Subgroups — C₁₉×#25569 #18031528

Order 4864.

1306 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2000	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1874	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#554	—	2	4	no	—
12	C₁₉×#554	—	2	4	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#127	—	2	1	no	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#121	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₁₉×#486	—	2	4	no	—
25	C₁₉×#460	—	2	4	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	4	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#392	—	2	2	no	—
33	C₁₉×#390	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#340	C₂²	1	4	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₁₉	—	2	4	no	—
47	C₂×SD₁₆×C₁₉	—	4	4	no	—
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	D₄	1	4	yes	complemented
52	C₁₉×#127	—	2	2	no	—
53	C₁₉×#127	—	2	2	no	—
54	C₁₉×#127	—	4	4	no	—
55	C₁₉×#125	—	2	8	no	—
56	C₁₉×C₂²⋊Q₈	—	2	16	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×#121	—	2	8	no	—
60	C₁₉×#121	—	4	4	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	D₄	1	4	yes	complemented
63	C₄×D₄×C₁₉	—	2	8	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	—	2	2	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#102	—	2	4	no	—
85	C₁₉×#102	—	2	8	no	—
86	C₁₉×C₂²⋊C₈	—	4	4	no	—
87	C₄×C₈×C₁₉	—	2	2	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	8	2	no	—
96	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	4	8	no	—
104	C₂×D₄×C₁₉	—	4	8	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	8	2	no	—
110	C₂×D₄×C₁₉	—	8	4	no	—
111	C₂×D₄×C₁₉	SD₁₆	1	4	yes	complemented
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	8	4	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	SD₁₆×C₁₉	—	4	8	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	8	no	—
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₁₉	#41	1	4	yes	—
143	C₂²⋊C₄×C₁₉	—	2	8	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	4	8	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	4	2	no	—
148	C₄²×C₁₉	C₂×D₄	1	2	yes	—
149	C₄²×C₁₉	C₂×D₄	1	2	yes	—
150	#25569	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
161	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₉	—	2	2	no	—
163	Q₈×C₁₉	—	2	2	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	8	4	no	—
166	D₄×C₁₉	—	2	8	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	8	4	no	—
171	D₄×C₁₉	—	8	16	no	—
172	D₄×C₁₉	—	8	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	#120	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₁₉	#137	1	2	yes	—
193	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₂×#554	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#2541	C₂×C₁₉	1	1	yes	characteristic
203	#2000	C₂×C₁₉	1	4	yes	complemented
204	#1987	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#1874	C₂×C₁₉	1	4	yes	complemented
207	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	8	no	—
210	C₂²×C₁₉	—	4	4	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	8	4	no	—
214	C₂²×C₁₉	—	8	2	no	—
215	C₂²×C₁₉	—	8	2	no	—
216	C₂²×C₁₉	—	8	2	no	—
217	C₂²×C₁₉	—	8	4	no	—
218	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
219	C₂²×C₁₉	#546	1	2	yes	—
220	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
221	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
222	C₂²×C₁₉	#576	1	2	yes	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	#448	1	4	yes	—
230	C₄×C₁₉	#532	1	1	yes	characteristic
231	C₄×C₁₉	#535	1	1	yes	characteristic
232	C₄×C₁₉	#550	1	2	yes	—
233	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
234	#554	—	2	4	no	—
235	#554	—	2	4	no	—
236	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#127	—	2	1	no	—
238	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#125	—	2	1	no	—
240	C₂×C₂²⋊Q₈	—	2	2	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
242	C₂×#121	C₂²×C₁₉	1	4	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×D₄	—	2	1	no	—
