Subgroups — C₁₉×#24577 #18030536

Order 4864.

826 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#483	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2503	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2344	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1949	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1928	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#483	—	2	4	no	—
18	C₂×C₁₉×#107	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	2	yes	—
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#400	—	2	2	no	—
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#387	—	2	2	no	—
32	C₁₉×#382	C₂²	1	2	yes	—
33	C₁₉×#381	—	2	1	no	—
34	C₁₉×#381	—	2	1	no	—
35	C₁₉×#381	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	4	no	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×C₂²⋊Q₈	—	2	2	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×#117	—	4	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#107	—	2	4	no	—
75	C₁₉×#107	—	2	4	no	—
76	C₁₉×#106	—	2	2	no	—
77	C₁₉×#106	—	2	2	no	—
78	C₁₉×C₄⋊C₈	—	2	4	no	—
79	C₁₉×#103	—	2	4	no	—
80	C₁₉×#103	—	2	2	no	—
81	C₁₉×#103	—	2	2	no	—
82	C₁₉×C₂²⋊C₈	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	D₄	1	2	yes	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	#41	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₉	—	2	8	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	#41	1	4	yes	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	4	2	no	—
136	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	4	4	no	—
145	#24577	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	#121	1	2	yes	—
149	C₂³×C₁₉	#135	1	2	yes	—
150	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
151	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	8	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	8	4	no	—
183	C₂×C₄×C₁₉	#121	1	2	yes	—
184	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₁₉	—	2	4	no	—
189	C₈×C₁₉	—	4	1	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₂×#483	C₂×C₁₉	1	1	yes	characteristic
192	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic
193	#2503	C₂×C₁₉	1	1	yes	characteristic
194	#2344	C₂×C₁₉	1	1	yes	characteristic
195	#2085	C₂×C₁₉	1	2	yes	complemented
196	#2068	C₂×C₁₉	1	2	yes	complemented
197	#1949	C₂×C₁₉	1	2	yes	complemented
198	#1928	C₂×C₁₉	1	2	yes	complemented
199	#1892	C₂×C₁₉	1	1	yes	characteristic
200	#1850	C₂×C₁₉	1	1	yes	characteristic
201	#1823	C₂×C₁₉	1	1	yes	characteristic
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	#463	1	4	yes	—
207	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
208	C₂²×C₁₉	#547	1	2	yes	—
209	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
210	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₁₉	#578	1	2	yes	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	#525	1	1	yes	characteristic
222	C₄×C₁₉	#536	1	1	yes	characteristic
223	C₄×C₁₉	#552	1	2	yes	—
224	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#117	—	2	1	no	—
227	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	#483	—	2	4	no	—
230	C₂×#107	—	2	4	no	—
231	C₂×#107	C₂²×C₁₉	1	2	yes	—
232	C₂×#107	C₂²×C₁₉	1	2	yes	—
233	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
236	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#103	C₂²×C₁₉	1	2	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
240	#400	—	2	2	no	—
241	#391	C₂²×C₁₉	1	2	yes	—
242	#389	C₂²×C₁₉	1	2	yes	—
243	#387	—	2	2	no	—
244	#382	C₂²×C₁₉	1	2	yes	—
245	#381	—	2	1	no	—
246	#381	—	2	1	no	—
247	#381	—	2	1	no	—
248	#380	C₂²×C₁₉	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
251	#340	C₂²×C₁₉	1	2	yes	—
252	#340	C₂²×C₁₉	1	2	yes	—
253	#340	C₂²×C₁₉	1	2	yes	—
254	#336	C₂²×C₁₉	1	2	yes	—
255	C₂×C₁₉	—	2	4	no	—
256	C₂×C₁₉	#2413	1	1	yes	characteristic
257	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
258	C₂×C₁₉	#3044	1	1	yes	characteristic
259	C₂×C₁₉	#3336	1	2	yes	—
260	C₂×C₁₉	#3343	1	2	yes	—
261	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
270	C₂²⋊Q₈	—	2	2	no	—
271	C₂²⋊Q₈	—	2	2	no	—
272	#117	—	4	4	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
292	#107	—	2	4	no	—
293	#107	—	2	4	no	—
294	#106	—	2	2	no	—
295	#106	—	2	2	no	—
296	C₄⋊C₈	—	2	4	no	—
297	#103	—	2	4	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₁₉	1	2	yes	—
309	C₁₉	#24577	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	#41×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	#41×C₁₉	1	4	yes	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
356	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	C₁₉×#121	1	2	yes	—
367	C₂³	C₁₉×#135	1	2	yes	—
368	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
369	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
370	Q₈	—	4	1	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	C₁₉×#121	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
404	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
406	C₈	—	2	4	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	C₁₉×#463	1	4	yes	—
414	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
415	C₂²	C₁₉×#547	1	2	yes	—
416	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₂²	C₁₉×#578	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₁₉×#525	1	1	yes	characteristic
429	C₄	C₁₉×#536	1	1	yes	characteristic
430	C₄	C₁₉×#552	1	2	yes	—
431	C₂	—	2	4	no	—
432	C₂	C₁₉×#2413	1	1	yes	characteristic
433	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
434	C₂	C₁₉×#3044	1	1	yes	characteristic
435	C₂	C₁₉×#3336	1	2	yes	—
436	C₂	C₁₉×#3343	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2068	C₂	semidirect
7. C₁₉×#1949	C₂	semidirect
8. C₁₉×#1928	C₂	semidirect
145. #24577	C₁₉	direct (N × H)
195. #2085	C₂×C₁₉	semidirect
196. #2068	C₂×C₁₉	semidirect
197. #1949	C₂×C₁₉	semidirect
198. #1928	C₂×C₁₉	semidirect
309. C₁₉	#24577	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×#483	2
C₂²×C₁₉×#107	2
C₁₉×#2503	2
C₁₉×#2344	2
C₁₉×#2085	2
C₁₉×#2068	2
C₁₉×#1949	2
C₁₉×#1928	2
C₁₉×#1892	2
C₁₉×#1850	2
C₁₉×#1823	2
#24577	19

Subgroups — C19×#24577 #18030536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24577 #18030536