Subgroups — C₁₉×#19376 #18025335

Order 4864.

722 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1685	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1667	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₁₉×#529	C₂²	1	1	yes	characteristic
21	C₁₉×#496	—	2	1	no	—
22	C₁₉×#496	—	2	1	no	—
23	C₁₉×#496	—	2	1	no	—
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#493	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#492	C₂²	1	1	yes	characteristic
28	C₁₉×#490	—	2	1	no	—
29	C₁₉×#478	—	2	1	no	—
30	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#469	—	2	1	no	—
33	C₁₉×#468	—	2	1	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#460	C₂²	1	1	yes	characteristic
37	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#459	C₂²	1	1	yes	characteristic
39	C₁₉×#459	C₂²	1	1	yes	characteristic
40	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#450	—	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×#423	C₂²	1	1	yes	characteristic
53	C₁₉×#405	—	2	1	no	—
54	C₄×M₁₆×C₁₉	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	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
72	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×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×D₈×C₁₉	—	2	1	no	—
84	C₂×D₈×C₁₉	—	2	1	no	—
85	C₂×D₈×C₁₉	—	2	1	no	—
86	C₂×D₈×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₁₉	—	2	1	no	—
92	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₉×#127	—	2	1	no	—
94	C₁₉×#127	—	2	1	no	—
95	C₁₉×#127	—	2	1	no	—
96	C₁₉×#127	C₂³	1	1	yes	characteristic
97	C₁₉×#127	C₂³	1	1	yes	characteristic
98	C₁₉×#127	C₂³	1	1	yes	characteristic
99	C₁₉×#126	—	2	1	no	—
100	C₁₉×#125	D₄	1	1	yes	characteristic
101	C₁₉×#124	—	2	1	no	—
102	C₁₉×#124	D₄	1	1	yes	characteristic
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#117	—	2	1	no	—
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#97	D₄	1	1	yes	characteristic
141	C₁₉×#97	D₄	1	1	yes	characteristic
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	—	2	1	no	—
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	4	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂×D₄×C₁₉	—	8	2	no	—
170	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
176	SD₁₆×C₁₉	—	4	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	SD₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	8	1	no	—
181	SD₁₆×C₁₉	—	8	1	no	—
182	SD₁₆×C₁₉	—	8	1	no	—
183	D₈×C₁₉	—	4	2	no	—
184	D₈×C₁₉	—	4	2	no	—
185	D₈×C₁₉	—	4	2	no	—
186	D₈×C₁₉	—	4	2	no	—
187	D₈×C₁₉	—	8	1	no	—
188	D₈×C₁₉	—	8	1	no	—
189	D₈×C₁₉	—	8	1	no	—
190	M₁₆×C₁₉	—	2	2	no	—
191	M₁₆×C₁₉	—	2	2	no	—
192	M₁₆×C₁₉	—	4	2	no	—
193	M₁₆×C₁₉	—	8	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	4	2	no	—
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	#41	1	1	yes	characteristic
224	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
225	#19376	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	8	2	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	—	8	2	no	—
233	C₂³×C₁₉	#121	1	1	yes	characteristic
234	Q₈×C₁₉	—	2	1	no	—
235	Q₈×C₁₉	—	2	1	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	2	1	no	—
239	D₄×C₁₉	—	2	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	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	8	1	no	—
253	D₄×C₁₉	—	8	1	no	—
254	D₄×C₁₉	—	8	1	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	1	no	—
259	D₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
278	C₈×C₁₉	—	2	1	no	—
279	C₈×C₁₉	—	2	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
287	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
288	#3251	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#3217	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#2969	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1685	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1667	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1553	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	—	16	4	no	—
