Subgroups — #18077760

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574210	C₂	1	1	yes	maximal, characteristic
2	#14564554	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562033	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561473	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926947	C₄	1	1	yes	characteristic, complemented
10	#11926920	C₄	1	1	yes	characteristic, complemented
11	#11926892	C₄	1	1	yes	characteristic, complemented
12	#11926890	C₄	1	1	yes	characteristic, complemented
13	#11926778	—	2	2	no	—
14	C₄×#64525	—	2	2	no	—
15	#11926597	C₂²	1	1	yes	characteristic
16	C₂×#10597282	—	2	1	no	—
17	C₂×#10597282	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926278	—	2	2	no	—
21	#11926271	—	2	1	no	—
22	#11926271	—	2	1	no	—
23	C₂×C₁₉×#131	—	2	1	no	—
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#436	—	2	1	no	—
26	C₁₉×#435	—	2	2	no	—
27	C₈×D₄×C₁₉	—	2	1	no	—
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#408	—	2	1	no	—
30	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#64541	—	2	1	no	—
33	C₁₉×#131	—	4	2	no	—
34	C₁₉×#131	—	4	2	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
41	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
42	C₁₉×#124	—	2	1	no	—
43	C₁₉×#121	—	2	1	no	—
44	C₁₉×#121	D₄	1	2	yes	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	D₄	1	2	yes	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×#64525	—	2	2	no	—
49	#10597376	—	2	1	no	—
50	#10597376	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	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×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
62	C₁₉×C₂²⋊C₈	—	2	2	no	—
63	C₁₉×C₂²⋊C₈	—	2	2	no	—
64	C₁₉×#97	—	2	1	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	#10597289	—	2	2	no	—
67	C₁₉⋊#95	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	#10597282	—	4	2	no	—
70	#10597282	—	4	2	no	—
71	#10597266	—	2	2	no	—
72	#10597264	—	2	2	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄×C₁₉⋊C₈	—	2	1	no	—
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
78	#41×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	—	2	2	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	#41	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₉	—	4	1	no	—
92	C₂²×Dic₁₉	—	4	1	no	—
93	#64541	—	4	1	no	—
94	#64541	—	4	1	no	—
95	#64541	—	4	1	no	—
96	#64541	—	4	1	no	—
97	C₂×D₇₆	—	2	1	no	—
98	C₂×D₇₆	—	2	1	no	—
99	C₂×D₇₆	—	2	1	no	—
100	C₂×C₄×D₁₉	—	4	1	no	—
101	C₂×Dic₃₈	—	2	1	no	—
102	M₁₆×C₁₉	—	2	1	no	—
103	M₁₆×C₁₉	—	2	1	no	—
104	M₁₆×C₁₉	—	2	1	no	—
105	M₁₆×C₁₉	—	4	4	no	—
106	M₁₆×C₁₉	D₈	1	2	yes	complemented
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	4	4	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	#64525	—	4	4	no	—
123	(C₂×D₁₉)⋊C₄	—	4	1	no	—
124	(C₂×D₁₉)⋊C₄	—	4	1	no	—
125	C₄⋊Dic₁₉	—	2	2	no	—
126	C₄⋊Dic₁₉	—	2	1	no	—
127	C₄⋊Dic₁₉	—	2	1	no	—
128	C₄⋊Dic₁₉	—	4	1	no	—
129	C₄×Dic₁₉	—	4	1	no	—
130	C₄×Dic₁₉	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	2	1	no	—
132	C₂×C₁₉⋊C₈	—	2	1	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	#9053	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	#121	1	1	yes	characteristic
138	C₂²×D₁₉	—	4	1	no	—
139	Q₈×C₁₉	—	4	1	no	—
140	Q₈×C₁₉	—	4	1	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
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	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²⋊D₁₉	—	8	1	no	—
