Subgroups — C₁₉×#11095 #18017054

Order 4864.

1230 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	2	yes	maximal
4	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
12	C₂×C₁₉×#106	—	2	2	no	—
13	C₂×C₁₉×#106	—	2	4	no	—
14	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
15	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
16	C₂×C₁₉×C₂²⋊C₈	C₄	1	4	yes	complemented
17	C₁₉×#380	—	2	4	no	—
18	C₁₉×#380	—	2	4	no	—
19	C₂×C₁₉×#95	—	2	2	no	—
20	C₁₉×#340	—	2	2	no	—
21	C₁₉×#340	—	2	4	no	—
22	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂³×C₄×C₁₉	—	2	2	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	2	no	—
30	C₂³×C₄×C₁₉	—	2	2	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₉	D₄	1	2	yes	—
46	C₂²×C₈×C₁₉	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
62	C₁₉×#106	—	2	8	no	—
63	C₁₉×C₂²⋊C₈	—	2	8	no	—
64	C₁₉×#95	—	2	8	no	—
65	C₂⁴×C₁₉	—	2	2	no	—
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	—	2	1	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
73	C₂⁴×C₁₉	SD₁₆	1	4	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₉	#41	1	2	yes	—
122	C₂×C₈×C₁₉	—	2	4	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	—	4	2	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	16	no	—
141	#11095	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	4	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	4	no	—
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	#106	1	4	yes	complemented
163	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₉	#120	1	2	yes	—
165	C₂³×C₁₉	#121	1	1	yes	characteristic
166	C₂³×C₁₉	#121	1	1	yes	characteristic
167	C₂³×C₁₉	#123	1	2	yes	—
168	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
169	C₂³×C₁₉	#135	1	2	yes	—
170	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂³×C₁₉	#137	1	2	yes	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	8	2	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	—	8	2	no	—
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#121	1	2	yes	—
203	C₂×C₄×C₁₉	#121	1	2	yes	—
204	C₂×C₄×C₁₉	#121	1	2	yes	—
205	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#123	1	2	yes	—
211	C₂×C₄×C₁₉	#124	1	2	yes	—
212	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#126	1	2	yes	—
214	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
215	C₈×C₁₉	—	2	4	no	—
216	C₈×C₁₉	—	4	2	no	—
217	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
218	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
219	C₂×#380	C₂×C₁₉	1	2	yes	—
220	C₂×#340	C₂×C₁₉	1	2	yes	complemented
221	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	8	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	—	4	4	no	—
231	C₂²×C₁₉	#380	1	1	yes	characteristic
232	C₂²×C₁₉	#385	1	2	yes	—
233	C₂²×C₁₉	#392	1	1	yes	characteristic
234	C₂²×C₁₉	#394	1	2	yes	—
235	C₂²×C₁₉	#397	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
237	C₂²×C₁₉	#427	1	1	yes	characteristic
238	C₂²×C₁₉	#428	1	2	yes	—
239	C₂²×C₁₉	#448	1	2	yes	—
240	C₂²×C₁₉	#449	1	2	yes	—
241	C₂²×C₁₉	#450	1	2	yes	—
242	C₂²×C₁₉	#452	1	2	yes	—
243	C₂²×C₁₉	#465	1	2	yes	—
244	C₂²×C₁₉	#465	1	2	yes	—
245	C₂²×C₁₉	#468	1	2	yes	—
246	C₂²×C₁₉	#469	1	1	yes	characteristic
247	C₂²×C₁₉	#470	1	1	yes	characteristic
248	C₂²×C₁₉	#481	1	2	yes	—
249	C₂²×C₁₉	#482	1	2	yes	—
250	C₂²×C₁₉	#483	1	2	yes	—
251	C₂²×C₁₉	#485	1	2	yes	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	8	4	no	—
254	C₄×C₁₉	—	8	4	no	—
255	C₄×C₁₉	#386	1	1	yes	characteristic
256	C₄×C₁₉	#388	1	2	yes	—
257	C₄×C₁₉	#390	1	1	yes	characteristic
258	C₄×C₁₉	#393	1	1	yes	characteristic
259	C₄×C₁₉	#396	1	2	yes	—
260	C₄×C₁₉	#399	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
266	C₂²×C₂²⋊C₄	—	2	2	no	—
267	C₂×#106	—	2	2	no	—
268	C₂×#106	—	2	4	no	—
269	C₂×C₂²⋊C₈	—	2	2	no	—
270	C₂×C₂²⋊C₈	—	2	2	no	—
271	C₂×C₂²⋊C₈	C₄×C₁₉	1	4	yes	complemented
272	#380	—	2	4	no	—
273	#380	—	2	4	no	—
274	C₂×#95	—	2	2	no	—
275	#340	—	2	2	no	—
276	#340	—	2	4	no	—
277	C₂×C₁₉	—	4	4	no	—
278	C₂×C₁₉	#1439	1	1	yes	characteristic
279	C₂×C₁₉	#1807	1	1	yes	characteristic
280	C₂×C₁₉	#1809	1	1	yes	characteristic
281	C₂×C₁₉	#1853	1	2	yes	—
282	C₂×C₁₉	#1854	1	2	yes	—
283	C₂×C₁₉	#2000	1	2	yes	—
284	C₂×C₁₉	#2034	1	2	yes	—
285	C₂×C₁₉	#2035	1	2	yes	—
286	C₂×C₁₉	#2077	1	2	yes	—
287	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
