Subgroups — C₁₉×#19582 #18025541

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#496	—	2	1	no	—
20	C₁₉×#493	C₂²	1	1	yes	characteristic
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#490	—	2	1	no	—
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#477	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#476	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#466	—	2	1	no	—
29	C₁₉×#465	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#460	C₂²	1	1	yes	characteristic
32	C₁₉×#460	C₂²	1	1	yes	characteristic
33	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#459	—	2	1	no	—
35	C₁₉×#459	—	2	1	no	—
36	C₁₉×#459	C₂²	1	1	yes	characteristic
37	C₁₉×#459	C₂²	1	1	yes	characteristic
38	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#450	—	2	1	no	—
40	C₁₉×#447	—	2	1	no	—
41	C₁₉×#447	—	2	1	no	—
42	C₁₉×#447	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#424	—	2	1	no	—
53	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×C₄⋊C₈	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×#331	C₂²	1	1	yes	characteristic
62	C₁₉×#331	C₂²	1	1	yes	characteristic
63	C₁₉×#331	C₂²	1	1	yes	characteristic
64	C₁₉×#331	C₂²	1	1	yes	characteristic
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	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×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×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×D₈×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₂²×C₈×C₁₉	—	2	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₉×#127	—	2	1	no	—
87	C₁₉×#127	—	2	1	no	—
88	C₁₉×#127	—	2	1	no	—
89	C₁₉×#127	C₂³	1	1	yes	characteristic
90	C₁₉×#127	C₂³	1	1	yes	characteristic
91	C₁₉×#127	C₂³	1	1	yes	characteristic
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#125	D₄	1	1	yes	characteristic
94	C₁₉×#124	—	2	1	no	—
95	C₁₉×#124	D₄	1	1	yes	characteristic
96	C₁₉×#123	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#117	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	—	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×#102	—	2	1	no	—
124	C₁₉×#102	—	2	1	no	—
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×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	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	C₂⁴×C₁₉	—	4	1	no	—
145	#41×C₁₉	—	8	2	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	8	1	no	—
163	C₂×D₄×C₁₉	—	8	1	no	—
164	C₂×D₄×C₁₉	—	8	1	no	—
165	C₂×D₄×C₁₉	—	8	1	no	—
166	C₂×D₄×C₁₉	—	8	2	no	—
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
173	SD₁₆×C₁₉	—	8	1	no	—
174	SD₁₆×C₁₉	—	8	1	no	—
175	SD₁₆×C₁₉	—	8	1	no	—
176	D₈×C₁₉	—	8	1	no	—
177	D₈×C₁₉	—	8	1	no	—
178	D₈×C₁₉	—	8	1	no	—
179	D₈×C₁₉	—	8	1	no	—
180	D₈×C₁₉	—	8	1	no	—
181	D₈×C₁₉	—	8	1	no	—
182	D₈×C₁₉	—	8	1	no	—
183	M₁₆×C₁₉	—	8	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	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	8	1	no	—
191	C₂×C₈×C₁₉	—	8	1	no	—
192	C₂×C₈×C₁₉	—	8	1	no	—
193	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₂²⋊C₄×C₁₉	—	4	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₉	#41	1	1	yes	characteristic
216	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
217	#19582	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	4	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	—	8	2	no	—
225	C₂³×C₁₉	#121	1	1	yes	characteristic
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	2	1	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	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	—	4	1	no	—
244	D₄×C₁₉	—	8	1	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	2	no	—
248	D₄×C₁₉	—	8	2	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	2	no	—
251	C₂×C₄×C₁₉	—	2	2	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	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	#3247	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2994	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1697	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂×#331	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	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	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	16	4	no	—
