Subgroups — #18088357

Order 4864.

1126 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926414	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	4	yes	maximal
4	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₁₉	—	2	2	no	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
11	#11926414	—	2	2	no	—
12	#11926414	C₄	1	4	yes	complemented
13	#11926306	—	2	8	no	—
14	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#384	—	2	2	no	—
18	C₁₉×#384	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₉	—	2	2	no	—
20	C₂³×C₄×C₁₉	D₄	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
36	C₂×C₄⋊Dic₁₉	—	2	4	no	—
37	C₂×C₄⋊Dic₁₉	—	2	4	no	—
38	C₂×C₄⋊Dic₁₉	—	2	8	no	—
39	C₂×C₄⋊Dic₁₉	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	4	4	no	—
41	C₂×C₄⋊Dic₁₉	—	4	4	no	—
42	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	2	no	—
45	C₂²×C₁₉⋊C₈	—	2	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	2	no	—
47	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
48	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
49	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
50	C₄×C₁₉⋊C₈	—	2	8	no	—
51	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	4	no	—
56	C₂²×C₄×C₁₉	—	4	4	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
60	C₂²×C₄×C₁₉	D₈	1	4	yes	—
61	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
62	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
63	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
72	C₂²×C₄×C₁₉	#41	1	2	yes	—
73	C₂²×C₄×C₁₉	#41	1	2	yes	—
74	C₂²×Dic₁₉	—	2	4	no	—
75	C₂²×Dic₁₉	—	4	2	no	—
76	C₂²×Dic₁₉	—	4	2	no	—
77	C₂²×Dic₁₉	—	4	4	no	—
78	C₂²×Dic₁₉	—	4	4	no	—
79	C₄⋊C₄×C₁₉	—	2	8	no	—
80	C₄⋊C₄×C₁₉	—	4	16	no	—
81	C₄⋊C₄×C₁₉	—	4	4	no	—
82	C₄²×C₁₉	C₄²	1	4	yes	—
83	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
84	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
85	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
86	C₄⋊Dic₁₉	—	2	8	no	—
87	C₄⋊Dic₁₉	—	4	16	no	—
88	C₄⋊Dic₁₉	—	4	4	no	—
89	C₂×C₁₉⋊C₈	—	2	4	no	—
90	C₂×C₁₉⋊C₈	—	2	4	no	—
91	C₂×C₁₉⋊C₈	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	2	4	no	—
93	C₂×C₁₉⋊C₈	—	2	4	no	—
94	C₂×C₁₉⋊C₈	—	2	4	no	—
95	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	complemented
96	#10841	—	19	1	no	maximal, Sylow
97	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂³×C₁₉	#124	1	1	yes	characteristic
101	C₂³×C₁₉	#124	1	1	yes	characteristic
102	C₂³×C₁₉	#127	1	1	yes	characteristic
103	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
104	C₂³×C₁₉	C₂×D₈	1	2	yes	—
105	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
106	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
107	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	4	8	no	—
110	C₂×C₄×C₁₉	—	8	4	no	—
111	C₂×C₄×C₁₉	—	8	2	no	—
112	C₂×C₄×C₁₉	—	8	2	no	—
113	C₂×C₄×C₁₉	#95	1	8	yes	—
