Subgroups — C₁₉×#19387 #18025346

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#474	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2972	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1683	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1669	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1571	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#533	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#494	C₂²	1	2	yes	complemented
14	C₁₉×#487	C₂²	1	2	yes	complemented
15	C₁₉×#478	—	2	2	no	—
16	C₁₉×#476	C₂²	1	2	yes	—
17	C₁₉×#474	—	2	2	no	—
18	C₁₉×#474	C₂²	1	2	yes	—
19	C₁₉×#474	C₂²	1	4	yes	—
20	C₁₉×#462	—	2	2	no	—
21	C₁₉×#451	—	2	2	no	—
22	C₈×D₄×C₁₉	—	2	2	no	—
23	C₈×D₄×C₁₉	C₂²	1	4	yes	—
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#428	—	2	1	no	—
27	C₂×C₁₉×#107	—	2	1	no	—
28	C₁₉×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#418	—	2	1	no	—
31	C₂×C₁₉×#102	—	2	1	no	—
32	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
33	C₁₉×#335	C₂²	1	4	yes	complemented
34	C₁₉×#333	C₂²	1	2	yes	complemented
35	C₁₉×#332	C₂²	1	2	yes	complemented
36	C₁₉×#332	C₂²	1	4	yes	complemented
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂×Q₁₆×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	1	no	—
43	C₂²×C₈×C₁₉	—	2	4	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
50	C₁₉×#125	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₁₉×C₂²⋊Q₈	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×Q₈×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	D₄	1	2	yes	—
58	C₄×D₄×C₁₉	C₂³	1	2	yes	—
59	C₁₉×#117	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#107	—	2	4	no	—
66	C₁₉×#107	—	2	2	no	—
67	C₁₉×#106	—	2	2	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×C₄⋊C₈	—	2	1	no	—
70	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₉×#103	—	2	4	no	—
75	C₁₉×#102	—	2	4	no	—
76	C₁₉×#102	—	2	2	no	—
77	C₁₉×#102	—	2	2	no	—
78	C₁₉×C₂²⋊C₈	—	2	1	no	—
79	C₁₉×C₂²⋊C₈	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₁₉	—	2	1	no	—
82	C₄×C₈×C₁₉	C₂³	1	2	yes	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	8	2	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	Q₁₆	1	4	yes	complemented
92	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	Q₁₆×C₁₉	—	8	4	no	—
102	M₁₆×C₁₉	—	4	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	4	2	no	—
107	C₂×C₈×C₁₉	—	8	4	no	—
108	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	#41	1	1	yes	characteristic
128	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
129	#19387	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	8	1	no	—
133	C₂³×C₁₉	—	8	1	no	—
134	C₂³×C₁₉	#121	1	1	yes	characteristic
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	4	4	no	—
137	Q₈×C₁₉	—	8	1	no	—
138	Q₈×C₁₉	—	8	2	no	—
139	D₄×C₁₉	—	2	2	no	—
140	D₄×C₁₉	—	2	4	no	—
141	D₄×C₁₉	C₂×Q₁₆	1	4	yes	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	8	2	no	—
150	C₂×C₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	—	8	2	no	—
152	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₁₉	#135	1	2	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₉	—	2	4	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₈×C₁₉	—	4	2	no	—
163	C₈×C₁₉	—	4	2	no	—
164	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
165	#3077	C₂×C₁₉	1	1	yes	characteristic
166	C₂×#474	C₂×C₁₉	1	1	yes	characteristic
167	#2972	C₂×C₁₉	1	1	yes	characteristic
168	#1683	C₂×C₁₉	1	4	yes	complemented
169	#1669	C₂×C₁₉	1	4	yes	complemented
170	#1571	C₂×C₁₉	1	1	yes	characteristic, complemented
171	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#1542	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	4	no	—
176	C₂²×C₁₉	—	4	2	no	—
177	C₂²×C₁₉	—	4	2	no	—
178	C₂²×C₁₉	—	8	4	no	—
179	C₂²×C₁₉	#467	1	2	yes	—
180	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	8	2	no	—
186	C₄×C₁₉	—	8	1	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₄×C₁₉	#467	1	2	yes	—
189	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
190	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
191	C₄×C₁₉	#576	1	2	yes	—
192	#533	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
195	#494	C₂²×C₁₉	1	2	yes	complemented
196	#487	C₂²×C₁₉	1	2	yes	complemented
197	#478	—	2	2	no	—
198	#476	C₂²×C₁₉	1	2	yes	—
