Subgroups — C₁₉×#26230 #18032189

Order 4864.

1070 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#480	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#127	—	2	1	no	—
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#480	—	2	8	no	—
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#392	—	2	2	no	—
32	C₁₉×#390	—	2	1	no	—
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#385	—	2	2	no	—
35	C₁₉×#384	C₂²	1	1	yes	characteristic
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#127	—	2	2	no	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#127	—	4	4	no	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	4	2	no	—
59	C₁₉×#121	—	4	2	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×#107	—	2	4	no	—
82	C₁₉×#107	—	2	2	no	—
83	C₁₉×#107	D₄	1	4	yes	complemented
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×#102	—	2	4	no	—
86	C₁₉×#102	—	2	4	no	—
87	C₁₉×#102	—	4	2	no	—
88	C₁₉×#102	—	4	2	no	—
89	C₁₉×C₂²⋊C₈	—	2	4	no	—
90	C₁₉×C₂²⋊C₈	—	4	2	no	—
91	C₄×C₈×C₁₉	—	2	2	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	8	1	no	—
114	C₂×D₄×C₁₉	—	8	1	no	—
115	C₂×D₄×C₁₉	—	8	2	no	—
116	C₂×D₄×C₁₉	—	8	2	no	—
117	C₂×D₄×C₁₉	D₈	1	4	yes	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
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	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	8	2	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
153	C₄⋊C₄×C₁₉	—	4	4	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	—	8	1	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₁₉	#41	1	2	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	4	no	—
163	C₄²×C₁₉	—	4	2	no	—
164	C₄²×C₁₉	—	4	2	no	—
165	C₄²×C₁₉	#41	1	2	yes	—
166	C₄²×C₁₉	#41	1	2	yes	—
167	#26230	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	C₂×D₈	1	4	yes	—
182	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	D₄×C₁₉	—	2	8	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	8	4	no	—
189	D₄×C₁₉	—	8	8	no	—
190	D₄×C₁₉	—	8	8	no	—
191	D₄×C₁₉	—	8	4	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	8	8	no	—
217	C₂×C₄×C₁₉	#123	1	2	yes	—
218	C₂×C₄×C₁₉	#123	1	2	yes	—
219	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
220	C₂×C₄×C₁₉	#137	1	2	yes	—
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
227	C₈×C₁₉	—	2	2	no	—
228	C₈×C₁₉	—	4	1	no	—
229	C₈×C₁₉	—	4	2	no	—
230	C₂×#480	C₂×C₁₉	1	2	yes	complemented
231	#2541	C₂×C₁₉	1	1	yes	characteristic
232	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2033	C₂×C₁₉	1	2	yes	complemented
234	#2033	C₂×C₁₉	1	2	yes	complemented
235	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1874	C₂×C₁₉	1	2	yes	complemented
240	C₄×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	—	8	2	no	—
251	C₂²×C₁₉	—	8	2	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
256	C₂²×C₁₉	D₄²	1	1	yes	characteristic
257	C₂²×C₁₉	#546	1	1	yes	characteristic
258	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
260	C₂²×C₁₉	#576	1	1	yes	characteristic
261	C₂²×C₁₉	#577	1	1	yes	characteristic
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	#480	1	4	yes	complemented
270	C₄×C₁₉	#532	1	1	yes	characteristic
271	C₄×C₁₉	#540	1	1	yes	characteristic
272	C₄×C₁₉	#550	1	1	yes	characteristic
273	C₄×C₁₉	#559	1	1	yes	characteristic
274	C₂×#127	—	2	1	no	—
275	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#121	C₂²×C₁₉	1	2	yes	—
277	C₂×#121	C₂²×C₁₉	1	2	yes	—
278	C₂×C₄×D₄	—	2	1	no	—
279	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
281	#480	—	2	8	no	—
282	C₂×#107	C₂²×C₁₉	1	2	yes	—
283	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₉	1	2	yes	—
287	C₂×#102	C₂²×C₁₉	1	2	yes	—
288	C₂×#102	C₂²×C₁₉	1	2	yes	—
289	C₂×#102	C₂²×C₁₉	1	2	yes	—
290	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
291	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
292	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
293	#392	—	2	2	no	—
294	#390	—	2	1	no	—
295	#389	—	2	1	no	—
296	#385	—	2	2	no	—
297	#384	C₂²×C₁₉	1	1	yes	characteristic
298	#380	C₂²×C₁₉	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
301	#340	C₂²×C₁₉	1	1	yes	characteristic
302	#340	C₂²×C₁₉	1	2	yes	—
303	#340	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×C₁₉	—	4	4	no	—