114	C₂×C₄×C₁₉	#102	1	8	yes	—
115	C₂×C₄×C₁₉	#102	1	8	yes	—
116	C₂×C₄×C₁₉	#103	1	8	yes	—
117	C₂×C₄×C₁₉	#103	1	8	yes	—
118	C₂×C₄×C₁₉	#106	1	8	yes	—
119	C₂×C₄×C₁₉	#107	1	8	yes	—
120	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	#117	1	2	yes	—
126	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
127	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
129	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
130	C₂×C₄×C₁₉	#121	1	2	yes	—
131	C₂×C₄×C₁₉	#121	1	2	yes	—
132	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
134	C₂×C₄×C₁₉	#125	1	2	yes	—
135	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
136	C₂×Dic₁₉	—	4	4	no	—
137	C₂×Dic₁₉	—	4	8	no	—
138	C₂×Dic₁₉	—	8	4	no	—
139	C₂×Dic₁₉	—	8	2	no	—
140	C₂×Dic₁₉	—	8	2	no	—
141	C₁₉⋊C₈	—	2	8	no	—
142	C₂²×C₄×C₈	—	19	1	no	—
143	C₂×#384	—	19	1	no	—
144	C₂×#384	D₁₉	1	1	yes	characteristic
145	C₂×#340	—	19	4	no	—
146	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
147	C₂²×C₁₉	#382	1	1	yes	characteristic
148	C₂²×C₁₉	#384	1	1	yes	characteristic
149	C₂²×C₁₉	#390	1	1	yes	characteristic
150	C₂²×C₁₉	#390	1	1	yes	characteristic
151	C₂²×C₁₉	#391	1	1	yes	characteristic
152	C₂²×C₁₉	#391	1	1	yes	characteristic
153	C₂²×C₁₉	C₂×#102	1	2	yes	—
154	C₂²×C₁₉	C₂×#102	1	2	yes	—
155	C₂²×C₁₉	C₂×#103	1	2	yes	—
156	C₂²×C₁₉	C₂×#103	1	2	yes	—
157	C₂²×C₁₉	C₂×#106	1	2	yes	—
158	C₂²×C₁₉	C₂×#107	1	2	yes	—
159	C₂²×C₁₉	#486	1	2	yes	—
160	C₂²×C₁₉	#486	1	2	yes	—
161	C₂²×C₁₉	#487	1	2	yes	—
162	C₂²×C₁₉	#487	1	2	yes	—
163	C₂²×C₁₉	#492	1	1	yes	characteristic
164	C₂²×C₁₉	#492	1	1	yes	characteristic
165	C₂²×C₁₉	#493	1	1	yes	characteristic
166	C₂²×C₁₉	#494	1	1	yes	characteristic
167	C₂²×C₁₉	#498	1	2	yes	—
168	C₂²×C₁₉	#500	1	2	yes	—
169	C₄×C₁₉	—	8	4	no	—
170	C₄×C₁₉	#340	1	16	yes	complemented
171	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
172	C₄×C₁₉	#380	1	2	yes	—
173	C₄×C₁₉	#389	1	2	yes	—
174	C₄×C₁₉	#389	1	2	yes	—
175	Dic₁₉	—	8	4	no	—
176	C₂³×C₈	—	19	2	no	—
177	C₂²×C₄⋊C₄	—	2	2	no	—
178	C₂²×C₄⋊C₄	—	19	2	no	—
179	C₂²×C₄⋊C₄	—	38	2	no	—
180	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
181	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
182	C₂×C₄×C₈	—	19	4	no	—
183	C₂×C₄×C₈	—	38	2	no	—
184	C₂×C₄×C₈	—	38	2	no	—
185	#384	—	2	2	no	—
186	#384	—	19	4	no	—
187	#384	—	38	2	no	—
188	#384	Dic₁₉	1	4	yes	complemented
189	#340	—	38	8	no	—
190	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₁₉	C₂×#340	1	2	yes	—
192	C₂×C₁₉	#1834	1	2	yes	—
193	C₂×C₁₉	#1844	1	1	yes	characteristic
194	C₂×C₁₉	#1845	1	1	yes	characteristic
195	C₂×C₁₉	#1956	1	1	yes	characteristic
196	C₂×C₁₉	#1956	1	1	yes	characteristic
197	C₂×C₁₉	#1957	1	1	yes	characteristic
198	C₂×C₁₉	#1957	1	1	yes	characteristic
199	C₂×C₁₉	#1990	1	2	yes	—
200	C₂×C₁₉	#1990	1	2	yes	—
201	C₂³×C₄	—	2	2	no	—
202	C₂³×C₄	—	38	2	no	—
203	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
