Subgroups — C₁₉×#24953 #18030912

Order 4864.

800 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2485	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1809	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#397	—	2	1	no	—
30	C₁₉×#394	—	2	1	no	—
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#388	—	2	1	no	—
35	C₁₉×#387	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#385	—	2	1	no	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₁₉×#380	C₂²	1	1	yes	characteristic
42	C₁₉×#380	C₂²	1	1	yes	characteristic
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#340	C₂²	1	1	yes	characteristic
46	C₁₉×#340	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	—	4	1	no	—
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	4	4	no	—
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	—	2	2	no	—
107	C₁₉×#107	—	4	1	no	—
108	C₁₉×#107	—	4	1	no	—
109	C₁₉×#106	—	2	2	no	—
110	C₁₉×C₂²⋊C₈	—	2	2	no	—
111	C₁₉×C₂²⋊C₈	—	2	2	no	—
112	C₁₉×C₂²⋊C₈	—	4	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	4	2	no	—
145	C₂²×C₄×C₁₉	—	4	2	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	8	1	no	—
149	C₂²×C₄×C₁₉	—	8	1	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	2	yes	—
155	C₂²×C₄×C₁₉	#41	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	M₁₆×C₁₉	—	4	4	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	#41	1	2	yes	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	4	2	no	—
189	C₄⋊C₄×C₁₉	—	4	2	no	—
190	C₄⋊C₄×C₁₉	—	8	1	no	—
191	C₄⋊C₄×C₁₉	—	8	1	no	—
192	C₄⋊C₄×C₁₉	#41	1	2	yes	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	4	2	no	—
196	C₂²⋊C₄×C₁₉	—	4	2	no	—
197	C₂²⋊C₄×C₁₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	8	1	no	—
200	C₂²⋊C₄×C₁₉	—	8	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	4	2	no	—
204	C₄²×C₁₉	—	4	2	no	—
205	#24953	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	#123	1	2	yes	—
219	C₂³×C₁₉	#137	1	2	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	D₄×C₁₉	—	2	8	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	8	4	no	—
265	C₂×C₄×C₁₉	—	8	4	no	—
266	C₂×C₄×C₁₉	#123	1	2	yes	—
267	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₁₉	—	2	2	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	#2485	C₂×C₁₉	1	1	yes	characteristic
279	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
280	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#2083	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1870	C₂×C₁₉	1	1	yes	characteristic
287	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1809	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1736	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
308	C₂²×C₁₉	#546	1	1	yes	characteristic
309	C₂²×C₁₉	#547	1	1	yes	characteristic
310	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
312	C₂²×C₁₉	#576	1	1	yes	characteristic
313	C₂²×C₁₉	#578	1	1	yes	characteristic
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	2	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	—	8	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	—	8	1	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	#529	1	1	yes	characteristic
327	C₄×C₁₉	#539	1	1	yes	characteristic
328	C₄×C₁₉	#551	1	1	yes	characteristic
329	C₄×C₁₉	#552	1	1	yes	characteristic
330	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×D₄	—	2	1	no	—
332	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	#397	—	2	1	no	—
344	#394	—	2	1	no	—
345	#389	—	2	1	no	—
346	#389	C₂²×C₁₉	1	1	yes	characteristic
347	#389	C₂²×C₁₉	1	1	yes	characteristic
348	#388	—	2	1	no	—
349	#387	—	2	1	no	—
350	#385	—	2	1	no	—
351	#385	—	2	1	no	—
352	#384	C₂²×C₁₉	1	1	yes	characteristic
353	#380	C₂²×C₁₉	1	1	yes	characteristic
354	#380	C₂²×C₁₉	1	1	yes	characteristic
355	#380	C₂²×C₁₉	1	1	yes	characteristic
356	#380	C₂²×C₁₉	1	1	yes	characteristic
357	#380	C₂²×C₁₉	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
359	#340	C₂²×C₁₉	1	1	yes	characteristic
360	#340	C₂²×C₁₉	1	1	yes	characteristic
361	#340	C₂²×C₁₉	1	1	yes	characteristic
362	#340	C₂²×C₁₉	1	1	yes	characteristic
363	#340	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	1	yes	characteristic
365	#340	C₂²×C₁₉	1	1	yes	characteristic
