Subgroups — C₁₉×#10179 #18016138

Order 4864.

560 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₉	—	2	1	no	—
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#492	—	2	1	no	—
13	C₁₉×#486	—	2	1	no	—
14	C₁₉×#479	—	2	2	no	—
15	C₁₉×#477	—	2	1	no	—
16	C₁₉×#475	—	2	1	no	—
17	C₁₉×#460	—	2	2	no	—
18	C₁₉×#460	—	2	2	no	—
19	C₁₉×#460	—	2	2	no	—
20	C₁₉×#450	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₁₉×#428	—	2	1	no	—
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#419	—	2	1	no	—
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₁₉×#331	—	2	2	no	—
29	C₁₉×Q₈⋊C₈	—	2	2	no	—
30	C₁₉×#324	—	2	2	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂×SD₁₆×C₁₉	—	2	4	no	—
36	C₂×SD₁₆×C₁₉	—	2	4	no	—
37	C₂×SD₁₆×C₁₉	—	4	2	no	—
38	C₂×SD₁₆×C₁₉	—	4	2	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	—	2	1	no	—
45	C₁₉×#127	—	2	1	no	—
46	C₁₉×#127	D₄	1	2	yes	—
47	C₁₉×#125	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×C₂²⋊Q₈	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×Q₈×C₁₉	—	2	1	no	—
55	C₄×Q₈×C₁₉	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	—	2	1	no	—
60	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×#107	—	2	2	no	—
62	C₁₉×#106	—	2	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
69	C₁₉×#103	—	2	2	no	—
70	C₁₉×#103	—	2	2	no	—
71	C₁₉×#102	—	2	4	no	—
72	C₁₉×#102	—	2	4	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	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	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	8	2	no	—
97	C₂×D₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	SD₁₆×C₁₉	—	4	8	no	—
104	SD₁₆×C₁₉	—	8	4	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	#10179	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	8	2	no	—
134	C₂³×C₁₉	—	8	2	no	—
135	C₂³×C₁₉	—	8	1	no	—
136	C₂³×C₁₉	—	8	1	no	—
137	C₂³×C₁₉	#121	1	1	yes	characteristic
138	Q₈×C₁₉	—	2	2	no	—
139	Q₈×C₁₉	—	2	2	no	—
140	Q₈×C₁₉	—	4	2	no	—
141	Q₈×C₁₉	—	4	1	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	8	2	no	—
148	D₄×C₁₉	—	8	2	no	—
149	D₄×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	8	1	no	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	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	#137	1	1	yes	characteristic
171	C₈×C₁₉	—	4	2	no	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	—	4	2	no	—
174	C₈×C₁₉	—	8	1	no	—
175	#3208	C₂×C₁₉	1	1	yes	characteristic
176	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
177	C₂×#460	C₂×C₁₉	1	1	yes	characteristic
178	#1545	C₂×C₁₉	1	1	yes	characteristic
179	#1481	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#1461	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1301	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	—	8	2	no	—
187	C₂²×C₁₉	—	16	2	no	—
188	C₂²×C₁₉	—	16	2	no	—
189	C₂²×C₁₉	#392	1	1	yes	characteristic
190	C₂²×C₁₉	#465	1	1	yes	characteristic
191	C₂²×C₁₉	#468	1	1	yes	characteristic
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	4	2	no	—
196	C₄×C₁₉	—	8	1	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	#448	1	1	yes	characteristic
200	C₄×C₁₉	#449	1	1	yes	characteristic
201	C₄×C₁₉	#450	1	1	yes	characteristic
202	C₄×C₁₉	#452	1	1	yes	characteristic
203	C₄×C₁₉	#471	1	2	yes	—
204	C₂²×SD₁₆	—	2	1	no	—
205	#533	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
208	#492	—	2	1	no	—
209	#486	—	2	1	no	—
210	#479	—	2	2	no	—
211	#477	—	2	1	no	—
212	#475	—	2	1	no	—
213	#460	—	2	2	no	—
214	#460	—	2	2	no	—
215	#460	—	2	2	no	—
216	#450	—	2	2	no	—
217	#431	C₂²×C₁₉	1	1	yes	characteristic
218	#431	C₂²×C₁₉	1	1	yes	characteristic
219	#428	—	2	1	no	—
220	#423	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
222	#419	—	2	1	no	—
223	C₂×#102	—	2	1	no	—
224	#331	—	2	2	no	—
225	Q₈⋊C₈	—	2	2	no	—
226	#324	—	2	2	no	—
227	C₂×C₁₉	—	2	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	16	2	no	—
230	C₂×C₁₉	#2000	1	1	yes	characteristic
231	C₂×C₁₉	#2008	1	1	yes	characteristic
232	C₂×C₁₉	#2019	1	1	yes	characteristic
233	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₂×SD₁₆	—	2	4	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×SD₁₆	—	4	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
244	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	D₄×C₁₉	1	2	yes	—
249	#125	—	2	1	no	—
250	C₂²⋊Q₈	—	2	1	no	—
251	C₂²⋊Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	#117	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#106	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
270	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#102	—	2	4	no	—
274	#102	—	2	4	no	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₁₉	#10179	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	4	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	complemented
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	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	—	8	2	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	8	4	no	—
308	M₁₆	—	4	1	no	—
309	M₁₆	—	4	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₄²	—	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	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂³	—	4	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	C₁₉×#121	1	1	yes	characteristic
340	Q₈	—	2	2	no	—
341	Q₈	—	2	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
364	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
365	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
366	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
367	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
368	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
369	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
370	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
371	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	—	8	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	16	2	no	—
383	C₂²	—	16	2	no	—
384	C₂²	C₁₉×#392	1	1	yes	characteristic
385	C₂²	C₁₉×#465	1	1	yes	characteristic
386	C₂²	C₁₉×#468	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	1	no	—
394	C₄	C₁₉×#448	1	1	yes	characteristic
395	C₄	C₁₉×#449	1	1	yes	characteristic
396	C₄	C₁₉×#450	1	1	yes	characteristic
397	C₄	C₁₉×#452	1	1	yes	characteristic
398	C₄	C₁₉×#471	1	2	yes	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	16	2	no	—
402	C₂	C₁₉×#2000	1	1	yes	characteristic
403	C₂	C₁₉×#2008	1	1	yes	characteristic
404	C₂	C₁₉×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
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×#3078	C₂	semidirect
5. C₁₉×#1481	C₂	semidirect
6. C₁₉×#1461	C₂	semidirect
7. C₁₉×#1301	C₂	semidirect
85. C₂×Q₈×C₁₉	SD₁₆	semidirect
131. #10179	C₁₉	direct (N × H)
176. #3078	C₂×C₁₉	semidirect
179. #1481	C₂×C₁₉	semidirect
180. #1461	C₂×C₁₉	semidirect
181. #1301	C₂×C₁₉	semidirect
279. C₁₉	#10179	direct (N × H)
288. C₂×Q₈	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3208	2
C₁₉×#3078	2
C₂×C₁₉×#460	2
C₁₉×#1545	2
C₁₉×#1481	2
C₁₉×#1461	2
C₁₉×#1301	2
#10179	19

Subgroups — C19×#10179 #18016138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10179 #18016138