204	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
205	C₂²×C₈	—	19	4	no	—
206	C₂²×C₈	—	19	4	no	—
207	C₂²×C₈	—	19	4	no	—
208	C₂²×C₈	—	38	2	no	—
209	C₂²×C₈	—	38	2	no	—
210	C₂²×C₈	—	38	2	no	—
211	C₂²×C₈	—	38	2	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	8	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	4	4	no	—
217	C₂×C₄⋊C₄	—	4	4	no	—
218	C₂×C₄⋊C₄	—	19	4	no	—
219	C₂×C₄⋊C₄	—	38	4	no	—
220	C₂×C₄⋊C₄	—	38	4	no	—
221	C₂×C₄⋊C₄	—	38	8	no	—
222	C₂×C₄⋊C₄	—	38	2	no	—
223	C₂×C₄⋊C₄	—	76	4	no	—
224	C₂×C₄⋊C₄	—	76	4	no	—
225	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
226	C₂×C₄²	Dic₃₈	1	2	yes	—
227	C₂×C₄²	C₄×D₁₉	1	2	yes	—
228	C₂×C₄²	C₄×D₁₉	1	2	yes	—
229	C₂×C₄²	D₇₆	1	2	yes	—
230	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
231	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
232	C₄×C₈	—	38	8	no	—
233	C₁₉	#10841	1	1	yes	characteristic, complemented, Sylow
234	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	4	4	no	—
237	C₂²×C₄	—	4	4	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	38	4	no	—
241	C₂²×C₄	—	76	4	no	—
242	C₂²×C₄	—	76	2	no	—
243	C₂²×C₄	—	76	4	no	—
244	C₂²×C₄	—	76	2	no	—
245	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
246	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
247	C₂²×C₄	#64525	1	4	yes	—
248	C₂²×C₄	#64526	1	4	yes	—
249	C₂²×C₄	#64527	1	4	yes	—
250	C₂²×C₄	#64528	1	4	yes	—
251	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
252	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
253	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
256	C₂²×C₄	D₄×D₁₉	1	2	yes	—
257	C₂²×C₄	#64543	1	2	yes	—
258	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
259	C₂²×C₄	#64545	1	2	yes	—
260	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₈	—	19	8	no	—
263	C₂×C₈	—	38	4	no	—
264	C₂×C₈	—	38	4	no	—
265	C₂×C₈	—	38	4	no	—
266	C₂×C₈	—	38	4	no	—
267	C₂×C₈	—	38	4	no	—
268	C₂×C₈	—	38	4	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	4	4	no	—
271	C₄⋊C₄	—	4	16	no	—
272	C₄⋊C₄	—	38	8	no	—
273	C₄⋊C₄	—	76	16	no	—
274	C₄⋊C₄	—	76	4	no	—
275	C₄²	C₄×Dic₁₉	1	4	yes	—
276	C₄²	Dic₁₉⋊C₄	1	4	yes	—
277	C₄²	C₄⋊Dic₁₉	1	4	yes	—
278	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
279	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
280	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
281	C₂³	C₂×#64525	1	2	yes	—
282	C₂³	C₂×#64526	1	2	yes	—
283	C₂³	#10597382	1	1	yes	characteristic
284	C₂³	#10597386	1	1	yes	characteristic
285	C₂³	C₂×#64527	1	2	yes	—
286	C₂³	C₂×#64528	1	2	yes	—
287	C₂³	#10597390	1	1	yes	characteristic
288	C₂³	#10597393	1	1	yes	characteristic
289	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
290	C₂×C₄	—	4	8	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	8	4	no	—
293	C₂×C₄	—	8	2	no	—
294	C₂×C₄	—	8	2	no	—
295	C₂×C₄	—	76	8	no	—
296	C₂×C₄	—	76	4	no	—
297	C₂×C₄	—	152	4	no	—
