Subgroups — C₁₉×#19538 #18025497

Order 4864.

662 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1701	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×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1681	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×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1545	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×#495	—	2	1	no	—
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#493	C₂²	1	1	yes	characteristic
23	C₁₉×#490	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#460	C₂²	1	1	yes	characteristic
30	C₁₉×#460	C₂²	1	1	yes	characteristic
31	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#459	—	2	1	no	—
33	C₁₉×#459	—	2	1	no	—
34	C₁₉×#459	C₂²	1	1	yes	characteristic
35	C₁₉×#459	C₂²	1	1	yes	characteristic
36	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#452	—	2	1	no	—
38	C₁₉×#450	—	2	1	no	—
39	C₁₉×#449	—	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	—	2	1	no	—
46	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#435	—	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×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#424	—	2	1	no	—
54	C₁₉×#423	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×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#332	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×Q₁₆×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	—	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×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₉×#127	—	2	1	no	—
88	C₁₉×#127	—	2	1	no	—
89	C₁₉×#127	—	2	1	no	—
90	C₁₉×#127	C₂³	1	1	yes	characteristic
91	C₁₉×#127	C₂³	1	1	yes	characteristic
92	C₁₉×#127	C₂³	1	1	yes	characteristic
93	C₁₉×#126	—	2	1	no	—
94	C₁₉×#125	D₄	1	1	yes	characteristic
95	C₁₉×#124	—	2	1	no	—
96	C₁₉×#124	D₄	1	1	yes	characteristic
97	C₁₉×#123	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
107	C₁₉×#117	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#102	—	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×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₄×C₈×C₁₉	—	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	1	no	—
146	#41×C₁₉	—	8	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	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	—	4	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	1	no	—
167	C₂×D₄×C₁₉	—	8	2	no	—
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
174	Q₁₆×C₁₉	—	8	1	no	—
175	SD₁₆×C₁₉	—	8	1	no	—
176	SD₁₆×C₁₉	—	8	1	no	—
177	SD₁₆×C₁₉	—	8	1	no	—
178	SD₁₆×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	D₈×C₁₉	—	8	1	no	—
184	D₈×C₁₉	—	8	1	no	—
185	D₈×C₁₉	—	8	1	no	—
186	M₁₆×C₁₉	—	8	1	no	—
187	M₁₆×C₁₉	—	8	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	8	1	no	—
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₉	#41	1	1	yes	characteristic
218	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
219	#19538	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	8	2	no	—
225	C₂³×C₁₉	—	8	2	no	—
226	C₂³×C₁₉	—	8	2	no	—
227	C₂³×C₁₉	#121	1	1	yes	characteristic
228	Q₈×C₁₉	—	2	1	no	—
229	Q₈×C₁₉	—	2	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	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	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	8	1	no	—
248	D₄×C₁₉	—	8	1	no	—
249	D₄×C₁₉	—	8	2	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	8	1	no	—
253	D₄×C₁₉	—	8	2	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	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	—	2	1	no	—
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#3212	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#2993	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	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	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	16	4	no	—
