Subgroups — C₁₉×#24774 #18030733

Order 4864.

882 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#472	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#471	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2045	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#472	—	2	4	no	—
27	C₁₉×#471	—	2	4	no	—
28	C₁₉×#464	—	2	1	no	—
29	C₁₉×#464	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#463	—	2	1	no	—
32	C₁₉×#463	—	2	1	no	—
33	C₁₉×#463	—	2	1	no	—
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#463	—	2	1	no	—
36	C₁₉×#442	—	2	1	no	—
37	C₁₉×#440	—	2	1	no	—
38	C₄×SD₁₆×C₁₉	—	2	1	no	—
39	C₄×D₈×C₁₉	—	2	1	no	—
40	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
42	C₁₉×#428	C₂²	1	1	yes	characteristic
43	C₁₉×#424	—	2	1	no	—
44	C₁₉×#424	—	2	1	no	—
45	C₁₉×#424	C₂²	1	1	yes	characteristic
46	C₁₉×#424	C₂²	1	1	yes	characteristic
47	C₁₉×#423	—	2	1	no	—
48	C₁₉×#423	C₂²	1	1	yes	characteristic
49	C₁₉×#423	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₉×#419	C₂²	1	1	yes	characteristic
53	C₁₉×#418	C₂²	1	1	yes	characteristic
54	C₁₉×#418	C₂²	1	1	yes	characteristic
55	C₁₉×#417	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
62	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
63	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
64	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
65	C₁₉×#343	C₂²	1	1	yes	characteristic
66	C₁₉×#343	C₂²	1	1	yes	characteristic
67	C₁₉×#341	C₂²	1	1	yes	characteristic
68	C₁₉×#341	C₂²	1	1	yes	characteristic
69	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₁₉×#137	—	2	2	no	—
75	C₁₉×#137	—	2	2	no	—
76	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
78	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
79	C₁₉×AGL(1,ℤ/8)	D₄	1	4	yes	—
80	C₂×Q₁₆×C₁₉	—	2	1	no	—
81	C₂×SD₁₆×C₁₉	—	2	1	no	—
82	C₂×SD₁₆×C₁₉	—	2	1	no	—
83	C₂×SD₁₆×C₁₉	—	2	1	no	—
84	C₂×SD₁₆×C₁₉	—	2	2	no	—
85	C₂×SD₁₆×C₁₉	—	2	1	no	—
86	C₂×SD₁₆×C₁₉	—	2	1	no	—
87	C₂×SD₁₆×C₁₉	—	4	1	no	—
88	C₂×D₈×C₁₉	—	2	1	no	—
89	C₂×D₈×C₁₉	—	2	1	no	—
90	C₂×D₈×C₁₉	—	2	2	no	—
91	C₂×D₈×C₁₉	—	2	1	no	—
92	C₂×D₈×C₁₉	—	2	1	no	—
93	C₂×D₈×C₁₉	—	4	1	no	—
94	C₁₉×#131	—	2	2	no	—
95	C₁₉×#131	—	2	2	no	—
96	C₁₉×#131	—	4	1	no	—
97	C₁₉×#131	—	4	1	no	—
98	C₂×M₁₆×C₁₉	—	2	1	no	—
99	C₂×M₁₆×C₁₉	—	2	1	no	—
100	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₉	—	2	1	no	—
107	C₂²×C₈×C₁₉	—	2	1	no	—
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#124	—	2	1	no	—
111	C₁₉×#124	—	2	1	no	—
112	C₁₉×#124	—	2	1	no	—
113	C₁₉×#124	—	2	1	no	—
114	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	—	2	1	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
123	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
124	C₁₉×#117	—	2	1	no	—
125	C₁₉×#117	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄²×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#108	—	2	2	no	—
133	C₁₉×#108	—	2	2	no	—
134	C₁₉×#107	—	2	1	no	—
135	C₁₉×#106	—	2	1	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×C₄⋊C₈	—	2	1	no	—
138	C₁₉×C₄⋊C₈	—	2	1	no	—
139	C₁₉×C₄⋊C₈	—	2	1	no	—
140	C₁₉×C₄⋊C₈	—	2	1	no	—
141	C₁₉×C₄⋊C₈	—	2	1	no	—
142	C₁₉×C₄⋊C₈	—	2	1	no	—
143	C₁₉×C₄⋊C₈	—	2	1	no	—
144	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
145	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
146	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
