Subgroups — C₁₉×#17757 #18023716

Order 4864.

972 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2920	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1561	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1560	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1554	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1553	C₂	1	4	yes	maximal, complemented
7	C₁₉×#533	C₂²	1	2	yes	—
8	C₁₉×#533	C₂²	1	1	yes	characteristic
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₂²	1	2	yes	—
11	C₁₉×#529	—	2	2	no	—
12	C₁₉×#529	—	2	2	no	—
13	C₁₉×#529	C₄	1	4	yes	—
14	C₁₉×#525	—	2	2	no	—
15	C₁₉×#525	C₄	1	2	yes	—
16	C₄×#41×C₁₉	—	2	2	no	—
17	C₄×#41×C₁₉	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#432	—	2	2	no	—
20	C₁₉×#432	C₂²	1	4	yes	—
21	C₁₉×#431	—	2	2	no	—
22	C₁₉×#431	C₂²	1	4	yes	—
23	C₁₉×#423	C₂²	1	4	yes	—
24	C₁₉×#407	—	2	2	no	—
25	C₄×M₁₆×C₁₉	—	2	2	no	—
26	C₁₉×#333	C₂²	1	4	yes	complemented
27	C₁₉×#332	C₂²	1	8	yes	complemented
28	C₁₉×#331	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	—	2	4	no	—
34	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
35	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
36	C₁₉×#127	C₂³	1	1	yes	characteristic
37	C₁₉×#126	—	2	4	no	—
38	C₁₉×#125	—	2	2	no	—
39	C₁₉×#125	C₂×C₄	1	2	yes	—
40	C₁₉×#124	—	2	2	no	—
41	C₁₉×#124	C₂×C₄	1	2	yes	—
42	C₁₉×#123	—	2	4	no	—
43	C₁₉×#123	—	2	2	no	—
44	C₁₉×C₂²⋊Q₈	—	2	2	no	—
45	C₁₉×C₂²⋊Q₈	—	2	2	no	—
46	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
47	C₁₉×#121	—	2	2	no	—
48	C₁₉×#121	—	2	2	no	—
49	C₁₉×#121	C₂×C₄	1	4	yes	—
50	C₁₉×#120	—	2	2	no	—
51	C₄×Q₈×C₁₉	—	2	2	no	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	2	2	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	4	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	D₄	1	2	yes	—
69	C₂×C₄²×C₁₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₁₉×C₄⋊C₈	—	2	4	no	—
73	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
74	C₁₉×C₂²⋊C₈	—	2	4	no	—
75	C₁₉×C₂²⋊C₈	—	2	4	no	—
76	C₁₉×#97	—	2	4	no	—
77	C₄×C₈×C₁₉	—	2	4	no	—
78	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	#41×C₁₉	—	4	8	no	—
80	#41×C₁₉	—	4	4	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	4	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	M₁₆×C₁₉	—	4	8	no	—
102	C₂×C₈×C₁₉	—	2	8	no	—
103	C₄⋊C₄×C₁₉	—	2	4	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	C₂²×C₄	1	4	yes	—
109	C₂²⋊C₄×C₁₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₄²×C₁₉	—	2	4	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	2	yes	—
123	C₄²×C₁₉	C₂×D₄	1	2	yes	—
124	C₄²×C₁₉	C₂×D₄	1	2	yes	—
125	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
126	#17757	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
132	Q₈×C₁₉	—	4	2	no	—
133	Q₈×C₁₉	—	4	4	no	—
134	D₄×C₁₉	—	4	2	no	—
135	D₄×C₁₉	—	4	4	no	—
136	D₄×C₁₉	—	4	8	no	—
137	D₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	8	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
159	C₈×C₁₉	—	4	8	no	—
160	#3444	C₂×C₁₉	1	1	yes	characteristic
161	#2920	C₂×C₁₉	1	2	yes	complemented
162	#1561	C₂×C₁₉	1	2	yes	complemented
163	#1560	C₂×C₁₉	1	2	yes	complemented
164	#1554	C₂×C₁₉	1	4	yes	complemented
165	#1553	C₂×C₁₉	1	4	yes	complemented
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	4	4	no	—
172	C₂²×C₁₉	—	4	2	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₄×C₁₉	—	2	2	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	2	no	—
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	4	2	no	—
181	C₄×C₁₉	—	4	4	no	—
182	C₄×C₁₉	#413	1	2	yes	—
183	C₄×C₁₉	#575	1	4	yes	—
184	#533	C₂²×C₁₉	1	2	yes	—
185	#533	C₂²×C₁₉	1	1	yes	characteristic
186	#532	C₂²×C₁₉	1	1	yes	characteristic
187	#532	C₂²×C₁₉	1	2	yes	—
188	#529	—	2	2	no	—
189	#529	—	2	2	no	—
190	#529	C₄×C₁₉	1	4	yes	—
191	#525	—	2	2	no	—
192	#525	C₄×C₁₉	1	2	yes	—
