Subgroups — C₁₉×#60869 #18066828

Order 4864.

1626 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3242	C₂	1	16	yes	maximal, complemented
4	C₁₉×#3166	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3139	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3095	C₂	1	4	yes	maximal
7	C₁₉×#3078	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2921	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#544	—	2	2	no	—
10	C₁₉×#544	C₂²	1	8	yes	—
11	C₁₉×#543	—	2	2	no	—
12	C₁₉×#541	—	2	4	no	—
13	C₁₉×#541	C₂²	1	8	yes	—
14	C₁₉×#533	—	2	4	no	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#126	—	2	2	no	—
19	C₂×C₁₉×#125	—	2	2	no	—
20	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#501	C₂²	1	8	yes	complemented
26	C₁₉×#499	C₂²	1	8	yes	complemented
27	C₁₉×#491	C₂²	1	8	yes	complemented
28	C₁₉×#487	C₂²	1	8	yes	complemented
29	C₁₉×#485	C₂²	1	16	yes	—
30	C₁₉×#484	C₂²	1	8	yes	—
31	C₁₉×#483	C₂²	1	8	yes	—
32	C₁₉×#479	C₂²	1	16	yes	complemented
33	C₁₉×#477	C₂²	1	8	yes	complemented
34	C₁₉×#475	C₂²	1	8	yes	complemented
35	C₁₉×#433	C₂²	1	8	yes	—
36	C₁₉×#428	C₂²	1	8	yes	—
37	C₁₉×#423	C₂²	1	2	yes	—
38	C₁₉×#419	C₂²	1	8	yes	—
39	C₁₉×#407	C₂²	1	2	yes	—
40	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
44	C₁₉×C₄⋊Q₈	—	2	8	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
47	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
48	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
49	C₁₉×#126	—	2	16	no	—
50	C₁₉×#125	—	2	16	no	—
51	C₁₉×#125	—	2	8	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	C₂³	1	4	yes	—
54	C₁₉×#125	C₂³	1	4	yes	—
55	C₁₉×#125	C₂³	1	4	yes	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	8	no	—
60	C₁₉×C₂²⋊Q₈	—	2	8	no	—
61	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
62	C₄×Q₈×C₁₉	—	2	4	no	—
63	C₄×Q₈×C₁₉	—	2	4	no	—
64	C₄×Q₈×C₁₉	—	2	4	no	—
65	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	D₄	1	4	yes	—
69	C₁₉×#117	C₂³	1	4	yes	—
70	C₁₉×#117	C₂³	1	4	yes	—
71	C₁₉×#117	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#107	C₂³	1	16	yes	—
87	C₁₉×#106	C₂³	1	16	yes	—
88	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
89	C₁₉×#103	C₂³	1	16	yes	—
90	C₁₉×#103	C₂³	1	16	yes	—
91	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
92	C₁₉×#97	C₂³	1	4	yes	—
93	C₄×C₈×C₁₉	C₂³	1	4	yes	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	4	no	—
97	C₂×Q₈×C₁₉	—	2	4	no	—
98	C₂×Q₈×C₁₉	—	2	8	no	—
99	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	2	8	no	—
111	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	8	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	8	no	—
122	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
123	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
124	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
129	C₄²×C₁₉	—	2	4	no	—
130	C₄²×C₁₉	—	2	4	no	—
131	C₄²×C₁₉	—	2	8	no	—
132	C₄²×C₁₉	C₂×D₄	1	2	yes	—
133	C₄²×C₁₉	C₂×D₄	1	2	yes	—
134	C₄²×C₁₉	C₂⁴	1	2	yes	—
135	C₄²×C₁₉	C₂⁴	1	2	yes	—
136	#60869	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	2	8	no	—
142	Q₈×C₁₉	—	4	4	no	—
143	Q₈×C₁₉	—	8	4	no	—
144	Q₈×C₁₉	—	8	4	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	4	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	8	4	no	—
156	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
161	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
162	C₈×C₁₉	—	2	8	no	—
163	#3458	C₂×C₁₉	1	1	yes	characteristic
164	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
165	#3242	C₂×C₁₉	1	16	yes	complemented
166	#3166	C₂×C₁₉	1	2	yes	complemented
167	#3139	C₂×C₁₉	1	2	yes	complemented
168	#3095	C₂×C₁₉	1	4	yes	—
169	#3078	C₂×C₁₉	1	4	yes	complemented
170	#2921	C₂×C₁₉	1	1	yes	characteristic
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	8	2	no	—
175	C₂²×C₁₉	#536	1	2	yes	—
176	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₁₉	—	2	4	no	—
178	C₄×C₁₉	—	2	4	no	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	4	4	no	—
181	C₄×C₁₉	—	4	8	no	—
182	C₄×C₁₉	—	4	4	no	—
183	C₄×C₁₉	#536	1	2	yes	—
184	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
185	#544	—	2	2	no	—
186	#544	C₂²×C₁₉	1	8	yes	—
187	#543	—	2	2	no	—
188	#541	—	2	4	no	—
