Subgroups — #18076749

Order 4864.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566586	C₂	1	1	yes	maximal, characteristic
2	#14564394	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563791	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563636	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×#10597338	—	2	1	no	—
10	C₂×#10597275	—	2	1	no	—
11	C₂×#10597265	—	2	2	no	—
12	C₂×#10597278	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926445	—	2	1	no	—
15	#11926434	—	2	2	no	—
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926401	—	2	1	no	—
18	C₄⋊C₄×Dic₁₉	—	2	1	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926307	—	2	1	no	—
21	#11926307	—	2	1	no	—
22	#11926271	C₄	1	4	yes	complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₉×#384	C₂²	1	1	yes	characteristic
26	C₂²×D₇₆	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
35	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
36	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	—	2	2	no	—
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	#10597338	—	4	2	no	—
47	#10597338	—	4	2	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	C₂×C₄	1	2	yes	—
51	C₄×D₇₆	Q₈	1	2	yes	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
56	C₁₉⋊#95	—	2	2	no	—
57	C₁₉⋊#95	—	2	1	no	—
58	#10597278	—	4	2	no	—
59	#10597275	—	4	2	no	—
60	#10597265	—	4	4	no	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
63	C₂³×D₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×Dic₁₉	—	2	1	no	—
69	C₂²×Dic₁₉	—	2	1	no	—
70	C₂²×Dic₁₉	—	2	1	no	—
71	C₂²×Dic₁₉	—	4	1	no	—
72	C₂×D₇₆	—	2	1	no	—
73	C₂×D₇₆	—	2	1	no	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
78	C₂×C₄×D₁₉	—	2	2	no	—
79	C₂×C₄×D₁₉	—	2	2	no	—
80	C₂×C₄×D₁₉	—	4	1	no	—
81	C₂×C₄×D₁₉	—	4	1	no	—
82	C₂×C₄×D₁₉	—	4	1	no	—
83	C₂×C₄×D₁₉	—	4	1	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	4	1	no	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₄²×C₁₉	#41	1	1	yes	characteristic
98	C₄²×C₁₉	#41	1	1	yes	characteristic
99	(C₂×D₁₉)⋊C₄	—	2	2	no	—
100	(C₂×D₁₉)⋊C₄	—	2	2	no	—
101	(C₂×D₁₉)⋊C₄	—	4	4	no	—
102	(C₂×D₁₉)⋊C₄	—	8	2	no	—
103	C₄⋊Dic₁₉	—	2	1	no	—
104	C₄⋊Dic₁₉	—	2	1	no	—
105	C₄⋊Dic₁₉	—	2	1	no	—
106	C₄⋊Dic₁₉	—	2	1	no	—
107	C₄⋊Dic₁₉	—	4	2	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
113	C₄⋊Dic₁₉	SD₁₆	1	2	yes	—
114	C₄×Dic₁₉	—	4	4	no	—
115	C₄×Dic₁₉	—	4	1	no	—
116	C₄×Dic₁₉	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	#8889	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	#120	1	1	yes	characteristic
122	C₂²×D₁₉	—	2	2	no	—
123	C₂²×D₁₉	—	4	1	no	—
124	C₂²×D₁₉	—	4	1	no	—
125	C₂²×D₁₉	—	4	1	no	—
126	C₂²×D₁₉	—	4	1	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
144	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
148	C₂×Dic₁₉	—	2	2	no	—
149	C₂×Dic₁₉	—	2	2	no	—
150	C₂×Dic₁₉	—	4	1	no	—
151	C₂×Dic₁₉	—	4	1	no	—
152	C₂×Dic₁₉	—	4	1	no	—
153	C₂×Dic₁₉	—	4	1	no	—
154	C₂×Dic₁₉	—	4	1	no	—
155	C₂×Dic₁₉	—	4	1	no	—
156	C₂×Dic₁₉	—	4	1	no	—
157	C₂×Dic₁₉	—	8	1	no	—
158	C₂×Dic₁₉	—	8	1	no	—
159	C₂×Dic₁₉	—	8	1	no	—
160	D₇₆	—	2	2	no	—
161	D₇₆	—	2	2	no	—
162	D₇₆	—	4	1	no	—
163	D₇₆	—	4	1	no	—
164	C₄×D₁₉	—	4	2	no	—
165	C₄×D₁₉	—	4	2	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₄×D₁₉	—	4	2	no	—
168	C₈×C₁₉	—	4	2	no	—
169	C₈×C₁₉	—	8	1	no	—
170	C₁₉⋊C₈	—	2	4	no	—
171	#2354	—	19	1	no	—
172	#1947	—	19	1	no	—
173	#1844	—	19	1	no	—
174	#1802	—	19	1	no	—
