Subgroups — C₁₉×#24550 #18030509

Order 4864.

1266 conjugacy classes of subgroups.

The subgroup lattice has 660 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	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2075	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1893	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1808	C₂	1	2	yes	maximal, complemented
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#120	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
21	C₁₉×#480	—	2	4	no	—
22	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
26	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#386	—	2	1	no	—
31	C₁₉×#386	—	2	1	no	—
32	C₁₉×#386	—	2	1	no	—
33	C₁₉×#380	—	2	1	no	—
34	C₁₉×#380	—	2	1	no	—
35	C₁₉×#380	C₂²	1	2	yes	—
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#380	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#95	—	2	1	no	—
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#340	C₂²	1	2	yes	complemented
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	—	2	4	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	—	4	2	no	—
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	—	2	4	no	—
63	C₂²×C₈×C₁₉	—	2	4	no	—
64	C₂²×C₈×C₁₉	—	4	2	no	—
65	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	4	no	—
70	C₁₉×#121	—	4	2	no	—
71	C₁₉×#120	—	4	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
91	C₁₉×#107	—	2	4	no	—
92	C₁₉×#107	—	4	2	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#102	—	4	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	2	no	—
96	C₁₉×C₂²⋊C₈	—	2	4	no	—
97	C₁₉×C₂²⋊C₈	D₄	1	4	yes	complemented
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	2	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	2	1	no	—
108	C₂⁴×C₁₉	—	4	1	no	—
109	C₂⁴×C₁₉	—	4	1	no	—
110	C₂⁴×C₁₉	D₈	1	4	yes	—
111	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	—	4	8	no	—
151	C₂²×C₄×C₁₉	—	4	8	no	—
152	C₂²×C₄×C₁₉	—	4	2	no	—
153	C₂²×C₄×C₁₉	—	4	2	no	—
154	C₂²×C₄×C₁₉	—	4	2	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	2	no	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	#41	1	2	yes	—
163	C₂²×C₄×C₁₉	#41	1	4	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	4	8	no	—
171	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₄⋊C₄×C₁₉	—	4	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	4	no	—
184	C₂²⋊C₄×C₁₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₉	—	4	2	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	—	4	2	no	—
190	#24550	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	1	no	—
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	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	8	no	—
206	C₂³×C₁₉	—	2	8	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	4	no	—
209	C₂³×C₁₉	—	4	4	no	—
210	C₂³×C₁₉	—	4	4	no	—
211	C₂³×C₁₉	—	4	4	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	#121	1	2	yes	—
220	C₂³×C₁₉	#123	1	2	yes	—
221	C₂³×C₁₉	C₂×D₈	1	2	yes	—
222	C₂³×C₁₉	C₂×D₈	1	2	yes	—
223	C₂³×C₁₉	C₂×D₈	1	2	yes	—
224	C₂³×C₁₉	#135	1	2	yes	—
225	C₂³×C₁₉	#137	1	2	yes	—
226	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	8	4	no	—
230	D₄×C₁₉	—	8	4	no	—
231	D₄×C₁₉	—	8	4	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	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	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	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	4	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	2	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	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	8	4	no	—
264	C₂×C₄×C₁₉	—	8	4	no	—
265	C₂×C₄×C₁₉	#121	1	2	yes	—
266	C₂×C₄×C₁₉	#123	1	2	yes	—
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
269	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₁₉	—	2	4	no	—
272	C₈×C₁₉	—	4	2	no	—
273	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#2847	C₂×C₁₉	1	1	yes	characteristic
276	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#2075	C₂×C₁₉	1	2	yes	complemented
278	#2033	C₂×C₁₉	1	2	yes	complemented
279	#1893	C₂×C₁₉	1	2	yes	complemented
280	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1808	C₂×C₁₉	1	2	yes	complemented
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	4	16	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	#466	1	4	yes	—
312	C₂²×C₁₉	#480	1	4	yes	complemented
313	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
314	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
315	C₂²×C₁₉	#534	1	1	yes	characteristic
316	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
317	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
318	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
319	C₂²×C₁₉	#575	1	1	yes	characteristic
320	C₄×C₁₉	—	2	2	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	2	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	2	no	—
327	C₄×C₁₉	—	8	1	no	—
328	C₄×C₁₉	#546	1	2	yes	—
329	C₄×C₁₉	#551	1	2	yes	—
330	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
332	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#120	—	2	1	no	—
336	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	—	2	1	no	—
339	#480	—	2	4	no	—
340	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
341	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
342	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
343	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
344	C₂×C₂²⋊C₈	—	2	4	no	—
345	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
346	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
348	#386	—	2	1	no	—
349	#386	—	2	1	no	—
350	#386	—	2	1	no	—
351	#380	—	2	1	no	—
352	#380	—	2	1	no	—
353	#380	C₂²×C₁₉	1	1	yes	characteristic
354	#380	C₂²×C₁₉	1	2	yes	—
355	#380	C₂²×C₁₉	1	1	yes	characteristic