147	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
148	C₁₉×#103	—	2	1	no	—
149	C₁₉×#103	—	2	1	no	—
150	C₁₉×#103	—	2	1	no	—
151	C₁₉×#103	—	2	1	no	—
152	C₁₉×#103	—	2	1	no	—
153	C₁₉×#102	—	2	1	no	—
154	C₁₉×#102	—	2	1	no	—
155	C₁₉×#102	—	2	1	no	—
156	C₁₉×#102	—	2	1	no	—
157	C₁₉×#102	—	2	1	no	—
158	C₁₉×#102	—	2	1	no	—
159	C₁₉×#102	—	2	1	no	—
160	C₁₉×#101	—	2	2	no	—
161	C₁₉×#101	—	4	1	no	—
162	C₁₉×#100	—	2	2	no	—
163	C₁₉×#100	—	2	2	no	—
164	C₁₉×#100	—	2	2	no	—
165	C₁₉×#100	—	4	1	no	—
166	C₁₉×#97	—	2	1	no	—
167	C₄×C₈×C₁₉	—	2	1	no	—
168	C₂⁴×C₁₉	—	2	1	no	—
169	C₂⁴×C₁₉	—	2	1	no	—
170	#41×C₁₉	—	2	1	no	—
171	#41×C₁₉	—	2	1	no	—
172	#41×C₁₉	C₂×D₄	1	2	yes	—
173	#41×C₁₉	#41	1	2	yes	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	1	no	—
180	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	8	2	no	—
203	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
206	Q₁₆×C₁₉	—	4	2	no	—
207	SD₁₆×C₁₉	—	2	4	no	—
208	SD₁₆×C₁₉	—	4	2	no	—
209	SD₁₆×C₁₉	—	4	2	no	—
210	SD₁₆×C₁₉	—	4	2	no	—
211	SD₁₆×C₁₉	—	4	2	no	—
212	D₈×C₁₉	—	2	4	no	—
213	D₈×C₁₉	—	4	2	no	—
214	D₈×C₁₉	—	4	2	no	—
215	D₈×C₁₉	—	4	2	no	—
216	M₁₆×C₁₉	—	2	1	no	—
217	M₁₆×C₁₉	—	2	1	no	—
218	M₁₆×C₁₉	—	2	1	no	—
219	M₁₆×C₁₉	—	2	1	no	—
220	M₁₆×C₁₉	—	2	1	no	—
221	M₁₆×C₁₉	—	2	1	no	—
222	M₁₆×C₁₉	—	2	1	no	—
223	M₁₆×C₁₉	—	2	1	no	—
224	M₁₆×C₁₉	—	2	1	no	—
225	M₁₆×C₁₉	—	2	1	no	—
226	M₁₆×C₁₉	—	2	1	no	—
227	M₁₆×C₁₉	—	4	2	no	—
228	M₁₆×C₁₉	—	4	2	no	—
229	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
230	C₂×C₈×C₁₉	—	2	1	no	—
231	C₂×C₈×C₁₉	—	2	1	no	—
232	C₂×C₈×C₁₉	—	2	1	no	—
233	C₂×C₈×C₁₉	—	2	1	no	—
234	C₂×C₈×C₁₉	—	2	1	no	—
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	4	2	no	—
241	C₂×C₈×C₁₉	—	4	2	no	—
242	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
243	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₉	—	2	1	no	—
247	C₄⋊C₄×C₁₉	—	2	1	no	—
248	C₄⋊C₄×C₁₉	—	2	1	no	—
249	C₄⋊C₄×C₁₉	—	2	1	no	—
250	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²⋊C₄×C₁₉	—	2	1	no	—
253	C₂²⋊C₄×C₁₉	—	2	1	no	—
254	C₂²⋊C₄×C₁₉	—	2	1	no	—
255	C₂²⋊C₄×C₁₉	—	4	1	no	—
256	C₂²⋊C₄×C₁₉	—	4	1	no	—
257	C₂²⋊C₄×C₁₉	—	4	1	no	—
258	C₂²⋊C₄×C₁₉	—	4	1	no	—
259	C₂²⋊C₄×C₁₉	—	4	1	no	—
260	C₂²⋊C₄×C₁₉	—	4	1	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	2	1	no	—
264	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
268	#24774	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	—	2	2	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	4	1	no	—
274	C₂³×C₁₉	—	4	1	no	—
275	C₂³×C₁₉	—	4	1	no	—
276	C₂³×C₁₉	—	8	1	no	—
277	C₂³×C₁₉	—	8	1	no	—
278	C₂³×C₁₉	—	8	1	no	—
279	C₂³×C₁₉	—	8	1	no	—
280	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
281	Q₈×C₁₉	—	2	1	no	—
282	Q₈×C₁₉	—	4	1	no	—
283	Q₈×C₁₉	—	4	1	no	—
284	Q₈×C₁₉	—	4	1	no	—
285	Q₈×C₁₉	—	4	1	no	—
286	Q₈×C₁₉	#121	1	2	yes	—
287	D₄×C₁₉	—	2	2	no	—
288	D₄×C₁₉	—	2	2	no	—
289	D₄×C₁₉	—	2	2	no	—
290	D₄×C₁₉	—	2	1	no	—
291	D₄×C₁₉	—	2	2	no	—
292	D₄×C₁₉	—	4	1	no	—
293	D₄×C₁₉	—	4	1	no	—
294	D₄×C₁₉	—	4	1	no	—
295	D₄×C₁₉	—	4	1	no	—
296	D₄×C₁₉	—	4	1	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	#121	1	2	yes	—
299	C₂×C₄×C₁₉	—	2	1	no	—
300	C₂×C₄×C₁₉	—	2	2	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	8	1	no	—
312	C₂×C₄×C₁₉	—	8	2	no	—
313	C₂×C₄×C₁₉	—	8	2	no	—
314	C₂×C₄×C₁₉	—	8	1	no	—
