Subgroups — C₁₉×#24914 #18030873

Order 4864.

982 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2420	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1924	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×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#448	—	2	4	no	—
24	C₁₉×#440	—	2	4	no	—
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
39	C₁₉×#397	—	2	1	no	—
40	C₁₉×#394	—	2	1	no	—
41	C₁₉×#391	—	2	1	no	—
42	C₁₉×#391	—	2	1	no	—
43	C₁₉×#391	C₂²	1	1	yes	characteristic
44	C₁₉×#391	C₂²	1	1	yes	characteristic
45	C₁₉×#390	C₂²	1	1	yes	characteristic
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#386	—	2	1	no	—
48	C₁₉×#382	C₂²	1	1	yes	characteristic
49	C₁₉×#381	—	2	1	no	—
50	C₁₉×#380	—	2	1	no	—
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	—	2	2	no	—
62	C₂²×Q₈×C₁₉	—	2	2	no	—
63	C₂²×Q₈×C₁₉	—	2	1	no	—
64	C₂²×Q₈×C₁₉	—	2	2	no	—
65	C₂²×Q₈×C₁₉	—	2	2	no	—
66	C₂²×Q₈×C₁₉	—	4	1	no	—
67	C₂²×Q₈×C₁₉	—	4	1	no	—
68	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	2	2	no	—
77	C₂×SD₁₆×C₁₉	—	2	2	no	—
78	C₂×SD₁₆×C₁₉	—	2	2	no	—
79	C₂×SD₁₆×C₁₉	—	4	1	no	—
80	C₂×SD₁₆×C₁₉	D₄	1	4	yes	—
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	4	1	no	—
87	C₄×Q₈×C₁₉	—	2	2	no	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	4	1	no	—
90	C₄×Q₈×C₁₉	—	4	1	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	4	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#107	—	2	2	no	—
114	C₁₉×#106	—	4	1	no	—
115	C₁₉×C₄⋊C₈	—	4	1	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	4	1	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	4	1	no	—
124	C₁₉×C₂²⋊C₈	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	4	1	no	—
126	C₁₉×#97	—	2	2	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	D₄	1	1	yes	characteristic
137	C₁₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₁₉	—	2	1	no	—
139	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₉	—	2	4	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	4	2	no	—
150	C₂×Q₈×C₁₉	—	4	2	no	—
151	C₂×Q₈×C₁₉	—	4	4	no	—
152	C₂×Q₈×C₁₉	—	4	4	no	—
153	C₂×Q₈×C₁₉	—	4	4	no	—
154	C₂×Q₈×C₁₉	—	4	4	no	—
155	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₁₉	#41	1	2	yes	—
157	C₂×Q₈×C₁₉	#41	1	2	yes	—
158	C₂×Q₈×C₁₉	#41	1	2	yes	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂×D₄×C₁₉	—	4	2	no	—
166	C₂×D₄×C₁₉	—	8	1	no	—
167	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	4	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	4	2	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	4	2	no	—
185	C₂²×C₄×C₁₉	—	4	2	no	—
186	C₂²×C₄×C₁₉	—	8	1	no	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
193	SD₁₆×C₁₉	—	2	8	no	—
194	SD₁₆×C₁₉	—	4	4	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	4	2	no	—
218	C₄⋊C₄×C₁₉	—	4	2	no	—
219	C₄⋊C₄×C₁₉	—	8	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₉	—	4	2	no	—
223	C₂²⋊C₄×C₁₉	—	4	2	no	—
224	C₂²⋊C₄×C₁₉	—	4	2	no	—
225	C₂²⋊C₄×C₁₉	—	8	1	no	—
226	C₂²⋊C₄×C₁₉	—	8	1	no	—
227	C₂²⋊C₄×C₁₉	—	8	1	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	—	2	1	no	—
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	4	2	no	—
233	C₄²×C₁₉	—	4	2	no	—
234	#24914	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	#137	1	2	yes	—
249	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	Q₈×C₁₉	—	2	2	no	—
251	Q₈×C₁₉	—	2	2	no	—
252	Q₈×C₁₉	—	2	2	no	—
253	Q₈×C₁₉	—	2	2	no	—
254	Q₈×C₁₉	—	2	2	no	—
255	Q₈×C₁₉	—	4	8	no	—
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	#123	1	4	yes	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	—	2	2	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	8	4	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	4	8	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	8	4	no	—
