Subgroups — C₁₉×#26198 #18032157

Order 4864.

944 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2416	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	—	2	1	no	—
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₉×#396	—	2	1	no	—
35	C₁₉×#394	—	2	1	no	—
36	C₁₉×#390	C₂²	1	1	yes	characteristic
37	C₁₉×#389	—	2	1	no	—
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#386	—	2	1	no	—
40	C₁₉×#385	—	2	1	no	—
41	C₁₉×#385	—	2	1	no	—
42	C₁₉×#384	C₂²	1	1	yes	characteristic
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₁₉×#380	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	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	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	—	2	2	no	—
69	C₂²×C₈×C₁₉	—	4	1	no	—
70	C₂²×C₈×C₁₉	—	4	1	no	—
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	4	1	no	—
79	C₁₉×#121	—	4	4	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	4	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	4	1	no	—
116	C₁₉×#102	—	2	2	no	—
117	C₁₉×#102	—	4	1	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×#102	—	4	1	no	—
120	C₁₉×C₂²⋊C₈	—	2	2	no	—
121	C₁₉×C₂²⋊C₈	—	4	1	no	—
122	C₁₉×C₂²⋊C₈	—	4	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₂⁴×C₁₉	—	2	1	no	—
129	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	2	no	—
143	C₂×D₄×C₁₉	—	4	2	no	—
144	C₂×D₄×C₁₉	—	8	1	no	—
145	C₂×D₄×C₁₉	D₈	1	4	yes	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	—	4	2	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	—	8	1	no	—
170	C₂²×C₄×C₁₉	—	8	1	no	—
171	C₂²×C₄×C₁₉	—	8	1	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	#41	1	2	yes	—
177	C₂²×C₄×C₁₉	#41	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	4	4	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	4	2	no	—
206	C₄⋊C₄×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	4	2	no	—
208	C₄⋊C₄×C₁₉	—	4	2	no	—
209	C₄⋊C₄×C₁₉	—	4	2	no	—
210	C₄⋊C₄×C₁₉	—	8	1	no	—
211	C₄⋊C₄×C₁₉	#41	1	2	yes	—
212	C₄⋊C₄×C₁₉	#41	1	2	yes	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	2	no	—
216	C₂²⋊C₄×C₁₉	—	4	2	no	—
217	C₂²⋊C₄×C₁₉	—	4	2	no	—
218	C₂²⋊C₄×C₁₉	—	4	2	no	—
219	C₂²⋊C₄×C₁₉	—	4	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	2	no	—
221	C₂²⋊C₄×C₁₉	—	8	1	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	4	2	no	—
225	#26198	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	#123	1	2	yes	—
244	C₂³×C₁₉	C₂×D₈	1	2	yes	—
245	C₂³×C₁₉	C₂×D₈	1	2	yes	—
246	C₂³×C₁₉	#137	1	2	yes	—
247	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	D₄×C₁₉	—	2	8	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	8	4	no	—
254	D₄×C₁₉	—	8	4	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	8	4	no	—
295	C₂×C₄×C₁₉	—	8	4	no	—
296	C₂×C₄×C₁₉	—	8	4	no	—
297	C₂×C₄×C₁₉	#123	1	2	yes	—
298	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
299	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
305	C₈×C₁₉	—	4	1	no	—
306	C₈×C₁₉	—	4	1	no	—
307	C₈×C₁₉	—	4	1	no	—
308	C₈×C₁₉	—	4	1	no	—
309	#2416	C₂×C₁₉	1	1	yes	characteristic
310	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#2075	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1869	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	2	2	no	—
327	C₂²×C₁₉	—	2	2	no	—
328	C₂²×C₁₉	—	2	2	no	—
329	C₂²×C₁₉	—	2	2	no	—
330	C₂²×C₁₉	—	2	2	no	—
331	C₂²×C₁₉	—	2	2	no	—
