Subgroups — C₁₉×#21898 #18027857

Order 4864.

1014 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1989	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1981	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1894	C₂	1	2	yes	maximal
7	C₁₉×#1892	C₂	1	2	yes	maximal
8	C₁₉×#1805	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1803	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#541	—	2	4	no	—
13	C₁₉×#541	C₄	1	8	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#126	—	2	2	no	—
16	C₂×C₁₉×#125	—	2	2	no	—
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#424	—	2	4	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₁₉×#388	—	2	2	no	—
29	C₁₉×#387	—	2	2	no	—
30	C₁₉×#384	C₂²	1	1	yes	characteristic
31	C₁₉×#382	C₂²	1	1	yes	characteristic
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	4	1	no	—
42	C₂×M₁₆×C₁₉	—	4	1	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₂²×C₈×C₁₉	—	4	1	no	—
45	C₂²×C₈×C₁₉	—	4	1	no	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₁₉×#126	—	2	16	no	—
51	C₁₉×#125	—	2	16	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	C₂×C₄	1	4	yes	—
54	C₁₉×C₂²⋊Q₈	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
56	C₄×Q₈×C₁₉	—	2	4	no	—
57	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
58	C₁₉×#117	C₂×C₄	1	4	yes	—
59	C₁₉×#117	D₄	1	4	yes	—
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	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊C₈	—	2	4	no	—
77	C₁₉×C₄⋊C₈	—	2	4	no	—
78	C₁₉×#103	—	4	2	no	—
79	C₁₉×#103	—	4	2	no	—
80	C₁₉×#103	—	4	2	no	—
81	C₁₉×#103	—	4	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
91	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₉	—	4	4	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	4	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	8	no	—
117	C₄⋊C₄×C₁₉	—	2	8	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	8	2	no	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
125	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
126	C₂²⋊C₄×C₁₉	—	2	8	no	—
127	C₂²⋊C₄×C₁₉	—	8	2	no	—
128	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
129	C₄²×C₁₉	—	2	8	no	—
130	C₄²×C₁₉	—	8	2	no	—
131	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
132	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₉	C₂×D₄	1	2	yes	—
134	C₄²×C₁₉	C₂×D₄	1	2	yes	—
135	#21898	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₉	—	2	4	no	—
143	Q₈×C₁₉	—	2	4	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
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	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	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	2	no	—
179	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
180	C₂×#424	C₂×C₁₉	1	1	yes	characteristic
181	#2314	C₂×C₁₉	1	1	yes	characteristic
182	#1989	C₂×C₁₉	1	2	yes	complemented
183	#1981	C₂×C₁₉	1	2	yes	complemented
184	#1894	C₂×C₁₉	1	2	yes	—
185	#1892	C₂×C₁₉	1	2	yes	—
186	#1805	C₂×C₁₉	1	2	yes	complemented
187	#1803	C₂×C₁₉	1	2	yes	complemented
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₉	#537	1	1	yes	characteristic
195	C₂²×C₁₉	#537	1	1	yes	characteristic
196	C₂²×C₁₉	#577	1	2	yes	—
197	C₂²×C₁₉	#578	1	2	yes	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	—	4	4	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	#520	1	1	yes	characteristic
206	C₄×C₁₉	#520	1	1	yes	characteristic
207	C₄×C₁₉	#535	1	1	yes	characteristic
208	C₄×C₁₉	#536	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
211	#541	—	2	4	no	—
212	#541	C₄×C₁₉	1	8	yes	complemented
213	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#126	—	2	2	no	—
215	C₂×#125	—	2	2	no	—
216	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
219	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
220	#424	—	2	4	no	—
221	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
223	C₂×#103	C₂²×C₁₉	1	2	yes	—
224	C₂×#103	C₂²×C₁₉	1	2	yes	—
225	C₂×#103	C₂²×C₁₉	1	2	yes	—
226	C₂×#103	C₂²×C₁₉	1	2	yes	—
227	#388	—	2	2	no	—
228	#387	—	2	2	no	—
229	#384	C₂²×C₁₉	1	1	yes	characteristic
230	#382	C₂²×C₁₉	1	1	yes	characteristic
231	#380	C₂²×C₁₉	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
233	#340	C₂²×C₁₉	1	2	yes	—
234	#340	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	2	yes	—
237	C₂×C₁₉	—	4	2	no	—
238	C₂×C₁₉	#2311	1	1	yes	characteristic
239	C₂×C₁₉	#2898	1	2	yes	—
240	C₂×C₁₉	#3258	1	2	yes	—
241	C₂×C₁₉	#3260	1	1	yes	characteristic
242	C₂×C₁₉	#3261	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	4	1	no	—
247	C₂×M₁₆	—	4	1	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	4	1	no	—
250	C₂²×C₈	—	4	1	no	—
251	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
255	#126	—	2	16	no	—
256	#125	—	2	16	no	—
257	#125	—	2	2	no	—
258	#125	C₂×C₄×C₁₉	1	4	yes	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
263	#117	C₂×C₄×C₁₉	1	4	yes	—
264	#117	D₄×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	2	4	no	—
283	#103	—	4	2	no	—
284	#103	—	4	2	no	—
285	#103	—	4	2	no	—
286	#103	—	4	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	C₁₉	#21898	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
312	M₁₆	—	4	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	4	4	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
331	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
335	C₄²	—	2	8	no	—
336	C₄²	—	8	2	no	—
337	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
338	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
339	C₄²	C₂×D₄×C₁₉	1	2	yes	—
340	C₄²	C₂×D₄×C₁₉	1	2	yes	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
346	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
381	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂²	C₁₉×#537	1	1	yes	characteristic
391	C₂²	C₁₉×#537	1	1	yes	characteristic
392	C₂²	C₁₉×#577	1	2	yes	—
393	C₂²	C₁₉×#578	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₁₉×#520	1	1	yes	characteristic
402	C₄	C₁₉×#520	1	1	yes	characteristic
403	C₄	C₁₉×#535	1	1	yes	characteristic
404	C₄	C₁₉×#536	1	1	yes	characteristic
405	C₂	—	4	2	no	—
406	C₂	C₁₉×#2311	1	1	yes	characteristic
407	C₂	C₁₉×#2898	1	2	yes	—
408	C₂	C₁₉×#3258	1	2	yes	—
409	C₂	C₁₉×#3260	1	1	yes	characteristic
410	C₂	C₁₉×#3261	1	1	yes	characteristic

	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
4. C₁₉×#1989	C₂	semidirect
5. C₁₉×#1981	C₂	semidirect
8. C₁₉×#1805	C₂	semidirect
9. C₁₉×#1803	C₂	semidirect
13. C₁₉×#541	C₄	semidirect
135. #21898	C₁₉	direct (N × H)
182. #1989	C₂×C₁₉	semidirect
183. #1981	C₂×C₁₉	semidirect
186. #1805	C₂×C₁₉	semidirect
187. #1803	C₂×C₁₉	semidirect
212. #541	C₄×C₁₉	semidirect
290. C₁₉	#21898	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×#541	2
C₂×C₁₉×#424	2
C₁₉×#2314	2
C₁₉×#1989	2
C₁₉×#1981	2
C₁₉×#1894	2
C₁₉×#1892	2
C₁₉×#1805	2
C₁₉×#1803	2
#21898	19

Subgroups — C19×#21898 #18027857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21898 #18027857