Subgroups — C₁₉×#2510 #14560367

Order 2432.

482 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#386	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#386	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#386	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₁₉×#95	C₂²	1	1	yes	characteristic
40	C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₁₉×#95	C₂²	1	1	yes	characteristic
43	C₁₉×#95	C₂²	1	1	yes	characteristic
44	C₁₉×#95	C₂²	1	1	yes	characteristic
45	C₁₉×#95	C₂²	1	1	yes	characteristic
46	C₁₉×#95	C₂²	1	1	yes	characteristic
47	C₁₉×#95	C₂²	1	1	yes	characteristic
48	C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₁₉×#95	C₂²	1	1	yes	characteristic
50	C₁₉×#95	C₂²	1	1	yes	characteristic
51	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
52	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	4	1	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂²⋊C₄×C₁₉	—	4	1	no	—
88	C₂²⋊C₄×C₁₉	—	4	1	no	—
89	C₂²⋊C₄×C₁₉	—	4	1	no	—
90	C₂²⋊C₄×C₁₉	—	4	1	no	—
91	C₄²×C₁₉	—	2	2	no	—
92	C₄²×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	2	1	no	—
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	2	1	no	—
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	2	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	—	2	1	no	—
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	#41	1	2	yes	—
105	C₂³×C₁₉	#41	1	2	yes	—
106	C₂³×C₁₉	#41	1	2	yes	—
107	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
108	D₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	#41	1	2	yes	—
150	C₂×C₄×C₁₉	#41	1	2	yes	—
151	#2510	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂²×C₁₉	—	2	2	no	—
153	C₂²×C₁₉	—	2	2	no	—
154	C₂²×C₁₉	—	2	2	no	—
155	C₂²×C₁₉	—	2	2	no	—
156	C₂²×C₁₉	—	2	2	no	—
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	4	1	no	—
159	C₂²×C₁₉	—	4	1	no	—
160	C₂²×C₁₉	—	4	1	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	1	no	—
163	C₂²×C₁₉	—	4	1	no	—
164	C₂²×C₁₉	—	4	1	no	—
165	C₂²×C₁₉	#126	1	4	yes	—
166	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
167	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
169	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₄×C₁₉	—	2	2	no	—
174	C₄×C₁₉	—	2	2	no	—
175	C₄×C₁₉	—	4	1	no	—
176	C₄×C₁₉	—	4	1	no	—
177	C₄×C₁₉	—	4	1	no	—
178	C₄×C₁₉	—	4	1	no	—
179	C₄×C₁₉	—	4	1	no	—
180	C₄×C₁₉	—	4	1	no	—
181	C₄×C₁₉	—	4	1	no	—
182	C₄×C₁₉	—	4	1	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	4	1	no	—
186	#401	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#400	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#397	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#397	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#388	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#388	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#387	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#386	C₂×C₁₉	1	1	yes	characteristic
194	#386	C₂×C₁₉	1	1	yes	characteristic
195	#386	C₂×C₁₉	1	1	yes	characteristic
196	#385	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#383	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#380	C₂×C₁₉	1	1	yes	characteristic, complemented
199	C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂×#95	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂×C₁₉	—	2	4	no	—
202	C₂×C₁₉	—	8	1	no	—
203	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
204	C₂×C₁₉	#529	1	1	yes	characteristic
205	C₂×C₁₉	#538	1	1	yes	characteristic
206	C₂×C₁₉	#551	1	1	yes	characteristic
207	C₂×C₁₉	#551	1	1	yes	characteristic
