Subgroups — C₁₉×#24867 #18030826

Order 4864.

1042 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2409	C₂	1	1	yes	maximal, characteristic
4	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1808	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	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#484	—	2	4	no	—
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	—	2	4	no	—
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×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₉×#395	—	2	1	no	—
42	C₁₉×#393	—	2	1	no	—
43	C₁₉×#391	C₂²	1	1	yes	characteristic
44	C₁₉×#391	C₂²	1	1	yes	characteristic
45	C₁₉×#389	—	2	1	no	—
46	C₁₉×#386	—	2	1	no	—
47	C₁₉×#385	—	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	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₁₉×#380	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊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	1	no	—
62	C₂²×Q₈×C₁₉	—	2	2	no	—
63	C₂²×Q₈×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	—	2	1	no	—
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	—	2	2	no	—
77	C₂²×C₈×C₁₉	—	2	2	no	—
78	C₂²×C₈×C₁₉	—	4	1	no	—
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	4	1	no	—
86	C₁₉×C₂²⋊Q₈	—	4	1	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	4	4	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₁₉×#107	—	2	2	no	—
117	C₁₉×#107	—	2	2	no	—
118	C₁₉×#107	—	4	1	no	—
119	C₁₉×#107	—	4	1	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#103	—	2	2	no	—
125	C₁₉×#103	—	4	1	no	—
126	C₁₉×#103	—	4	1	no	—
127	C₁₉×#103	D₄	1	4	yes	complemented
128	C₁₉×C₂²⋊C₈	—	2	2	no	—
129	C₁₉×C₂²⋊C₈	—	2	2	no	—
130	C₁₉×C₂²⋊C₈	—	4	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	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₁₉×#95	—	2	1	no	—
139	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	8	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	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	4	4	no	—
155	C₂×Q₈×C₁₉	—	4	4	no	—
156	C₂×Q₈×C₁₉	—	4	4	no	—
157	C₂×Q₈×C₁₉	—	4	2	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×Q₈×C₁₉	#41	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	Q₁₆	1	4	yes	—
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	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	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	—	4	2	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	—	4	2	no	—
187	C₂²×C₄×C₁₉	—	4	2	no	—
188	C₂²×C₄×C₁₉	—	8	1	no	—
189	C₂²×C₄×C₁₉	—	8	1	no	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	#41	1	2	yes	—
195	C₂²×C₄×C₁₉	#41	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	4	4	no	—
209	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	2	1	no	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	4	2	no	—
223	C₄⋊C₄×C₁₉	—	4	2	no	—
224	C₄⋊C₄×C₁₉	—	4	2	no	—
225	C₄⋊C₄×C₁₉	—	4	2	no	—
226	C₄⋊C₄×C₁₉	—	4	2	no	—
227	C₄⋊C₄×C₁₉	—	8	1	no	—
228	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
229	C₂²⋊C₄×C₁₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	4	2	no	—
232	C₂²⋊C₄×C₁₉	—	4	2	no	—
233	C₂²⋊C₄×C₁₉	—	4	2	no	—
234	C₂²⋊C₄×C₁₉	—	4	2	no	—
235	C₂²⋊C₄×C₁₉	—	4	2	no	—
236	C₄²×C₁₉	—	2	1	no	—
237	C₄²×C₁₉	—	2	1	no	—
238	C₄²×C₁₉	—	4	2	no	—
239	#24867	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	1	no	—
247	C₂³×C₁₉	—	2	1	no	—
248	C₂³×C₁₉	—	2	1	no	—
249	C₂³×C₁₉	—	2	1	no	—
250	C₂³×C₁₉	#123	1	2	yes	—
251	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
252	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
253	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
254	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₉	—	2	2	no	—
256	Q₈×C₁₉	—	2	2	no	—
257	Q₈×C₁₉	—	2	2	no	—
258	Q₈×C₁₉	—	2	2	no	—
259	Q₈×C₁₉	—	4	8	no	—
260	Q₈×C₁₉	—	4	1	no	—
261	Q₈×C₁₉	—	4	1	no	—
262	Q₈×C₁₉	—	4	1	no	—
263	Q₈×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	2	8	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	2	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	—	4	8	no	—
283	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	8	4	no	—
309	C₂×C₄×C₁₉	—	8	4	no	—
310	C₂×C₄×C₁₉	#123	1	2	yes	—
311	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
