Subgroups — C₁₉×#26174 #18032133

Order 4864.

1016 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#123	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₁₉×#459	—	2	4	no	—
26	C₁₉×#442	—	2	4	no	—
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×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	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×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
39	C₁₉×#394	—	2	1	no	—
40	C₁₉×#394	—	2	1	no	—
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#390	C₂²	1	1	yes	characteristic
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×#386	—	2	1	no	—
48	C₁₉×#385	—	2	1	no	—
49	C₁₉×#385	—	2	1	no	—
50	C₁₉×#384	C₂²	1	1	yes	characteristic
51	C₁₉×#380	—	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×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	—	2	2	no	—
71	C₂×D₈×C₁₉	—	2	2	no	—
72	C₂×D₈×C₁₉	—	2	2	no	—
73	C₂×D₈×C₁₉	—	2	2	no	—
74	C₂×D₈×C₁₉	—	2	2	no	—
75	C₂×D₈×C₁₉	D₄	1	4	yes	—
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#127	—	2	2	no	—
81	C₁₉×#127	—	4	1	no	—
82	C₁₉×#123	—	4	4	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	4	1	no	—
89	C₄×D₄×C₁₉	—	4	1	no	—
90	C₄×D₄×C₁₉	—	4	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	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	—	4	4	no	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#106	—	2	2	no	—
118	C₁₉×#106	—	4	1	no	—
119	C₁₉×C₄⋊C₈	—	2	2	no	—
120	C₁₉×#102	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	2	2	no	—
127	C₁₉×#102	—	4	1	no	—
128	C₁₉×#97	—	2	2	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	D₄	1	1	yes	characteristic
133	C₁₉×#95	D₄	1	1	yes	characteristic
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂⁴×C₁₉	—	2	1	no	—
136	C₂⁴×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	8	1	no	—
156	C₂×D₄×C₁₉	—	8	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₉	#41	1	2	yes	—
160	C₂×D₄×C₁₉	#41	1	2	yes	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	4	2	no	—
172	C₂²×C₄×C₁₉	—	4	2	no	—
173	C₂²×C₄×C₁₉	—	4	2	no	—
174	C₂²×C₄×C₁₉	—	4	2	no	—
175	C₂²×C₄×C₁₉	—	8	1	no	—
176	C₂²×C₄×C₁₉	—	8	1	no	—
177	C₂²×C₄×C₁₉	—	8	1	no	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	D₈×C₁₉	—	2	8	no	—
186	D₈×C₁₉	—	4	4	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
211	C₄⋊C₄×C₁₉	—	4	2	no	—
212	C₄⋊C₄×C₁₉	—	4	2	no	—
213	C₄⋊C₄×C₁₉	—	4	2	no	—
214	C₄⋊C₄×C₁₉	—	8	1	no	—
215	C₄⋊C₄×C₁₉	#41	1	2	yes	—
216	C₂²⋊C₄×C₁₉	—	2	4	no	—
217	C₂²⋊C₄×C₁₉	—	4	2	no	—
218	C₂²⋊C₄×C₁₉	—	4	2	no	—
219	C₂²⋊C₄×C₁₉	—	4	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	2	no	—
221	C₂²⋊C₄×C₁₉	—	4	2	no	—
222	C₂²⋊C₄×C₁₉	—	4	2	no	—
223	C₂²⋊C₄×C₁₉	—	8	1	no	—
224	C₂²⋊C₄×C₁₉	—	8	1	no	—
225	C₂²⋊C₄×C₁₉	—	8	1	no	—
226	C₄²×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	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	#26174	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	2	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	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	—	4	1	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	4	1	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	D₄×C₁₉	—	2	2	no	—
256	D₄×C₁₉	—	2	2	no	—
257	D₄×C₁₉	—	2	2	no	—
258	D₄×C₁₉	—	2	2	no	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	8	4	no	—
267	D₄×C₁₉	—	8	4	no	—
268	D₄×C₁₉	#123	1	4	yes	complemented
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	2	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	—	2	1	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	4	8	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	—	8	4	no	—
302	C₂×C₄×C₁₉	—	8	4	no	—
303	C₂×C₄×C₁₉	—	8	4	no	—
304	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
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	2₋¹⁺⁴	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×#459	C₂×C₁₉	1	1	yes	characteristic
