Subgroups — C₁₉×#19789 #18025748

Order 4864.

680 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1619	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	—	2	1	no	—
17	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	D₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#492	C₂²	1	1	yes	characteristic
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#481	—	2	1	no	—
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#476	—	2	1	no	—
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#465	—	2	1	no	—
36	C₁₉×#465	—	2	1	no	—
37	C₁₉×#463	—	2	1	no	—
38	C₁₉×#463	—	2	1	no	—
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#442	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×D₈×C₁₉	—	2	1	no	—
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	4	4	no	—
76	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×D₈×C₁₉	—	2	1	no	—
80	C₂×D₈×C₁₉	—	4	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#127	C₂³	1	1	yes	characteristic
87	C₁₉×#127	C₂³	1	1	yes	characteristic
88	C₁₉×#125	—	2	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#123	—	4	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	4	1	no	—
95	C₁₉×C₂²⋊Q₈	—	4	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	1	no	—
98	C₁₉×#120	—	4	1	no	—
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
111	C₁₉×#106	D₄	1	1	yes	characteristic
112	C₁₉×#106	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	4	1	no	—
123	C₁₉×#103	D₄	1	1	yes	characteristic
124	C₁₉×#103	D₄	1	1	yes	characteristic
125	C₁₉×#102	—	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×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	4	2	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	SD₁₆×C₁₉	—	2	2	no	—
173	SD₁₆×C₁₉	—	2	2	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	8	1	no	—
178	SD₁₆×C₁₉	—	8	1	no	—
179	D₈×C₁₉	—	4	2	no	—
180	D₈×C₁₉	—	4	2	no	—
181	D₈×C₁₉	—	8	2	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	4	2	no	—
188	C₂×C₈×C₁₉	—	8	1	no	—
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₂²⋊C₄×C₁₉	—	4	1	no	—
213	C₂²⋊C₄×C₁₉	—	4	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
217	#19789	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	8	2	no	—
223	C₂³×C₁₉	—	8	2	no	—
224	C₂³×C₁₉	—	16	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	2	1	no	—
228	Q₈×C₁₉	—	2	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	8	1	no	—
232	Q₈×C₁₉	—	8	2	no	—
233	D₄×C₁₉	—	2	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	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	—	8	1	no	—
244	D₄×C₁₉	—	8	1	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	8	2	no	—
247	D₄×C₁₉	#135	1	2	yes	—
248	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	16	1	no	—
263	C₂×C₄×C₁₉	—	16	1	no	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₁₉	—	2	1	no	—
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	4	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	#3373	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#3361	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3295	C₂×C₁₉	1	1	yes	characteristic, complemented
279	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1717	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1643	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1637	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1620	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1619	C₂×C₁₉	1	1	yes	characteristic
289	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
290	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	16	4	no	—
304	C₂²×C₁₉	D₄²	1	1	yes	characteristic
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	8	1	no	—
313	C₄×C₁₉	—	8	1	no	—
314	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
315	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₄×C₁₉	#577	1	1	yes	characteristic
317	C₄×C₁₉	#577	1	1	yes	characteristic
318	C₂²×SD₁₆	—	2	1	no	—
319	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#554	C₂²×C₁₉	1	1	yes	characteristic
321	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	D₄²	C₂²×C₁₉	1	1	yes	characteristic
323	#493	C₂²×C₁₉	1	1	yes	characteristic
324	#492	C₂²×C₁₉	1	1	yes	characteristic
325	#489	—	2	1	no	—
326	#488	—	2	1	no	—
327	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
328	#486	C₂²×C₁₉	1	1	yes	characteristic
329	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
331	#481	—	2	1	no	—
332	#478	—	2	1	no	—
333	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	#476	—	2	1	no	—
335	#476	C₂²×C₁₉	1	1	yes	characteristic
336	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#465	—	2	1	no	—
338	#465	—	2	1	no	—
339	#463	—	2	1	no	—
340	#463	—	2	1	no	—
341	#461	C₂²×C₁₉	1	1	yes	characteristic
342	#460	C₂²×C₁₉	1	1	yes	characteristic
343	#460	C₂²×C₁₉	1	1	yes	characteristic
344	#459	C₂²×C₁₉	1	1	yes	characteristic
345	#459	C₂²×C₁₉	1	1	yes	characteristic
346	#450	—	2	1	no	—
347	#450	—	2	1	no	—
348	#448	—	2	1	no	—
349	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
350	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	#442	—	2	1	no	—
352	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
353	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
354	C₄×D₈	—	2	1	no	—
355	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#102	—	2	1	no	—
