Subgroups — C₁₉×#24478 #18030437

Order 4864.

1232 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2041	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1926	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#127	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#120	—	2	1	no	—
17	C₂×C₁₉×#120	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#481	—	2	4	no	—
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#102	—	2	4	no	—
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×#102	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₉×#392	—	2	2	no	—
33	C₁₉×#390	C₂²	1	2	yes	—
34	C₁₉×#389	C₂²	1	2	yes	complemented
35	C₁₉×#387	—	2	2	no	—
36	C₁₉×#380	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	4	2	no	—
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	—	2	2	no	—
57	C₂²×C₈×C₁₉	—	4	2	no	—
58	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×#127	—	2	4	no	—
62	C₁₉×#127	—	4	2	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#120	—	4	4	no	—
66	C₁₉×#120	—	4	4	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	—	2	2	no	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×#106	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	4	2	no	—
86	C₁₉×#102	—	2	4	no	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×#102	—	4	2	no	—
93	C₁₉×C₂²⋊C₈	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₁₉×#95	D₄	1	2	yes	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	1	no	—
100	C₂⁴×C₁₉	—	4	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	4	2	no	—
104	C₂⁴×C₁₉	—	8	2	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	4	8	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	2	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	4	no	—
127	C₂×D₄×C₁₉	—	8	2	no	—
128	C₂×D₄×C₁₉	—	8	2	no	—
129	C₂×D₄×C₁₉	#41	1	4	yes	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	8	2	no	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	#41	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	4	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	8	2	no	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	4	2	no	—
166	C₂²⋊C₄×C₁₉	—	4	4	no	—
167	C₂²⋊C₄×C₁₉	SD₁₆	1	4	yes	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	8	2	no	—
171	#24478	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	4	8	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	—	4	2	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	8	8	no	—
188	C₂³×C₁₉	—	8	8	no	—
189	C₂³×C₁₉	—	8	4	no	—
190	C₂³×C₁₉	—	8	4	no	—
191	C₂³×C₁₉	#121	1	2	yes	—
192	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
193	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	D₄×C₁₉	—	2	4	no	—
196	D₄×C₁₉	—	2	4	no	—
197	D₄×C₁₉	—	4	8	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	8	8	no	—
204	D₄×C₁₉	—	8	8	no	—
205	D₄×C₁₉	—	8	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	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	8	4	no	—
226	C₂×C₄×C₁₉	#121	1	2	yes	—
227	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
232	C₈×C₁₉	—	4	1	no	—
233	C₈×C₁₉	—	4	1	no	—
234	C₈×C₁₉	—	4	2	no	—
235	C₂×#481	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2433	C₂×C₁₉	1	1	yes	characteristic
238	#2345	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2065	C₂×C₁₉	1	2	yes	complemented
240	#2041	C₂×C₁₉	1	2	yes	complemented
241	#1982	C₂×C₁₉	1	2	yes	complemented
242	#1926	C₂×C₁₉	1	2	yes	complemented
243	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	4	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	4	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	4	no	—
253	C₂²×C₁₉	—	8	16	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	—	8	2	no	—
256	C₂²×C₁₉	—	8	2	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	—	8	1	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	1	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	#460	1	4	yes	—
264	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
265	C₂²×C₁₉	#546	1	2	yes	—
266	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂²×C₁₉	#576	1	2	yes	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	2	4	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	2	no	—
276	C₄×C₁₉	#525	1	1	yes	characteristic
277	C₄×C₁₉	#535	1	1	yes	characteristic
278	C₄×C₁₉	#551	1	2	yes	—
279	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
280	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#127	C₂²×C₁₉	1	2	yes	—
282	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#120	—	2	1	no	—
284	C₂×#120	—	2	1	no	—
285	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
286	#481	—	2	4	no	—
287	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
289	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
290	C₂×#102	—	2	4	no	—
291	C₂×#102	C₂²×C₁₉	1	2	yes	—
292	C₂×#102	C₂²×C₁₉	1	2	yes	—
293	C₂×#102	C₂²×C₁₉	1	2	yes	—
294	C₂×#102	C₂²×C₁₉	1	2	yes	—
295	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
296	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
298	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
299	#392	—	2	2	no	—
300	#390	C₂²×C₁₉	1	2	yes	—
