Subgroups — C₁₉×#14226 #18020185

Order 4864.

1462 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#398	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#389	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1436	C₂	1	2	yes	maximal
9	C₁₉×#1436	C₂	1	2	yes	maximal
10	C₁₉×#1436	C₂	1	2	yes	maximal
11	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#398	C₄	1	8	yes	complemented
24	C₁₉×#389	—	2	8	no	—
25	C₁₉×#389	—	2	4	no	—
26	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂×C₁₉×#95	C₂²	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	—	2	4	no	—
76	C₂×C₄²×C₁₉	—	4	2	no	—
77	C₂×C₄²×C₁₉	—	4	2	no	—
78	C₂×C₄²×C₁₉	—	4	2	no	—
79	C₂×C₄²×C₁₉	D₄	1	4	yes	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	4	no	—
83	C₁₉×#95	—	2	4	no	—
84	C₁₉×#95	—	2	4	no	—
85	C₁₉×#95	—	2	4	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	4	no	—
88	C₁₉×#95	—	4	2	no	—
89	C₁₉×#95	C₂×C₄	1	8	yes	—
90	C₁₉×#95	C₂×C₄	1	4	yes	—
91	C₁₉×#95	Q₈	1	8	yes	—
92	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
153	C₂²×C₄×C₁₉	#41	1	2	yes	—
154	C₂²×C₄×C₁₉	#41	1	2	yes	—
155	C₂²×C₄×C₁₉	#41	1	2	yes	—
156	C₂²×C₄×C₁₉	#41	1	4	yes	—
157	C₂²×C₄×C₁₉	#41	1	2	yes	—
158	C₄⋊C₄×C₁₉	—	2	8	no	—
159	C₄⋊C₄×C₁₉	—	2	16	no	—
160	C₄⋊C₄×C₁₉	—	2	8	no	—
161	C₄⋊C₄×C₁₉	—	2	8	no	—
162	C₄⋊C₄×C₁₉	—	4	8	no	—
163	C₄⋊C₄×C₁₉	—	4	4	no	—
164	C₄⋊C₄×C₁₉	—	4	8	no	—
165	C₄²×C₁₉	—	2	8	no	—
166	C₄²×C₁₉	—	4	4	no	—
167	C₄²×C₁₉	—	4	8	no	—
168	C₄²×C₁₉	—	4	4	no	—
169	#14226	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
171	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
174	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
175	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
176	C₂³×C₁₉	C₂×#41	1	2	yes	—
177	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
178	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
180	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	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	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
242	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
243	C₂×C₄×C₁₉	C₄×Q₈	1	8	yes	—
244	C₂×C₄×C₁₉	#121	1	4	yes	—
245	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
246	C₂×#398	C₂×C₁₉	1	1	yes	characteristic
247	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
248	C₂×#389	C₂×C₁₉	1	2	yes	—
249	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
250	#1445	C₂×C₁₉	1	1	yes	characteristic
251	#1444	C₂×C₁₉	1	1	yes	characteristic
252	#1441	C₂×C₁₉	1	1	yes	characteristic
253	#1436	C₂×C₁₉	1	2	yes	—
254	#1436	C₂×C₁₉	1	2	yes	—
255	#1436	C₂×C₁₉	1	2	yes	—
256	C₄×#95	C₂×C₁₉	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
260	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
261	C₂²×C₁₉	#520	1	2	yes	—
262	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
263	C₂²×C₁₉	#525	1	1	yes	characteristic
264	C₂²×C₁₉	#529	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
266	C₂²×C₁₉	#532	1	1	yes	characteristic
267	C₂²×C₁₉	#532	1	1	yes	characteristic
268	C₂²×C₁₉	#533	1	2	yes	—
269	C₂²×C₁₉	#534	1	1	yes	characteristic
270	C₂²×C₁₉	#536	1	1	yes	characteristic
271	C₂²×C₁₉	#539	1	2	yes	—
272	C₂²×C₁₉	#546	1	2	yes	—
273	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
274	C₂²×C₁₉	#552	1	2	yes	—
275	C₂²×C₁₉	#552	1	2	yes	—
276	C₂²×C₁₉	#553	1	2	yes	—
277	C₂²×C₁₉	#554	1	2	yes	—
278	C₂²×C₁₉	#554	1	2	yes	—
279	C₂²×C₁₉	#557	1	2	yes	—
280	C₄×C₁₉	—	2	4	no	—
281	C₄×C₁₉	—	2	4	no	—
282	C₄×C₁₉	—	2	8	no	—
283	C₄×C₁₉	—	2	4	no	—
284	C₄×C₁₉	—	2	4	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	4	no	—
289	C₄×C₁₉	—	4	4	no	—
290	C₄×C₁₉	—	8	2	no	—
291	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
292	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
293	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
294	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
300	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
302	#398	C₄×C₁₉	1	8	yes	complemented
303	#389	—	2	8	no	—
304	#389	—	2	4	no	—
305	C₄×C₄⋊C₄	—	2	4	no	—
306	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#95	C₂²×C₁₉	1	2	yes	—
308	C₂×#95	C₂²×C₁₉	1	2	yes	—
309	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#95	C₂²×C₁₉	1	2	yes	—
311	C₂×#95	C₂²×C₁₉	1	2	yes	—
312	C₂×#95	C₂²×C₁₉	1	2	yes	—
313	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#95	C₂²×C₁₉	1	2	yes	—
315	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#95	C₂²×C₁₉	1	2	yes	—
317	C₂×#95	C₂²×C₁₉	1	2	yes	—
318	C₂×C₁₉	C₄×#121	1	1	yes	characteristic
