Subgroups — C₁₉×#21893 #18027852

Order 4864.

1410 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×C₁₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1987	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1895	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1802	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₉	—	2	1	no	—
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#532	—	2	4	no	—
11	C₁₉×#532	C₄	1	8	yes	complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	—	2	1	no	—
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	—	2	1	no	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#423	—	2	4	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	8	yes	—
25	C₁₉×#384	C₂²	1	2	yes	—
26	C₁₉×#382	—	2	1	no	—
27	C₁₉×#380	—	2	1	no	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	8	yes	—
32	C₂×#41×C₁₉	—	2	8	no	—
33	C₂×#41×C₁₉	—	4	8	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	2	4	no	—
44	C₂×M₁₆×C₁₉	—	4	4	no	—
45	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
48	C₁₉×#127	—	2	2	no	—
49	C₁₉×#127	C₂×C₄	1	4	yes	—
50	C₁₉×#124	—	2	8	no	—
51	C₁₉×#121	—	2	8	no	—
52	C₁₉×#121	—	2	4	no	—
53	C₁₉×#121	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₁₉	—	2	8	no	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
57	C₁₉×#117	—	4	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	D₄	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊C₈	—	2	4	no	—
74	C₁₉×C₄⋊C₈	—	2	4	no	—
75	C₁₉×#102	—	4	8	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	#41×C₁₉	—	4	32	no	—
81	C₂×Q₈×C₁₉	—	2	4	no	—
82	C₂×Q₈×C₁₉	—	4	4	no	—
83	C₂×D₄×C₁₉	—	2	8	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	8	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
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	2	no	—
100	C₂²×C₄×C₁₉	—	2	8	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	4	8	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₁₉	—	4	8	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	4	4	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₁₉	—	2	8	no	—
124	C₂²⋊C₄×C₁₉	—	2	8	no	—
125	C₂²⋊C₄×C₁₉	—	4	4	no	—
126	C₄²×C₁₉	—	4	4	no	—
127	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
129	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₉	C₂×D₄	1	2	yes	—
132	C₄²×C₁₉	C₂×D₄	1	2	yes	—
133	#21893	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₉	—	4	8	no	—
146	D₄×C₁₉	—	2	8	no	—
147	D₄×C₁₉	—	4	8	no	—
148	D₄×C₁₉	—	4	16	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	8	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	16	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
174	C₂×C₄×C₁₉	#137	1	2	yes	—
175	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₁₉	—	4	4	no	—
180	C₂×#532	C₂×C₁₉	1	1	yes	characteristic
181	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1987	C₂×C₁₉	1	2	yes	complemented
184	#1982	C₂×C₁₉	1	2	yes	complemented
185	#1895	C₂×C₁₉	1	4	yes	complemented
186	#1802	C₂×C₁₉	1	4	yes	complemented
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	8	4	no	—
196	C₂²×C₁₉	—	8	4	no	—
197	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₁₉	#537	1	2	yes	—
199	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	8	4	no	—
207	C₄×C₁₉	#417	1	4	yes	—
208	C₄×C₁₉	#418	1	4	yes	—
209	C₄×C₁₉	#520	1	2	yes	—
210	C₄×C₁₉	#535	1	1	yes	characteristic
211	C₄×C₁₉	#536	1	1	yes	characteristic
212	C₂²×#41	—	2	1	no	—
213	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
214	#532	—	2	4	no	—
215	#532	C₄×C₁₉	1	8	yes	complemented
216	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₂²×C₁₉	1	2	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
223	C₂×#117	—	2	1	no	—
224	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
225	#423	—	2	4	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
228	C₂×#102	C₂²×C₁₉	1	8	yes	—
229	#384	C₂²×C₁₉	1	2	yes	—
230	#382	—	2	1	no	—
231	#380	—	2	1	no	—
232	#380	C₂²×C₁₉	1	2	yes	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	8	yes	—
236	C₂×C₁₉	—	4	2	no	—
237	C₂×C₁₉	—	8	4	no	—
238	C₂×C₁₉	#2311	1	1	yes	characteristic
239	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
240	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
241	C₂×C₁₉	#3253	1	2	yes	—
242	C₂×C₁₉	#3254	1	2	yes	—
243	C₂×#41	—	2	8	no	—
244	C₂×#41	—	4	8	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	4	4	no	—
256	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
259	#127	—	2	2	no	—
260	#127	C₂×C₄×C₁₉	1	4	yes	—
261	#124	—	2	8	no	—
262	#121	—	2	8	no	—
263	#121	—	2	4	no	—
264	#121	C₂×C₄×C₁₉	1	8	yes	—
265	C₄×D₄	—	2	8	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
268	#117	—	4	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	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	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
279	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₉	1	4	yes	—
282	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊C₈	—	2	4	no	—
285	C₄⋊C₈	—	2	4	no	—
286	#102	—	4	8	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₁₉	#21893	1	1	yes	characteristic, direct product factor, Sylow
290	C₂⁴	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	#41	—	4	32	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	4	8	no	—
315	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
316	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
325	M₁₆	—	4	8	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	8	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	4	4	no	—
339	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
340	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
341	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
342	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
343	C₄²	C₂×D₄×C₁₉	1	2	yes	—
344	C₄²	C₂×D₄×C₁₉	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
355	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
356	Q₈	—	4	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	4	8	no	—
359	D₄	—	4	16	no	—
360	D₄	—	4	8	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
384	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
385	C₂×C₄	C₁₉×#137	1	2	yes	—
386	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
389	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
390	C₈	—	4	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂²	C₁₉×#537	1	2	yes	—
403	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
405	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	4	no	—
411	C₄	C₁₉×#417	1	4	yes	—
412	C₄	C₁₉×#418	1	4	yes	—
413	C₄	C₁₉×#520	1	2	yes	—
414	C₄	C₁₉×#535	1	1	yes	characteristic
415	C₄	C₁₉×#536	1	1	yes	characteristic
416	C₂	—	4	2	no	—
417	C₂	—	8	4	no	—
418	C₂	C₁₉×#2311	1	1	yes	characteristic
419	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
420	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
421	C₂	C₁₉×#3253	1	2	yes	—
422	C₂	C₁₉×#3254	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	C₂×C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#423	C₂	semidirect
3. C₁₉×#2285	C₂	semidirect
4. C₁₉×#1987	C₂	semidirect
5. C₁₉×#1982	C₂	semidirect
6. C₁₉×#1895	C₂	semidirect
7. C₁₉×#1802	C₂	semidirect
11. C₁₉×#532	C₄	semidirect
133. #21893	C₁₉	direct (N × H)
181. C₂×#423	C₂×C₁₉	semidirect
182. #2285	C₂×C₁₉	semidirect
183. #1987	C₂×C₁₉	semidirect
184. #1982	C₂×C₁₉	semidirect
185. #1895	C₂×C₁₉	semidirect
186. #1802	C₂×C₁₉	semidirect
215. #532	C₄×C₁₉	semidirect
289. C₁₉	#21893	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×#532	2
C₂×C₁₉×#423	2
C₁₉×#2285	2
C₁₉×#1987	2
C₁₉×#1982	2
C₁₉×#1895	2
C₁₉×#1802	2
#21893	19

Subgroups — C19×#21893 #18027852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21893 #18027852