Subgroups — C₁₉×#19306 #18025265

Order 4864.

732 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂²×M₁₆×C₁₉	—	2	1	no	—
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#481	—	2	1	no	—
26	C₁₉×#476	C₂²	1	1	yes	characteristic
27	C₁₉×#476	C₂²	1	1	yes	characteristic
28	C₁₉×#469	—	2	1	no	—
29	C₁₉×#469	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#463	—	2	1	no	—
32	C₁₉×#461	C₂²	1	1	yes	characteristic
33	C₁₉×#461	C₂²	1	1	yes	characteristic
34	C₁₉×#459	C₂²	1	1	yes	characteristic
35	C₁₉×#459	C₂²	1	1	yes	characteristic
36	C₁₉×#459	C₂²	1	1	yes	characteristic
37	C₁₉×#459	C₂²	1	1	yes	characteristic
38	C₁₉×#447	—	2	1	no	—
39	C₁₉×#442	—	2	1	no	—
40	C₁₉×#442	—	2	1	no	—
41	C₁₉×#442	—	2	1	no	—
42	C₁₉×#442	—	2	1	no	—
43	C₁₉×#436	C₂²	1	1	yes	characteristic
44	C₁₉×#436	C₂²	1	1	yes	characteristic
45	C₁₉×#435	—	2	1	no	—
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#432	C₂²	1	1	yes	characteristic
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#417	—	2	1	no	—
53	C₁₉×#407	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×D₈×C₁₉	—	2	1	no	—
75	C₂×D₈×C₁₉	—	2	1	no	—
76	C₂×D₈×C₁₉	—	2	1	no	—
77	C₂×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	4	4	no	—
85	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
87	C₂²×C₈×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×#127	C₂³	1	1	yes	characteristic
92	C₁₉×#127	C₂³	1	1	yes	characteristic
93	C₁₉×#124	—	2	1	no	—
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×#97	—	2	1	no	—
142	C₁₉×#97	D₄	1	1	yes	characteristic
143	C₁₉×#97	D₄	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	2	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	4	2	no	—
149	#41×C₁₉	—	8	2	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	4	1	no	—
163	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	4	2	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	D₈×C₁₉	—	4	2	no	—
180	D₈×C₁₉	—	4	2	no	—
181	D₈×C₁₉	—	4	2	no	—
182	D₈×C₁₉	—	4	2	no	—
183	D₈×C₁₉	—	4	2	no	—
184	D₈×C₁₉	—	4	2	no	—
185	M₁₆×C₁₉	—	2	2	no	—
186	M₁₆×C₁₉	—	4	1	no	—
187	M₁₆×C₁₉	—	4	2	no	—
188	M₁₆×C₁₉	—	4	2	no	—
189	M₁₆×C₁₉	—	4	2	no	—
190	M₁₆×C₁₉	—	4	2	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	4	2	no	—
198	C₂×C₈×C₁₉	—	4	2	no	—
199	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	1	no	—
215	C₂²⋊C₄×C₁₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₉	#41	1	1	yes	characteristic
221	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
222	#19306	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	4	2	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	8	1	no	—
230	C₂³×C₁₉	#121	1	1	yes	characteristic
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	2	1	no	—
236	D₄×C₁₉	—	2	1	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	1	no	—
248	D₄×C₁₉	—	8	2	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₈×C₁₉	—	2	1	no	—
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	2	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
285	#3184	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3109	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3036	C₂×C₁₉	1	1	yes	characteristic, complemented
288	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1697	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	8	4	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₄×C₁₉	#575	1	1	yes	characteristic