299	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	Q₈×C₁₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
309	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
310	C₂²×C₈	D₄×C₁₉	1	2	yes	—
311	C₂²×C₈	D₄×C₁₉	1	2	yes	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
323	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
324	C₂×C₂²⋊C₄	—	2	8	no	—
325	C₂×C₂²⋊C₄	—	4	4	no	—
326	C₂×C₂²⋊C₄	—	4	4	no	—
327	#106	—	2	8	no	—
328	C₂²⋊C₈	—	2	8	no	—
329	#95	—	2	8	no	—
330	C₁₉	#11095	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	1	no	—
333	C₂⁴	—	2	1	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	2	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	—
339	C₂⁴	SD₁₆×C₁₉	1	4	yes	—
340	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
383	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	#41×C₁₉	1	2	yes	—
387	C₂²×C₄	#41×C₁₉	1	2	yes	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	16	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₁₉×#106	1	4	yes	complemented
428	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
429	C₂³	C₁₉×#120	1	2	yes	—
430	C₂³	C₁₉×#121	1	1	yes	characteristic
431	C₂³	C₁₉×#121	1	1	yes	characteristic
432	C₂³	C₁₉×#123	1	2	yes	—
433	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
434	C₂³	C₁₉×#135	1	2	yes	—
435	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
436	C₂³	C₁₉×#137	1	2	yes	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	2	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
464	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
465	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
466	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
467	C₂×C₄	C₁₉×#121	1	2	yes	—
468	C₂×C₄	C₁₉×#121	1	2	yes	—
469	C₂×C₄	C₁₉×#121	1	2	yes	—
470	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
471	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
472	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
473	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
474	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
475	C₂×C₄	C₁₉×#123	1	2	yes	—
476	C₂×C₄	C₁₉×#124	1	2	yes	—
477	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
478	C₂×C₄	C₁₉×#126	1	2	yes	—
479	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
480	C₈	—	2	4	no	—
481	C₈	—	4	2	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	8	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	C₁₉×#380	1	1	yes	characteristic
492	C₂²	C₁₉×#385	1	2	yes	—
493	C₂²	C₁₉×#392	1	1	yes	characteristic
494	C₂²	C₁₉×#394	1	2	yes	—
495	C₂²	C₁₉×#397	1	1	yes	characteristic
496	C₂²	C₂×C₁₉×#106	1	1	yes	characteristic
497	C₂²	C₁₉×#427	1	1	yes	characteristic
498	C₂²	C₁₉×#428	1	2	yes	—
499	C₂²	C₁₉×#448	1	2	yes	—
500	C₂²	C₁₉×#449	1	2	yes	—
501	C₂²	C₁₉×#450	1	2	yes	—
502	C₂²	C₁₉×#452	1	2	yes	—
503	C₂²	C₁₉×#465	1	2	yes	—
504	C₂²	C₁₉×#465	1	2	yes	—
505	C₂²	C₁₉×#468	1	2	yes	—
506	C₂²	C₁₉×#469	1	1	yes	characteristic
507	C₂²	C₁₉×#470	1	1	yes	characteristic
508	C₂²	C₁₉×#481	1	2	yes	—
509	C₂²	C₁₉×#482	1	2	yes	—
510	C₂²	C₁₉×#483	1	2	yes	—
511	C₂²	C₁₉×#485	1	2	yes	—
512	C₄	—	4	2	no	—
513	C₄	—	8	4	no	—
514	C₄	—	8	4	no	—
515	C₄	C₁₉×#386	1	1	yes	characteristic
516	C₄	C₁₉×#388	1	2	yes	—
517	C₄	C₁₉×#390	1	1	yes	characteristic
518	C₄	C₁₉×#393	1	1	yes	characteristic
519	C₄	C₁₉×#396	1	2	yes	—
520	C₄	C₁₉×#399	1	1	yes	characteristic
521	C₂	—	4	4	no	—
522	C₂	C₁₉×#1439	1	1	yes	characteristic
523	C₂	C₁₉×#1807	1	1	yes	characteristic
524	C₂	C₁₉×#1809	1	1	yes	characteristic
525	C₂	C₁₉×#1853	1	2	yes	—
526	C₂	C₁₉×#1854	1	2	yes	—
527	C₂	C₁₉×#2000	1	2	yes	—
528	C₂	C₁₉×#2034	1	2	yes	—
529	C₂	C₁₉×#2035	1	2	yes	—
530	C₂	C₁₉×#2077	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#106	C₂	semidirect
4. C₂×C₁₉×#340	C₂	semidirect
5. C₂×C₁₉×#340	C₂	semidirect
16. C₂×C₁₉×C₂²⋊C₈	C₄	semidirect
131. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
141. #11095	C₁₉	direct (N × H)
162. C₂³×C₁₉	#106	semidirect
217. C₂²×#106	C₂×C₁₉	semidirect
220. C₂×#340	C₂×C₁₉	semidirect
221. C₂×#340	C₂×C₁₉	semidirect
271. C₂×C₂²⋊C₈	C₄×C₁₉	semidirect
330. C₁₉	#11095	direct (N × H)
397. C₂×C₈	C₂²⋊C₄×C₁₉	semidirect
427. C₂³	C₁₉×#106	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#106	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#380	2
C₂×C₁₉×#340	2
#11095	19

Subgroups — C19×#11095 #18017054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11095 #18017054