Subgroups — #18077639

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572199	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562060	C₂	1	2	yes	maximal, complemented
3	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561538	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2392	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	—	2	1	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926571	—	2	4	no	—
9	#11926568	—	2	1	no	—
10	#11926568	C₂²	1	2	yes	—
11	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#398	C₄	1	1	yes	characteristic
18	C₁₉×#397	C₄	1	1	yes	characteristic
19	C₁₉×#396	—	2	1	no	—
20	C₁₉×#394	—	2	1	no	—
21	C₁₉×#394	C₄	1	1	yes	characteristic
22	C₁₉×#392	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₄×D₄×C₁₉	—	4	2	no	—
32	C₄×D₄×C₁₉	—	4	2	no	—
33	C₁₉×#117	—	2	2	no	—
34	C₁₉×#117	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×#64520	—	2	2	no	—
51	C₂×#64520	—	2	2	no	—
52	C₂×#64520	—	4	2	no	—
53	C₂×#64520	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
58	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂×D₄×C₁₉	—	4	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	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	—	4	1	no	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	D₈	1	2	yes	—
89	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	4	2	no	—
98	C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	2	no	—
102	C₂²⋊C₄×C₁₉	—	4	2	no	—
103	C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	2	1	no	—
106	C₄²×C₁₉	—	2	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	C₂×D₄	1	2	yes	—
110	C₄²×C₁₉	#41	1	2	yes	—
111	#64520	—	4	4	no	—
112	#64520	—	4	2	no	—
113	#64520	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	C₂×C₁₉⋊C₈	—	4	4	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	#9035	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	#102	1	2	yes	—
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	D₄×C₁₉	—	2	4	no	—
132	D₄×C₁₉	—	4	2	no	—
133	D₄×C₁₉	—	4	8	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	8	1	no	—
156	C₂×C₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	#102	1	2	yes	—
160	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	2	yes	—
163	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₁₉⋊C₈	—	4	4	no	—
169	C₁₉⋊C₈	—	8	2	no	—
170	#2905	—	19	1	no	—
171	#2392	D₁₉	1	1	yes	characteristic
172	#1486	—	19	2	no	—
173	#1458	—	19	1	no	—
174	#1303	—	19	2	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	4	2	no	—
179	C₂²×C₁₉	—	4	2	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	1	no	—
183	C₂²×C₁₉	—	4	2	no	—
184	C₂²×C₁₉	—	8	1	no	—
185	C₂²×C₁₉	—	8	1	no	—
186	C₂²×C₁₉	—	8	1	no	—
187	C₂²×C₁₉	—	8	1	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	#386	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
191	C₂²×C₁₉	#417	1	1	yes	characteristic
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	4	2	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	#447	1	1	yes	characteristic
201	C₄×C₁₉	#448	1	1	yes	characteristic
202	C₄×C₁₉	#480	1	1	yes	characteristic
203	C₄×C₁₉	#481	1	1	yes	characteristic
204	C₂²×M₁₆	—	38	1	no	—
205	C₂×C₄×D₄	—	2	1	no	—
206	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
207	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
208	#431	—	19	2	no	—
209	#424	—	38	4	no	—
210	#423	—	19	2	no	—
211	#423	—	38	1	no	—
212	#398	Dic₁₉	1	1	yes	characteristic
213	#397	Dic₁₉	1	1	yes	characteristic
214	#396	—	2	1	no	—
215	#394	—	2	1	no	—
216	#394	Dic₁₉	1	1	yes	characteristic
217	#392	Dic₁₉	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	—	2	1	no	—
220	D₄⋊C₈	—	38	4	no	—
221	#324	—	38	1	no	—
222	#323	—	38	1	no	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	4	2	no	—
226	C₂×C₁₉	—	8	2	no	—
227	C₂×C₁₉	#1874	1	1	yes	characteristic
228	C₂×C₁₉	#1884	1	1	yes	characteristic
229	C₂×C₁₉	#1891	1	1	yes	characteristic
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂×M₁₆	—	38	2	no	—
235	C₂×M₁₆	—	38	2	no	—
236	C₂×M₁₆	—	76	2	no	—
237	C₂×M₁₆	—	76	2	no	—
238	C₂²×C₈	—	38	2	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	4	2	no	—
242	C₄×D₄	—	4	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
260	C₄⋊C₈	—	19	4	no	—
261	C₄⋊C₈	—	38	4	no	—
262	C₄⋊C₈	—	38	2	no	—
263	C₄⋊C₈	—	38	2	no	—
264	C₂²⋊C₈	—	38	2	no	—
265	C₄×C₈	—	38	2	no	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	C₂×Dic₁₉	1	1	yes	characteristic
269	#95	C₂×Dic₁₉	1	1	yes	characteristic
270	C₁₉	#9035	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	2	1	no	—
272	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	#64525	1	2	yes	—
292	C₂²×C₄	#64526	1	2	yes	—
293	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	M₁₆	—	76	4	no	—
300	M₁₆	—	76	2	no	—
301	M₁₆	—	76	2	no	—
302	C₂×C₈	—	38	4	no	—
303	C₂×C₈	—	76	4	no	—
304	C₂×C₈	—	76	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	1	no	—
321	C₄²	D₄×D₁₉	1	2	yes	—
322	C₄²	#64543	1	2	yes	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	#10597289	1	2	yes	—
335	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
336	D₄	—	2	4	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	8	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	—	8	1	no	—
364	C₂×C₄	#10597289	1	2	yes	—
365	C₂×C₄	C₂×#64525	1	1	yes	characteristic
366	C₂×C₄	C₂×#64526	1	1	yes	characteristic
367	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
368	C₂×C₄	#10597381	1	1	yes	characteristic
369	C₂×C₄	#10597383	1	1	yes	characteristic
370	C₂×C₄	#10597385	1	2	yes	—
371	C₂×C₄	#10597395	1	1	yes	characteristic
372	C₂×C₄	#10597397	1	1	yes	characteristic
373	C₈	—	76	4	no	—
374	C₈	—	152	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	#11926424	1	1	yes	characteristic
390	C₂²	C₂×#10597289	1	1	yes	characteristic
391	C₂²	#11926545	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	#11926677	1	1	yes	characteristic
401	C₄	#11926682	1	1	yes	characteristic
402	C₄	#11926855	1	1	yes	characteristic
403	C₄	#11926860	1	1	yes	characteristic
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	4	2	no	—
407	C₂	—	8	2	no	—
408	C₂	#14563953	1	1	yes	characteristic
409	C₂	#14564019	1	1	yes	characteristic
410	C₂	#14564054	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2392	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#392	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2392	D₁₉
hypocenter	C₁₉	#9035
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2392

Complements

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

N	H ≅ G/N	type
1. #14572199	C₂	semidirect
2. #14562060	C₂	semidirect
3. #14561949	C₂	semidirect
4. #14561538	C₂	semidirect
63. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
270. C₁₉	#9035	semidirect

Maximal subgroups

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

subgroup	index
#14572199	2
#14562060	2
#14561949	2
#14561538	2
C₁₉×#2392	2
#9035	19