Subgroups — C₁₉×#32954 #18038913

Order 4864.

1332 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#475	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1865	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1853	C₂	1	2	yes	maximal
6	C₁₉×#1803	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1787	C₂	1	2	yes	maximal
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
13	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	—	2	1	no	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#475	—	2	8	no	—
22	C₂×C₁₉×#106	C₂²	1	4	yes	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	4	yes	—
25	C₂×C₁₉×#103	C₂²	1	4	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₉×#391	—	2	1	no	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#384	C₂²	1	1	yes	characteristic
31	C₁₉×#380	—	2	1	no	—
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	4	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	Q₈	1	4	yes	complemented
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
48	C₁₉×C₄⋊Q₈	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	4	4	no	—
50	C₄×Q₈×C₁₉	—	2	8	no	—
51	C₄×Q₈×C₁₉	—	2	8	no	—
52	C₄×Q₈×C₁₉	—	2	4	no	—
53	C₄×Q₈×C₁₉	—	2	4	no	—
54	C₄×Q₈×C₁₉	—	2	4	no	—
55	C₄×Q₈×C₁₉	D₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	8	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	4	no	—
73	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#106	—	2	8	no	—
78	C₁₉×C₄⋊C₈	—	2	4	no	—
79	C₁₉×#103	—	2	8	no	—
80	C₁₉×#103	—	2	8	no	—
81	C₁₉×C₂²⋊C₈	—	2	4	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×Q₈×C₁₉	—	2	16	no	—
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	2	16	no	—
89	C₂×Q₈×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂×Q₈×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	4	2	no	—
96	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
97	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
98	C₂×Q₈×C₁₉	#41	1	4	yes	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₉	—	2	4	no	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	4	2	no	—
136	C₄⋊C₄×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	4	4	no	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₄²×C₁₉	—	2	8	no	—
141	C₄²×C₁₉	—	2	8	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	C₂×D₄	1	4	yes	—
146	#32954	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
152	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
153	C₂³×C₁₉	#137	1	2	yes	—
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	16	no	—
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	—	2	4	no	—
158	Q₈×C₁₉	—	2	4	no	—
159	Q₈×C₁₉	—	8	4	no	—
160	Q₈×C₁₉	C₂²⋊Q₈	1	8	yes	complemented
161	C₂×C₄×C₁₉	—	2	16	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	8	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	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	2	no	—
188	C₂×C₄×C₁₉	#120	1	2	yes	—
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₁₉	#137	1	2	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₈×C₁₉	—	4	4	no	—
199	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
200	C₂×#475	C₂×C₁₉	1	2	yes	complemented
201	#2857	C₂×C₁₉	1	1	yes	characteristic
202	#1865	C₂×C₁₉	1	4	yes	complemented
203	#1853	C₂×C₁₉	1	2	yes	—
204	#1803	C₂×C₁₉	1	2	yes	complemented
205	#1797	C₂×C₁₉	1	1	yes	characteristic
206	#1787	C₂×C₁₉	1	2	yes	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	#475	1	4	yes	complemented
214	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₁₉	#525	1	1	yes	characteristic
217	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
220	C₂²×C₁₉	#575	1	1	yes	characteristic
221	C₄×C₁₉	—	2	8	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	#448	1	4	yes	—
230	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
231	C₄×C₁₉	#525	1	2	yes	—
232	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	—	2	1	no	—
235	C₂×C₄×Q₈	—	2	8	no	—
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
240	C₂²×C₄⋊C₄	—	2	1	no	—
241	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×C₄²	—	2	1	no	—
243	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
244	#475	—	2	8	no	—
245	C₂×#106	C₂²×C₁₉	1	4	yes	—
246	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
247	C₂×#103	C₂²×C₁₉	1	4	yes	—