317	C₂×#442	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#2445	C₂×C₁₉	1	1	yes	characteristic, complemented
319	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#2094	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#2088	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
331	C₂²×C₁₉	—	2	4	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	4	2	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	4	2	no	—
337	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
346	C₂²×C₁₉	—	8	1	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	—	8	1	no	—
349	C₂²×C₁₉	—	8	1	no	—
350	C₂²×C₁₉	—	8	1	no	—
351	C₂²×C₁₉	—	8	1	no	—
352	C₂²×C₁₉	#525	1	1	yes	characteristic
353	C₂²×C₁₉	D₄²	1	1	yes	characteristic
354	C₂²×C₁₉	#548	1	1	yes	characteristic
355	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₁₉	#576	1	1	yes	characteristic
358	C₂²×C₁₉	#577	1	1	yes	characteristic
359	C₄×C₁₉	—	2	2	no	—
360	C₄×C₁₉	—	2	2	no	—
361	C₄×C₁₉	—	4	2	no	—
362	C₄×C₁₉	—	4	1	no	—
363	C₄×C₁₉	—	4	1	no	—
364	C₄×C₁₉	—	4	1	no	—
365	C₄×C₁₉	—	4	1	no	—
366	C₄×C₁₉	—	8	1	no	—
367	C₄×C₁₉	—	8	1	no	—
368	C₄×C₁₉	—	8	1	no	—
369	C₄×C₁₉	—	8	1	no	—
370	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
371	C₄×C₁₉	#539	1	1	yes	characteristic
372	C₄×C₁₉	#547	1	1	yes	characteristic
373	C₄×C₁₉	#553	1	1	yes	characteristic
374	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
375	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#123	—	2	1	no	—
378	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	—	2	1	no	—
383	#459	—	2	4	no	—
384	#442	—	2	4	no	—
385	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
397	#394	—	2	1	no	—
398	#394	—	2	1	no	—
399	#390	C₂²×C₁₉	1	1	yes	characteristic
400	#390	C₂²×C₁₉	1	1	yes	characteristic
401	#390	C₂²×C₁₉	1	1	yes	characteristic
402	#389	C₂²×C₁₉	1	1	yes	characteristic
403	#389	C₂²×C₁₉	1	1	yes	characteristic
404	#389	C₂²×C₁₉	1	1	yes	characteristic
405	#386	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#384	C₂²×C₁₉	1	1	yes	characteristic
409	#380	—	2	1	no	—
410	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
411	#340	C₂²×C₁₉	1	1	yes	characteristic
412	#340	C₂²×C₁₉	1	1	yes	characteristic
413	#340	C₂²×C₁₉	1	1	yes	characteristic
414	#340	C₂²×C₁₉	1	1	yes	characteristic
415	#336	C₂²×C₁₉	1	1	yes	characteristic
416	#336	C₂²×C₁₉	1	1	yes	characteristic
417	#336	C₂²×C₁₉	1	1	yes	characteristic
418	#336	C₂²×C₁₉	1	1	yes	characteristic
419	C₂×C₁₉	—	4	4	no	—
420	C₂×C₁₉	—	8	2	no	—
421	C₂×C₁₉	—	16	1	no	—
422	C₂×C₁₉	#2443	1	1	yes	characteristic
423	C₂×C₁₉	#3109	1	1	yes	characteristic
424	C₂×C₁₉	#3119	1	1	yes	characteristic
425	C₂×C₁₉	#3264	1	1	yes	characteristic
426	C₂×C₁₉	#3272	1	1	yes	characteristic
427	C₂×C₁₉	#3366	1	1	yes	characteristic
428	C₂×C₁₉	#3373	1	1	yes	characteristic
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂×D₈	—	2	2	no	—
439	C₂×D₈	—	2	2	no	—
440	C₂×D₈	—	2	2	no	—
441	C₂×D₈	—	2	2	no	—
442	C₂×D₈	—	2	2	no	—
443	C₂×D₈	D₄×C₁₉	1	4	yes	—
444	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	#127	—	2	2	no	—
449	#127	—	4	1	no	—
450	#123	—	4	4	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	4	1	no	—
457	C₄×D₄	—	4	1	no	—
458	C₄×D₄	—	4	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	4	4	no	—
465	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
485	#106	—	2	2	no	—
486	#106	—	4	1	no	—
487	C₄⋊C₈	—	2	2	no	—
488	#102	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	2	2	no	—
492	#102	—	2	2	no	—
493	#102	—	2	2	no	—
494	#102	—	2	2	no	—
495	#102	—	4	1	no	—
496	#97	—	2	2	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	D₄×C₁₉	1	1	yes	characteristic
501	#95	D₄×C₁₉	1	1	yes	characteristic
502	C₁₉	#26174	1	1	yes	characteristic, direct product factor, Sylow
503	C₂⁴	—	2	1	no	—
504	C₂⁴	—	2	1	no	—
