Subgroups — C₁₉×#18677 #18024636

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1648	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1645	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1636	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1633	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1493	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₁₉	—	2	1	no	—
13	Q₈²×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#557	—	2	2	no	—
16	C₁₉×#557	—	2	2	no	—
17	C₁₉×#557	C₂²	1	2	yes	—
18	C₁₉×#544	—	2	2	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#533	—	2	2	no	—
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₁₉×#533	C₂²	1	1	yes	characteristic
24	C₁₉×#519	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#500	C₂²	1	1	yes	characteristic
27	C₁₉×#494	C₂²	1	1	yes	characteristic
28	C₁₉×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#487	C₂²	1	1	yes	characteristic
30	C₁₉×#479	—	2	2	no	—
31	C₁₉×#477	—	2	1	no	—
32	C₁₉×#477	C₂²	1	2	yes	—
33	C₁₉×#477	C₂²	1	2	yes	—
34	C₁₉×#475	C₂²	1	2	yes	—
35	C₁₉×#467	—	2	2	no	—
36	C₁₉×#467	—	2	2	no	—
37	C₁₉×#462	—	2	1	no	—
38	C₁₉×#462	C₂²	1	2	yes	—
39	C₄×Q₁₆×C₁₉	—	2	2	no	—
40	C₁₉×#428	—	2	1	no	—
41	C₁₉×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₉×#419	—	2	1	no	—
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	4	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×C₄⋊Q₈	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	4	no	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₉×#125	—	2	4	no	—
70	C₁₉×#125	—	2	4	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	4	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
83	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	4	no	—
87	C₄×Q₈×C₁₉	—	2	2	no	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	D₄	1	2	yes	—
98	C₄×Q₈×C₁₉	D₄	1	2	yes	—
99	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
100	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
101	C₁₉×#117	—	2	4	no	—
102	C₁₉×#117	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#107	—	2	2	no	—
110	C₁₉×#107	—	2	2	no	—
111	C₁₉×#107	—	2	2	no	—
112	C₁₉×#106	—	2	2	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
116	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₄×C₈×C₁₉	—	2	1	no	—
124	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	Q₁₆	1	4	yes	complemented
134	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	Q₁₆×C₁₉	—	4	4	no	—
143	Q₁₆×C₁₉	—	8	2	no	—
144	M₁₆×C₁₉	—	4	2	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	4	2	no	—
150	C₂×C₈×C₁₉	—	8	1	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	4	1	no	—
174	C₄⋊C₄×C₁₉	—	4	1	no	—
175	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	2	4	no	—
182	C₄²×C₁₉	—	2	4	no	—
183	C₄²×C₁₉	—	2	2	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	4	1	no	—
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
192	#18677	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂³×C₁₉	#120	1	1	yes	characteristic
194	Q₈×C₁₉	—	2	2	no	—
195	Q₈×C₁₉	—	2	4	no	—
196	Q₈×C₁₉	—	2	2	no	—
197	Q₈×C₁₉	—	2	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	4	1	no	—
201	Q₈×C₁₉	—	4	1	no	—
202	Q₈×C₁₉	—	4	1	no	—
203	Q₈×C₁₉	—	4	1	no	—
204	Q₈×C₁₉	—	8	1	no	—
205	Q₈×C₁₉	—	8	4	no	—
206	Q₈×C₁₉	C₂×Q₁₆	1	4	yes	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	8	1	no	—
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
224	C₂×C₄×C₁₉	#137	1	2	yes	—
225	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₁₉	—	2	2	no	—
229	C₈×C₁₉	—	4	1	no	—
230	C₈×C₁₉	—	4	2	no	—
231	C₈×C₁₉	—	4	2	no	—
232	#3502	C₂×C₁₉	1	1	yes	characteristic
233	#3249	C₂×C₁₉	1	1	yes	characteristic
234	#3170	C₂×C₁₉	1	1	yes	characteristic
235	#3078	C₂×C₁₉	1	1	yes	characteristic
236	#1648	C₂×C₁₉	1	2	yes	complemented
237	#1645	C₂×C₁₉	1	2	yes	complemented
238	#1636	C₂×C₁₉	1	2	yes	complemented
239	#1633	C₂×C₁₉	1	2	yes	complemented
240	#1550	C₂×C₁₉	1	1	yes	characteristic
241	#1493	C₂×C₁₉	1	1	yes	characteristic
242	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	#451	1	2	yes	—
246	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
247	C₄×C₁₉	—	2	4	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	4	2	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	8	1	no	—
257	C₄×C₁₉	—	8	1	no	—
258	C₄×C₁₉	#451	1	2	yes	—
259	C₄×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
260	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
261	C₄×C₁₉	#577	1	1	yes	characteristic
262	C₄×C₁₉	#578	1	1	yes	characteristic
263	Q₈²	—	2	1	no	—
264	Q₈²	C₂²×C₁₉	1	2	yes	—
265	#557	—	2	1	no	—
266	#557	—	2	2	no	—
267	#557	—	2	2	no	—