306	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
312	C₈×C₁₉	—	2	2	no	—
313	C₈×C₁₉	—	4	1	no	—
314	C₈×C₁₉	—	4	1	no	—
315	C₈×C₁₉	—	4	1	no	—
316	C₂×#448	C₂×C₁₉	1	1	yes	characteristic
317	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#2420	C₂×C₁₉	1	1	yes	characteristic
319	Q₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2097	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2055	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#2034	C₂×C₁₉	1	1	yes	characteristic
324	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#1924	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
331	C₂²×C₁₉	—	2	2	no	—
332	C₂²×C₁₉	—	2	2	no	—
333	C₂²×C₁₉	—	2	2	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	1	no	—
336	C₂²×C₁₉	—	4	1	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	2	no	—
339	C₂²×C₁₉	—	4	2	no	—
340	C₂²×C₁₉	—	4	2	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	#525	1	1	yes	characteristic
346	C₂²×C₁₉	D₄²	1	1	yes	characteristic
347	C₂²×C₁₉	#546	1	1	yes	characteristic
348	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
349	C₂²×C₁₉	#575	1	1	yes	characteristic
350	C₂²×C₁₉	#577	1	1	yes	characteristic
351	C₂²×C₁₉	#577	1	1	yes	characteristic
352	C₄×C₁₉	—	2	4	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	2	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	8	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	—	8	1	no	—
363	C₄×C₁₉	—	8	1	no	—
364	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
365	C₄×C₁₉	#538	1	1	yes	characteristic
366	C₄×C₁₉	#546	1	1	yes	characteristic
367	C₄×C₁₉	#551	1	1	yes	characteristic
368	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
370	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
375	#448	—	2	4	no	—
376	#440	—	2	4	no	—
377	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
391	#397	—	2	1	no	—
392	#394	—	2	1	no	—
393	#391	—	2	1	no	—
394	#391	—	2	1	no	—
395	#391	C₂²×C₁₉	1	1	yes	characteristic
396	#391	C₂²×C₁₉	1	1	yes	characteristic
397	#390	C₂²×C₁₉	1	1	yes	characteristic
398	#389	C₂²×C₁₉	1	1	yes	characteristic
399	#386	—	2	1	no	—
400	#382	C₂²×C₁₉	1	1	yes	characteristic
401	#381	—	2	1	no	—
402	#380	—	2	1	no	—
403	#380	C₂²×C₁₉	1	1	yes	characteristic
404	#380	C₂²×C₁₉	1	1	yes	characteristic
405	C₄×C₂²⋊C₄	—	2	1	no	—
406	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
407	#340	C₂²×C₁₉	1	1	yes	characteristic
408	#340	C₂²×C₁₉	1	1	yes	characteristic
409	#340	C₂²×C₁₉	1	1	yes	characteristic
410	#340	C₂²×C₁₉	1	1	yes	characteristic
411	#336	C₂²×C₁₉	1	1	yes	characteristic
412	#336	C₂²×C₁₉	1	1	yes	characteristic
413	C₂×C₁₉	—	4	2	no	—
414	C₂×C₁₉	—	8	2	no	—
415	C₂×C₁₉	#2418	1	1	yes	characteristic
416	C₂×C₁₉	#3117	1	1	yes	characteristic
417	C₂×C₁₉	#3126	1	1	yes	characteristic
418	C₂×C₁₉	#3266	1	1	yes	characteristic
419	C₂×C₁₉	#3275	1	1	yes	characteristic
420	C₂×C₁₉	#3320	1	1	yes	characteristic
421	C₂×C₁₉	#3321	1	1	yes	characteristic
422	C₂²×Q₈	—	2	2	no	—
423	C₂²×Q₈	—	2	2	no	—
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	—	2	2	no	—
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	4	1	no	—
428	C₂²×Q₈	—	4	1	no	—
429	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×SD₁₆	—	2	2	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	2	2	no	—
439	C₂×SD₁₆	—	2	2	no	—
440	C₂×SD₁₆	—	4	1	no	—
441	C₂×SD₁₆	D₄×C₁₉	1	4	yes	—
442	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	#121	—	2	2	no	—
447	#121	—	4	1	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	—	4	1	no	—
451	C₄×Q₈	—	4	1	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	4	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
474	#107	—	2	2	no	—
475	#106	—	4	1	no	—
476	C₄⋊C₈	—	4	1	no	—
477	#103	—	2	2	no	—
