Subgroups — C₁₉×#26189 #18032148

Order 4864.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2448	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2092	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	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	C₁₉×#464	—	2	4	no	—
24	C₁₉×#441	—	2	4	no	—
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	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×#97	C₂²	1	1	yes	characteristic
37	C₁₉×#399	—	2	1	no	—
38	C₁₉×#397	—	2	1	no	—
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#389	—	2	1	no	—
43	C₁₉×#389	—	2	1	no	—
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#388	—	2	1	no	—
48	C₁₉×#388	—	2	1	no	—
49	C₁₉×#382	—	2	1	no	—
50	C₁₉×#382	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₄×C₄⋊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×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×Q₁₆×C₁₉	—	2	2	no	—
66	C₂×Q₁₆×C₁₉	D₄	1	4	yes	—
67	C₂×SD₁₆×C₁₉	—	2	2	no	—
68	C₂×SD₁₆×C₁₉	—	2	2	no	—
69	C₂×SD₁₆×C₁₉	—	2	2	no	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	4	1	no	—
82	C₄×Q₈×C₁₉	—	4	1	no	—
83	C₄×Q₈×C₁₉	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	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	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	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×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	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₁₉×#107	—	4	1	no	—
112	C₁₉×#106	—	2	2	no	—
113	C₁₉×C₄⋊C₈	—	2	2	no	—
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#102	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	4	1	no	—
122	C₁₉×#97	—	2	2	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	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	D₄	1	1	yes	characteristic
131	C₁₉×#95	D₄	1	1	yes	characteristic
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₁₉	#41	1	2	yes	—
144	C₂×Q₈×C₁₉	#41	1	2	yes	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×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	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₁₉	—	2	8	no	—
166	SD₁₆×C₁₉	—	4	4	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₁₉	—	2	4	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	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	2	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	8	1	no	—
197	C₄⋊C₄×C₁₉	#41	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	4	2	no	—
200	C₂²⋊C₄×C₁₉	—	4	2	no	—
201	C₂²⋊C₄×C₁₉	—	4	2	no	—
202	C₂²⋊C₄×C₁₉	—	8	1	no	—
203	C₂²⋊C₄×C₁₉	—	8	1	no	—
204	C₄²×C₁₉	—	2	4	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	4	2	no	—
212	C₄²×C₁₉	—	4	2	no	—
213	C₄²×C₁₉	—	4	2	no	—
214	#26189	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	4	1	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	2	2	no	—
225	Q₈×C₁₉	—	2	2	no	—
226	Q₈×C₁₉	—	2	2	no	—
227	Q₈×C₁₉	—	2	2	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	#123	1	4	yes	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	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	—	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	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	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	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
280	C₈×C₁₉	—	2	2	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₂×#464	C₂×C₁₉	1	1	yes	characteristic
285	C₂×#441	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#2448	C₂×C₁₉	1	1	yes	characteristic
287	#2351	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#2092	C₂×C₁₉	1	1	yes	characteristic
289	#2088	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#2074	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#2042	C₂×C₁₉	1	1	yes	characteristic
292	#1936	C₂×C₁₉	1	1	yes	characteristic
293	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1880	C₂×C₁₉	1	1	yes	characteristic
295	#1880	C₂×C₁₉	1	1	yes	characteristic
296	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	#525	1	1	yes	characteristic
307	C₂²×C₁₉	D₄²	1	1	yes	characteristic
308	C₂²×C₁₉	#548	1	1	yes	characteristic
309	C₂²×C₁₉	#575	1	1	yes	characteristic
310	C₂²×C₁₉	#575	1	1	yes	characteristic
311	C₂²×C₁₉	#577	1	1	yes	characteristic
312	C₂²×C₁₉	#578	1	1	yes	characteristic
313	C₄×C₁₉	—	2	4	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	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	C₂×#123	1	1	yes	characteristic
327	C₄×C₁₉	#539	1	1	yes	characteristic
