Subgroups — C₁₉×#23660 #18029619

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2085	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2083	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#428	—	2	4	no	—
18	C₂×C₁₉×#107	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	2	yes	—
20	C₂×C₁₉×#107	C₂²	1	4	yes	—
21	C₂×C₁₉×#106	C₂²	1	2	yes	—
22	C₁₉×#389	—	2	2	no	—
23	C₁₉×#389	—	2	2	no	—
24	C₁₉×#389	C₂²	1	4	yes	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₁₉×#380	—	2	2	no	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	4	yes	—
32	C₁₉×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₁₉×#117	—	2	2	no	—
45	C₁₉×#117	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	—	2	2	no	—
49	C₁₉×#117	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#107	—	2	8	no	—
71	C₁₉×#107	—	2	4	no	—
72	C₁₉×#106	—	2	4	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	8	2	no	—
84	C₂²×C₄×C₁₉	—	8	2	no	—
85	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₉	#41	1	2	yes	—
91	C₂²×C₄×C₁₉	#41	1	2	yes	—
92	C₂²×C₄×C₁₉	#41	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₉	—	2	8	no	—
95	C₂×C₈×C₁₉	—	2	8	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
101	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	8	4	no	—
115	C₄⋊C₄×C₁₉	—	8	4	no	—
116	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	4	2	no	—
123	C₄²×C₁₉	—	4	2	no	—
124	#23660	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	#121	1	2	yes	—
128	C₂³×C₁₉	#123	1	2	yes	—
129	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
130	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	4	4	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	8	4	no	—
146	C₂×C₄×C₁₉	—	8	4	no	—
147	C₂×C₄×C₁₉	#121	1	2	yes	—
148	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₁₉	#123	1	2	yes	—
151	C₂×C₄×C₁₉	#125	1	4	yes	—
152	C₂×C₄×C₁₉	#125	1	4	yes	—
153	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₉	—	2	4	no	—
161	C₈×C₁₉	—	2	4	no	—
162	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
163	C₂²×#107	C₂×C₁₉	1	1	yes	characteristic
164	#2317	C₂×C₁₉	1	1	yes	characteristic
165	#2316	C₂×C₁₉	1	1	yes	characteristic
166	#2085	C₂×C₁₉	1	4	yes	complemented
167	#2083	C₂×C₁₉	1	4	yes	complemented
168	#1736	C₂×C₁₉	1	1	yes	characteristic
169	#1735	C₂×C₁₉	1	1	yes	characteristic
170	#1729	C₂×C₁₉	1	1	yes	characteristic
171	C₂²×C₁₉	—	2	4	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	#398	1	4	yes	—
176	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
179	C₂²×C₁₉	#576	1	2	yes	—
180	C₂²×C₁₉	#578	1	2	yes	—
181	C₄×C₁₉	—	4	4	no	—
182	C₄×C₁₉	—	4	4	no	—
183	C₄×C₁₉	—	8	2	no	—
184	C₄×C₁₉	—	8	1	no	—
185	C₄×C₁₉	—	8	2	no	—
186	C₄×C₁₉	—	8	1	no	—
187	C₄×C₁₉	#398	1	4	yes	—
188	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
191	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
192	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
199	#428	—	2	4	no	—
200	C₂×#107	—	2	4	no	—
201	C₂×#107	C₂²×C₁₉	1	2	yes	—
202	C₂×#107	C₂²×C₁₉	1	4	yes	—
203	C₂×#106	C₂²×C₁₉	1	2	yes	—
204	#389	—	2	2	no	—
205	#389	—	2	2	no	—
206	#389	C₂²×C₁₉	1	4	yes	—
207	#385	—	2	2	no	—
208	#384	C₂²×C₁₉	1	2	yes	—
209	#382	C₂²×C₁₉	1	2	yes	—
210	#380	—	2	2	no	—
211	#340	C₂²×C₁₉	1	2	yes	—
212	#340	C₂²×C₁₉	1	4	yes	—
213	#340	C₂²×C₁₉	1	2	yes	—
214	#336	C₂²×C₁₉	1	4	yes	—
215	C₂×C₁₉	—	2	4	no	—
216	C₂×C₁₉	C₂×#398	1	1	yes	characteristic
217	C₂×C₁₉	#3041	1	1	yes	characteristic
218	C₂×C₁₉	#3044	1	1	yes	characteristic
219	C₂×C₁₉	#3098	1	2	yes	—
220	C₂×C₁₉	#3164	1	2	yes	—
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	—	2	1	no	—
223	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	Q₈×C₁₉	1	4	yes	—
230	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
246	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
258	#107	—	2	8	no	—
259	#107	—	2	4	no	—
260	#106	—	2	4	no	—
261	#95	—	2	4	no	—
262	#95	—	2	4	no	—
263	C₁₉	#23660	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	8	2	no	—
273	C₂²×C₄	—	8	2	no	—
274	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
275	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
278	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
279	C₂²×C₄	#41×C₁₉	1	2	yes	—
280	C₂²×C₄	#41×C₁₉	1	2	yes	—
281	C₂²×C₄	#41×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
283	M₁₆	—	2	8	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
290	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	8	4	no	—
304	C₄⋊C₄	—	8	4	no	—
305	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	C₁₉×#121	1	2	yes	—
316	C₂³	C₁₉×#123	1	2	yes	—
317	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
318	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	—	8	4	no	—
335	C₂×C₄	C₁₉×#121	1	2	yes	—
336	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
337	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
338	C₂×C₄	C₁₉×#123	1	2	yes	—
339	C₂×C₄	C₁₉×#125	1	4	yes	—
340	C₂×C₄	C₁₉×#125	1	4	yes	—
341	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	C₁₉×#398	1	4	yes	—
355	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
356	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
357	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
358	C₂²	C₁₉×#576	1	2	yes	—
359	C₂²	C₁₉×#578	1	2	yes	—
360	C₄	—	4	4	no	—
361	C₄	—	4	4	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	C₁₉×#398	1	4	yes	—
367	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
368	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
369	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
370	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
371	C₂	—	2	4	no	—
372	C₂	C₂×C₁₉×#398	1	1	yes	characteristic
373	C₂	C₁₉×#3041	1	1	yes	characteristic
374	C₂	C₁₉×#3044	1	1	yes	characteristic
375	C₂	C₁₉×#3098	1	2	yes	—
376	C₂	C₁₉×#3164	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2083	C₂	semidirect
124. #23660	C₁₉	direct (N × H)
166. #2085	C₂×C₁₉	semidirect
167. #2083	C₂×C₁₉	semidirect
263. C₁₉	#23660	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₂²×C₁₉×#107	2
C₁₉×#2317	2
C₁₉×#2316	2
C₁₉×#2085	2
C₁₉×#2083	2
C₁₉×#1736	2
C₁₉×#1735	2
C₁₉×#1729	2
#23660	19

Subgroups — C19×#23660 #18029619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23660 #18029619