313	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	#576	1	1	yes	characteristic
323	C₄×C₁₉	#576	1	1	yes	characteristic
324	C₄×C₁₉	#576	1	1	yes	characteristic
325	C₄×C₁₉	#577	1	1	yes	characteristic
326	#532	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
328	#529	C₂²×C₁₉	1	1	yes	characteristic
329	#496	—	2	1	no	—
330	#495	—	2	1	no	—
331	#493	C₂²×C₁₉	1	1	yes	characteristic
332	#493	C₂²×C₁₉	1	1	yes	characteristic
333	#490	—	2	1	no	—
334	#488	—	2	1	no	—
335	#486	C₂²×C₁₉	1	1	yes	characteristic
336	#486	C₂²×C₁₉	1	1	yes	characteristic
337	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#460	C₂²×C₁₉	1	1	yes	characteristic
340	#460	C₂²×C₁₉	1	1	yes	characteristic
341	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	#459	—	2	1	no	—
343	#459	—	2	1	no	—
344	#459	C₂²×C₁₉	1	1	yes	characteristic
345	#459	C₂²×C₁₉	1	1	yes	characteristic
346	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#452	—	2	1	no	—
348	#450	—	2	1	no	—
349	#449	—	2	1	no	—
350	#447	—	2	1	no	—
351	#447	—	2	1	no	—
352	#447	—	2	1	no	—
353	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#436	—	2	1	no	—
356	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#435	—	2	1	no	—
358	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	#433	—	2	1	no	—
360	#432	C₂²×C₁₉	1	1	yes	characteristic
361	#431	C₂²×C₁₉	1	1	yes	characteristic
362	#431	C₂²×C₁₉	1	1	yes	characteristic
363	#424	—	2	1	no	—
364	#423	C₂²×C₁₉	1	1	yes	characteristic
365	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#331	C₂²×C₁₉	1	1	yes	characteristic
372	#331	C₂²×C₁₉	1	1	yes	characteristic
373	#331	C₂²×C₁₉	1	1	yes	characteristic
374	#331	C₂²×C₁₉	1	1	yes	characteristic
375	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	C₂×C₁₉	—	4	1	no	—
378	C₂×C₁₉	—	8	1	no	—
379	C₂×C₁₉	—	16	1	no	—
380	C₂×C₁₉	—	16	1	no	—
381	C₂×C₁₉	—	16	1	no	—
382	C₂×C₁₉	#3045	1	1	yes	characteristic
383	C₂×C₁₉	#3058	1	1	yes	characteristic
384	C₂×C₁₉	#3068	1	1	yes	characteristic
385	C₂×#41	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂×Q₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×D₈	—	2	1	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	—	2	1	no	—
399	C₂×D₈	—	2	1	no	—
400	C₂×D₈	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
405	#127	—	2	1	no	—
406	#127	—	2	1	no	—
407	#127	—	2	1	no	—
408	#127	C₂³×C₁₉	1	1	yes	characteristic
409	#127	C₂³×C₁₉	1	1	yes	characteristic
410	#127	C₂³×C₁₉	1	1	yes	characteristic
411	#126	—	2	1	no	—
412	#125	D₄×C₁₉	1	1	yes	characteristic
413	#124	—	2	1	no	—
414	#124	D₄×C₁₉	1	1	yes	characteristic
415	#123	—	2	1	no	—
416	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	D₄×C₁₉	1	1	yes	characteristic
420	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
425	#117	—	2	1	no	—
426	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
431	C₄⋊C₈	D₄×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	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
438	#103	—	2	1	no	—
439	#103	—	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	#102	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	C₂²⋊C₈	—	2	1	no	—
453	C₂²⋊C₈	—	2	1	no	—
454	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
455	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
456	#97	—	2	1	no	—
457	#97	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	2	1	no	—
460	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
461	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₁₉	#19538	1	1	yes	characteristic, direct product factor, Sylow
463	C₂⁴	—	4	1	no	—
464	#41	—	8	1	no	—
465	#41	—	8	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	8	1	no	—
483	C₂×D₄	—	8	1	no	—
484	C₂×D₄	—	8	1	no	—
485	C₂×D₄	—	8	1	no	—
486	C₂×D₄	—	8	2	no	—
