Subgroups — C₁₉×#2334 #14560191

Order 2432.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#126	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#388	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#388	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#388	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#385	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#385	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#126	C₄	1	8	yes	complemented
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊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×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊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×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	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	C₁₉×#95	C₂²	1	1	yes	characteristic
52	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
78	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
79	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
80	C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂²⋊C₄×C₁₉	—	4	1	no	—
82	C₂²⋊C₄×C₁₉	—	4	1	no	—
83	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
84	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
85	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
86	C₄²×C₁₉	—	2	2	no	—
87	C₄²×C₁₉	—	4	1	no	—
88	C₄²×C₁₉	—	4	1	no	—
89	C₄²×C₁₉	—	4	1	no	—
90	C₄²×C₁₉	—	4	1	no	—
91	C₄²×C₁₉	C₂×C₄	1	4	yes	complemented
92	C₂³×C₁₉	—	2	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	C₂²×C₄	1	2	yes	—
99	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	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	—	4	4	no	—
135	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
136	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
138	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
140	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂×C₄×C₁₉	#41	1	2	yes	—
142	C₂×C₄×C₁₉	#41	1	2	yes	—
143	#2334	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂²×C₁₉	—	2	2	no	—
145	C₂²×C₁₉	—	2	2	no	—
146	C₂²×C₁₉	—	2	2	no	—
147	C₂²×C₁₉	—	4	1	no	—
148	C₂²×C₁₉	—	4	1	no	—
149	C₂²×C₁₉	—	4	1	no	—
150	C₂²×C₁₉	—	4	1	no	—
151	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
152	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
153	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
154	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
158	C₄×C₁₉	—	2	2	no	—
159	C₄×C₁₉	—	2	2	no	—
160	C₄×C₁₉	—	2	2	no	—
161	C₄×C₁₉	—	2	2	no	—
162	C₄×C₁₉	—	2	2	no	—
163	C₄×C₁₉	—	2	2	no	—
164	C₄×C₁₉	—	2	2	no	—
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	4	1	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	—	4	1	no	—
170	C₄×C₁₉	—	4	1	no	—
171	C₄×C₁₉	—	4	1	no	—
172	C₂×#126	C₂×C₁₉	1	1	yes	characteristic
173	#389	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#389	C₂×C₁₉	1	1	yes	characteristic, complemented
175	#388	C₂×C₁₉	1	1	yes	characteristic
176	#388	C₂×C₁₉	1	1	yes	characteristic
177	#388	C₂×C₁₉	1	1	yes	characteristic
178	#387	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#387	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#387	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#385	C₂×C₁₉	1	1	yes	characteristic
182	#385	C₂×C₁₉	1	1	yes	characteristic
183	#382	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
187	C₂×C₁₉	—	4	2	no	—
188	C₂×C₁₉	C₄×#41	1	1	yes	characteristic
189	C₂×C₁₉	#520	1	1	yes	characteristic
190	C₂×C₁₉	#520	1	1	yes	characteristic
191	C₂×C₁₉	#538	1	1	yes	characteristic
192	C₂×C₁₉	#539	1	1	yes	characteristic
193	C₂×C₁₉	#541	1	1	yes	characteristic
194	C₂×C₁₉	#542	1	1	yes	characteristic
195	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
196	#126	C₄×C₁₉	1	8	yes	complemented
197	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