319	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	1	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	8	1	no	—
328	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
329	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
330	C₄×C₁₉	#576	1	1	yes	characteristic
331	C₄×C₁₉	#577	1	1	yes	characteristic
332	C₂×AGL(1,ℤ/8)	—	2	1	no	—
333	C₂×AGL(1,ℤ/8)	—	2	1	no	—
334	#532	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
336	#529	C₂²×C₁₉	1	1	yes	characteristic
337	#496	—	2	1	no	—
338	#496	—	2	1	no	—
339	#496	—	2	1	no	—
340	#493	C₂²×C₁₉	1	1	yes	characteristic
341	#493	C₂²×C₁₉	1	1	yes	characteristic
342	#492	C₂²×C₁₉	1	1	yes	characteristic
343	#492	C₂²×C₁₉	1	1	yes	characteristic
344	#490	—	2	1	no	—
345	#478	—	2	1	no	—
346	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#469	—	2	1	no	—
349	#468	—	2	1	no	—
350	#463	—	2	1	no	—
351	#460	C₂²×C₁₉	1	1	yes	characteristic
352	#460	C₂²×C₁₉	1	1	yes	characteristic
353	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#459	C₂²×C₁₉	1	1	yes	characteristic
355	#459	C₂²×C₁₉	1	1	yes	characteristic
356	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#450	—	2	1	no	—
358	#447	—	2	1	no	—
359	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#436	—	2	1	no	—
362	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	#435	—	2	1	no	—
364	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#433	—	2	1	no	—
366	#432	C₂²×C₁₉	1	1	yes	characteristic
367	#431	C₂²×C₁₉	1	1	yes	characteristic
368	#423	C₂²×C₁₉	1	1	yes	characteristic
369	#405	—	2	1	no	—
370	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
371	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#331	C₂²×C₁₉	1	1	yes	characteristic
378	#331	C₂²×C₁₉	1	1	yes	characteristic
379	#331	C₂²×C₁₉	1	1	yes	characteristic
380	#331	C₂²×C₁₉	1	1	yes	characteristic
381	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	C₂×C₁₉	—	4	1	no	—
384	C₂×C₁₉	—	8	1	no	—
385	C₂×C₁₉	—	16	1	no	—
386	C₂×C₁₉	—	16	1	no	—
387	C₂×C₁₉	—	16	1	no	—
388	C₂×C₁₉	#3038	1	1	yes	characteristic
389	C₂×C₁₉	#3062	1	1	yes	characteristic
390	C₂×C₁₉	#3068	1	1	yes	characteristic
391	C₂×#41	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	AGL(1,ℤ/8)	—	4	4	no	—
396	AGL(1,ℤ/8)	—	4	4	no	—
397	C₂×SD₁₆	—	2	1	no	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×SD₁₆	—	2	1	no	—
400	C₂×SD₁₆	—	2	1	no	—
401	C₂×SD₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂×D₈	—	2	1	no	—
405	C₂×D₈	—	2	1	no	—
406	C₂×D₈	—	2	1	no	—
407	C₂×D₈	—	2	1	no	—
408	C₂×D₈	—	2	1	no	—
409	C₂×D₈	—	2	1	no	—
410	C₂×D₈	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
414	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₈	—	2	1	no	—
416	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	#127	—	2	1	no	—
418	#127	—	2	1	no	—
419	#127	—	2	1	no	—
420	#127	C₂³×C₁₉	1	1	yes	characteristic
421	#127	C₂³×C₁₉	1	1	yes	characteristic
422	#127	C₂³×C₁₉	1	1	yes	characteristic
423	#126	—	2	1	no	—
424	#125	D₄×C₁₉	1	1	yes	characteristic
425	#124	—	2	1	no	—
426	#124	D₄×C₁₉	1	1	yes	characteristic
427	#123	—	2	1	no	—
428	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
429	#121	—	2	1	no	—
430	#121	—	2	1	no	—
431	#121	D₄×C₁₉	1	1	yes	characteristic
432	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
437	#117	—	2	1	no	—
438	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
439	#107	—	2	1	no	—
440	#106	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
450	#103	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	#97	—	2	1	no	—
463	#97	—	2	1	no	—
464	#97	D₄×C₁₉	1	1	yes	characteristic
465	#97	D₄×C₁₉	1	1	yes	characteristic
466	C₄×C₈	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
469	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
470	C₁₉	#19376	1	1	yes	characteristic, direct product factor, Sylow