487	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
493	Q₁₆	—	8	1	no	—
494	SD₁₆	—	8	1	no	—
495	SD₁₆	—	8	1	no	—
496	SD₁₆	—	8	1	no	—
497	SD₁₆	—	8	1	no	—
498	D₈	—	8	1	no	—
499	D₈	—	8	1	no	—
500	D₈	—	8	1	no	—
501	D₈	—	8	1	no	—
502	D₈	—	8	1	no	—
503	D₈	—	8	1	no	—
504	D₈	—	8	1	no	—
505	M₁₆	—	8	1	no	—
506	M₁₆	—	8	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	8	1	no	—
514	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₄²	#41×C₁₉	1	1	yes	characteristic
537	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
538	C₂³	—	2	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	8	2	no	—
543	C₂³	—	8	2	no	—
544	C₂³	—	8	2	no	—
545	C₂³	C₁₉×#121	1	1	yes	characteristic
546	Q₈	—	2	1	no	—
547	Q₈	—	2	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	D₄	—	2	1	no	—
551	D₄	—	2	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	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	8	1	no	—
565	D₄	—	8	1	no	—
566	D₄	—	8	1	no	—
567	D₄	—	8	2	no	—
568	D₄	—	8	2	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	1	no	—
571	D₄	—	8	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	8	2	no	—
584	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
585	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	16	4	no	—
616	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₁₉×#576	1	1	yes	characteristic
626	C₄	C₁₉×#576	1	1	yes	characteristic
627	C₄	C₁₉×#576	1	1	yes	characteristic
628	C₄	C₁₉×#577	1	1	yes	characteristic
629	C₂	—	4	1	no	—
630	C₂	—	8	1	no	—
631	C₂	—	16	1	no	—
632	C₂	—	16	1	no	—
633	C₂	—	16	1	no	—
634	C₂	C₁₉×#3045	1	1	yes	characteristic
635	C₂	C₁₉×#3058	1	1	yes	characteristic
636	C₂	C₁₉×#3068	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×#3217	C₂	semidirect
2. C₁₉×#3212	C₂	semidirect
3. C₁₉×#3205	C₂	semidirect
4. C₁₉×#2993	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1701	C₂	semidirect
7. C₁₉×#1688	C₂	semidirect
8. C₁₉×#1687	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1681	C₂	semidirect
11. C₁₉×#1668	C₂	semidirect
12. C₁₉×#1667	C₂	semidirect
13. C₁₉×#1572	C₂	semidirect
14. C₁₉×#1557	C₂	semidirect
15. C₁₉×#1545	C₂	semidirect
27. C₁₉×#462	C₂²	semidirect
28. C₁₉×#461	C₂²	semidirect
31. C₁₉×#460	C₂²	semidirect
36. C₁₉×#459	C₂²	semidirect
43. C₁₉×#446	C₂²	semidirect
44. C₈×Q₈×C₁₉	C₂²	semidirect
46. 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×#332	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
65. C₁₉×#331	C₂²	semidirect
66. C₁₉×#331	C₂²	semidirect
219. #19538	C₁₉	direct (N × H)
282. #3217	C₂×C₁₉	semidirect
283. #3212	C₂×C₁₉	semidirect
284. #3205	C₂×C₁₉	semidirect
285. #2993	C₂×C₁₉	semidirect
286. #1702	C₂×C₁₉	semidirect
287. #1701	C₂×C₁₉	semidirect
288. #1688	C₂×C₁₉	semidirect
289. #1687	C₂×C₁₉	semidirect
290. #1682	C₂×C₁₉	semidirect
291. #1681	C₂×C₁₉	semidirect
292. #1668	C₂×C₁₉	semidirect
293. #1667	C₂×C₁₉	semidirect
294. #1572	C₂×C₁₉	semidirect
295. #1557	C₂×C₁₉	semidirect
296. #1545	C₂×C₁₉	semidirect
337. #462	C₂²×C₁₉	semidirect
338. #461	C₂²×C₁₉	semidirect
341. #460	C₂²×C₁₉	semidirect
346. #459	C₂²×C₁₉	semidirect
353. #446	C₂²×C₁₉	semidirect
354. C₈×Q₈	C₂²×C₁₉	semidirect
356. #436	C₂²×C₁₉	semidirect
358. C₈×D₄	C₂²×C₁₉	semidirect
365. #335	C₂²×C₁₉	semidirect
366. #335	C₂²×C₁₉	semidirect
367. #334	C₂²×C₁₉	semidirect
368. #334	C₂²×C₁₉	semidirect
369. #332	C₂²×C₁₉	semidirect
370. #332	C₂²×C₁₉	semidirect
375. #331	C₂²×C₁₉	semidirect
376. #331	C₂²×C₁₉	semidirect
462. C₁₉	#19538	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×#3217	2
C₁₉×#3212	2
C₁₉×#3205	2
C₁₉×#2993	2
C₁₉×#1702	2
C₁₉×#1701	2
C₁₉×#1688	2
C₁₉×#1687	2
C₁₉×#1682	2
C₁₉×#1681	2
C₁₉×#1668	2
C₁₉×#1667	2
C₁₉×#1572	2
C₁₉×#1557	2
C₁₉×#1545	2
#19538	19

Subgroups — C19×#19538 #18025497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19538 #18025497