305	C₂×C₁₉	—	16	2	no	—
306	C₂×C₁₉	#2445	1	1	yes	characteristic
307	C₂×C₁₉	C₂×#480	1	1	yes	characteristic
308	C₂×C₁₉	#3096	1	1	yes	characteristic
309	C₂×C₁₉	#3278	1	1	yes	characteristic
310	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
311	C₂×C₁₉	#3294	1	1	yes	characteristic
312	C₂×C₁₉	#3333	1	1	yes	characteristic
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
321	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
324	#127	—	2	2	no	—
325	#127	—	2	2	no	—
326	#127	—	4	4	no	—
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	4	2	no	—
330	#121	—	4	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	4	4	no	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	4	2	no	—
339	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
352	#107	—	2	4	no	—
353	#107	—	2	2	no	—
354	#107	D₄×C₁₉	1	4	yes	complemented
355	C₄⋊C₈	—	2	2	no	—
356	#102	—	2	4	no	—
357	#102	—	2	4	no	—
358	#102	—	4	2	no	—
359	#102	—	4	2	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	C₂²⋊C₈	—	4	2	no	—
362	C₄×C₈	—	2	2	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	2	no	—
366	C₁₉	#26230	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	—	2	2	no	—
368	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	8	1	no	—
386	C₂×D₄	—	8	1	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂×D₄	D₈×C₁₉	1	4	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	8	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	8	1	no	—
428	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
430	C₄⋊C₄	#41×C₁₉	1	2	yes	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₄²	—	4	2	no	—
436	C₄²	—	4	2	no	—
437	C₄²	#41×C₁₉	1	2	yes	—
438	C₄²	#41×C₁₉	1	2	yes	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂×D₈×C₁₉	1	4	yes	—
453	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	8	no	—
461	D₄	—	8	8	no	—
462	D₄	—	8	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	C₁₉×#123	1	2	yes	—
489	C₂×C₄	C₁₉×#123	1	2	yes	—
490	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
491	C₂×C₄	C₁₉×#137	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
516	C₂²	D₄²×C₁₉	1	1	yes	characteristic
517	C₂²	C₁₉×#546	1	1	yes	characteristic
518	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
519	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
520	C₂²	C₁₉×#576	1	1	yes	characteristic
521	C₂²	C₁₉×#577	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	1	no	—
529	C₄	C₁₉×#480	1	4	yes	complemented
530	C₄	C₁₉×#532	1	1	yes	characteristic
531	C₄	C₁₉×#540	1	1	yes	characteristic
532	C₄	C₁₉×#550	1	1	yes	characteristic
533	C₄	C₁₉×#559	1	1	yes	characteristic
534	C₂	—	4	4	no	—
535	C₂	—	16	2	no	—
536	C₂	C₁₉×#2445	1	1	yes	characteristic
537	C₂	C₂×C₁₉×#480	1	1	yes	characteristic
538	C₂	C₁₉×#3096	1	1	yes	characteristic
539	C₂	C₁₉×#3278	1	1	yes	characteristic
540	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
541	C₂	C₁₉×#3294	1	1	yes	characteristic
542	C₂	C₁₉×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2541	C₂
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×#480	C₂	semidirect
3. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#2033	C₂	semidirect
5. C₁₉×#2033	C₂	semidirect
6. C₁₉×#1982	C₂	semidirect
7. C₁₉×#1957	C₂	semidirect
8. C₁₉×#1954	C₂	semidirect
9. C₁₉×#1947	C₂	semidirect
10. C₁₉×#1874	C₂	semidirect
11. C₄×C₁₉×#107	C₂	semidirect
83. C₁₉×#107	D₄	semidirect
167. #26230	C₁₉	direct (N × H)
230. C₂×#480	C₂×C₁₉	semidirect
232. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
233. #2033	C₂×C₁₉	semidirect
234. #2033	C₂×C₁₉	semidirect
235. #1982	C₂×C₁₉	semidirect
236. #1957	C₂×C₁₉	semidirect
237. #1954	C₂×C₁₉	semidirect
238. #1947	C₂×C₁₉	semidirect
239. #1874	C₂×C₁₉	semidirect
240. C₄×#107	C₂×C₁₉	semidirect
269. C₄×C₁₉	#480	semidirect
354. #107	D₄×C₁₉	semidirect
366. C₁₉	#26230	direct (N × H)
529. C₄	C₁₉×#480	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#480	2
C₁₉×#2541	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2033	2
C₁₉×#1982	2
C₁₉×#1957	2
C₁₉×#1954	2
C₁₉×#1947	2
C₁₉×#1874	2
C₄×C₁₉×#107	2
#26230	19

Subgroups — C19×#26230 #18032189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26230 #18032189