Subgroups — C₁₉×#24530 #18030489

Order 4864.

1198 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2071	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1877	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₁₉×#450	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#102	—	2	4	no	—
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#398	—	2	2	no	—
30	C₁₉×#391	C₂²	1	2	yes	complemented
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#386	—	2	2	no	—
33	C₁₉×#385	—	2	1	no	—
34	C₁₉×#385	—	2	1	no	—
35	C₁₉×#384	C₂²	1	2	yes	complemented
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#379	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	complemented
40	C₁₉×#340	C₂²	1	2	yes	complemented
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	4	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	4	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	4	2	no	—
59	C₂²×C₈×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₁₉×C₄⋊C₈	—	4	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	4	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	2	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	D₄	1	2	yes	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	4	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	8	2	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	8	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₉	#41	1	4	yes	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	8	2	no	—
132	C₂²×C₄×C₁₉	—	8	2	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	#41	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₁₉	—	4	4	no	—
140	SD₁₆×C₁₉	—	4	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	4	4	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	4	2	no	—
156	C₄⋊C₄×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	—	8	2	no	—
158	C₄⋊C₄×C₁₉	—	8	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	4	2	no	—
163	C₂²⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	8	2	no	—
165	C₂²⋊C₄×C₁₉	SD₁₆	1	4	yes	complemented
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	#24530	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	8	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	8	no	—
183	C₂³×C₁₉	—	8	4	no	—
184	C₂³×C₁₉	—	8	8	no	—
185	C₂³×C₁₉	—	8	8	no	—
186	C₂³×C₁₉	#121	1	2	yes	—
187	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
188	C₂³×C₁₉	#137	1	2	yes	—
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	2	2	no	—
196	D₄×C₁₉	—	2	4	no	—
197	D₄×C₁₉	—	4	8	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	#123	1	4	yes	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	8	8	no	—
220	C₂×C₄×C₁₉	—	8	4	no	—
221	C₂×C₄×C₁₉	#121	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
227	C₈×C₁₉	—	4	1	no	—
228	C₈×C₁₉	—	4	2	no	—
229	C₈×C₁₉	—	4	1	no	—
230	C₂×#450	C₂×C₁₉	1	1	yes	characteristic
231	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
232	#2502	C₂×C₁₉	1	1	yes	characteristic, complemented
233	D₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
234	#2071	C₂×C₁₉	1	2	yes	complemented
235	#2055	C₂×C₁₉	1	2	yes	complemented
236	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1877	C₂×C₁₉	1	2	yes	complemented
238	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1802	C₂×C₁₉	1	2	yes	complemented
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	8	16	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	#461	1	4	yes	—
257	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
258	C₂²×C₁₉	#546	1	2	yes	—
259	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
261	C₂²×C₁₉	#576	1	2	yes	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	4	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	2	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	2	no	—
269	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
270	C₄×C₁₉	#534	1	1	yes	characteristic
271	C₄×C₁₉	#551	1	2	yes	—
272	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
273	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
274	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
275	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	—	2	1	no	—
280	#450	—	2	4	no	—
281	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
282	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
283	C₂×#102	—	2	4	no	—
284	C₂×#102	C₂²×C₁₉	1	2	yes	—
285	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₉	1	2	yes	—
287	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
289	#398	—	2	2	no	—
290	#391	C₂²×C₁₉	1	2	yes	complemented
291	#390	C₂²×C₁₉	1	2	yes	—
292	#386	—	2	2	no	—
293	#385	—	2	1	no	—
294	#385	—	2	1	no	—
295	#384	C₂²×C₁₉	1	2	yes	complemented
296	#380	C₂²×C₁₉	1	1	yes	characteristic
