Subgroups — C₁₉×#21897 #18027856

Order 4864.

1142 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1989	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1895	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1893	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1802	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×#540	—	2	4	no	—
13	C₁₉×#540	C₄	1	8	yes	complemented
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#123	—	2	2	no	—
17	C₂×C₁₉×#121	—	2	2	no	—
18	C₂×C₁₉×#121	C₂²	1	2	yes	—
19	C₂×C₄×D₄×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×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	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×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	4	1	no	—
45	C₂×M₁₆×C₁₉	—	4	1	no	—
46	C₂²×C₈×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	—	4	1	no	—
48	C₂²×C₈×C₁₉	—	4	1	no	—
49	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#127	C₂×C₄	1	4	yes	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	C₂×C₄	1	4	yes	—
55	C₁₉×#123	—	2	16	no	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	16	no	—
58	C₁₉×#121	C₂×C₄	1	8	yes	—
59	C₄×D₄×C₁₉	—	2	4	no	—
60	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
61	C₁₉×#117	C₂×C₄	1	4	yes	—
62	C₁₉×#117	D₄	1	4	yes	—
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	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
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×#102	—	4	2	no	—
79	C₁₉×#102	—	4	2	no	—
80	C₁₉×#102	—	4	2	no	—
81	C₁₉×#102	—	4	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₁₉	—	2	8	no	—
88	C₂×D₄×C₁₉	—	2	8	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	8	2	no	—
95	C₂×D₄×C₁₉	—	8	2	no	—
96	C₂×D₄×C₁₉	—	8	2	no	—
97	C₂×D₄×C₁₉	—	8	2	no	—
98	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	8	2	no	—
108	C₂²×C₄×C₁₉	—	8	2	no	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₁₉	—	4	4	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	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	4	4	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	8	2	no	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂²⋊C₄×C₁₉	—	2	8	no	—
133	C₂²⋊C₄×C₁₉	—	2	8	no	—
134	C₂²⋊C₄×C₁₉	—	8	2	no	—
135	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
136	C₄²×C₁₉	—	8	2	no	—
137	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
139	C₄²×C₁₉	C₂×D₄	1	2	yes	—
140	C₄²×C₁₉	C₂×D₄	1	2	yes	—
141	#21897	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	D₄×C₁₉	—	2	4	no	—
156	D₄×C₁₉	—	2	4	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	8	8	no	—
160	D₄×C₁₉	—	8	8	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	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	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	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	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	8	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₁₉	—	4	2	no	—
191	C₈×C₁₉	—	4	2	no	—
192	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
193	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#2314	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1989	C₂×C₁₉	1	2	yes	complemented
196	#1982	C₂×C₁₉	1	2	yes	complemented
197	#1895	C₂×C₁₉	1	2	yes	complemented
198	#1893	C₂×C₁₉	1	2	yes	complemented
199	#1804	C₂×C₁₉	1	2	yes	complemented
200	#1802	C₂×C₁₉	1	2	yes	complemented
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	4	4	no	—
208	C₂²×C₁₉	—	4	4	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	8	2	no	—
211	C₂²×C₁₉	—	8	2	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₁₉	#537	1	1	yes	characteristic
215	C₂²×C₁₉	#537	1	1	yes	characteristic
216	C₂²×C₁₉	#576	1	2	yes	—
217	C₂²×C₁₉	#577	1	2	yes	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	4	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	#520	1	1	yes	characteristic
225	C₄×C₁₉	#520	1	1	yes	characteristic
