Subgroups — #18086419

Order 4864.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926821	C₂	1	1	yes	maximal, characteristic
2	#14564429	C₂	1	1	yes	maximal, characteristic
3	#14563632	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	#11926821	—	2	2	no	—
10	#11926821	—	2	2	no	—
11	C₂×#10597264	—	2	1	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597266	—	2	1	no	—
16	C₂×#10597266	—	2	1	no	—
17	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
18	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
19	#11926306	—	2	1	no	—
20	#11926297	—	2	2	no	—
21	#11926290	—	2	2	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	—	2	1	no	—
24	C₂×C₁₉×#103	—	2	1	no	—
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×D₇₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₄×D₇₆	—	2	1	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	2	1	no	—
51	C₁₉×#103	—	4	2	no	—
52	C₁₉×#103	—	4	2	no	—
53	C₄×C₈×C₁₉	—	2	1	no	—
54	C₄×C₈×C₁₉	—	2	1	no	—
55	(C₂×D₁₉)⋊C₈	—	4	2	no	—
56	(C₂×D₁₉)⋊C₈	—	4	2	no	—
57	#10597266	—	2	4	no	—
58	#10597266	—	4	2	no	—
59	#10597264	—	2	4	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)	D₄	1	2	yes	—
66	C₂³×D₁₉	—	2	1	no	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
78	C₂²×Dic₁₉	—	2	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	—	2	1	no	—
81	C₂×D₇₆	—	2	1	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	Q₁₆	1	2	yes	—
85	C₂×C₄×D₁₉	—	4	1	no	—
86	C₂×C₄×D₁₉	—	4	1	no	—
87	C₂×C₄×D₁₉	—	4	1	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	2	1	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	D₈	1	2	yes	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	8	1	no	—
106	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	(C₂×D₁₉)⋊C₄	—	4	1	no	—
111	(C₂×D₁₉)⋊C₄	—	4	1	no	—
112	C₄⋊Dic₁₉	—	2	1	no	—
113	C₄⋊Dic₁₉	—	2	1	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	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	#10485	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	#121	1	1	yes	characteristic
125	C₂²×D₁₉	—	2	2	no	—
126	C₂²×D₁₉	—	4	1	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	Q₈×C₁₉	—	4	2	no	—
133	Q₈×C₁₉	—	4	2	no	—
134	Q₈×C₁₉	—	8	1	no	—
135	Q₈×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	—	8	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
158	C₂×Dic₁₉	—	4	1	no	—
159	C₂×Dic₁₉	—	4	1	no	—
160	C₂×Dic₁₉	—	4	1	no	—
161	D₇₆	—	2	2	no	—
162	D₇₆	—	2	2	no	—
163	D₇₆	—	4	1	no	—
164	D₇₆	—	4	1	no	—
165	C₄×D₁₉	—	8	1	no	—
166	C₄×D₁₉	—	8	1	no	—
167	C₄×D₁₉	—	8	1	no	—
168	C₄×D₁₉	—	8	1	no	—
169	C₈×C₁₉	—	2	2	no	—
170	C₈×C₁₉	—	4	1	no	—
171	C₁₉⋊C₈	—	4	2	no	—
172	C₁₉⋊C₈	—	8	1	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	C₂×#474	—	19	1	no	—
175	#1956	D₁₉	1	1	yes	characteristic, complemented
176	#1954	—	19	1	no	—
177	#1802	—	19	1	no	—
178	C₂×#335	—	19	1	no	—
179	C₂×#332	—	19	1	no	—
180	#1296	—	19	1	no	—
181	C₂²×C₁₉	#394	1	1	yes	characteristic
182	C₂²×C₁₉	#459	1	1	yes	characteristic
183	C₂²×C₁₉	#463	1	1	yes	characteristic
184	C₂²×C₁₉	#467	1	1	yes	characteristic
185	C₂²×C₁₉	#468	1	1	yes	characteristic
186	C₂²×C₁₉	#471	1	1	yes	characteristic
187	C₂²×C₁₉	#473	1	1	yes	characteristic
