Subgroups — C₁₉×#26389 #18032348

Order 4864.

790 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2451	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2096	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1943	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	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	C₁₉×#475	—	2	4	no	—
23	C₁₉×#441	—	2	4	no	—
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
37	C₁₉×#398	—	2	1	no	—
38	C₁₉×#395	—	2	1	no	—
39	C₁₉×#391	—	2	1	no	—
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#389	—	2	1	no	—
43	C₁₉×#389	—	2	1	no	—
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#389	C₂²	1	1	yes	characteristic
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#384	—	2	1	no	—
50	C₁₉×#384	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₄×C₄⋊C₄×C₁₉	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	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	—	2	1	no	—
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	—	2	2	no	—
65	C₂×Q₁₆×C₁₉	—	2	2	no	—
66	C₂×Q₁₆×C₁₉	Q₈	1	4	yes	complemented
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	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	—	4	1	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	4	1	no	—
79	C₄×Q₈×C₁₉	—	4	1	no	—
80	C₄×Q₈×C₁₉	—	4	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	2	no	—
108	C₁₉×#106	—	2	2	no	—
109	C₁₉×#106	—	2	2	no	—
110	C₁₉×#106	—	2	2	no	—
111	C₁₉×#106	—	4	1	no	—
112	C₁₉×C₄⋊C₈	—	2	2	no	—
113	C₁₉×#103	—	2	2	no	—
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	4	1	no	—
118	C₁₉×#103	D₄	1	4	yes	—
119	C₁₉×#97	—	2	2	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	D₄	1	1	yes	characteristic
129	C₁₉×#95	D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	4	2	no	—
139	C₂×Q₈×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	8	1	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
144	C₂×Q₈×C₁₉	#41	1	2	yes	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₁₉	—	2	8	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	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	2	no	—
188	C₄⋊C₄×C₁₉	—	4	2	no	—
189	C₄⋊C₄×C₁₉	—	4	2	no	—
190	C₄⋊C₄×C₁₉	—	4	2	no	—
191	C₄⋊C₄×C₁₉	—	8	1	no	—
192	C₄⋊C₄×C₁₉	—	8	1	no	—
193	C₄⋊C₄×C₁₉	—	8	1	no	—
194	C₄⋊C₄×C₁₉	—	8	1	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	#41	1	2	yes	—
198	C₄²×C₁₉	—	2	4	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	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	4	2	no	—
206	C₄²×C₁₉	—	4	2	no	—
207	C₄²×C₁₉	—	4	2	no	—
208	#26389	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₉	—	2	2	no	—
211	Q₈×C₁₉	—	2	2	no	—
212	Q₈×C₁₉	—	2	2	no	—
213	Q₈×C₁₉	—	2	2	no	—
214	Q₈×C₁₉	—	2	2	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	8	4	no	—
218	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	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	2	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	2	no	—
232	C₂×C₄×C₁₉	—	2	2	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	—	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	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	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	1	no	—
259	C₂×C₄×C₁₉	#137	1	2	yes	—
260	C₂×C₄×C₁₉	#137	1	2	yes	—
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	2	2	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	C₂×#475	C₂×C₁₉	1	1	yes	characteristic
272	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
273	#2451	C₂×C₁₉	1	1	yes	characteristic
274	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
275	#2096	C₂×C₁₉	1	1	yes	characteristic
276	#2084	C₂×C₁₉	1	1	yes	characteristic
277	#2068	C₂×C₁₉	1	1	yes	characteristic
278	#2058	C₂×C₁₉	1	1	yes	characteristic
279	#1943	C₂×C₁₉	1	1	yes	characteristic
280	#1917	C₂×C₁₉	1	1	yes	characteristic
281	#1878	C₂×C₁₉	1	1	yes	characteristic
282	#1878	C₂×C₁₉	1	1	yes	characteristic
283	#1865	C₂×C₁₉	1	1	yes	characteristic
284	#1865	C₂×C₁₉	1	1	yes	characteristic
285	#1863	C₂×C₁₉	1	1	yes	characteristic
286	C₂²×C₁₉	#525	1	1	yes	characteristic
287	C₂²×C₁₉	D₄²	1	1	yes	characteristic
288	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
291	C₂²×C₁₉	#577	1	1	yes	characteristic
292	C₂²×C₁₉	#577	1	1	yes	characteristic
293	C₄×C₁₉	—	2	2	no	—
294	C₄×C₁₉	—	2	4	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
308	C₄×C₁₉	#539	1	1	yes	characteristic
309	C₄×C₁₉	#547	1	1	yes	characteristic
