Subgroups — C₁₉×#20912 #18026871

Order 4864.

2278 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#418	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1875	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₉	—	2	1	no	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×#121	—	2	4	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	C₄	1	8	yes	complemented
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	—	2	1	no	—
19	C₂×C₁₉×#117	—	2	1	no	—
20	C₂×C₁₉×#117	—	2	8	no	—
21	C₂×C₁₉×#117	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄²×C₁₉	—	2	1	no	—
28	C₁₉×#418	—	2	8	no	—
29	C₂×C₁₉×#102	C₂²	1	8	yes	complemented
30	C₁₉×#407	—	2	4	no	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
33	C₁₉×#340	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₉	—	2	1	no	—
35	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	—	2	8	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	—	4	8	no	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	4	no	—
47	C₂³×C₄×C₁₉	—	2	4	no	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	D₄	1	4	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₉	—	2	4	no	—
59	C₂×M₁₆×C₁₉	—	2	4	no	—
60	C₂×M₁₆×C₁₉	—	2	4	no	—
61	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
62	C₁₉×#121	—	2	8	no	—
63	C₁₉×#121	—	2	8	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	C₂×C₄	1	8	yes	—
67	C₁₉×#121	C₂×C₄	1	8	yes	complemented
68	C₁₉×#117	—	2	8	no	—
69	C₁₉×#117	—	2	8	no	—
70	C₁₉×#117	—	2	4	no	—
71	C₁₉×#117	—	2	8	no	—
72	C₁₉×#117	D₄	1	8	yes	complemented
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄²×C₁₉	—	2	8	no	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	—	2	2	no	—
89	C₁₉×#102	—	2	16	no	—
90	C₁₉×C₂²⋊C₈	—	2	4	no	—
91	C₁₉×C₂²⋊C₈	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	4	2	no	—
98	C₂⁴×C₁₉	—	4	4	no	—
99	C₂⁴×C₁₉	—	4	4	no	—
100	C₂⁴×C₁₉	—	4	2	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	16	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	4	no	—
113	C₂×D₄×C₁₉	—	4	32	no	—
114	C₂×D₄×C₁₉	—	4	8	no	—
115	C₂×D₄×C₁₉	—	4	8	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	8	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	16	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	16	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	4	4	no	—
137	C₂²×C₄×C₁₉	—	4	4	no	—
138	C₂²×C₄×C₁₉	—	4	4	no	—
139	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	#41	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	M₁₆×C₁₉	—	4	8	no	—
155	C₂×C₈×C₁₉	—	2	4	no	—
156	C₂×C₈×C₁₉	—	2	4	no	—
157	C₂×C₈×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	8	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	complemented
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	—	2	8	no	—
169	C₄²×C₁₉	—	2	8	no	—
170	#20912	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	8	no	—
181	C₂³×C₁₉	—	2	8	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	8	no	—
185	C₂³×C₁₉	—	4	8	no	—
186	C₂³×C₁₉	—	4	8	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	4	8	no	—
193	C₂³×C₁₉	—	8	8	no	—
194	C₂³×C₁₉	—	8	8	no	—
195	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂³×C₁₉	#120	1	2	yes	—
199	C₂³×C₁₉	#123	1	2	yes	—
200	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
201	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	D₄×C₁₉	—	2	8	no	—
203	D₄×C₁₉	—	4	16	no	—
204	D₄×C₁₉	—	4	16	no	—
205	D₄×C₁₉	—	4	4	no	—
206	D₄×C₁₉	—	4	8	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	8	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	8	no	—
217	C₂×C₄×C₁₉	—	2	8	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	8	no	—
220	C₂×C₄×C₁₉	—	4	16	no	—
221	C₂×C₄×C₁₉	—	4	8	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	#121	1	8	yes	—
231	C₂×C₄×C₁₉	#123	1	2	yes	—
232	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
236	C₈×C₁₉	—	4	4	no	—
237	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
238	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#418	C₂×C₁₉	1	2	yes	complemented
