Subgroups — C₁₉×#24490 #18030449

Order 4864.

1022 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2431	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#480	—	2	4	no	—
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×#417	—	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×#103	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×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₉×#392	—	2	1	no	—
42	C₁₉×#392	—	2	1	no	—
43	C₁₉×#391	C₂²	1	1	yes	characteristic
44	C₁₉×#390	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#387	—	2	1	no	—
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#386	—	2	1	no	—
50	C₁₉×#386	—	2	1	no	—
51	C₁₉×#380	—	2	1	no	—
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₄×C₂²⋊C₄×C₁₉	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	—	2	2	no	—
65	C₂×#41×C₁₉	—	4	1	no	—
66	C₂×#41×C₁₉	—	4	1	no	—
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	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	—	2	1	no	—
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	—	2	2	no	—
78	C₂×M₁₆×C₁₉	—	4	1	no	—
79	C₂×M₁₆×C₁₉	—	4	1	no	—
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#127	—	2	2	no	—
85	C₁₉×#127	—	4	1	no	—
86	C₁₉×#124	—	2	2	no	—
87	C₁₉×#124	—	4	1	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	complemented
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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#107	—	2	2	no	—
113	C₁₉×#107	—	2	2	no	—
114	C₁₉×C₄⋊C₈	—	4	1	no	—
115	C₁₉×C₄⋊C₈	—	4	1	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	4	1	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	4	1	no	—
126	C₁₉×#102	—	4	1	no	—
127	C₁₉×#102	—	4	1	no	—
128	C₁₉×C₂²⋊C₈	—	2	2	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	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	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	#41	1	2	yes	—
151	C₂×D₄×C₁₉	—	2	1	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	—	4	2	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	—	4	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	2	no	—
170	C₂×D₄×C₁₉	—	8	1	no	—
171	C₂×D₄×C₁₉	—	8	1	no	—
172	C₂×D₄×C₁₉	—	8	1	no	—
173	C₂×D₄×C₁₉	—	8	1	no	—
174	C₂×D₄×C₁₉	#41	1	2	yes	—
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	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	4	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	4	2	no	—
187	C₂²×C₄×C₁₉	—	4	2	no	—
188	C₂²×C₄×C₁₉	—	4	2	no	—
189	C₂²×C₄×C₁₉	—	8	1	no	—
190	C₂²×C₄×C₁₉	—	8	1	no	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	#41	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
199	M₁₆×C₁₉	—	4	4	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	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	4	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	8	1	no	—
222	C₄⋊C₄×C₁₉	—	8	1	no	—
223	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
224	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	4	1	no	—
227	C₂²⋊C₄×C₁₉	—	4	2	no	—
228	C₂²⋊C₄×C₁₉	—	4	2	no	—
229	C₂²⋊C₄×C₁₉	—	4	2	no	—
230	C₂²⋊C₄×C₁₉	—	4	2	no	—
231	C₂²⋊C₄×C₁₉	—	8	1	no	—
232	C₂²⋊C₄×C₁₉	—	8	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	—	2	1	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	—	8	1	no	—
238	C₄²×C₁₉	—	8	1	no	—
239	#24490	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	—	4	1	no	—
265	Q₈×C₁₉	—	4	1	no	—
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	D₄×C₁₉	—	8	4	no	—
277	D₄×C₁₉	—	8	4	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	2	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	2	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	2	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	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	1	no	—
298	C₂×C₄×C₁₉	—	4	8	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	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	8	4	no	—
315	C₂×C₄×C₁₉	#121	1	2	yes	—
316	C₂×C₄×C₁₉	#137	1	2	yes	—
317	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
323	C₈×C₁₉	—	4	1	no	—
324	C₈×C₁₉	—	4	1	no	—
325	C₈×C₁₉	—	4	1	no	—
326	C₈×C₁₉	—	4	1	no	—
327	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
