Subgroups — C₁₉×#24576 #18030535

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2501	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2083	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1947	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1925	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#123	—	2	1	no	—
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#480	—	2	4	no	—
20	C₂×C₁₉×#107	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	2	yes	—
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	2	yes	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#399	—	2	2	no	—
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#389	C₂²	1	2	yes	—
33	C₁₉×#387	—	2	2	no	—
34	C₁₉×#384	C₂²	1	2	yes	—
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×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	4	no	—
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₁₉×#123	—	4	4	no	—
54	C₁₉×#123	—	4	4	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#117	—	4	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#107	—	2	4	no	—
81	C₁₉×#107	—	2	4	no	—
82	C₁₉×#107	—	2	2	no	—
83	C₁₉×#107	—	2	2	no	—
84	C₁₉×C₄⋊C₈	—	2	4	no	—
85	C₁₉×#102	—	2	4	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	D₄	1	2	yes	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	#41	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₉	—	2	8	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	#41	1	4	yes	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	4	no	—
141	C₄⋊C₄×C₁₉	—	4	4	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	4	4	no	—
146	C₂²⋊C₄×C₁₉	—	4	2	no	—
147	C₂²⋊C₄×C₁₉	—	4	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₉	D₈	1	4	yes	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	4	4	no	—
153	#24576	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	#121	1	2	yes	—
162	C₂³×C₁₉	C₂×D₈	1	2	yes	—
163	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
164	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	8	4	no	—
195	C₂×C₄×C₁₉	#121	1	2	yes	—
196	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	—	4	1	no	—
203	C₈×C₁₉	—	4	1	no	—
204	C₂×#480	C₂×C₁₉	1	1	yes	characteristic
205	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2501	C₂×C₁₉	1	1	yes	characteristic
207	#2344	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2083	C₂×C₁₉	1	2	yes	complemented
209	#2067	C₂×C₁₉	1	2	yes	complemented
210	#1947	C₂×C₁₉	1	2	yes	complemented
211	#1925	C₂×C₁₉	1	2	yes	complemented
212	#1893	C₂×C₁₉	1	1	yes	characteristic
213	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	8	2	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	—	8	1	no	—
222	C₂²×C₁₉	—	8	1	no	—
223	C₂²×C₁₉	—	8	1	no	—
224	C₂²×C₁₉	#459	1	4	yes	—
225	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
226	C₂²×C₁₉	#547	1	2	yes	—
227	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
228	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂²×C₁₉	#578	1	2	yes	—
230	C₄×C₁₉	—	2	4	no	—
231	C₄×C₁₉	—	2	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	—	8	2	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	#525	1	1	yes	characteristic
239	C₄×C₁₉	#536	1	1	yes	characteristic
240	C₄×C₁₉	#552	1	2	yes	—
241	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#123	—	2	1	no	—
243	C₂×#123	—	2	1	no	—
244	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#117	—	2	1	no	—
246	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
248	#480	—	2	4	no	—
249	C₂×#107	—	2	4	no	—
250	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#107	C₂²×C₁₉	1	2	yes	—
253	C₂×#107	C₂²×C₁₉	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
255	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₉	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
259	#399	—	2	2	no	—
260	#390	C₂²×C₁₉	1	2	yes	—
261	#389	C₂²×C₁₉	1	2	yes	—
262	#387	—	2	2	no	—
263	#384	C₂²×C₁₉	1	2	yes	—
264	#381	—	2	1	no	—
265	#380	C₂²×C₁₉	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
268	#340	C₂²×C₁₉	1	2	yes	—
269	#340	C₂²×C₁₉	1	2	yes	—
270	#340	C₂²×C₁₉	1	2	yes	—
271	#336	C₂²×C₁₉	1	2	yes	—
272	C₂×C₁₉	—	2	4	no	—
273	C₂×C₁₉	—	16	1	no	—
274	C₂×C₁₉	#2413	1	1	yes	characteristic
275	C₂×C₁₉	C₂×#459	1	1	yes	characteristic
276	C₂×C₁₉	#3044	1	1	yes	characteristic
277	C₂×C₁₉	#3334	1	2	yes	—
278	C₂×C₁₉	#3343	1	2	yes	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
289	#123	—	4	4	no	—
290	#123	—	4	4	no	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	#117	—	4	4	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
316	#107	—	2	4	no	—
317	#107	—	2	4	no	—
318	#107	—	2	2	no	—
319	#107	—	2	2	no	—
320	C₄⋊C₈	—	2	4	no	—
321	#102	—	2	4	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	D₄×C₁₉	1	2	yes	—
329	C₁₉	#24576	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
356	C₂²×C₄	#41×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
358	C₂×C₈	—	2	8	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	#41×C₁₉	1	4	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	D₈×C₁₉	1	4	yes	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	4	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₁₉×#121	1	2	yes	—
398	C₂³	C₂×D₈×C₁₉	1	2	yes	—
399	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
400	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	2	no	—
404	D₄	—	8	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	4	no	—
431	C₂×C₄	C₁₉×#121	1	2	yes	—
432	C₂×C₄	C₂×D₈×C₁₉	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
435	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
437	C₈	—	2	4	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₁₉×#459	1	4	yes	—
450	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
451	C₂²	C₁₉×#547	1	2	yes	—
452	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
453	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₂²	C₁₉×#578	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	C₁₉×#525	1	1	yes	characteristic
464	C₄	C₁₉×#536	1	1	yes	characteristic
465	C₄	C₁₉×#552	1	2	yes	—
466	C₂	—	2	4	no	—
467	C₂	—	16	1	no	—
468	C₂	C₁₉×#2413	1	1	yes	characteristic
469	C₂	C₂×C₁₉×#459	1	1	yes	characteristic
470	C₂	C₁₉×#3044	1	1	yes	characteristic
471	C₂	C₁₉×#3334	1	2	yes	—
472	C₂	C₁₉×#3343	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
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
2. C₂²×C₁₉×#107	C₂	semidirect
4. C₁₉×#2344	C₂	semidirect
5. C₁₉×#2083	C₂	semidirect
6. C₁₉×#2067	C₂	semidirect
7. C₁₉×#1947	C₂	semidirect
8. C₁₉×#1925	C₂	semidirect
10. C₁₉×#1850	C₂	semidirect
11. C₁₉×#1823	C₂	semidirect
153. #24576	C₁₉	direct (N × H)
205. C₂²×#107	C₂×C₁₉	semidirect
207. #2344	C₂×C₁₉	semidirect
208. #2083	C₂×C₁₉	semidirect
209. #2067	C₂×C₁₉	semidirect
210. #1947	C₂×C₁₉	semidirect
211. #1925	C₂×C₁₉	semidirect
213. #1850	C₂×C₁₉	semidirect
214. #1823	C₂×C₁₉	semidirect
329. C₁₉	#24576	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×#480	2
C₂²×C₁₉×#107	2
C₁₉×#2501	2
C₁₉×#2344	2
C₁₉×#2083	2
C₁₉×#2067	2
C₁₉×#1947	2
C₁₉×#1925	2
C₁₉×#1893	2
C₁₉×#1850	2
C₁₉×#1823	2
#24576	19

Subgroups — C19×#24576 #18030535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24576 #18030535