175	C₂×D₄⋊C₈	—	19	1	no	—
176	#1296	D₁₉	1	1	yes	characteristic, complemented
177	#1279	—	19	1	no	—
178	C₂²×C₁₉	#385	1	1	yes	characteristic
179	C₂²×C₁₉	#449	1	1	yes	characteristic
180	C₂²×C₁₉	#449	1	1	yes	characteristic
181	C₂²×C₁₉	#450	1	1	yes	characteristic
182	C₂²×C₁₉	#452	1	1	yes	characteristic
183	C₂²×C₁₉	#453	1	1	yes	characteristic
184	C₂²×C₁₉	#456	1	1	yes	characteristic
185	C₂×D₁₉	—	4	2	no	—
186	C₂×D₁₉	—	4	2	no	—
187	C₂×D₁₉	—	4	2	no	—
188	C₂×D₁₉	—	8	1	no	—
189	C₂×D₁₉	—	8	1	no	—
190	C₂×D₁₉	—	8	1	no	—
191	C₂×D₁₉	—	8	1	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	8	2	no	—
195	C₄×C₁₉	#427	1	1	yes	characteristic
196	C₄×C₁₉	#428	1	1	yes	characteristic
197	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
198	C₄×C₁₉	#442	1	1	yes	characteristic
199	C₄×C₁₉	#476	1	1	yes	characteristic
200	C₄×C₁₉	#478	1	1	yes	characteristic
201	C₄×C₁₉	#482	1	1	yes	characteristic
202	C₄×C₁₉	#485	1	1	yes	characteristic
203	Dic₁₉	—	4	2	no	—
204	Dic₁₉	—	4	2	no	—
205	Dic₁₉	—	8	1	no	—
206	Dic₁₉	—	16	1	no	—
207	C₂×C₄×D₄	—	19	1	no	—
208	C₂×#117	—	38	1	no	—
209	C₂×#107	—	38	1	no	—
210	C₂×#106	—	38	2	no	—
211	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
213	C₂×#102	—	38	1	no	—
214	C₂×C₄×C₈	—	19	1	no	—
215	#390	—	38	1	no	—
216	#388	—	38	2	no	—
217	#384	—	19	1	no	—
218	#384	C₂×D₁₉	1	1	yes	characteristic
219	#380	—	38	1	no	—
220	C₄×C₄⋊C₄	—	19	1	no	—
221	C₄×C₄⋊C₄	—	38	1	no	—
222	#340	—	38	1	no	—
223	#340	—	38	1	no	—
224	D₄⋊C₈	—	19	4	no	—
225	C₂×C₁₉	#1624	1	1	yes	characteristic
226	C₂×C₁₉	#1631	1	1	yes	characteristic
227	C₂×C₁₉	#1652	1	1	yes	characteristic
228	C₂×C₁₉	#1654	1	1	yes	characteristic
229	C₂×C₁₉	#1854	1	1	yes	characteristic
230	C₂×C₁₉	#1859	1	1	yes	characteristic
231	C₂×C₁₉	#1864	1	1	yes	characteristic
232	D₁₉	—	8	2	no	—
233	C₂²×D₄	—	19	1	no	—
234	C₂³×C₄	—	38	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	38	1	no	—
238	C₄×D₄	—	19	2	no	—
239	C₄×D₄	—	19	2	no	—
240	C₄×D₄	—	38	1	no	—
241	C₄×D₄	—	38	1	no	—
242	#117	—	76	2	no	—
243	#117	—	76	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	19	1	no	—
247	C₂×C₄⋊C₄	—	19	1	no	—
248	C₂×C₄⋊C₄	—	19	1	no	—
249	C₂×C₄⋊C₄	—	38	1	no	—
250	C₂×C₄⋊C₄	—	38	1	no	—
251	C₂×C₄⋊C₄	—	38	1	no	—
252	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
253	C₂×C₂²⋊C₄	—	38	1	no	—
254	C₂×C₂²⋊C₄	—	38	2	no	—
255	C₂×C₂²⋊C₄	—	38	2	no	—
256	C₂×C₄²	—	38	2	no	—
257	C₂×C₄²	—	38	1	no	—
258	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
259	#107	—	76	2	no	—
260	#106	—	76	4	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
265	#102	—	76	2	no	—
266	C₄×C₈	—	19	2	no	—
267	C₄×C₈	—	38	1	no	—
268	#95	—	38	2	no	—
269	#95	—	38	1	no	—
270	C₁₉	#8889	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	38	1	no	—
272	C₂×D₄	—	19	2	no	—
273	C₂×D₄	—	38	1	no	—
274	C₂×D₄	—	38	1	no	—
275	C₂×D₄	—	38	1	no	—
276	C₂×D₄	—	38	1	no	—
277	C₂×D₄	—	38	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	38	1	no	—
280	C₂²×C₄	—	38	1	no	—
281	C₂²×C₄	—	38	2	no	—
282	C₂²×C₄	—	38	2	no	—
283	C₂²×C₄	—	38	1	no	—
284	C₂²×C₄	—	76	1	no	—
285	C₂²×C₄	—	76	1	no	—
286	C₂²×C₄	—	76	1	no	—
287	C₂²×C₄	—	76	1	no	—
288	C₂²×C₄	—	76	1	no	—
289	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	38	2	no	—
299	C₂×C₈	—	38	2	no	—
300	C₂×C₈	—	38	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	19	2	no	—
307	C₄⋊C₄	—	19	2	no	—
308	C₄⋊C₄	—	38	1	no	—
309	C₄⋊C₄	—	38	1	no	—
310	C₄⋊C₄	—	38	1	no	—
311	C₄⋊C₄	—	38	1	no	—
