Subgroups — C₁₉×#24817 #18030776

Order 4864.

806 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#477	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2567	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2083	C₂	1	2	yes	maximal
6	C₁₉×#2068	C₂	1	2	yes	maximal
7	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1878	C₂	1	2	yes	maximal
10	C₁₉×#1803	C₂	1	2	yes	maximal
11	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#477	—	2	4	no	—
18	C₄×Q₁₆×C₁₉	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#395	—	2	2	no	—
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#389	—	2	2	no	—
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#389	—	2	1	no	—
33	C₁₉×#389	C₂²	1	2	yes	—
34	C₁₉×#384	—	2	1	no	—
35	C₁₉×#384	C₂²	1	1	yes	characteristic
36	C₁₉×#384	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₉	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	4	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	—	2	2	no	—
58	C₄×Q₈×C₁₉	—	4	2	no	—
59	C₄×Q₈×C₁₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	4	no	—
82	C₁₉×C₄⋊C₈	—	2	2	no	—
83	C₁₉×C₄⋊C₈	—	4	2	no	—
84	C₁₉×#103	—	2	2	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₄×C₈×C₁₉	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	D₄	1	2	yes	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	—	8	1	no	—
103	C₂×Q₈×C₁₉	—	8	1	no	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂×Q₈×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	Q₁₆×C₁₉	—	2	8	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	8	1	no	—
143	C₄⋊C₄×C₁₉	—	8	2	no	—
144	C₄⋊C₄×C₁₉	—	8	2	no	—
145	C₄⋊C₄×C₁₉	—	8	2	no	—
146	C₄⋊C₄×C₁₉	Q₁₆	1	4	yes	complemented
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	4	4	no	—
152	C₄²×C₁₉	—	4	2	no	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	#41	1	2	yes	—
155	#24817	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	2	2	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	8	4	no	—
165	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	#121	1	2	yes	—
192	C₂×C₄×C₁₉	#121	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
194	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
195	C₂×C₄×C₁₉	#137	1	2	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
202	C₈×C₁₉	—	2	2	no	—
203	C₈×C₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₂×#477	C₂×C₁₉	1	1	yes	characteristic
206	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
207	#2567	C₂×C₁₉	1	1	yes	characteristic
208	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
209	#2083	C₂×C₁₉	1	2	yes	—
210	#2068	C₂×C₁₉	1	2	yes	—
211	#1990	C₂×C₁₉	1	1	yes	characteristic
212	#1939	C₂×C₁₉	1	1	yes	characteristic
213	#1878	C₂×C₁₉	1	2	yes	—
214	#1803	C₂×C₁₉	1	1	yes	characteristic
215	#1803	C₂×C₁₉	1	2	yes	—
216	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
217	C₂²×C₁₉	#546	1	1	yes	characteristic
218	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
219	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
221	C₂²×C₁₉	#576	1	1	yes	characteristic
222	C₂²×C₁₉	#577	1	1	yes	characteristic
223	C₄×C₁₉	—	2	4	no	—
224	C₄×C₁₉	—	2	4	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	#462	1	4	yes	—
233	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₄×C₁₉	#537	1	1	yes	characteristic
235	C₄×C₁₉	#552	1	1	yes	characteristic
236	C₄×C₁₉	#554	1	1	yes	characteristic
237	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	#477	—	2	4	no	—
243	C₄×Q₁₆	—	2	4	no	—
244	C₂×#107	C₂²×C₁₉	1	2	yes	—
245	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
248	C₂×#103	C₂²×C₁₉	1	2	yes	—
249	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#103	C₂²×C₁₉	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
