Subgroups — #18078652

Order 4864.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597394	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562227	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562074	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561526	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561471	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	—	2	1	no	—
9	#11926568	C₂²	1	1	yes	characteristic
10	#11926500	—	2	2	no	—
11	#11926500	—	2	1	no	—
12	C₄×#64520	—	2	1	no	—
13	C₄×#64520	C₂²	1	1	yes	characteristic
14	C₄×#64520	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926284	—	2	2	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#482	—	2	1	no	—
25	C₁₉×#477	C₄	1	1	yes	characteristic
26	C₁₉×#476	C₄	1	1	yes	characteristic
27	C₁₉×#460	C₄	1	1	yes	characteristic
28	C₁₉×#459	C₄	1	1	yes	characteristic
29	C₁₉×#449	—	2	1	no	—
30	C₄×SD₁₆×C₁₉	—	2	1	no	—
31	C₄×D₈×C₁₉	—	2	1	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#124	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	#10597394	—	2	4	no	—
55	#10597394	—	2	4	no	—
56	C₂×#64520	—	2	2	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂×#64520	—	2	1	no	—
59	C₂×#64520	—	2	1	no	—
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₂²×C₁₉⋊C₈	—	2	1	no	—
62	C₁₉×#107	—	2	1	no	—
63	C₁₉×#106	—	2	1	no	—
64	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×C₂²⋊C₈	—	2	1	no	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	#10597260	—	2	2	no	—
75	#10597260	—	2	1	no	—
76	#10597260	D₄	1	2	yes	—
77	C₄×C₁₉⋊C₈	—	2	2	no	—
78	C₄×C₁₉⋊C₈	—	2	1	no	—
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
82	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
83	#41×C₁₉	—	2	2	no	—
84	#41×C₁₉	—	2	2	no	—
85	#41×C₁₉	—	8	1	no	—
86	#41×C₁₉	—	8	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	SD₁₆×C₁₉	—	4	2	no	—
103	D₈×C₁₉	—	4	2	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	#64520	—	2	8	no	—
125	#64520	—	2	2	no	—
126	#64520	—	2	2	no	—
127	#64520	—	2	2	no	—
128	#64520	—	4	1	no	—
129	#64520	—	8	1	no	—
130	C₂×C₁₉⋊C₈	—	2	8	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	1	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#9211	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	#123	1	1	yes	characteristic
142	Q₈×C₁₉	—	2	1	no	—
143	Q₈×C₁₉	—	8	1	no	—
144	Q₈×C₁₉	#104	1	2	yes	—
145	D₄×C₁₉	—	2	4	no	—
146	D₄×C₁₉	—	2	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	1	no	—
149	D₄×C₁₉	—	4	1	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	#104	1	2	yes	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₈×C₁₉	—	4	1	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₁₉⋊C₈	—	2	2	no	—
180	C₁₉⋊C₈	—	2	4	no	—
181	C₁₉⋊C₈	—	2	2	no	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₁₉⋊C₈	—	8	1	no	—
184	#3106	D₁₉	1	1	yes	characteristic
185	C₄×#131	—	19	1	no	—
186	#1525	—	19	1	no	—
187	#1492	—	19	1	no	—
188	#1489	—	19	1	no	—
189	#1299	—	19	1	no	—
190	#1278	—	19	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	#386	1	1	yes	characteristic
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
209	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
210	C₄×C₁₉	#443	1	1	yes	characteristic
211	C₄×C₁₉	#444	1	1	yes	characteristic
212	C₄×C₁₉	#471	1	1	yes	characteristic
213	C₄×C₁₉	#472	1	1	yes	characteristic
214	C₂×#131	—	38	1	no	—
215	#532	C₂×D₁₉	1	1	yes	characteristic
216	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
217	#482	—	2	1	no	—
218	#477	Dic₁₉	1	1	yes	characteristic
219	#476	Dic₁₉	1	1	yes	characteristic
220	#460	Dic₁₉	1	1	yes	characteristic
221	#459	Dic₁₉	1	1	yes	characteristic
222	#449	—	2	1	no	—
223	C₄×SD₁₆	—	2	1	no	—
224	C₄×D₈	—	2	1	no	—
225	#431	C₂×D₁₉	1	1	yes	characteristic
226	#423	—	19	1	no	—
227	#405	—	38	2	no	—
228	#405	—	38	1	no	—
229	C₄×M₁₆	—	19	1	no	—
230	C₄×M₁₆	—	19	1	no	—
231	C₄×M₁₆	—	38	1	no	—
232	C₂×C₄×C₈	—	19	1	no	—
233	C₂×C₄×C₈	—	38	1	no	—
234	#329	—	38	2	no	—
235	Q₈⋊C₈	—	38	1	no	—
236	D₄⋊C₈	—	38	1	no	—
237	D₄⋊C₈	—	38	1	no	—
238	D₄⋊C₈	—	38	1	no	—