366	#340	C₂²×C₁₉	1	1	yes	characteristic
367	#340	C₂²×C₁₉	1	1	yes	characteristic
368	#340	C₂²×C₁₉	1	1	yes	characteristic
369	#340	C₂²×C₁₉	1	1	yes	characteristic
370	#340	C₂²×C₁₉	1	1	yes	characteristic
371	#336	C₂²×C₁₉	1	1	yes	characteristic
372	#336	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₁₉	—	4	2	no	—
374	C₂×C₁₉	—	4	2	no	—
375	C₂×C₁₉	#2419	1	1	yes	characteristic
376	C₂×C₁₉	#3092	1	1	yes	characteristic
377	C₂×C₁₉	#3098	1	1	yes	characteristic
378	C₂×C₁₉	#3312	1	1	yes	characteristic
379	C₂×C₁₉	#3325	1	1	yes	characteristic
380	C₂×C₁₉	#3346	1	1	yes	characteristic
381	C₂×C₁₉	#3353	1	1	yes	characteristic
382	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	4	1	no	—
390	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	4	4	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	4	1	no	—
408	C₂×C₄⋊C₄	—	4	1	no	—
409	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
429	#107	—	2	2	no	—
430	#107	—	4	1	no	—
431	#107	—	4	1	no	—
432	#106	—	2	2	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	C₂²⋊C₈	—	2	2	no	—
435	C₂²⋊C₈	—	4	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	C₁₉	#24953	1	1	yes	characteristic, direct product factor, Sylow
445	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	8	1	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	#41×C₁₉	1	2	yes	—
479	C₂²×C₄	#41×C₁₉	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
481	M₁₆	—	4	4	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	#41×C₁₉	1	2	yes	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	8	1	no	—
515	C₄⋊C₄	—	8	1	no	—
516	C₄⋊C₄	#41×C₁₉	1	2	yes	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	8	1	no	—
524	C₂²⋊C₄	—	8	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	4	2	no	—
528	C₄²	—	4	2	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	C₁₉×#123	1	2	yes	—
542	C₂³	C₁₉×#137	1	2	yes	—
543	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	D₄	—	2	8	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	—	8	4	no	—
589	C₂×C₄	C₁₉×#123	1	2	yes	—
590	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
591	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
595	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
616	C₂²	C₁₉×#546	1	1	yes	characteristic
617	C₂²	C₁₉×#547	1	1	yes	characteristic
618	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
619	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
620	C₂²	C₁₉×#576	1	1	yes	characteristic
621	C₂²	C₁₉×#578	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	C₁₉×#529	1	1	yes	characteristic
635	C₄	C₁₉×#539	1	1	yes	characteristic
636	C₄	C₁₉×#551	1	1	yes	characteristic
637	C₄	C₁₉×#552	1	1	yes	characteristic
638	C₂	—	4	2	no	—
639	C₂	—	4	2	no	—
640	C₂	C₁₉×#2419	1	1	yes	characteristic
641	C₂	C₁₉×#3092	1	1	yes	characteristic
642	C₂	C₁₉×#3098	1	1	yes	characteristic
643	C₂	C₁₉×#3312	1	1	yes	characteristic
644	C₂	C₁₉×#3325	1	1	yes	characteristic
645	C₂	C₁₉×#3346	1	1	yes	characteristic
646	C₂	C₁₉×#3353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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
3. C₁₉×#2099	C₂	semidirect
4. C₁₉×#2083	C₂	semidirect
5. C₁₉×#2077	C₂	semidirect
6. C₁₉×#2076	C₂	semidirect
7. C₁₉×#1920	C₂	semidirect
8. C₁₉×#1918	C₂	semidirect
10. C₁₉×#1852	C₂	semidirect
11. C₁₉×#1852	C₂	semidirect
12. C₁₉×#1825	C₂	semidirect
13. C₁₉×#1824	C₂	semidirect
14. C₁₉×#1809	C₂	semidirect
15. C₁₉×#1736	C₂	semidirect
205. #24953	C₁₉	direct (N × H)
280. #2099	C₂×C₁₉	semidirect
281. #2083	C₂×C₁₉	semidirect
282. #2077	C₂×C₁₉	semidirect
283. #2076	C₂×C₁₉	semidirect
284. #1920	C₂×C₁₉	semidirect
285. #1918	C₂×C₁₉	semidirect
287. #1852	C₂×C₁₉	semidirect
288. #1852	C₂×C₁₉	semidirect
289. #1825	C₂×C₁₉	semidirect
290. #1824	C₂×C₁₉	semidirect
291. #1809	C₂×C₁₉	semidirect
292. #1736	C₂×C₁₉	semidirect
444. C₁₉	#24953	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×#2485	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2099	2
C₁₉×#2083	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#1920	2
C₁₉×#1918	2
C₁₉×#1870	2
C₁₉×#1852	2
C₁₉×#1825	2
C₁₉×#1824	2
C₁₉×#1809	2
C₁₉×#1736	2
#24953	19

Subgroups — C19×#24953 #18030912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24953 #18030912