193	C₄×#41	—	2	2	no	—
194	C₄×#41	C₄×C₁₉	1	2	yes	—
195	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
196	#432	—	2	2	no	—
197	#432	C₂²×C₁₉	1	4	yes	—
198	#431	—	2	2	no	—
199	#431	C₂²×C₁₉	1	4	yes	—
200	#423	C₂²×C₁₉	1	4	yes	—
201	#407	—	2	2	no	—
202	C₄×M₁₆	—	2	2	no	—
203	#333	C₂²×C₁₉	1	4	yes	complemented
204	#332	C₂²×C₁₉	1	8	yes	complemented
205	#331	C₂²×C₁₉	1	4	yes	complemented
206	C₂×C₁₉	—	4	1	no	—
207	C₂×C₁₉	—	4	2	no	—
208	C₂×C₁₉	—	8	2	no	—
209	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
210	C₂×C₁₉	#2896	1	2	yes	—
211	C₂×#41	—	2	2	no	—
212	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
213	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₉	1	2	yes	—
215	C₂×M₁₆	—	2	4	no	—
216	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
217	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
218	#127	C₂³×C₁₉	1	1	yes	characteristic
219	#126	—	2	4	no	—
220	#125	—	2	2	no	—
221	#125	C₂×C₄×C₁₉	1	2	yes	—
222	#124	—	2	2	no	—
223	#124	C₂×C₄×C₁₉	1	2	yes	—
224	#123	—	2	4	no	—
225	#123	—	2	2	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
229	#121	—	2	2	no	—
230	#121	—	2	2	no	—
231	#121	C₂×C₄×C₁₉	1	4	yes	—
232	#120	—	2	2	no	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₄×D₄	—	2	4	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
242	#117	—	2	2	no	—
243	#117	—	2	4	no	—
244	#117	—	2	2	no	—
245	#117	C₂×C₄×C₁₉	1	2	yes	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
249	C₂×C₄²	D₄×C₁₉	1	2	yes	—
250	C₂×C₄²	D₄×C₁₉	1	2	yes	—
251	C₂×C₄²	D₄×C₁₉	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	#97	—	2	4	no	—
259	C₄×C₈	—	2	4	no	—
260	C₁₉	#17757	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
262	#41	—	4	8	no	—
263	#41	—	4	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
278	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
284	M₁₆	—	4	8	no	—
285	C₂×C₈	—	2	8	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
300	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
301	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
302	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
303	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
304	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₁₉	1	2	yes	—
306	C₄²	C₂×D₄×C₁₉	1	2	yes	—
307	C₄²	C₂×D₄×C₁₉	1	2	yes	—
308	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
309	C₂³	—	2	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	2	no	—
312	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
313	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	4	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	4	no	—
318	D₄	—	4	8	no	—
319	D₄	—	4	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
341	C₈	—	4	8	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	4	no	—
350	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	4	no	—
358	C₄	C₁₉×#413	1	2	yes	—
359	C₄	C₁₉×#575	1	4	yes	—
360	C₂	—	4	1	no	—
361	C₂	—	4	2	no	—
362	C₂	—	8	2	no	—
363	C₂	C₂×C₁₉×#413	1	1	yes	characteristic
364	C₂	C₁₉×#2896	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2920	C₂	semidirect
3. C₁₉×#1561	C₂	semidirect
4. C₁₉×#1560	C₂	semidirect
5. C₁₉×#1554	C₂	semidirect
6. C₁₉×#1553	C₂	semidirect
26. C₁₉×#333	C₂²	semidirect
27. C₁₉×#332	C₂²	semidirect
28. C₁₉×#331	C₂²	semidirect
126. #17757	C₁₉	direct (N × H)
161. #2920	C₂×C₁₉	semidirect
162. #1561	C₂×C₁₉	semidirect
163. #1560	C₂×C₁₉	semidirect
164. #1554	C₂×C₁₉	semidirect
165. #1553	C₂×C₁₉	semidirect
203. #333	C₂²×C₁₉	semidirect
204. #332	C₂²×C₁₉	semidirect
205. #331	C₂²×C₁₉	semidirect
260. C₁₉	#17757	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×#3444	2
C₁₉×#2920	2
C₁₉×#1561	2
C₁₉×#1560	2
C₁₉×#1554	2
C₁₉×#1553	2
#17757	19

Subgroups — C19×#17757 #18023716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17757 #18023716