Subgroups — C₁₉×#26290 #18032249

Order 4864.

660 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2584	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
25	C₁₉×#398	—	2	1	no	—
26	C₁₉×#395	—	2	1	no	—
27	C₁₉×#389	—	2	1	no	—
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#389	—	2	1	no	—
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#384	C₂²	1	1	yes	characteristic
37	C₁₉×#384	C₂²	1	1	yes	characteristic
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#340	C₂²	1	1	yes	characteristic
44	C₁₉×#340	C₂²	1	1	yes	characteristic
45	C₁₉×#340	C₂²	1	1	yes	characteristic
46	C₁₉×#340	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	4	4	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	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	Q₈	1	4	yes	complemented
100	C₁₉×#106	—	2	2	no	—
101	C₁₉×#106	—	2	2	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×C₄⋊C₈	—	2	2	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
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	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	2	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	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	8	1	no	—
167	C₄⋊C₄×C₁₉	—	8	1	no	—
168	C₄⋊C₄×C₁₉	—	8	1	no	—
169	C₄⋊C₄×C₁₉	—	8	1	no	—
170	C₄⋊C₄×C₁₉	—	8	1	no	—
171	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
173	C₄⋊C₄×C₁₉	#41	1	2	yes	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	4	2	no	—
179	C₄²×C₁₉	—	4	2	no	—
180	C₄²×C₁₉	—	4	2	no	—
181	C₄²×C₁₉	—	8	1	no	—
182	C₄²×C₁₉	#41	1	2	yes	—
183	C₄²×C₁₉	#41	1	2	yes	—
184	#26290	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	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	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	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	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	#123	1	2	yes	—
226	C₂×C₄×C₁₉	#123	1	2	yes	—
227	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₉	#137	1	2	yes	—
229	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₈×C₁₉	—	2	2	no	—
236	C₈×C₁₉	—	4	1	no	—
237	C₈×C₁₉	—	4	1	no	—
238	C₈×C₁₉	—	4	1	no	—
239	#2584	C₂×C₁₉	1	1	yes	characteristic
240	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
241	#2100	C₂×C₁₉	1	1	yes	characteristic
242	#2099	C₂×C₁₉	1	1	yes	characteristic
243	#2084	C₂×C₁₉	1	1	yes	characteristic
244	#2084	C₂×C₁₉	1	1	yes	characteristic
245	#1992	C₂×C₁₉	1	1	yes	characteristic
246	#1989	C₂×C₁₉	1	1	yes	characteristic
247	#1985	C₂×C₁₉	1	1	yes	characteristic
248	#1948	C₂×C₁₉	1	1	yes	characteristic
249	#1921	C₂×C₁₉	1	1	yes	characteristic
250	#1920	C₂×C₁₉	1	1	yes	characteristic
251	#1919	C₂×C₁₉	1	1	yes	characteristic
252	#1918	C₂×C₁₉	1	1	yes	characteristic
253	#1776	C₂×C₁₉	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
255	C₂²×C₁₉	#548	1	1	yes	characteristic
256	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
259	C₂²×C₁₉	#577	1	1	yes	characteristic
260	C₂²×C₁₉	#577	1	1	yes	characteristic
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	#533	1	1	yes	characteristic
276	C₄×C₁₉	#541	1	1	yes	characteristic
277	C₄×C₁₉	#556	1	1	yes	characteristic
278	C₄×C₁₉	#557	1	1	yes	characteristic
279	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×C₄×Q₈	—	2	1	no	—
281	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
288	#398	—	2	1	no	—
289	#395	—	2	1	no	—
290	#389	—	2	1	no	—
291	#389	—	2	1	no	—
292	#389	—	2	1	no	—
293	#389	—	2	1	no	—
294	#389	—	2	1	no	—
295	#389	C₂²×C₁₉	1	1	yes	characteristic
296	#389	C₂²×C₁₉	1	1	yes	characteristic
297	#389	C₂²×C₁₉	1	1	yes	characteristic
298	#389	C₂²×C₁₉	1	1	yes	characteristic
299	#384	C₂²×C₁₉	1	1	yes	characteristic
300	#384	C₂²×C₁₉	1	1	yes	characteristic
301	#384	C₂²×C₁₉	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
306	#340	C₂²×C₁₉	1	1	yes	characteristic
307	#340	C₂²×C₁₉	1	1	yes	characteristic
308	#340	C₂²×C₁₉	1	1	yes	characteristic
309	#340	C₂²×C₁₉	1	1	yes	characteristic
