Subgroups — #18073539

Order 4864.

522 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	#14572329	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562127	C₂	1	1	yes	maximal, characteristic
4	#14562124	C₂	1	1	yes	maximal, characteristic
5	#14561523	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561521	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597347	C₄	1	1	yes	characteristic, complemented
9	#11927055	C₂²	1	1	yes	characteristic
10	#11926615	—	2	1	no	—
11	#11926615	—	2	1	no	—
12	C₈×C₂²⋊D₁₉	—	2	1	no	—
13	C₈×C₂²⋊D₁₉	—	2	1	no	—
14	#11926570	C₄	1	1	yes	characteristic, complemented
15	#11926510	C₄	1	1	yes	characteristic, complemented
16	#11926508	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
18	#11926499	C₄	1	1	yes	characteristic, complemented
19	C₂×C₈×Dic₁₉	—	2	1	no	—
20	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926298	—	2	1	no	—
22	#11926282	C₄	1	2	yes	complemented
23	#11926280	C₄	1	2	yes	complemented
24	#11926279	C₄	1	2	yes	complemented
25	#11926277	C₄	1	2	yes	complemented
26	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#336	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×#64541	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	4	2	no	—
35	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	#10597399	—	2	1	no	—
44	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
45	#10597376	C₂×C₄	1	1	yes	characteristic
46	#10597376	C₂×C₄	1	1	yes	characteristic
47	#10597375	—	2	1	no	—
48	C₄×C₂²⋊D₁₉	—	2	1	no	—
49	C₄×C₂²⋊D₁₉	—	2	1	no	—
50	#10597372	C₂×C₄	1	1	yes	characteristic
51	#10597370	C₂×C₄	1	1	yes	characteristic
52	#10597370	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×#64520	C₂×C₄	1	1	yes	characteristic
55	C₂×#64520	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	#10597347	—	4	2	no	—
58	C₂×#64515	—	2	1	no	—
59	C₂×C₈×D₁₉	—	2	1	no	—
60	C₁₉×C₂²⋊C₈	—	2	1	no	—
61	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₉×#97	—	4	2	no	—
63	C₁₉×#95	C₂×C₄	1	2	yes	—
64	C₁₉⋊#95	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
69	(C₂×D₁₉)⋊C₈	—	2	1	no	—
70	(C₂×D₁₉)⋊C₈	—	2	1	no	—
71	#10597272	—	2	1	no	—
72	Dic₁₉⋊C₈	—	2	1	no	—
73	Dic₁₉⋊C₈	—	2	1	no	—
74	C₈×Dic₁₉	—	2	1	no	—
75	C₈×Dic₁₉	—	4	2	no	—
76	C₂⁴×C₁₉	#41	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₉	—	2	1	no	—
87	C₂×C₂²⋊D₁₉	—	2	1	no	—
88	C₂×C₂²⋊D₁₉	—	2	1	no	—
89	C₂²×Dic₁₉	—	2	2	no	—
90	#64541	—	4	1	no	—
91	#64541	—	4	1	no	—
92	C₂×D₇₆	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×Dic₃₈	C₄²	1	1	yes	characteristic
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²⋊C₄×C₁₉	—	4	2	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₂²⋊Dic₁₉	—	2	4	no	—
112	C₂²⋊Dic₁₉	—	2	1	no	—
113	C₂²⋊Dic₁₉	—	2	1	no	—
114	C₂²⋊Dic₁₉	—	2	1	no	—
115	(C₂×D₁₉)⋊C₄	—	2	1	no	—
116	(C₂×D₁₉)⋊C₄	—	2	1	no	—
117	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
118	C₄⋊Dic₁₉	C₄²	1	1	yes	characteristic
119	Dic₁₉⋊C₄	—	2	1	no	—
120	Dic₁₉⋊C₄	—	2	1	no	—
121	C₄×Dic₁₉	—	2	1	no	—
122	C₄×Dic₁₉	—	4	1	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	#64520	—	4	1	no	—
125	#64520	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	2	1	no	—
127	C₂×C₁₉⋊C₈	—	2	1	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	#64515	—	4	2	no	—
132	C₈×D₁₉	—	4	2	no	—
133	#8240	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	#117	1	1	yes	characteristic
138	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