332	C₂²×C₁₉	—	2	2	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	1	no	—
336	C₂²×C₁₉	—	4	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	—	8	1	no	—
339	C₂²×C₁₉	—	8	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	#480	1	4	yes	—
345	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
346	C₂²×C₁₉	#546	1	1	yes	characteristic
347	C₂²×C₁₉	#546	1	1	yes	characteristic
348	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
349	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
350	C₂²×C₁₉	#577	1	1	yes	characteristic
351	C₂²×C₁₉	#577	1	1	yes	characteristic
352	C₄×C₁₉	—	2	2	no	—
353	C₄×C₁₉	—	2	2	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	2	no	—
357	C₄×C₁₉	—	4	2	no	—
358	C₄×C₁₉	—	8	1	no	—
359	C₄×C₁₉	—	8	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	—	8	1	no	—
363	C₄×C₁₉	#529	1	1	yes	characteristic
364	C₄×C₁₉	#538	1	1	yes	characteristic
365	C₄×C₁₉	#553	1	1	yes	characteristic
366	C₄×C₁₉	#553	1	1	yes	characteristic
367	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#121	—	2	1	no	—
369	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×C₄×D₄	—	2	1	no	—
372	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
385	#396	—	2	1	no	—
386	#394	—	2	1	no	—
387	#390	C₂²×C₁₉	1	1	yes	characteristic
388	#389	—	2	1	no	—
389	#389	C₂²×C₁₉	1	1	yes	characteristic
390	#386	—	2	1	no	—
391	#385	—	2	1	no	—
392	#385	—	2	1	no	—
393	#384	C₂²×C₁₉	1	1	yes	characteristic
394	#380	C₂²×C₁₉	1	1	yes	characteristic
395	#380	C₂²×C₁₉	1	1	yes	characteristic
396	#380	C₂²×C₁₉	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
398	#340	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#340	C₂²×C₁₉	1	1	yes	characteristic
402	#340	C₂²×C₁₉	1	1	yes	characteristic
403	#340	C₂²×C₁₉	1	1	yes	characteristic
404	#340	C₂²×C₁₉	1	1	yes	characteristic
405	#340	C₂²×C₁₉	1	1	yes	characteristic
406	#340	C₂²×C₁₉	1	1	yes	characteristic
407	#340	C₂²×C₁₉	1	1	yes	characteristic
408	#336	C₂²×C₁₉	1	1	yes	characteristic
409	#336	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×C₁₉	—	2	4	no	—
411	C₂×C₁₉	—	4	2	no	—
412	C₂×C₁₉	—	16	1	no	—
413	C₂×C₁₉	#2444	1	1	yes	characteristic
414	C₂×C₁₉	C₂×#480	1	1	yes	characteristic
415	C₂×C₁₉	#3099	1	1	yes	characteristic
416	C₂×C₁₉	#3294	1	1	yes	characteristic
417	C₂×C₁₉	#3294	1	1	yes	characteristic
418	C₂×C₁₉	#3316	1	1	yes	characteristic
419	C₂×C₁₉	#3320	1	1	yes	characteristic
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂³×C₄	—	2	1	no	—
425	C₂³×C₄	—	2	1	no	—
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	—	2	2	no	—
430	C₂²×C₈	—	4	1	no	—
431	C₂²×C₈	—	4	1	no	—
432	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	#121	—	2	2	no	—
437	#121	—	2	2	no	—
438	#121	—	2	2	no	—
439	#121	—	4	1	no	—
440	#121	—	4	4	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	4	4	no	—
444	C₂×C₄⋊C₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	4	1	no	—
454	C₂×C₄⋊C₄	—	4	1	no	—
455	C₂×C₄⋊C₄	—	4	1	no	—
456	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
475	#107	—	2	2	no	—
476	#107	—	4	1	no	—
477	#102	—	2	2	no	—
478	#102	—	4	1	no	—
479	#102	—	4	1	no	—
480	#102	—	4	1	no	—
481	C₂²⋊C₈	—	2	2	no	—
482	C₂²⋊C₈	—	4	1	no	—
483	C₂²⋊C₈	—	4	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	C₁₉	#26198	1	1	yes	characteristic, direct product factor, Sylow
490	C₂⁴	—	2	1	no	—