505	C₂⁴	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	—	8	1	no	—
526	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
528	C₂×D₄	#41×C₁₉	1	2	yes	—
529	C₂×D₄	#41×C₁₉	1	2	yes	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	1	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	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂⁴×C₁₉	1	1	yes	characteristic
554	D₈	—	2	8	no	—
555	D₈	—	4	4	no	—
556	C₂×C₈	—	2	1	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	C₂×D₄×C₁₉	1	2	yes	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	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	—	4	2	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	8	1	no	—
584	C₄⋊C₄	#41×C₁₉	1	2	yes	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	8	1	no	—
593	C₂²⋊C₄	—	8	1	no	—
594	C₂²⋊C₄	—	8	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
623	D₄	—	2	2	no	—
624	D₄	—	2	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	8	4	no	—
635	D₄	—	8	4	no	—
636	D₄	C₁₉×#123	1	4	yes	complemented
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	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	4	8	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	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	8	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	8	4	no	—
672	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
673	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
675	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
676	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
678	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	C₁₉×#525	1	1	yes	characteristic
706	C₂²	D₄²×C₁₉	1	1	yes	characteristic
707	C₂²	C₁₉×#548	1	1	yes	characteristic
708	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
709	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
710	C₂²	C₁₉×#576	1	1	yes	characteristic
711	C₂²	C₁₉×#577	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
724	C₄	C₁₉×#539	1	1	yes	characteristic
725	C₄	C₁₉×#547	1	1	yes	characteristic
726	C₄	C₁₉×#553	1	1	yes	characteristic
727	C₂	—	4	4	no	—
728	C₂	—	8	2	no	—
729	C₂	—	16	1	no	—
730	C₂	C₁₉×#2443	1	1	yes	characteristic
731	C₂	C₁₉×#3109	1	1	yes	characteristic
732	C₂	C₁₉×#3119	1	1	yes	characteristic
733	C₂	C₁₉×#3264	1	1	yes	characteristic
734	C₂	C₁₉×#3272	1	1	yes	characteristic
735	C₂	C₁₉×#3366	1	1	yes	characteristic
736	C₂	C₁₉×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#459	C₂
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
2. C₂×C₁₉×#442	C₂	semidirect
3. C₁₉×#2445	C₂	semidirect
4. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#2094	C₂	semidirect
6. C₁₉×#2088	C₂	semidirect
7. C₁₉×#2071	C₂	semidirect
8. C₁₉×#2041	C₂	semidirect
9. C₁₉×#1936	C₂	semidirect
10. C₁₉×#1917	C₂	semidirect
11. C₁₉×#1879	C₂	semidirect
12. C₁₉×#1879	C₂	semidirect
13. C₁₉×#1879	C₂	semidirect
14. C₁₉×#1864	C₂	semidirect
15. C₁₉×#1864	C₂	semidirect
232. #26174	C₁₉	direct (N × H)
268. D₄×C₁₉	#123	semidirect
317. C₂×#442	C₂×C₁₉	semidirect
318. #2445	C₂×C₁₉	semidirect
319. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
320. #2094	C₂×C₁₉	semidirect
321. #2088	C₂×C₁₉	semidirect
322. #2071	C₂×C₁₉	semidirect
323. #2041	C₂×C₁₉	semidirect
324. #1936	C₂×C₁₉	semidirect
325. #1917	C₂×C₁₉	semidirect
326. #1879	C₂×C₁₉	semidirect
327. #1879	C₂×C₁₉	semidirect
328. #1879	C₂×C₁₉	semidirect
329. #1864	C₂×C₁₉	semidirect
330. #1864	C₂×C₁₉	semidirect
502. C₁₉	#26174	direct (N × H)
636. D₄	C₁₉×#123	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#459	2
C₂×C₁₉×#442	2
C₁₉×#2445	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2094	2
C₁₉×#2088	2
C₁₉×#2071	2
C₁₉×#2041	2
C₁₉×#1936	2
C₁₉×#1917	2
C₁₉×#1879	2
C₁₉×#1864	2
#26174	19

Subgroups — C19×#26174 #18032133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26174 #18032133