315	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
325	C₈×C₁₉	—	2	2	no	—
326	C₈×C₁₉	—	2	1	no	—
327	C₈×C₁₉	—	2	1	no	—
328	C₈×C₁₉	—	2	1	no	—
329	C₈×C₁₉	—	2	1	no	—
330	C₈×C₁₉	—	4	1	no	—
331	C₈×C₁₉	—	4	1	no	—
332	C₈×C₁₉	—	4	1	no	—
333	C₈×C₁₉	—	4	1	no	—
334	C₈×C₁₉	—	4	1	no	—
335	C₂×#472	C₂×C₁₉	1	1	yes	characteristic
336	C₂×#471	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#3040	C₂×C₁₉	1	1	yes	characteristic, complemented
338	C₂×#463	C₂×C₁₉	1	1	yes	characteristic, complemented
339	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#2906	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
343	#2046	C₂×C₁₉	1	1	yes	characteristic, complemented
344	#2045	C₂×C₁₉	1	1	yes	characteristic, complemented
345	#1967	C₂×C₁₉	1	1	yes	characteristic, complemented
346	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#1908	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#1907	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
350	C₂²×C₁₉	—	2	1	no	—
351	C₂²×C₁₉	—	2	1	no	—
352	C₂²×C₁₉	—	2	2	no	—
353	C₂²×C₁₉	—	4	1	no	—
354	C₂²×C₁₉	—	4	1	no	—
355	C₂²×C₁₉	—	4	2	no	—
356	C₂²×C₁₉	—	8	2	no	—
357	C₂²×C₁₉	—	8	2	no	—
358	C₂²×C₁₉	—	8	1	no	—
359	C₂²×C₁₉	—	8	1	no	—
360	C₂²×C₁₉	—	8	1	no	—
361	C₂²×C₁₉	—	8	1	no	—
362	C₂²×C₁₉	—	8	1	no	—
363	C₂²×C₁₉	—	16	1	no	—
364	C₂²×C₁₉	—	16	1	no	—
365	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
366	C₂²×C₁₉	#547	1	1	yes	characteristic
367	C₂²×C₁₉	#553	1	1	yes	characteristic
368	C₄×C₁₉	—	2	2	no	—
369	C₄×C₁₉	—	2	1	no	—
370	C₄×C₁₉	—	2	1	no	—
371	C₄×C₁₉	—	2	1	no	—
372	C₄×C₁₉	—	2	1	no	—
373	C₄×C₁₉	—	4	1	no	—
374	C₄×C₁₉	—	4	1	no	—
375	C₄×C₁₉	—	8	1	no	—
376	C₄×C₁₉	—	8	1	no	—
377	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
378	C₄×C₁₉	#537	1	1	yes	characteristic
379	C₄×C₁₉	D₄²	1	1	yes	characteristic
380	C₄×C₁₉	#548	1	1	yes	characteristic
381	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
385	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
389	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
391	#472	—	2	4	no	—
392	#471	—	2	4	no	—
393	#464	—	2	1	no	—
394	#464	—	2	1	no	—
395	#463	—	2	1	no	—
396	#463	—	2	1	no	—
397	#463	—	2	1	no	—
398	#463	—	2	1	no	—
399	#463	—	2	1	no	—
400	#463	—	2	1	no	—
401	#442	—	2	1	no	—
402	#440	—	2	1	no	—
403	C₄×SD₁₆	—	2	1	no	—
404	C₄×D₈	—	2	1	no	—
405	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
407	#428	C₂²×C₁₉	1	1	yes	characteristic
408	#424	—	2	1	no	—
409	#424	—	2	1	no	—
410	#424	C₂²×C₁₉	1	1	yes	characteristic
411	#424	C₂²×C₁₉	1	1	yes	characteristic
412	#423	—	2	1	no	—
413	#423	C₂²×C₁₉	1	1	yes	characteristic
414	#423	C₂²×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₈	—	2	1	no	—
416	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
417	#419	C₂²×C₁₉	1	1	yes	characteristic
418	#418	C₂²×C₁₉	1	1	yes	characteristic
419	#418	C₂²×C₁₉	1	1	yes	characteristic
420	#417	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
423	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
424	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
425	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
429	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
430	#343	C₂²×C₁₉	1	1	yes	characteristic
431	#343	C₂²×C₁₉	1	1	yes	characteristic
432	#341	C₂²×C₁₉	1	1	yes	characteristic