165	C₂²⋊D₁₉	—	8	1	no	—
166	C₂×Dic₁₉	—	4	2	no	—
167	C₂×Dic₁₉	—	4	1	no	—
168	C₂×Dic₁₉	—	8	1	no	—
169	C₂×Dic₁₉	—	8	1	no	—
170	D₇₆	—	4	2	no	—
171	D₇₆	—	4	1	no	—
172	D₇₆	—	4	1	no	—
173	D₇₆	—	4	1	no	—
174	D₇₆	—	4	1	no	—
175	C₄×D₁₉	—	8	1	no	—
176	C₄×D₁₉	—	8	1	no	—
177	Dic₃₈	—	4	1	no	—
178	Dic₃₈	—	4	1	no	—
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₁₉⋊C₈	—	2	2	no	—
184	C₁₉⋊C₈	—	4	1	no	—
185	C₁₉⋊C₈	—	8	1	no	—
186	#3169	—	19	1	no	—
187	#2935	D₁₉	1	1	yes	characteristic, complemented
188	#1980	—	19	1	no	—
189	#1502	—	19	1	no	—
190	#1480	—	19	1	no	—
191	#1279	—	19	1	no	—
192	#1278	—	19	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	#386	1	1	yes	characteristic
199	C₂²×C₁₉	#459	1	1	yes	characteristic
200	C₂²×C₁₉	#463	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	C₄×D₈	1	1	yes	characteristic
209	C₄×C₁₉	#442	1	1	yes	characteristic
210	C₄×C₁₉	#443	1	1	yes	characteristic
211	C₄×C₁₉	#444	1	1	yes	characteristic
212	C₄×C₁₉	#447	1	1	yes	characteristic
213	C₄×C₁₉	#449	1	1	yes	characteristic
214	Dic₁₉	—	8	2	no	—
215	Dic₁₉	—	8	1	no	—
216	C₂×#131	—	2	1	no	—
217	#532	—	19	1	no	—
218	#532	C₂×D₁₉	1	1	yes	characteristic
219	#500	—	19	1	no	—
220	#493	—	19	1	no	—
221	#486	—	19	1	no	—
222	#486	—	19	1	no	—
223	#466	—	38	2	no	—
224	C₄×D₈	—	38	2	no	—
225	#436	—	2	1	no	—
226	#435	—	2	2	no	—
227	C₈×D₄	—	2	1	no	—
228	#431	—	19	1	no	—
229	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
230	C₂×#104	—	38	1	no	—
231	C₂×#104	—	38	1	no	—
232	#408	—	2	1	no	—
233	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
234	C₂×C₄×C₈	—	19	1	no	—
235	C₄×C₄⋊C₄	—	19	1	no	—
236	#327	—	38	2	no	—
237	D₄⋊C₈	—	38	1	no	—
238	D₄⋊C₈	—	38	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	8	2	no	—
242	C₂×C₁₉	#1876	1	1	yes	characteristic
243	C₂×C₁₉	#1879	1	1	yes	characteristic
244	C₂×C₁₉	#1884	1	1	yes	characteristic
245	D₁₉	—	16	1	no	—
246	C₂×#41	—	2	1	no	—
247	C₂×#41	—	38	1	no	—
248	C₂×D₈	—	38	2	no	—
249	#131	—	4	2	no	—
250	#131	—	4	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₄⋊Q₈	—	19	1	no	—
258	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
259	#127	—	19	1	no	—
260	#127	C₄×D₁₉	1	1	yes	characteristic
261	#124	—	2	1	no	—
262	#124	—	38	1	no	—
263	#121	—	2	1	no	—
264	#121	—	38	1	no	—
265	#121	—	38	1	no	—
266	#121	D₇₆	1	2	yes	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	38	1	no	—
269	C₄×D₄	—	38	1	no	—
270	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	—	38	1	no	—
272	C₂×C₄²	—	38	1	no	—
273	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
274	#107	—	38	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
279	#104	—	76	2	no	—
280	#104	—	76	2	no	—
281	#102	—	38	2	no	—
282	#102	—	38	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	38	1	no	—
286	#97	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	19	1	no	—
289	C₄×C₈	—	19	1	no	—
290	C₄×C₈	—	38	1	no	—
291	C₄×C₈	—	38	1	no	—
292	#95	—	38	1	no	—
293	C₁₉	#9053	1	1	yes	characteristic, complemented, Sylow
294	#41	—	4	1	no	—
295	#41	—	4	1	no	—
296	#41	—	4	1	no	—
297	#41	—	4	1	no	—
298	#41	—	76	1	no	—
299	#41	—	76	1	no	—
300	#41	—	76	1	no	—
301	#41	—	76	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	38	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	38	1	no	—
308	C₂×D₄	—	38	1	no	—
309	C₂×D₄	—	38	1	no	—
310	C₂×D₄	—	76	1	no	—
311	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	76	1	no	—
314	C₂²×C₄	—	76	1	no	—
