Subgroups — C₂×C₁₉×#1863 #18026829

Order 4864.

1542 conjugacy classes of subgroups.

The subgroup lattice has 482 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	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1863	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
14	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	—	2	1	no	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	—	2	4	no	—
24	C₂×C₁₉×#107	C₂²	1	4	yes	—
25	C₂×C₁₉×#103	—	2	4	no	—
26	C₂×C₁₉×#103	C₄	1	8	yes	complemented
27	C₂×C₁₉×#103	C₂²	1	4	yes	—
28	C₂×C₁₉×#103	C₂²	1	4	yes	—
29	C₁₉×#389	—	2	2	no	—
30	C₁₉×#389	C₂²	1	4	yes	—
31	C₂×C₁₉×#95	—	2	1	no	—
32	C₁₉×#340	C₂²	1	4	yes	—
33	C₁₉×#336	C₂²	1	4	yes	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
39	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
40	C₂²×Q₈×C₁₉	Q₈	1	4	yes	—
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	—	2	1	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₄×Q₈×C₁₉	—	2	16	no	—
58	C₄×Q₈×C₁₉	—	2	8	no	—
59	C₄×Q₈×C₁₉	—	2	8	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₉	—	2	8	no	—
77	C₂×C₄²×C₁₉	—	2	4	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	D₄	1	2	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₁₉×#107	—	2	8	no	—
83	C₁₉×#103	—	2	8	no	—
84	C₁₉×#103	C₂×C₄	1	16	yes	complemented
85	C₁₉×#95	—	2	4	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	2	8	no	—
89	C₂×Q₈×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	—	2	4	no	—
91	C₂×Q₈×C₁₉	—	2	8	no	—
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	C₄⋊C₄	1	16	yes	complemented
97	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
98	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
99	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	4	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	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₉	—	2	8	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	4	no	—
139	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
140	C₄⋊C₄×C₁₉	—	2	16	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	4	8	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₄²×C₁₉	—	2	16	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₂×#1863	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	C₄×D₄	1	2	yes	—
157	C₂³×C₁₉	#120	1	2	yes	—
158	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
160	C₂³×C₁₉	#135	1	2	yes	—
161	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
162	C₂³×C₁₉	#137	1	2	yes	—
163	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	4	no	—
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	2	16	no	—
168	Q₈×C₁₉	C₂×C₄⋊C₄	1	8	yes	complemented
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	16	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	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	8	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	8	4	no	—
192	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
193	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₉	#120	1	2	yes	—
196	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
197	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₁₉	#123	1	4	yes	—
199	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
200	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₉	—	2	4	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
209	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic
210	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
211	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
212	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
213	#1863	C₂×C₁₉	1	8	yes	direct product factor
214	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
216	C₂²×C₁₉	#385	1	4	yes	—
217	C₂²×C₁₉	C₄×Q₁₆	1	4	yes	—
218	C₂²×C₁₉	#440	1	4	yes	—
219	C₂²×C₁₉	#449	1	4	yes	—
220	C₂²×C₁₉	#451	1	4	yes	—
221	C₂²×C₁₉	#477	1	4	yes	—
222	C₂²×C₁₉	#479	1	4	yes	—
223	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
225	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
227	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
228	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
230	C₄×C₁₉	—	2	4	no	—
231	C₄×C₁₉	—	2	8	no	—
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	4	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	#385	1	4	yes	—
237	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
241	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×Q₈	—	2	4	no	—
245	C₂×C₄×Q₈	—	2	4	no	—
246	C₂×C₄×Q₈	—	2	2	no	—
247	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
248	C₂²×C₄⋊C₄	—	2	1	no	—
249	C₂²×C₄⋊C₄	—	2	1	no	—
250	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
253	C₂²×C₄²	—	2	1	no	—
254	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#107	—	2	4	no	—
256	C₂×#107	C₂²×C₁₉	1	4	yes	—
257	C₂×#103	—	2	4	no	—
258	C₂×#103	C₄×C₁₉	1	8	yes	complemented
259	C₂×#103	C₂²×C₁₉	1	4	yes	—
260	C₂×#103	C₂²×C₁₉	1	4	yes	—
261	#389	—	2	2	no	—
262	#389	C₂²×C₁₉	1	4	yes	—
263	C₂×#95	—	2	1	no	—