471	C₂⁴	—	4	1	no	—
472	#41	—	4	2	no	—
473	#41	—	4	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	—	8	2	no	—
495	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
501	SD₁₆	—	4	2	no	—
502	SD₁₆	—	4	2	no	—
503	SD₁₆	—	4	2	no	—
504	SD₁₆	—	4	2	no	—
505	SD₁₆	—	8	1	no	—
506	SD₁₆	—	8	1	no	—
507	SD₁₆	—	8	1	no	—
508	D₈	—	4	2	no	—
509	D₈	—	4	2	no	—
510	D₈	—	4	2	no	—
511	D₈	—	4	2	no	—
512	D₈	—	8	1	no	—
513	D₈	—	8	1	no	—
514	D₈	—	8	1	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	2	2	no	—
517	M₁₆	—	4	2	no	—
518	M₁₆	—	8	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	4	2	no	—
526	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₄²	#41×C₁₉	1	1	yes	characteristic
549	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
550	C₂³	—	2	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	8	2	no	—
555	C₂³	—	8	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₁₉×#121	1	1	yes	characteristic
558	Q₈	—	2	1	no	—
559	Q₈	—	2	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	D₄	—	2	1	no	—
563	D₄	—	2	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	8	1	no	—
577	D₄	—	8	1	no	—
578	D₄	—	8	1	no	—
579	D₄	—	8	2	no	—
580	D₄	—	8	2	no	—
581	D₄	—	8	2	no	—
582	D₄	—	8	1	no	—
583	D₄	—	8	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
597	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
598	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
602	C₈	—	2	1	no	—
603	C₈	—	2	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
611	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	16	4	no	—
628	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
638	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
639	C₄	C₁₉×#576	1	1	yes	characteristic
640	C₄	C₁₉×#577	1	1	yes	characteristic
641	C₂	—	4	1	no	—
642	C₂	—	8	1	no	—
643	C₂	—	16	1	no	—
644	C₂	—	16	1	no	—
645	C₂	—	16	1	no	—
646	C₂	C₁₉×#3038	1	1	yes	characteristic
647	C₂	C₁₉×#3062	1	1	yes	characteristic
648	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×#3251	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#3151	C₂	semidirect
4. C₁₉×#2969	C₂	semidirect
5. C₁₉×#1688	C₂	semidirect
6. C₁₉×#1687	C₂	semidirect
7. C₁₉×#1686	C₂	semidirect
8. C₁₉×#1685	C₂	semidirect
9. C₁₉×#1668	C₂	semidirect
10. C₁₉×#1667	C₂	semidirect
11. C₁₉×#1666	C₂	semidirect
12. C₁₉×#1665	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1553	C₂	semidirect
15. C₁₉×#1545	C₂	semidirect
30. C₁₉×#475	C₂²	semidirect
31. C₁₉×#474	C₂²	semidirect
37. C₁₉×#460	C₂²	semidirect
40. 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
225. #19376	C₁₉	direct (N × H)
288. #3251	C₂×C₁₉	semidirect
289. #3217	C₂×C₁₉	semidirect
290. #3151	C₂×C₁₉	semidirect
291. #2969	C₂×C₁₉	semidirect
292. #1688	C₂×C₁₉	semidirect
293. #1687	C₂×C₁₉	semidirect
294. #1686	C₂×C₁₉	semidirect
295. #1685	C₂×C₁₉	semidirect
296. #1668	C₂×C₁₉	semidirect
297. #1667	C₂×C₁₉	semidirect
298. #1666	C₂×C₁₉	semidirect
299. #1665	C₂×C₁₉	semidirect
300. #1569	C₂×C₁₉	semidirect
301. #1553	C₂×C₁₉	semidirect
302. #1545	C₂×C₁₉	semidirect
346. #475	C₂²×C₁₉	semidirect
347. #474	C₂²×C₁₉	semidirect
353. #460	C₂²×C₁₉	semidirect
356. #459	C₂²×C₁₉	semidirect
359. #446	C₂²×C₁₉	semidirect
360. C₈×Q₈	C₂²×C₁₉	semidirect
362. #436	C₂²×C₁₉	semidirect
364. C₈×D₄	C₂²×C₁₉	semidirect
371. #335	C₂²×C₁₉	semidirect
372. #335	C₂²×C₁₉	semidirect
373. #334	C₂²×C₁₉	semidirect
374. #334	C₂²×C₁₉	semidirect
375. #332	C₂²×C₁₉	semidirect
376. #332	C₂²×C₁₉	semidirect
381. #331	C₂²×C₁₉	semidirect
382. #331	C₂²×C₁₉	semidirect
470. C₁₉	#19376	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×#3251	2
C₁₉×#3217	2
C₁₉×#3151	2
C₁₉×#2969	2
C₁₉×#1688	2
C₁₉×#1687	2
C₁₉×#1686	2
C₁₉×#1685	2
C₁₉×#1668	2
C₁₉×#1667	2
C₁₉×#1666	2
C₁₉×#1665	2
C₁₉×#1569	2
C₁₉×#1553	2
C₁₉×#1545	2
#19376	19

Subgroups — C19×#19376 #18025335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19376 #18025335