315	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
316	C₂²×C₄	#64541	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	D₈	—	76	4	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	1	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	4	4	no	—
323	M₁₆	#64525	1	2	yes	complemented
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	4	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	38	1	no	—
332	C₂×C₈	—	38	1	no	—
333	C₂×C₈	—	76	2	no	—
334	C₂×C₈	—	76	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	38	2	no	—
337	C₄⋊C₄	—	38	1	no	—
338	C₄⋊C₄	—	38	1	no	—
339	C₄⋊C₄	—	76	1	no	—
340	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	76	1	no	—
344	C₂²⋊C₄	—	76	1	no	—
345	C₄²	—	76	1	no	—
346	C₄²	—	76	1	no	—
347	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
348	C₄²	#64541	1	1	yes	characteristic
349	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
350	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	76	1	no	—
353	C₂³	#10597376	1	1	yes	characteristic
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	76	1	no	—
357	Q₈	—	76	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	76	2	no	—
366	D₄	—	76	1	no	—
367	D₄	—	76	1	no	—
368	D₄	—	76	1	no	—
369	D₄	—	76	1	no	—
370	D₄	—	152	1	no	—
371	D₄	—	152	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	76	2	no	—
379	C₂×C₄	—	76	1	no	—
380	C₂×C₄	—	152	1	no	—
381	C₂×C₄	—	152	1	no	—
382	C₂×C₄	—	152	1	no	—
383	C₂×C₄	—	152	1	no	—
384	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
387	C₂×C₄	#10597375	1	1	yes	characteristic
388	C₂×C₄	#10597376	1	1	yes	characteristic
389	C₂×C₄	C₂×#64525	1	1	yes	characteristic
390	C₂×C₄	#10597378	1	1	yes	characteristic
391	C₂×C₄	#10597395	1	1	yes	characteristic
392	C₂×C₄	#10597396	1	1	yes	characteristic
393	C₂×C₄	#10597399	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	38	2	no	—
399	C₈	—	76	1	no	—
400	C₈	—	152	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	152	1	no	—
407	C₂²	—	152	1	no	—
408	C₂²	—	152	1	no	—
409	C₂²	#11926423	1	1	yes	characteristic
410	C₂²	#11926739	1	1	yes	characteristic
411	C₂²	#11926759	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	152	2	no	—
417	C₄	—	152	1	no	—
418	C₄	C₄×#64525	1	1	yes	characteristic
419	C₄	#11926654	1	1	yes	characteristic
420	C₄	#11926659	1	1	yes	characteristic
421	C₄	#11926664	1	1	yes	characteristic
422	C₄	#11926678	1	1	yes	characteristic
423	C₄	#11926689	1	1	yes	characteristic
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	304	1	no	—
428	C₂	#14563962	1	1	yes	characteristic
429	C₂	#14563983	1	1	yes	characteristic
430	C₂	#14564018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2935	C₂
socle	C₂²×C₁₉	#386
prime radical	#14574210	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2935	D₁₉
hypocenter	C₁₉	#9053
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #14564554	C₂	semidirect
3. #14562130	C₂	semidirect
4. #14562033	C₂	semidirect
5. #14561474	C₂	semidirect
6. #14561473	C₂	semidirect
7. C₁₉×#2935	C₂	semidirect
9. #11926947	C₄	semidirect
10. #11926920	C₄	semidirect
11. #11926892	C₄	semidirect
12. #11926890	C₄	semidirect
106. M₁₆×C₁₉	D₈	semidirect
187. #2935	D₁₉	semidirect
293. C₁₉	#9053	semidirect
323. M₁₆	#64525	semidirect

Maximal subgroups

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

subgroup	index
#14574210	2
#14564554	2
#14562130	2
#14562033	2
#14561474	2
#14561473	2
C₁₉×#2935	2
#9053	19