297	#379	—	2	1	no	—
298	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
299	#340	C₂²×C₁₉	1	2	yes	complemented
300	#340	C₂²×C₁₉	1	2	yes	complemented
301	#340	C₂²×C₁₉	1	2	yes	complemented
302	#336	C₂²×C₁₉	1	2	yes	complemented
303	C₂×C₁₉	—	2	4	no	—
304	C₂×C₁₉	—	4	4	no	—
305	C₂×C₁₉	—	8	2	no	—
306	C₂×C₁₉	#2412	1	1	yes	characteristic
307	C₂×C₁₉	C₂×#461	1	1	yes	characteristic
308	C₂×C₁₉	#3041	1	1	yes	characteristic
309	C₂×C₁₉	#3295	1	2	yes	—
310	C₂×C₁₉	#3314	1	2	yes	—
311	C₂⁵	—	2	1	no	—
312	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	4	2	no	—
317	C₂²×D₄	D₄×C₁₉	1	4	yes	—
318	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	4	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	4	2	no	—
329	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	4	4	no	—
351	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
354	C₄⋊C₈	—	4	2	no	—
355	#103	—	4	2	no	—
356	#102	—	2	4	no	—
357	#102	—	2	4	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	#95	—	2	1	no	—
362	#95	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	D₄×C₁₉	1	2	yes	—
365	C₁₉	#24530	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	—	2	1	no	—
367	C₂⁴	—	2	1	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	4	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	8	2	no	—
373	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂×D₄	#41×C₁₉	1	4	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	8	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	#41×C₁₉	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	SD₁₆	—	4	4	no	—
409	SD₁₆	—	4	4	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	8	2	no	—
427	C₄⋊C₄	—	8	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	8	2	no	—
434	C₂²⋊C₄	SD₁₆×C₁₉	1	4	yes	complemented
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	8	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	8	4	no	—
452	C₂³	—	8	8	no	—
453	C₂³	—	8	8	no	—
454	C₂³	C₁₉×#121	1	2	yes	—
455	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
456	C₂³	C₁₉×#137	1	2	yes	—
457	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	4	no	—
465	D₄	—	4	8	no	—
466	D₄	—	4	2	no	—
467	D₄	C₁₉×#123	1	4	yes	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	C₁₉×#121	1	2	yes	—
490	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
493	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
494	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
495	C₈	—	4	1	no	—
496	C₈	—	4	2	no	—
497	C₈	—	4	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	16	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	C₁₉×#461	1	4	yes	—
514	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
515	C₂²	C₁₉×#546	1	2	yes	—
516	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
517	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
518	C₂²	C₁₉×#576	1	2	yes	—
519	C₄	—	2	2	no	—
520	C₄	—	2	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
527	C₄	C₁₉×#534	1	1	yes	characteristic
528	C₄	C₁₉×#551	1	2	yes	—
529	C₂	—	2	4	no	—
530	C₂	—	4	4	no	—
531	C₂	—	8	2	no	—
532	C₂	C₁₉×#2412	1	1	yes	characteristic
533	C₂	C₂×C₁₉×#461	1	1	yes	characteristic
534	C₂	C₁₉×#3041	1	1	yes	characteristic
535	C₂	C₁₉×#3295	1	2	yes	—
536	C₂	C₁₉×#3314	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	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
3. C₁₉×#2502	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#1892	C₂	semidirect
8. C₁₉×#1877	C₂	semidirect
9. C₁₉×#1850	C₂	semidirect
10. C₁₉×#1824	C₂	semidirect
11. C₁₉×#1802	C₂	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₉×#103	C₂²	semidirect
30. C₁₉×#391	C₂²	semidirect
35. C₁₉×#384	C₂²	semidirect
39. C₁₉×#340	C₂²	semidirect
40. C₁₉×#340	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
165. C₂²⋊C₄×C₁₉	SD₁₆	semidirect
168. #24530	C₁₉	direct (N × H)
232. #2502	C₂×C₁₉	semidirect
234. #2071	C₂×C₁₉	semidirect
235. #2055	C₂×C₁₉	semidirect
236. #1892	C₂×C₁₉	semidirect
237. #1877	C₂×C₁₉	semidirect
238. #1850	C₂×C₁₉	semidirect
239. #1824	C₂×C₁₉	semidirect
240. #1802	C₂×C₁₉	semidirect
281. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
282. C₂×#103	C₂²×C₁₉	semidirect
290. #391	C₂²×C₁₉	semidirect
295. #384	C₂²×C₁₉	semidirect
299. #340	C₂²×C₁₉	semidirect
300. #340	C₂²×C₁₉	semidirect
301. #340	C₂²×C₁₉	semidirect
302. #336	C₂²×C₁₉	semidirect
365. C₁₉	#24530	direct (N × H)
434. C₂²⋊C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#450	2
C₂²×C₁₉×#102	2
C₁₉×#2502	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#2071	2
C₁₉×#2055	2
C₁₉×#1892	2
C₁₉×#1877	2
C₁₉×#1850	2
C₁₉×#1824	2
C₁₉×#1802	2
#24530	19

Subgroups — C19×#24530 #18030489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24530 #18030489