199	#474	—	2	2	no	—
200	#474	C₂²×C₁₉	1	2	yes	—
201	#474	C₂²×C₁₉	1	4	yes	—
202	#462	—	2	2	no	—
203	#451	—	2	2	no	—
204	C₈×D₄	—	2	2	no	—
205	C₈×D₄	C₂²×C₁₉	1	4	yes	—
206	#431	C₂²×C₁₉	1	1	yes	characteristic
207	#431	C₂²×C₁₉	1	1	yes	characteristic
208	#428	—	2	1	no	—
209	C₂×#107	—	2	1	no	—
210	#423	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
212	#418	—	2	1	no	—
213	C₂×#102	—	2	1	no	—
214	C₂×C₂²⋊C₈	—	2	2	no	—
215	#335	C₂²×C₁₉	1	4	yes	complemented
216	#333	C₂²×C₁₉	1	2	yes	complemented
217	#332	C₂²×C₁₉	1	2	yes	complemented
218	#332	C₂²×C₁₉	1	4	yes	complemented
219	C₂×C₁₉	—	2	2	no	—
220	C₂×C₁₉	—	4	4	no	—
221	C₂×C₁₉	#3041	1	1	yes	characteristic
222	C₂×C₁₉	C₂×#467	1	1	yes	characteristic
223	C₂×C₁₉	#3069	1	1	yes	characteristic
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×Q₁₆	—	2	4	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	4	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
235	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
236	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
237	#125	—	2	1	no	—
238	C₂²⋊Q₈	—	2	1	no	—
239	C₂²⋊Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	D₄×C₁₉	1	2	yes	—
245	C₄×D₄	C₂³×C₁₉	1	2	yes	—
246	#117	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	#107	—	2	4	no	—
253	#107	—	2	2	no	—
254	#106	—	2	2	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
258	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
260	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
261	#103	—	2	4	no	—
262	#102	—	2	4	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	C₂³×C₁₉	1	2	yes	—
270	C₁₉	#19387	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁴	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	8	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	Q₁₆×C₁₉	1	4	yes	complemented
280	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	8	2	no	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
289	Q₁₆	—	8	4	no	—
290	M₁₆	—	4	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	8	4	no	—
296	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
315	C₄²	#41×C₁₉	1	1	yes	characteristic
316	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	8	1	no	—
321	C₂³	C₁₉×#121	1	1	yes	characteristic
322	Q₈	—	4	2	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	8	1	no	—
325	Q₈	—	8	2	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	C₂×Q₁₆×C₁₉	1	4	yes	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
340	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
341	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
342	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
343	C₂×C₄	C₁₉×#135	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	8	4	no	—
357	C₂²	C₁₉×#467	1	2	yes	—
358	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	C₁₉×#467	1	2	yes	—
367	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
368	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
369	C₄	C₁₉×#576	1	2	yes	—
370	C₂	—	2	2	no	—
371	C₂	—	4	4	no	—
372	C₂	C₁₉×#3041	1	1	yes	characteristic
373	C₂	C₂×C₁₉×#467	1	1	yes	characteristic
374	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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×#3209	C₂	semidirect
5. C₁₉×#1683	C₂	semidirect
6. C₁₉×#1669	C₂	semidirect
7. C₁₉×#1571	C₂	semidirect
8. C₁₉×#1549	C₂	semidirect
9. C₁₉×#1542	C₂	semidirect
13. C₁₉×#494	C₂²	semidirect
14. C₁₉×#487	C₂²	semidirect
33. C₁₉×#335	C₂²	semidirect
34. C₁₉×#333	C₂²	semidirect
35. C₁₉×#332	C₂²	semidirect
36. C₁₉×#332	C₂²	semidirect
91. C₂×D₄×C₁₉	Q₁₆	semidirect
129. #19387	C₁₉	direct (N × H)
164. #3209	C₂×C₁₉	semidirect
168. #1683	C₂×C₁₉	semidirect
169. #1669	C₂×C₁₉	semidirect
170. #1571	C₂×C₁₉	semidirect
171. #1549	C₂×C₁₉	semidirect
172. #1542	C₂×C₁₉	semidirect
195. #494	C₂²×C₁₉	semidirect
196. #487	C₂²×C₁₉	semidirect
215. #335	C₂²×C₁₉	semidirect
216. #333	C₂²×C₁₉	semidirect
217. #332	C₂²×C₁₉	semidirect
218. #332	C₂²×C₁₉	semidirect
270. C₁₉	#19387	direct (N × H)
279. C₂×D₄	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3209	2
C₁₉×#3077	2
C₂×C₁₉×#474	2
C₁₉×#2972	2
C₁₉×#1683	2
C₁₉×#1669	2
C₁₉×#1571	2
C₁₉×#1549	2
C₁₉×#1542	2
#19387	19

Subgroups — C19×#19387 #18025346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19387 #18025346