309	C₂²×C₁₉	#472	1	2	yes	—
310	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	8	1	no	—
319	C₄×C₁₉	#576	1	1	yes	characteristic
320	C₄×C₁₉	#576	1	1	yes	characteristic
321	C₄×C₁₉	#577	1	1	yes	characteristic
322	C₄×C₁₉	#577	1	1	yes	characteristic
323	#532	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
325	#529	C₂²×C₁₉	1	1	yes	characteristic
326	#496	—	2	1	no	—
327	#493	C₂²×C₁₉	1	1	yes	characteristic
328	#493	C₂²×C₁₉	1	1	yes	characteristic
329	#490	—	2	1	no	—
330	#486	C₂²×C₁₉	1	1	yes	characteristic
331	#486	C₂²×C₁₉	1	1	yes	characteristic
332	#478	—	2	1	no	—
333	#477	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	#476	C₂²×C₁₉	1	1	yes	characteristic, complemented
335	#466	—	2	1	no	—
336	#465	—	2	1	no	—
337	#463	—	2	1	no	—
338	#460	C₂²×C₁₉	1	1	yes	characteristic
339	#460	C₂²×C₁₉	1	1	yes	characteristic
340	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#459	—	2	1	no	—
342	#459	—	2	1	no	—
343	#459	C₂²×C₁₉	1	1	yes	characteristic
344	#459	C₂²×C₁₉	1	1	yes	characteristic
345	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
346	#450	—	2	1	no	—
347	#447	—	2	1	no	—
348	#447	—	2	1	no	—
349	#447	—	2	1	no	—
350	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
351	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	#435	—	2	1	no	—
354	C₈×D₄	—	2	1	no	—
355	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#433	—	2	1	no	—
357	#432	C₂²×C₁₉	1	1	yes	characteristic
358	#431	C₂²×C₁₉	1	1	yes	characteristic
359	#424	—	2	1	no	—
360	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#331	C₂²×C₁₉	1	1	yes	characteristic
369	#331	C₂²×C₁₉	1	1	yes	characteristic
370	#331	C₂²×C₁₉	1	1	yes	characteristic
371	#331	C₂²×C₁₉	1	1	yes	characteristic
372	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	C₂×C₁₉	—	2	2	no	—
375	C₂×C₁₉	—	8	1	no	—
376	C₂×C₁₉	—	16	1	no	—
377	C₂×C₁₉	—	16	1	no	—
378	C₂×C₁₉	—	16	1	no	—
379	C₂×C₁₉	#3045	1	1	yes	characteristic
380	C₂×C₁₉	#3062	1	1	yes	characteristic
381	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
382	C₂×#41	—	2	1	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×D₈	—	2	1	no	—
390	C₂×D₈	—	2	1	no	—
391	C₂×D₈	—	2	1	no	—
392	C₂×D₈	—	2	1	no	—
393	C₂×D₈	—	2	1	no	—
394	C₂×D₈	—	2	1	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	2	1	no	—
400	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
401	#127	—	2	1	no	—
402	#127	—	2	1	no	—
403	#127	—	2	1	no	—
404	#127	C₂³×C₁₉	1	1	yes	characteristic
405	#127	C₂³×C₁₉	1	1	yes	characteristic
406	#127	C₂³×C₁₉	1	1	yes	characteristic
407	#126	—	2	1	no	—
408	#125	D₄×C₁₉	1	1	yes	characteristic
409	#124	—	2	1	no	—
410	#124	D₄×C₁₉	1	1	yes	characteristic
411	#123	—	2	1	no	—
412	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
413	#121	—	2	1	no	—
414	#121	—	2	1	no	—
415	#121	D₄×C₁₉	1	1	yes	characteristic
416	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
421	#117	—	2	1	no	—
422	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
423	#107	—	2	1	no	—
424	#106	—	2	1	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
430	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
431	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
437	#103	—	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	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
453	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
454	#97	—	2	1	no	—
455	#97	—	2	1	no	—
456	C₄×C₈	—	2	1	no	—
457	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
458	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
459	C₁₉	#19582	1	1	yes	characteristic, direct product factor, Sylow
460	C₂⁴	—	4	1	no	—
461	#41	—	8	2	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	8	1	no	—