312	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
318	C₈×C₁₉	—	2	2	no	—
319	C₈×C₁₉	—	4	1	no	—
320	C₈×C₁₉	—	4	1	no	—
321	C₈×C₁₉	—	4	1	no	—
322	C₂×#484	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2409	C₂×C₁₉	1	1	yes	characteristic
325	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
326	#2095	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2072	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#2036	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1869	C₂×C₁₉	1	1	yes	characteristic
334	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
336	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	2	2	no	—
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	2	2	no	—
343	C₂²×C₁₉	—	2	2	no	—
344	C₂²×C₁₉	—	2	2	no	—
345	C₂²×C₁₉	—	2	2	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	1	no	—
349	C₂²×C₁₉	—	4	1	no	—
350	C₂²×C₁₉	#484	1	4	yes	complemented
351	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
352	C₂²×C₁₉	D₄²	1	1	yes	characteristic
353	C₂²×C₁₉	#546	1	1	yes	characteristic
354	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
355	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₁₉	#577	1	1	yes	characteristic
357	C₂²×C₁₉	#578	1	1	yes	characteristic
358	C₄×C₁₉	—	2	2	no	—
359	C₄×C₁₉	—	2	2	no	—
360	C₄×C₁₉	—	4	1	no	—
361	C₄×C₁₉	—	4	1	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	—	4	2	no	—
364	C₄×C₁₉	—	4	2	no	—
365	C₄×C₁₉	—	8	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	#525	1	1	yes	characteristic
371	C₄×C₁₉	#538	1	1	yes	characteristic
372	C₄×C₁₉	#546	1	1	yes	characteristic
373	C₄×C₁₉	#551	1	1	yes	characteristic
374	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
375	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₄×D₄	—	2	1	no	—
379	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
380	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
381	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
382	#484	—	2	4	no	—
383	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#103	—	2	4	no	—
388	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
394	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
399	#395	—	2	1	no	—
400	#393	—	2	1	no	—
401	#391	C₂²×C₁₉	1	1	yes	characteristic
402	#391	C₂²×C₁₉	1	1	yes	characteristic
403	#389	—	2	1	no	—
404	#386	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#384	C₂²×C₁₉	1	1	yes	characteristic
409	#380	C₂²×C₁₉	1	1	yes	characteristic
410	#380	C₂²×C₁₉	1	1	yes	characteristic
411	#380	C₂²×C₁₉	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
413	#340	C₂²×C₁₉	1	1	yes	characteristic
414	#340	C₂²×C₁₉	1	1	yes	characteristic
415	#340	C₂²×C₁₉	1	1	yes	characteristic
416	#340	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	—	2	4	no	—
420	C₂×C₁₉	—	4	2	no	—
421	C₂×C₁₉	#2418	1	1	yes	characteristic
422	C₂×C₁₉	C₂×#484	1	1	yes	characteristic
423	C₂×C₁₉	#3097	1	1	yes	characteristic
424	C₂×C₁₉	#3265	1	1	yes	characteristic
425	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
426	C₂×C₁₉	#3299	1	1	yes	characteristic
427	C₂×C₁₉	#3308	1	1	yes	characteristic
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	2	no	—
430	C₂²×Q₈	—	2	2	no	—
431	C₂²×Q₈	—	2	2	no	—
432	C₂²×Q₈	—	2	2	no	—
433	C₂²×Q₈	—	4	1	no	—
434	C₂²×Q₈	—	4	1	no	—
435	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	—	2	1	no	—
441	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
443	C₂²×C₈	—	2	2	no	—
444	C₂²×C₈	—	2	2	no	—
445	C₂²×C₈	—	4	1	no	—
446	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	4	1	no	—
453	C₂²⋊Q₈	—	4	1	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	4	4	no	—
457	C₂×C₄⋊C₄	—	2	2	no	—
458	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
465	C₂×C₄⋊C₄	—	4	1	no	—
466	C₂×C₄⋊C₄	—	4	1	no	—
467	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	D₄×C₁₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
483	#107	—	2	2	no	—
484	#107	—	2	2	no	—
485	#107	—	4	1	no	—
486	#107	—	4	1	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#103	—	2	2	no	—
490	#103	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	4	1	no	—
493	#103	—	4	1	no	—
494	#103	D₄×C₁₉	1	4	yes	complemented
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	—	2	2	no	—