240	C₂×#407	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1875	C₂×C₁₉	1	4	yes	complemented
242	#1874	C₂×C₁₉	1	4	yes	complemented
243	#1736	C₂×C₁₉	1	2	yes	complemented
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	2	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	4	no	—
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	—	2	2	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	4	16	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	4	no	—
259	C₂²×C₁₉	—	4	4	no	—
260	C₂²×C₁₉	—	4	4	no	—
261	C₂²×C₁₉	—	8	16	no	—
262	C₂²×C₁₉	—	8	4	no	—
263	C₂²×C₁₉	—	8	4	no	—
264	C₂²×C₁₉	#386	1	4	yes	—
265	C₂²×C₁₉	#418	1	4	yes	complemented
266	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
268	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
270	C₂²×C₁₉	#575	1	2	yes	—
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	4	4	no	—
274	C₄×C₁₉	—	4	8	no	—
275	C₄×C₁₉	#386	1	4	yes	—
276	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
277	C₄×C₁₉	C₂×#121	1	2	yes	—
278	C₂³×D₄	—	2	1	no	—
279	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
280	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
282	C₂×#121	—	2	4	no	—
283	C₂×#121	—	2	1	no	—
284	C₂×#121	—	2	1	no	—
285	C₂×#121	C₄×C₁₉	1	8	yes	complemented
286	C₂×#121	C₂²×C₁₉	1	2	yes	—
287	C₂×#121	C₂²×C₁₉	1	2	yes	—
288	C₂×#117	—	2	1	no	—
289	C₂×#117	—	2	1	no	—
290	C₂×#117	—	2	8	no	—
291	C₂×#117	C₂²×C₁₉	1	2	yes	—
292	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
293	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
295	C₂²×C₂²⋊C₄	—	2	1	no	—
296	C₂²×C₂²⋊C₄	—	2	1	no	—
297	C₂²×C₄²	—	2	1	no	—
298	#418	—	2	8	no	—
299	C₂×#102	C₂²×C₁₉	1	8	yes	complemented
300	#407	—	2	4	no	—
301	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
302	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
303	#340	C₂²×C₁₉	1	8	yes	complemented
304	C₂×C₁₉	—	2	4	no	—
305	C₂×C₁₉	—	2	4	no	—
306	C₂×C₁₉	—	4	2	no	—
307	C₂×C₁₉	—	8	4	no	—
308	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
309	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
310	C₂×C₁₉	#2896	1	1	yes	characteristic
311	C₂×C₁₉	#3006	1	2	yes	—
312	C₂×C₁₉	#3094	1	2	yes	—
313	C₂⁵	—	2	1	no	—
314	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
315	C₂²×D₄	—	2	8	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	4	no	—
322	C₂²×D₄	—	4	8	no	—
323	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
324	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	—	2	4	no	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
330	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
331	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₁₉	1	4	yes	—
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂×M₁₆	—	2	4	no	—
338	C₂×M₁₆	—	2	4	no	—
339	C₂×M₁₆	—	2	4	no	—
340	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
341	#121	—	2	8	no	—
342	#121	—	2	8	no	—
343	#121	—	2	4	no	—
344	#121	—	2	4	no	—
345	#121	C₂×C₄×C₁₉	1	8	yes	—
346	#121	C₂×C₄×C₁₉	1	8	yes	complemented
347	#117	—	2	8	no	—
348	#117	—	2	8	no	—
349	#117	—	2	4	no	—
350	#117	—	2	8	no	—
351	#117	D₄×C₁₉	1	8	yes	complemented
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	8	no	—
356	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
359	C₂×C₂²⋊C₄	—	2	8	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	8	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₄²	—	2	8	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	#102	—	2	16	no	—
369	C₂²⋊C₈	—	2	4	no	—
370	C₂²⋊C₈	—	2	4	no	—
371	C₁₉	#20912	1	1	yes	characteristic, direct product factor, Sylow
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	4	4	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	—	4	2	no	—
382	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
383	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	16	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	4	32	no	—
394	C₂×D₄	—	4	8	no	—
395	C₂×D₄	—	4	8	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	16	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
420	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
