Subgroups — C₁₉×#11051 #18017010

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#102	C₂	1	2	yes	maximal
2	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#102	—	2	4	no	—
13	C₂×C₁₉×#102	—	2	4	no	—
14	C₂×C₁₉×#102	—	2	4	no	—
15	C₁₉×#390	—	2	2	no	—
16	C₁₉×#390	C₄	1	4	yes	complemented
17	C₁₉×#382	—	2	4	no	—
18	C₂×C₁₉×#95	—	2	2	no	—
19	C₁₉×#340	—	2	4	no	—
20	C₁₉×#336	—	2	2	no	—
21	C₂⁵×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	2	no	—
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₉	D₄	1	2	yes	—
31	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₉	—	2	2	no	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	2	no	—
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	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	D₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	1	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₉	D₄	1	2	yes	—
59	C₁₉×#102	—	2	16	no	—
60	C₁₉×#95	—	2	8	no	—
61	C₂⁴×C₁₉	—	2	2	no	—
62	C₂⁴×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	2	2	no	—
64	C₂⁴×C₁₉	—	4	1	no	—
65	C₂⁴×C₁₉	—	4	1	no	—
66	C₂⁴×C₁₉	—	4	1	no	—
67	C₂⁴×C₁₉	—	4	1	no	—
68	C₂⁴×C₁₉	—	4	4	no	—
69	C₂⁴×C₁₉	—	4	4	no	—
70	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	4	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	2	4	no	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	4	no	—
80	C₂×D₄×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	4	2	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	4	no	—
98	C₂²×C₄×C₁₉	—	4	4	no	—
99	C₂²×C₄×C₁₉	—	4	4	no	—
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	2	yes	—
111	C₂×C₈×C₁₉	—	2	4	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	4	2	no	—
116	C₂×C₈×C₁₉	—	4	2	no	—
117	C₂×C₈×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	16	no	—
125	C₄²×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	#11051	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	8	no	—
138	C₂³×C₁₉	—	4	8	no	—
139	C₂³×C₁₉	—	8	4	no	—
140	C₂³×C₁₉	—	8	4	no	—
141	C₂³×C₁₉	—	8	2	no	—
142	C₂³×C₁₉	—	8	2	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂³×C₁₉	#123	1	1	yes	characteristic
150	C₂³×C₁₉	#124	1	1	yes	characteristic
151	C₂³×C₁₉	#127	1	1	yes	characteristic
152	C₂³×C₁₉	#135	1	4	yes	—
153	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
154	D₄×C₁₉	—	2	8	no	—
155	D₄×C₁₉	—	4	4	no	—
156	D₄×C₁₉	—	4	4	no	—
157	D₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	8	no	—
167	C₂×C₄×C₁₉	—	8	4	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	8	2	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	2	yes	—
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	2	yes	—
180	C₂×C₄×C₁₉	#121	1	2	yes	—
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#123	1	2	yes	—
185	C₂×C₄×C₁₉	#123	1	2	yes	—
186	C₂×C₄×C₁₉	#124	1	2	yes	—
187	C₂×C₄×C₁₉	#126	1	2	yes	—
188	C₈×C₁₉	—	4	4	no	—
189	C₂²×#102	C₂×C₁₉	1	2	yes	—
190	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
191	C₂×#382	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂×#340	C₂×C₁₉	1	2	yes	complemented
193	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	4	8	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	—	8	4	no	—
197	C₂²×C₁₉	—	8	4	no	—
198	C₂²×C₁₉	—	8	4	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	4	no	—
202	C₂²×C₁₉	—	8	4	no	—
203	C₂²×C₁₉	#380	1	1	yes	characteristic
204	C₂²×C₁₉	#386	1	1	yes	characteristic
205	C₂²×C₁₉	#390	1	1	yes	characteristic
206	C₂²×C₁₉	#392	1	1	yes	characteristic
207	C₂²×C₁₉	#393	1	1	yes	characteristic
208	C₂²×C₁₉	#397	1	1	yes	characteristic
209	C₂²×C₁₉	#399	1	1	yes	characteristic
210	C₂²×C₁₉	#416	1	2	yes	—
211	C₂²×C₁₉	#418	1	2	yes	—
212	C₂²×C₁₉	#449	1	4	yes	—
213	C₂²×C₁₉	#463	1	4	yes	—
214	C₂²×C₁₉	#478	1	4	yes	—
215	C₂²×C₁₉	#482	1	4	yes	—
216	C₂²×C₁₉	#488	1	2	yes	—
217	C₂²×C₁₉	#490	1	2	yes	—
218	C₂²×C₁₉	#495	1	2	yes	—
219	C₂²×C₁₉	#496	1	2	yes	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	4	no	—
223	C₄×C₁₉	#385	1	2	yes	—
224	C₄×C₁₉	#388	1	2	yes	—
225	C₄×C₁₉	#394	1	2	yes	—
226	C₄×C₁₉	#396	1	2	yes	—
227	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
231	C₂²×C₂²⋊C₄	—	2	2	no	—
232	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#102	—	2	4	no	—
234	C₂×#102	—	2	4	no	—
