Subgroups — C₁₉×#8375 #18014334

Order 4864.

1518 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1786	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1519	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	—	2	1	no	—
7	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	D₄²×C₁₉	—	2	4	no	—
10	D₄²×C₁₉	—	2	4	no	—
11	C₂×C₁₉×#127	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#121	—	2	1	no	—
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#120	—	2	1	no	—
16	C₂×C₁₉×#120	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#102	—	2	4	no	—
20	C₂×C₁₉×#99	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
22	C₁₉×#380	C₂²	1	2	yes	complemented
23	C₁₉×#342	—	2	1	no	—
24	C₁₉×#327	—	2	4	no	—
25	C₁₉×#324	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂⁵×C₁₉	—	2	1	no	—
28	C₂⁵×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	8	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	4	4	no	—
40	C₂²×D₄×C₁₉	—	4	4	no	—
41	C₂²×D₄×C₁₉	—	4	4	no	—
42	C₂²×D₄×C₁₉	—	4	2	no	—
43	C₂²×D₄×C₁₉	—	4	2	no	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	D₄	1	4	yes	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₁₉×#127	—	2	2	no	—
54	C₁₉×#127	—	2	2	no	—
55	C₁₉×#121	—	2	8	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	2	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	D₄	1	4	yes	—
60	C₁₉×#120	—	2	8	no	—
61	C₁₉×#120	—	2	8	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₁₉×#102	—	4	8	no	—
77	C₁₉×#99	—	4	2	no	—
78	C₁₉×C₂²⋊C₈	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	4	4	no	—
87	C₂⁴×C₁₉	—	4	4	no	—
88	C₂⁴×C₁₉	—	4	2	no	—
89	C₂⁴×C₁₉	—	4	2	no	—
90	C₂⁴×C₁₉	—	4	1	no	—
91	C₂⁴×C₁₉	—	4	1	no	—
92	C₂⁴×C₁₉	—	4	2	no	—
93	C₂⁴×C₁₉	—	8	2	no	—
94	C₂⁴×C₁₉	—	8	2	no	—
95	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	4	8	no	—
115	C₂×D₄×C₁₉	—	4	8	no	—
116	C₂×D₄×C₁₉	—	4	16	no	—
117	C₂×D₄×C₁₉	—	4	16	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	4	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	2	no	—
126	C₂×D₄×C₁₉	—	4	4	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	8	2	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₂×D₄×C₁₉	D₈	1	2	yes	—
133	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	4	2	no	—
143	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×C₈×C₁₉	—	4	4	no	—
151	C₂×C₈×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	2	no	—
162	C₂²⋊C₄×C₁₉	—	4	2	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	—	2	1	no	—
165	#8375	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	8	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	8	no	—
181	C₂³×C₁₉	—	4	8	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	8	4	no	—
193	C₂³×C₁₉	—	8	4	no	—
194	C₂³×C₁₉	—	8	4	no	—
195	C₂³×C₁₉	—	8	4	no	—
196	C₂³×C₁₉	—	8	8	no	—
197	C₂³×C₁₉	—	8	8	no	—
198	C₂³×C₁₉	—	8	8	no	—
199	C₂³×C₁₉	#102	1	2	yes	complemented
200	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₁₉	#120	1	2	yes	—
202	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
203	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
204	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	2	no	—
209	D₄×C₁₉	—	2	4	no	—
210	D₄×C₁₉	—	4	8	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	8	no	—
214	D₄×C₁₉	—	4	8	no	—
215	D₄×C₁₉	—	4	8	no	—
216	D₄×C₁₉	—	4	4	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	8	4	no	—
220	D₄×C₁₉	#99	1	4	yes	complemented
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	8	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	#102	1	2	yes	complemented
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#120	1	2	yes	—
244	C₈×C₁₉	—	8	2	no	—
245	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic
246	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1786	C₂×C₁₉	1	2	yes	complemented
248	#1519	C₂×C₁₉	1	2	yes	complemented
249	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	4	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	4	no	—
261	C₂²×C₁₉	—	4	4	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	8	8	no	—
274	C₂²×C₁₉	—	8	8	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	—	8	2	no	—
277	C₂²×C₁₉	—	8	2	no	—
278	C₂²×C₁₉	—	8	2	no	—
279	C₂²×C₁₉	—	8	16	no	—
280	C₂²×C₁₉	#379	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
282	C₂²×C₁₉	#418	1	1	yes	characteristic
283	C₂²×C₁₉	#447	1	2	yes	—
284	C₂²×C₁₉	#450	1	2	yes	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	2	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	16	2	no	—
292	C₄×C₁₉	C₂×#99	1	2	yes	—
293	C₂³×D₄	—	2	1	no	—
294	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
295	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
296	D₄²	—	2	4	no	—
297	D₄²	—	2	4	no	—
298	C₂×#127	C₄×C₁₉	1	1	yes	characteristic, complemented
299	C₂×#121	—	2	1	no	—
300	C₂×#121	C₄×C₁₉	1	1	yes	characteristic, complemented
301	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#120	—	2	1	no	—
303	C₂×#120	—	2	1	no	—
304	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
305	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#102	—	2	4	no	—
307	C₂×#99	—	2	1	no	—
