Subgroups — C₁₉×#22769 #18028728

Order 4864.

794 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2356	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1933	C₂	1	2	yes	maximal
5	C₁₉×#1918	C₂	1	2	yes	maximal
6	C₁₉×#1878	C₂	1	2	yes	maximal
7	C₁₉×#1835	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×#103	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₁₉	C₄	1	8	yes	complemented
17	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#389	—	2	2	no	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#387	—	2	2	no	—
29	C₁₉×#383	—	2	1	no	—
30	C₁₉×#382	—	2	1	no	—
31	C₁₉×#382	C₂²	1	1	yes	characteristic
32	C₁₉×#382	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#376	—	2	1	no	—
37	C₁₉×#340	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₉	—	2	2	no	—
45	C₂×Q₁₆×C₁₉	—	2	2	no	—
46	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₉	—	2	2	no	—
51	C₄×Q₈×C₁₉	—	2	2	no	—
52	C₄×Q₈×C₁₉	—	2	4	no	—
53	C₄×Q₈×C₁₉	—	4	2	no	—
54	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#107	C₂×C₄	1	4	yes	—
72	C₁₉×C₄⋊C₈	—	2	2	no	—
73	C₁₉×#103	—	2	4	no	—
74	C₁₉×#103	—	4	2	no	—
75	C₁₉×#103	C₂×C₄	1	4	yes	—
76	C₁₉×#103	C₂×C₄	1	4	yes	—
77	C₄×C₈×C₁₉	—	4	2	no	—
78	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	D₄	1	1	yes	characteristic
88	C₁₉×#95	D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₁₉	#41	1	2	yes	—
100	C₂×Q₈×C₁₉	#41	1	2	yes	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₁₉	—	2	8	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
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	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	4	4	no	—
132	C₄⋊C₄×C₁₉	—	4	4	no	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	4	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	4	4	no	—
140	C₄²×C₁₉	—	4	4	no	—
141	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₉	#41	1	2	yes	—
143	#22769	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₉	—	2	2	no	—
146	Q₈×C₁₉	—	2	2	no	—
147	Q₈×C₁₉	—	2	2	no	—
148	Q₈×C₁₉	—	2	2	no	—
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	#117	1	4	yes	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	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	2	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	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	#135	1	4	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₁₉	—	2	2	no	—
186	C₈×C₁₉	—	2	2	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
189	#2356	C₂×C₁₉	1	1	yes	characteristic
190	#2351	C₂×C₁₉	1	1	yes	characteristic
191	#1933	C₂×C₁₉	1	2	yes	—
192	#1918	C₂×C₁₉	1	2	yes	—
193	#1878	C₂×C₁₉	1	2	yes	—
194	#1835	C₂×C₁₉	1	1	yes	characteristic
195	#1805	C₂×C₁₉	1	1	yes	characteristic
196	#1805	C₂×C₁₉	1	1	yes	characteristic
197	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
198	C₄×#103	C₂×C₁₉	1	2	yes	—
199	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₁₉	#546	1	1	yes	characteristic
201	C₂²×C₁₉	#548	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#135	1	2	yes	—
203	C₂²×C₁₉	#578	1	2	yes	—
204	C₄×C₁₉	—	2	4	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
215	C₄×C₁₉	#520	1	1	yes	characteristic
216	C₄×C₁₉	#552	1	1	yes	characteristic
217	C₄×C₁₉	#553	1	1	yes	characteristic
218	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
220	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₄×Q₁₆	C₄×C₁₉	1	8	yes	complemented
223	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₉	1	2	yes	—
226	C₂×#103	C₂²×C₁₉	1	2	yes	—
227	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
231	#391	C₂²×C₁₉	1	2	yes	—
232	#389	—	2	2	no	—
233	#389	C₂²×C₁₉	1	2	yes	—
234	#387	—	2	2	no	—
235	#383	—	2	1	no	—
236	#382	—	2	1	no	—
237	#382	C₂²×C₁₉	1	1	yes	characteristic
238	#382	C₂²×C₁₉	1	1	yes	characteristic
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	#376	—	2	1	no	—
243	#340	C₂²×C₁₉	1	2	yes	—
244	#340	C₂²×C₁₉	1	2	yes	—
245	#340	C₂²×C₁₉	1	2	yes	—
246	#340	C₂²×C₁₉	1	2	yes	—
247	#336	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	#2352	1	1	yes	characteristic
249	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
250	C₂×C₁₉	#2950	1	1	yes	characteristic
251	C₂×C₁₉	#3300	1	2	yes	—
252	C₂×C₁₉	#3364	1	2	yes	—
253	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
258	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	4	2	no	—
265	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
266	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	#107	C₂×C₄×C₁₉	1	4	yes	—
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	4	no	—
285	#103	—	4	2	no	—
286	#103	C₂×C₄×C₁₉	1	4	yes	—
287	#103	C₂×C₄×C₁₉	1	4	yes	—
288	C₄×C₈	—	4	2	no	—
289	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
290	#95	—	2	1	no	—
291	#95	—	2	2	no	—
292	#95	—	2	1	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	1	no	—
297	#95	—	2	2	no	—
298	#95	D₄×C₁₉	1	1	yes	characteristic
299	#95	D₄×C₁₉	1	1	yes	characteristic
300	C₁₉	#22769	1	1	yes	characteristic, direct product factor, Sylow
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
310	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂×Q₈	#41×C₁₉	1	2	yes	—
312	C₂×Q₈	#41×C₁₉	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	Q₁₆	—	2	8	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
346	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	4	4	no	—
353	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
354	C₄²	#41×C₁₉	1	2	yes	—
355	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	Q₈	C₁₉×#117	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
389	C₂×C₄	C₁₉×#135	1	4	yes	—
390	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
400	C₂²	C₁₉×#546	1	1	yes	characteristic
401	C₂²	C₁₉×#548	1	1	yes	characteristic
402	C₂²	C₂×C₁₉×#135	1	2	yes	—
403	C₂²	C₁₉×#578	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
415	C₄	C₁₉×#520	1	1	yes	characteristic
416	C₄	C₁₉×#552	1	1	yes	characteristic
417	C₄	C₁₉×#553	1	1	yes	characteristic
418	C₂	C₁₉×#2352	1	1	yes	characteristic
419	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
420	C₂	C₁₉×#2950	1	1	yes	characteristic
421	C₂	C₁₉×#3300	1	2	yes	—
422	C₂	C₁₉×#3364	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
16. C₄×Q₁₆×C₁₉	C₄	semidirect
143. #22769	C₁₉	direct (N × H)
222. C₄×Q₁₆	C₄×C₁₉	semidirect
300. C₁₉	#22769	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×C₄×Q₁₆×C₁₉	2
C₁₉×#2356	2
C₁₉×#2351	2
C₁₉×#1933	2
C₁₉×#1918	2
C₁₉×#1878	2
C₁₉×#1835	2
C₁₉×#1805	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#103	2
#22769	19

Subgroups — C19×#22769 #18028728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22769 #18028728