Subgroups — C₁₉×#18805 #18024764

Order 4864.

968 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1650	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1647	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1646	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1643	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	—	2	1	no	—
13	C₁₉×#556	C₂²	1	1	yes	characteristic
14	C₁₉×#555	C₂²	1	1	yes	characteristic
15	C₁₉×#554	C₂²	1	1	yes	characteristic
16	C₁₉×#553	—	2	1	no	—
17	C₁₉×#552	—	2	1	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#551	—	2	2	no	—
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#546	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	—	2	2	no	—
25	C₁₉×#529	—	2	1	no	—
26	C₁₉×#525	—	2	1	no	—
27	C₄×#41×C₁₉	—	2	1	no	—
28	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	—	2	1	no	—
31	C₁₉×#500	C₂²	1	2	yes	complemented
32	C₁₉×#487	C₂²	1	2	yes	complemented
33	C₁₉×#484	—	2	2	no	—
34	C₁₉×#477	—	2	2	no	—
35	C₁₉×#477	—	2	1	no	—
36	C₁₉×#476	—	2	1	no	—
37	C₁₉×#475	C₂²	1	2	yes	complemented
38	C₁₉×#474	C₂²	1	2	yes	complemented
39	C₁₉×#461	—	2	1	no	—
40	C₁₉×#461	—	2	1	no	—
41	C₁₉×#461	C₂²	1	2	yes	—
42	C₁₉×#461	C₂²	1	2	yes	—
43	C₁₉×#431	C₂²	1	1	yes	characteristic
44	C₁₉×#428	—	2	1	no	—
45	C₁₉×#423	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₉×#417	—	2	1	no	—
48	C₂×C₁₉×#103	—	2	1	no	—
49	C₁₉×#333	C₂²	1	2	yes	complemented
50	C₁₉×#332	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	4	4	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#126	—	2	2	no	—
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#120	—	2	2	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	D₄	1	2	yes	—
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	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	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
108	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
110	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#117	—	2	2	no	—
114	C₁₉×#117	—	2	2	no	—
115	C₁₉×#117	—	2	2	no	—
116	C₁₉×#117	—	2	1	no	—
117	C₁₉×#117	—	2	1	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	—	2	1	no	—
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	—	2	2	no	—
130	C₂×C₄²×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#107	—	2	2	no	—
133	C₁₉×#107	—	2	4	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×C₄⋊C₈	—	2	1	no	—
138	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
140	C₁₉×#103	—	2	2	no	—
141	C₁₉×#103	—	2	4	no	—
142	C₁₉×#103	—	2	2	no	—
143	C₁₉×#103	—	2	2	no	—
144	C₁₉×#102	—	2	2	no	—
145	C₁₉×C₂²⋊C₈	—	2	1	no	—
146	C₄×C₈×C₁₉	C₂³	1	2	yes	—
147	C₂⁴×C₁₉	—	2	1	no	—
148	#41×C₁₉	—	2	2	no	—
149	#41×C₁₉	—	2	2	no	—
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	4	2	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	2	no	—
154	C₂×Q₈×C₁₉	—	4	2	no	—
155	C₂×Q₈×C₁₉	—	4	2	no	—
156	C₂×Q₈×C₁₉	—	4	1	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	4	1	no	—
165	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	4	2	no	—
179	C₂²×C₄×C₁₉	—	4	2	no	—
180	C₂²×C₄×C₁₉	—	4	1	no	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	SD₁₆×C₁₉	—	4	4	no	—
185	SD₁₆×C₁₉	—	4	4	no	—
186	M₁₆×C₁₉	—	4	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	2	2	no	—
190	C₂×C₈×C₁₉	—	4	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₄²×C₁₉	—	2	2	no	—
227	C₄²×C₁₉	—	2	2	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	—	2	2	no	—
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
236	#18805	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	8	1	no	—
243	C₂³×C₁₉	#120	1	1	yes	characteristic
244	Q₈×C₁₉	—	2	1	no	—
245	Q₈×C₁₉	—	2	1	no	—
246	Q₈×C₁₉	—	4	2	no	—
247	Q₈×C₁₉	—	4	1	no	—
248	Q₈×C₁₉	—	4	1	no	—
249	Q₈×C₁₉	—	4	2	no	—
250	Q₈×C₁₉	—	4	2	no	—
251	Q₈×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	2	1	no	—
253	D₄×C₁₉	—	2	1	no	—
254	D₄×C₁₉	—	2	1	no	—
255	D₄×C₁₉	—	2	1	no	—
256	D₄×C₁₉	—	2	1	no	—
257	D₄×C₁₉	—	4	2	no	—
258	D₄×C₁₉	—	4	4	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	8	2	no	—
261	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	4	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	2	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	8	1	no	—
