Subgroups — C₁₉×#10404 #18016363

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2639	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#103	—	2	1	no	—
12	C₂×C₁₉×#102	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#400	—	2	1	no	—
16	C₁₉×#397	—	2	1	no	—
17	C₁₉×#394	—	2	1	no	—
18	C₁₉×#393	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₂×C₁₉×#95	—	2	1	no	—
22	C₂×C₁₉×#95	—	2	1	no	—
23	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
25	C₁₉×#340	—	2	1	no	—
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#328	—	2	2	no	—
28	C₁₉×#327	—	2	2	no	—
29	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×C₂²⋊Q₈	—	2	1	no	—
40	C₁₉×C₂²⋊Q₈	—	2	1	no	—
41	C₁₉×C₂²⋊Q₈	—	2	1	no	—
42	C₁₉×C₂²⋊Q₈	—	2	1	no	—
43	C₁₉×#121	—	2	1	no	—
44	C₁₉×#121	—	2	1	no	—
45	C₁₉×#121	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₁₉×#103	—	4	2	no	—
60	C₁₉×#102	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₁₉×C₂²⋊C₈	—	2	1	no	—
63	C₁₉×C₂²⋊C₈	—	2	1	no	—
64	C₁₉×C₂²⋊C₈	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	C₁₉×#95	—	2	1	no	—
68	C₁₉×#95	—	2	1	no	—
69	C₁₉×#95	—	2	1	no	—
70	C₁₉×#95	—	2	1	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	4	2	no	—
73	C₁₉×#95	—	4	2	no	—
74	C₁₉×#95	D₄	1	2	yes	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
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	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	8	1	no	—
147	C₂²⋊C₄×C₁₉	—	8	1	no	—
148	C₂²⋊C₄×C₁₉	—	8	1	no	—
149	C₂²⋊C₄×C₁₉	—	8	1	no	—
150	#10404	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	—	2	1	no	—
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	#120	1	1	yes	characteristic
163	C₂³×C₁₉	#121	1	1	yes	characteristic
164	C₂³×C₁₉	#124	1	1	yes	characteristic
165	C₂³×C₁₉	#135	1	1	yes	characteristic
166	C₂³×C₁₉	#135	1	1	yes	characteristic
167	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂³×C₁₉	#137	1	1	yes	characteristic
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	8	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	1	no	—
176	D₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	8	1	no	—
209	C₂×C₄×C₁₉	—	8	1	no	—
210	C₂×C₄×C₁₉	—	8	1	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	8	1	no	—
216	C₂×C₄×C₁₉	—	8	1	no	—
217	C₂×C₄×C₁₉	—	8	1	no	—
218	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
222	C₈×C₁₉	—	8	1	no	—
223	C₈×C₁₉	—	8	1	no	—
224	#2639	C₂×C₁₉	1	1	yes	characteristic
225	#1874	C₂×C₁₉	1	1	yes	characteristic
226	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂×#327	C₂×C₁₉	1	1	yes	characteristic
229	#1442	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	—	8	1	no	—
250	C₂²×C₁₉	#394	1	1	yes	characteristic
251	C₂²×C₁₉	#449	1	1	yes	characteristic
252	C₂²×C₁₉	#452	1	1	yes	characteristic
253	C₂²×C₁₉	#454	1	1	yes	characteristic
254	C₂²×C₁₉	#455	1	1	yes	characteristic
255	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₁₉	#458	1	1	yes	characteristic
257	C₂²×C₁₉	#463	1	1	yes	characteristic
258	C₂²×C₁₉	#464	1	1	yes	characteristic
259	C₂²×C₁₉	#488	1	1	yes	characteristic
260	C₂²×C₁₉	#489	1	1	yes	characteristic
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	2	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#103	—	2	1	no	—
276	C₂×#102	—	2	1	no	—
277	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
279	#400	—	2	1	no	—
280	#397	—	2	1	no	—
281	#394	—	2	1	no	—
282	#393	—	2	1	no	—
283	#386	—	2	1	no	—
284	#386	—	2	1	no	—
285	C₂×#95	—	2	1	no	—
286	C₂×#95	—	2	1	no	—
287	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
289	#340	—	2	1	no	—
