Subgroups — C₁₉×#29424 #18035383

Order 4864.

780 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2324	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	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	C₁₉×#391	C₂²	1	1	yes	characteristic
34	C₁₉×#390	—	2	1	no	—
35	C₁₉×#390	C₂²	1	1	yes	characteristic
36	C₁₉×#389	—	2	1	no	—
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#388	—	2	1	no	—
40	C₁₉×#388	—	2	1	no	—
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#386	—	2	1	no	—
44	C₁₉×#385	—	2	1	no	—
45	C₁₉×#380	C₂²	1	1	yes	characteristic
46	C₁₉×#380	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	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×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	—	2	1	no	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂×SD₁₆×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	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×D₄×C₁₉	—	4	1	no	—
78	C₄×D₄×C₁₉	—	4	1	no	—
79	C₁₉×#117	—	4	1	no	—
80	C₁₉×#117	—	4	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	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#106	—	2	2	no	—
108	C₁₉×#106	—	2	2	no	—
109	C₁₉×#106	—	4	1	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#103	—	4	1	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	4	1	no	—
116	C₁₉×C₂²⋊C₈	—	4	1	no	—
117	C₁₉×C₂²⋊C₈	—	4	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	#41	1	2	yes	—
134	C₂×D₄×C₁₉	—	2	4	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	—	2	1	no	—
140	C₂×D₄×C₁₉	—	8	1	no	—
141	C₂×D₄×C₁₉	—	8	1	no	—
142	C₂×D₄×C₁₉	#41	1	2	yes	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	8	1	no	—
158	C₂²×C₄×C₁₉	—	8	1	no	—
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	SD₁₆×C₁₉	—	4	4	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	—	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	C₄⋊C₄×C₁₉	—	2	4	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	—	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	—	8	1	no	—
193	C₄⋊C₄×C₁₉	—	8	1	no	—
194	C₄⋊C₄×C₁₉	#41	1	2	yes	—
195	C₄⋊C₄×C₁₉	#41	1	2	yes	—
196	C₂²⋊C₄×C₁₉	—	2	4	no	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	2	no	—
201	C₂²⋊C₄×C₁₉	—	8	1	no	—
202	C₂²⋊C₄×C₁₉	—	8	1	no	—
203	C₂²⋊C₄×C₁₉	—	8	1	no	—
204	C₂²⋊C₄×C₁₉	—	8	1	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	—	4	2	no	—
210	C₄²×C₁₉	—	8	1	no	—
211	C₄²×C₁₉	—	8	1	no	—
212	#29424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₁₉	—	2	2	no	—
229	Q₈×C₁₉	—	2	2	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	2	2	no	—
233	D₄×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	8	4	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	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	1	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	—	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	—	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	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	8	4	no	—
278	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	—	4	1	no	—
287	C₈×C₁₉	—	4	1	no	—
288	#2324	C₂×C₁₉	1	1	yes	characteristic
289	#2323	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#2034	C₂×C₁₉	1	1	yes	characteristic
293	#2000	C₂×C₁₉	1	1	yes	characteristic
294	#1927	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	2	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	#525	1	1	yes	characteristic
318	C₂²×C₁₉	#525	1	1	yes	characteristic
319	C₂²×C₁₉	#534	1	1	yes	characteristic
320	C₂²×C₁₉	#577	1	1	yes	characteristic
321	C₂²×C₁₉	#577	1	1	yes	characteristic
322	C₂²×C₁₉	#577	1	1	yes	characteristic
323	C₂²×C₁₉	#577	1	1	yes	characteristic
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	2	no	—
327	C₄×C₁₉	—	4	2	no	—
328	C₄×C₁₉	—	4	1	no	—
329	C₄×C₁₉	—	4	1	no	—
330	C₄×C₁₉	—	4	1	no	—
331	C₄×C₁₉	—	4	1	no	—
332	C₄×C₁₉	—	8	1	no	—
333	C₄×C₁₉	—	8	1	no	—
334	C₄×C₁₉	—	8	1	no	—
335	C₄×C₁₉	—	8	1	no	—
336	C₄×C₁₉	#551	1	1	yes	characteristic
337	C₄×C₁₉	#553	1	1	yes	characteristic
338	C₄×C₁₉	#553	1	1	yes	characteristic
339	C₄×C₁₉	#559	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
352	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
357	#391	C₂²×C₁₉	1	1	yes	characteristic
358	#390	—	2	1	no	—
359	#390	C₂²×C₁₉	1	1	yes	characteristic
360	#389	—	2	1	no	—
361	#389	C₂²×C₁₉	1	1	yes	characteristic
362	#389	C₂²×C₁₉	1	1	yes	characteristic
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#387	—	2	1	no	—
367	#386	—	2	1	no	—
368	#385	—	2	1	no	—
369	#380	C₂²×C₁₉	1	1	yes	characteristic
370	#380	C₂²×C₁₉	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