285	C₂×C₄×C₁₉	—	8	2	no	—
286	C₂×C₄×C₁₉	—	8	2	no	—
287	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
288	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
290	C₂×C₄×C₁₉	#135	1	2	yes	—
291	C₂×C₄×C₁₉	#137	1	2	yes	—
292	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
295	C₈×C₁₉	—	4	2	no	—
296	C₈×C₁₉	—	4	2	no	—
297	C₈×C₁₉	—	4	2	no	—
298	#3475	C₂×C₁₉	1	1	yes	characteristic
299	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
301	C₂×#461	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1650	C₂×C₁₉	1	2	yes	complemented
303	#1647	C₂×C₁₉	1	2	yes	complemented
304	#1646	C₂×C₁₉	1	2	yes	complemented
305	#1643	C₂×C₁₉	1	2	yes	complemented
306	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1477	C₂×C₁₉	1	1	yes	characteristic, complemented
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	2	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	8	4	no	—
321	C₂²×C₁₉	#452	1	2	yes	—
322	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	—	2	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	4	1	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	—	4	1	no	—
330	C₄×C₁₉	—	4	2	no	—
331	C₄×C₁₉	—	4	1	no	—
332	C₄×C₁₉	—	4	2	no	—
333	C₄×C₁₉	—	8	2	no	—
334	C₄×C₁₉	#452	1	2	yes	—
335	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
336	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
338	C₄×C₁₉	#575	1	1	yes	characteristic
339	C₂²×SD₁₆	—	2	1	no	—
340	#556	C₂²×C₁₉	1	1	yes	characteristic
341	#555	C₂²×C₁₉	1	1	yes	characteristic
342	#554	C₂²×C₁₉	1	1	yes	characteristic
343	#553	—	2	1	no	—
344	#552	—	2	1	no	—
345	#552	—	2	1	no	—
346	#551	—	2	2	no	—
347	#547	C₂²×C₁₉	1	1	yes	characteristic
348	#546	—	2	1	no	—
349	#533	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
351	#529	—	2	2	no	—
352	#529	—	2	1	no	—
353	#525	—	2	1	no	—
354	C₄×#41	—	2	1	no	—
355	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#117	—	2	1	no	—
358	#500	C₂²×C₁₉	1	2	yes	complemented
359	#487	C₂²×C₁₉	1	2	yes	complemented
360	#484	—	2	2	no	—
361	#477	—	2	1	no	—
362	#477	—	2	2	no	—
363	#476	—	2	1	no	—
364	#475	C₂²×C₁₉	1	2	yes	complemented
365	#474	C₂²×C₁₉	1	2	yes	complemented
366	#461	—	2	1	no	—
367	#461	—	2	1	no	—
368	#461	C₂²×C₁₉	1	2	yes	—
369	#461	C₂²×C₁₉	1	2	yes	—
370	#431	C₂²×C₁₉	1	1	yes	characteristic
371	#428	—	2	1	no	—
372	#423	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
374	#417	—	2	1	no	—
375	C₂×#103	—	2	1	no	—
376	#333	C₂²×C₁₉	1	2	yes	complemented
377	#332	C₂²×C₁₉	1	2	yes	complemented
378	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
379	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
380	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
381	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
382	C₂×C₁₉	—	2	2	no	—
383	C₂×C₁₉	—	4	2	no	—
384	C₂×C₁₉	—	8	1	no	—
385	C₂×C₁₉	—	8	1	no	—
386	C₂×C₁₉	C₂×#452	1	1	yes	characteristic
387	C₂×C₁₉	#3006	1	1	yes	characteristic
388	C₂×C₁₉	#3022	1	1	yes	characteristic
389	C₂×#41	—	2	1	no	—
390	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
391	C₂²×Q₈	—	2	1	no	—
392	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
393	C₂³×C₄	—	2	1	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	—	4	4	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
403	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
405	#126	—	2	2	no	—
406	#126	—	2	2	no	—
407	#126	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	1	no	—
410	#125	—	2	1	no	—
411	#124	—	2	2	no	—
412	#124	—	2	1	no	—
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	#123	—	2	2	no	—
416	#123	—	2	2	no	—
417	C₂²⋊Q₈	—	2	1	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
423	#121	—	2	2	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#120	—	2	2	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
431	C₄×Q₈	D₄×C₁₉	1	2	yes	—
432	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
442	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
443	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
444	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	—	2	2	no	—
450	#117	—	2	1	no	—
451	#117	—	2	1	no	—
452	#117	—	2	1	no	—
453	#117	—	2	1	no	—
454	#117	—	2	1	no	—
