Subgroups — C₁₉×#24760 #18030719

Order 4864.

960 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#470	C₂	1	2	yes	maximal
2	C₂×C₁₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2056	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1894	C₂	1	2	yes	maximal
11	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#470	—	2	8	no	—
20	C₁₉×#462	—	2	4	no	—
21	C₂×C₁₉×#106	C₂²	1	2	yes	—
22	C₁₉×#423	—	2	4	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₁₉×#391	C₂²	1	1	yes	characteristic
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#389	—	2	1	no	—
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#387	—	2	1	no	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#384	C₂²	1	1	yes	characteristic
38	C₁₉×#380	—	2	1	no	—
39	C₁₉×#380	—	2	1	no	—
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₉	—	2	4	no	—
52	C₂×Q₁₆×C₁₉	—	2	4	no	—
53	C₂×Q₁₆×C₁₉	—	4	2	no	—
54	C₂×M₁₆×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	4	no	—
56	C₂×M₁₆×C₁₉	—	4	2	no	—
57	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
65	C₄×Q₈×C₁₉	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#106	—	2	4	no	—
91	C₁₉×C₄⋊C₈	—	2	4	no	—
92	C₁₉×C₄⋊C₈	—	2	2	no	—
93	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
94	C₁₉×#103	—	2	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#103	—	2	4	no	—
97	C₁₉×#103	—	4	2	no	—
98	C₁₉×#95	—	2	1	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₁₉×#95	—	2	2	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	2	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	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	Q₁₆×C₁₉	—	4	8	no	—
143	M₁₆×C₁₉	—	4	8	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	—	2	2	no	—
149	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	4	2	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	4	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	4	2	no	—
174	C₄²×C₁₉	—	4	2	no	—
175	C₄²×C₁₉	C₂×D₄	1	2	yes	—
176	C₄²×C₁₉	#41	1	2	yes	—
177	#24760	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	1	no	—
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	#121	1	2	yes	—
185	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	2	2	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
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	1	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	4	no	—
215	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	#121	1	2	yes	—
228	C₂×C₄×C₁₉	#121	1	2	yes	—
229	C₂×C₄×C₁₉	#121	1	2	yes	—
230	C₂×C₄×C₁₉	#137	1	2	yes	—
231	C₂×C₄×C₁₉	#137	1	2	yes	—
232	C₂×C₄×C₁₉	#137	1	2	yes	—
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₉	—	2	4	no	—
240	C₈×C₁₉	—	4	2	no	—
241	C₂×#470	C₂×C₁₉	1	2	yes	—
242	C₂×#462	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂×#423	C₂×C₁₉	1	1	yes	characteristic
244	#2857	C₂×C₁₉	1	1	yes	characteristic
245	C₄×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
246	#2066	C₂×C₁₉	1	2	yes	complemented
247	#2056	C₂×C₁₉	1	2	yes	complemented
248	#1981	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1948	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1894	C₂×C₁₉	1	2	yes	—
251	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	2	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	1	no	—
259	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
261	C₂²×C₁₉	#537	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
265	C₂²×C₁₉	#575	1	1	yes	characteristic
266	C₄×C₁₉	—	2	2	no	—
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	8	2	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	2	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	#470	1	4	yes	complemented
277	C₄×C₁₉	D₄²	1	1	yes	characteristic
278	C₄×C₁₉	#547	1	1	yes	characteristic
279	C₄×C₁₉	#548	1	1	yes	characteristic
280	C₄×C₁₉	#553	1	1	yes	characteristic
281	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
282	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
283	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
288	#470	—	2	8	no	—
289	#462	—	2	4	no	—
290	C₂×#106	C₂²×C₁₉	1	2	yes	—
291	#423	—	2	4	no	—