478	#103	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	4	1	no	—
483	#102	—	2	2	no	—
484	#102	—	4	1	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	—	4	1	no	—
487	#97	—	2	2	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	D₄×C₁₉	1	1	yes	characteristic
498	#95	D₄×C₁₉	1	1	yes	characteristic
499	C₁₉	#24914	1	1	yes	characteristic, direct product factor, Sylow
500	C₂⁴	—	2	1	no	—
501	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	—	4	4	no	—
515	C₂×Q₈	—	4	4	no	—
516	C₂×Q₈	—	4	4	no	—
517	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
518	C₂×Q₈	#41×C₁₉	1	2	yes	—
519	C₂×Q₈	#41×C₁₉	1	2	yes	—
520	C₂×Q₈	#41×C₁₉	1	2	yes	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	8	1	no	—
529	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	8	1	no	—
549	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
555	SD₁₆	—	2	8	no	—
556	SD₁₆	—	4	4	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	8	1	no	—
588	C₂²⋊C₄	—	8	1	no	—
589	C₂²⋊C₄	—	8	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	4	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	C₁₉×#137	1	2	yes	—
610	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
611	Q₈	—	2	2	no	—
612	Q₈	—	2	2	no	—
613	Q₈	—	2	2	no	—
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	4	8	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	C₁₉×#123	1	4	yes	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	8	4	no	—
667	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
668	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
669	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
670	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
671	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₁₉×#525	1	1	yes	characteristic
692	C₂²	D₄²×C₁₉	1	1	yes	characteristic
693	C₂²	C₁₉×#546	1	1	yes	characteristic
694	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
695	C₂²	C₁₉×#575	1	1	yes	characteristic
696	C₂²	C₁₉×#577	1	1	yes	characteristic
697	C₂²	C₁₉×#577	1	1	yes	characteristic
698	C₄	—	2	4	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
711	C₄	C₁₉×#538	1	1	yes	characteristic
712	C₄	C₁₉×#546	1	1	yes	characteristic
713	C₄	C₁₉×#551	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₁₉×#2418	1	1	yes	characteristic
717	C₂	C₁₉×#3117	1	1	yes	characteristic
718	C₂	C₁₉×#3126	1	1	yes	characteristic
719	C₂	C₁₉×#3266	1	1	yes	characteristic
720	C₂	C₁₉×#3275	1	1	yes	characteristic
721	C₂	C₁₉×#3320	1	1	yes	characteristic
722	C₂	C₁₉×#3321	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 ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#440	C₂	semidirect
4. Q₈×C₂²⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#2097	C₂	semidirect
6. C₁₉×#2076	C₂	semidirect
7. C₁₉×#2055	C₂	semidirect
9. C₁₉×#1935	C₂	semidirect
10. C₁₉×#1924	C₂	semidirect
11. C₁₉×#1880	C₂	semidirect
12. C₁₉×#1877	C₂	semidirect
13. C₁₉×#1865	C₂	semidirect
14. C₁₉×#1805	C₂	semidirect
15. C₁₉×#1787	C₂	semidirect
234. #24914	C₁₉	direct (N × H)
317. C₂×#440	C₂×C₁₉	semidirect
319. Q₈×C₂²⋊C₄	C₂×C₁₉	semidirect
320. #2097	C₂×C₁₉	semidirect
321. #2076	C₂×C₁₉	semidirect
322. #2055	C₂×C₁₉	semidirect
324. #1935	C₂×C₁₉	semidirect
325. #1924	C₂×C₁₉	semidirect
326. #1880	C₂×C₁₉	semidirect
327. #1877	C₂×C₁₉	semidirect
328. #1865	C₂×C₁₉	semidirect
329. #1805	C₂×C₁₉	semidirect
330. #1787	C₂×C₁₉	semidirect
499. C₁₉	#24914	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×#448	2
C₂×C₁₉×#440	2
C₁₉×#2420	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2097	2
C₁₉×#2076	2
C₁₉×#2055	2
C₁₉×#2034	2
C₁₉×#1935	2
C₁₉×#1924	2
C₁₉×#1880	2
C₁₉×#1877	2
C₁₉×#1865	2
C₁₉×#1805	2
C₁₉×#1787	2
#24914	19

Subgroups — C19×#24914 #18030873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24914 #18030873