Subgroups — C₁₉×#29513 #18035472

Order 4864.

734 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2860	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2094	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1941	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1934	C₂	1	2	yes	maximal
9	C₁₉×#1926	C₂	1	2	yes	maximal
10	C₁₉×#1919	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#126	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₂×C₁₉×#106	C₂²	1	2	yes	—
17	C₂×C₁₉×#102	C₂²	1	2	yes	—
18	C₂×C₁₉×#102	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#391	—	2	1	no	—
21	C₁₉×#390	C₂²	1	1	yes	characteristic
22	C₁₉×#390	C₂²	1	1	yes	characteristic
23	C₁₉×#390	C₂²	1	1	yes	characteristic
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	C₂²	1	1	yes	characteristic
26	C₁₉×#389	C₂²	1	2	yes	—
27	C₁₉×#389	C₂²	1	1	yes	characteristic
28	C₁₉×#389	C₂²	1	1	yes	characteristic
29	C₁₉×#388	—	2	1	no	—
30	C₁₉×#388	—	2	1	no	—
31	C₁₉×#388	—	2	1	no	—
32	C₁₉×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₄³×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₁₉×C₄⋊Q₈	—	2	4	no	—
48	C₁₉×#126	—	4	4	no	—
49	C₄×Q₈×C₁₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#106	—	2	4	no	—
77	C₁₉×#106	—	2	4	no	—
78	C₁₉×#102	—	2	4	no	—
79	C₁₉×#102	—	2	4	no	—
80	C₄×C₈×C₁₉	—	2	4	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	#41	1	4	yes	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	4	4	no	—
126	C₄⋊C₄×C₁₉	#41	1	4	yes	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	4	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₉	—	4	2	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	1	no	—
138	C₄²×C₁₉	—	2	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	4	4	no	—
141	C₄²×C₁₉	SD₁₆	1	4	yes	—
142	#29513	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	8	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₉	#135	1	2	yes	—
186	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₁₉	—	2	4	no	—
192	C₈×C₁₉	—	4	2	no	—
193	#2860	C₂×C₁₉	1	1	yes	characteristic
194	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#2100	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2094	C₂×C₁₉	1	1	yes	characteristic
197	#2058	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2023	C₂×C₁₉	1	1	yes	characteristic
199	#1941	C₂×C₁₉	1	2	yes	complemented
200	#1934	C₂×C₁₉	1	2	yes	—
201	#1926	C₂×C₁₉	1	2	yes	—
202	#1919	C₂×C₁₉	1	2	yes	complemented
203	#1744	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	#525	1	1	yes	characteristic
212	C₂²×C₁₉	#532	1	1	yes	characteristic
213	C₂²×C₁₉	#536	1	1	yes	characteristic
214	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₁₉	#575	1	1	yes	characteristic
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	—	8	1	no	—
229	C₄×C₁₉	#552	1	2	yes	—
230	C₄×C₁₉	#556	1	2	yes	—
231	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#126	—	2	1	no	—
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×#106	C₂²×C₁₉	1	2	yes	—
235	C₂×#106	C₂²×C₁₉	1	2	yes	—
236	C₂×#102	C₂²×C₁₉	1	2	yes	—
237	C₂×#102	C₂²×C₁₉	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
239	#391	—	2	1	no	—
240	#390	C₂²×C₁₉	1	1	yes	characteristic
241	#390	C₂²×C₁₉	1	1	yes	characteristic
242	#390	C₂²×C₁₉	1	1	yes	characteristic
243	#389	—	2	1	no	—
244	#389	C₂²×C₁₉	1	2	yes	—
245	#389	C₂²×C₁₉	1	1	yes	characteristic
246	#389	C₂²×C₁₉	1	1	yes	characteristic
247	#389	C₂²×C₁₉	1	1	yes	characteristic
248	#388	—	2	1	no	—
249	#388	—	2	1	no	—
250	#388	—	2	1	no	—
251	#384	C₂²×C₁₉	1	1	yes	characteristic
252	C₄×C₄⋊C₄	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
254	C₄³	C₂²×C₁₉	1	1	yes	characteristic
255	#340	C₂²×C₁₉	1	2	yes	—
256	#340	C₂²×C₁₉	1	2	yes	—
257	#340	C₂²×C₁₉	1	2	yes	—
258	#340	C₂²×C₁₉	1	2	yes	—
259	#336	C₂²×C₁₉	1	1	yes	characteristic
260	#336	C₂²×C₁₉	1	1	yes	characteristic
261	#336	C₂²×C₁₉	1	2	yes	—
262	C₂×C₁₉	—	16	1	no	—
263	C₂×C₁₉	#2604	1	1	yes	characteristic
264	C₂×C₁₉	#3103	1	1	yes	characteristic
265	C₂×C₁₉	#3105	1	1	yes	characteristic
266	C₂×C₁₉	#3167	1	1	yes	characteristic
267	C₂×C₁₉	#3180	1	1	yes	characteristic
268	C₂×C₁₉	#3227	1	1	yes	characteristic
269	C₂×C₁₉	#3233	1	1	yes	characteristic
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
274	C₄⋊Q₈	—	2	4	no	—
275	#126	—	4	4	no	—
276	C₄×Q₈	—	4	4	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	#106	—	2	4	no	—
304	#106	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	C₄×C₈	—	2	4	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	1	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	C₁₉	#29513	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁴	—	2	1	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	#41×C₁₉	1	4	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	#41×C₁₉	1	4	yes	—
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	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	4	no	—
369	C₄²	SD₁₆×C₁₉	1	4	yes	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
378	Q₈	—	4	8	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
410	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
411	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
412	C₂×C₄	C₁₉×#135	1	2	yes	—
413	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
414	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
415	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
416	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₁₉×#525	1	1	yes	characteristic
428	C₂²	C₁₉×#532	1	1	yes	characteristic
429	C₂²	C₁₉×#536	1	1	yes	characteristic
430	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
431	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
432	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
433	C₂²	C₁₉×#575	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	4	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₁₉×#552	1	2	yes	—
446	C₄	C₁₉×#556	1	2	yes	—
447	C₂	—	16	1	no	—
448	C₂	C₁₉×#2604	1	1	yes	characteristic
449	C₂	C₁₉×#3103	1	1	yes	characteristic
450	C₂	C₁₉×#3105	1	1	yes	characteristic
451	C₂	C₁₉×#3167	1	1	yes	characteristic
452	C₂	C₁₉×#3180	1	1	yes	characteristic
453	C₂	C₁₉×#3227	1	1	yes	characteristic
454	C₂	C₁₉×#3233	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
3. C₁₉×#2100	C₂	semidirect
5. C₁₉×#2058	C₂	semidirect
7. C₁₉×#1941	C₂	semidirect
10. C₁₉×#1919	C₂	semidirect
11. C₁₉×#1744	C₂	semidirect
142. #29513	C₁₉	direct (N × H)
194. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
195. #2100	C₂×C₁₉	semidirect
197. #2058	C₂×C₁₉	semidirect
199. #1941	C₂×C₁₉	semidirect
202. #1919	C₂×C₁₉	semidirect
203. #1744	C₂×C₁₉	semidirect
313. C₁₉	#29513	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2860	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2100	2
C₁₉×#2094	2
C₁₉×#2058	2
C₁₉×#2023	2
C₁₉×#1941	2
C₁₉×#1934	2
C₁₉×#1926	2
C₁₉×#1919	2
C₁₉×#1744	2
#29513	19

Subgroups — C19×#29513 #18035472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29513 #18035472