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#103	C₂²×C₁₉	1	2	yes	—
296	C₂×#103	C₂²×C₁₉	1	2	yes	—
297	C₂×#103	C₂²×C₁₉	1	2	yes	—
298	C₂×#103	C₂²×C₁₉	1	2	yes	—
299	#391	C₂²×C₁₉	1	1	yes	characteristic
300	#391	C₂²×C₁₉	1	2	yes	—
301	#389	—	2	1	no	—
302	#389	—	2	1	no	—
303	#389	C₂²×C₁₉	1	1	yes	characteristic
304	#387	—	2	1	no	—
305	#385	—	2	1	no	—
306	#384	C₂²×C₁₉	1	1	yes	characteristic
307	#380	—	2	1	no	—
308	#380	—	2	1	no	—
309	#380	C₂²×C₁₉	1	1	yes	characteristic
310	C₄×C₄⋊C₄	—	2	1	no	—
311	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	—	2	1	no	—
313	#340	C₂²×C₁₉	1	2	yes	—
314	#340	C₂²×C₁₉	1	2	yes	—
315	C₂×C₁₉	—	4	2	no	—
316	C₂×C₁₉	#2416	1	1	yes	characteristic
317	C₂×C₁₉	#3037	1	1	yes	characteristic
318	C₂×C₁₉	#3039	1	1	yes	characteristic
319	C₂×C₁₉	C₂×#470	1	1	yes	characteristic
320	C₂×C₁₉	#3056	1	1	yes	characteristic
321	C₂×C₁₉	#3252	1	1	yes	characteristic
322	C₂×C₁₉	#3255	1	1	yes	characteristic
323	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
324	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
326	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×Q₁₆	—	2	4	no	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	—	4	2	no	—
331	C₂×M₁₆	—	2	4	no	—
332	C₂×M₁₆	—	2	4	no	—
333	C₂×M₁₆	—	4	2	no	—
334	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
335	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	#106	—	2	4	no	—
368	C₄⋊C₈	—	2	4	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
371	#103	—	2	4	no	—
372	#103	—	2	4	no	—
373	#103	—	2	4	no	—
374	#103	—	4	2	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	C₁₉	#24760	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	#41×C₁₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
420	Q₁₆	—	4	8	no	—
421	M₁₆	—	4	8	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	C₂×D₄×C₁₉	1	4	yes	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	4	2	no	—
452	C₄²	—	4	2	no	—
453	C₄²	C₂×D₄×C₁₉	1	2	yes	—
454	C₄²	#41×C₁₉	1	2	yes	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	C₁₉×#121	1	2	yes	—
462	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	C₁₉×#121	1	2	yes	—
505	C₂×C₄	C₁₉×#121	1	2	yes	—
506	C₂×C₄	C₁₉×#121	1	2	yes	—
507	C₂×C₄	C₁₉×#137	1	2	yes	—
508	C₂×C₄	C₁₉×#137	1	2	yes	—
509	C₂×C₄	C₁₉×#137	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
516	C₈	—	2	4	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
527	C₂²	C₁₉×#537	1	1	yes	characteristic
528	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
529	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
530	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
531	C₂²	C₁₉×#575	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	8	2	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	2	no	—
541	C₄	—	8	1	no	—
542	C₄	C₁₉×#470	1	4	yes	complemented
543	C₄	D₄²×C₁₉	1	1	yes	characteristic
544	C₄	C₁₉×#547	1	1	yes	characteristic
545	C₄	C₁₉×#548	1	1	yes	characteristic
546	C₄	C₁₉×#553	1	1	yes	characteristic
547	C₂	—	4	2	no	—
548	C₂	C₁₉×#2416	1	1	yes	characteristic
549	C₂	C₁₉×#3037	1	1	yes	characteristic
550	C₂	C₁₉×#3039	1	1	yes	characteristic
551	C₂	C₂×C₁₉×#470	1	1	yes	characteristic
552	C₂	C₁₉×#3056	1	1	yes	characteristic
553	C₂	C₁₉×#3252	1	1	yes	characteristic
554	C₂	C₁₉×#3255	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#462	C₂	semidirect
6. C₁₉×#2066	C₂	semidirect
7. C₁₉×#2056	C₂	semidirect
8. C₁₉×#1981	C₂	semidirect
9. C₁₉×#1948	C₂	semidirect
11. C₁₉×#1803	C₂	semidirect
177. #24760	C₁₉	direct (N × H)
242. C₂×#462	C₂×C₁₉	semidirect
246. #2066	C₂×C₁₉	semidirect
247. #2056	C₂×C₁₉	semidirect
248. #1981	C₂×C₁₉	semidirect
249. #1948	C₂×C₁₉	semidirect
251. #1803	C₂×C₁₉	semidirect
276. C₄×C₁₉	#470	semidirect
382. C₁₉	#24760	direct (N × H)
542. C₄	C₁₉×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#470	2
C₂×C₁₉×#462	2
C₂×C₁₉×#423	2
C₁₉×#2857	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2066	2
C₁₉×#2056	2
C₁₉×#1981	2
C₁₉×#1948	2
C₁₉×#1894	2
C₁₉×#1803	2
#24760	19

Subgroups — C19×#24760 #18030719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24760 #18030719