Subgroups — C₁₉×#23561 #18029520

Order 4864.

1074 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2911	C₂	1	2	yes	maximal
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2061	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2060	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1733	C₂	1	2	yes	maximal
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#544	—	2	4	no	—
10	C₁₉×#544	—	2	2	no	—
11	C₁₉×#544	C₂²	1	4	yes	—
12	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₂×C₁₉×#125	—	2	2	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₁₉×#117	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#428	—	2	2	no	—
20	C₁₉×#428	—	2	2	no	—
21	C₁₉×#428	C₂²	1	4	yes	—
22	C₁₉×#428	C₂²	1	4	yes	—
23	C₁₉×#427	—	2	4	no	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₁₉×#343	C₂²	1	4	yes	—
29	C₁₉×#339	C₂²	1	8	yes	—
30	C₂²×Q₈×C₁₉	—	2	2	no	—
31	C₂³×C₄×C₁₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	2	4	no	—
35	C₂×M₁₆×C₁₉	Q₈	1	8	yes	complemented
36	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₁₉×C₄⋊Q₈	—	2	8	no	—
39	C₁₉×C₄⋊Q₈	—	2	8	no	—
40	C₁₉×#125	—	2	8	no	—
41	C₁₉×#125	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	8	no	—
43	C₁₉×C₂²⋊Q₈	—	2	8	no	—
44	C₁₉×#117	—	2	2	no	—
45	C₁₉×#117	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	—	2	2	no	—
49	C₁₉×#117	D₄	1	4	yes	—
50	C₁₉×#117	Q₈	1	4	yes	complemented
51	C₁₉×#117	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#107	—	2	4	no	—
71	C₁₉×#107	—	2	4	no	—
72	C₁₉×#106	—	2	4	no	—
73	C₁₉×#106	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₁₉	—	2	8	no	—
77	C₂×Q₈×C₁₉	—	8	4	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	8	2	no	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₉	#41	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₉	—	2	8	no	—
95	M₁₆×C₁₉	—	2	4	no	—
96	M₁₆×C₁₉	C₂×Q₈	1	8	yes	complemented
97	C₂×C₈×C₁₉	—	2	8	no	—
98	C₂×C₈×C₁₉	—	2	4	no	—
99	C₄⋊C₄×C₁₉	—	2	8	no	—
100	C₄⋊C₄×C₁₉	—	2	16	no	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	8	4	no	—
109	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
110	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	2	4	no	—
117	C₄²×C₁₉	—	2	4	no	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	4	2	no	—
120	C₄²×C₁₉	C₂×Q₈	1	4	yes	complemented
121	#23561	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	#120	1	1	yes	characteristic
125	C₂³×C₁₉	#120	1	1	yes	characteristic
126	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
127	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
128	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₉	—	8	8	no	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	8	2	no	—
145	C₂×C₄×C₁₉	#120	1	2	yes	—
146	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
147	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
148	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
150	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
151	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
156	C₈×C₁₉	—	2	8	no	—
157	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
158	#2911	C₂×C₁₉	1	2	yes	—
159	#2317	C₂×C₁₉	1	1	yes	characteristic
160	#2061	C₂×C₁₉	1	4	yes	complemented
161	#2060	C₂×C₁₉	1	4	yes	complemented
162	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
163	#1733	C₂×C₁₉	1	2	yes	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	4	2	no	—
171	C₂²×C₁₉	—	4	2	no	—
172	C₂²×C₁₉	#395	1	2	yes	—
173	C₂²×C₁₉	#395	1	2	yes	—
174	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
176	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₄×C₁₉	—	4	4	no	—
178	C₄×C₁₉	—	4	4	no	—
179	C₄×C₁₉	—	4	4	no	—
180	C₄×C₁₉	—	4	4	no	—
181	C₄×C₁₉	—	8	1	no	—
182	C₄×C₁₉	—	8	1	no	—
183	C₄×C₁₉	#395	1	4	yes	—
184	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
185	C₄×C₁₉	C₂×C₄⋊Q₈	1	2	yes	—
186	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
187	#544	—	2	4	no	—
188	#544	—	2	2	no	—
189	#544	C₂²×C₁₉	1	4	yes	—
190	C₂×C₄⋊Q₈	—	2	2	no	—
191	C₂×#125	—	2	2	no	—
192	C₂×C₂²⋊Q₈	—	2	2	no	—
193	C₂×#117	C₂²×C₁₉	1	2	yes	—
194	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
197	#428	—	2	2	no	—
198	#428	—	2	2	no	—
