Subgroups — #18091251

Order 4864.

822 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	C₂×#11926584	C₂	1	2	yes	maximal
2	#14566253	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926304	C₂	1	2	yes	maximal
5	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂×#10597372	C₂²	1	2	yes	—
8	#11926584	—	2	4	no	—
9	#11926584	—	2	4	no	—
10	C₂×#10597264	—	2	2	no	—
11	C₂×#10597265	—	2	2	no	—
12	#11926443	—	2	2	no	—
13	#11926443	—	2	2	no	—
14	#11926404	—	2	2	no	—
15	#11926313	C₄	1	4	yes	complemented
16	#11926304	—	2	4	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#95	—	2	2	no	—
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	D₄	1	2	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
33	C₂×C₄²×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
37	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
38	#10597372	—	2	2	no	—
39	#10597372	—	2	2	no	—
40	#10597372	—	2	2	no	—
41	#10597372	—	2	2	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
44	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
46	C₂×C₄×Dic₁₉	—	2	2	no	—
47	C₂×#64520	—	2	2	no	—
48	C₂×#64520	—	2	2	no	—
49	C₂×#64520	—	2	2	no	—
50	C₂×#64520	C₂×C₄	1	4	yes	—
51	C₂×#64520	D₄	1	4	yes	—
52	C₂×#64520	Q₈	1	4	yes	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₁₉×#95	—	4	4	no	—
55	C₁₉⋊#95	—	2	4	no	—
56	#10597265	—	2	8	no	—
57	#10597264	—	2	8	no	—
58	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	—	4	1	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
76	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	2	yes	—
86	C₂²×Dic₁₉	—	2	2	no	—
87	C₂²×Dic₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₄⋊C₄×C₁₉	—	2	4	no	—
90	C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₄⋊C₄×C₁₉	—	4	2	no	—
92	C₄²×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	—	4	2	no	—
94	C₂²⋊Dic₁₉	—	4	2	no	—
95	C₂²⋊Dic₁₉	—	4	2	no	—
96	C₄⋊Dic₁₉	—	2	2	no	—
97	C₄⋊Dic₁₉	—	2	2	no	—
98	C₄⋊Dic₁₉	—	2	2	no	—
99	C₄⋊Dic₁₉	—	2	2	no	—
100	C₄⋊Dic₁₉	—	8	2	no	—
101	C₄⋊Dic₁₉	—	8	2	no	—
102	C₄×Dic₁₉	—	4	2	no	—
103	C₄×Dic₁₉	—	4	2	no	—
104	#64520	—	2	4	no	—
105	#64520	—	2	4	no	—
106	#64520	—	2	4	no	—
107	#64520	C₄⋊C₄	1	8	yes	complemented
108	C₂×C₁₉⋊C₈	—	2	4	no	—
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	#11342	—	19	1	no	maximal, Sylow
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₁₉	#120	1	1	yes	characteristic
118	C₂³×C₁₉	#121	1	1	yes	characteristic
119	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
120	C₂³×C₁₉	#123	1	1	yes	characteristic
121	C₂³×C₁₉	#127	1	1	yes	characteristic
122	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	2	4	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	—	4	4	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	8	2	no	—
137	C₂×C₄×C₁₉	—	8	2	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#120	1	2	yes	—
145	C₂×C₄×C₁₉	#121	1	2	yes	—
146	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₁₉	#123	1	2	yes	—
151	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#125	1	2	yes	—
153	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
155	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
