Subgroups — C₁₉×#11228 #18017187

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#340	C₂	1	2	yes	maximal
4	C₂×C₁₉×#340	C₂	1	2	yes	maximal
5	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	—	2	4	no	—
13	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
14	C₁₉×#389	—	2	2	no	—
15	C₁₉×#389	C₄	1	4	yes	complemented
16	C₂×C₁₉×#95	—	2	1	no	—
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₁₉×#340	—	2	4	no	—
20	C₁₉×#340	—	2	4	no	—
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂²×C₈×C₁₉	—	2	2	no	—
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₂²×C₈×C₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	D₄	1	4	yes	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
52	C₂×C₄²×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	—	2	2	no	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	D₄	1	2	yes	—
56	C₁₉×C₄⋊C₈	—	2	8	no	—
57	C₁₉×#95	—	2	4	no	—
58	C₁₉×#95	—	4	2	no	—
59	C₁₉×#95	—	4	2	no	—
60	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	C₂×C₈×C₁₉	—	2	4	no	—
99	C₂×C₈×C₁₉	—	2	4	no	—
100	C₂×C₈×C₁₉	—	2	4	no	—
101	C₂×C₈×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	—	4	2	no	—
103	C₂×C₈×C₁₉	—	4	2	no	—
104	C₂×C₈×C₁₉	—	4	2	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	4	8	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
117	C₄²×C₁₉	—	2	4	no	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	2	2	no	—
120	#11228	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	#121	1	1	yes	characteristic
123	C₂³×C₁₉	#121	1	2	yes	—
124	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
126	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
127	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
128	C₂³×C₁₉	#135	1	2	yes	—
129	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
130	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
131	C₂³×C₁₉	#137	1	1	yes	characteristic
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	—	8	2	no	—
154	C₂×C₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	—	8	2	no	—
158	C₂×C₄×C₁₉	#103	1	4	yes	—
159	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	2	yes	—
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#123	1	2	yes	—
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#125	1	2	yes	—
173	C₂×C₄×C₁₉	#125	1	2	yes	—
174	C₂×C₄×C₁₉	#126	1	2	yes	—
175	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
177	C₈×C₁₉	—	4	4	no	—
178	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
179	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
180	C₂×#340	C₂×C₁₉	1	2	yes	—
181	C₂×#340	C₂×C₁₉	1	2	yes	—
182	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
183	C₂²×C₁₉	#380	1	1	yes	characteristic
184	C₂²×C₁₉	#386	1	1	yes	characteristic
185	C₂²×C₁₉	#391	1	1	yes	characteristic
186	C₂²×C₁₉	#396	1	2	yes	—
187	C₂²×C₁₉	#398	1	2	yes	—
188	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
189	C₂²×C₁₉	#416	1	1	yes	characteristic
190	C₂²×C₁₉	#417	1	1	yes	characteristic
191	C₂²×C₁₉	#418	1	1	yes	characteristic
192	C₂²×C₁₉	#460	1	1	yes	characteristic
193	C₂²×C₁₉	#462	1	1	yes	characteristic
194	C₂²×C₁₉	#463	1	2	yes	—
195	C₂²×C₁₉	#465	1	2	yes	—
196	C₂²×C₁₉	#467	1	2	yes	—
197	C₂²×C₁₉	#468	1	2	yes	—
198	C₂²×C₁₉	#469	1	2	yes	—
199	C₂²×C₁₉	#475	1	1	yes	characteristic
200	C₂²×C₁₉	#476	1	2	yes	—
201	C₂²×C₁₉	#477	1	1	yes	characteristic
202	C₂²×C₁₉	#477	1	2	yes	—
203	C₂²×C₁₉	#478	1	2	yes	—
204	C₂²×C₁₉	#478	1	2	yes	—
205	C₂²×C₁₉	#479	1	2	yes	—
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	8	4	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#387	1	2	yes	—
212	C₄×C₁₉	#389	1	2	yes	—
213	C₄×C₁₉	#394	1	1	yes	characteristic
214	C₄×C₁₉	#395	1	1	yes	characteristic
215	C₄×C₁₉	#398	1	1	yes	characteristic
216	C₄×C₁₉	#400	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
218	C₂²×C₄⋊C₄	—	2	1	no	—
219	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₄⋊C₈	—	2	4	no	—
224	C₂×C₄⋊C₈	—	2	2	no	—
225	#389	—	2	2	no	—
226	#389	C₄×C₁₉	1	4	yes	complemented
227	C₂×#95	—	2	1	no	—
228	C₂×#95	—	2	1	no	—
229	C₂×#95	—	2	1	no	—
230	#340	—	2	4	no	—
231	#340	—	2	4	no	—
232	C₂×C₁₉	#1441	1	1	yes	characteristic
233	C₂×C₁₉	#1803	1	1	yes	characteristic