199	#428	C₂²×C₁₉	1	4	yes	—
200	#428	C₂²×C₁₉	1	4	yes	—
201	#427	—	2	4	no	—
202	#389	—	2	2	no	—
203	#385	—	2	2	no	—
204	#384	C₂²×C₁₉	1	2	yes	—
205	#382	C₂²×C₁₉	1	2	yes	—
206	#343	C₂²×C₁₉	1	4	yes	—
207	#339	C₂²×C₁₉	1	8	yes	—
208	C₂×C₁₉	—	2	1	no	—
209	C₂×C₁₉	—	2	1	no	—
210	C₂×C₁₉	—	2	2	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	C₂×#395	1	1	yes	characteristic
213	C₂×C₁₉	#3019	1	1	yes	characteristic
214	C₂×C₁₉	#3020	1	1	yes	characteristic
215	C₂²×Q₈	—	2	2	no	—
216	C₂³×C₄	D₄×C₁₉	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	Q₈×C₁₉	1	8	yes	complemented
221	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
222	C₂²×C₈	—	2	2	no	—
223	C₄⋊Q₈	—	2	8	no	—
224	C₄⋊Q₈	—	2	8	no	—
225	#125	—	2	8	no	—
226	#125	—	2	8	no	—
227	C₂²⋊Q₈	—	2	8	no	—
228	C₂²⋊Q₈	—	2	8	no	—
229	#117	—	2	2	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	D₄×C₁₉	1	4	yes	—
235	#117	Q₈×C₁₉	1	4	yes	complemented
236	#117	C₂³×C₁₉	1	4	yes	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
244	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
245	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
255	#107	—	2	4	no	—
256	#107	—	2	4	no	—
257	#106	—	2	4	no	—
258	#106	—	2	4	no	—
259	#95	—	2	4	no	—
260	C₁₉	#23561	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
262	C₂×Q₈	—	2	8	no	—
263	C₂×Q₈	—	8	4	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	8	2	no	—
272	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
273	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
276	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
278	C₂²×C₄	#41×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
280	M₁₆	—	2	8	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	C₂×Q₈×C₁₉	1	8	yes	complemented
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	8	4	no	—
295	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
296	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	1	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	C₂×Q₈×C₁₉	1	4	yes	complemented
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₁₉×#120	1	1	yes	characteristic
310	C₂³	C₁₉×#120	1	1	yes	characteristic
311	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
312	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
313	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
314	Q₈	—	8	8	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	C₁₉×#120	1	2	yes	—
331	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
332	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
333	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
334	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
335	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
336	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
338	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
339	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	C₁₉×#395	1	2	yes	—
351	C₂²	C₁₉×#395	1	2	yes	—
352	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
353	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
355	C₄	—	4	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	4	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	1	no	—
360	C₄	—	8	1	no	—
361	C₄	C₁₉×#395	1	4	yes	—
362	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
363	C₄	C₂×C₁₉×C₄⋊Q₈	1	2	yes	—
364	C₂	—	2	1	no	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	—	2	1	no	—
368	C₂	C₂×C₁₉×#395	1	1	yes	characteristic
369	C₂	C₁₉×#3019	1	1	yes	characteristic
370	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2061	C₂	semidirect
5. C₁₉×#2060	C₂	semidirect
35. C₂×M₁₆×C₁₉	Q₈	semidirect
50. C₁₉×#117	Q₈	semidirect
96. M₁₆×C₁₉	C₂×Q₈	semidirect
120. C₄²×C₁₉	C₂×Q₈	semidirect
121. #23561	C₁₉	direct (N × H)
160. #2061	C₂×C₁₉	semidirect
161. #2060	C₂×C₁₉	semidirect
220. C₂×M₁₆	Q₈×C₁₉	semidirect
235. #117	Q₈×C₁₉	semidirect
260. C₁₉	#23561	direct (N × H)
282. M₁₆	C₂×Q₈×C₁₉	semidirect
306. C₄²	C₂×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#544	2
C₁₉×#2911	2
C₁₉×#2317	2
C₁₉×#2061	2
C₁₉×#2060	2
C₂×C₁₉×#343	2
C₁₉×#1733	2
#23561	19

Subgroups — C19×#23561 #18029520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23561 #18029520