156	C₂×Dic₁₉	—	4	2	no	—
157	C₂×Dic₁₉	—	4	2	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	4	2	no	—
161	C₂×Dic₁₉	—	4	2	no	—
162	C₁₉⋊C₈	—	2	8	no	—
163	C₂×#428	—	19	2	no	—
164	#2316	—	19	1	no	—
165	C₂×#343	—	19	1	no	—
166	C₂×#339	—	19	2	no	—
167	C₄⋊#95	D₁₉	1	1	yes	characteristic
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	#384	1	1	yes	characteristic
181	C₂²×C₁₉	#385	1	1	yes	characteristic
182	C₂²×C₁₉	#389	1	1	yes	characteristic
183	C₂²×C₁₉	#392	1	1	yes	characteristic
184	C₂²×C₁₉	#395	1	1	yes	characteristic
185	C₂²×C₁₉	#398	1	1	yes	characteristic
186	C₂²×C₁₉	#399	1	1	yes	characteristic
187	C₂²×C₁₉	#453	1	1	yes	characteristic
188	C₂²×C₁₉	#454	1	1	yes	characteristic
189	C₂²×C₁₉	#455	1	1	yes	characteristic
190	C₂²×C₁₉	#456	1	1	yes	characteristic
191	C₄×C₁₉	—	4	4	no	—
192	C₄×C₁₉	—	4	4	no	—
193	C₄×C₁₉	—	8	2	no	—
194	C₄×C₁₉	#385	1	2	yes	—
195	C₄×C₁₉	#389	1	2	yes	—
196	C₄×C₁₉	#395	1	2	yes	—
197	C₄×C₁₉	#398	1	2	yes	—
198	Dic₁₉	—	8	2	no	—
199	Dic₁₉	—	8	2	no	—
200	C₂²×M₁₆	—	19	2	no	—
201	C₂×#117	—	19	2	no	—
202	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
204	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
205	#428	—	38	4	no	—
206	#428	—	38	4	no	—
207	C₂×#107	—	38	2	no	—
208	C₂×#106	—	38	2	no	—
209	#389	—	38	2	no	—
210	#389	—	38	2	no	—
211	#380	—	38	2	no	—
212	C₂×#95	—	2	2	no	—
213	#343	—	19	4	no	—
214	#339	—	38	4	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	2	1	no	—
217	C₂×C₁₉	—	2	1	no	—
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	#1444	1	1	yes	characteristic
220	C₂×C₁₉	#1856	1	1	yes	characteristic
221	C₂×C₁₉	#1857	1	1	yes	characteristic
222	C₂×C₁₉	#2006	1	1	yes	characteristic
223	C₂×C₁₉	#2007	1	1	yes	characteristic
224	C₂×C₁₉	#2060	1	1	yes	characteristic
225	C₂×C₁₉	#2061	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	—	2	1	no	—
228	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
229	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
230	C₂×M₁₆	—	19	4	no	—
231	C₂×M₁₆	—	19	4	no	—
232	C₂×M₁₆	—	19	4	no	—
233	C₂×M₁₆	—	38	2	no	—
234	C₂×M₁₆	—	38	2	no	—
235	C₂×M₁₆	—	38	2	no	—
236	C₂²×C₈	—	38	2	no	—
237	#117	—	38	2	no	—
238	#117	—	38	2	no	—
239	#117	—	38	2	no	—
240	#117	—	38	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	19	2	no	—
247	C₂×C₄⋊C₄	—	19	2	no	—
248	C₂×C₄⋊C₄	—	38	2	no	—
249	C₂×C₄⋊C₄	—	38	2	no	—
250	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
251	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
252	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
253	C₂×C₂²⋊C₄	—	38	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	38	2	no	—
258	C₂×C₄²	Dic₃₈	1	2	yes	—
259	#107	—	38	8	no	—
260	#106	—	38	8	no	—
261	#95	—	4	4	no	—
262	#95	—	38	4	no	—
263	C₁₉	#11342	1	1	yes	characteristic, complemented, Sylow
264	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	38	2	no	—
282	C₂²×C₄	—	38	2	no	—
283	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
284	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
288	C₂²×C₄	#64541	1	1	yes	characteristic
289	C₂²×C₄	#64541	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₁₉	1	2	yes	—