264	#340	C₂²×C₁₉	1	4	yes	—
265	#336	C₂²×C₁₉	1	4	yes	—
266	C₂×C₁₉	#1863	1	8	yes	direct product factor
267	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
268	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
269	C₂×C₁₉	C₂×#440	1	1	yes	characteristic
270	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
272	C₂×C₁₉	C₂×#477	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#479	1	1	yes	characteristic
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
280	C₂²×Q₈	Q₈×C₁₉	1	4	yes	—
281	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
295	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
297	C₄×Q₈	—	2	16	no	—
298	C₄×Q₈	—	2	8	no	—
299	C₄×Q₈	—	2	8	no	—
300	C₂×C₄⋊C₄	—	2	8	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	4	4	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
316	C₂×C₄²	—	2	8	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	D₄×C₁₉	1	2	yes	—
321	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
322	#107	—	2	8	no	—
323	#103	—	2	8	no	—
324	#103	C₂×C₄×C₁₉	1	16	yes	complemented
325	#95	—	2	4	no	—
326	C₁₉	C₂×#1863	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂×Q₈	—	2	8	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	8	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₄⋊C₄×C₁₉	1	16	yes	complemented
338	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
339	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
340	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	Q₁₆×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
370	C₂²×C₄	#41×C₁₉	1	2	yes	—
371	C₂²×C₄	#41×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₂×C₈	—	2	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	8	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
391	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
392	C₄²	—	2	16	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₂³	C₄×D₄×C₁₉	1	2	yes	—
397	C₂³	C₁₉×#120	1	2	yes	—
398	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
399	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
400	C₂³	C₁₉×#135	1	2	yes	—
401	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
402	C₂³	C₁₉×#137	1	2	yes	—
403	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
404	Q₈	—	2	16	no	—
405	Q₈	—	2	4	no	—
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	C₂×C₄⋊C₄×C₁₉	1	8	yes	complemented
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
433	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
434	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
435	C₂×C₄	C₁₉×#120	1	2	yes	—
436	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
437	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
438	C₂×C₄	C₁₉×#123	1	4	yes	—
439	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
440	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
446	C₈	—	2	4	no	—
447	C₈	—	4	2	no	—
448	C₂²	C₁₉×#385	1	4	yes	—
449	C₂²	C₄×Q₁₆×C₁₉	1	4	yes	—
450	C₂²	C₁₉×#440	1	4	yes	—
451	C₂²	C₁₉×#449	1	4	yes	—
452	C₂²	C₁₉×#451	1	4	yes	—
453	C₂²	C₁₉×#477	1	4	yes	—
454	C₂²	C₁₉×#479	1	4	yes	—
455	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
456	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
457	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
458	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
459	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
460	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
462	C₄	—	2	4	no	—
463	C₄	—	2	8	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	8	2	no	—
468	C₄	C₁₉×#385	1	4	yes	—
469	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
470	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
471	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
472	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
473	C₂	C₁₉×#1863	1	8	yes	direct product factor
474	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
475	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#440	1	1	yes	characteristic
477	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
478	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
479	C₂	C₂×C₁₉×#477	1	1	yes	characteristic
480	C₂	C₂×C₁₉×#479	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1863	C₂	direct (N × H)
26. C₂×C₁₉×#103	C₄	semidirect
84. C₁₉×#103	C₂×C₄	semidirect
96. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
155. C₂×#1863	C₁₉	direct (N × H)
168. Q₈×C₁₉	C₂×C₄⋊C₄	semidirect
213. #1863	C₂×C₁₉	direct (N × H)
258. C₂×#103	C₄×C₁₉	semidirect
266. C₂×C₁₉	#1863	direct (N × H)
324. #103	C₂×C₄×C₁₉	semidirect
326. C₁₉	C₂×#1863	direct (N × H)
337. C₂×Q₈	C₄⋊C₄×C₁₉	semidirect
408. Q₈	C₂×C₄⋊C₄×C₁₉	semidirect
473. C₂	C₁₉×#1863	direct (N × H)

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
C₂²×C₁₉×#107	2
C₂²×C₁₉×#103	2
C₂×C₁₉×#389	2
C₁₉×#1863	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
C₂×#1863	19

Subgroups — C2×C19×#1863 #18026829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1863 #18026829