319	C₂×C₁₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
320	C₂×C₁₉	#2322	1	1	yes	characteristic
321	C₂×C₁₉	#2360	1	2	yes	—
322	C₂×C₁₉	#2370	1	2	yes	—
323	C₂×C₁₉	#2543	1	1	yes	characteristic
324	C₂×C₁₉	#2546	1	1	yes	characteristic
325	C₂×C₁₉	#2556	1	2	yes	—
326	C₂×C₁₉	#2583	1	1	yes	characteristic
327	C₂×C₁₉	#2585	1	2	yes	—
328	C₂×C₁₉	#2611	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
331	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	—	4	2	no	—
356	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
357	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
358	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
359	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	—	4	2	no	—
367	C₂×C₄²	—	4	2	no	—
368	C₂×C₄²	—	4	2	no	—
369	C₂×C₄²	D₄×C₁₉	1	4	yes	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	4	no	—
373	#95	—	2	4	no	—
374	#95	—	2	4	no	—
375	#95	—	2	4	no	—
376	#95	—	2	2	no	—
377	#95	—	2	4	no	—
378	#95	—	4	2	no	—
379	#95	C₂×C₄×C₁₉	1	8	yes	—
380	#95	C₂×C₄×C₁₉	1	4	yes	—
381	#95	Q₈×C₁₉	1	8	yes	—
382	C₁₉	#14226	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
432	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
442	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
443	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
444	C₂²×C₄	#41×C₁₉	1	2	yes	—
445	C₂²×C₄	#41×C₁₉	1	2	yes	—
446	C₂²×C₄	#41×C₁₉	1	2	yes	—
447	C₂²×C₄	#41×C₁₉	1	4	yes	—
448	C₂²×C₄	#41×C₁₉	1	2	yes	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	16	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	4	8	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	8	no	—
456	C₄²	—	2	8	no	—
457	C₄²	—	4	4	no	—
458	C₄²	—	4	8	no	—
459	C₄²	—	4	4	no	—
460	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
461	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
462	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
463	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
464	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
465	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
466	C₂³	C₂×#41×C₁₉	1	2	yes	—
467	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
468	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
469	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
470	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
532	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
533	C₂×C₄	C₄×Q₈×C₁₉	1	8	yes	—
534	C₂×C₄	C₁₉×#121	1	4	yes	—
535	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
536	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
537	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
538	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
539	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
540	C₂²	C₁₉×#520	1	2	yes	—
541	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
542	C₂²	C₁₉×#525	1	1	yes	characteristic
543	C₂²	C₁₉×#529	1	1	yes	characteristic
544	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
545	C₂²	C₁₉×#532	1	1	yes	characteristic
546	C₂²	C₁₉×#532	1	1	yes	characteristic
547	C₂²	C₁₉×#533	1	2	yes	—
548	C₂²	C₁₉×#534	1	1	yes	characteristic
549	C₂²	C₁₉×#536	1	1	yes	characteristic
550	C₂²	C₁₉×#539	1	2	yes	—
551	C₂²	C₁₉×#546	1	2	yes	—
552	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
553	C₂²	C₁₉×#552	1	2	yes	—
554	C₂²	C₁₉×#552	1	2	yes	—
555	C₂²	C₁₉×#553	1	2	yes	—
556	C₂²	C₁₉×#554	1	2	yes	—
557	C₂²	C₁₉×#554	1	2	yes	—
558	C₂²	C₁₉×#557	1	2	yes	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	2	4	no	—
562	C₄	—	2	4	no	—
563	C₄	—	2	8	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	4	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	2	no	—
570	C₂	C₄×C₁₉×#121	1	1	yes	characteristic
571	C₂	C₄×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
572	C₂	C₁₉×#2322	1	1	yes	characteristic
573	C₂	C₁₉×#2360	1	2	yes	—
574	C₂	C₁₉×#2370	1	2	yes	—
575	C₂	C₁₉×#2543	1	1	yes	characteristic
576	C₂	C₁₉×#2546	1	1	yes	characteristic
577	C₂	C₁₉×#2556	1	2	yes	—
578	C₂	C₁₉×#2583	1	1	yes	characteristic
579	C₂	C₁₉×#2585	1	2	yes	—
580	C₂	C₁₉×#2611	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
23. C₁₉×#398	C₄	semidirect
169. #14226	C₁₉	direct (N × H)
302. #398	C₄×C₁₉	semidirect
382. C₁₉	#14226	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×#398	2
C₂×C₁₉×#389	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1445	2
C₁₉×#1444	2
C₁₉×#1441	2
C₁₉×#1436	2
C₄×C₁₉×#95	2
#14226	19

Subgroups — C19×#14226 #18020185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14226 #18020185