Subgroups — C₁₉×#24482 #18030441

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2434	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2345	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2068	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2043	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1981	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×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#484	—	2	4	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#395	—	2	2	no	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#389	C₂²	1	2	yes	—
33	C₁₉×#387	—	2	2	no	—
34	C₁₉×#385	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₁₉×#380	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	4	2	no	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	4	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	—	2	4	no	—
59	C₁₉×C₄⋊Q₈	—	4	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×C₄⋊C₈	—	4	2	no	—
82	C₁₉×#103	—	2	4	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#103	—	2	4	no	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#103	—	4	2	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	D₄	1	2	yes	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	8	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	4	8	no	—
109	C₂×Q₈×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	#41	1	4	yes	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	4	4	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	8	2	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	4	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	4	4	no	—
146	C₄⋊C₄×C₁₉	—	4	4	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	8	2	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	2	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	Q₁₆	1	4	yes	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	—	8	2	no	—
158	#24482	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	#121	1	2	yes	—
162	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
163	C₂³×C₁₉	#137	1	2	yes	—
164	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	4	8	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	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	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	8	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	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	8	4	no	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
204	C₈×C₁₉	—	4	1	no	—
205	C₈×C₁₉	—	4	1	no	—
206	C₈×C₁₉	—	4	2	no	—
207	C₂×#484	C₂×C₁₉	1	1	yes	characteristic
208	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
209	#2434	C₂×C₁₉	1	1	yes	characteristic
210	#2345	C₂×C₁₉	1	1	yes	characteristic
211	#2068	C₂×C₁₉	1	2	yes	complemented
212	#2043	C₂×C₁₉	1	2	yes	complemented
213	#1981	C₂×C₁₉	1	2	yes	complemented
214	#1928	C₂×C₁₉	1	2	yes	complemented
215	#1892	C₂×C₁₉	1	1	yes	characteristic
216	#1850	C₂×C₁₉	1	1	yes	characteristic
217	#1787	C₂×C₁₉	1	1	yes	characteristic
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	4	no	—
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	#462	1	4	yes	—
223	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
224	C₂²×C₁₉	#546	1	2	yes	—
225	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
226	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
227	C₂²×C₁₉	#577	1	2	yes	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	—	8	2	no	—
237	C₄×C₁₉	#525	1	1	yes	characteristic
238	C₄×C₁₉	#535	1	1	yes	characteristic
239	C₄×C₁₉	#551	1	2	yes	—
240	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
245	#484	—	2	4	no	—
246	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
249	C₂×#103	—	2	4	no	—
250	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#103	C₂²×C₁₉	1	2	yes	—
253	C₂×#103	C₂²×C₁₉	1	2	yes	—
254	C₂×#103	C₂²×C₁₉	1	2	yes	—
255	C₂×#103	C₂²×C₁₉	1	2	yes	—
256	C₂×#103	C₂²×C₁₉	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
258	#395	—	2	2	no	—
259	#391	C₂²×C₁₉	1	2	yes	—
260	#389	C₂²×C₁₉	1	2	yes	—
261	#387	—	2	2	no	—
262	#385	—	2	1	no	—
263	#385	—	2	1	no	—
264	#380	—	2	1	no	—
265	#380	C₂²×C₁₉	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
267	C₄×C₂²⋊C₄	—	2	1	no	—
268	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
269	#340	C₂²×C₁₉	1	2	yes	—
270	#336	C₂²×C₁₉	1	2	yes	—
271	C₂×C₁₉	—	2	4	no	—
272	C₂×C₁₉	#2411	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#462	1	1	yes	characteristic
274	C₂×C₁₉	#3042	1	1	yes	characteristic
275	C₂×C₁₉	#3299	1	2	yes	—
276	C₂×C₁₉	#3320	1	2	yes	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	4	no	—
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×Q₈	—	4	2	no	—
282	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	4	2	no	—
289	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
292	C₄⋊Q₈	—	2	4	no	—
293	C₄⋊Q₈	—	4	2	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	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	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
313	#107	—	2	2	no	—
314	#107	—	2	2	no	—
315	C₄⋊C₈	—	4	2	no	—
316	#103	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	—	2	4	no	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	4	2	no	—
322	#103	—	4	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₁₉	1	2	yes	—
330	C₁₉	#24482	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	8	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	#41×C₁₉	1	4	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	8	2	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂²×C₄	#41×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	Q₁₆×C₁₉	1	4	yes	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	8	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	C₁₉×#121	1	2	yes	—
396	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
397	C₂³	C₁₉×#137	1	2	yes	—
398	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	Q₈	—	2	4	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	4	8	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	C₁₉×#121	1	2	yes	—
433	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
436	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
438	C₈	—	4	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	C₁₉×#462	1	4	yes	—
446	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
447	C₂²	C₁₉×#546	1	2	yes	—
448	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
449	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
450	C₂²	C₁₉×#577	1	2	yes	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	C₁₉×#525	1	1	yes	characteristic
461	C₄	C₁₉×#535	1	1	yes	characteristic
462	C₄	C₁₉×#551	1	2	yes	—
463	C₂	—	2	4	no	—
464	C₂	C₁₉×#2411	1	1	yes	characteristic
465	C₂	C₂×C₁₉×#462	1	1	yes	characteristic
466	C₂	C₁₉×#3042	1	1	yes	characteristic
467	C₂	C₁₉×#3299	1	2	yes	—
468	C₂	C₁₉×#3320	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×#2068	C₂	semidirect
6. C₁₉×#2043	C₂	semidirect
7. C₁₉×#1981	C₂	semidirect
8. C₁₉×#1928	C₂	semidirect
158. #24482	C₁₉	direct (N × H)
211. #2068	C₂×C₁₉	semidirect
212. #2043	C₂×C₁₉	semidirect
213. #1981	C₂×C₁₉	semidirect
214. #1928	C₂×C₁₉	semidirect
330. C₁₉	#24482	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×#484	2
C₂²×C₁₉×#103	2
C₁₉×#2434	2
C₁₉×#2345	2
C₁₉×#2068	2
C₁₉×#2043	2
C₁₉×#1981	2
C₁₉×#1928	2
C₁₉×#1892	2
C₁₉×#1850	2
C₁₉×#1787	2
#24482	19

Subgroups — C19×#24482 #18030441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24482 #18030441