Subgroups — C₁₉×#21064 #18027023

Order 4864.

1078 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1928	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1927	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#428	—	2	4	no	—
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	C₂²	1	2	yes	—
20	C₁₉×#419	C₄	1	8	yes	complemented
21	C₂×C₁₉×#103	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	4	yes	—
23	C₂×C₁₉×#103	C₂²	1	4	yes	—
24	C₁₉×#391	—	2	2	no	—
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	2	yes	—
27	C₁₉×#381	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
30	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	4	yes	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₁₉×#117	—	2	2	no	—
54	C₁₉×#117	—	2	2	no	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	—	2	4	no	—
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#107	—	2	4	no	—
75	C₁₉×#106	—	2	4	no	—
76	C₁₉×#103	—	2	8	no	—
77	C₁₉×#103	C₂×C₄	1	16	yes	complemented
78	C₁₉×#95	—	2	4	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₁₉×#95	—	2	4	no	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	4	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	8	no	—
85	C₂×Q₈×C₁₉	—	2	8	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	4	2	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	4	no	—
93	C₂×Q₈×C₁₉	—	4	4	no	—
94	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	8	2	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	2	yes	—
112	C₂²×C₄×C₁₉	#41	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₁₉	—	2	8	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	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	—	4	4	no	—
121	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
131	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	2	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	4	2	no	—
139	C₄²×C₁₉	—	8	4	no	—
140	#21064	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	C₄×D₄	1	2	yes	—
144	C₂³×C₁₉	#121	1	2	yes	—
145	C₂³×C₁₉	#123	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	4	no	—
148	Q₈×C₁₉	—	2	4	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	8	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	8	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	#117	1	4	yes	—
170	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
171	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	#123	1	2	yes	—
174	C₂×C₄×C₁₉	#124	1	4	yes	—
175	C₂×C₄×C₁₉	#126	1	4	yes	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	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	C₈×C₁₉	—	2	4	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
185	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
186	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
187	#2310	C₂×C₁₉	1	1	yes	characteristic
188	#2274	C₂×C₁₉	1	1	yes	characteristic
189	#1928	C₂×C₁₉	1	4	yes	complemented
190	#1927	C₂×C₁₉	1	4	yes	complemented
191	#1735	C₂×C₁₉	1	1	yes	characteristic
192	#1729	C₂×C₁₉	1	1	yes	characteristic
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	#388	1	4	yes	—
198	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
200	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
201	C₂²×C₁₉	#577	1	2	yes	—
202	C₂²×C₁₉	#578	1	2	yes	—
203	C₄×C₁₉	—	4	4	no	—
204	C₄×C₁₉	—	4	4	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	4	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	#388	1	4	yes	—
210	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
211	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
213	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
214	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
221	#428	—	2	4	no	—
222	C₂×#107	C₂²×C₁₉	1	2	yes	—
223	C₂×#106	C₂²×C₁₉	1	2	yes	—
224	#419	C₄×C₁₉	1	8	yes	complemented
225	C₂×#103	—	2	4	no	—
226	C₂×#103	C₂²×C₁₉	1	4	yes	—
227	C₂×#103	C₂²×C₁₉	1	4	yes	—
228	#391	—	2	2	no	—
229	#391	C₂²×C₁₉	1	2	yes	—
230	#391	C₂²×C₁₉	1	2	yes	—
231	#381	—	2	2	no	—
232	C₄×C₄⋊C₄	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
234	C₄×C₂²⋊C₄	—	2	2	no	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	2	yes	—
237	#336	C₂²×C₁₉	1	4	yes	—
238	C₂×C₁₉	—	2	4	no	—
239	C₂×C₁₉	C₂×#388	1	1	yes	characteristic
240	C₂×C₁₉	#2947	1	2	yes	—
241	C₂×C₁₉	#3042	1	1	yes	characteristic
242	C₂×C₁₉	#3044	1	1	yes	characteristic
243	C₂×C₁₉	#3097	1	2	yes	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	2	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
251	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₁₉	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
284	#107	—	2	4	no	—
285	#106	—	2	4	no	—
286	#103	—	2	8	no	—
287	#103	C₂×C₄×C₁₉	1	16	yes	complemented
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	#95	—	2	4	no	—
291	C₁₉	#21064	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	8	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	8	2	no	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	#41×C₁₉	1	2	yes	—
321	C₂²×C₄	#41×C₁₉	1	2	yes	—
322	C₂²×C₄	#41×C₁₉	1	2	yes	—
323	C₂²×C₄	#41×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
325	M₁₆	—	2	8	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
342	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	8	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₄×D₄×C₁₉	1	2	yes	—
354	C₂³	C₁₉×#121	1	2	yes	—
355	C₂³	C₁₉×#123	1	2	yes	—
356	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	2	4	no	—
359	Q₈	—	4	8	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	C₁₉×#117	1	4	yes	—
380	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
382	C₂×C₄	C₁₉×#121	1	2	yes	—
383	C₂×C₄	C₁₉×#123	1	2	yes	—
384	C₂×C₄	C₁₉×#124	1	4	yes	—
385	C₂×C₄	C₁₉×#126	1	4	yes	—
386	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	C₁₉×#388	1	4	yes	—
399	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
400	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
401	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
402	C₂²	C₁₉×#577	1	2	yes	—
403	C₂²	C₁₉×#578	1	2	yes	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	C₁₉×#388	1	4	yes	—
411	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
412	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
413	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
414	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
415	C₂	—	2	4	no	—
416	C₂	C₂×C₁₉×#388	1	1	yes	characteristic
417	C₂	C₁₉×#2947	1	2	yes	—
418	C₂	C₁₉×#3042	1	1	yes	characteristic
419	C₂	C₁₉×#3044	1	1	yes	characteristic
420	C₂	C₁₉×#3097	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 ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1928	C₂	semidirect
7. C₁₉×#1927	C₂	semidirect
20. C₁₉×#419	C₄	semidirect
77. C₁₉×#103	C₂×C₄	semidirect
140. #21064	C₁₉	direct (N × H)
189. #1928	C₂×C₁₉	semidirect
190. #1927	C₂×C₁₉	semidirect
224. #419	C₄×C₁₉	semidirect
287. #103	C₂×C₄×C₁₉	semidirect
291. C₁₉	#21064	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×#428	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#103	2
C₁₉×#2310	2
C₁₉×#2274	2
C₁₉×#1928	2
C₁₉×#1927	2
C₁₉×#1735	2
C₁₉×#1729	2
#21064	19

Subgroups — C19×#21064 #18027023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21064 #18027023