433	#341	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×C₁₉	—	2	1	no	—
435	C₂×C₁₉	—	2	1	no	—
436	C₂×C₁₉	—	4	2	no	—
437	C₂×C₁₉	—	8	2	no	—
438	C₂×C₁₉	—	16	1	no	—
439	C₂×C₁₉	#2416	1	1	yes	characteristic
440	C₂×C₁₉	#3067	1	1	yes	characteristic
441	C₂×C₁₉	#3068	1	1	yes	characteristic
442	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂³×C₄	—	2	1	no	—
447	#137	—	2	2	no	—
448	#137	—	2	2	no	—
449	AGL(1,ℤ/8)	—	2	2	no	—
450	AGL(1,ℤ/8)	—	2	2	no	—
451	AGL(1,ℤ/8)	—	2	2	no	—
452	AGL(1,ℤ/8)	D₄×C₁₉	1	4	yes	—
453	C₂×Q₁₆	—	2	1	no	—
454	C₂×SD₁₆	—	2	1	no	—
455	C₂×SD₁₆	—	2	1	no	—
456	C₂×SD₁₆	—	2	2	no	—
457	C₂×SD₁₆	—	2	1	no	—
458	C₂×SD₁₆	—	2	1	no	—
459	C₂×SD₁₆	—	2	1	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×D₈	—	2	1	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	1	no	—
464	C₂×D₈	—	2	1	no	—
465	C₂×D₈	—	2	1	no	—
466	C₂×D₈	—	4	1	no	—
467	#131	—	2	2	no	—
468	#131	—	2	2	no	—
469	#131	—	4	1	no	—
470	#131	—	4	1	no	—
471	C₂×M₁₆	—	2	1	no	—
472	C₂×M₁₆	—	2	1	no	—
473	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
475	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
476	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
477	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
479	C₂²×C₈	—	2	1	no	—
480	C₂²×C₈	—	2	1	no	—
481	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
483	#124	—	2	1	no	—
484	#124	—	2	1	no	—
485	#124	—	2	1	no	—
486	#124	—	2	1	no	—
487	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
488	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	—	2	1	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
496	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
497	#117	—	2	1	no	—
498	#117	C₂³×C₁₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
505	#108	—	2	2	no	—
506	#108	—	2	2	no	—
507	#107	—	2	1	no	—
508	#106	—	2	1	no	—
509	C₄⋊C₈	—	2	1	no	—
510	C₄⋊C₈	—	2	1	no	—
511	C₄⋊C₈	—	2	1	no	—
512	C₄⋊C₈	—	2	1	no	—
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	C₄⋊C₈	—	2	1	no	—
516	C₄⋊C₈	—	2	1	no	—
517	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
518	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
519	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
520	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#103	—	2	1	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	1	no	—
528	#102	—	2	1	no	—
529	#102	—	2	1	no	—
530	#102	—	2	1	no	—
531	#102	—	2	1	no	—
532	#102	—	2	1	no	—
533	#101	—	2	2	no	—
534	#101	—	4	1	no	—
535	#100	—	2	2	no	—
536	#100	—	2	2	no	—
537	#100	—	2	2	no	—
538	#100	—	4	1	no	—
539	#97	—	2	1	no	—
540	C₄×C₈	—	2	1	no	—
541	C₁₉	#24774	1	1	yes	characteristic, direct product factor, Sylow
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	1	no	—
544	#41	—	2	1	no	—
545	#41	—	2	1	no	—
546	#41	C₂×D₄×C₁₉	1	2	yes	—
547	#41	#41×C₁₉	1	2	yes	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
568	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	8	2	no	—
577	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
580	Q₁₆	—	4	2	no	—
581	SD₁₆	—	2	4	no	—
582	SD₁₆	—	4	2	no	—
583	SD₁₆	—	4	2	no	—
584	SD₁₆	—	4	2	no	—
585	SD₁₆	—	4	2	no	—
586	D₈	—	2	4	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	2	no	—
589	D₈	—	4	2	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	1	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	2	1	no	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	1	no	—