358	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#331	C₂²×C₁₉	1	1	yes	characteristic
363	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
367	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
368	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	—	4	2	no	—
371	C₂×C₁₉	—	16	1	no	—
372	C₂×C₁₉	—	16	1	no	—
373	C₂×C₁₉	#3265	1	1	yes	characteristic
374	C₂×C₁₉	#3282	1	1	yes	characteristic
375	C₂×C₁₉	#3288	1	1	yes	characteristic
376	C₂²×Q₈	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×SD₁₆	—	2	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	4	4	no	—
385	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
386	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	4	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	#127	C₂³×C₁₉	1	1	yes	characteristic
396	#127	C₂³×C₁₉	1	1	yes	characteristic
397	#125	—	2	1	no	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#123	—	4	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	4	1	no	—
404	C₂²⋊Q₈	—	4	1	no	—
405	#121	—	2	1	no	—
406	#121	—	2	1	no	—
407	#120	—	4	1	no	—
408	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	2	1	no	—
417	#107	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	—	2	1	no	—
420	#106	D₄×C₁₉	1	1	yes	characteristic
421	#106	D₄×C₁₉	1	1	yes	characteristic
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#103	—	4	1	no	—
432	#103	D₄×C₁₉	1	1	yes	characteristic
433	#103	D₄×C₁₉	1	1	yes	characteristic
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	D₄×C₁₉	1	1	yes	characteristic
446	#102	D₄×C₁₉	1	1	yes	characteristic
447	C₂²⋊C₈	—	2	1	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	#97	—	2	1	no	—
450	C₄×C₈	—	2	1	no	—
451	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
452	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
454	C₁₉	#19789	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁴	—	4	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	4	1	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	—	8	1	no	—
461	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	8	1	no	—
474	C₂×D₄	—	8	1	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	SD₁₆	—	2	2	no	—
483	SD₁₆	—	2	2	no	—
484	SD₁₆	—	4	2	no	—
485	SD₁₆	—	4	2	no	—
486	SD₁₆	—	4	2	no	—
487	SD₁₆	—	8	1	no	—
488	SD₁₆	—	8	1	no	—
489	D₈	—	4	2	no	—
490	D₈	—	4	2	no	—
491	D₈	—	8	2	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	4	2	no	—
498	C₂×C₈	—	8	1	no	—
499	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	8	2	no	—
532	C₂³	—	8	2	no	—
533	C₂³	—	16	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	8	1	no	—
541	Q₈	—	8	2	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	1	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	C₁₉×#135	1	2	yes	—
557	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	16	1	no	—
572	C₂×C₄	—	16	1	no	—
573	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	16	4	no	—
598	C₂²	D₄²×C₁₉	1	1	yes	characteristic
599	C₄	—	2	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
609	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
610	C₄	C₁₉×#577	1	1	yes	characteristic
611	C₄	C₁₉×#577	1	1	yes	characteristic
612	C₂	—	4	2	no	—
613	C₂	—	4	2	no	—
614	C₂	—	16	1	no	—
615	C₂	—	16	1	no	—
616	C₂	C₁₉×#3265	1	1	yes	characteristic
617	C₂	C₁₉×#3282	1	1	yes	characteristic
618	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#1619	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3373	C₂	semidirect
2. C₁₉×#3361	C₂	semidirect
3. C₁₉×#3295	C₂	semidirect
4. D₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1717	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1681	C₂	semidirect
8. C₁₉×#1677	C₂	semidirect
9. C₁₉×#1666	C₂	semidirect
10. C₁₉×#1643	C₂	semidirect
11. C₁₉×#1637	C₂	semidirect
12. C₁₉×#1620	C₂	semidirect
14. C₁₉×#1582	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
17. C₁₉×#559	C₂²	semidirect
25. C₁₉×#487	C₂²	semidirect
27. C₁₉×#486	C₂²	semidirect
28. C₁₉×#486	C₂²	semidirect
31. C₁₉×#477	C₂²	semidirect
34. C₁₉×#475	C₂²	semidirect
47. C₁₉×#446	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
217. #19789	C₁₉	direct (N × H)
276. #3373	C₂×C₁₉	semidirect
277. #3361	C₂×C₁₉	semidirect
278. #3295	C₂×C₁₉	semidirect
279. D₄×SD₁₆	C₂×C₁₉	semidirect
280. #1717	C₂×C₁₉	semidirect
281. #1698	C₂×C₁₉	semidirect
282. #1681	C₂×C₁₉	semidirect
283. #1677	C₂×C₁₉	semidirect
284. #1666	C₂×C₁₉	semidirect
285. #1643	C₂×C₁₉	semidirect
286. #1637	C₂×C₁₉	semidirect
287. #1620	C₂×C₁₉	semidirect
289. #1582	C₂×C₁₉	semidirect
290. SD₁₆⋊C₈	C₂×C₁₉	semidirect
319. #559	C₂²×C₁₉	semidirect
327. #487	C₂²×C₁₉	semidirect
329. #486	C₂²×C₁₉	semidirect
330. #486	C₂²×C₁₉	semidirect
333. #477	C₂²×C₁₉	semidirect
336. #475	C₂²×C₁₉	semidirect
349. #446	C₂²×C₁₉	semidirect
350. C₈×Q₈	C₂²×C₁₉	semidirect
358. #335	C₂²×C₁₉	semidirect
359. #334	C₂²×C₁₉	semidirect
360. #333	C₂²×C₁₉	semidirect
361. #332	C₂²×C₁₉	semidirect
363. #331	C₂²×C₁₉	semidirect
364. Q₈⋊C₈	C₂²×C₁₉	semidirect
365. Q₈⋊C₈	C₂²×C₁₉	semidirect
368. #322	C₂²×C₁₉	semidirect
454. C₁₉	#19789	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×#3373	2
C₁₉×#3361	2
C₁₉×#3295	2
D₄×SD₁₆×C₁₉	2
C₁₉×#1717	2
C₁₉×#1698	2
C₁₉×#1681	2
C₁₉×#1677	2
C₁₉×#1666	2
C₁₉×#1643	2
C₁₉×#1637	2
C₁₉×#1620	2
C₁₉×#1619	2
C₁₉×#1582	2
C₁₉×SD₁₆⋊C₈	2
#19789	19

Subgroups — C19×#19789 #18025748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19789 #18025748