139	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
140	C₂²×D₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	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	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
157	C₂²⋊D₁₉	—	4	2	no	—
158	C₂²⋊D₁₉	—	4	2	no	—
159	C₂²⋊D₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	2	4	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	2	1	no	—
163	C₂×Dic₁₉	—	2	1	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	D₇₆	—	4	1	no	—
167	C₄×D₁₉	—	4	1	no	—
168	C₄×D₁₉	—	4	1	no	—
169	Dic₃₈	—	4	1	no	—
170	C₈×C₁₉	—	2	1	no	—
171	C₈×C₁₉	—	2	1	no	—
172	C₈×C₁₉	—	2	1	no	—
173	C₈×C₁₉	—	4	2	no	—
174	C₈×C₁₉	#99	1	2	yes	—
175	C₁₉⋊C₈	—	4	2	no	—
176	C₁₉⋊C₈	—	4	1	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	#2929	—	19	1	no	—
179	#1752	D₁₉	1	1	yes	characteristic, complemented
180	C₈×C₂²⋊C₄	—	19	1	no	—
181	#1501	—	19	1	no	—
182	#1501	—	19	1	no	—
183	#1298	—	19	1	no	—
184	#1297	—	19	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₉	#443	1	2	yes	—
195	C₂²×C₁₉	#444	1	2	yes	—
196	C₂×D₁₉	—	4	1	no	—
197	C₂×D₁₉	—	4	1	no	—
198	C₂×D₁₉	—	4	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
204	C₄×C₁₉	#410	1	1	yes	characteristic
205	Dic₁₉	—	4	4	no	—
206	Dic₁₉	—	4	1	no	—
207	Dic₁₉	—	4	1	no	—
208	Dic₁₉	—	4	1	no	—
209	C₂×#131	—	19	1	no	—
210	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
211	#525	—	19	1	no	—
212	#435	—	38	1	no	—
213	#435	—	38	1	no	—
214	C₈×D₄	—	38	1	no	—
215	C₈×D₄	—	38	1	no	—
216	#424	—	19	1	no	—
217	#408	—	19	1	no	—
218	#407	—	19	1	no	—
219	C₂×C₂²⋊C₈	—	19	1	no	—
220	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
221	#405	—	19	1	no	—
222	C₂×#97	—	2	1	no	—
223	C₂×C₄×C₈	—	38	1	no	—
224	C₄×C₂²⋊C₄	—	19	1	no	—
225	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
226	#336	—	2	1	no	—
227	#336	—	38	1	no	—
228	#328	—	19	2	no	—
229	#328	—	19	2	no	—
230	#327	—	19	2	no	—
231	#327	—	19	2	no	—
232	C₂×C₁₉	—	2	2	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	4	1	no	—
235	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
236	C₂×C₁₉	#1764	1	1	yes	characteristic
237	C₂×C₁₉	#1765	1	1	yes	characteristic
238	D₁₉	—	8	1	no	—
239	C₂×#41	—	19	1	no	—
240	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
241	#131	—	76	2	no	—
242	C₂×M₁₆	—	19	1	no	—
243	C₂×M₁₆	—	19	1	no	—
244	C₂×M₁₆	—	38	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	4	2	no	—
247	C₂²×C₈	—	38	1	no	—
248	C₂²×C₈	—	38	1	no	—
249	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
251	C₂²×C₈	D₇₆	1	1	yes	characteristic
252	C₂²×C₈	D₇₆	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
255	#123	—	38	1	no	—
256	C₂²⋊Q₈	—	19	1	no	—
257	C₂²⋊Q₈	—	19	1	no	—
258	#121	—	19	1	no	—
259	#121	—	19	1	no	—
260	#120	—	38	1	no	—
261	C₄×D₄	—	38	1	no	—
262	C₄×D₄	—	38	1	no	—
263	#117	—	19	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	38	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	38	1	no	—
268	C₄⋊C₈	—	38	1	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	19	2	no	—
272	C₂²⋊C₈	—	38	1	no	—
273	C₂²⋊C₈	—	38	1	no	—
274	C₂²⋊C₈	—	38	1	no	—
275	C₂²⋊C₈	—	38	1	no	—
276	C₂²⋊C₈	—	38	1	no	—
277	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
278	#97	—	4	2	no	—
279	#97	—	38	1	no	—
280	C₄×C₈	—	38	1	no	—
281	C₄×C₈	—	76	2	no	—
282	#95	—	19	2	no	—
283	#95	C₄×D₁₉	1	2	yes	—
284	C₁₉	#8240	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	#64541	1	1	yes	characteristic