301	#389	C₂²×C₁₉	1	2	yes	complemented
302	#387	—	2	2	no	—
303	#380	—	2	1	no	—
304	#380	C₂²×C₁₉	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
306	C₄×C₂²⋊C₄	—	2	1	no	—
307	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	#340	C₂²×C₁₉	1	2	yes	complemented
309	#336	C₂²×C₁₉	1	2	yes	complemented
310	C₂×C₁₉	—	2	4	no	—
311	C₂×C₁₉	—	8	4	no	—
312	C₂×C₁₉	—	16	1	no	—
313	C₂×C₁₉	#2411	1	1	yes	characteristic
314	C₂×C₁₉	C₂×#460	1	1	yes	characteristic
315	C₂×C₁₉	#3041	1	1	yes	characteristic
316	C₂×C₁₉	#3295	1	2	yes	—
317	C₂×C₁₉	#3318	1	2	yes	—
318	C₂⁵	—	2	1	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	4	2	no	—
327	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	4	2	no	—
333	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
334	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	#127	—	2	4	no	—
337	#127	—	4	2	no	—
338	#121	—	2	2	no	—
339	#121	—	2	2	no	—
340	#120	—	4	4	no	—
341	#120	—	4	4	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	complemented
346	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
358	#106	—	2	2	no	—
359	#106	—	2	2	no	—
360	C₄⋊C₈	—	4	2	no	—
361	#102	—	2	4	no	—
362	#102	—	2	4	no	—
363	#102	—	2	4	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	4	2	no	—
367	#102	—	4	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	1	no	—
372	#95	D₄×C₁₉	1	2	yes	—
373	C₁₉	#24478	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	4	4	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	8	2	no	—
381	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	#41×C₁₉	1	4	yes	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	8	2	no	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²×C₄	#41×C₁₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	8	2	no	—
436	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	SD₁₆×C₁₉	1	4	yes	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	8	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	8	8	no	—
463	C₂³	—	8	8	no	—
464	C₂³	—	8	4	no	—
465	C₂³	—	8	4	no	—
466	C₂³	C₁₉×#121	1	2	yes	—
467	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
468	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
469	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	8	no	—
479	D₄	—	8	8	no	—
480	D₄	—	8	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	C₁₉×#121	1	2	yes	—
502	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
505	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
507	C₈	—	4	1	no	—
508	C₈	—	4	2	no	—
509	C₈	—	4	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	8	16	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	2	no	—
527	C₂²	C₁₉×#460	1	4	yes	—
528	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
529	C₂²	C₁₉×#546	1	2	yes	—
530	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
531	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
532	C₂²	C₁₉×#576	1	2	yes	—
533	C₄	—	2	2	no	—
534	C₄	—	2	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	2	no	—
540	C₄	C₁₉×#525	1	1	yes	characteristic
541	C₄	C₁₉×#535	1	1	yes	characteristic
542	C₄	C₁₉×#551	1	2	yes	—
543	C₂	—	2	4	no	—
544	C₂	—	8	4	no	—
545	C₂	—	16	1	no	—
546	C₂	C₁₉×#2411	1	1	yes	characteristic
547	C₂	C₂×C₁₉×#460	1	1	yes	characteristic
548	C₂	C₁₉×#3041	1	1	yes	characteristic
549	C₂	C₁₉×#3295	1	2	yes	—
550	C₂	C₁₉×#3318	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2433	C₂
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
1. C₂×C₁₉×#481	C₂	semidirect
2. C₂²×C₁₉×#102	C₂	semidirect
4. C₁₉×#2345	C₂	semidirect
5. C₁₉×#2065	C₂	semidirect
6. C₁₉×#2041	C₂	semidirect
7. C₁₉×#1982	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1850	C₂	semidirect
11. C₁₉×#1786	C₂	semidirect
20. C₂×C₁₉×#106	C₂²	semidirect
21. C₂×C₁₉×#106	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
28. C₂×C₁₉×#102	C₂²	semidirect
29. C₂×C₁₉×#102	C₂²	semidirect
30. C₂×C₁₉×#102	C₂²	semidirect
34. C₁₉×#389	C₂²	semidirect
38. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
70. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
171. #24478	C₁₉	direct (N × H)
235. C₂×#481	C₂×C₁₉	semidirect
236. C₂²×#102	C₂×C₁₉	semidirect
238. #2345	C₂×C₁₉	semidirect
239. #2065	C₂×C₁₉	semidirect
240. #2041	C₂×C₁₉	semidirect
241. #1982	C₂×C₁₉	semidirect
242. #1926	C₂×C₁₉	semidirect
243. #1893	C₂×C₁₉	semidirect
244. #1850	C₂×C₁₉	semidirect
245. #1786	C₂×C₁₉	semidirect
287. C₂×#106	C₂²×C₁₉	semidirect
288. C₂×#106	C₂²×C₁₉	semidirect
289. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
295. C₂×#102	C₂²×C₁₉	semidirect
296. C₂×#102	C₂²×C₁₉	semidirect
297. C₂×#102	C₂²×C₁₉	semidirect
301. #389	C₂²×C₁₉	semidirect
305. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
308. #340	C₂²×C₁₉	semidirect
309. #336	C₂²×C₁₉	semidirect
345. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
373. C₁₉	#24478	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×#481	2
C₂²×C₁₉×#102	2
C₁₉×#2433	2
C₁₉×#2345	2
C₁₉×#2065	2
C₁₉×#2041	2
C₁₉×#1982	2
C₁₉×#1926	2
C₁₉×#1893	2
C₁₉×#1850	2
C₁₉×#1786	2
#24478	19

Subgroups — C19×#24478 #18030437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24478 #18030437