Subgroups — C₁₉×#18295 #18024254

Order 4864.

940 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3189	C₂	1	2	yes	maximal
3	C₁₉×#2627	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1617	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1605	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1520	C₂	1	2	yes	maximal
7	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#544	—	2	4	no	—
9	C₁₉×#544	—	2	2	no	—
10	C₁₉×#544	C₂²	1	4	yes	—
11	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₁₉×#125	—	2	2	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#484	—	2	2	no	—
19	C₁₉×#484	C₂²	1	4	yes	—
20	C₁₉×#467	—	2	4	no	—
21	C₁₉×#451	—	2	2	no	—
22	C₁₉×#451	C₂²	1	4	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#400	C₂²	1	2	yes	—
25	C₁₉×#398	—	2	2	no	—
26	C₁₉×#395	C₂²	1	2	yes	—
27	C₁₉×#385	—	2	1	no	—
28	C₁₉×#381	—	2	1	no	—
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#328	C₂²	1	8	yes	—
31	C₁₉×#324	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
34	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₁₉	—	2	4	no	—
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₁₉×C₄⋊Q₈	—	2	8	no	—
41	C₁₉×C₄⋊Q₈	—	2	8	no	—
42	C₁₉×#125	—	2	8	no	—
43	C₁₉×#125	—	2	8	no	—
44	C₁₉×C₂²⋊Q₈	—	2	4	no	—
45	C₁₉×C₂²⋊Q₈	—	2	4	no	—
46	C₁₉×C₂²⋊Q₈	—	2	2	no	—
47	C₁₉×C₂²⋊Q₈	—	2	2	no	—
48	C₁₉×C₂²⋊Q₈	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
51	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
52	C₁₉×#117	—	2	4	no	—
53	C₁₉×#117	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₁₉×#107	—	2	4	no	—
73	C₁₉×#103	—	2	4	no	—
74	C₁₉×#103	—	2	4	no	—
75	C₁₉×C₂²⋊C₈	—	2	2	no	—
76	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	C₂³	1	2	yes	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	4	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	8	1	no	—
86	C₂×Q₈×C₁₉	—	8	2	no	—
87	C₂×Q₈×C₁₉	—	8	2	no	—
88	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	8	1	no	—
100	C₂²×C₄×C₁₉	—	8	1	no	—
101	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	complemented
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₁₉	—	8	4	no	—
109	C₂×C₈×C₁₉	—	2	4	no	—
110	C₂×C₈×C₁₉	—	8	2	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	8	1	no	—
123	C₄⋊C₄×C₁₉	—	8	2	no	—
124	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	2	no	—
130	C₄²×C₁₉	—	2	8	no	—
131	#18295	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂³×C₁₉	#120	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
137	C₂³×C₁₉	#137	1	2	yes	—
138	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₉	—	4	4	no	—
140	Q₈×C₁₉	—	4	4	no	—
141	Q₈×C₁₉	—	8	2	no	—
142	Q₈×C₁₉	—	8	4	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	#120	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
169	C₈×C₁₉	—	4	4	no	—
170	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
171	#3189	C₂×C₁₉	1	2	yes	—
172	#2627	C₂×C₁₉	1	1	yes	characteristic
173	#1617	C₂×C₁₉	1	4	yes	complemented
174	#1605	C₂×C₁₉	1	4	yes	complemented
175	#1520	C₂×C₁₉	1	2	yes	—
176	C₂×#324	C₂×C₁₉	1	1	yes	characteristic
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	4	2	no	—
184	C₂²×C₁₉	—	4	2	no	—
185	C₂²×C₁₉	#451	1	2	yes	—
186	C₂²×C₁₉	#451	1	2	yes	—
187	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
188	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
190	C₄×C₁₉	—	2	4	no	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	4	4	no	—
194	C₄×C₁₉	—	4	2	no	—
195	C₄×C₁₉	—	4	4	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	#544	—	2	4	no	—
200	#544	—	2	2	no	—
201	#544	C₂²×C₁₉	1	4	yes	—
202	C₂×C₄⋊Q₈	—	2	2	no	—
203	C₂×#125	—	2	2	no	—
204	C₂×C₂²⋊Q₈	—	2	1	no	—
205	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
206	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#117	—	2	1	no	—
208	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
209	#484	—	2	2	no	—
210	#484	C₂²×C₁₉	1	4	yes	—
211	#467	—	2	4	no	—
212	#451	—	2	2	no	—
213	#451	C₂²×C₁₉	1	4	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
215	#400	C₂²×C₁₉	1	2	yes	—
216	#398	—	2	2	no	—
217	#395	C₂²×C₁₉	1	2	yes	—
218	#385	—	2	1	no	—
219	#381	—	2	1	no	—
220	#380	C₂²×C₁₉	1	1	yes	characteristic
221	#328	C₂²×C₁₉	1	8	yes	—
222	#324	C₂²×C₁₉	1	4	yes	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	2	2	no	—
226	C₂×C₁₉	—	2	2	no	—
227	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
228	C₂×C₁₉	#3020	1	1	yes	characteristic
229	C₂×C₁₉	#3026	1	1	yes	characteristic
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
232	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
233	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂×Q₁₆	—	2	4	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	8	no	—
239	C₄⋊Q₈	—	2	8	no	—
240	#125	—	2	8	no	—
241	#125	—	2	8	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
249	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
250	#117	—	2	4	no	—
251	#117	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	—	2	2	no	—
270	#107	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	2	4	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	C₂³×C₁₉	1	2	yes	—
279	C₁₉	#18295	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	8	1	no	—
285	C₂×Q₈	—	8	2	no	—
286	C₂×Q₈	—	8	2	no	—
287	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	8	1	no	—
299	C₂²×C₄	—	8	1	no	—
300	C₂²×C₄	Q₁₆×C₁₉	1	4	yes	complemented
301	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
307	Q₁₆	—	8	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	8	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	1	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	8	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₁₉×#120	1	1	yes	characteristic
333	C₂³	C₁₉×#120	1	1	yes	characteristic
334	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
335	C₂³	C₁₉×#137	1	2	yes	—
336	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	8	2	no	—
340	Q₈	—	8	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	1	no	—
364	C₂×C₄	C₁₉×#120	1	2	yes	—
365	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
366	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
367	C₈	—	4	4	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₁₉×#451	1	2	yes	—
377	C₂²	C₁₉×#451	1	2	yes	—
378	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
379	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
380	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	2	no	—
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
395	C₂	C₁₉×#3020	1	1	yes	characteristic
396	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
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
4. C₁₉×#1617	C₂	semidirect
5. C₁₉×#1605	C₂	semidirect
101. C₂²×C₄×C₁₉	Q₁₆	semidirect
131. #18295	C₁₉	direct (N × H)
173. #1617	C₂×C₁₉	semidirect
174. #1605	C₂×C₁₉	semidirect
279. C₁₉	#18295	direct (N × H)
300. C₂²×C₄	Q₁₆×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×#544	2
C₁₉×#3189	2
C₁₉×#2627	2
C₁₉×#1617	2
C₁₉×#1605	2
C₁₉×#1520	2
C₂×C₁₉×#324	2
#18295	19

Subgroups — C19×#18295 #18024254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18295 #18024254