310	C₄×C₁₉	#554	1	1	yes	characteristic
311	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	#475	—	2	4	no	—
318	#441	—	2	4	no	—
319	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
332	#398	—	2	1	no	—
333	#395	—	2	1	no	—
334	#391	—	2	1	no	—
335	#391	C₂²×C₁₉	1	1	yes	characteristic
336	#391	C₂²×C₁₉	1	1	yes	characteristic
337	#389	—	2	1	no	—
338	#389	—	2	1	no	—
339	#389	C₂²×C₁₉	1	1	yes	characteristic
340	#389	C₂²×C₁₉	1	1	yes	characteristic
341	#389	C₂²×C₁₉	1	1	yes	characteristic
342	#389	C₂²×C₁₉	1	1	yes	characteristic
343	#387	—	2	1	no	—
344	#384	—	2	1	no	—
345	#384	C₂²×C₁₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	—	2	1	no	—
347	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#340	C₂²×C₁₉	1	1	yes	characteristic
350	#340	C₂²×C₁₉	1	1	yes	characteristic
351	#340	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	C₂×C₁₉	#2449	1	1	yes	characteristic
357	C₂×C₁₉	#3113	1	1	yes	characteristic
358	C₂×C₁₉	#3125	1	1	yes	characteristic
359	C₂×C₁₉	#3266	1	1	yes	characteristic
360	C₂×C₁₉	#3278	1	1	yes	characteristic
361	C₂×C₁₉	#3387	1	1	yes	characteristic
362	C₂×C₁₉	#3387	1	1	yes	characteristic
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×Q₁₆	Q₈×C₁₉	1	4	yes	complemented
369	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	—	4	1	no	—
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	4	1	no	—
381	C₄×Q₈	—	4	1	no	—
382	C₄×Q₈	—	4	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
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	#107	—	2	2	no	—
410	#106	—	2	2	no	—
411	#106	—	2	2	no	—
412	#106	—	2	2	no	—
413	#106	—	4	1	no	—
414	C₄⋊C₈	—	2	2	no	—
415	#103	—	2	2	no	—
416	#103	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	—	2	2	no	—
419	#103	—	4	1	no	—
420	#103	D₄×C₁₉	1	4	yes	—
421	#97	—	2	2	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	D₄×C₁₉	1	1	yes	characteristic
431	#95	D₄×C₁₉	1	1	yes	characteristic
432	C₁₉	#26389	1	1	yes	characteristic, direct product factor, Sylow
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	4	2	no	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	—	8	1	no	—
444	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
445	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
446	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
447	C₂×Q₈	#41×C₁₉	1	2	yes	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
463	Q₁₆	—	2	8	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	C₂×D₄×C₁₉	1	2	yes	—
475	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	8	1	no	—
495	C₄⋊C₄	—	8	1	no	—
496	C₄⋊C₄	—	8	1	no	—
497	C₄⋊C₄	—	8	1	no	—
498	C₄⋊C₄	—	8	1	no	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₄⋊C₄	#41×C₁₉	1	2	yes	—
501	C₄²	—	2	4	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	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	—	4	2	no	—
511	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	8	4	no	—
520	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	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	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	C₁₉×#137	1	2	yes	—
562	C₂×C₄	C₁₉×#137	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₂²	C₁₉×#525	1	1	yes	characteristic
574	C₂²	D₄²×C₁₉	1	1	yes	characteristic
575	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
576	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
577	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
578	C₂²	C₁₉×#577	1	1	yes	characteristic
579	C₂²	C₁₉×#577	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
595	C₄	C₁₉×#539	1	1	yes	characteristic
596	C₄	C₁₉×#547	1	1	yes	characteristic
597	C₄	C₁₉×#554	1	1	yes	characteristic
598	C₂	C₁₉×#2449	1	1	yes	characteristic
599	C₂	C₁₉×#3113	1	1	yes	characteristic
600	C₂	C₁₉×#3125	1	1	yes	characteristic
601	C₂	C₁₉×#3266	1	1	yes	characteristic
602	C₂	C₁₉×#3278	1	1	yes	characteristic
603	C₂	C₁₉×#3387	1	1	yes	characteristic
604	C₂	C₁₉×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
66. C₂×Q₁₆×C₁₉	Q₈	semidirect
208. #26389	C₁₉	direct (N × H)
368. C₂×Q₁₆	Q₈×C₁₉	semidirect
432. C₁₉	#26389	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×#475	2
C₂×C₁₉×#441	2
C₁₉×#2451	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2096	2
C₁₉×#2084	2
C₁₉×#2068	2
C₁₉×#2058	2
C₁₉×#1943	2
C₁₉×#1917	2
C₁₉×#1878	2
C₁₉×#1865	2
C₁₉×#1863	2
#26389	19

Subgroups — C19×#26389 #18032348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26389 #18032348