600	M₁₆	—	2	1	no	—
601	M₁₆	—	4	2	no	—
602	M₁₆	—	4	2	no	—
603	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	4	2	no	—
615	C₂×C₈	—	4	2	no	—
616	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
617	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
618	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
619	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	4	1	no	—
633	C₂²⋊C₄	—	4	1	no	—
634	C₂²⋊C₄	—	4	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	—	8	1	no	—
651	C₂³	—	8	1	no	—
652	C₂³	—	8	1	no	—
653	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
654	Q₈	—	2	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	C₁₉×#121	1	2	yes	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	2	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	C₁₉×#121	1	2	yes	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	—	8	1	no	—
688	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
689	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
690	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
691	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
695	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
696	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	8	2	no	—
715	C₂²	—	8	2	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	16	1	no	—
722	C₂²	—	16	1	no	—
723	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
724	C₂²	C₁₉×#547	1	1	yes	characteristic
725	C₂²	C₁₉×#553	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	8	1	no	—
734	C₄	—	8	1	no	—
735	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
736	C₄	C₁₉×#537	1	1	yes	characteristic
737	C₄	D₄²×C₁₉	1	1	yes	characteristic
738	C₄	C₁₉×#548	1	1	yes	characteristic
739	C₂	—	2	1	no	—
740	C₂	—	2	1	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	2	no	—
743	C₂	—	16	1	no	—
744	C₂	C₁₉×#2416	1	1	yes	characteristic
745	C₂	C₁₉×#3067	1	1	yes	characteristic
746	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₂×C₁₉×#471	C₂	semidirect
3. C₁₉×#3040	C₂	semidirect
4. C₂×C₁₉×#463	C₂	semidirect
5. C₄×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
6. C₁₉×#2906	C₂	semidirect
7. C₁₉×#2064	C₂	semidirect
8. C₁₉×#2063	C₂	semidirect
9. C₁₉×#2046	C₂	semidirect
10. C₁₉×#2045	C₂	semidirect
11. C₁₉×#1967	C₂	semidirect
12. C₁₉×#1950	C₂	semidirect
13. C₁₉×#1908	C₂	semidirect
14. C₁₉×#1907	C₂	semidirect
15. C₁₉×#1800	C₂	semidirect
268. #24774	C₁₉	direct (N × H)
336. C₂×#471	C₂×C₁₉	semidirect
337. #3040	C₂×C₁₉	semidirect
338. C₂×#463	C₂×C₁₉	semidirect
339. C₄×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
340. #2906	C₂×C₁₉	semidirect
341. #2064	C₂×C₁₉	semidirect
342. #2063	C₂×C₁₉	semidirect
343. #2046	C₂×C₁₉	semidirect
344. #2045	C₂×C₁₉	semidirect
345. #1967	C₂×C₁₉	semidirect
346. #1950	C₂×C₁₉	semidirect
347. #1908	C₂×C₁₉	semidirect
348. #1907	C₂×C₁₉	semidirect
349. #1800	C₂×C₁₉	semidirect
541. C₁₉	#24774	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#472	2
C₂×C₁₉×#471	2
C₁₉×#3040	2
C₂×C₁₉×#463	2
C₄×C₁₉×AGL(1,ℤ/8)	2
C₁₉×#2906	2
C₁₉×#2064	2
C₁₉×#2063	2
C₁₉×#2046	2
C₁₉×#2045	2
C₁₉×#1967	2
C₁₉×#1950	2
C₁₉×#1908	2
C₁₉×#1907	2
C₁₉×#1800	2
#24774	19

Subgroups — C19×#24774 #18030733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24774 #18030733