Subgroups — C₁₉×#22294 #18028253

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2396	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1753	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1753	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#400	C₄	1	1	yes	characteristic
33	C₁₉×#399	C₄	1	1	yes	characteristic
34	C₁₉×#398	C₄	1	1	yes	characteristic
35	C₁₉×#398	C₄	1	1	yes	characteristic
36	C₁₉×#396	C₄	1	1	yes	characteristic
37	C₁₉×#396	C₄	1	1	yes	characteristic
38	C₁₉×#395	C₄	1	1	yes	characteristic
39	C₁₉×#393	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	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	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#336	C₂²	1	1	yes	characteristic
46	C₁₉×#336	C₂²	1	1	yes	characteristic
47	C₁₉×#336	C₂²	1	1	yes	characteristic
48	C₁₉×#336	C₂²	1	1	yes	characteristic
49	C₁₉×#336	C₂²	1	1	yes	characteristic
50	C₁₉×#336	C₂²	1	1	yes	characteristic
51	C₁₉×#336	C₂²	1	1	yes	characteristic
52	C₁₉×#336	C₂²	1	1	yes	characteristic
53	C₁₉×#336	C₂²	1	1	yes	characteristic
54	C₁₉×#336	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	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₁₉	—	4	1	no	—
62	C₂×M₁₆×C₁₉	—	4	1	no	—
63	C₂×M₁₆×C₁₉	Q₈	1	4	yes	complemented
64	C₂²×C₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	—	4	1	no	—
66	C₂²×C₈×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	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	C₄×Q₈×C₁₉	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₁₉×#117	—	4	1	no	—
78	C₁₉×#117	—	4	1	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×C₄⋊C₈	—	4	1	no	—
103	C₁₉×C₄⋊C₈	—	4	1	no	—
104	C₁₉×C₄⋊C₈	—	4	1	no	—
105	C₁₉×C₄⋊C₈	—	4	1	no	—
106	C₁₉×C₄⋊C₈	—	4	1	no	—
107	C₁₉×C₄⋊C₈	—	4	1	no	—
108	C₁₉×C₂²⋊C₈	—	2	2	no	—
109	C₁₉×C₂²⋊C₈	—	2	2	no	—
110	C₁₉×#97	—	4	1	no	—
111	C₁₉×#97	—	4	1	no	—
112	C₄×C₈×C₁₉	—	4	1	no	—
113	C₄×C₈×C₁₉	—	4	1	no	—
114	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
120	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
121	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
122	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
123	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
124	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	4	1	no	—
127	C₂×Q₈×C₁₉	—	4	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	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₁₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₁₉	—	4	4	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	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	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	—	4	4	no	—
172	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
173	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	4	1	no	—
188	C₂²⋊C₄×C₁₉	—	4	1	no	—
189	C₂²⋊C₄×C₁₉	—	4	1	no	—
190	C₂²⋊C₄×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	#22294	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
211	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
212	Q₈×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	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	C₄×Q₈	1	2	yes	—
254	C₂×C₄×C₁₉	#131	1	2	yes	—
255	C₂×C₄×C₁₉	#131	1	2	yes	—
256	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
262	C₈×C₁₉	—	2	2	no	—
263	C₈×C₁₉	—	2	2	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	#2396	C₂×C₁₉	1	1	yes	characteristic
271	#1985	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1984	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1940	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1939	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1916	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1916	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1850	C₂×C₁₉	1	1	yes	characteristic
280	#1850	C₂×C₁₉	1	1	yes	characteristic
281	#1798	C₂×C₁₉	1	1	yes	characteristic
282	#1753	C₂×C₁₉	1	1	yes	characteristic
283	#1753	C₂×C₁₉	1	1	yes	characteristic
284	#1729	C₂×C₁₉	1	1	yes	characteristic
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
293	C₂²×C₁₉	#518	1	1	yes	characteristic
294	C₂²×C₁₉	#520	1	1	yes	characteristic
295	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
297	C₂²×C₁₉	#568	1	1	yes	characteristic
298	C₂²×C₁₉	#568	1	1	yes	characteristic
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	#538	1	1	yes	characteristic
313	C₄×C₁₉	#539	1	1	yes	characteristic
314	C₄×C₁₉	#543	1	1	yes	characteristic
315	C₄×C₁₉	#544	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
317	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
332	#400	C₄×C₁₉	1	1	yes	characteristic
333	#399	C₄×C₁₉	1	1	yes	characteristic
334	#398	C₄×C₁₉	1	1	yes	characteristic
