Subgroups — #18078832

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573635	C₂	1	1	yes	maximal, characteristic
2	#14564463	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562129	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561538	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926857	—	2	1	no	—
10	#11926824	C₄	1	2	yes	complemented
11	#11926739	C₄	1	2	yes	complemented
12	#11926678	—	2	1	no	—
13	C₄×#64525	—	2	2	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926597	C₂²	1	1	yes	characteristic
16	#11926568	C₂²	1	1	yes	characteristic
17	C₂×#10597262	—	2	1	no	—
18	C₂×#10597262	—	2	1	no	—
19	#11926277	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	—	2	1	no	—
23	C₁₉×#390	—	2	1	no	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#388	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₄³×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂×#64541	—	2	1	no	—
32	C₄×D₄×C₁₉	—	2	1	no	—
33	C₄×D₄×C₁₉	—	2	1	no	—
34	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×D₄×C₁₉	D₄	1	2	yes	—
36	C₁₉×#117	—	4	2	no	—
37	C₁₉×#117	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×#64525	—	2	2	no	—
51	#10597376	—	2	1	no	—
52	#10597376	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	#10597321	—	2	1	no	—
55	#10597320	C₂×C₄	1	1	yes	characteristic
56	C₄×D₇₆	—	2	1	no	—
57	C₄×D₇₆	—	2	1	no	—
58	#10597315	C₂×C₄	1	1	yes	characteristic
59	C₁₉×#95	—	2	2	no	—
60	C₁₉×#95	D₄	1	2	yes	—
61	#10597289	—	2	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
64	#10597266	—	2	2	no	—
65	#10597264	—	2	2	no	—
66	#10597262	—	4	2	no	—
67	#10597262	—	4	2	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₉	—	4	1	no	—
92	#64541	—	4	1	no	—
93	#64541	—	4	1	no	—
94	#64541	—	4	1	no	—
95	#64541	—	4	1	no	—
96	C₂×D₇₆	—	2	1	no	—
97	C₂×D₇₆	—	2	1	no	—
98	C₂×D₇₆	—	2	1	no	—
99	C₂×C₄×D₁₉	—	4	1	no	—
100	C₂×Dic₃₈	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	4	4	no	—
104	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂²⋊C₄×C₁₉	—	4	4	no	—
108	C₂²⋊C₄×C₁₉	—	4	4	no	—
109	C₄²×C₁₉	—	2	1	no	—
110	C₄²×C₁₉	—	2	1	no	—
111	C₄²×C₁₉	—	2	1	no	—
112	C₄²×C₁₉	—	4	2	no	—
113	C₄²×C₁₉	—	4	2	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	D₈	1	2	yes	complemented
117	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	#41	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	#64525	—	4	4	no	—
122	(C₂×D₁₉)⋊C₄	—	4	1	no	—
123	(C₂×D₁₉)⋊C₄	—	4	1	no	—
124	C₄⋊Dic₁₉	—	2	1	no	—
125	C₄⋊Dic₁₉	—	2	1	no	—
126	#64520	—	4	1	no	—
127	#64520	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	#9237	—	19	1	no	maximal, Sylow
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	#120	1	1	yes	characteristic
138	C₂²×D₁₉	—	4	1	no	—
139	D₄×C₁₉	—	2	2	no	—
140	D₄×C₁₉	—	2	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	4	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	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂²⋊D₁₉	—	8	1	no	—
171	C₂²⋊D₁₉	—	8	1	no	—
172	C₂×Dic₁₉	—	4	1	no	—
173	D₇₆	—	4	2	no	—
174	D₇₆	—	4	1	no	—
175	D₇₆	—	4	1	no	—
176	D₇₆	—	8	1	no	—
177	C₄×D₁₉	—	8	1	no	—
178	C₄×D₁₉	—	8	1	no	—
179	Dic₃₈	—	4	1	no	—
180	Dic₃₈	—	4	1	no	—
181	C₁₉⋊C₈	—	4	2	no	—
182	C₁₉⋊C₈	—	8	1	no	—
183	C₁₉⋊C₈	—	8	1	no	—
184	#3100	—	19	1	no	—
185	#2293	D₁₉	1	1	yes	characteristic, complemented
186	#1962	—	19	1	no	—
187	#1502	—	19	1	no	—
188	#1486	—	19	1	no	—
189	#1303	—	19	1	no	—
190	#1276	—	19	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	#386	1	1	yes	characteristic
199	C₂²×C₁₉	#447	1	1	yes	characteristic
200	C₂²×C₁₉	#449	1	1	yes	characteristic
201	C₂×D₁₉	—	8	1	no	—
202	C₂×D₁₉	—	8	1	no	—
203	C₂×D₁₉	—	8	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#421	1	2	yes	—
212	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
213	C₄×C₁₉	#442	1	1	yes	characteristic
214	C₄×C₁₉	#459	1	1	yes	characteristic
215	C₄×C₁₉	#463	1	1	yes	characteristic
216	Dic₁₉	—	8	1	no	—
217	#532	—	19	1	no	—
218	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
219	C₂×#117	—	2	1	no	—
220	#480	—	38	1	no	—
221	#474	—	19	2	no	—
222	#459	—	19	2	no	—
223	#447	—	38	1	no	—
224	C₄×D₈	—	38	2	no	—
225	#431	—	19	1	no	—
226	#431	—	19	1	no	—
227	#423	—	19	1	no	—
228	C₂×#104	—	38	1	no	—
229	C₂×#104	—	38	1	no	—
230	#390	—	2	1	no	—
231	#389	—	2	1	no	—
232	#388	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	—	2	1	no	—
235	C₄³	C₂×D₁₉	1	1	yes	characteristic