312	C₄⋊C₄	—	76	2	no	—
313	C₄⋊C₄	—	76	1	no	—
314	C₄⋊C₄	—	76	1	no	—
315	C₄⋊C₄	—	76	1	no	—
316	C₄⋊C₄	—	76	1	no	—
317	C₂²⋊C₄	—	38	2	no	—
318	C₂²⋊C₄	—	38	2	no	—
319	C₂²⋊C₄	—	76	4	no	—
320	C₂²⋊C₄	—	152	2	no	—
321	C₄²	—	76	4	no	—
322	C₄²	—	76	1	no	—
323	C₄²	—	76	1	no	—
324	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
325	C₄²	#64541	1	1	yes	characteristic
326	C₄²	#64543	1	1	yes	characteristic
327	C₄²	Q₈×D₁₉	1	1	yes	characteristic
328	C₂³	—	38	2	no	—
329	C₂³	—	76	1	no	—
330	C₂³	—	76	1	no	—
331	C₂³	—	76	1	no	—
332	C₂³	—	76	1	no	—
333	C₂³	—	76	1	no	—
334	C₂³	—	76	1	no	—
335	C₂³	#10597328	1	1	yes	characteristic
336	D₄	—	38	2	no	—
337	D₄	—	38	2	no	—
338	D₄	—	76	1	no	—
339	D₄	—	76	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	38	2	no	—
346	C₂×C₄	—	38	2	no	—
347	C₂×C₄	—	76	1	no	—
348	C₂×C₄	—	76	1	no	—
349	C₂×C₄	—	76	1	no	—
350	C₂×C₄	—	76	1	no	—
351	C₂×C₄	—	76	2	no	—
352	C₂×C₄	—	76	2	no	—
353	C₂×C₄	—	76	2	no	—
354	C₂×C₄	—	76	2	no	—
355	C₂×C₄	—	76	1	no	—
356	C₂×C₄	—	76	1	no	—
357	C₂×C₄	—	76	1	no	—
358	C₂×C₄	—	152	1	no	—
359	C₂×C₄	—	152	1	no	—
360	C₂×C₄	—	152	1	no	—
361	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
362	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	#10597329	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597342	1	1	yes	characteristic
366	C₂×C₄	#10597343	1	1	yes	characteristic
367	C₂×C₄	#10597357	1	1	yes	characteristic
368	C₂×C₄	#10597358	1	1	yes	characteristic
369	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597360	1	1	yes	characteristic
371	C₂×C₄	#10597360	1	1	yes	characteristic
372	C₂×C₄	#10597361	1	1	yes	characteristic
373	C₂×C₄	#10597365	1	1	yes	characteristic
374	C₂×C₄	#10597365	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	8	1	no	—
377	C₈	—	38	4	no	—
378	C₂²	—	76	2	no	—
379	C₂²	—	76	2	no	—
380	C₂²	—	76	2	no	—
381	C₂²	—	152	1	no	—
382	C₂²	—	152	1	no	—
383	C₂²	—	152	1	no	—
384	C₂²	—	152	1	no	—
385	C₂²	#11926418	1	1	yes	characteristic
386	C₂²	#11926692	1	1	yes	characteristic
387	C₂²	#11926692	1	1	yes	characteristic
388	C₂²	#11926696	1	1	yes	characteristic
389	C₂²	#11926707	1	1	yes	characteristic
390	C₂²	#11926714	1	1	yes	characteristic
391	C₂²	#11926729	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	304	1	no	—
396	C₄	—	76	2	no	—
397	C₄	—	76	2	no	—
398	C₄	—	152	1	no	—
399	C₄	#11926581	1	1	yes	characteristic
400	C₄	#11926583	1	1	yes	characteristic
401	C₄	#11926629	1	1	yes	characteristic
402	C₄	#11926653	1	1	yes	characteristic
403	C₄	#11926833	1	1	yes	characteristic
404	C₄	#11926847	1	1	yes	characteristic
405	C₄	#11926866	1	1	yes	characteristic
406	C₄	#11926884	1	1	yes	characteristic
407	C₂	—	152	2	no	—
408	C₂	#14562719	1	1	yes	characteristic
409	C₂	#14562763	1	1	yes	characteristic
410	C₂	#14562906	1	1	yes	characteristic
411	C₂	#14562920	1	1	yes	characteristic
412	C₂	#14563837	1	1	yes	characteristic
413	C₂	#14563864	1	1	yes	characteristic
414	C₂	#14563897	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8889
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #14564394	C₂	semidirect
3. #14563791	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
22. #11926271	C₄	semidirect
176. #1296	D₁₉	semidirect
270. C₁₉	#8889	semidirect

Maximal subgroups

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

subgroup	index
#14566586	2
#14564394	2
#14563791	2
#14563636	2
C₂×#11926271	2
#14561474	2
C₁₉×#1296	2
#8889	19