Subgroups — C₁₉×#22567 #18028526

Order 4864.

962 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2345	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1935	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1927	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1865	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1763	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1752	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×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#106	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₄	1	8	yes	complemented
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#97	C₂²	1	2	yes	—
26	C₁₉×#391	—	2	2	no	—
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#387	—	2	2	no	—
30	C₁₉×#380	—	2	1	no	—
31	C₁₉×#380	—	2	1	no	—
32	C₁₉×#380	C₂²	1	1	yes	characteristic
33	C₁₉×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	4	2	no	—
46	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	—	4	2	no	—
53	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₁₉	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	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	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	—	2	2	no	—
74	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
75	C₁₉×#106	—	4	2	no	—
76	C₁₉×#103	—	2	4	no	—
77	C₁₉×#103	—	4	2	no	—
78	C₁₉×#103	C₂×C₄	1	4	yes	—
79	C₁₉×#103	C₂×C₄	1	4	yes	—
80	C₁₉×#103	C₂×C₄	1	4	yes	—
81	C₁₉×#103	C₂×C₄	1	4	yes	—
82	C₁₉×C₂²⋊C₈	—	2	2	no	—
83	C₁₉×#97	—	4	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	D₄	1	2	yes	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	8	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	4	4	no	—
100	C₂×Q₈×C₁₉	—	4	4	no	—
101	C₂×Q₈×C₁₉	—	4	8	no	—
102	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂×Q₈×C₁₉	#41	1	4	yes	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	—	8	2	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	4	4	no	—
129	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
131	C₄⋊C₄×C₁₉	—	2	4	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	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	—	8	2	no	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	2	no	—
145	C₂²⋊C₄×C₁₉	—	4	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	4	4	no	—
149	C₄²×C₁₉	—	8	2	no	—
150	#22567	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	C₄×D₄	1	2	yes	—
154	C₂³×C₁₉	#137	1	2	yes	—
155	C₂³×C₁₉	#137	1	2	yes	—
156	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	4	no	—
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	4	8	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	#117	1	4	yes	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	4	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	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	2	no	—
179	C₂×C₄×C₁₉	—	4	8	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	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	—	8	4	no	—
190	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
195	C₈×C₁₉	—	2	2	no	—
196	C₈×C₁₉	—	2	2	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
199	#2345	C₂×C₁₉	1	1	yes	characteristic
200	Q₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
201	#1935	C₂×C₁₉	1	2	yes	complemented
202	#1927	C₂×C₁₉	1	2	yes	complemented
203	#1865	C₂×C₁₉	1	2	yes	complemented
204	#1824	C₂×C₁₉	1	1	yes	characteristic
205	#1807	C₂×C₁₉	1	1	yes	characteristic
206	#1787	C₂×C₁₉	1	1	yes	characteristic
207	#1763	C₂×C₁₉	1	2	yes	complemented
208	#1752	C₂×C₁₉	1	1	yes	characteristic
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	4	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	#441	1	4	yes	—
214	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₁₉	#546	1	2	yes	—
216	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
218	C₂²×C₁₉	#577	1	2	yes	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
229	C₄×C₁₉	#518	1	1	yes	characteristic
230	C₄×C₁₉	#551	1	2	yes	—
231	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×#106	C₂²×C₁₉	1	2	yes	—
236	C₂×#103	C₄×C₁₉	1	8	yes	complemented
237	C₂×#103	C₂²×C₁₉	1	2	yes	—
238	C₂×#103	C₂²×C₁₉	1	2	yes	—
239	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#97	C₂²×C₁₉	1	2	yes	—
245	#391	—	2	2	no	—
246	#391	C₂²×C₁₉	1	2	yes	—
247	#389	C₂²×C₁₉	1	2	yes	—
248	#387	—	2	2	no	—
249	#380	—	2	1	no	—
250	#380	—	2	1	no	—
251	#380	C₂²×C₁₉	1	1	yes	characteristic
252	#380	C₂²×C₁₉	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
254	C₄×C₂²⋊C₄	—	2	1	no	—
255	C₄×C₂²⋊C₄	—	2	1	no	—
256	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	#340	C₂²×C₁₉	1	2	yes	—
258	#340	C₂²×C₁₉	1	2	yes	—
259	#340	C₂²×C₁₉	1	2	yes	—
260	#336	C₂²×C₁₉	1	2	yes	—
261	C₂×C₁₉	—	2	4	no	—
262	C₂×C₁₉	#2342	1	1	yes	characteristic
263	C₂×C₁₉	C₂×#441	1	1	yes	characteristic
264	C₂×C₁₉	#2949	1	1	yes	characteristic
265	C₂×C₁₉	#3316	1	2	yes	—
266	C₂×C₁₉	#3320	1	2	yes	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	—	2	4	no	—
270	C₂²×Q₈	—	4	2	no	—
271	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
272	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂²×C₈	—	4	2	no	—
278	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
300	#106	—	4	2	no	—
301	#103	—	2	4	no	—
302	#103	—	4	2	no	—
303	#103	C₂×C₄×C₁₉	1	4	yes	—
304	#103	C₂×C₄×C₁₉	1	4	yes	—
305	#103	C₂×C₄×C₁₉	1	4	yes	—
306	#103	C₂×C₄×C₁₉	1	4	yes	—
307	C₂²⋊C₈	—	2	2	no	—
308	#97	—	4	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	D₄×C₁₉	1	2	yes	—
316	C₁₉	#22567	1	1	yes	characteristic, direct product factor, Sylow
317	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	8	no	—
328	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
329	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
330	C₂×Q₈	#41×C₁₉	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	#41×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
356	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
367	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	8	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₄×D₄×C₁₉	1	2	yes	—
379	C₂³	C₁₉×#137	1	2	yes	—
380	C₂³	C₁₉×#137	1	2	yes	—
381	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	8	no	—
387	Q₈	—	4	2	no	—
388	Q₈	C₁₉×#117	1	4	yes	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
418	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	C₁₉×#441	1	4	yes	—
428	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
429	C₂²	C₁₉×#546	1	2	yes	—
430	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
431	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
432	C₂²	C₁₉×#577	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
443	C₄	C₁₉×#518	1	1	yes	characteristic
444	C₄	C₁₉×#551	1	2	yes	—
445	C₂	—	2	4	no	—
446	C₂	C₁₉×#2342	1	1	yes	characteristic
447	C₂	C₂×C₁₉×#441	1	1	yes	characteristic
448	C₂	C₁₉×#2949	1	1	yes	characteristic
449	C₂	C₁₉×#3316	1	2	yes	—
450	C₂	C₁₉×#3320	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×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
4. C₁₉×#1935	C₂	semidirect
5. C₁₉×#1927	C₂	semidirect
6. C₁₉×#1865	C₂	semidirect
10. C₁₉×#1763	C₂	semidirect
17. C₂×C₁₉×#103	C₄	semidirect
150. #22567	C₁₉	direct (N × H)
201. #1935	C₂×C₁₉	semidirect
202. #1927	C₂×C₁₉	semidirect
203. #1865	C₂×C₁₉	semidirect
207. #1763	C₂×C₁₉	semidirect
236. C₂×#103	C₄×C₁₉	semidirect
316. C₁₉	#22567	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#103	2
C₁₉×#2345	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#1935	2
C₁₉×#1927	2
C₁₉×#1865	2
C₁₉×#1824	2
C₁₉×#1807	2
C₁₉×#1787	2
C₁₉×#1763	2
C₁₉×#1752	2
#22567	19

Subgroups — C19×#22567 #18028526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22567 #18028526