	2	yes	—
93	C₂⁴×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	8	4	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	4	4	no	—
98	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	—	8	4	no	—
109	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	SD₁₆×C₁₉	—	4	8	no	—
116	SD₁₆×C₁₉	—	4	8	no	—
117	SD₁₆×C₁₉	—	8	4	no	—
118	D₈×C₁₉	—	8	4	no	—
119	C₂×C₈×C₁₉	—	2	4	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	C₂×D₄	1	2	yes	—
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
147	#18684	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	8	4	no	—
151	C₂³×C₁₉	—	8	2	no	—
152	C₂³×C₁₉	#120	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	4	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	8	2	no	—
157	Q₈×C₁₉	—	8	2	no	—
158	D₄×C₁₉	—	2	4	no	—
159	D₄×C₁₉	—	4	4	no	—
160	D₄×C₁₉	—	4	4	no	—
161	D₄×C₁₉	—	4	4	no	—
162	D₄×C₁₉	—	4	4	no	—
163	D₄×C₁₉	—	8	2	no	—
164	D₄×C₁₉	—	8	4	no	—
165	D₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	8	4	no	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
180	C₈×C₁₉	—	2	4	no	—
181	C₈×C₁₉	—	4	4	no	—
182	#3544	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#3217	C₂×C₁₉	1	2	yes	complemented
184	C₂×#492	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1624	C₂×C₁₉	1	2	yes	complemented
186	#1623	C₂×C₁₉	1	2	yes	complemented
187	#1622	C₂×C₁₉	1	4	yes	complemented
188	#1558	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1494	C₂×C₁₉	1	2	yes	complemented
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	8	4	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	16	4	no	—
197	C₂²×C₁₉	#453	1	2	yes	—
198	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	#577	1	4	yes	—
208	C₂²×SD₁₆	—	2	2	no	—
209	#563	—	2	2	no	—
210	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
211	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
212	#554	C₂²×C₁₉	1	2	yes	complemented
213	#552	—	2	2	no	—
214	#547	—	2	2	no	—
215	#544	—	2	2	no	—
216	#542	—	2	2	no	—
217	#536	—	2	2	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
220	#529	C₂²×C₁₉	1	2	yes	—
221	#496	—	2	2	no	—
222	#492	—	2	2	no	—
223	#492	C₂²×C₁₉	1	2	yes	—
224	#492	C₂²×C₁₉	1	2	yes	—
225	#490	—	2	2	no	—
226	#460	C₂²×C₁₉	1	4	yes	—
227	#459	C₂²×C₁₉	1	4	yes	—
228	#450	—	2	2	no	—
229	#447	—	2	2	no	—
230	#432	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
232	#333	C₂²×C₁₉	1	2	yes	complemented
233	#333	C₂²×C₁₉	1	2	yes	complemented
234	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
235	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
236	C₂×C₁₉	—	2	2	no	—
237	C₂×C₁₉	—	8	2	no	—
238	C₂×C₁₉	—	16	2	no	—
239	C₂×C₁₉	#3010	1	2	yes	—
240	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
241	C₂×#41	—	2	2	no	—
242	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	—	4	8	no	—
249	C₂×D₈	—	2	4	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
258	#127	—	2	2	no	—
259	#127	—	2	1	no	—
260	#127	C₂³×C₁₉	1	2	yes	—
261	#126	—	2	4	no	—
262	#126	—	2	2	no	—
263	#125	—	2	4	no	—
264	#125	—	2	2	no	—
265	#125	D₄×C₁₉	1	2	yes	—
266	#124	—	2	2	no	—
267	#124	—	2	2	no	—
268	#124	D₄×C₁₉	1	2	yes	—
269	#123	—	2	4	no	—
270	#123	—	2	4	no	—
271	#123	—	2	2	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
277	#121	—	2	2	no	—
278	#121	D₄×C₁₉	1	2	yes	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	C₂³×C₁₉	1	2	yes	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
291	#102	—	2	4	no	—
292	#102	—	2	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	#97	—	2	2	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	C₂³×C₁₉	1	2	yes	—
297	C₁₉	#18684	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	4	1	no	—
299	#41	—	8	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
304	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
305	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	SD₁₆	—	4	8	no	—
321	SD₁₆	—	4	8	no	—
322	SD₁₆	—	8	4	no	—
323	D₈	—	8	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
338	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₁₉	1	2	yes	—
351	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	4	no	—
355	C₂³	—	8	2	no	—
356	C₂³	C₁₉×#120	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	Q₈	—	8	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	4	no	—
369	D₄	—	8	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₁₉×#120	1	2	yes	—
381	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	16	4	no	—
393	C₂²	C₁₉×#453	1	2	yes	—
394	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	C₁₉×#577	1	4	yes	—
404	C₂	—	2	2	no	—
405	C₂	—	8	2	no	—
406	C₂	—	16	2	no	—
407	C₂	C₁₉×#3010	1	2	yes	—
408	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
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×#3544	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₂×C₁₉×#492	C₂	semidirect
4. C₁₉×#1624	C₂	semidirect
5. C₁₉×#1623	C₂	semidirect
6. C₁₉×#1622	C₂	semidirect
7. C₁₉×#1558	C₂	semidirect
8. C₁₉×#1494	C₂	semidirect
11. Q₈²×C₁₉	C₂²	semidirect
12. C₁₉×#555	C₂²	semidirect
13. C₁₉×#554	C₂²	semidirect
33. C₁₉×#333	C₂²	semidirect
34. C₁₉×#333	C₂²	semidirect
35. C₁₉×Q₈⋊C₈	C₂²	semidirect
36. C₁₉×D₄⋊C₈	C₂²	semidirect
147. #18684	C₁₉	direct (N × H)
182. #3544	C₂×C₁₉	semidirect
183. #3217	C₂×C₁₉	semidirect
184. C₂×#492	C₂×C₁₉	semidirect
185. #1624	C₂×C₁₉	semidirect
186. #1623	C₂×C₁₉	semidirect
187. #1622	C₂×C₁₉	semidirect
188. #1558	C₂×C₁₉	semidirect
189. #1494	C₂×C₁₉	semidirect
210. Q₈²	C₂²×C₁₉	semidirect
211. #555	C₂²×C₁₉	semidirect
212. #554	C₂²×C₁₉	semidirect
232. #333	C₂²×C₁₉	semidirect
233. #333	C₂²×C₁₉	semidirect
234. Q₈⋊C₈	C₂²×C₁₉	semidirect
235. D₄⋊C₈	C₂²×C₁₉	semidirect
297. C₁₉	#18684	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3544	2
C₁₉×#3217	2
C₂×C₁₉×#492	2
C₁₉×#1624	2
C₁₉×#1623	2
C₁₉×#1622	2
C₁₉×#1558	2
C₁₉×#1494	2
#18684	19

Subgroups — C19×#18684 #18024643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18684 #18024643