290	#340	—	2	1	no	—
291	#328	—	2	2	no	—
292	#327	—	2	2	no	—
293	C₂×C₁₉	—	2	1	no	—
294	C₂×C₁₉	—	2	1	no	—
295	C₂×C₁₉	—	2	1	no	—
296	C₂×C₁₉	—	2	1	no	—
297	C₂×C₁₉	—	16	1	no	—
298	C₂×C₁₉	#1597	1	1	yes	characteristic
299	C₂×C₁₉	#1606	1	1	yes	characteristic
300	C₂×C₁₉	#1612	1	1	yes	characteristic
301	C₂×C₁₉	#1615	1	1	yes	characteristic
302	C₂×C₁₉	#2040	1	1	yes	characteristic
303	C₂×C₁₉	#2042	1	1	yes	characteristic
304	C₂×C₁₉	#2044	1	1	yes	characteristic
305	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	4	2	no	—
327	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	#103	—	4	2	no	—
336	#102	—	4	2	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	4	2	no	—
349	#95	—	4	2	no	—
350	#95	D₄×C₁₉	1	2	yes	—
351	C₁₉	#10404	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁴	—	2	1	no	—
353	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
403	C₂×C₈	—	4	1	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₂×C₈	—	4	1	no	—
407	C₂×C₈	—	4	1	no	—
408	C₂×C₈	—	4	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	4	1	no	—
422	C₂²⋊C₄	—	4	1	no	—
423	C₂²⋊C₄	—	8	1	no	—
424	C₂²⋊C₄	—	8	1	no	—
425	C₂²⋊C₄	—	8	1	no	—
426	C₂²⋊C₄	—	8	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	C₁₉×#120	1	1	yes	characteristic
439	C₂³	C₁₉×#121	1	1	yes	characteristic
440	C₂³	C₁₉×#124	1	1	yes	characteristic
441	C₂³	C₁₉×#135	1	1	yes	characteristic
442	C₂³	C₁₉×#135	1	1	yes	characteristic
443	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₂³	C₁₉×#137	1	1	yes	characteristic
445	Q₈	—	4	2	no	—
446	Q₈	—	8	1	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	1	no	—
449	D₄	—	8	1	no	—
450	D₄	—	8	1	no	—
451	D₄	—	8	1	no	—
452	D₄	—	8	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	1	no	—
488	C₂×C₄	—	8	1	no	—
489	C₂×C₄	—	8	1	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
495	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
496	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
498	C₈	—	8	1	no	—
499	C₈	—	8	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	C₁₉×#394	1	1	yes	characteristic
520	C₂²	C₁₉×#449	1	1	yes	characteristic
521	C₂²	C₁₉×#452	1	1	yes	characteristic
522	C₂²	C₁₉×#454	1	1	yes	characteristic
523	C₂²	C₁₉×#455	1	1	yes	characteristic
524	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
525	C₂²	C₁₉×#458	1	1	yes	characteristic
526	C₂²	C₁₉×#463	1	1	yes	characteristic
527	C₂²	C₁₉×#464	1	1	yes	characteristic
528	C₂²	C₁₉×#488	1	1	yes	characteristic
529	C₂²	C₁₉×#489	1	1	yes	characteristic
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	8	2	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	2	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	2	1	no	—
545	C₂	—	16	1	no	—
546	C₂	C₁₉×#1597	1	1	yes	characteristic
547	C₂	C₁₉×#1606	1	1	yes	characteristic
548	C₂	C₁₉×#1612	1	1	yes	characteristic
549	C₂	C₁₉×#1615	1	1	yes	characteristic
550	C₂	C₁₉×#2040	1	1	yes	characteristic
551	C₂	C₁₉×#2042	1	1	yes	characteristic
552	C₂	C₁₉×#2044	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1872	C₂	semidirect
4. C₂×C₁₉×#328	C₂	semidirect
6. C₁₉×#1442	C₂	semidirect
7. C₁₉×#1280	C₂	semidirect
150. #10404	C₁₉	direct (N × H)
226. #1872	C₂×C₁₉	semidirect
227. C₂×#328	C₂×C₁₉	semidirect
229. #1442	C₂×C₁₉	semidirect
230. #1280	C₂×C₁₉	semidirect
351. C₁₉	#10404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2639	2
C₁₉×#1874	2
C₁₉×#1872	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₁₉×#1442	2
C₁₉×#1280	2
#10404	19

Subgroups — C19×#10404 #18016363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10404 #18016363