328	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#2431	C₂×C₁₉	1	1	yes	characteristic
330	#2345	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#2068	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#2067	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1983	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
341	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
342	C₂²×C₁₉	—	2	2	no	—
343	C₂²×C₁₉	—	2	2	no	—
344	C₂²×C₁₉	—	2	2	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	2	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
361	C₂²×C₁₉	—	8	1	no	—
362	C₂²×C₁₉	—	8	1	no	—
363	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
364	C₂²×C₁₉	#546	1	1	yes	characteristic
365	C₂²×C₁₉	#546	1	1	yes	characteristic
366	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
367	C₂²×C₁₉	#575	1	1	yes	characteristic
368	C₂²×C₁₉	#576	1	1	yes	characteristic
369	C₂²×C₁₉	#576	1	1	yes	characteristic
370	C₄×C₁₉	—	2	2	no	—
371	C₄×C₁₉	—	2	2	no	—
372	C₄×C₁₉	—	4	1	no	—
373	C₄×C₁₉	—	4	2	no	—
374	C₄×C₁₉	—	4	2	no	—
375	C₄×C₁₉	—	4	2	no	—
376	C₄×C₁₉	—	4	1	no	—
377	C₄×C₁₉	—	4	1	no	—
378	C₄×C₁₉	—	8	1	no	—
379	C₄×C₁₉	—	8	1	no	—
380	C₄×C₁₉	—	8	1	no	—
381	C₄×C₁₉	#525	1	1	yes	characteristic
382	C₄×C₁₉	#535	1	1	yes	characteristic
383	C₄×C₁₉	#551	1	1	yes	characteristic
384	C₄×C₁₉	#551	1	1	yes	characteristic
385	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
386	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
391	#480	—	2	4	no	—
392	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
396	#417	—	2	4	no	—
397	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
408	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
410	#392	—	2	1	no	—
411	#392	—	2	1	no	—
412	#391	C₂²×C₁₉	1	1	yes	characteristic
413	#390	C₂²×C₁₉	1	1	yes	characteristic
414	#389	C₂²×C₁₉	1	1	yes	characteristic
415	#389	C₂²×C₁₉	1	1	yes	characteristic
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#386	—	2	1	no	—
419	#386	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	C₂²×C₁₉	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
424	C₄×C₂²⋊C₄	—	2	1	no	—
425	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
426	#340	C₂²×C₁₉	1	1	yes	characteristic
427	#340	C₂²×C₁₉	1	1	yes	characteristic
428	#336	C₂²×C₁₉	1	1	yes	characteristic
429	#336	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×C₁₉	—	4	2	no	—
431	C₂×C₁₉	—	8	2	no	—
432	C₂×C₁₉	—	16	1	no	—
433	C₂×C₁₉	#2411	1	1	yes	characteristic
434	C₂×C₁₉	#3037	1	1	yes	characteristic
435	C₂×C₁₉	#3041	1	1	yes	characteristic
436	C₂×C₁₉	#3309	1	1	yes	characteristic
437	C₂×C₁₉	#3314	1	1	yes	characteristic
438	C₂×C₁₉	#3322	1	1	yes	characteristic
439	C₂×C₁₉	#3333	1	1	yes	characteristic
440	C₂×#41	—	2	2	no	—
441	C₂×#41	—	2	2	no	—
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	4	1	no	—
445	C₂×#41	—	4	1	no	—
446	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
453	C₂³×C₄	—	2	1	no	—
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
456	C₂×M₁₆	—	2	2	no	—
457	C₂×M₁₆	—	4	1	no	—
458	C₂×M₁₆	—	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	#127	—	2	2	no	—
464	#127	—	4	1	no	—
465	#124	—	2	2	no	—
466	#124	—	4	1	no	—
467	#121	—	2	2	no	—
468	#121	—	2	2	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	complemented
474	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₁₉	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
491	#107	—	2	2	no	—
492	#107	—	2	2	no	—
493	C₄⋊C₈	—	4	1	no	—
494	C₄⋊C₈	—	4	1	no	—
495	#103	—	2	2	no	—
496	#103	—	2	2	no	—
497	#103	—	2	2	no	—
498	#103	—	4	1	no	—
499	#102	—	2	2	no	—
500	#102	—	2	2	no	—
501	#102	—	2	2	no	—
502	#102	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	4	1	no	—
505	#102	—	4	1	no	—
506	#102	—	4	1	no	—
507	C₂²⋊C₈	—	2	2	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	D₄×C₁₉	1	1	yes	characteristic
516	#95	D₄×C₁₉	1	1	yes	characteristic
517	C₁₉	#24490	1	1	yes	characteristic, direct product factor, Sylow
518	C₂⁴	—	2	1	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
521	#41	—	2	8	no	—
522	#41	—	4	4	no	—
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	#41×C₁₉	1	2	yes	—