328	C₄×C₁₉	#575	1	1	yes	characteristic
329	C₂×AGL(1,ℤ/8)	—	2	1	no	—
330	C₂²×M₁₆	—	2	1	no	—
331	#532	C₂²×C₁₉	1	1	yes	characteristic
332	#532	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
334	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
335	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#481	—	2	1	no	—
339	#476	C₂²×C₁₉	1	1	yes	characteristic
340	#476	C₂²×C₁₉	1	1	yes	characteristic
341	#469	—	2	1	no	—
342	#469	—	2	1	no	—
343	#463	—	2	1	no	—
344	#463	—	2	1	no	—
345	#461	C₂²×C₁₉	1	1	yes	characteristic
346	#461	C₂²×C₁₉	1	1	yes	characteristic
347	#459	C₂²×C₁₉	1	1	yes	characteristic
348	#459	C₂²×C₁₉	1	1	yes	characteristic
349	#459	C₂²×C₁₉	1	1	yes	characteristic
350	#459	C₂²×C₁₉	1	1	yes	characteristic
351	#447	—	2	1	no	—
352	#442	—	2	1	no	—
353	#442	—	2	1	no	—
354	#442	—	2	1	no	—
355	#442	—	2	1	no	—
356	#436	C₂²×C₁₉	1	1	yes	characteristic
357	#436	C₂²×C₁₉	1	1	yes	characteristic
358	#435	—	2	1	no	—
359	#435	—	2	1	no	—
360	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
361	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
362	#432	C₂²×C₁₉	1	1	yes	characteristic
363	#423	C₂²×C₁₉	1	1	yes	characteristic
364	#423	C₂²×C₁₉	1	1	yes	characteristic
365	#417	—	2	1	no	—
366	#407	—	2	1	no	—
367	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
368	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
379	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	C₂×C₁₉	—	4	1	no	—
381	C₂×C₁₉	—	4	2	no	—
382	C₂×C₁₉	—	8	1	no	—
383	C₂×C₁₉	—	16	1	no	—
384	C₂×C₁₉	—	16	1	no	—
385	C₂×C₁₉	#3036	1	1	yes	characteristic
386	C₂×C₁₉	#3055	1	1	yes	characteristic
387	C₂×C₁₉	#3068	1	1	yes	characteristic
388	C₂×#41	—	2	1	no	—
389	C₂×#41	—	2	1	no	—
390	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	AGL(1,ℤ/8)	—	4	4	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	—	2	1	no	—
399	C₂×D₈	—	2	1	no	—
400	C₂×D₈	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	2	1	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	—	4	4	no	—
406	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
407	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
412	#127	C₂³×C₁₉	1	1	yes	characteristic
413	#127	C₂³×C₁₉	1	1	yes	characteristic
414	#124	—	2	1	no	—
415	#124	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
427	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
428	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#106	—	2	1	no	—
434	#106	—	2	1	no	—
435	#106	—	2	1	no	—
436	#106	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	C₂²⋊C₈	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	#97	—	2	1	no	—
463	#97	D₄×C₁₉	1	1	yes	characteristic
464	#97	D₄×C₁₉	1	1	yes	characteristic
465	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
466	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
467	C₁₉	#19306	1	1	yes	characteristic, direct product factor, Sylow
468	C₂⁴	—	2	1	no	—
469	#41	—	4	2	no	—
470	#41	—	4	2	no	—
471	#41	—	8	2	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	4	2	no	—
501	D₈	—	4	2	no	—
502	D₈	—	4	2	no	—
503	D₈	—	4	2	no	—
504	D₈	—	4	2	no	—
505	D₈	—	4	2	no	—
506	D₈	—	4	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	4	1	no	—
509	M₁₆	—	4	2	no	—
510	M₁₆	—	4	2	no	—
511	M₁₆	—	4	2	no	—
512	M₁₆	—	4	2	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	4	2	no	—
520	C₂×C₈	—	4	2	no	—