291	C₂²×C₄	D₄×D₁₉	1	2	yes	—
292	C₂²×C₄	#64543	1	2	yes	—
293	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
294	M₁₆	—	19	8	no	—
295	M₁₆	—	38	4	no	—
296	M₁₆	—	38	4	no	—
297	M₁₆	—	38	4	no	—
298	C₂×C₈	—	38	4	no	—
299	C₂×C₈	—	38	4	no	—
300	C₂×C₈	—	38	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	38	2	no	—
306	C₄⋊C₄	—	38	2	no	—
307	C₄⋊C₄	—	38	2	no	—
308	C₄⋊C₄	—	38	2	no	—
309	C₄⋊C₄	—	152	2	no	—
310	C₄⋊C₄	—	152	2	no	—
311	C₂²⋊C₄	—	76	2	no	—
312	C₂²⋊C₄	—	76	2	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	76	2	no	—
316	C₄²	—	76	2	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
322	C₂³	#10597370	1	1	yes	characteristic
323	C₂³	#10597376	1	1	yes	characteristic
324	C₂³	#10597381	1	1	yes	characteristic
325	C₂³	#10597383	1	1	yes	characteristic
326	C₂³	#10597386	1	1	yes	characteristic
327	C₂³	#10597390	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	—	76	2	no	—
346	C₂×C₄	—	76	2	no	—
347	C₂×C₄	—	76	2	no	—
348	C₂×C₄	—	76	2	no	—
349	C₂×C₄	—	76	2	no	—
350	C₂×C₄	—	76	2	no	—
351	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
352	C₂×C₄	#10597315	1	1	yes	characteristic
353	C₂×C₄	#10597316	1	1	yes	characteristic
354	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
355	C₂×C₄	#10597324	1	2	yes	—
356	C₂×C₄	#10597324	1	2	yes	—
357	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
358	C₂×C₄	#10597328	1	2	yes	—
359	C₂×C₄	#10597329	1	2	yes	—
360	C₂×C₄	#10597330	1	2	yes	—
361	C₂×C₄	#10597334	1	2	yes	—
362	C₂×C₄	#10597334	1	2	yes	—
363	C₂×C₄	#10597335	1	2	yes	—
364	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
365	C₂×C₄	#10597342	1	2	yes	—
366	C₂×C₄	#10597343	1	2	yes	—
367	C₈	—	38	8	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	#11926413	1	1	yes	characteristic
381	C₂²	#11926416	1	1	yes	characteristic
382	C₂²	#11926442	1	1	yes	characteristic
383	C₂²	#11926453	1	1	yes	characteristic
384	C₂²	#11926464	1	1	yes	characteristic
385	C₂²	#11926474	1	1	yes	characteristic
386	C₂²	#11926480	1	1	yes	characteristic
387	C₂²	#11926711	1	1	yes	characteristic
388	C₂²	#11926716	1	1	yes	characteristic
389	C₂²	#11926721	1	1	yes	characteristic
390	C₂²	#11926726	1	1	yes	characteristic
391	C₄	—	4	4	no	—
392	C₄	—	4	4	no	—
393	C₄	—	8	2	no	—
394	C₄	—	152	2	no	—
395	C₄	—	152	2	no	—
396	C₄	#11926418	1	2	yes	—
397	C₄	#11926441	1	2	yes	—
398	C₄	#11926465	1	2	yes	—
399	C₄	#11926478	1	2	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#14561899	1	1	yes	characteristic
405	C₂	#14563844	1	1	yes	characteristic
406	C₂	#14563849	1	1	yes	characteristic
407	C₂	#14564676	1	1	yes	characteristic
408	C₂	#14564681	1	1	yes	characteristic
409	C₂	#14564980	1	1	yes	characteristic
410	C₂	#14564985	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊#95	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄⋊#95	D₁₉
hypocenter	C₁₉	#11342
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
15. #11926313	C₄	semidirect
107. #64520	C₄⋊C₄	semidirect
263. C₁₉	#11342	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926584	2
#14566253	2
C₂×#11926313	2
C₂×#11926304	2
C₁₉×C₄⋊#95	2
#11342	19