497	C₂²⋊C₈	—	4	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	C₁₉	#24867	1	1	yes	characteristic, direct product factor, Sylow
507	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	8	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	4	2	no	—
521	C₂×Q₈	—	4	2	no	—
522	C₂×Q₈	—	4	4	no	—
523	C₂×Q₈	—	4	4	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
527	C₂×Q₈	#41×C₁₉	1	2	yes	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	Q₁₆×C₁₉	1	4	yes	—
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	—	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	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	8	1	no	—
557	C₂²×C₄	—	8	1	no	—
558	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₂²×C₄	#41×C₁₉	1	2	yes	—
563	C₂²×C₄	#41×C₁₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	4	4	no	—
577	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	8	1	no	—
596	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	4	2	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	C₁₉×#123	1	2	yes	—
618	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
619	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
620	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
621	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
622	Q₈	—	2	2	no	—
623	Q₈	—	2	2	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	2	2	no	—
626	Q₈	—	4	8	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	D₄	—	2	8	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	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	4	8	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	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	C₁₉×#123	1	2	yes	—
678	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
680	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
681	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
682	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
683	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	C₁₉×#484	1	4	yes	complemented
703	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
704	C₂²	D₄²×C₁₉	1	1	yes	characteristic
705	C₂²	C₁₉×#546	1	1	yes	characteristic
706	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
707	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₂²	C₁₉×#577	1	1	yes	characteristic
709	C₂²	C₁₉×#578	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	—	8	1	no	—
722	C₄	C₁₉×#525	1	1	yes	characteristic
723	C₄	C₁₉×#538	1	1	yes	characteristic
724	C₄	C₁₉×#546	1	1	yes	characteristic
725	C₄	C₁₉×#551	1	1	yes	characteristic
726	C₂	—	2	4	no	—
727	C₂	—	4	2	no	—
728	C₂	C₁₉×#2418	1	1	yes	characteristic
729	C₂	C₂×C₁₉×#484	1	1	yes	characteristic
730	C₂	C₁₉×#3097	1	1	yes	characteristic
731	C₂	C₁₉×#3265	1	1	yes	characteristic
732	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
733	C₂	C₁₉×#3299	1	1	yes	characteristic
734	C₂	C₁₉×#3308	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#484	C₂	semidirect
2. C₂²×C₁₉×#103	C₂	semidirect
5. C₁₉×#2095	C₂	semidirect
6. C₁₉×#2072	C₂	semidirect
7. C₁₉×#2036	C₂	semidirect
8. C₁₉×#2036	C₂	semidirect
9. C₁₉×#1928	C₂	semidirect
10. C₁₉×#1928	C₂	semidirect
11. C₁₉×#1872	C₂	semidirect
13. C₁₉×#1852	C₂	semidirect
14. C₁₉×#1808	C₂	semidirect
15. C₁₉×#1787	C₂	semidirect
127. C₁₉×#103	D₄	semidirect
239. #24867	C₁₉	direct (N × H)
322. C₂×#484	C₂×C₁₉	semidirect
323. C₂²×#103	C₂×C₁₉	semidirect
326. #2095	C₂×C₁₉	semidirect
327. #2072	C₂×C₁₉	semidirect
328. #2036	C₂×C₁₉	semidirect
329. #2036	C₂×C₁₉	semidirect
330. #1928	C₂×C₁₉	semidirect
331. #1928	C₂×C₁₉	semidirect
332. #1872	C₂×C₁₉	semidirect
334. #1852	C₂×C₁₉	semidirect
335. #1808	C₂×C₁₉	semidirect
336. #1787	C₂×C₁₉	semidirect
350. C₂²×C₁₉	#484	semidirect
494. #103	D₄×C₁₉	semidirect
506. C₁₉	#24867	direct (N × H)
702. C₂²	C₁₉×#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#484	2
C₂²×C₁₉×#103	2
C₁₉×#2409	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2095	2
C₁₉×#2072	2
C₁₉×#2036	2
C₁₉×#1928	2
C₁₉×#1872	2
C₁₉×#1869	2
C₁₉×#1852	2
C₁₉×#1808	2
C₁₉×#1787	2
#24867	19

Subgroups — C19×#24867 #18030826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24867 #18030826