Subgroups — #18081392

Order 4864.

554 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564572	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564430	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926299	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
16	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₈×C₁₉⋊C₈	—	2	2	no	—
18	C₂²×SD₁₆×C₁₉	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₄×SD₁₆×C₁₉	—	2	2	no	—
22	C₄×SD₁₆×C₁₉	—	2	2	no	—
23	C₂×C₁₉×#106	C₄	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₄	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₄	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂×SD₁₆×C₁₉	—	2	2	no	—
31	C₂×SD₁₆×C₁₉	—	2	2	no	—
32	C₂×SD₁₆×C₁₉	C₈	1	4	yes	complemented
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×D₄×C₁₉	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
53	C₁₉×#106	—	2	2	no	—
54	C₁₉×#103	—	2	2	no	—
55	C₁₉×#102	—	2	2	no	—
56	C₄×C₈×C₁₉	D₄	1	2	yes	—
57	C₄×C₈×C₁₉	D₄	1	2	yes	—
58	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
67	C₂⁴×C₁₉	—	2	1	no	—
68	C₂×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	SD₁₆×C₁₉	—	2	8	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
96	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₂²⋊C₄×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	C₂×C₁₉⋊C₈	—	2	4	no	—
112	C₂×C₁₉⋊C₈	—	2	2	no	—
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	2	2	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	complemented
120	#9655	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
127	Q₈×C₁₉	—	2	2	no	—
128	Q₈×C₁₉	—	2	2	no	—
129	Q₈×C₁₉	—	4	1	no	—
130	Q₈×C₁₉	—	4	1	no	—
131	D₄×C₁₉	—	2	2	no	—
132	D₄×C₁₉	—	2	2	no	—
133	D₄×C₁₉	—	4	1	no	—
134	D₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	8	2	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₁₉	#135	1	2	yes	—
158	C₈×C₁₉	—	2	2	no	—
159	C₈×C₁₉	C₂²⋊C₈	1	4	yes	complemented
160	C₁₉⋊C₈	—	2	4	no	—
161	C₁₉⋊C₈	—	2	4	no	—
162	C₁₉⋊C₈	—	8	1	no	—
163	C₁₉⋊C₈	—	8	1	no	—
164	C₂×C₄×SD₁₆	D₁₉	1	1	yes	characteristic
165	#1984	—	19	1	no	—
166	#1954	—	19	1	no	—
167	C₂×#334	—	19	1	no	—
168	C₂×Q₈⋊C₈	—	19	1	no	—
169	C₂×D₄⋊C₈	—	19	1	no	—
170	C₂×C₈²	—	19	1	no	—
171	C₂²×C₁₉	—	4	4	no	—
172	C₂²×C₁₉	—	4	2	no	—
173	C₂²×C₁₉	—	8	2	no	—
174	C₂²×C₁₉	—	8	1	no	—
175	C₂²×C₁₉	—	8	1	no	—
176	C₂²×C₁₉	#390	1	1	yes	characteristic
177	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
178	C₂²×C₁₉	#436	1	1	yes	characteristic
179	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
180	C₂²×C₁₉	#443	1	2	yes	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	4	2	no	—
184	C₄×C₁₉	—	8	1	no	—
185	C₄×C₁₉	—	8	1	no	—
186	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
187	C₄×C₁₉	#408	1	1	yes	characteristic
188	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
189	C₄×C₁₉	#436	1	1	yes	characteristic
190	C₄×C₁₉	#465	1	2	yes	—
191	C₄×C₁₉	#492	1	1	yes	characteristic
192	C₄×C₁₉	#495	1	1	yes	characteristic
193	C₂²×SD₁₆	Dic₁₉	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
196	C₄×SD₁₆	—	2	2	no	—
197	C₄×SD₁₆	—	2	2	no	—
198	C₂×#106	Dic₁₉	1	1	yes	characteristic
199	C₂×C₄⋊C₈	—	19	1	no	—
200	C₂×C₄⋊C₈	—	19	1	no	—
201	C₂×#103	Dic₁₉	1	1	yes	characteristic
202	C₂×#102	Dic₁₉	1	1	yes	characteristic
203	C₂×C₂²⋊C₈	—	38	2	no	—
204	C₂×C₄×C₈	—	19	1	no	—
205	C₂×C₄×C₈	—	19	1	no	—
206	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
207	#336	—	38	2	no	—
208	#334	—	38	2	no	—
209	Q₈⋊C₈	—	38	2	no	—
210	D₄⋊C₈	—	38	2	no	—
211	C₈²	—	38	2	no	—
212	C₂×C₁₉	—	8	2	no	—
213	C₂×C₁₉	C₈×SD₁₆	1	2	yes	—
214	C₂×C₁₉	#1590	1	2	yes	—
215	C₂×C₁₉	#1954	1	1	yes	characteristic
216	C₂×C₁₉	#1968	1	1	yes	characteristic
217	C₂×C₁₉	#1974	1	1	yes	characteristic
218	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
219	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