335	#398	C₄×C₁₉	1	1	yes	characteristic
336	#396	C₄×C₁₉	1	1	yes	characteristic
337	#396	C₄×C₁₉	1	1	yes	characteristic
338	#395	C₄×C₁₉	1	1	yes	characteristic
339	#393	C₄×C₁₉	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	#336	C₂²×C₁₉	1	1	yes	characteristic
346	#336	C₂²×C₁₉	1	1	yes	characteristic
347	#336	C₂²×C₁₉	1	1	yes	characteristic
348	#336	C₂²×C₁₉	1	1	yes	characteristic
349	#336	C₂²×C₁₉	1	1	yes	characteristic
350	#336	C₂²×C₁₉	1	1	yes	characteristic
351	#336	C₂²×C₁₉	1	1	yes	characteristic
352	#336	C₂²×C₁₉	1	1	yes	characteristic
353	#336	C₂²×C₁₉	1	1	yes	characteristic
354	#336	C₂²×C₁₉	1	1	yes	characteristic
355	#336	C₂²×C₁₉	1	1	yes	characteristic
356	#336	C₂²×C₁₉	1	1	yes	characteristic
357	#336	C₂²×C₁₉	1	1	yes	characteristic
358	#336	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₁₉	—	4	2	no	—
360	C₂×C₁₉	#2329	1	1	yes	characteristic
361	C₂×C₁₉	#2962	1	1	yes	characteristic
362	C₂×C₁₉	#2962	1	1	yes	characteristic
363	C₂×C₁₉	#2976	1	1	yes	characteristic
364	C₂×C₁₉	#2981	1	1	yes	characteristic
365	C₂×C₁₉	#2994	1	1	yes	characteristic
366	C₂×C₁₉	#2995	1	1	yes	characteristic
367	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×M₁₆	—	4	1	no	—
370	C₂×M₁₆	—	4	1	no	—
371	C₂×M₁₆	Q₈×C₁₉	1	4	yes	complemented
372	C₂²×C₈	—	2	2	no	—
373	C₂²×C₈	—	4	1	no	—
374	C₂²×C₈	—	4	1	no	—
375	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄×Q₈	—	4	1	no	—
384	C₄×Q₈	—	4	1	no	—
385	#117	—	4	1	no	—
386	#117	—	4	1	no	—
387	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊C₈	—	4	1	no	—
411	C₄⋊C₈	—	4	1	no	—
412	C₄⋊C₈	—	4	1	no	—
413	C₄⋊C₈	—	4	1	no	—
414	C₄⋊C₈	—	4	1	no	—
415	C₄⋊C₈	—	4	1	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	#97	—	4	1	no	—
419	#97	—	4	1	no	—
420	C₄×C₈	—	4	1	no	—
421	C₄×C₈	—	4	1	no	—
422	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
423	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
424	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
425	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
426	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
427	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
428	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
429	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
430	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
431	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
432	C₁₉	#22294	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	—	4	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
455	C₂²×C₄	#41×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
457	M₁₆	—	4	4	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	4	no	—
481	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
482	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₄×Q₈×C₁₉	1	2	yes	—
519	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
520	Q₈	—	4	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
562	C₂×C₄	C₁₉×#131	1	2	yes	—
563	C₂×C₄	C₁₉×#131	1	2	yes	—
564	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
586	C₂²	C₁₉×#518	1	1	yes	characteristic
587	C₂²	C₁₉×#520	1	1	yes	characteristic
588	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
589	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
590	C₂²	C₁₉×#568	1	1	yes	characteristic
591	C₂²	C₁₉×#568	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	C₁₉×#538	1	1	yes	characteristic
606	C₄	C₁₉×#539	1	1	yes	characteristic
607	C₄	C₁₉×#543	1	1	yes	characteristic
608	C₄	C₁₉×#544	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	C₁₉×#2329	1	1	yes	characteristic
611	C₂	C₁₉×#2962	1	1	yes	characteristic
612	C₂	C₁₉×#2962	1	1	yes	characteristic
613	C₂	C₁₉×#2976	1	1	yes	characteristic
614	C₂	C₁₉×#2981	1	1	yes	characteristic
615	C₂	C₁₉×#2994	1	1	yes	characteristic
616	C₂	C₁₉×#2995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1985	C₂	semidirect
3. C₁₉×#1984	C₂	semidirect
4. C₁₉×#1940	C₂	semidirect
5. C₁₉×#1939	C₂	semidirect
6. C₁₉×#1917	C₂	semidirect
7. C₁₉×#1917	C₂	semidirect
8. C₁₉×#1916	C₂	semidirect
9. C₁₉×#1916	C₂	semidirect
63. C₂×M₁₆×C₁₉	Q₈	semidirect
203. #22294	C₁₉	direct (N × H)
271. #1985	C₂×C₁₉	semidirect
272. #1984	C₂×C₁₉	semidirect
273. #1940	C₂×C₁₉	semidirect
274. #1939	C₂×C₁₉	semidirect
275. #1917	C₂×C₁₉	semidirect
276. #1917	C₂×C₁₉	semidirect
277. #1916	C₂×C₁₉	semidirect
278. #1916	C₂×C₁₉	semidirect
371. C₂×M₁₆	Q₈×C₁₉	semidirect
432. C₁₉	#22294	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×#2396	2
C₁₉×#1985	2
C₁₉×#1984	2
C₁₉×#1940	2
C₁₉×#1939	2
C₁₉×#1917	2
C₁₉×#1916	2
C₁₉×#1850	2
C₁₉×#1798	2
C₁₉×#1753	2
C₁₉×#1729	2
#22294	19

Subgroups — C19×#22294 #18028253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22294 #18028253