Subgroups — C₁₉×#19481 #18025440

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3115	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1690	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1669	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#494	C₂²	1	1	yes	characteristic
20	C₁₉×#492	C₂²	1	1	yes	characteristic
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#482	—	2	1	no	—
24	C₁₉×#479	—	2	1	no	—
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#477	C₂²	1	1	yes	characteristic
27	C₁₉×#476	C₂²	1	1	yes	characteristic
28	C₁₉×#475	C₂²	1	1	yes	characteristic
29	C₁₉×#475	C₂²	1	1	yes	characteristic
30	C₁₉×#474	C₂²	1	1	yes	characteristic
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#464	—	2	1	no	—
33	C₁₉×#464	—	2	1	no	—
34	C₁₉×#460	C₂²	1	1	yes	characteristic
35	C₁₉×#459	C₂²	1	1	yes	characteristic
36	C₁₉×#452	—	2	1	no	—
37	C₁₉×#452	—	2	1	no	—
38	C₁₉×#449	—	2	1	no	—
39	C₁₉×#446	C₂²	1	1	yes	characteristic
40	C₁₉×#446	C₂²	1	1	yes	characteristic
41	C₁₉×#442	—	2	1	no	—
42	C₁₉×#440	—	2	1	no	—
43	C₁₉×#435	—	2	1	no	—
44	C₁₉×#435	—	2	1	no	—
45	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#432	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#431	C₂²	1	1	yes	characteristic
50	C₁₉×#427	—	2	1	no	—
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₉×#416	—	2	1	no	—
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×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×D₈×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	—	2	1	no	—
76	C₂²×C₈×C₁₉	—	2	1	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×#127	C₂³	1	1	yes	characteristic
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×#121	—	2	1	no	—
88	C₁₉×#121	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	D₄	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×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×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	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×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₁₉×#97	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	4	1	no	—
146	#41×C₁₉	—	8	1	no	—
147	#41×C₁₉	—	8	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	—	2	1	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	—	4	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
165	Q₁₆×C₁₉	—	8	1	no	—
166	Q₁₆×C₁₉	—	8	1	no	—
167	SD₁₆×C₁₉	—	4	2	no	—
168	SD₁₆×C₁₉	—	8	1	no	—
169	SD₁₆×C₁₉	—	8	1	no	—
170	D₈×C₁₉	—	4	2	no	—
171	M₁₆×C₁₉	—	8	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	—	8	1	no	—
180	C₂×C₈×C₁₉	—	8	1	no	—
181	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	#41	1	1	yes	characteristic
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19481	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	#121	1	1	yes	characteristic
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	2	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	8	1	no	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	8	2	no	—
230	D₄×C₁₉	#137	1	2	yes	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	8	2	no	—
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
253	C₈×C₁₉	—	2	1	no	—
254	C₈×C₁₉	—	2	1	no	—
255	C₈×C₁₉	—	2	1	no	—
256	C₈×C₁₉	—	2	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	#3210	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#3115	C₂×C₁₉	1	1	yes	characteristic
265	#3076	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2990	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1690	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1669	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
299	C₄×C₁₉	#575	1	1	yes	characteristic
300	C₄×C₁₉	#576	1	1	yes	characteristic
301	C₄×C₁₉	#577	1	1	yes	characteristic
302	#533	C₂²×C₁₉	1	1	yes	characteristic
303	#532	C₂²×C₁₉	1	1	yes	characteristic
304	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
305	#494	C₂²×C₁₉	1	1	yes	characteristic
306	#492	C₂²×C₁₉	1	1	yes	characteristic
307	#487	C₂²×C₁₉	1	1	yes	characteristic
308	#486	C₂²×C₁₉	1	1	yes	characteristic
309	#482	—	2	1	no	—
310	#479	—	2	1	no	—
311	#478	—	2	1	no	—
312	#477	C₂²×C₁₉	1	1	yes	characteristic
313	#476	C₂²×C₁₉	1	1	yes	characteristic
314	#475	C₂²×C₁₉	1	1	yes	characteristic
315	#475	C₂²×C₁₉	1	1	yes	characteristic
316	#474	C₂²×C₁₉	1	1	yes	characteristic
317	#474	C₂²×C₁₉	1	1	yes	characteristic
318	#464	—	2	1	no	—
319	#464	—	2	1	no	—
320	#460	C₂²×C₁₉	1	1	yes	characteristic
321	#459	C₂²×C₁₉	1	1	yes	characteristic
322	#452	—	2	1	no	—
323	#452	—	2	1	no	—
324	#449	—	2	1	no	—
