Subgroups — C₁₉×#8154 #18014113

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1749	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#324	C₂	1	2	yes	maximal
5	C₁₉×#1280	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₉×#97	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	—	2	1	no	—
13	C₁₉×#387	—	2	1	no	—
14	C₁₉×#387	—	2	1	no	—
15	C₁₉×#387	—	2	1	no	—
16	C₁₉×#387	—	2	1	no	—
17	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
18	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
19	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
20	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#324	C₄	1	8	yes	complemented
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₁₉	—	4	2	no	—
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₁₉×C₂²⋊C₈	—	2	2	no	—
47	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
48	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
49	C₁₉×#97	—	4	2	no	—
50	C₄×C₈×C₁₉	—	4	2	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
85	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	2	yes	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₂×C₈×C₁₉	—	4	2	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	#8154	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
114	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₁₉	#117	1	1	yes	characteristic
116	C₂³×C₁₉	#131	1	2	yes	—
117	C₂³×C₁₉	#131	1	2	yes	—
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	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	4	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	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	—	8	2	no	—
154	C₂×C₄×C₁₉	#99	1	2	yes	—
155	C₂×C₄×C₁₉	#101	1	2	yes	—
156	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
158	C₈×C₁₉	—	4	4	no	—
159	C₈×C₁₉	—	4	4	no	—
160	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
161	#1749	C₂×C₁₉	1	1	yes	characteristic
162	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
163	C₂×#324	C₂×C₁₉	1	2	yes	—
164	#1280	C₂×C₁₉	1	2	yes	—
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₁₉	#405	1	2	yes	—
175	C₂²×C₁₉	#408	1	1	yes	characteristic
176	C₂²×C₁₉	#408	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
178	C₂²×C₁₉	#410	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
180	C₂²×C₁₉	#413	1	1	yes	characteristic
181	C₂²×C₁₉	#433	1	2	yes	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	1	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	8	1	no	—
191	C₄×C₁₉	—	8	1	no	—
192	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
194	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
197	C₂×#97	—	2	1	no	—
198	C₂×C₄×C₈	—	2	1	no	—
199	#387	—	2	1	no	—
200	#387	—	2	1	no	—
201	#387	—	2	1	no	—
202	#387	—	2	1	no	—
203	C₂×#95	C₄×C₁₉	1	1	yes	characteristic
204	C₂×#95	C₄×C₁₉	1	1	yes	characteristic
205	C₂×#95	C₄×C₁₉	1	1	yes	characteristic
206	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
207	#336	—	2	1	no	—
208	#336	—	2	1	no	—
209	#324	C₄×C₁₉	1	8	yes	complemented
210	C₂×C₁₉	—	2	2	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	#1468	1	1	yes	characteristic
213	C₂×C₁₉	#1470	1	1	yes	characteristic
214	C₂×C₁₉	#1472	1	1	yes	characteristic
215	C₂×C₁₉	#1473	1	1	yes	characteristic
216	C₂×C₁₉	#1750	1	1	yes	characteristic
217	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
218	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
222	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	4	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
235	C₂×C₄²	—	4	2	no	—
236	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
243	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
244	#97	—	4	2	no	—
245	C₄×C₈	—	4	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	C₁₉	#8154	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	C₄²×C₁₉	1	2	yes	—
281	C₂²×C₄	C₄²×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	#41×C₁₉	1	2	yes	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	2	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	4	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
309	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
310	C₂³	C₁₉×#117	1	1	yes	characteristic
311	C₂³	C₁₉×#131	1	2	yes	—
312	C₂³	C₁₉×#131	1	2	yes	—
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	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	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	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	C₁₉×#99	1	2	yes	—
350	C₂×C₄	C₁₉×#101	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
352	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
353	C₈	—	4	4	no	—
354	C₈	—	4	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
364	C₂²	C₁₉×#405	1	2	yes	—
365	C₂²	C₁₉×#408	1	1	yes	characteristic
366	C₂²	C₁₉×#408	1	1	yes	characteristic
367	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
368	C₂²	C₁₉×#410	1	1	yes	characteristic
369	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
370	C₂²	C₁₉×#413	1	1	yes	characteristic
371	C₂²	C₁₉×#433	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	1	no	—
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	C₁₉×#1468	1	1	yes	characteristic
385	C₂	C₁₉×#1470	1	1	yes	characteristic
386	C₂	C₁₉×#1472	1	1	yes	characteristic
387	C₂	C₁₉×#1473	1	1	yes	characteristic
388	C₂	C₁₉×#1750	1	1	yes	characteristic
389	C₂	C₄×C₁₉×#99	1	1	yes	characteristic
390	C₂	C₄×C₁₉×#101	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₁₉×#324	C₄	semidirect
108. #8154	C₁₉	direct (N × H)
209. #324	C₄×C₁₉	semidirect
254. C₁₉	#8154	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×#387	2
C₁₉×#1749	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#324	2
C₁₉×#1280	2
#8154	19

Subgroups — C19×#8154 #18014113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8154 #18014113