308	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
309	#380	C₂²×C₁₉	1	2	yes	complemented
310	#342	—	2	1	no	—
311	#327	—	2	4	no	—
312	#324	—	2	1	no	—
313	#323	—	2	1	no	—
314	C₂×C₁₉	—	2	2	no	—
315	C₂×C₁₉	—	2	1	no	—
316	C₂×C₁₉	—	2	1	no	—
317	C₂×C₁₉	—	2	2	no	—
318	C₂×C₁₉	—	4	4	no	—
319	C₂×C₁₉	—	4	2	no	—
320	C₂×C₁₉	—	8	2	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	#1781	1	1	yes	characteristic
323	C₂×C₁₉	#1786	1	1	yes	characteristic
324	C₂×C₁₉	#1795	1	1	yes	characteristic
325	C₂⁵	—	2	1	no	—
326	C₂⁵	—	2	1	no	—
327	C₂²×D₄	—	2	8	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	4	4	no	—
338	C₂²×D₄	—	4	4	no	—
339	C₂²×D₄	—	4	4	no	—
340	C₂²×D₄	—	4	2	no	—
341	C₂²×D₄	—	4	2	no	—
342	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
343	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
344	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
345	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂²×D₄	D₄×C₁₉	1	4	yes	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂²×C₈	—	2	2	no	—
351	#127	—	2	2	no	—
352	#127	—	2	2	no	—
353	#121	—	2	8	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	D₄×C₁₉	1	4	yes	—
358	#120	—	2	8	no	—
359	#120	—	2	8	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
374	#102	—	4	8	no	—
375	#99	—	4	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	#95	—	2	2	no	—
379	C₁₉	#8375	1	1	yes	characteristic, direct product factor, Sylow
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	4	no	—
382	C₂⁴	—	2	1	no	—
383	C₂⁴	—	2	1	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	4	4	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	2	no	—
388	C₂⁴	—	4	1	no	—
389	C₂⁴	—	4	1	no	—
390	C₂⁴	—	4	2	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	—	8	2	no	—
393	C₂⁴	—	8	2	no	—
394	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	8	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	—	4	16	no	—
416	C₂×D₄	—	4	16	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
429	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
430	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
431	C₂×D₄	D₈×C₁₉	1	2	yes	—
432	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₈	—	4	4	no	—
450	C₂×C₈	—	4	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	8	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	—	8	4	no	—
494	C₂³	—	8	8	no	—
495	C₂³	—	8	8	no	—
496	C₂³	—	8	8	no	—
497	C₂³	C₁₉×#102	1	2	yes	complemented
498	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
499	C₂³	C₁₉×#120	1	2	yes	—
500	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
501	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
502	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
503	D₄	—	2	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	4	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	8	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	2	no	—
517	D₄	—	8	4	no	—
518	D₄	C₁₉×#99	1	4	yes	complemented
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	C₁₉×#102	1	2	yes	complemented
539	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
540	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
541	C₂×C₄	C₁₉×#120	1	2	yes	—
542	C₈	—	8	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	8	8	no	—
567	C₂²	—	8	8	no	—
568	C₂²	—	8	2	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	16	no	—
573	C₂²	C₁₉×#379	1	1	yes	characteristic
574	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
575	C₂²	C₁₉×#418	1	1	yes	characteristic
576	C₂²	C₁₉×#447	1	2	yes	—
577	C₂²	C₁₉×#450	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	16	2	no	—
585	C₄	C₂×C₁₉×#99	1	2	yes	—
586	C₂	—	2	2	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	2	no	—
590	C₂	—	4	4	no	—
591	C₂	—	4	2	no	—
592	C₂	—	8	2	no	—
593	C₂	—	8	2	no	—
594	C₂	C₁₉×#1781	1	1	yes	characteristic
595	C₂	C₁₉×#1786	1	1	yes	characteristic
596	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×D₄²×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1799	C₂	semidirect
3. C₁₉×#1786	C₂	semidirect
4. C₁₉×#1519	C₂	semidirect
5. C₁₉×#1459	C₂	semidirect
7. C₂³×D₄×C₁₉	C₄	semidirect
11. C₂×C₁₉×#127	C₄	semidirect
13. C₂×C₁₉×#121	C₄	semidirect
17. C₂×C₄×D₄×C₁₉	C₄	semidirect
21. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
22. C₁₉×#380	C₂²	semidirect
165. #8375	C₁₉	direct (N × H)
199. C₂³×C₁₉	#102	semidirect
220. D₄×C₁₉	#99	semidirect
240. C₂×C₄×C₁₉	#102	semidirect
246. #1799	C₂×C₁₉	semidirect
247. #1786	C₂×C₁₉	semidirect
248. #1519	C₂×C₁₉	semidirect
249. #1459	C₂×C₁₉	semidirect
294. C₂³×D₄	C₄×C₁₉	semidirect
298. C₂×#127	C₄×C₁₉	semidirect
300. C₂×#121	C₄×C₁₉	semidirect
304. C₂×C₄×D₄	C₄×C₁₉	semidirect
308. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
309. #380	C₂²×C₁₉	semidirect
379. C₁₉	#8375	direct (N × H)
497. C₂³	C₁₉×#102	semidirect
518. D₄	C₁₉×#99	semidirect
538. C₂×C₄	C₁₉×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₉	2
C₁₉×#1799	2
C₁₉×#1786	2
C₁₉×#1519	2
C₁₉×#1459	2
#8375	19

Subgroups — C19×#8375 #18014334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8375 #18014334