479	C₂×D₄	—	8	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	—	8	1	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
489	SD₁₆	—	8	1	no	—
490	SD₁₆	—	8	1	no	—
491	SD₁₆	—	8	1	no	—
492	D₈	—	8	1	no	—
493	D₈	—	8	1	no	—
494	D₈	—	8	1	no	—
495	D₈	—	8	1	no	—
496	D₈	—	8	1	no	—
497	D₈	—	8	1	no	—
498	D₈	—	8	1	no	—
499	M₁₆	—	8	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	8	1	no	—
507	C₂×C₈	—	8	1	no	—
508	C₂×C₈	—	8	1	no	—
509	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄²	#41×C₁₉	1	1	yes	characteristic
532	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	8	2	no	—
538	C₂³	—	8	2	no	—
539	C₂³	—	8	2	no	—
540	C₂³	C₁₉×#121	1	1	yes	characteristic
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	8	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	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	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	8	1	no	—
560	D₄	—	8	1	no	—
561	D₄	—	8	1	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	2	no	—
564	D₄	—	8	2	no	—
565	D₄	—	8	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
579	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
580	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
583	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	2	1	no	—
587	C₈	—	2	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	16	4	no	—
609	C₂²	C₁₉×#472	1	2	yes	—
610	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	8	1	no	—
619	C₄	C₁₉×#576	1	1	yes	characteristic
620	C₄	C₁₉×#576	1	1	yes	characteristic
621	C₄	C₁₉×#577	1	1	yes	characteristic
622	C₄	C₁₉×#577	1	1	yes	characteristic
623	C₂	—	2	2	no	—
624	C₂	—	8	1	no	—
625	C₂	—	16	1	no	—
626	C₂	—	16	1	no	—
627	C₂	—	16	1	no	—
628	C₂	C₁₉×#3045	1	1	yes	characteristic
629	C₂	C₁₉×#3062	1	1	yes	characteristic
630	C₂	C₂×C₁₉×#472	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×#3247	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3205	C₂	semidirect
4. C₁₉×#2994	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1697	C₂	semidirect
7. C₁₉×#1688	C₂	semidirect
8. C₁₉×#1687	C₂	semidirect
9. C₁₉×#1678	C₂	semidirect
10. C₁₉×#1677	C₂	semidirect
11. C₁₉×#1668	C₂	semidirect
12. C₁₉×#1667	C₂	semidirect
13. C₁₉×#1573	C₂	semidirect
14. C₁₉×#1551	C₂	semidirect
15. C₂×C₁₉×#331	C₂	semidirect
26. C₁₉×#477	C₂²	semidirect
27. C₁₉×#476	C₂²	semidirect
33. C₁₉×#460	C₂²	semidirect
38. C₁₉×#459	C₂²	semidirect
43. C₁₉×#446	C₂²	semidirect
44. C₈×Q₈×C₁₉	C₂²	semidirect
45. C₁₉×#436	C₂²	semidirect
48. C₈×D₄×C₁₉	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
65. C₁₉×#331	C₂²	semidirect
66. C₁₉×#331	C₂²	semidirect
217. #19582	C₁₉	direct (N × H)
279. #3247	C₂×C₁₉	semidirect
280. #3217	C₂×C₁₉	semidirect
281. #3205	C₂×C₁₉	semidirect
282. #2994	C₂×C₁₉	semidirect
283. #1698	C₂×C₁₉	semidirect
284. #1697	C₂×C₁₉	semidirect
285. #1688	C₂×C₁₉	semidirect
286. #1687	C₂×C₁₉	semidirect
287. #1678	C₂×C₁₉	semidirect
288. #1677	C₂×C₁₉	semidirect
289. #1668	C₂×C₁₉	semidirect
290. #1667	C₂×C₁₉	semidirect
291. #1573	C₂×C₁₉	semidirect
292. #1551	C₂×C₁₉	semidirect
293. C₂×#331	C₂×C₁₉	semidirect
333. #477	C₂²×C₁₉	semidirect
334. #476	C₂²×C₁₉	semidirect
340. #460	C₂²×C₁₉	semidirect
345. #459	C₂²×C₁₉	semidirect
350. #446	C₂²×C₁₉	semidirect
351. C₈×Q₈	C₂²×C₁₉	semidirect
352. #436	C₂²×C₁₉	semidirect
355. C₈×D₄	C₂²×C₁₉	semidirect
362. #335	C₂²×C₁₉	semidirect
363. #335	C₂²×C₁₉	semidirect
364. #334	C₂²×C₁₉	semidirect
365. #334	C₂²×C₁₉	semidirect
366. #333	C₂²×C₁₉	semidirect
367. #333	C₂²×C₁₉	semidirect
372. #331	C₂²×C₁₉	semidirect
373. #331	C₂²×C₁₉	semidirect
459. C₁₉	#19582	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×#3247	2
C₁₉×#3217	2
C₁₉×#3205	2
C₁₉×#2994	2
C₁₉×#1698	2
C₁₉×#1697	2
C₁₉×#1688	2
C₁₉×#1687	2
C₁₉×#1678	2
C₁₉×#1677	2
C₁₉×#1668	2
C₁₉×#1667	2
C₁₉×#1573	2
C₁₉×#1551	2
C₂×C₁₉×#331	2
#19582	19

Subgroups — C19×#19582 #18025541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19582 #18025541