373	#340	C₂²×C₁₉	1	1	yes	characteristic
374	#340	C₂²×C₁₉	1	1	yes	characteristic
375	#340	C₂²×C₁₉	1	1	yes	characteristic
376	#340	C₂²×C₁₉	1	1	yes	characteristic
377	#340	C₂²×C₁₉	1	1	yes	characteristic
378	#340	C₂²×C₁₉	1	1	yes	characteristic
379	#336	C₂²×C₁₉	1	1	yes	characteristic
380	#336	C₂²×C₁₉	1	1	yes	characteristic
381	#336	C₂²×C₁₉	1	1	yes	characteristic
382	#336	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×C₁₉	—	8	1	no	—
384	C₂×C₁₉	—	8	2	no	—
385	C₂×C₁₉	#2600	1	1	yes	characteristic
386	C₂×C₁₉	#3123	1	1	yes	characteristic
387	C₂×C₁₉	#3125	1	1	yes	characteristic
388	C₂×C₁₉	#3125	1	1	yes	characteristic
389	C₂×C₁₉	#3126	1	1	yes	characteristic
390	C₂×C₁₉	#3200	1	1	yes	characteristic
391	C₂×C₁₉	#3204	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	4	1	no	—
400	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	C₄×Q₈	—	4	1	no	—
409	C₄×Q₈	—	4	1	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	#117	—	4	1	no	—
413	#117	—	4	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
440	#106	—	2	2	no	—
441	#106	—	2	2	no	—
442	#106	—	4	1	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	4	1	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	4	1	no	—
449	C₂²⋊C₈	—	4	1	no	—
450	C₂²⋊C₈	—	4	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	C₁₉	#29424	1	1	yes	characteristic, direct product factor, Sylow
460	C₂⁴	—	2	1	no	—
461	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	#41×C₁₉	1	2	yes	—
468	C₂×D₄	—	2	4	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	C₂×D₄	—	8	1	no	—
475	C₂×D₄	—	8	1	no	—
476	C₂×D₄	#41×C₁₉	1	2	yes	—
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	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	8	1	no	—
492	C₂²×C₄	—	8	1	no	—
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
499	SD₁₆	—	4	4	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	8	1	no	—
527	C₄⋊C₄	—	8	1	no	—
528	C₄⋊C₄	#41×C₁₉	1	2	yes	—
529	C₄⋊C₄	#41×C₁₉	1	2	yes	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	8	1	no	—
536	C₂²⋊C₄	—	8	1	no	—
537	C₂²⋊C₄	—	8	1	no	—
538	C₂²⋊C₄	—	8	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	4	2	no	—
544	C₄²	—	8	1	no	—
545	C₄²	—	8	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	8	4	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	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	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	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	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
615	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	C₁₉×#525	1	1	yes	characteristic
636	C₂²	C₁₉×#525	1	1	yes	characteristic
637	C₂²	C₁₉×#534	1	1	yes	characteristic
638	C₂²	C₁₉×#577	1	1	yes	characteristic
639	C₂²	C₁₉×#577	1	1	yes	characteristic
640	C₂²	C₁₉×#577	1	1	yes	characteristic
641	C₂²	C₁₉×#577	1	1	yes	characteristic
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	C₁₉×#551	1	1	yes	characteristic
655	C₄	C₁₉×#553	1	1	yes	characteristic
656	C₄	C₁₉×#553	1	1	yes	characteristic
657	C₄	C₁₉×#559	1	1	yes	characteristic
658	C₂	—	8	1	no	—
659	C₂	—	8	2	no	—
660	C₂	C₁₉×#2600	1	1	yes	characteristic
661	C₂	C₁₉×#3123	1	1	yes	characteristic
662	C₂	C₁₉×#3125	1	1	yes	characteristic
663	C₂	C₁₉×#3125	1	1	yes	characteristic
664	C₂	C₁₉×#3126	1	1	yes	characteristic
665	C₂	C₁₉×#3200	1	1	yes	characteristic
666	C₂	C₁₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2323	C₂	semidirect
3. C₁₉×#2077	C₂	semidirect
4. C₁₉×#2035	C₂	semidirect
7. C₁₉×#1927	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1920	C₂	semidirect
10. C₁₉×#1919	C₂	semidirect
11. C₁₉×#1880	C₂	semidirect
12. C₁₉×#1877	C₂	semidirect
13. C₁₉×#1865	C₂	semidirect
14. C₁₉×#1864	C₂	semidirect
15. C₁₉×#1818	C₂	semidirect
212. #29424	C₁₉	direct (N × H)
289. #2323	C₂×C₁₉	semidirect
290. #2077	C₂×C₁₉	semidirect
291. #2035	C₂×C₁₉	semidirect
294. #1927	C₂×C₁₉	semidirect
295. #1926	C₂×C₁₉	semidirect
296. #1920	C₂×C₁₉	semidirect
297. #1919	C₂×C₁₉	semidirect
298. #1880	C₂×C₁₉	semidirect
299. #1877	C₂×C₁₉	semidirect
300. #1865	C₂×C₁₉	semidirect
301. #1864	C₂×C₁₉	semidirect
302. #1818	C₂×C₁₉	semidirect
459. C₁₉	#29424	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×#2324	2
C₁₉×#2323	2
C₁₉×#2077	2
C₁₉×#2035	2
C₁₉×#2034	2
C₁₉×#2000	2
C₁₉×#1927	2
C₁₉×#1926	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1880	2
C₁₉×#1877	2
C₁₉×#1865	2
C₁₉×#1864	2
C₁₉×#1818	2
#29424	19

Subgroups — C19×#29424 #18035383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29424 #18035383