Subgroups — C₁₉×#26009 #18031968

Order 4864.

740 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2440	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2346	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1809	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#398	—	2	1	no	—
29	C₁₉×#395	—	2	1	no	—
30	C₁₉×#389	C₂²	1	1	yes	characteristic
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#388	—	2	1	no	—
35	C₁₉×#388	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#384	C₂²	1	1	yes	characteristic
38	C₁₉×#382	—	2	1	no	—
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#376	—	2	1	no	—
45	C₁₉×#340	C₂²	1	1	yes	characteristic
46	C₁₉×#340	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×Q₈×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	—	4	1	no	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	—	2	2	no	—
70	C₁₉×C₄⋊Q₈	—	4	1	no	—
71	C₁₉×C₂²⋊Q₈	—	4	4	no	—
72	C₁₉×#117	—	2	2	no	—
73	C₁₉×#117	Q₈	1	4	yes	complemented
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	2	no	—
103	C₁₉×#106	—	2	2	no	—
104	C₁₉×#106	—	4	1	no	—
105	C₁₉×#106	—	4	1	no	—
106	C₁₉×C₄⋊C₈	—	2	2	no	—
107	C₁₉×C₄⋊C₈	—	4	1	no	—
108	C₁₉×C₂²⋊C₈	—	2	2	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₁₉×#95	D₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	8	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	2	no	—
137	C₂²×C₄×C₁₉	—	8	1	no	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₉	#41	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	M₁₆×C₁₉	—	4	4	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	#41	1	2	yes	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	—	4	2	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	4	2	no	—
177	C₄⋊C₄×C₁₉	—	8	1	no	—
178	C₄⋊C₄×C₁₉	—	8	1	no	—
179	C₄⋊C₄×C₁₉	—	8	1	no	—
180	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
182	C₄⋊C₄×C₁₉	#41	1	2	yes	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	4	2	no	—
187	C₂²⋊C₄×C₁₉	—	8	1	no	—
188	C₄²×C₁₉	—	2	4	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	4	2	no	—
194	C₄²×C₁₉	—	4	2	no	—
195	#26009	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	2	1	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
247	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
248	C₂×C₄×C₁₉	#137	1	2	yes	—
249	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
255	C₈×C₁₉	—	2	2	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	#2440	C₂×C₁₉	1	1	yes	characteristic
260	#2346	C₂×C₁₉	1	1	yes	characteristic
261	#2100	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2088	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#2087	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#2058	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1948	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1918	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1853	C₂×C₁₉	1	1	yes	characteristic
270	#1851	C₂×C₁₉	1	1	yes	characteristic
271	#1825	C₂×C₁₉	1	1	yes	characteristic
272	#1809	C₂×C₁₉	1	1	yes	characteristic
273	#1736	C₂×C₁₉	1	1	yes	characteristic
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
282	C₂²×C₁₉	#546	1	1	yes	characteristic
283	C₂²×C₁₉	#547	1	1	yes	characteristic
284	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
286	C₂²×C₁₉	#577	1	1	yes	characteristic
287	C₂²×C₁₉	#577	1	1	yes	characteristic
288	C₄×C₁₉	—	2	2	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	#533	1	1	yes	characteristic
302	C₄×C₁₉	#544	1	1	yes	characteristic
303	C₄×C₁₉	#551	1	1	yes	characteristic
304	C₄×C₁₉	#552	1	1	yes	characteristic
305	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	—	2	1	no	—
308	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
317	#398	—	2	1	no	—
318	#395	—	2	1	no	—
319	#389	C₂²×C₁₉	1	1	yes	characteristic
320	#389	C₂²×C₁₉	1	1	yes	characteristic
321	#389	C₂²×C₁₉	1	1	yes	characteristic
322	#389	C₂²×C₁₉	1	1	yes	characteristic
323	#388	—	2	1	no	—
324	#388	—	2	1	no	—
325	#385	—	2	1	no	—
326	#384	C₂²×C₁₉	1	1	yes	characteristic
327	#382	—	2	1	no	—
328	#380	C₂²×C₁₉	1	1	yes	characteristic
329	#380	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
333	#376	—	2	1	no	—
334	#340	C₂²×C₁₉	1	1	yes	characteristic
335	#340	C₂²×C₁₉	1	1	yes	characteristic
336	#340	C₂²×C₁₉	1	1	yes	characteristic
337	#340	C₂²×C₁₉	1	1	yes	characteristic
338	#340	C₂²×C₁₉	1	1	yes	characteristic