234	C₂×C₁₉	#1804	1	1	yes	characteristic
235	C₂×C₁₉	#1892	1	1	yes	characteristic
236	C₂×C₁₉	#1895	1	1	yes	characteristic
237	C₂×C₁₉	#1987	1	1	yes	characteristic
238	C₂×C₁₉	#1989	1	1	yes	characteristic
239	C₂×C₁₉	#2065	1	2	yes	—
240	C₂×C₁₉	#2068	1	2	yes	—
241	C₂×C₁₉	#2087	1	2	yes	—
242	C₂×C₁₉	#2088	1	2	yes	—
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	D₄×C₁₉	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	4	4	no	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	Q₈×C₁₉	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
277	C₂×C₄²	D₄×C₁₉	1	2	yes	—
278	C₄⋊C₈	—	2	8	no	—
279	#95	—	2	4	no	—
280	#95	—	4	2	no	—
281	#95	—	4	2	no	—
282	C₁₉	#11228	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
309	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
310	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
317	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₉	1	2	yes	—
320	C₂²×C₄	#41×C₁₉	1	2	yes	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	C₄⋊C₄×C₁₉	1	4	yes	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
344	C₂³	C₁₉×#121	1	1	yes	characteristic
345	C₂³	C₁₉×#121	1	2	yes	—
346	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
347	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
348	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
349	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
350	C₂³	C₁₉×#135	1	2	yes	—
351	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
353	C₂³	C₁₉×#137	1	1	yes	characteristic
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	C₁₉×#103	1	4	yes	—
381	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
383	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
384	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
385	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
386	C₂×C₄	C₁₉×#121	1	2	yes	—
387	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
389	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
390	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#123	1	2	yes	—
392	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#125	1	2	yes	—
395	C₂×C₄	C₁₉×#125	1	2	yes	—
396	C₂×C₄	C₁₉×#126	1	2	yes	—
397	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
398	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
399	C₈	—	4	4	no	—
400	C₂²	C₁₉×#380	1	1	yes	characteristic
401	C₂²	C₁₉×#386	1	1	yes	characteristic
402	C₂²	C₁₉×#391	1	1	yes	characteristic
403	C₂²	C₁₉×#396	1	2	yes	—
404	C₂²	C₁₉×#398	1	2	yes	—
405	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
406	C₂²	C₁₉×#416	1	1	yes	characteristic
407	C₂²	C₁₉×#417	1	1	yes	characteristic
408	C₂²	C₁₉×#418	1	1	yes	characteristic
409	C₂²	C₁₉×#460	1	1	yes	characteristic
410	C₂²	C₁₉×#462	1	1	yes	characteristic
411	C₂²	C₁₉×#463	1	2	yes	—
412	C₂²	C₁₉×#465	1	2	yes	—
413	C₂²	C₁₉×#467	1	2	yes	—
414	C₂²	C₁₉×#468	1	2	yes	—
415	C₂²	C₁₉×#469	1	2	yes	—
416	C₂²	C₁₉×#475	1	1	yes	characteristic
417	C₂²	C₁₉×#476	1	2	yes	—
418	C₂²	C₁₉×#477	1	2	yes	—
419	C₂²	C₁₉×#477	1	1	yes	characteristic
420	C₂²	C₁₉×#478	1	2	yes	—
421	C₂²	C₁₉×#478	1	2	yes	—
422	C₂²	C₁₉×#479	1	2	yes	—
423	C₄	—	2	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	4	no	—
428	C₄	C₁₉×#387	1	2	yes	—
429	C₄	C₁₉×#389	1	2	yes	—
430	C₄	C₁₉×#394	1	1	yes	characteristic
431	C₄	C₁₉×#395	1	1	yes	characteristic
432	C₄	C₁₉×#398	1	1	yes	characteristic
433	C₄	C₁₉×#400	1	1	yes	characteristic
434	C₂	C₁₉×#1441	1	1	yes	characteristic
435	C₂	C₁₉×#1803	1	1	yes	characteristic
436	C₂	C₁₉×#1804	1	1	yes	characteristic
437	C₂	C₁₉×#1892	1	1	yes	characteristic
438	C₂	C₁₉×#1895	1	1	yes	characteristic
439	C₂	C₁₉×#1987	1	1	yes	characteristic
440	C₂	C₁₉×#1989	1	1	yes	characteristic
441	C₂	C₁₉×#2065	1	2	yes	—
442	C₂	C₁₉×#2068	1	2	yes	—
443	C₂	C₁₉×#2087	1	2	yes	—
444	C₂	C₁₉×#2088	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₉×#389	C₄	semidirect
120. #11228	C₁₉	direct (N × H)
226. #389	C₄×C₁₉	semidirect
282. C₁₉	#11228	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×C₄⋊C₈	2
C₂×C₁₉×#389	2
C₂×C₁₉×#340	2
C₁₉×C₄⋊#95	2
#11228	19

Subgroups — C19×#11228 #18017187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11228 #18017187