521	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₄²	#41×C₁₉	1	1	yes	characteristic
543	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	8	1	no	—
551	C₂³	C₁₉×#121	1	1	yes	characteristic
552	Q₈	—	4	1	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	8	1	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	2	1	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	8	1	no	—
568	D₄	—	8	1	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	2	no	—
571	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
591	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
592	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	complemented
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	8	4	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
632	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₄	C₁₉×#575	1	1	yes	characteristic
634	C₄	C₁₉×#575	1	1	yes	characteristic
635	C₂	—	4	1	no	—
636	C₂	—	4	2	no	—
637	C₂	—	8	1	no	—
638	C₂	—	16	1	no	—
639	C₂	—	16	1	no	—
640	C₂	C₁₉×#3036	1	1	yes	characteristic
641	C₂	C₁₉×#3055	1	1	yes	characteristic
642	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3184	C₂	semidirect
2. C₁₉×#3109	C₂	semidirect
3. C₁₉×#3036	C₂	semidirect
4. D₄×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1701	C₂	semidirect
6. C₁₉×#1697	C₂	semidirect
7. C₁₉×#1691	C₂	semidirect
8. C₁₉×#1687	C₂	semidirect
9. C₁₉×#1681	C₂	semidirect
10. C₁₉×#1677	C₂	semidirect
11. C₁₉×#1671	C₂	semidirect
12. C₁₉×#1667	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1560	C₂	semidirect
15. C₁₉×#1557	C₂	semidirect
21. C₁₉×#498	C₂²	semidirect
22. C₁₉×#493	C₂²	semidirect
23. C₁₉×#486	C₂²	semidirect
24. C₁₉×#486	C₂²	semidirect
55. C₁₉×#335	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#334	C₂²	semidirect
59. C₁₉×#333	C₂²	semidirect
60. C₁₉×#333	C₂²	semidirect
61. C₁₉×#332	C₂²	semidirect
62. C₁₉×#332	C₂²	semidirect
63. C₁₉×#331	C₂²	semidirect
64. C₁₉×#331	C₂²	semidirect
65. C₁₉×#331	C₂²	semidirect
66. C₁₉×#331	C₂²	semidirect
222. #19306	C₁₉	direct (N × H)
284. C₈×C₁₉	AGL(1,ℤ/8)	semidirect
285. #3184	C₂×C₁₉	semidirect
286. #3109	C₂×C₁₉	semidirect
287. #3036	C₂×C₁₉	semidirect
288. D₄×M₁₆	C₂×C₁₉	semidirect
289. #1701	C₂×C₁₉	semidirect
290. #1697	C₂×C₁₉	semidirect
291. #1691	C₂×C₁₉	semidirect
292. #1687	C₂×C₁₉	semidirect
293. #1681	C₂×C₁₉	semidirect
294. #1677	C₂×C₁₉	semidirect
295. #1671	C₂×C₁₉	semidirect
296. #1667	C₂×C₁₉	semidirect
297. #1569	C₂×C₁₉	semidirect
298. #1560	C₂×C₁₉	semidirect
299. #1557	C₂×C₁₉	semidirect
334. #498	C₂²×C₁₉	semidirect
335. #493	C₂²×C₁₉	semidirect
336. #486	C₂²×C₁₉	semidirect
337. #486	C₂²×C₁₉	semidirect
368. #335	C₂²×C₁₉	semidirect
369. #335	C₂²×C₁₉	semidirect
370. #334	C₂²×C₁₉	semidirect
371. #334	C₂²×C₁₉	semidirect
372. #333	C₂²×C₁₉	semidirect
373. #333	C₂²×C₁₉	semidirect
374. #332	C₂²×C₁₉	semidirect
375. #332	C₂²×C₁₉	semidirect
376. #331	C₂²×C₁₉	semidirect
377. #331	C₂²×C₁₉	semidirect
378. #331	C₂²×C₁₉	semidirect
379. #331	C₂²×C₁₉	semidirect
467. C₁₉	#19306	direct (N × H)
605. C₈	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3184	2
C₁₉×#3109	2
C₁₉×#3036	2
D₄×M₁₆×C₁₉	2
C₁₉×#1701	2
C₁₉×#1697	2
C₁₉×#1691	2
C₁₉×#1687	2
C₁₉×#1681	2
C₁₉×#1677	2
C₁₉×#1671	2
C₁₉×#1667	2
C₁₉×#1569	2
C₁₉×#1560	2
C₁₉×#1557	2
#19306	19

Subgroups — C19×#19306 #18025265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19306 #18025265