Subgroups — C₁₉×#22113 #18028072

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#477	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1942	C₂	1	2	yes	maximal
7	C₁₉×#1933	C₂	1	2	yes	maximal
8	C₁₉×#1928	C₂	1	2	yes	maximal
9	C₁₉×#1921	C₂	1	2	yes	maximal
10	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#477	C₄	1	8	yes	complemented
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#391	C₂²	1	1	yes	characteristic
25	C₁₉×#391	C₂²	1	1	yes	characteristic
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	1	yes	characteristic
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	1	yes	characteristic
30	C₁₉×#387	—	2	1	no	—
31	C₁₉×#387	—	2	1	no	—
32	C₁₉×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#376	—	2	1	no	—
38	C₄³×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₁₉	—	2	2	no	—
51	C₄×Q₈×C₁₉	—	4	4	no	—
52	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#107	—	4	2	no	—
76	C₁₉×#107	C₂×C₄	1	8	yes	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
79	C₁₉×#103	—	4	2	no	—
80	C₁₉×#103	C₂×C₄	1	8	yes	—
81	C₄×C₈×C₁₉	—	4	2	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	4	2	no	—
98	C₂×Q₈×C₁₉	—	4	2	no	—
99	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	4	2	no	—
130	C₄⋊C₄×C₁₉	—	4	2	no	—
131	C₄⋊C₄×C₁₉	—	4	2	no	—
132	C₄⋊C₄×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
136	C₄²×C₁₉	—	2	4	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	1	no	—
140	C₄²×C₁₉	—	2	1	no	—
141	C₄²×C₁₉	—	2	1	no	—
142	C₄²×C₁₉	—	2	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	—	4	4	no	—
145	C₄²×C₁₉	—	4	2	no	—
146	C₄²×C₁₉	Q₁₆	1	4	yes	—
147	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₉	#41	1	2	yes	—
149	#22113	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	2	2	no	—
153	Q₈×C₁₉	—	4	8	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	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	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
189	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
190	C₂×C₄×C₁₉	#135	1	2	yes	—
191	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₉	—	2	4	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₂×#477	C₂×C₁₉	1	1	yes	characteristic
201	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
202	#2295	C₂×C₁₉	1	1	yes	characteristic
203	#1987	C₂×C₁₉	1	1	yes	characteristic
204	#1947	C₂×C₁₉	1	1	yes	characteristic
205	#1942	C₂×C₁₉	1	2	yes	—
206	#1933	C₂×C₁₉	1	2	yes	—
207	#1928	C₂×C₁₉	1	2	yes	—
208	#1921	C₂×C₁₉	1	2	yes	—
209	#1803	C₂×C₁₉	1	1	yes	characteristic
210	C₄×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₁₉	#536	1	1	yes	characteristic
213	C₂²×C₁₉	#537	1	1	yes	characteristic
214	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₁₉	#575	1	1	yes	characteristic
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	C₄×Q₁₆	1	4	yes	—
230	C₄×C₁₉	#519	1	1	yes	characteristic
231	C₄×C₁₉	#520	1	1	yes	characteristic
232	C₄×C₁₉	#541	1	1	yes	characteristic
233	C₄×C₁₉	#542	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄×Q₈	—	2	1	no	—
236	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	#477	C₄×C₁₉	1	8	yes	complemented
238	C₂×#107	C₂²×C₁₉	1	2	yes	—
239	C₂×#107	C₂²×C₁₉	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#103	C₂²×C₁₉	1	2	yes	—
243	C₂×#103	C₂²×C₁₉	1	2	yes	—
244	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
245	#391	—	2	1	no	—
246	#391	C₂²×C₁₉	1	1	yes	characteristic
247	#391	C₂²×C₁₉	1	1	yes	characteristic
248	#389	—	2	1	no	—
249	#389	C₂²×C₁₉	1	2	yes	—
250	#389	C₂²×C₁₉	1	1	yes	characteristic
251	#389	C₂²×C₁₉	1	1	yes	characteristic
252	#387	—	2	1	no	—
253	#387	—	2	1	no	—
254	#384	C₂²×C₁₉	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	2	1	no	—
256	C₄×C₄⋊C₄	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
259	#376	—	2	1	no	—
260	C₄³	C₂²×C₁₉	1	1	yes	characteristic
261	#340	C₂²×C₁₉	1	2	yes	—
262	#340	C₂²×C₁₉	1	2	yes	—
263	#340	C₂²×C₁₉	1	2	yes	—
264	#340	C₂²×C₁₉	1	2	yes	—
265	#336	C₂²×C₁₉	1	2	yes	—
266	C₂×C₁₉	#2323	1	1	yes	characteristic
267	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
268	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₂×C₁₉	#3230	1	1	yes	characteristic
270	C₂×C₁₉	#3233	1	1	yes	characteristic
271	C₂×C₁₉	#3247	1	1	yes	characteristic
272	C₂×C₁₉	#3249	1	1	yes	characteristic
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	4	4	no	—
281	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	#107	—	4	2	no	—
305	#107	C₂×C₄×C₁₉	1	8	yes	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
308	#103	—	4	2	no	—
309	#103	C₂×C₄×C₁₉	1	8	yes	—
310	C₄×C₈	—	4	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	C₁₉	#22113	1	1	yes	characteristic, direct product factor, Sylow
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	1	4	yes	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
365	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	4	2	no	—
376	C₄²	Q₁₆×C₁₉	1	4	yes	—
377	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
378	C₄²	#41×C₁₉	1	2	yes	—
379	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	8	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	4	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
415	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
416	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
417	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
418	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
419	C₂×C₄	C₁₉×#135	1	2	yes	—
420	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
421	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
425	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	4	2	no	—
429	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
430	C₂²	C₁₉×#536	1	1	yes	characteristic
431	C₂²	C₁₉×#537	1	1	yes	characteristic
432	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
433	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
434	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂²	C₁₉×#575	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	C₄×Q₁₆×C₁₉	1	4	yes	—
448	C₄	C₁₉×#519	1	1	yes	characteristic
449	C₄	C₁₉×#520	1	1	yes	characteristic
450	C₄	C₁₉×#541	1	1	yes	characteristic
451	C₄	C₁₉×#542	1	1	yes	characteristic
452	C₂	C₁₉×#2323	1	1	yes	characteristic
453	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
454	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂	C₁₉×#3230	1	1	yes	characteristic
456	C₂	C₁₉×#3233	1	1	yes	characteristic
457	C₂	C₁₉×#3247	1	1	yes	characteristic
458	C₂	C₁₉×#3249	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₉×#477	C₄	semidirect
149. #22113	C₁₉	direct (N × H)
237. #477	C₄×C₁₉	semidirect
320. C₁₉	#22113	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×#477	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2295	2
C₁₉×#1987	2
C₁₉×#1947	2
C₁₉×#1942	2
C₁₉×#1933	2
C₁₉×#1928	2
C₁₉×#1921	2
C₁₉×#1803	2
C₄×C₁₉×C₄⋊C₈	2
#22113	19

Subgroups — C19×#22113 #18028072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22113 #18028072