239	C₂×C₁₉	—	4	1	no	—
240	C₂×C₁₉	—	4	2	no	—
241	C₂×C₁₉	—	16	1	no	—
242	C₂×C₁₉	#1876	1	1	yes	characteristic
243	C₂×C₁₉	#1896	1	1	yes	characteristic
244	C₂×C₁₉	#1907	1	1	yes	characteristic
245	C₂×#41	—	2	1	no	—
246	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	#131	—	38	4	no	—
250	#131	—	38	4	no	—
251	C₂×M₁₆	—	38	2	no	—
252	C₂×M₁₆	—	38	1	no	—
253	C₂×M₁₆	—	38	1	no	—
254	C₂×M₁₆	—	38	1	no	—
255	C₂²×C₈	—	38	2	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
258	#127	C₂×Dic₁₉	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	—	2	1	no	—
262	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
263	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
269	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
270	#117	—	2	1	no	—
271	#117	C₂²⋊D₁₉	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
274	#107	—	2	1	no	—
275	#106	—	2	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	—	38	1	no	—
278	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
279	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
280	#103	—	2	1	no	—
281	#102	—	2	1	no	—
282	#102	—	2	1	no	—
283	#102	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	#97	—	19	2	no	—
286	#97	—	38	2	no	—
287	#97	—	38	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	19	1	no	—
290	C₄×C₈	—	19	1	no	—
291	C₄×C₈	—	38	2	no	—
292	C₄×C₈	—	38	1	no	—
293	C₄×C₈	—	38	1	no	—
294	C₄×C₈	—	38	1	no	—
295	C₁₉	#9211	1	1	yes	characteristic, complemented, Sylow
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	8	1	no	—
299	#41	—	8	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	#64543	1	1	yes	characteristic
313	C₂²×C₄	#64543	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
315	SD₁₆	—	4	2	no	—
316	D₈	—	4	2	no	—
317	M₁₆	—	38	8	no	—
318	M₁₆	—	38	2	no	—
319	M₁₆	—	38	2	no	—
320	M₁₆	—	38	2	no	—
321	M₁₆	—	76	1	no	—
322	M₁₆	—	152	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	38	8	no	—
326	C₂×C₈	—	38	2	no	—
327	C₂×C₈	—	38	2	no	—
328	C₂×C₈	—	38	1	no	—
329	C₂×C₈	—	38	1	no	—
330	C₂×C₈	—	38	2	no	—
331	C₂×C₈	—	76	1	no	—
332	C₂×C₈	—	76	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	D₄×D₁₉	1	1	yes	characteristic
348	C₄²	D₄×D₁₉	1	1	yes	characteristic
349	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
350	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
351	C₂³	—	2	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	#10597381	1	1	yes	characteristic
354	Q₈	—	2	1	no	—
355	Q₈	—	8	1	no	—
356	Q₈	#10597294	1	2	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	2	no	—
365	D₄	#10597294	1	2	yes	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
384	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
385	C₂×C₄	#10597383	1	1	yes	characteristic
386	C₂×C₄	#10597385	1	1	yes	characteristic
387	C₂×C₄	#10597385	1	1	yes	characteristic
388	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	38	2	no	—
392	C₈	—	38	2	no	—
393	C₈	—	38	4	no	—
394	C₈	—	76	2	no	—
395	C₈	—	152	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	#11926424	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₂×#10597294	1	1	yes	characteristic
414	C₄	C₂×#10597294	1	1	yes	characteristic
415	C₄	#11926661	1	1	yes	characteristic
416	C₄	#11926666	1	1	yes	characteristic
417	C₄	#11926805	1	1	yes	characteristic
418	C₄	#11926812	1	1	yes	characteristic
419	C₂	—	4	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	16	1	no	—
422	C₂	#14563964	1	1	yes	characteristic
423	C₂	#14564079	1	1	yes	characteristic
424	C₂	#14564145	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3106	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3106	D₁₉
hypocenter	C₁₉	#9211
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
1. C₄×#10597394	C₂	semidirect
2. #14562227	C₂	semidirect
3. #14562086	C₂	semidirect
4. #14562074	C₂	semidirect
5. #14561526	C₂	semidirect
6. #14561471	C₂	semidirect
295. C₁₉	#9211	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597394	2
#14562227	2
#14562086	2
#14562074	2
#14561526	2
#14561471	2
C₁₉×#3106	2
#9211	19