253	#395	—	2	2	no	—
254	#391	C₂²×C₁₉	1	2	yes	—
255	#389	—	2	1	no	—
256	#389	—	2	1	no	—
257	#389	—	2	2	no	—
258	#389	C₂²×C₁₉	1	2	yes	—
259	#384	—	2	1	no	—
260	#384	C₂²×C₁₉	1	2	yes	—
261	#384	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×C₄⋊C₄	—	2	1	no	—
263	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
264	#340	C₂²×C₁₉	1	2	yes	—
265	#340	C₂²×C₁₉	1	2	yes	—
266	#340	C₂²×C₁₉	1	2	yes	—
267	#336	C₂²×C₁₉	1	2	yes	—
268	C₂×C₁₉	#2417	1	1	yes	characteristic
269	C₂×C₁₉	C₂×#462	1	1	yes	characteristic
270	C₂×C₁₉	#3045	1	1	yes	characteristic
271	C₂×C₁₉	#3299	1	1	yes	characteristic
272	C₂×C₁₉	#3333	1	1	yes	characteristic
273	C₂×C₁₉	Q₈×Q₁₆	1	1	yes	characteristic
274	C₂×C₁₉	#3387	1	1	yes	characteristic
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	Q₈×C₁₉	1	4	yes	complemented
281	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	4	2	no	—
291	C₄×Q₈	D₄×C₁₉	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	#107	—	2	2	no	—
313	#107	—	2	4	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	4	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	4	no	—
318	#103	—	2	2	no	—
319	#103	—	4	2	no	—
320	C₄×C₈	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	D₄×C₁₉	1	2	yes	—
325	C₁₉	#24817	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×Q₈	—	8	1	no	—
337	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
338	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
339	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
340	C₂×Q₈	#41×C₁₉	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
352	Q₁₆	—	2	8	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	8	1	no	—
376	C₄⋊C₄	—	8	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₄⋊C₄	—	8	2	no	—
379	C₄⋊C₄	Q₁₆×C₁₉	1	4	yes	complemented
380	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	4	no	—
385	C₄²	—	4	2	no	—
386	C₄²	C₂×D₄×C₁₉	1	2	yes	—
387	C₄²	#41×C₁₉	1	2	yes	—
388	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	8	4	no	—
397	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	C₁₉×#121	1	2	yes	—
424	C₂×C₄	C₁₉×#121	1	2	yes	—
425	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
426	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
427	C₂×C₄	C₁₉×#137	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
438	C₂²	C₁₉×#546	1	1	yes	characteristic
439	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
440	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
442	C₂²	C₁₉×#576	1	1	yes	characteristic
443	C₂²	C₁₉×#577	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	2	no	—
453	C₄	C₁₉×#462	1	4	yes	—
454	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
455	C₄	C₁₉×#537	1	1	yes	characteristic
456	C₄	C₁₉×#552	1	1	yes	characteristic
457	C₄	C₁₉×#554	1	1	yes	characteristic
458	C₂	C₁₉×#2417	1	1	yes	characteristic
459	C₂	C₂×C₁₉×#462	1	1	yes	characteristic
460	C₂	C₁₉×#3045	1	1	yes	characteristic
461	C₂	C₁₉×#3299	1	1	yes	characteristic
462	C₂	C₁₉×#3333	1	1	yes	characteristic
463	C₂	Q₈×Q₁₆×C₁₉	1	1	yes	characteristic
464	C₂	C₁₉×#3387	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
48. C₂×Q₁₆×C₁₉	Q₈	semidirect
146. C₄⋊C₄×C₁₉	Q₁₆	semidirect
155. #24817	C₁₉	direct (N × H)
280. C₂×Q₁₆	Q₈×C₁₉	semidirect
325. C₁₉	#24817	direct (N × H)
379. C₄⋊C₄	Q₁₆×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×#477	2
C₂×C₄×Q₁₆×C₁₉	2
C₁₉×#2567	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2083	2
C₁₉×#2068	2
C₁₉×#1990	2
C₁₉×#1939	2
C₁₉×#1878	2
C₁₉×#1803	2
#24817	19

Subgroups — C19×#24817 #18030776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24817 #18030776