421	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
422	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
423	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
432	C₂²×C₄	#41×C₁₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
434	M₁₆	—	4	8	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	2	4	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	complemented
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₄²	—	2	8	no	—
449	C₄²	—	2	8	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	8	8	no	—
473	C₂³	—	8	8	no	—
474	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
475	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
476	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
477	C₂³	C₁₉×#120	1	2	yes	—
478	C₂³	C₁₉×#123	1	2	yes	—
479	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
480	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
481	D₄	—	2	8	no	—
482	D₄	—	4	16	no	—
483	D₄	—	4	16	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	4	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
505	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
506	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
507	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
508	C₂×C₄	C₁₉×#120	1	2	yes	—
509	C₂×C₄	C₁₉×#121	1	8	yes	—
510	C₂×C₄	C₁₉×#123	1	2	yes	—
511	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
515	C₈	—	4	4	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	4	16	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	8	16	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	4	no	—
536	C₂²	C₁₉×#386	1	4	yes	—
537	C₂²	C₁₉×#418	1	4	yes	complemented
538	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
539	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
540	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
541	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
542	C₂²	C₁₉×#575	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	8	no	—
546	C₄	—	4	4	no	—
547	C₄	C₁₉×#386	1	4	yes	—
548	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
549	C₄	C₂×C₁₉×#121	1	2	yes	—
550	C₂	—	2	4	no	—
551	C₂	—	2	4	no	—
552	C₂	—	4	2	no	—
553	C₂	—	8	4	no	—
554	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
555	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
556	C₂	C₁₉×#2896	1	1	yes	characteristic
557	C₂	C₁₉×#3006	1	2	yes	—
558	C₂	C₁₉×#3094	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#117	C₂	semidirect
3. C₂×C₁₉×#418	C₂	semidirect
4. C₂×C₁₉×#407	C₂	semidirect
5. C₁₉×#1875	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1736	C₂	semidirect
15. C₂×C₁₉×#121	C₄	semidirect
22. C₂×C₁₉×#117	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
29. C₂×C₁₉×#102	C₂²	semidirect
31. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
44. C₂²×D₄×C₁₉	C₂×C₄	semidirect
67. C₁₉×#121	C₂×C₄	semidirect
72. C₁₉×#117	D₄	semidirect
77. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
163. C₄⋊C₄×C₁₉	C₂×D₄	semidirect
170. #20912	C₁₉	direct (N × H)
238. C₂²×#117	C₂×C₁₉	semidirect
239. C₂×#418	C₂×C₁₉	semidirect
240. C₂×#407	C₂×C₁₉	semidirect
241. #1875	C₂×C₁₉	semidirect
242. #1874	C₂×C₁₉	semidirect
243. #1736	C₂×C₁₉	semidirect
265. C₂²×C₁₉	#418	semidirect
285. C₂×#121	C₄×C₁₉	semidirect
292. C₂×#117	C₂²×C₁₉	semidirect
294. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
299. C₂×#102	C₂²×C₁₉	semidirect
301. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
302. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
303. #340	C₂²×C₁₉	semidirect
323. C₂²×D₄	C₂×C₄×C₁₉	semidirect
346. #121	C₂×C₄×C₁₉	semidirect
351. #117	D₄×C₁₉	semidirect
356. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
371. C₁₉	#20912	direct (N × H)
443. C₄⋊C₄	C₂×D₄×C₁₉	semidirect
537. C₂²	C₁₉×#418	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#121	2
C₂²×C₁₉×#117	2
C₂×C₁₉×#418	2
C₂×C₁₉×#407	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1736	2
#20912	19

Subgroups — C19×#20912 #18026871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20912 #18026871