310	#340	C₂²×C₁₉	1	1	yes	characteristic
311	#340	C₂²×C₁₉	1	1	yes	characteristic
312	#340	C₂²×C₁₉	1	1	yes	characteristic
313	#340	C₂²×C₁₉	1	1	yes	characteristic
314	#340	C₂²×C₁₉	1	1	yes	characteristic
315	#340	C₂²×C₁₉	1	1	yes	characteristic
316	#340	C₂²×C₁₉	1	1	yes	characteristic
317	#340	C₂²×C₁₉	1	1	yes	characteristic
318	#336	C₂²×C₁₉	1	1	yes	characteristic
319	#336	C₂²×C₁₉	1	1	yes	characteristic
320	#336	C₂²×C₁₉	1	1	yes	characteristic
321	#336	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₁₉	#2446	1	1	yes	characteristic
323	C₂×C₁₉	#3092	1	1	yes	characteristic
324	C₂×C₁₉	#3099	1	1	yes	characteristic
325	C₂×C₁₉	#3368	1	1	yes	characteristic
326	C₂×C₁₉	#3372	1	1	yes	characteristic
327	C₂×C₁₉	#3384	1	1	yes	characteristic
328	C₂×C₁₉	#3387	1	1	yes	characteristic
329	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
334	#125	—	2	2	no	—
335	#125	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	4	4	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	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	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
369	#107	Q₈×C₁₉	1	4	yes	complemented
370	#106	—	2	2	no	—
371	#106	—	2	2	no	—
372	#106	—	2	2	no	—
373	C₄⋊C₈	—	2	2	no	—
374	#97	—	2	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	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	C₁₉	#26290	1	1	yes	characteristic, direct product factor, Sylow
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	—	4	2	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	8	1	no	—
438	C₄⋊C₄	—	8	1	no	—
439	C₄⋊C₄	—	8	1	no	—
440	C₄⋊C₄	—	8	1	no	—
441	C₄⋊C₄	—	8	1	no	—
442	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
443	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
444	C₄⋊C₄	#41×C₁₉	1	2	yes	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	4	2	no	—
450	C₄²	—	4	2	no	—
451	C₄²	—	4	2	no	—
452	C₄²	—	8	1	no	—
453	C₄²	#41×C₁₉	1	2	yes	—
454	C₄²	#41×C₁₉	1	2	yes	—
455	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	Q₈	—	2	8	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	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	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	C₁₉×#123	1	2	yes	—
496	C₂×C₄	C₁₉×#123	1	2	yes	—
497	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
498	C₂×C₄	C₁₉×#137	1	2	yes	—
499	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
504	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
505	C₈	—	2	2	no	—
506	C₈	—	4	1	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	1	no	—
509	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
510	C₂²	C₁₉×#548	1	1	yes	characteristic
511	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
512	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
513	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
514	C₂²	C₁₉×#577	1	1	yes	characteristic
515	C₂²	C₁₉×#577	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	1	no	—
530	C₄	C₁₉×#533	1	1	yes	characteristic
531	C₄	C₁₉×#541	1	1	yes	characteristic
532	C₄	C₁₉×#556	1	1	yes	characteristic
533	C₄	C₁₉×#557	1	1	yes	characteristic
534	C₂	C₁₉×#2446	1	1	yes	characteristic
535	C₂	C₁₉×#3092	1	1	yes	characteristic
536	C₂	C₁₉×#3099	1	1	yes	characteristic
537	C₂	C₁₉×#3368	1	1	yes	characteristic
538	C₂	C₁₉×#3372	1	1	yes	characteristic
539	C₂	C₁₉×#3384	1	1	yes	characteristic
540	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 ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
99. C₁₉×#107	Q₈	semidirect
184. #26290	C₁₉	direct (N × H)
369. #107	Q₈×C₁₉	semidirect
383. C₁₉	#26290	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×#2584	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2084	2
C₁₉×#1992	2
C₁₉×#1989	2
C₁₉×#1985	2
C₁₉×#1948	2
C₁₉×#1921	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1918	2
C₁₉×#1776	2
#26290	19

Subgroups — C19×#26290 #18032249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26290 #18032249