188	C₂×D₁₉	—	4	2	no	—
189	C₂×D₁₉	—	4	2	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	8	1	no	—
192	C₂×D₁₉	—	8	1	no	—
193	C₂×D₁₉	—	8	1	no	—
194	C₂×D₁₉	—	8	1	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	—	16	1	no	—
199	C₄×C₁₉	#449	1	1	yes	characteristic
200	C₄×C₁₉	#451	1	1	yes	characteristic
201	C₄×C₁₉	#459	1	1	yes	characteristic
202	C₄×C₁₉	#463	1	1	yes	characteristic
203	C₄×C₁₉	#466	1	1	yes	characteristic
204	C₄×C₁₉	#469	1	1	yes	characteristic
205	C₄×C₁₉	#484	1	1	yes	characteristic
206	C₄×C₁₉	#485	1	1	yes	characteristic
207	Dic₁₉	—	8	1	no	—
208	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
209	C₂×C₄×D₄	—	19	1	no	—
210	#474	—	38	2	no	—
211	#474	—	38	2	no	—
212	C₂×#107	—	38	1	no	—
213	C₂×C₄⋊C₈	—	19	1	no	—
214	C₂×C₄⋊C₈	—	19	1	no	—
215	C₂×C₄⋊C₈	—	19	1	no	—
216	C₂×#103	—	2	1	no	—
217	C₂×#103	—	2	1	no	—
218	C₂×#102	—	38	1	no	—
219	C₂×#102	—	38	1	no	—
220	C₂×C₂²⋊C₈	—	38	1	no	—
221	C₂×C₂²⋊C₈	—	38	1	no	—
222	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
223	#384	C₂×D₁₉	1	1	yes	characteristic
224	#340	—	38	1	no	—
225	#335	—	38	2	no	—
226	#332	—	38	2	no	—
227	C₂×C₁₉	#1669	1	1	yes	characteristic
228	C₂×C₁₉	#1683	1	1	yes	characteristic
229	C₂×C₁₉	#1685	1	1	yes	characteristic
230	C₂×C₁₉	#1699	1	1	yes	characteristic
231	C₂×C₁₉	#2036	1	1	yes	characteristic
232	C₂×C₁₉	#2052	1	1	yes	characteristic
233	C₂×C₁₉	#2054	1	1	yes	characteristic
234	D₁₉	—	8	2	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×D₄	—	19	1	no	—
237	C₂³×C₄	—	38	1	no	—
238	C₂²×C₈	—	38	1	no	—
239	C₂²×C₈	—	38	1	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	D₇₆	1	2	yes	—
247	C₄×D₄	—	38	1	no	—
248	C₄×D₄	—	38	1	no	—
249	C₄×D₄	—	38	1	no	—
250	C₄×D₄	—	38	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	19	1	no	—
257	C₂×C₂²⋊C₄	—	38	1	no	—
258	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
259	#107	—	38	4	no	—
260	C₄⋊C₈	—	19	2	no	—
261	C₄⋊C₈	—	38	1	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	—	38	1	no	—
264	C₄⋊C₈	—	38	1	no	—
265	C₄⋊C₈	—	38	1	no	—
266	#103	—	4	2	no	—
267	#103	—	4	2	no	—
268	#102	—	38	4	no	—
269	#102	—	76	2	no	—
270	C₂²⋊C₈	—	76	2	no	—
271	C₂²⋊C₈	—	76	2	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₁₉	#10485	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	38	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×D₄	—	19	2	no	—
283	C₂×D₄	—	38	1	no	—
284	C₂×D₄	—	38	1	no	—
285	C₂×D₄	—	38	1	no	—
286	C₂×D₄	—	38	1	no	—
287	C₂×D₄	—	38	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	76	1	no	—
292	C₂²×C₄	—	76	1	no	—
293	C₂²×C₄	—	76	1	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	—	76	1	no	—
297	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	#64543	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	38	2	no	—
306	C₂×C₈	—	76	1	no	—
307	C₂×C₈	—	76	1	no	—
308	C₂×C₈	—	76	1	no	—
309	C₂×C₈	—	76	1	no	—
310	C₂×C₈	—	76	1	no	—
311	C₂×C₈	—	76	1	no	—
312	C₂×C₈	—	76	1	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	#64525	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	8	1	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₄⋊C₄	—	38	1	no	—
326	C₂²⋊C₄	—	76	1	no	—