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	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	—	4	2	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	8	1	no	—
551	C₂×D₄	—	8	1	no	—
552	C₂×D₄	—	8	1	no	—
553	C₂×D₄	—	8	1	no	—
554	C₂×D₄	#41×C₁₉	1	2	yes	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	8	1	no	—
570	C₂²×C₄	—	8	1	no	—
571	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
577	C₂²×C₄	#41×C₁₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
579	M₁₆	—	4	4	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	8	1	no	—
602	C₄⋊C₄	—	8	1	no	—
603	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
604	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	4	1	no	—
607	C₂²⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₂²⋊C₄	—	8	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	8	1	no	—
618	C₄²	—	8	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	2	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	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	C₁₉×#121	1	2	yes	—
640	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	4	8	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	8	4	no	—
655	D₄	—	8	4	no	—
656	D₄	—	8	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	8	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	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₁₉×#121	1	2	yes	—
695	C₂×C₄	C₁₉×#137	1	2	yes	—
696	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
697	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
698	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
699	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
700	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	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	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
728	C₂²	C₁₉×#546	1	1	yes	characteristic
729	C₂²	C₁₉×#546	1	1	yes	characteristic
730	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
731	C₂²	C₁₉×#575	1	1	yes	characteristic
732	C₂²	C₁₉×#576	1	1	yes	characteristic
733	C₂²	C₁₉×#576	1	1	yes	characteristic
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	8	1	no	—
743	C₄	—	8	1	no	—
744	C₄	—	8	1	no	—
745	C₄	C₁₉×#525	1	1	yes	characteristic
746	C₄	C₁₉×#535	1	1	yes	characteristic
747	C₄	C₁₉×#551	1	1	yes	characteristic
748	C₄	C₁₉×#551	1	1	yes	characteristic
749	C₂	—	4	2	no	—
750	C₂	—	8	2	no	—
751	C₂	—	16	1	no	—
752	C₂	C₁₉×#2411	1	1	yes	characteristic
753	C₂	C₁₉×#3037	1	1	yes	characteristic
754	C₂	C₁₉×#3041	1	1	yes	characteristic
755	C₂	C₁₉×#3309	1	1	yes	characteristic
756	C₂	C₁₉×#3314	1	1	yes	characteristic
757	C₂	C₁₉×#3322	1	1	yes	characteristic
758	C₂	C₁₉×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2431	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
1. C₂×C₁₉×#480	C₂	semidirect
2. C₂×C₁₉×#417	C₂	semidirect
4. C₁₉×#2345	C₂	semidirect
5. C₁₉×#2068	C₂	semidirect
6. C₁₉×#2067	C₂	semidirect
7. C₁₉×#2042	C₂	semidirect
8. C₁₉×#2041	C₂	semidirect
9. C₁₉×#1983	C₂	semidirect
10. C₁₉×#1982	C₂	semidirect
11. C₁₉×#1928	C₂	semidirect
12. C₁₉×#1925	C₂	semidirect
13. C₁₉×#1895	C₂	semidirect
14. C₁₉×#1851	C₂	semidirect
15. C₁₉×#1788	C₂	semidirect
94. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
239. #24490	C₁₉	direct (N × H)
327. C₂×#480	C₂×C₁₉	semidirect
328. C₂×#417	C₂×C₁₉	semidirect
330. #2345	C₂×C₁₉	semidirect
331. #2068	C₂×C₁₉	semidirect
332. #2067	C₂×C₁₉	semidirect
333. #2042	C₂×C₁₉	semidirect
334. #2041	C₂×C₁₉	semidirect
335. #1983	C₂×C₁₉	semidirect
336. #1982	C₂×C₁₉	semidirect
337. #1928	C₂×C₁₉	semidirect
338. #1925	C₂×C₁₉	semidirect
339. #1895	C₂×C₁₉	semidirect
340. #1851	C₂×C₁₉	semidirect
341. #1788	C₂×C₁₉	semidirect
473. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
517. C₁₉	#24490	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×#480	2
C₂×C₁₉×#417	2
C₁₉×#2431	2
C₁₉×#2345	2
C₁₉×#2068	2
C₁₉×#2067	2
C₁₉×#2042	2
C₁₉×#2041	2
C₁₉×#1983	2
C₁₉×#1982	2
C₁₉×#1928	2
C₁₉×#1925	2
C₁₉×#1895	2
C₁₉×#1851	2
C₁₉×#1788	2
#24490	19

Subgroups — C19×#24490 #18030449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24490 #18030449