236	#327	—	38	2	no	—
237	D₄⋊C₈	—	38	2	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	8	2	no	—
241	C₂×C₁₉	#1879	1	1	yes	characteristic
242	C₂×C₁₉	#1897	1	1	yes	characteristic
243	C₂×C₁₉	#1906	1	1	yes	characteristic
244	D₁₉	—	16	1	no	—
245	C₂×#41	—	38	1	no	—
246	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂×D₈	—	38	2	no	—
249	C₂×M₁₆	—	38	1	no	—
250	C₄⋊Q₈	—	19	1	no	—
251	#127	—	19	1	no	—
252	#124	—	38	1	no	—
253	#121	—	38	1	no	—
254	#121	—	38	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	38	1	no	—
258	C₄×D₄	—	38	1	no	—
259	C₄×D₄	C₄×D₁₉	1	2	yes	—
260	C₄×D₄	D₇₆	1	2	yes	—
261	#117	—	4	2	no	—
262	#117	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
275	#107	—	38	2	no	—
276	C₄⋊C₈	—	19	2	no	—
277	C₄⋊C₈	—	38	1	no	—
278	C₄⋊C₈	—	38	1	no	—
279	C₄⋊C₈	—	38	1	no	—
280	#104	—	76	2	no	—
281	#104	—	76	2	no	—
282	#102	—	38	2	no	—
283	#102	—	38	2	no	—
284	C₂²⋊C₈	—	38	1	no	—
285	C₂²⋊C₈	—	38	1	no	—
286	C₄×C₈	—	38	1	no	—
287	C₄×C₈	—	38	1	no	—
288	#95	—	2	2	no	—
289	#95	C₂²⋊D₁₉	1	2	yes	—
290	C₁₉	#9237	1	1	yes	characteristic, complemented, Sylow
291	C₂⁴	—	2	1	no	—
292	#41	—	76	1	no	—
293	#41	—	76	1	no	—
294	#41	—	76	1	no	—
295	#41	—	76	1	no	—
296	C₂×Q₈	—	38	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	38	1	no	—
300	C₂×D₄	—	38	1	no	—
301	C₂×D₄	—	38	1	no	—
302	C₂×D₄	—	76	1	no	—
303	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	76	1	no	—
315	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	D₈	—	76	4	no	—
319	M₁₆	—	76	1	no	—
320	M₁₆	—	76	1	no	—
321	C₂×C₈	—	38	2	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	38	1	no	—
328	C₄⋊C₄	—	38	1	no	—
329	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	76	1	no	—
335	C₂²⋊C₄	—	76	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	#64525	1	2	yes	complemented
344	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
345	C₄²	C₂×D₇₆	1	1	yes	characteristic
346	C₄²	#64541	1	1	yes	characteristic
347	C₄²	#64541	1	1	yes	characteristic
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	76	1	no	—
354	C₂³	#10597399	1	1	yes	characteristic
355	Q₈	—	76	1	no	—
356	Q₈	—	76	1	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	76	2	no	—
361	D₄	—	76	1	no	—
362	D₄	—	76	1	no	—
363	D₄	—	152	1	no	—
364	D₄	—	152	1	no	—
365	D₄	—	152	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	152	1	no	—
386	C₂×C₄	—	152	1	no	—
387	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
389	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
390	C₂×C₄	#10597375	1	1	yes	characteristic
391	C₂×C₄	#10597376	1	1	yes	characteristic
392	C₂×C₄	#10597376	1	1	yes	characteristic
393	C₂×C₄	C₂×#64525	1	1	yes	characteristic
394	C₂×C₄	#10597378	1	1	yes	characteristic
395	C₂×C₄	#10597395	1	1	yes	characteristic
396	C₂×C₄	#10597396	1	1	yes	characteristic
397	C₈	—	76	2	no	—
398	C₈	—	152	1	no	—
399	C₈	—	152	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	152	1	no	—
408	C₂²	—	152	1	no	—
409	C₂²	—	152	1	no	—
410	C₂²	#11926423	1	1	yes	characteristic
411	C₂²	#11926678	1	1	yes	characteristic
412	C₂²	#11926689	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	152	1	no	—
421	C₄	#11926562	1	2	yes	—
422	C₄	C₄×#64525	1	1	yes	characteristic
423	C₄	#11926654	1	1	yes	characteristic
424	C₄	#11926739	1	1	yes	characteristic
425	C₄	#11926759	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	8	2	no	—
429	C₂	—	304	1	no	—
430	C₂	#14563983	1	1	yes	characteristic
431	C₂	#14564083	1	1	yes	characteristic
432	C₂	#14564136	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2293	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573635	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2293	D₁₉
hypocenter	C₁₉	#9237
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2293

Complements

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

N	H ≅ G/N	type
2. #14564463	C₂	semidirect
3. #14562129	C₂	semidirect
4. #14562060	C₂	semidirect
5. #14561538	C₂	semidirect
6. #14561468	C₂	semidirect
7. C₁₉×#2293	C₂	semidirect
10. #11926824	C₄	semidirect
11. #11926739	C₄	semidirect
116. C₄²×C₁₉	D₈	semidirect
185. #2293	D₁₉	semidirect
290. C₁₉	#9237	semidirect
343. C₄²	#64525	semidirect

Maximal subgroups

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

subgroup	index
#14573635	2
#14564463	2
#14562129	2
#14562060	2
#14561538	2
#14561468	2
C₁₉×#2293	2
#9237	19