235	C₂×#102	—	2	4	no	—
236	#390	—	2	2	no	—
237	#390	C₄×C₁₉	1	4	yes	complemented
238	#382	—	2	4	no	—
239	C₂×#95	—	2	2	no	—
240	#340	—	2	4	no	—
241	#336	—	2	2	no	—
242	C₂×C₁₉	—	8	4	no	—
243	C₂×C₁₉	#1439	1	1	yes	characteristic
244	C₂×C₁₉	#1804	1	2	yes	—
245	C₂×C₁₉	#1875	1	2	yes	—
246	C₂×C₁₉	#1958	1	1	yes	characteristic
247	C₂×C₁₉	#1961	1	1	yes	characteristic
248	C₂×C₁₉	#2012	1	2	yes	—
249	C₂×C₁₉	#2025	1	2	yes	—
250	C₂×C₁₉	#2073	1	2	yes	—
251	C₂×C₁₉	#2092	1	2	yes	—
252	C₂⁵	—	2	1	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
261	C₂²×D₄	D₄×C₁₉	1	2	yes	—
262	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	D₄×C₁₉	1	2	yes	—
266	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	D₄×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
283	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	—	4	8	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
289	C₂×C₄²	D₄×C₁₉	1	2	yes	—
290	#102	—	2	16	no	—
291	#95	—	2	8	no	—
292	C₁₉	#11051	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	4	1	no	—
297	C₂⁴	—	4	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	—	4	1	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	#41×C₁₉	1	2	yes	—
342	C₂²×C₄	#41×C₁₉	1	2	yes	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	16	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	8	4	no	—
371	C₂³	—	8	4	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	8	2	no	—
376	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
377	C₂³	C₁₉×#120	1	1	yes	characteristic
378	C₂³	C₁₉×#121	1	1	yes	characteristic
379	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂³	C₁₉×#123	1	1	yes	characteristic
381	C₂³	C₁₉×#124	1	1	yes	characteristic
382	C₂³	C₁₉×#127	1	1	yes	characteristic
383	C₂³	C₁₉×#135	1	4	yes	—
384	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
385	D₄	—	2	8	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
405	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
406	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
407	C₂×C₄	C₁₉×#120	1	2	yes	—
408	C₂×C₄	C₁₉×#121	1	2	yes	—
409	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
410	C₂×C₄	C₁₉×#121	1	2	yes	—
411	C₂×C₄	C₁₉×#121	1	2	yes	—
412	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
413	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
414	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#123	1	2	yes	—
416	C₂×C₄	C₁₉×#123	1	2	yes	—
417	C₂×C₄	C₁₉×#124	1	2	yes	—
418	C₂×C₄	C₁₉×#126	1	2	yes	—
419	C₈	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	8	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	8	4	no	—
429	C₂²	C₁₉×#380	1	1	yes	characteristic
430	C₂²	C₁₉×#386	1	1	yes	characteristic
431	C₂²	C₁₉×#390	1	1	yes	characteristic
432	C₂²	C₁₉×#392	1	1	yes	characteristic
433	C₂²	C₁₉×#393	1	1	yes	characteristic
434	C₂²	C₁₉×#397	1	1	yes	characteristic
435	C₂²	C₁₉×#399	1	1	yes	characteristic
436	C₂²	C₁₉×#416	1	2	yes	—
437	C₂²	C₁₉×#418	1	2	yes	—
438	C₂²	C₁₉×#449	1	4	yes	—
439	C₂²	C₁₉×#463	1	4	yes	—
440	C₂²	C₁₉×#478	1	4	yes	—
441	C₂²	C₁₉×#482	1	4	yes	—
442	C₂²	C₁₉×#488	1	2	yes	—
443	C₂²	C₁₉×#490	1	2	yes	—
444	C₂²	C₁₉×#495	1	2	yes	—
445	C₂²	C₁₉×#496	1	2	yes	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	4	no	—
449	C₄	C₁₉×#385	1	2	yes	—
450	C₄	C₁₉×#388	1	2	yes	—
451	C₄	C₁₉×#394	1	2	yes	—
452	C₄	C₁₉×#396	1	2	yes	—
453	C₂	—	8	4	no	—
454	C₂	C₁₉×#1439	1	1	yes	characteristic
455	C₂	C₁₉×#1804	1	2	yes	—
456	C₂	C₁₉×#1875	1	2	yes	—
457	C₂	C₁₉×#1958	1	1	yes	characteristic
458	C₂	C₁₉×#1961	1	1	yes	characteristic
459	C₂	C₁₉×#2012	1	2	yes	—
460	C₂	C₁₉×#2025	1	2	yes	—
461	C₂	C₁₉×#2073	1	2	yes	—
462	C₂	C₁₉×#2092	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	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#382	C₂	semidirect
4. C₂×C₁₉×#340	C₂	semidirect
5. C₂×C₁₉×#336	C₂	semidirect
16. C₁₉×#390	C₄	semidirect
127. #11051	C₁₉	direct (N × H)
191. C₂×#382	C₂×C₁₉	semidirect
192. C₂×#340	C₂×C₁₉	semidirect
193. C₂×#336	C₂×C₁₉	semidirect
237. #390	C₄×C₁₉	semidirect
292. C₁₉	#11051	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#382	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
#11051	19

Subgroups — C19×#11051 #18017010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11051 #18017010