189	#541	C₂²×C₁₉	1	8	yes	—
190	#533	—	2	4	no	—
191	#533	C₂²×C₁₉	1	2	yes	—
192	#533	C₂²×C₁₉	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×#126	—	2	2	no	—
195	C₂×#125	—	2	2	no	—
196	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
199	C₂×#117	C₂²×C₁₉	1	2	yes	—
200	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
201	#501	C₂²×C₁₉	1	8	yes	complemented
202	#499	C₂²×C₁₉	1	8	yes	complemented
203	#491	C₂²×C₁₉	1	8	yes	complemented
204	#487	C₂²×C₁₉	1	8	yes	complemented
205	#485	C₂²×C₁₉	1	16	yes	—
206	#484	C₂²×C₁₉	1	8	yes	—
207	#483	C₂²×C₁₉	1	8	yes	—
208	#479	C₂²×C₁₉	1	16	yes	complemented
209	#477	C₂²×C₁₉	1	8	yes	complemented
210	#475	C₂²×C₁₉	1	8	yes	complemented
211	#433	C₂²×C₁₉	1	8	yes	—
212	#428	C₂²×C₁₉	1	8	yes	—
213	#423	C₂²×C₁₉	1	2	yes	—
214	#419	C₂²×C₁₉	1	8	yes	—
215	#407	C₂²×C₁₉	1	2	yes	—
216	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
217	C₂×C₁₉	—	2	2	no	—
218	C₂×C₁₉	—	4	2	no	—
219	C₂×C₁₉	C₂×#536	1	1	yes	characteristic
220	C₂×C₁₉	#3586	1	2	yes	—
221	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
223	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
224	C₄⋊Q₈	—	2	8	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
227	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
228	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
229	#126	—	2	16	no	—
230	#125	—	2	16	no	—
231	#125	—	2	8	no	—
232	#125	—	2	2	no	—
233	#125	C₂³×C₁₉	1	4	yes	—
234	#125	C₂³×C₁₉	1	4	yes	—
235	#125	C₂³×C₁₉	1	4	yes	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	8	no	—
240	C₂²⋊Q₈	—	2	8	no	—
241	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	D₄×C₁₉	1	4	yes	—
249	#117	C₂³×C₁₉	1	4	yes	—
250	#117	C₂³×C₁₉	1	4	yes	—
251	#117	C₂³×C₁₉	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
266	#107	C₂³×C₁₉	1	16	yes	—
267	#106	C₂³×C₁₉	1	16	yes	—
268	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
269	#103	C₂³×C₁₉	1	16	yes	—
270	#103	C₂³×C₁₉	1	16	yes	—
271	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
272	#97	C₂³×C₁₉	1	4	yes	—
273	C₄×C₈	C₂³×C₁₉	1	4	yes	—
274	C₁₉	#60869	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
291	M₁₆	—	2	8	no	—
292	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
304	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
305	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	8	no	—
313	C₄²	C₂×D₄×C₁₉	1	2	yes	—
314	C₄²	C₂×D₄×C₁₉	1	2	yes	—
315	C₄²	C₂⁴×C₁₉	1	2	yes	—
316	C₄²	C₂⁴×C₁₉	1	2	yes	—
317	C₂³	—	2	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
320	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
321	Q₈	—	2	8	no	—
322	Q₈	—	4	4	no	—
323	Q₈	—	8	4	no	—
324	Q₈	—	8	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
341	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
342	C₈	—	2	8	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	8	2	no	—
347	C₂²	C₁₉×#536	1	2	yes	—
348	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	2	4	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	8	no	—
355	C₄	C₁₉×#536	1	2	yes	—
356	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
357	C₂	—	2	2	no	—
358	C₂	—	4	2	no	—
359	C₂	C₂×C₁₉×#536	1	1	yes	characteristic
360	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3242	C₂	semidirect
4. C₁₉×#3166	C₂	semidirect
5. C₁₉×#3139	C₂	semidirect
7. C₁₉×#3078	C₂	semidirect
25. C₁₉×#501	C₂²	semidirect
26. C₁₉×#499	C₂²	semidirect
27. C₁₉×#491	C₂²	semidirect
28. C₁₉×#487	C₂²	semidirect
32. C₁₉×#479	C₂²	semidirect
33. C₁₉×#477	C₂²	semidirect
34. C₁₉×#475	C₂²	semidirect
136. #60869	C₁₉	direct (N × H)
165. #3242	C₂×C₁₉	semidirect
166. #3166	C₂×C₁₉	semidirect
167. #3139	C₂×C₁₉	semidirect
169. #3078	C₂×C₁₉	semidirect
201. #501	C₂²×C₁₉	semidirect
202. #499	C₂²×C₁₉	semidirect
203. #491	C₂²×C₁₉	semidirect
204. #487	C₂²×C₁₉	semidirect
208. #479	C₂²×C₁₉	semidirect
209. #477	C₂²×C₁₉	semidirect
210. #475	C₂²×C₁₉	semidirect
274. C₁₉	#60869	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×#3458	2
C₂×C₁₉×#541	2
C₁₉×#3242	2
C₁₉×#3166	2
C₁₉×#3139	2
C₁₉×#3095	2
C₁₉×#3078	2
C₁₉×#2921	2
#60869	19

Subgroups — C19×#60869 #18066828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60869 #18066828