248	C₂×#103	C₂²×C₁₉	1	4	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
250	#391	—	2	1	no	—
251	#389	—	2	1	no	—
252	#389	C₂²×C₁₉	1	2	yes	—
253	#384	C₂²×C₁₉	1	1	yes	characteristic
254	#380	—	2	1	no	—
255	#380	C₂²×C₁₉	1	2	yes	—
256	#340	C₂²×C₁₉	1	4	yes	—
257	#336	C₂²×C₁₉	1	2	yes	—
258	C₂×C₁₉	—	2	4	no	—
259	C₂×C₁₉	#2848	1	1	yes	characteristic
260	C₂×C₁₉	C₂×#448	1	1	yes	characteristic
261	C₂×C₁₉	#3007	1	1	yes	characteristic
262	C₂×C₁₉	C₂×#475	1	1	yes	characteristic
263	C₂×C₁₉	#3078	1	1	yes	characteristic
264	C₂×C₁₉	#3103	1	1	yes	characteristic
265	C₂×C₁₉	#3113	1	1	yes	characteristic
266	C₂²×Q₈	—	2	4	no	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	Q₈×C₁₉	1	4	yes	complemented
272	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
279	C₄⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	4	4	no	—
281	C₄×Q₈	—	2	8	no	—
282	C₄×Q₈	—	2	8	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	D₄×C₁₉	1	8	yes	—
287	C₂×C₄⋊C₄	—	2	8	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
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	C₂³×C₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²	—	2	8	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	4	no	—
304	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
308	#106	—	2	8	no	—
309	C₄⋊C₈	—	2	4	no	—
310	#103	—	2	8	no	—
311	#103	—	2	8	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₁₉	#32954	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	16	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	16	no	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
329	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
330	C₂×Q₈	#41×C₁₉	1	4	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
355	C₂²×C₄	#41×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	4	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₄²	—	2	8	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₄×C₁₉	1	4	yes	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
383	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
384	C₂³	C₁₉×#137	1	2	yes	—
385	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	Q₈	—	2	16	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	8	4	no	—
391	Q₈	C₁₉×C₂²⋊Q₈	1	8	yes	complemented
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	C₁₉×#120	1	2	yes	—
420	C₂×C₄	C₁₉×#120	1	2	yes	—
421	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
422	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
423	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
424	C₂×C₄	C₁₉×#137	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
426	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
428	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
429	C₈	—	4	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	C₁₉×#475	1	4	yes	complemented
437	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
438	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂²	C₁₉×#525	1	1	yes	characteristic
440	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
443	C₂²	C₁₉×#575	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	4	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₁₉×#448	1	4	yes	—
453	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
454	C₄	C₁₉×#525	1	2	yes	—
455	C₂	—	2	4	no	—
456	C₂	C₁₉×#2848	1	1	yes	characteristic
457	C₂	C₂×C₁₉×#448	1	1	yes	characteristic
458	C₂	C₁₉×#3007	1	1	yes	characteristic
459	C₂	C₂×C₁₉×#475	1	1	yes	characteristic
460	C₂	C₁₉×#3078	1	1	yes	characteristic
461	C₂	C₁₉×#3103	1	1	yes	characteristic
462	C₂	C₁₉×#3113	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×#475	C₂	semidirect
4. C₁₉×#1865	C₂	semidirect
6. C₁₉×#1803	C₂	semidirect
40. C₂²×Q₈×C₁₉	Q₈	semidirect
146. #32954	C₁₉	direct (N × H)
160. Q₈×C₁₉	C₂²⋊Q₈	semidirect
200. C₂×#475	C₂×C₁₉	semidirect
202. #1865	C₂×C₁₉	semidirect
204. #1803	C₂×C₁₉	semidirect
213. C₂²×C₁₉	#475	semidirect
271. C₂²×Q₈	Q₈×C₁₉	semidirect
315. C₁₉	#32954	direct (N × H)
391. Q₈	C₁₉×C₂²⋊Q₈	semidirect
436. C₂²	C₁₉×#475	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₉	2
C₂×C₁₉×#475	2
C₁₉×#2857	2
C₁₉×#1865	2
C₁₉×#1853	2
C₁₉×#1803	2
C₁₉×#1797	2
C₁₉×#1787	2
#32954	19

Subgroups — C19×#32954 #18038913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32954 #18038913