226	C₄×C₁₉	#535	1	1	yes	characteristic
227	C₄×C₁₉	#536	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
230	#540	—	2	4	no	—
231	#540	C₄×C₁₉	1	8	yes	complemented
232	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#123	—	2	2	no	—
235	C₂×#121	—	2	2	no	—
236	C₂×#121	C₂²×C₁₉	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
238	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
239	#424	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
242	C₂×#102	C₂²×C₁₉	1	2	yes	—
243	C₂×#102	C₂²×C₁₉	1	2	yes	—
244	C₂×#102	C₂²×C₁₉	1	2	yes	—
245	C₂×#102	C₂²×C₁₉	1	2	yes	—
246	#388	—	2	2	no	—
247	#387	—	2	2	no	—
248	#384	C₂²×C₁₉	1	1	yes	characteristic
249	#382	C₂²×C₁₉	1	1	yes	characteristic
250	#380	C₂²×C₁₉	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
252	#340	C₂²×C₁₉	1	2	yes	—
253	#340	C₂²×C₁₉	1	2	yes	—
254	#340	C₂²×C₁₉	1	2	yes	—
255	#340	C₂²×C₁₉	1	2	yes	—
256	C₂×C₁₉	—	4	2	no	—
257	C₂×C₁₉	—	8	4	no	—
258	C₂×C₁₉	#2311	1	1	yes	characteristic
259	C₂×C₁₉	#2897	1	2	yes	—
260	C₂×C₁₉	#3257	1	2	yes	—
261	C₂×C₁₉	#3259	1	1	yes	characteristic
262	C₂×C₁₉	#3260	1	1	yes	characteristic
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	4	1	no	—
270	C₂×M₁₆	—	4	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	4	1	no	—
273	C₂²×C₈	—	4	1	no	—
274	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
276	#127	—	2	2	no	—
277	#127	C₂×C₄×C₁₉	1	4	yes	—
278	#125	—	2	2	no	—
279	#125	C₂×C₄×C₁₉	1	4	yes	—
280	#123	—	2	16	no	—
281	#121	—	2	4	no	—
282	#121	—	2	16	no	—
283	#121	C₂×C₄×C₁₉	1	8	yes	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
286	#117	C₂×C₄×C₁₉	1	4	yes	—
287	#117	D₄×C₁₉	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₄⋊C₈	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	#102	—	4	2	no	—
304	#102	—	4	2	no	—
305	#102	—	4	2	no	—
306	#102	—	4	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₁₉	#21897	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	2	2	no	—
312	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	4	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
362	C₄²	—	8	2	no	—
363	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
364	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
365	C₄²	C₂×D₄×C₁₉	1	2	yes	—
366	C₄²	C₂×D₄×C₁₉	1	2	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	8	no	—
385	D₄	—	8	8	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
414	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₂²	C₁₉×#537	1	1	yes	characteristic
431	C₂²	C₁₉×#537	1	1	yes	characteristic
432	C₂²	C₁₉×#576	1	2	yes	—
433	C₂²	C₁₉×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	2	no	—
440	C₄	C₁₉×#520	1	1	yes	characteristic
441	C₄	C₁₉×#520	1	1	yes	characteristic
442	C₄	C₁₉×#535	1	1	yes	characteristic
443	C₄	C₁₉×#536	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₁₉×#2311	1	1	yes	characteristic
447	C₂	C₁₉×#2897	1	2	yes	—
448	C₂	C₁₉×#3257	1	2	yes	—
449	C₂	C₁₉×#3259	1	1	yes	characteristic
450	C₂	C₁₉×#3260	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	C₂×C₁₉×#540	C₂
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
2. C₂×C₁₉×#424	C₂	semidirect
3. C₁₉×#2314	C₂	semidirect
4. C₁₉×#1989	C₂	semidirect
5. C₁₉×#1982	C₂	semidirect
6. C₁₉×#1895	C₂	semidirect
7. C₁₉×#1893	C₂	semidirect
8. C₁₉×#1804	C₂	semidirect
9. C₁₉×#1802	C₂	semidirect
13. C₁₉×#540	C₄	semidirect
141. #21897	C₁₉	direct (N × H)
193. C₂×#424	C₂×C₁₉	semidirect
194. #2314	C₂×C₁₉	semidirect
195. #1989	C₂×C₁₉	semidirect
196. #1982	C₂×C₁₉	semidirect
197. #1895	C₂×C₁₉	semidirect
198. #1893	C₂×C₁₉	semidirect
199. #1804	C₂×C₁₉	semidirect
200. #1802	C₂×C₁₉	semidirect
231. #540	C₄×C₁₉	semidirect
310. C₁₉	#21897	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×#540	2
C₂×C₁₉×#424	2
C₁₉×#2314	2
C₁₉×#1989	2
C₁₉×#1982	2
C₁₉×#1895	2
C₁₉×#1893	2
C₁₉×#1804	2
C₁₉×#1802	2
#21897	19

Subgroups — C19×#21897 #18027856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21897 #18027856