Subgroups — C₁₉×#24535 #18030494

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#449	—	2	4	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×#416	—	2	4	no	—
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#394	—	2	1	no	—
38	C₁₉×#394	—	2	1	no	—
39	C₁₉×#390	—	2	1	no	—
40	C₁₉×#390	—	2	1	no	—
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#390	C₂²	1	1	yes	characteristic
44	C₁₉×#390	C₂²	1	1	yes	characteristic
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#388	—	2	1	no	—
47	C₁₉×#384	C₂²	1	1	yes	characteristic
48	C₁₉×#382	C₂²	1	1	yes	characteristic
49	C₁₉×#380	—	2	1	no	—
50	C₁₉×#380	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₁₉	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×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂×#41×C₁₉	—	2	2	no	—
62	C₂×#41×C₁₉	—	2	2	no	—
63	C₂×#41×C₁₉	—	2	2	no	—
64	C₂×#41×C₁₉	—	4	1	no	—
65	C₂×#41×C₁₉	—	4	1	no	—
66	C₂×#41×C₁₉	D₄	1	4	yes	—
67	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×SD₁₆×C₁₉	—	2	2	no	—
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	2	2	no	—
77	C₂×D₈×C₁₉	—	2	2	no	—
78	C₂×D₈×C₁₉	—	4	1	no	—
79	C₂×D₈×C₁₉	—	4	1	no	—
80	C₂²×C₈×C₁₉	—	2	2	no	—
81	C₂²×C₈×C₁₉	—	4	1	no	—
82	C₂²×C₈×C₁₉	—	4	1	no	—
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	4	1	no	—
92	C₄×Q₈×C₁₉	—	4	1	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	—	4	1	no	—
123	C₁₉×C₄⋊C₈	—	4	1	no	—
124	C₁₉×#103	—	2	2	no	—
125	C₁₉×#103	—	2	2	no	—
126	C₁₉×#103	—	2	2	no	—
127	C₁₉×#102	—	2	2	no	—
128	C₁₉×#102	—	2	2	no	—
129	C₁₉×#102	—	2	2	no	—
130	C₁₉×#102	—	4	1	no	—
131	C₁₉×#102	—	4	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	2	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	D₄	1	1	yes	characteristic
137	C₁₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₁₉	—	2	1	no	—
139	C₂⁴×C₁₉	—	2	1	no	—
140	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
141	#41×C₁₉	—	2	8	no	—
142	#41×C₁₉	—	4	4	no	—
143	#41×C₁₉	—	4	4	no	—
144	#41×C₁₉	—	4	4	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₉	#41	1	2	yes	—
150	C₂×Q₈×C₁₉	#41	1	2	yes	—
151	C₂×D₄×C₁₉	—	2	4	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	8	1	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	4	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	4	2	no	—
181	C₂²×C₄×C₁₉	—	4	2	no	—
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	#41	1	2	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
190	SD₁₆×C₁₉	—	4	4	no	—
191	D₈×C₁₉	—	4	4	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	4	4	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	4	2	no	—
216	C₄⋊C₄×C₁₉	—	4	2	no	—
217	C₄⋊C₄×C₁₉	—	8	1	no	—
218	C₄⋊C₄×C₁₉	—	8	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	2	no	—
222	C₂²⋊C₄×C₁₉	—	4	2	no	—
223	C₂²⋊C₄×C₁₉	—	4	2	no	—
224	C₂²⋊C₄×C₁₉	—	4	2	no	—
225	C₂²⋊C₄×C₁₉	—	4	2	no	—
226	C₂²⋊C₄×C₁₉	—	4	2	no	—
227	C₂²⋊C₄×C₁₉	—	8	1	no	—
228	C₂²⋊C₄×C₁₉	—	8	1	no	—
229	C₂²⋊C₄×C₁₉	—	8	1	no	—
230	C₂²⋊C₄×C₁₉	—	8	1	no	—
231	C₂²⋊C₄×C₁₉	—	8	1	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	2	1	no	—
236	C₄²×C₁₉	—	4	2	no	—
237	C₄²×C₁₉	—	4	2	no	—
238	C₄²×C₁₉	—	4	2	no	—
239	#24535	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	—	4	1	no	—
256	C₂³×C₁₉	—	4	1	no	—
257	C₂³×C₁₉	—	4	1	no	—
258	C₂³×C₁₉	—	4	1	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	#121	1	2	yes	—
261	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	Q₈×C₁₉	—	2	2	no	—
263	Q₈×C₁₉	—	2	2	no	—
264	Q₈×C₁₉	—	2	2	no	—
265	Q₈×C₁₉	#123	1	4	yes	—
266	D₄×C₁₉	—	2	2	no	—
267	D₄×C₁₉	—	2	2	no	—
268	D₄×C₁₉	—	4	8	no	—
269	D₄×C₁₉	—	4	1	no	—
270	D₄×C₁₉	—	4	1	no	—
271	D₄×C₁₉	—	4	1	no	—
272	D₄×C₁₉	—	4	1	no	—
273	D₄×C₁₉	—	4	1	no	—
274	D₄×C₁₉	—	4	1	no	—
275	D₄×C₁₉	—	8	4	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	4	8	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	#121	1	2	yes	—
313	C₂×C₄×C₁₉	#135	1	2	yes	—