356	#380	C₂²×C₁₉	1	2	yes	—
357	#380	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#95	—	2	1	no	—
359	#340	C₂²×C₁₉	1	2	yes	complemented
360	#340	C₂²×C₁₉	1	2	yes	complemented
361	#340	C₂²×C₁₉	1	2	yes	complemented
362	#340	C₂²×C₁₉	1	2	yes	complemented
363	C₂×C₁₉	—	2	4	no	—
364	C₂×C₁₉	—	2	4	no	—
365	C₂×C₁₉	—	4	2	no	—
366	C₂×C₁₉	—	16	1	no	—
367	C₂×C₁₉	#2412	1	1	yes	characteristic
368	C₂×C₁₉	C₂×#466	1	1	yes	characteristic
369	C₂×C₁₉	#3056	1	1	yes	characteristic
370	C₂×C₁₉	C₂×#480	1	1	yes	characteristic
371	C₂×C₁₉	#3091	1	1	yes	characteristic
372	C₂×C₁₉	#3186	1	1	yes	characteristic
373	C₂×C₁₉	#3190	1	1	yes	characteristic
374	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	—	2	2	no	—
380	C₂³×C₄	—	2	2	no	—
381	C₂³×C₄	—	2	4	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	—	4	2	no	—
385	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
387	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂²×C₈	—	2	4	no	—
392	C₂²×C₈	—	2	4	no	—
393	C₂²×C₈	—	4	2	no	—
394	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
395	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
396	#121	—	2	2	no	—
397	#121	—	2	2	no	—
398	#121	—	2	4	no	—
399	#121	—	4	2	no	—
400	#120	—	4	4	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	4	2	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	2	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	4	4	no	—
420	#107	—	2	4	no	—
421	#107	—	4	2	no	—
422	#102	—	2	4	no	—
423	#102	—	4	2	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	4	no	—
426	C₂²⋊C₈	D₄×C₁₉	1	4	yes	complemented
427	#95	—	2	2	no	—
428	#95	—	2	2	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	C₁₉	#24550	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	—	2	2	no	—
434	C₂⁴	—	2	2	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	4	1	no	—
439	C₂⁴	—	4	1	no	—
440	C₂⁴	D₈×C₁₉	1	4	yes	—
441	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	8	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
491	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	#41×C₁₉	1	2	yes	—
493	C₂²×C₄	#41×C₁₉	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	4	8	no	—
501	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	4	4	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	8	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	C₁₉×#121	1	2	yes	—
549	C₂³	C₁₉×#123	1	2	yes	—
550	C₂³	C₂×D₈×C₁₉	1	2	yes	—
551	C₂³	C₂×D₈×C₁₉	1	2	yes	—
552	C₂³	C₂×D₈×C₁₉	1	2	yes	—
553	C₂³	C₁₉×#135	1	2	yes	—
554	C₂³	C₁₉×#137	1	2	yes	—
555	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	8	4	no	—
559	D₄	—	8	4	no	—
560	D₄	—	8	4	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	4	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	C₁₉×#121	1	2	yes	—
595	C₂×C₄	C₁₉×#123	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
598	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
599	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
600	C₈	—	2	4	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	4	16	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	C₁₉×#466	1	4	yes	—
630	C₂²	C₁₉×#480	1	4	yes	complemented
631	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
632	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
633	C₂²	C₁₉×#534	1	1	yes	characteristic
634	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
635	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
636	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
637	C₂²	C₁₉×#575	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	8	2	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	2	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₁₉×#546	1	2	yes	—
647	C₄	C₁₉×#551	1	2	yes	—
648	C₂	—	2	4	no	—
649	C₂	—	2	4	no	—
650	C₂	—	4	2	no	—
651	C₂	—	16	1	no	—
652	C₂	C₁₉×#2412	1	1	yes	characteristic
653	C₂	C₂×C₁₉×#466	1	1	yes	characteristic
654	C₂	C₁₉×#3056	1	1	yes	characteristic
655	C₂	C₂×C₁₉×#480	1	1	yes	characteristic
656	C₂	C₁₉×#3091	1	1	yes	characteristic
657	C₂	C₁₉×#3186	1	1	yes	characteristic
658	C₂	C₁₉×#3190	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×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. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
4. C₂×C₁₉×#380	C₂	semidirect
5. C₁₉×#2075	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1893	C₂	semidirect
8. C₁₉×#1874	C₂	semidirect
9. C₁₉×#1852	C₂	semidirect
10. C₁₉×#1823	C₂	semidirect
11. C₁₉×#1808	C₂	semidirect
22. C₂×C₁₉×#107	C₂²	semidirect
23. C₂×C₁₉×#107	C₂²	semidirect
24. C₂×C₁₉×#102	C₂²	semidirect
25. C₂×C₁₉×#102	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#340	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#340	C₂²	semidirect
97. C₁₉×C₂²⋊C₈	D₄	semidirect
190. #24550	C₁₉	direct (N × H)
273. C₂×#480	C₂×C₁₉	semidirect
274. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
276. C₂×#380	C₂×C₁₉	semidirect
277. #2075	C₂×C₁₉	semidirect
278. #2033	C₂×C₁₉	semidirect
279. #1893	C₂×C₁₉	semidirect
280. #1874	C₂×C₁₉	semidirect
281. #1852	C₂×C₁₉	semidirect
282. #1823	C₂×C₁₉	semidirect
283. #1808	C₂×C₁₉	semidirect
312. C₂²×C₁₉	#480	semidirect
340. C₂×#107	C₂²×C₁₉	semidirect
341. C₂×#107	C₂²×C₁₉	semidirect
342. C₂×#102	C₂²×C₁₉	semidirect
343. C₂×#102	C₂²×C₁₉	semidirect
359. #340	C₂²×C₁₉	semidirect
360. #340	C₂²×C₁₉	semidirect
361. #340	C₂²×C₁₉	semidirect
362. #340	C₂²×C₁₉	semidirect
426. C₂²⋊C₈	D₄×C₁₉	semidirect
432. C₁₉	#24550	direct (N × H)
630. C₂²	C₁₉×#480	semidirect

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
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#2847	2
C₂×C₁₉×#380	2
C₁₉×#2075	2
C₁₉×#2033	2
C₁₉×#1893	2
C₁₉×#1874	2
C₁₉×#1852	2
C₁₉×#1823	2
C₁₉×#1808	2
#24550	19

Subgroups — C19×#24550 #18030509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24550 #18030509