339	#340	C₂²×C₁₉	1	1	yes	characteristic
340	#340	C₂²×C₁₉	1	1	yes	characteristic
341	#340	C₂²×C₁₉	1	1	yes	characteristic
342	#340	C₂²×C₁₉	1	1	yes	characteristic
343	#340	C₂²×C₁₉	1	1	yes	characteristic
344	#340	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	1	yes	characteristic
346	#336	C₂²×C₁₉	1	1	yes	characteristic
347	#336	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×C₁₉	—	4	2	no	—
349	C₂×C₁₉	#2438	1	1	yes	characteristic
350	C₂×C₁₉	#3079	1	1	yes	characteristic
351	C₂×C₁₉	#3084	1	1	yes	characteristic
352	C₂×C₁₉	#3310	1	1	yes	characteristic
353	C₂×C₁₉	#3329	1	1	yes	characteristic
354	C₂×C₁₉	#3344	1	1	yes	characteristic
355	C₂×C₁₉	#3354	1	1	yes	characteristic
356	C₂²×Q₈	—	2	1	no	—
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	4	1	no	—
362	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	4	1	no	—
368	C₂²⋊Q₈	—	4	4	no	—
369	#117	—	2	2	no	—
370	#117	Q₈×C₁₉	1	4	yes	complemented
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	4	1	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
399	#107	—	2	2	no	—
400	#106	—	2	2	no	—
401	#106	—	4	1	no	—
402	#106	—	4	1	no	—
403	C₄⋊C₈	—	2	2	no	—
404	C₄⋊C₈	—	4	1	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	D₄×C₁₉	1	1	yes	characteristic
415	#95	D₄×C₁₉	1	1	yes	characteristic
416	C₁₉	#26009	1	1	yes	characteristic, direct product factor, Sylow
417	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	—	8	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	8	1	no	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
442	C₂²×C₄	#41×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
444	M₁₆	—	4	4	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	#41×C₁₉	1	2	yes	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	8	1	no	—
476	C₄⋊C₄	—	8	1	no	—
477	C₄⋊C₄	—	8	1	no	—
478	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
479	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
480	C₄⋊C₄	#41×C₁₉	1	2	yes	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	8	1	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	4	2	no	—
492	C₄²	—	4	2	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	Q₈	—	8	4	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	8	4	no	—
543	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
544	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
545	C₂×C₄	C₁₉×#137	1	2	yes	—
546	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
548	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
549	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
550	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
564	C₂²	C₁₉×#546	1	1	yes	characteristic
565	C₂²	C₁₉×#547	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
568	C₂²	C₁₉×#577	1	1	yes	characteristic
569	C₂²	C₁₉×#577	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	C₁₉×#533	1	1	yes	characteristic
584	C₄	C₁₉×#544	1	1	yes	characteristic
585	C₄	C₁₉×#551	1	1	yes	characteristic
586	C₄	C₁₉×#552	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	C₁₉×#2438	1	1	yes	characteristic
589	C₂	C₁₉×#3079	1	1	yes	characteristic
590	C₂	C₁₉×#3084	1	1	yes	characteristic
591	C₂	C₁₉×#3310	1	1	yes	characteristic
592	C₂	C₁₉×#3329	1	1	yes	characteristic
593	C₂	C₁₉×#3344	1	1	yes	characteristic
594	C₂	C₁₉×#3354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
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
3. C₁₉×#2100	C₂	semidirect
4. C₁₉×#2088	C₂	semidirect
5. C₁₉×#2087	C₂	semidirect
6. C₁₉×#2058	C₂	semidirect
7. C₁₉×#1988	C₂	semidirect
8. C₁₉×#1948	C₂	semidirect
9. C₁₉×#1920	C₂	semidirect
10. C₁₉×#1918	C₂	semidirect
73. C₁₉×#117	Q₈	semidirect
195. #26009	C₁₉	direct (N × H)
261. #2100	C₂×C₁₉	semidirect
262. #2088	C₂×C₁₉	semidirect
263. #2087	C₂×C₁₉	semidirect
264. #2058	C₂×C₁₉	semidirect
265. #1988	C₂×C₁₉	semidirect
266. #1948	C₂×C₁₉	semidirect
267. #1920	C₂×C₁₉	semidirect
268. #1918	C₂×C₁₉	semidirect
370. #117	Q₈×C₁₉	semidirect
416. C₁₉	#26009	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×#2440	2
C₁₉×#2346	2
C₁₉×#2100	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2058	2
C₁₉×#1988	2
C₁₉×#1948	2
C₁₉×#1920	2
C₁₉×#1918	2
C₁₉×#1853	2
C₁₉×#1851	2
C₁₉×#1825	2
C₁₉×#1809	2
C₁₉×#1736	2
#26009	19

Subgroups — C19×#26009 #18031968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26009 #18031968