314	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	C₈×C₁₉	—	4	1	no	—
323	C₈×C₁₉	—	4	1	no	—
324	C₂×#449	C₂×C₁₉	1	1	yes	characteristic
325	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#2500	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2341	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#2073	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#2054	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#2054	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	8	1	no	—
350	C₂²×C₁₉	—	8	1	no	—
351	C₂²×C₁₉	—	8	1	no	—
352	C₂²×C₁₉	—	8	1	no	—
353	C₂²×C₁₉	—	8	1	no	—
354	C₂²×C₁₉	—	8	1	no	—
355	C₂²×C₁₉	—	8	1	no	—
356	C₂²×C₁₉	—	8	1	no	—
357	C₂²×C₁₉	—	8	1	no	—
358	C₂²×C₁₉	—	8	1	no	—
359	C₂²×C₁₉	—	8	1	no	—
360	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
361	C₂²×C₁₉	#546	1	1	yes	characteristic
362	C₂²×C₁₉	#546	1	1	yes	characteristic
363	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
364	C₂²×C₁₉	#575	1	1	yes	characteristic
365	C₂²×C₁₉	#576	1	1	yes	characteristic
366	C₂²×C₁₉	#577	1	1	yes	characteristic
367	C₄×C₁₉	—	2	2	no	—
368	C₄×C₁₉	—	2	4	no	—
369	C₄×C₁₉	—	2	2	no	—
370	C₄×C₁₉	—	4	1	no	—
371	C₄×C₁₉	—	4	1	no	—
372	C₄×C₁₉	—	4	1	no	—
373	C₄×C₁₉	—	8	1	no	—
374	C₄×C₁₉	—	8	1	no	—
375	C₄×C₁₉	—	8	1	no	—
376	C₄×C₁₉	—	8	1	no	—
377	C₄×C₁₉	—	8	1	no	—
378	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
379	C₄×C₁₉	#534	1	1	yes	characteristic
380	C₄×C₁₉	#551	1	1	yes	characteristic
381	C₄×C₁₉	#551	1	1	yes	characteristic
382	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
385	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
390	#449	—	2	4	no	—
391	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
393	#416	—	2	4	no	—
394	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
403	#394	—	2	1	no	—
404	#394	—	2	1	no	—
405	#390	—	2	1	no	—
406	#390	—	2	1	no	—
407	#390	C₂²×C₁₉	1	1	yes	characteristic
408	#390	C₂²×C₁₉	1	1	yes	characteristic
409	#390	C₂²×C₁₉	1	1	yes	characteristic
410	#390	C₂²×C₁₉	1	1	yes	characteristic
411	#388	—	2	1	no	—
412	#388	—	2	1	no	—
413	#384	C₂²×C₁₉	1	1	yes	characteristic
414	#382	C₂²×C₁₉	1	1	yes	characteristic
415	#380	—	2	1	no	—
416	#380	C₂²×C₁₉	1	1	yes	characteristic
417	C₄×C₂²⋊C₄	—	2	1	no	—
418	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
419	#340	C₂²×C₁₉	1	1	yes	characteristic
420	#340	C₂²×C₁₉	1	1	yes	characteristic
421	#340	C₂²×C₁₉	1	1	yes	characteristic
422	#340	C₂²×C₁₉	1	1	yes	characteristic
423	#340	C₂²×C₁₉	1	1	yes	characteristic
424	#340	C₂²×C₁₉	1	1	yes	characteristic
425	#336	C₂²×C₁₉	1	1	yes	characteristic
426	#336	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×C₁₉	—	4	2	no	—
428	C₂×C₁₉	—	8	2	no	—
429	C₂×C₁₉	—	16	1	no	—
430	C₂×C₁₉	#2412	1	1	yes	characteristic
431	C₂×C₁₉	#3035	1	1	yes	characteristic
432	C₂×C₁₉	#3045	1	1	yes	characteristic
433	C₂×C₁₉	#3301	1	1	yes	characteristic
434	C₂×C₁₉	#3305	1	1	yes	characteristic
435	C₂×C₁₉	#3309	1	1	yes	characteristic
436	C₂×C₁₉	#3321	1	1	yes	characteristic
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	2	2	no	—
439	C₂×#41	—	2	2	no	—
440	C₂×#41	—	4	1	no	—
441	C₂×#41	—	4	1	no	—
442	C₂×#41	D₄×C₁₉	1	4	yes	—
443	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×SD₁₆	—	2	2	no	—
451	C₂×SD₁₆	—	2	2	no	—
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×D₈	—	2	2	no	—
454	C₂×D₈	—	4	1	no	—
455	C₂×D₈	—	4	1	no	—
456	C₂²×C₈	—	2	2	no	—
457	C₂²×C₈	—	4	1	no	—
458	C₂²×C₈	—	4	1	no	—
459	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	4	1	no	—
468	C₄×Q₈	—	4	1	no	—
469	#117	—	2	2	no	—
470	#117	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
498	C₄⋊C₈	—	4	1	no	—
499	C₄⋊C₈	—	4	1	no	—
500	#103	—	2	2	no	—
501	#103	—	2	2	no	—
502	#103	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	2	2	no	—
505	#102	—	2	2	no	—
506	#102	—	4	1	no	—
507	#102	—	4	1	no	—