328	C₄×C₁₉	#547	1	1	yes	characteristic
329	C₄×C₁₉	#553	1	1	yes	characteristic
330	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
331	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	#464	—	2	4	no	—
338	#441	—	2	4	no	—
339	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
351	#399	—	2	1	no	—
352	#397	—	2	1	no	—
353	#391	C₂²×C₁₉	1	1	yes	characteristic
354	#390	C₂²×C₁₉	1	1	yes	characteristic
355	#390	C₂²×C₁₉	1	1	yes	characteristic
356	#389	—	2	1	no	—
357	#389	—	2	1	no	—
358	#389	C₂²×C₁₉	1	1	yes	characteristic
359	#389	C₂²×C₁₉	1	1	yes	characteristic
360	#389	C₂²×C₁₉	1	1	yes	characteristic
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#382	—	2	1	no	—
364	#382	C₂²×C₁₉	1	1	yes	characteristic
365	C₄×C₄⋊C₄	—	2	1	no	—
366	C₄×C₄⋊C₄	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	#336	C₂²×C₁₉	1	1	yes	characteristic
374	#336	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×C₁₉	—	16	1	no	—
376	C₂×C₁₉	#2443	1	1	yes	characteristic
377	C₂×C₁₉	#3111	1	1	yes	characteristic
378	C₂×C₁₉	#3121	1	1	yes	characteristic
379	C₂×C₁₉	#3271	1	1	yes	characteristic
380	C₂×C₁₉	#3277	1	1	yes	characteristic
381	C₂×C₁₉	#3371	1	1	yes	characteristic
382	C₂×C₁₉	#3377	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×Q₁₆	—	2	2	no	—
388	C₂×Q₁₆	D₄×C₁₉	1	4	yes	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	2	no	—
392	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
396	#124	—	2	2	no	—
397	#124	—	4	1	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	4	1	no	—
404	C₄×Q₈	—	4	1	no	—
405	C₄×Q₈	—	4	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	—	4	1	no	—
434	#106	—	2	2	no	—
435	C₄⋊C₈	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	4	1	no	—
444	#97	—	2	2	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	D₄×C₁₉	1	1	yes	characteristic
453	#95	D₄×C₁₉	1	1	yes	characteristic
454	C₁₉	#26189	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁴	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
465	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
466	C₂×Q₈	#41×C₁₉	1	2	yes	—
467	C₂×Q₈	#41×C₁₉	1	2	yes	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
488	Q₁₆	—	2	8	no	—
489	SD₁₆	—	4	4	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
502	C₄⋊C₄	—	2	4	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	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	8	1	no	—
520	C₄⋊C₄	#41×C₁₉	1	2	yes	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	8	1	no	—
526	C₂²⋊C₄	—	8	1	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	4	2	no	—
536	C₄²	—	4	2	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	C₁₉×#123	1	4	yes	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	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	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
600	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₁₉×#525	1	1	yes	characteristic
614	C₂²	D₄²×C₁₉	1	1	yes	characteristic
615	C₂²	C₁₉×#548	1	1	yes	characteristic
616	C₂²	C₁₉×#575	1	1	yes	characteristic
617	C₂²	C₁₉×#575	1	1	yes	characteristic
618	C₂²	C₁₉×#577	1	1	yes	characteristic
619	C₂²	C₁₉×#578	1	1	yes	characteristic
620	C₄	—	2	4	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
634	C₄	C₁₉×#539	1	1	yes	characteristic
635	C₄	C₁₉×#547	1	1	yes	characteristic
636	C₄	C₁₉×#553	1	1	yes	characteristic
637	C₂	—	16	1	no	—
638	C₂	C₁₉×#2443	1	1	yes	characteristic
639	C₂	C₁₉×#3111	1	1	yes	characteristic
640	C₂	C₁₉×#3121	1	1	yes	characteristic
641	C₂	C₁₉×#3271	1	1	yes	characteristic
642	C₂	C₁₉×#3277	1	1	yes	characteristic
643	C₂	C₁₉×#3371	1	1	yes	characteristic
644	C₂	C₁₉×#3377	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#441	C₂	semidirect
4. C₁₉×#2351	C₂	semidirect
6. C₁₉×#2088	C₂	semidirect
7. C₁₉×#2074	C₂	semidirect
10. C₁₉×#1917	C₂	semidirect
13. C₁₉×#1878	C₂	semidirect
14. C₁₉×#1863	C₂	semidirect
15. C₁₉×#1863	C₂	semidirect
214. #26189	C₁₉	direct (N × H)
285. C₂×#441	C₂×C₁₉	semidirect
287. #2351	C₂×C₁₉	semidirect
289. #2088	C₂×C₁₉	semidirect
290. #2074	C₂×C₁₉	semidirect
293. #1917	C₂×C₁₉	semidirect
296. #1878	C₂×C₁₉	semidirect
297. #1863	C₂×C₁₉	semidirect
298. #1863	C₂×C₁₉	semidirect
454. C₁₉	#26189	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×#464	2
C₂×C₁₉×#441	2
C₁₉×#2448	2
C₁₉×#2351	2
C₁₉×#2092	2
C₁₉×#2088	2
C₁₉×#2074	2
C₁₉×#2042	2
C₁₉×#1936	2
C₁₉×#1917	2
C₁₉×#1880	2
C₁₉×#1878	2
C₁₉×#1863	2
#26189	19

Subgroups — C19×#26189 #18032148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26189 #18032148