Subgroups — C₁₉×#21033 #18026992

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1921	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1920	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1919	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1918	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#428	C₄	1	8	yes	complemented
21	C₂×C₁₉×#107	C₂²	1	2	yes	—
22	C₂×C₁₉×#106	C₂²	1	2	yes	—
23	C₁₉×#389	C₂²	1	1	yes	characteristic
24	C₁₉×#389	C₂²	1	1	yes	characteristic
25	C₁₉×#389	C₂²	1	1	yes	characteristic
26	C₁₉×#389	C₂²	1	1	yes	characteristic
27	C₁₉×#385	—	2	1	no	—
28	C₁₉×#385	—	2	1	no	—
29	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	—	2	1	no	—
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×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	2	yes	—
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	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	2	2	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	—	4	4	no	—
86	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#107	C₂×C₄	1	8	yes	complemented
91	C₁₉×#106	C₂×C₄	1	8	yes	complemented
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	1	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	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	C₂²×C₄	1	2	yes	—
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×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₁₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₁₉	—	2	8	no	—
130	M₁₆×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	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	C₂²×C₄	1	4	yes	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	—	4	2	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
155	C₂²⋊C₄×C₁₉	—	2	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	2	no	—
157	C₄²×C₁₉	—	2	4	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	—	4	4	no	—
165	C₄²×C₁₉	—	4	2	no	—
166	C₄²×C₁₉	—	4	4	no	—
167	#21033	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	C₄×D₄	1	2	yes	—
173	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
174	C₂³×C₁₉	#123	1	2	yes	—
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	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	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	8	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	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	#117	1	4	yes	—
209	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
211	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
212	C₂×C₄×C₁₉	#123	1	2	yes	—
213	C₂×C₄×C₁₉	#125	1	4	yes	—
214	C₂×C₄×C₁₉	#126	1	4	yes	—
215	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₁₉	#137	1	2	yes	—
217	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₉	—	2	4	no	—
224	C₈×C₁₉	—	4	2	no	—
225	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
226	#2296	C₂×C₁₉	1	1	yes	characteristic
227	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
228	#1921	C₂×C₁₉	1	2	yes	complemented
229	#1920	C₂×C₁₉	1	2	yes	complemented
230	#1919	C₂×C₁₉	1	2	yes	complemented
231	#1918	C₂×C₁₉	1	2	yes	complemented
232	#1736	C₂×C₁₉	1	1	yes	characteristic
233	#1736	C₂×C₁₉	1	1	yes	characteristic
234	#1736	C₂×C₁₉	1	1	yes	characteristic
235	#1728	C₂×C₁₉	1	1	yes	characteristic
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	#387	1	4	yes	—
243	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
245	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
248	C₂²×C₁₉	#575	1	1	yes	characteristic
249	C₂²×C₁₉	#575	1	1	yes	characteristic
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	—	2	2	no	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	4	1	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	—	4	2	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	#387	1	4	yes	—
261	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
262	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
264	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
265	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
271	C₂²×C₄²	—	2	1	no	—
272	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
273	#428	C₄×C₁₉	1	8	yes	complemented
274	C₂×#107	C₂²×C₁₉	1	2	yes	—
275	C₂×#106	C₂²×C₁₉	1	2	yes	—
276	#389	C₂²×C₁₉	1	1	yes	characteristic
277	#389	C₂²×C₁₉	1	1	yes	characteristic
278	#389	C₂²×C₁₉	1	1	yes	characteristic
279	#389	C₂²×C₁₉	1	1	yes	characteristic
280	#385	—	2	1	no	—
281	#385	—	2	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	—	2	1	no	—
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
287	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
288	C₂×#95	—	2	1	no	—
289	#340	C₂²×C₁₉	1	2	yes	—
290	#340	C₂²×C₁₉	1	2	yes	—
291	#340	C₂²×C₁₉	1	2	yes	—
292	#340	C₂²×C₁₉	1	2	yes	—
293	#340	C₂²×C₁₉	1	2	yes	—
294	#340	C₂²×C₁₉	1	2	yes	—
295	#336	C₂²×C₁₉	1	2	yes	—
296	#336	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	2	4	no	—
298	C₂×C₁₉	C₂×#387	1	1	yes	characteristic
299	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
301	C₂×C₁₉	#3077	1	1	yes	characteristic
302	C₂×C₁₉	#3078	1	1	yes	characteristic
303	C₂×C₁₉	#3092	1	1	yes	characteristic
304	C₂×C₁₉	#3093	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
316	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
317	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	#117	—	2	2	no	—
321	#117	C₂×C₄×C₁₉	1	4	yes	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
331	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	4	4	no	—
347	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
351	#107	C₂×C₄×C₁₉	1	8	yes	complemented
352	#106	C₂×C₄×C₁₉	1	8	yes	complemented
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	C₁₉	#21033	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
386	C₂²×C₄	#41×C₁₉	1	2	yes	—
387	C₂²×C₄	#41×C₁₉	1	2	yes	—
388	C₂²×C₄	#41×C₁₉	1	2	yes	—
389	C₂²×C₄	#41×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
391	M₁₆	—	2	8	no	—
392	M₁₆	—	4	4	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
415	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
416	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	4	4	no	—
427	C₄²	—	4	2	no	—
428	C₄²	—	4	4	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	C₄×D₄×C₁₉	1	2	yes	—
434	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
435	C₂³	C₁₉×#123	1	2	yes	—
436	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	C₁₉×#117	1	4	yes	—
470	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
471	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
472	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
473	C₂×C₄	C₁₉×#123	1	2	yes	—
474	C₂×C₄	C₁₉×#125	1	4	yes	—
475	C₂×C₄	C₁₉×#126	1	4	yes	—
476	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
477	C₂×C₄	C₁₉×#137	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
479	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
484	C₈	—	2	4	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	C₁₉×#387	1	4	yes	—
493	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
494	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
495	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
496	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
497	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
498	C₂²	C₁₉×#575	1	1	yes	characteristic
499	C₂²	C₁₉×#575	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	1	no	—
510	C₄	C₁₉×#387	1	4	yes	—
511	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
512	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
513	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
514	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
515	C₂	—	2	4	no	—
516	C₂	C₂×C₁₉×#387	1	1	yes	characteristic
517	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
519	C₂	C₁₉×#3077	1	1	yes	characteristic
520	C₂	C₁₉×#3078	1	1	yes	characteristic
521	C₂	C₁₉×#3092	1	1	yes	characteristic
522	C₂	C₁₉×#3093	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×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
4. C₁₉×#1921	C₂	semidirect
5. C₁₉×#1920	C₂	semidirect
6. C₁₉×#1919	C₂	semidirect
7. C₁₉×#1918	C₂	semidirect
20. C₁₉×#428	C₄	semidirect
90. C₁₉×#107	C₂×C₄	semidirect
91. C₁₉×#106	C₂×C₄	semidirect
167. #21033	C₁₉	direct (N × H)
228. #1921	C₂×C₁₉	semidirect
229. #1920	C₂×C₁₉	semidirect
230. #1919	C₂×C₁₉	semidirect
231. #1918	C₂×C₁₉	semidirect
273. #428	C₄×C₁₉	semidirect
351. #107	C₂×C₄×C₁₉	semidirect
352. #106	C₂×C₄×C₁₉	semidirect
359. C₁₉	#21033	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₁₉×#2296	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1921	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1918	2
C₁₉×#1736	2
C₁₉×#1728	2
#21033	19

Subgroups — C19×#21033 #18026992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21033 #18026992