220	C₂³×C₄	—	2	1	no	—
221	C₂×SD₁₆	—	2	2	no	—
222	C₂×SD₁₆	—	2	2	no	—
223	C₂×SD₁₆	C₁₉⋊C₈	1	4	yes	complemented
224	C₂²×C₈	—	19	2	no	—
225	C₂²×C₈	—	38	1	no	—
226	C₂²×C₈	—	38	1	no	—
227	C₂²×C₈	—	38	1	no	—
228	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
229	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
244	#106	—	2	2	no	—
245	C₄⋊C₈	—	38	1	no	—
246	C₄⋊C₈	—	38	1	no	—
247	C₄⋊C₈	—	38	1	no	—
248	C₄⋊C₈	—	38	1	no	—
249	#103	—	2	2	no	—
250	#102	—	2	2	no	—
251	C₂²⋊C₈	—	76	4	no	—
252	C₄×C₈	—	19	2	no	—
253	C₄×C₈	—	38	1	no	—
254	C₄×C₈	—	38	1	no	—
255	C₄×C₈	—	38	1	no	—
256	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
257	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
258	C₁₉	#9655	1	1	yes	characteristic, complemented, Sylow
259	C₂⁴	—	2	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	C₂×C₁₉⋊C₈	1	2	yes	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	C₂×C₁₉⋊C₈	1	2	yes	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
280	C₂²×C₄	#64543	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
282	SD₁₆	—	2	8	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	19	4	no	—
286	C₂×C₈	—	38	4	no	—
287	C₂×C₈	—	38	2	no	—
288	C₂×C₈	—	38	2	no	—
289	C₂×C₈	—	38	2	no	—
290	C₂×C₈	—	76	1	no	—
291	C₂×C₈	—	76	1	no	—
292	C₂×C₈	—	76	2	no	—
293	C₂×C₈	—	76	2	no	—
294	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
295	C₂×C₈	#64520	1	2	yes	—
296	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
297	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	D₄×D₁₉	1	1	yes	characteristic
309	C₄²	#64543	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	1	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
338	C₂×C₄	#10597362	1	2	yes	—
339	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
340	C₂×C₄	C₂×#64520	1	1	yes	characteristic
341	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
342	C₂×C₄	#10597382	1	1	yes	characteristic
343	C₂×C₄	#10597384	1	1	yes	characteristic
344	C₂×C₄	#10597384	1	1	yes	characteristic
345	C₂×C₄	#10597386	1	1	yes	characteristic
346	C₂×C₄	#10597394	1	1	yes	characteristic
347	C₂×C₄	#10597394	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	38	4	no	—
351	C₈	—	38	4	no	—
352	C₈	—	152	1	no	—
353	C₈	—	152	1	no	—
354	C₈	C₂²⋊(C₁₉⋊C₈)	1	4	yes	complemented
355	C₂²	—	4	2	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	2	no	—
360	C₂²	#11926447	1	1	yes	characteristic
361	C₂²	D₄×C₁₉⋊C₈	1	1	yes	characteristic
362	C₂²	#11926622	1	1	yes	characteristic
363	C₂²	SD₁₆×Dic₁₉	1	2	yes	—
364	C₂²	#11926661	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	8	1	no	—
369	C₄	—	8	1	no	—
370	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
371	C₄	#11926511	1	1	yes	characteristic
372	C₄	D₄×C₁₉⋊C₈	1	1	yes	characteristic
373	C₄	#11926622	1	1	yes	characteristic
374	C₄	#11926770	1	2	yes	—
375	C₄	#11926915	1	1	yes	characteristic
376	C₄	#11926925	1	1	yes	characteristic
377	C₂	—	8	2	no	—
378	C₂	SD₁₆×C₁₉⋊C₈	1	2	yes	—
379	C₂	#14562526	1	2	yes	—
380	C₂	#14564430	1	1	yes	characteristic
381	C₂	#14564491	1	1	yes	characteristic
382	C₂	#14564524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₄×SD₁₆×C₁₉	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×SD₁₆	D₁₉
hypocenter	C₁₉	#9655
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #14564572	C₂	semidirect
3. C₂×#11926295	C₂	semidirect
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
6. C₂×C₈×C₁₉⋊C₈	C₂	semidirect
32. C₂×SD₁₆×C₁₉	C₈	semidirect
119. C₂×C₁₉⋊C₈	SD₁₆	semidirect
159. C₈×C₁₉	C₂²⋊C₈	semidirect
223. C₂×SD₁₆	C₁₉⋊C₈	semidirect
258. C₁₉	#9655	semidirect
354. C₈	C₂²⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#14564572	2
#14564430	2
C₂×#11926295	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×D₄⋊(C₁₉⋊C₈)	2
C₂×C₈×C₁₉⋊C₈	2
C₂×C₄×SD₁₆×C₁₉	2
#9655	19