286	#41	—	76	1	no	—
287	#41	—	76	1	no	—
288	C₂×Q₈	—	19	1	no	—
289	C₂×D₄	—	19	1	no	—
290	C₂×D₄	—	38	1	no	—
291	C₂×D₄	—	38	1	no	—
292	C₂×D₄	—	38	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	38	2	no	—
297	C₂²×C₄	—	38	1	no	—
298	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
302	C₂²×C₄	#64541	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
304	M₁₆	—	76	2	no	—
305	M₁₆	—	76	1	no	—
306	M₁₆	—	76	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	38	1	no	—
318	C₂×C₈	—	38	1	no	—
319	C₂×C₈	—	76	2	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
323	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
324	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
325	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
326	C₄⋊C₄	—	19	1	no	—
327	C₄⋊C₄	—	19	1	no	—
328	C₄⋊C₄	—	38	1	no	—
329	C₄⋊C₄	—	38	1	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	38	4	no	—
332	C₂²⋊C₄	—	38	1	no	—
333	C₂²⋊C₄	—	38	1	no	—
334	C₂²⋊C₄	—	38	1	no	—
335	C₂²⋊C₄	—	38	1	no	—
336	C₂²⋊C₄	—	38	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	38	1	no	—
340	C₄²	—	76	1	no	—
341	C₄²	—	76	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	38	1	no	—
346	C₂³	#10597318	1	1	yes	characteristic
347	C₂³	C₄×D₇₆	1	1	yes	characteristic
348	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
349	Q₈	—	76	1	no	—
350	D₄	—	76	1	no	—
351	D₄	—	76	2	no	—
352	D₄	—	76	2	no	—
353	D₄	—	76	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	38	4	no	—
367	C₂×C₄	—	38	1	no	—
368	C₂×C₄	—	38	1	no	—
369	C₂×C₄	—	38	1	no	—
370	C₂×C₄	—	76	2	no	—
371	C₂×C₄	—	76	2	no	—
372	C₂×C₄	—	76	1	no	—
373	C₂×C₄	—	76	1	no	—
374	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
375	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
376	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	2	no	—
382	C₈	—	76	2	no	—
383	C₈	—	76	1	no	—
384	C₈	—	76	1	no	—
385	C₈	#10597263	1	2	yes	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	76	1	no	—
395	C₂²	—	76	1	no	—
396	C₂²	—	76	1	no	—
397	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
398	C₂²	#11926659	1	2	yes	—
399	C₂²	#11926667	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	76	4	no	—
405	C₄	—	76	1	no	—
406	C₄	—	76	1	no	—
407	C₄	—	76	1	no	—
408	C₄	C₂×#10597263	1	1	yes	characteristic
409	C₄	#11926517	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	152	1	no	—
414	C₂	C₄×#10597263	1	1	yes	characteristic
415	C₂	#14563474	1	1	yes	characteristic
416	C₂	#14563479	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1752	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	#11927055	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1752	D₁₉
hypocenter	C₁₉	#8240
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #1752

Complements

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

N	H ≅ G/N	type
2. C₈×C₂²⋊Dic₁₉	C₂	semidirect
5. #14561523	C₂	semidirect
6. #14561521	C₂	semidirect
7. C₁₉×#1752	C₂	semidirect
8. C₂×#10597347	C₄	semidirect
14. #11926570	C₄	semidirect
15. #11926510	C₄	semidirect
18. #11926499	C₄	semidirect
22. #11926282	C₄	semidirect
23. #11926280	C₄	semidirect
24. #11926279	C₄	semidirect
25. #11926277	C₄	semidirect
179. #1752	D₁₉	semidirect
284. C₁₉	#8240	semidirect

Maximal subgroups

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

subgroup	index
#14572329	2
C₈×C₂²⋊Dic₁₉	2
#14562127	2
#14562124	2
#14561523	2
#14561521	2
C₁₉×#1752	2
#8240	19