298	C₂×C₄	—	152	2	no	—
299	C₂×C₄	—	152	2	no	—
300	C₂×C₄	#10597264	1	8	yes	—
301	C₂×C₄	#10597265	1	8	yes	—
302	C₂×C₄	#10597266	1	8	yes	—
303	C₂×C₄	#10597267	1	8	yes	—
304	C₂×C₄	C₁₉⋊#95	1	8	yes	—
305	C₂×C₄	#10597289	1	8	yes	—
306	C₂×C₄	#10597292	1	8	yes	—
307	C₂×C₄	#10597333	1	2	yes	—
308	C₂×C₄	#10597334	1	2	yes	—
309	C₂×C₄	#10597336	1	2	yes	—
310	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
311	C₂×C₄	#10597338	1	2	yes	—
312	C₂×C₄	#10597339	1	2	yes	—
313	C₂×C₄	#10597341	1	2	yes	—
314	C₂×C₄	#10597343	1	2	yes	—
315	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
316	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
318	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
319	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
320	C₂×C₄	#10597384	1	2	yes	—
321	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
322	C₂×C₄	#10597392	1	2	yes	—
323	C₈	—	38	8	no	—
324	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
325	C₂²	#11926409	1	1	yes	characteristic
326	C₂²	#11926413	1	1	yes	characteristic
327	C₂²	#11926445	1	1	yes	characteristic
328	C₂²	#11926447	1	1	yes	characteristic
329	C₂²	#11926449	1	1	yes	characteristic
330	C₂²	#11926451	1	1	yes	characteristic
331	C₂²	C₂×#10597266	1	2	yes	—
332	C₂²	C₂×#10597289	1	2	yes	—
333	C₂²	C₂×#10597267	1	2	yes	—
334	C₂²	C₂×#10597292	1	2	yes	—
335	C₂²	C₂×#10597265	1	2	yes	—
336	C₂²	C₂×#10597264	1	2	yes	—
337	C₂²	#11926890	1	2	yes	—
338	C₂²	#11926892	1	2	yes	—
339	C₂²	#11926894	1	2	yes	—
340	C₂²	#11926896	1	2	yes	—
341	C₂²	#11926916	1	1	yes	characteristic
342	C₂²	#11926918	1	1	yes	characteristic
343	C₂²	#11926920	1	1	yes	characteristic
344	C₂²	#11926923	1	1	yes	characteristic
345	C₂²	#11926940	1	2	yes	—
346	C₂²	#11926947	1	2	yes	—
347	C₄	—	8	4	no	—
348	C₄	—	152	4	no	—
349	C₄	#11926306	1	16	yes	complemented
350	C₄	C₄⋊C₄×Dic₁₉	1	2	yes	—
351	C₄	#11926401	1	2	yes	—
352	C₄	#11926440	1	2	yes	—
353	C₄	#11926443	1	2	yes	—
354	C₂	#14561864	1	1	yes	characteristic
355	C₂	C₂×#11926306	1	2	yes	—
356	C₂	#14563762	1	2	yes	—
357	C₂	#14563791	1	1	yes	characteristic
358	C₂	#14563794	1	1	yes	characteristic
359	C₂	#14564436	1	1	yes	characteristic
360	C₂	#14564438	1	1	yes	characteristic
361	C₂	#14564440	1	1	yes	characteristic
362	C₂	#14564442	1	1	yes	characteristic
363	C₂	#14564595	1	2	yes	—
364	C₂	#14564597	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#384	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#384	D₁₉
hypocenter	C₁₉	#10841
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₁₉⋊C₈	C₄	semidirect
12. #11926414	C₄	semidirect
18. C₁₉×#384	C₄	semidirect
95. C₂×C₁₉⋊C₈	C₄⋊C₄	semidirect
170. C₄×C₁₉	#340	semidirect
188. #384	Dic₁₉	semidirect
233. C₁₉	#10841	semidirect
349. C₄	#11926306	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₉⋊C₈	2
C₂×#11926414	2
C₂×#11926306	2
C₂×C₁₉×#384	2
#10841	19