455	#117	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	2	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₄²	—	2	2	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
466	#107	—	2	2	no	—
467	#107	—	2	4	no	—
468	#106	—	2	2	no	—
469	C₄⋊C₈	—	2	1	no	—
470	C₄⋊C₈	—	2	1	no	—
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
473	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
474	#103	—	2	2	no	—
475	#103	—	2	4	no	—
476	#103	—	2	2	no	—
477	#103	—	2	2	no	—
478	#102	—	2	2	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	C₄×C₈	C₂³×C₁₉	1	2	yes	—
481	C₁₉	#18805	1	1	yes	characteristic, direct product factor, Sylow
482	C₂⁴	—	2	1	no	—
483	#41	—	2	2	no	—
484	#41	—	2	2	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	4	2	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	1	no	—
492	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	4	1	no	—
500	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	1	no	—
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	SD₁₆	—	4	4	no	—
520	SD₁₆	—	4	4	no	—
521	M₁₆	—	4	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	4	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	2	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	8	1	no	—
577	C₂³	C₁₉×#120	1	1	yes	characteristic
578	Q₈	—	2	1	no	—
579	Q₈	—	2	1	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	2	no	—
584	Q₈	—	4	2	no	—
585	Q₈	—	8	2	no	—
586	D₄	—	2	1	no	—
587	D₄	—	2	1	no	—
588	D₄	—	2	1	no	—
589	D₄	—	2	1	no	—
590	D₄	—	2	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	2	no	—
594	D₄	—	8	2	no	—
595	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	8	1	no	—
619	C₂×C₄	—	8	2	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
622	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
623	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
624	C₂×C₄	C₁₉×#135	1	2	yes	—
625	C₂×C₄	C₁₉×#137	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
627	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
629	C₈	—	4	2	no	—
630	C₈	—	4	2	no	—
631	C₈	—	4	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	8	4	no	—
644	C₂²	C₁₉×#452	1	2	yes	—
645	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	2	no	—
656	C₄	—	8	2	no	—
657	C₄	C₁₉×#452	1	2	yes	—
658	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
659	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
660	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
661	C₄	C₁₉×#575	1	1	yes	characteristic
662	C₂	—	2	2	no	—
663	C₂	—	4	2	no	—
664	C₂	—	8	1	no	—
665	C₂	—	8	1	no	—
666	C₂	C₂×C₁₉×#452	1	1	yes	characteristic
667	C₂	C₁₉×#3006	1	1	yes	characteristic
668	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3475	C₂
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
2. C₁₉×#3230	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₂×C₁₉×#461	C₂	semidirect
5. C₁₉×#1650	C₂	semidirect
6. C₁₉×#1647	C₂	semidirect
7. C₁₉×#1646	C₂	semidirect
8. C₁₉×#1643	C₂	semidirect
9. C₁₉×#1550	C₂	semidirect
10. C₁₉×#1486	C₂	semidirect
11. C₁₉×#1477	C₂	semidirect
31. C₁₉×#500	C₂²	semidirect
32. C₁₉×#487	C₂²	semidirect
37. C₁₉×#475	C₂²	semidirect
38. C₁₉×#474	C₂²	semidirect
49. C₁₉×#333	C₂²	semidirect
50. C₁₉×#332	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
54. C₁₉×D₄⋊C₈	C₂²	semidirect
236. #18805	C₁₉	direct (N × H)
299. #3230	C₂×C₁₉	semidirect
300. #3079	C₂×C₁₉	semidirect
301. C₂×#461	C₂×C₁₉	semidirect
302. #1650	C₂×C₁₉	semidirect
303. #1647	C₂×C₁₉	semidirect
304. #1646	C₂×C₁₉	semidirect
305. #1643	C₂×C₁₉	semidirect
306. #1550	C₂×C₁₉	semidirect
307. #1486	C₂×C₁₉	semidirect
308. #1477	C₂×C₁₉	semidirect
358. #500	C₂²×C₁₉	semidirect
359. #487	C₂²×C₁₉	semidirect
364. #475	C₂²×C₁₉	semidirect
365. #474	C₂²×C₁₉	semidirect
376. #333	C₂²×C₁₉	semidirect
377. #332	C₂²×C₁₉	semidirect
378. Q₈⋊C₈	C₂²×C₁₉	semidirect
381. D₄⋊C₈	C₂²×C₁₉	semidirect
481. C₁₉	#18805	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×#3475	2
C₁₉×#3230	2
C₁₉×#3079	2
C₂×C₁₉×#461	2
C₁₉×#1650	2
C₁₉×#1647	2
C₁₉×#1646	2
C₁₉×#1643	2
C₁₉×#1550	2
C₁₉×#1486	2
C₁₉×#1477	2
#18805	19

Subgroups — C19×#18805 #18024764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18805 #18024764