245	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
247	#486	—	2	4	no	—
248	#460	—	2	4	no	—
249	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₉	1	2	yes	—
251	C₂×#102	C₂²×C₁₉	1	4	yes	—
252	C₂×#102	C₂²×C₁₉	1	2	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
254	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
255	#392	—	2	2	no	—
256	#390	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	#340	C₂²×C₁₉	1	2	yes	—
259	#340	C₂²×C₁₉	1	4	yes	—
260	C₂×C₁₉	—	4	4	no	—
261	C₂×C₁₉	—	16	2	no	—
262	C₂×C₁₉	#2431	1	1	yes	characteristic
263	C₂×C₁₉	C₂×#448	1	1	yes	characteristic
264	C₂×C₁₉	#3008	1	1	yes	characteristic
265	C₂×C₁₉	#3295	1	2	yes	—
266	C₂×C₁₉	#3333	1	2	yes	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
276	C₂×SD₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	4	4	no	—
278	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	D₄×C₁₉	1	4	yes	complemented
282	#127	—	2	2	no	—
283	#127	—	2	2	no	—
284	#127	—	4	4	no	—
285	#125	—	2	8	no	—
286	C₂²⋊Q₈	—	2	16	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	#121	—	2	8	no	—
290	#121	—	4	4	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	D₄×C₁₉	1	4	yes	complemented
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊C₈	—	2	2	no	—
313	#103	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	8	no	—
316	C₂²⋊C₈	—	4	4	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	C₁₉	#25569	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	4	8	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	—	8	4	no	—
342	C₂×D₄	SD₁₆×C₁₉	1	4	yes	complemented
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	8	4	no	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
357	SD₁₆	—	4	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
373	C₄⋊C₄	#41×C₁₉	1	4	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	4	2	no	—
379	C₄²	C₂×D₄×C₁₉	1	2	yes	—
380	C₄²	C₂×D₄×C₁₉	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
391	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	16	no	—
402	D₄	—	8	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₁₉×#120	1	2	yes	—
420	C₂×C₄	C₁₉×#120	1	2	yes	—
421	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
422	C₂×C₄	C₁₉×#137	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
426	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	8	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	4	no	—
439	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
440	C₂²	C₁₉×#546	1	2	yes	—
441	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
443	C₂²	C₁₉×#576	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	C₁₉×#448	1	4	yes	—
451	C₄	C₁₉×#532	1	1	yes	characteristic
452	C₄	C₁₉×#535	1	1	yes	characteristic
453	C₄	C₁₉×#550	1	2	yes	—
454	C₂	—	4	4	no	—
455	C₂	—	16	2	no	—
456	C₂	C₁₉×#2431	1	1	yes	characteristic
457	C₂	C₂×C₁₉×#448	1	1	yes	characteristic
458	C₂	C₁₉×#3008	1	1	yes	characteristic
459	C₂	C₁₉×#3295	1	2	yes	—
460	C₂	C₁₉×#3333	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#554	C₂	semidirect
2. C₂×C₁₉×#486	C₂	semidirect
3. C₂×C₁₉×#460	C₂	semidirect
5. C₁₉×#2000	C₂	semidirect
6. C₁₉×#1987	C₂	semidirect
7. C₁₉×#1954	C₂	semidirect
8. C₁₉×#1874	C₂	semidirect
9. C₄×C₁₉×#103	C₂	semidirect
51. C₁₉×C₄⋊Q₈	D₄	semidirect
62. C₄×Q₈×C₁₉	D₄	semidirect
111. C₂×D₄×C₁₉	SD₁₆	semidirect
150. #25569	C₁₉	direct (N × H)
199. C₂×#554	C₂×C₁₉	semidirect
200. C₂×#486	C₂×C₁₉	semidirect
201. C₂×#460	C₂×C₁₉	semidirect
203. #2000	C₂×C₁₉	semidirect
204. #1987	C₂×C₁₉	semidirect
205. #1954	C₂×C₁₉	semidirect
206. #1874	C₂×C₁₉	semidirect
207. C₄×#103	C₂×C₁₉	semidirect
281. C₄⋊Q₈	D₄×C₁₉	semidirect
292. C₄×Q₈	D₄×C₁₉	semidirect
319. C₁₉	#25569	direct (N × H)
342. C₂×D₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#554	2
C₂×C₁₉×#486	2
C₂×C₁₉×#460	2
C₁₉×#2541	2
C₁₉×#2000	2
C₁₉×#1987	2
C₁₉×#1954	2
C₁₉×#1874	2
C₄×C₁₉×#103	2
#25569	19

Subgroups — C19×#25569 #18031528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#25569 #18031528