325	#446	C₂²×C₁₉	1	1	yes	characteristic
326	#446	C₂²×C₁₉	1	1	yes	characteristic
327	#442	—	2	1	no	—
328	#440	—	2	1	no	—
329	#435	—	2	1	no	—
330	#435	—	2	1	no	—
331	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
332	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	#432	—	2	1	no	—
334	#432	C₂²×C₁₉	1	1	yes	characteristic
335	#431	C₂²×C₁₉	1	1	yes	characteristic
336	#427	—	2	1	no	—
337	#423	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₄⋊C₈	—	2	1	no	—
339	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
340	#416	—	2	1	no	—
341	#335	C₂²×C₁₉	1	1	yes	characteristic
342	#335	C₂²×C₁₉	1	1	yes	characteristic
343	#334	C₂²×C₁₉	1	1	yes	characteristic
344	#334	C₂²×C₁₉	1	1	yes	characteristic
345	#333	C₂²×C₁₉	1	1	yes	characteristic
346	#333	C₂²×C₁₉	1	1	yes	characteristic
347	#332	C₂²×C₁₉	1	1	yes	characteristic
348	#332	C₂²×C₁₉	1	1	yes	characteristic
349	#332	C₂²×C₁₉	1	1	yes	characteristic
350	#332	C₂²×C₁₉	1	1	yes	characteristic
351	#331	C₂²×C₁₉	1	1	yes	characteristic
352	#331	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₁₉	—	4	1	no	—
354	C₂×C₁₉	—	4	2	no	—
355	C₂×C₁₉	—	16	1	no	—
356	C₂×C₁₉	#3045	1	1	yes	characteristic
357	C₂×C₁₉	#3056	1	1	yes	characteristic
358	C₂×C₁₉	#3067	1	1	yes	characteristic
359	C₂×#41	—	2	1	no	—
360	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
361	C₂×Q₁₆	—	2	1	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×D₈	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	#127	C₂³×C₁₉	1	1	yes	characteristic
375	#125	—	2	1	no	—
376	#124	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
384	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
390	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
396	#107	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
407	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
430	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
431	#97	—	2	1	no	—
432	#97	—	2	1	no	—
433	#97	—	2	1	no	—
434	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₁₉	#19481	1	1	yes	characteristic, direct product factor, Sylow
437	#41	—	2	2	no	—
438	#41	—	4	1	no	—
439	#41	—	8	1	no	—
440	#41	—	8	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
458	Q₁₆	—	8	1	no	—
459	Q₁₆	—	8	1	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	8	1	no	—
462	SD₁₆	—	8	1	no	—
463	D₈	—	4	2	no	—
464	M₁₆	—	8	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	2	no	—
472	C₂×C₈	—	8	1	no	—
473	C₂×C₈	—	8	1	no	—
474	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	4	1	no	—
500	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₄²	#41×C₁₉	1	1	yes	characteristic
503	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	C₁₉×#121	1	1	yes	characteristic
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	8	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	8	1	no	—
521	D₄	—	8	2	no	—
522	D₄	C₁₉×#137	1	2	yes	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
540	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
576	C₄	C₁₉×#575	1	1	yes	characteristic
577	C₄	C₁₉×#576	1	1	yes	characteristic
578	C₄	C₁₉×#577	1	1	yes	characteristic
579	C₂	—	4	1	no	—
580	C₂	—	4	2	no	—
581	C₂	—	16	1	no	—
582	C₂	C₁₉×#3045	1	1	yes	characteristic
583	C₂	C₁₉×#3056	1	1	yes	characteristic
584	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3115	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
1. C₁₉×#3210	C₂	semidirect
3. C₁₉×#3076	C₂	semidirect
4. C₁₉×#2990	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1690	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1683	C₂	semidirect
10. C₁₉×#1677	C₂	semidirect
11. C₁₉×#1669	C₂	semidirect
12. C₁₉×#1665	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1559	C₂	semidirect
15. C₁₉×#1547	C₂	semidirect
211. #19481	C₁₉	direct (N × H)
263. #3210	C₂×C₁₉	semidirect
265. #3076	C₂×C₁₉	semidirect
266. #2990	C₂×C₁₉	semidirect
267. #1704	C₂×C₁₉	semidirect
268. #1698	C₂×C₁₉	semidirect
269. #1690	C₂×C₁₉	semidirect
270. #1686	C₂×C₁₉	semidirect
271. #1683	C₂×C₁₉	semidirect
272. #1677	C₂×C₁₉	semidirect
273. #1669	C₂×C₁₉	semidirect
274. #1665	C₂×C₁₉	semidirect
275. #1573	C₂×C₁₉	semidirect
276. #1559	C₂×C₁₉	semidirect
277. #1547	C₂×C₁₉	semidirect
436. C₁₉	#19481	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×#3210	2
C₁₉×#3115	2
C₁₉×#3076	2
C₁₉×#2990	2
C₁₉×#1704	2
C₁₉×#1698	2
C₁₉×#1690	2
C₁₉×#1686	2
C₁₉×#1683	2
C₁₉×#1677	2
C₁₉×#1669	2
C₁₉×#1665	2
C₁₉×#1573	2
C₁₉×#1559	2
C₁₉×#1547	2
#19481	19

Subgroups — C19×#19481 #18025440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19481 #18025440