491	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	4	2	no	—
505	C₂×D₄	—	4	2	no	—
506	C₂×D₄	—	8	1	no	—
507	C₂×D₄	D₈×C₁₉	1	4	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²×C₄	#41×C₁₉	1	2	yes	—
539	C₂²×C₄	#41×C₁₉	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	8	1	no	—
573	C₄⋊C₄	#41×C₁₉	1	2	yes	—
574	C₄⋊C₄	#41×C₁₉	1	2	yes	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	4	2	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	C₁₉×#123	1	2	yes	—
605	C₂³	C₂×D₈×C₁₉	1	2	yes	—
606	C₂³	C₂×D₈×C₁₉	1	2	yes	—
607	C₂³	C₁₉×#137	1	2	yes	—
608	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
609	D₄	—	2	8	no	—
610	D₄	—	4	1	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	8	4	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	8	4	no	—
656	C₂×C₄	—	8	4	no	—
657	C₂×C₄	—	8	4	no	—
658	C₂×C₄	C₁₉×#123	1	2	yes	—
659	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
660	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
661	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
664	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	C₁₉×#480	1	4	yes	—
691	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
692	C₂²	C₁₉×#546	1	1	yes	characteristic
693	C₂²	C₁₉×#546	1	1	yes	characteristic
694	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
695	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
696	C₂²	C₁₉×#577	1	1	yes	characteristic
697	C₂²	C₁₉×#577	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	C₁₉×#529	1	1	yes	characteristic
710	C₄	C₁₉×#538	1	1	yes	characteristic
711	C₄	C₁₉×#553	1	1	yes	characteristic
712	C₄	C₁₉×#553	1	1	yes	characteristic
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	—	16	1	no	—
716	C₂	C₁₉×#2444	1	1	yes	characteristic
717	C₂	C₂×C₁₉×#480	1	1	yes	characteristic
718	C₂	C₁₉×#3099	1	1	yes	characteristic
719	C₂	C₁₉×#3294	1	1	yes	characteristic
720	C₂	C₁₉×#3294	1	1	yes	characteristic
721	C₂	C₁₉×#3316	1	1	yes	characteristic
722	C₂	C₁₉×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2416	C₂
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
2. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
3. C₁₉×#2099	C₂	semidirect
4. C₁₉×#2075	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1925	C₂	semidirect
8. C₁₉×#1918	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1874	C₂	semidirect
11. C₁₉×#1874	C₂	semidirect
12. C₁₉×#1869	C₂	semidirect
13. C₁₉×#1852	C₂	semidirect
14. C₁₉×#1823	C₂	semidirect
15. C₂×C₁₉×#340	C₂	semidirect
225. #26198	C₁₉	direct (N × H)
310. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
311. #2099	C₂×C₁₉	semidirect
312. #2075	C₂×C₁₉	semidirect
313. #2071	C₂×C₁₉	semidirect
314. #2033	C₂×C₁₉	semidirect
315. #1925	C₂×C₁₉	semidirect
316. #1918	C₂×C₁₉	semidirect
317. #1893	C₂×C₁₉	semidirect
318. #1874	C₂×C₁₉	semidirect
319. #1874	C₂×C₁₉	semidirect
320. #1869	C₂×C₁₉	semidirect
321. #1852	C₂×C₁₉	semidirect
322. #1823	C₂×C₁₉	semidirect
323. C₂×#340	C₂×C₁₉	semidirect
489. C₁₉	#26198	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×#2416	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2099	2
C₁₉×#2075	2
C₁₉×#2071	2
C₁₉×#2033	2
C₁₉×#1925	2
C₁₉×#1918	2
C₁₉×#1893	2
C₁₉×#1874	2
C₁₉×#1869	2
C₁₉×#1852	2
C₁₉×#1823	2
C₂×C₁₉×#340	2
#26198	19

Subgroups — C19×#26198 #18032157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26198 #18032157