327	C₂²⋊C₄	—	76	1	no	—
328	C₄²	C₂×D₇₆	1	1	yes	characteristic
329	C₄²	#64541	1	1	yes	characteristic
330	C₄²	D₄×D₁₉	1	1	yes	characteristic
331	C₄²	#64543	1	1	yes	characteristic
332	C₂³	—	38	2	no	—
333	C₂³	—	76	1	no	—
334	C₂³	—	76	1	no	—
335	C₂³	—	76	1	no	—
336	C₂³	—	76	1	no	—
337	C₂³	—	76	1	no	—
338	C₂³	—	76	1	no	—
339	C₂³	#10597384	1	1	yes	characteristic
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	8	1	no	—
343	Q₈	—	8	1	no	—
344	D₄	—	38	2	no	—
345	D₄	—	38	2	no	—
346	D₄	—	76	1	no	—
347	D₄	—	76	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	8	1	no	—
356	C₂×C₄	—	76	1	no	—
357	C₂×C₄	—	76	1	no	—
358	C₂×C₄	—	76	1	no	—
359	C₂×C₄	—	152	1	no	—
360	C₂×C₄	—	152	1	no	—
361	C₂×C₄	—	152	1	no	—
362	C₂×C₄	—	152	1	no	—
363	C₂×C₄	#10597328	1	1	yes	characteristic
364	C₂×C₄	#10597329	1	1	yes	characteristic
365	C₂×C₄	#10597331	1	1	yes	characteristic
366	C₂×C₄	#10597332	1	1	yes	characteristic
367	C₂×C₄	#10597360	1	1	yes	characteristic
368	C₂×C₄	#10597361	1	1	yes	characteristic
369	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597365	1	1	yes	characteristic
371	C₂×C₄	#10597376	1	1	yes	characteristic
372	C₂×C₄	C₂×#64525	1	1	yes	characteristic
373	C₂×C₄	#10597378	1	1	yes	characteristic
374	C₂×C₄	#10597385	1	1	yes	characteristic
375	C₂×C₄	#10597395	1	1	yes	characteristic
376	C₂×C₄	#10597396	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	76	2	no	—
380	C₈	—	152	1	no	—
381	C₈	—	152	1	no	—
382	C₂²	—	76	2	no	—
383	C₂²	—	76	2	no	—
384	C₂²	—	76	2	no	—
385	C₂²	—	152	1	no	—
386	C₂²	—	152	1	no	—
387	C₂²	—	152	1	no	—
388	C₂²	—	152	1	no	—
389	C₂²	#11926460	1	1	yes	characteristic
390	C₂²	#11926736	1	1	yes	characteristic
391	C₂²	#11926756	1	1	yes	characteristic
392	C₂²	#11926782	1	1	yes	characteristic
393	C₂²	#11926787	1	1	yes	characteristic
394	C₂²	#11926804	1	1	yes	characteristic
395	C₂²	#11926816	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	8	2	no	—
399	C₄	—	16	1	no	—
400	C₄	—	152	1	no	—
401	C₄	#11926692	1	1	yes	characteristic
402	C₄	#11926701	1	1	yes	characteristic
403	C₄	#11926739	1	1	yes	characteristic
404	C₄	#11926759	1	1	yes	characteristic
405	C₄	#11926778	1	1	yes	characteristic
406	C₄	#11926795	1	1	yes	characteristic
407	C₄	#11926878	1	1	yes	characteristic
408	C₄	#11926884	1	1	yes	characteristic
409	C₂	—	152	2	no	—
410	C₂	#14562997	1	1	yes	characteristic
411	C₂	#14563083	1	1	yes	characteristic
412	C₂	#14563097	1	1	yes	characteristic
413	C₂	#14563179	1	1	yes	characteristic
414	C₂	#14564837	1	1	yes	characteristic
415	C₂	#14564935	1	1	yes	characteristic
416	C₂	#14564945	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597384
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#10485
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

Complements

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

N	H ≅ G/N	type
4. C₂×#11926297	C₂	semidirect
5. C₂×#11926290	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#1956	C₂	semidirect
175. #1956	D₁₉	semidirect
274. C₁₉	#10485	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926821	2
#14564429	2
#14563632	2
C₂×#11926297	2
C₂×#11926290	2
#14561518	2
C₁₉×#1956	2
#10485	19