219	#95	C₂²×C₁₉	1	1	yes	characteristic
220	#95	C₂²×C₁₉	1	1	yes	characteristic
221	#95	C₂²×C₁₉	1	1	yes	characteristic
222	#95	C₂²×C₁₉	1	1	yes	characteristic
223	#95	C₂²×C₁₉	1	1	yes	characteristic
224	#95	C₂²×C₁₉	1	1	yes	characteristic
225	#95	C₂²×C₁₉	1	1	yes	characteristic
226	#95	C₂²×C₁₉	1	1	yes	characteristic
227	#95	C₂²×C₁₉	1	1	yes	characteristic
228	#95	C₂²×C₁₉	1	1	yes	characteristic
229	#95	C₂²×C₁₉	1	1	yes	characteristic
230	#95	C₂²×C₁₉	1	1	yes	characteristic
231	C₁₉	#2334	1	1	yes	characteristic, direct product factor, Sylow
232	C₂⁴	C₂³×C₁₉	1	1	yes	characteristic
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	4	1	no	—
235	C₂²×C₄	—	4	1	no	—
236	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
237	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
238	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
239	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	4	1	no	—
254	C₄⋊C₄	—	4	1	no	—
255	C₄⋊C₄	—	4	1	no	—
256	C₄⋊C₄	—	4	1	no	—
257	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
258	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
259	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
260	C₂²⋊C₄	—	2	2	no	—
261	C₂²⋊C₄	—	4	1	no	—
262	C₂²⋊C₄	—	4	1	no	—
263	C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
264	C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
265	C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
266	C₄²	—	2	2	no	—
267	C₄²	—	4	1	no	—
268	C₄²	—	4	1	no	—
269	C₄²	—	4	1	no	—
270	C₄²	—	4	1	no	—
271	C₄²	C₂×C₄×C₁₉	1	4	yes	complemented
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	1	no	—
278	C₂³	C₂²×C₄×C₁₉	1	2	yes	—
279	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	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	—	4	4	no	—
315	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
316	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
317	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
318	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
319	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
320	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
321	C₂×C₄	#41×C₁₉	1	2	yes	—
322	C₂×C₄	#41×C₁₉	1	2	yes	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	C₂³×C₄×C₁₉	1	1	yes	characteristic
331	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
332	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
333	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₂	—	4	2	no	—
352	C₂	C₄×#41×C₁₉	1	1	yes	characteristic
353	C₂	C₁₉×#520	1	1	yes	characteristic
354	C₂	C₁₉×#520	1	1	yes	characteristic
355	C₂	C₁₉×#538	1	1	yes	characteristic
356	C₂	C₁₉×#539	1	1	yes	characteristic
357	C₂	C₁₉×#541	1	1	yes	characteristic
358	C₂	C₁₉×#542	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#389	C₂	semidirect
3. C₁₉×#389	C₂	semidirect
7. C₁₉×#387	C₂	semidirect
8. C₁₉×#387	C₂	semidirect
9. C₁₉×#387	C₂	semidirect
12. C₁₉×#382	C₂	semidirect
13. C₄×C₄⋊C₄×C₁₉	C₂	semidirect
14. C₄×C₄⋊C₄×C₁₉	C₂	semidirect
17. C₁₉×#126	C₄	semidirect
77. C₄⋊C₄×C₁₉	C₂×C₄	semidirect
78. C₄⋊C₄×C₁₉	C₂×C₄	semidirect
79. C₄⋊C₄×C₁₉	C₂×C₄	semidirect
91. C₄²×C₁₉	C₂×C₄	semidirect
143. #2334	C₁₉	direct (N × H)
173. #389	C₂×C₁₉	semidirect
174. #389	C₂×C₁₉	semidirect
178. #387	C₂×C₁₉	semidirect
179. #387	C₂×C₁₉	semidirect
180. #387	C₂×C₁₉	semidirect
183. #382	C₂×C₁₉	semidirect
184. C₄×C₄⋊C₄	C₂×C₁₉	semidirect
185. C₄×C₄⋊C₄	C₂×C₁₉	semidirect
196. #126	C₄×C₁₉	semidirect
231. C₁₉	#2334	direct (N × H)
257. C₄⋊C₄	C₂×C₄×C₁₉	semidirect
258. C₄⋊C₄	C₂×C₄×C₁₉	semidirect
259. C₄⋊C₄	C₂×C₄×C₁₉	semidirect
271. C₄²	C₂×C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#126	2
C₁₉×#389	2
C₁₉×#388	2
C₁₉×#387	2
C₁₉×#385	2
C₁₉×#382	2
C₄×C₄⋊C₄×C₁₉	2
C₄×C₂²⋊C₄×C₁₉	2
#2334	19

Subgroups — C19×#2334 #14560191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2334 #14560191