508	C₂²⋊C₈	—	2	2	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	D₄×C₁₉	1	1	yes	characteristic
513	#95	D₄×C₁₉	1	1	yes	characteristic
514	C₁₉	#24535	1	1	yes	characteristic, direct product factor, Sylow
515	C₂⁴	—	2	1	no	—
516	C₂⁴	—	2	1	no	—
517	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
518	#41	—	2	8	no	—
519	#41	—	4	4	no	—
520	#41	—	4	4	no	—
521	#41	—	4	4	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
526	C₂×Q₈	#41×C₁₉	1	2	yes	—
527	C₂×Q₈	#41×C₁₉	1	2	yes	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	8	1	no	—
544	C₂×D₄	—	8	1	no	—
545	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	#41×C₁₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
567	SD₁₆	—	4	4	no	—
568	D₈	—	4	4	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	4	4	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	8	1	no	—
595	C₄⋊C₄	—	8	1	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	—	8	1	no	—
605	C₂²⋊C₄	—	8	1	no	—
606	C₂²⋊C₄	—	8	1	no	—
607	C₂²⋊C₄	—	8	1	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	4	2	no	—
614	C₄²	—	4	2	no	—
615	C₄²	—	4	2	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	C₁₉×#121	1	2	yes	—
637	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	C₁₉×#123	1	4	yes	—
642	D₄	—	2	2	no	—
643	D₄	—	2	2	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	8	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	4	8	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	C₁₉×#121	1	2	yes	—
689	C₂×C₄	C₁₉×#135	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
692	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
693	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
694	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
696	C₈	—	4	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
722	C₂²	C₁₉×#546	1	1	yes	characteristic
723	C₂²	C₁₉×#546	1	1	yes	characteristic
724	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
725	C₂²	C₁₉×#575	1	1	yes	characteristic
726	C₂²	C₁₉×#576	1	1	yes	characteristic
727	C₂²	C₁₉×#577	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	8	1	no	—
735	C₄	—	8	1	no	—
736	C₄	—	8	1	no	—
737	C₄	—	8	1	no	—
738	C₄	—	8	1	no	—
739	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
740	C₄	C₁₉×#534	1	1	yes	characteristic
741	C₄	C₁₉×#551	1	1	yes	characteristic
742	C₄	C₁₉×#551	1	1	yes	characteristic
743	C₂	—	4	2	no	—
744	C₂	—	8	2	no	—
745	C₂	—	16	1	no	—
746	C₂	C₁₉×#2412	1	1	yes	characteristic
747	C₂	C₁₉×#3035	1	1	yes	characteristic
748	C₂	C₁₉×#3045	1	1	yes	characteristic
749	C₂	C₁₉×#3301	1	1	yes	characteristic
750	C₂	C₁₉×#3305	1	1	yes	characteristic
751	C₂	C₁₉×#3309	1	1	yes	characteristic
752	C₂	C₁₉×#3321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#416	C₂	semidirect
3. C₁₉×#2500	C₂	semidirect
4. C₁₉×#2341	C₂	semidirect
5. C₁₉×#2073	C₂	semidirect
6. C₁₉×#2071	C₂	semidirect
7. C₁₉×#2054	C₂	semidirect
8. C₁₉×#2054	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1880	C₂	semidirect
11. C₁₉×#1880	C₂	semidirect
12. C₁₉×#1850	C₂	semidirect
13. C₁₉×#1825	C₂	semidirect
14. C₁₉×#1805	C₂	semidirect
15. C₁₉×#1803	C₂	semidirect
239. #24535	C₁₉	direct (N × H)
325. C₂×#416	C₂×C₁₉	semidirect
326. #2500	C₂×C₁₉	semidirect
327. #2341	C₂×C₁₉	semidirect
328. #2073	C₂×C₁₉	semidirect
329. #2071	C₂×C₁₉	semidirect
330. #2054	C₂×C₁₉	semidirect
331. #2054	C₂×C₁₉	semidirect
332. #1893	C₂×C₁₉	semidirect
333. #1880	C₂×C₁₉	semidirect
334. #1880	C₂×C₁₉	semidirect
335. #1850	C₂×C₁₉	semidirect
336. #1825	C₂×C₁₉	semidirect
337. #1805	C₂×C₁₉	semidirect
338. #1803	C₂×C₁₉	semidirect
514. C₁₉	#24535	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×#449	2
C₂×C₁₉×#416	2
C₁₉×#2500	2
C₁₉×#2341	2
C₁₉×#2073	2
C₁₉×#2071	2
C₁₉×#2054	2
C₁₉×#1893	2
C₁₉×#1880	2
C₁₉×#1850	2
C₁₉×#1825	2
C₁₉×#1805	2
C₁₉×#1803	2
#24535	19

Subgroups — C19×#24535 #18030494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24535 #18030494