268	#557	C₂²×C₁₉	1	2	yes	—
269	#544	—	2	2	no	—
270	#544	—	2	1	no	—
271	#533	—	2	2	no	—
272	#533	C₂²×C₁₉	1	1	yes	characteristic
273	#533	C₂²×C₁₉	1	1	yes	characteristic
274	#533	C₂²×C₁₉	1	1	yes	characteristic
275	#519	—	2	1	no	—
276	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	#500	C₂²×C₁₉	1	1	yes	characteristic
278	#494	C₂²×C₁₉	1	1	yes	characteristic
279	#487	C₂²×C₁₉	1	1	yes	characteristic
280	#487	C₂²×C₁₉	1	1	yes	characteristic
281	#479	—	2	2	no	—
282	#477	—	2	1	no	—
283	#477	C₂²×C₁₉	1	2	yes	—
284	#477	C₂²×C₁₉	1	2	yes	—
285	#475	C₂²×C₁₉	1	2	yes	—
286	#467	—	2	2	no	—
287	#467	—	2	2	no	—
288	#462	—	2	1	no	—
289	#462	C₂²×C₁₉	1	2	yes	—
290	C₄×Q₁₆	—	2	2	no	—
291	#428	—	2	1	no	—
292	#423	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
294	#419	—	2	1	no	—
295	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
296	#333	C₂²×C₁₉	1	2	yes	—
297	#332	C₂²×C₁₉	1	2	yes	—
298	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
299	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
300	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
301	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
302	C₂×C₁₉	—	2	2	no	—
303	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
304	C₂×C₁₉	#3013	1	1	yes	characteristic
305	C₂×C₁₉	#3018	1	1	yes	characteristic
306	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
319	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
324	#125	—	2	4	no	—
325	#125	—	2	4	no	—
326	#125	—	2	2	no	—
327	#125	—	2	4	no	—
328	#125	—	2	2	no	—
329	#125	—	2	1	no	—
330	#125	—	2	1	no	—
331	#125	—	2	1	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
338	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	D₄×C₁₉	1	2	yes	—
353	C₄×Q₈	D₄×C₁₉	1	2	yes	—
354	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
355	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
356	#117	—	2	4	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#107	—	2	2	no	—
366	#107	—	2	2	no	—
367	#106	—	2	2	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
371	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	C₄×C₈	—	2	1	no	—
379	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₁₉	#18677	1	1	yes	characteristic, direct product factor, Sylow
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	Q₁₆×C₁₉	1	4	yes	complemented
390	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
391	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
392	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	Q₁₆	—	4	4	no	—
399	Q₁₆	—	8	2	no	—
400	M₁₆	—	4	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	8	1	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	4	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	4	1	no	—
444	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
448	C₂³	C₁₉×#120	1	1	yes	characteristic
449	Q₈	—	2	4	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	8	1	no	—
460	Q₈	—	8	4	no	—
461	Q₈	C₂×Q₁₆×C₁₉	1	4	yes	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
476	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
477	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
478	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
479	C₂×C₄	C₁₉×#137	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	4	1	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	C₁₉×#451	1	2	yes	—
490	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
491	C₄	—	2	4	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	8	1	no	—
501	C₄	—	8	1	no	—
502	C₄	C₁₉×#451	1	2	yes	—
503	C₄	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
504	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
505	C₄	C₁₉×#577	1	1	yes	characteristic
506	C₄	C₁₉×#578	1	1	yes	characteristic
507	C₂	—	2	2	no	—
508	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
509	C₂	C₁₉×#3013	1	1	yes	characteristic
510	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
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
5. C₁₉×#1648	C₂	semidirect
6. C₁₉×#1645	C₂	semidirect
7. C₁₉×#1636	C₂	semidirect
8. C₁₉×#1633	C₂	semidirect
133. C₂×Q₈×C₁₉	Q₁₆	semidirect
192. #18677	C₁₉	direct (N × H)
236. #1648	C₂×C₁₉	semidirect
237. #1645	C₂×C₁₉	semidirect
238. #1636	C₂×C₁₉	semidirect
239. #1633	C₂×C₁₉	semidirect
381. C₁₉	#18677	direct (N × H)
389. C₂×Q₈	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×#3502	2
C₁₉×#3249	2
C₁₉×#3170	2
C₁₉×#3078	2
C₁₉×#1648	2
C₁₉×#1645	2
C₁₉×#1636	2
C₁₉×#1633	2
C₁₉×#1550	2
C₁₉×#1493	2
C₂×C₁₉×Q₈⋊C₈	2
#18677	19

Subgroups — C19×#18677 #18024636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18677 #18024636