208	C₂×C₁₉	#553	1	1	yes	characteristic
209	C₂×C₁₉	#553	1	1	yes	characteristic
210	C₂²×D₄	C₂²×C₁₉	1	1	yes	characteristic
211	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
212	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
229	#95	C₂²×C₁₉	1	1	yes	characteristic
230	#95	C₂²×C₁₉	1	1	yes	characteristic
231	#95	C₂²×C₁₉	1	1	yes	characteristic
232	#95	C₂²×C₁₉	1	1	yes	characteristic
233	#95	C₂²×C₁₉	1	1	yes	characteristic
234	#95	C₂²×C₁₉	1	1	yes	characteristic
235	#95	C₂²×C₁₉	1	1	yes	characteristic
236	#95	C₂²×C₁₉	1	1	yes	characteristic
237	#95	C₂²×C₁₉	1	1	yes	characteristic
238	#95	C₂²×C₁₉	1	1	yes	characteristic
239	#95	C₂²×C₁₉	1	1	yes	characteristic
240	#95	C₂²×C₁₉	1	1	yes	characteristic
241	#95	C₂²×C₁₉	1	1	yes	characteristic
242	#95	C₂²×C₁₉	1	1	yes	characteristic
243	#95	C₂²×C₁₉	1	1	yes	characteristic
244	#95	C₂²×C₁₉	1	1	yes	characteristic
245	C₁₉	#2510	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	C₂³×C₁₉	1	1	yes	characteristic
247	C₂⁴	C₂³×C₁₉	1	1	yes	characteristic
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
270	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	4	1	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₂²⋊C₄	—	2	2	no	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	4	1	no	—
283	C₂²⋊C₄	—	4	1	no	—
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	4	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	#41×C₁₉	1	2	yes	—
300	C₂³	#41×C₁₉	1	2	yes	—
301	C₂³	#41×C₁₉	1	2	yes	—
302	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
303	D₄	—	4	4	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	#41×C₁₉	1	2	yes	—
345	C₂×C₄	#41×C₁₉	1	2	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	C₁₉×#126	1	4	yes	—
360	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
361	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
362	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
363	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
364	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
365	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₂	—	2	4	no	—
381	C₂	—	8	1	no	—
382	C₂	C₂×C₁₉×#126	1	1	yes	characteristic
383	C₂	C₁₉×#529	1	1	yes	characteristic
384	C₂	C₁₉×#538	1	1	yes	characteristic
385	C₂	C₁₉×#551	1	1	yes	characteristic
386	C₂	C₁₉×#551	1	1	yes	characteristic
387	C₂	C₁₉×#553	1	1	yes	characteristic
388	C₂	C₁₉×#553	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₉×#401	C₂	semidirect
2. C₁₉×#400	C₂	semidirect
3. C₁₉×#397	C₂	semidirect
4. C₁₉×#397	C₂	semidirect
5. C₁₉×#388	C₂	semidirect
6. C₁₉×#388	C₂	semidirect
7. C₁₉×#387	C₂	semidirect
11. C₁₉×#385	C₂	semidirect
12. C₁₉×#383	C₂	semidirect
13. C₁₉×#380	C₂	semidirect
14. C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
15. C₂×C₁₉×#95	C₂	semidirect
151. #2510	C₁₉	direct (N × H)
186. #401	C₂×C₁₉	semidirect
187. #400	C₂×C₁₉	semidirect
188. #397	C₂×C₁₉	semidirect
189. #397	C₂×C₁₉	semidirect
190. #388	C₂×C₁₉	semidirect
191. #388	C₂×C₁₉	semidirect
192. #387	C₂×C₁₉	semidirect
196. #385	C₂×C₁₉	semidirect
197. #383	C₂×C₁₉	semidirect
198. #380	C₂×C₁₉	semidirect
199. C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
200. C₂×#95	C₂×C₁₉	semidirect
245. C₁₉	#2510	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×#401	2
C₁₉×#400	2
C₁₉×#397	2
C₁₉×#388	2
C₁₉×#387	2
C₁₉×#386	2
C₁₉×#385	2
C₁₉×#383	2
C₁₉×#380	2
C₄×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#95	2
#2510	19

Subgroups — C19×#2510 #14560367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2510 #14560367