Subgroups — #18077393

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#64520	C₂	1	1	yes	maximal, characteristic
2	#14564580	C₂	1	1	yes	maximal, characteristic
3	C₄×#10597292	C₂	1	1	yes	maximal, characteristic
4	#14562090	C₂	1	1	yes	maximal, characteristic
5	#14561537	C₂	1	1	yes	maximal, characteristic
6	#14561471	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#3104	C₂	1	1	yes	maximal, characteristic
8	#11926675	—	2	2	no	—
9	#11926675	—	2	1	no	—
10	Q₈×C₁₉⋊C₈	—	2	1	no	—
11	#11926568	—	2	1	no	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×#10597292	—	2	1	no	—
14	C₄×#64520	—	2	1	no	—
15	C₄×#64520	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	#11926306	—	2	1	no	—
19	#11926303	—	2	1	no	—
20	#11926303	—	2	1	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#484	—	2	1	no	—
25	C₁₉×#477	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#477	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#462	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#462	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#451	—	2	1	no	—
30	C₄×Q₁₆×C₁₉	—	2	1	no	—
31	C₄×Q₁₆×C₁₉	—	2	1	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂×Q₁₆×C₁₉	—	2	1	no	—
35	C₂×Q₁₆×C₁₉	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#125	—	2	1	no	—
39	C₁₉×C₂²⋊Q₈	—	2	1	no	—
40	C₁₉×C₂²⋊Q₈	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₁₉×#117	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	D₄	1	1	yes	characteristic
58	C₂×#64520	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#107	—	2	1	no	—
62	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#103	—	2	1	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	#10597292	—	2	4	no	—
71	C₁₉⋊#95	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
76	#10597260	—	2	2	no	—
77	#10597260	—	2	1	no	—
78	C₄×C₁₉⋊C₈	—	2	2	no	—
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	4	1	no	—
87	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×Dic₁₉	—	4	1	no	—
95	Q₁₆×C₁₉	—	4	2	no	—
96	Q₁₆×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	2	1	no	—
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	—	2	1	no	—
114	C₄²×C₁₉	—	2	1	no	—
115	C₄²×C₁₉	—	2	1	no	—
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	4	1	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	C₄⋊Dic₁₉	—	2	2	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₄×Dic₁₉	—	4	1	no	—
126	#64520	—	2	1	no	—
127	#64520	—	2	1	no	—
128	#64520	—	2	1	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	Q₁₆	1	2	yes	complemented
132	C₂×C₁₉⋊C₈	—	2	1	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#8990	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	#121	1	1	yes	characteristic
140	Q₈×C₁₉	—	2	1	no	—
141	Q₈×C₁₉	—	2	1	no	—
142	Q₈×C₁₉	—	2	1	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	4	1	no	—
147	Q₈×C₁₉	#104	1	2	yes	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
169	C₂×Dic₁₉	—	4	2	no	—
170	C₂×Dic₁₉	—	8	1	no	—
171	C₂×Dic₁₉	—	8	1	no	—
172	C₈×C₁₉	—	4	1	no	—
173	C₈×C₁₉	—	4	1	no	—
174	C₁₉⋊C₈	—	2	2	no	—
175	C₁₉⋊C₈	—	4	2	no	—
176	C₁₉⋊C₈	—	4	1	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	#3104	D₁₉	1	1	yes	characteristic
179	Q₈×M₁₆	—	19	1	no	—
180	#1986	—	19	1	no	—
181	C₄×#103	—	19	1	no	—
182	#1493	—	19	1	no	—
183	#1303	—	19	1	no	—
184	#1278	—	19	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	#386	1	1	yes	characteristic
188	C₂²×C₁₉	#462	1	1	yes	characteristic
189	C₂²×C₁₉	#464	1	1	yes	characteristic
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	4	1	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
200	C₄×C₁₉	#421	1	1	yes	characteristic
201	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
202	C₄×C₁₉	#441	1	1	yes	characteristic
203	C₄×C₁₉	#451	1	1	yes	characteristic
204	C₄×C₁₉	#452	1	1	yes	characteristic
205	Dic₁₉	—	8	2	no	—
206	#533	C₂×D₁₉	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
208	#484	—	2	1	no	—
209	#477	Dic₁₉	1	1	yes	characteristic, complemented
210	#477	Dic₁₉	1	1	yes	characteristic, complemented
211	#462	Dic₁₉	1	1	yes	characteristic, complemented
212	#462	Dic₁₉	1	1	yes	characteristic, complemented
213	#451	—	2	1	no	—
214	#446	—	38	2	no	—
215	#446	—	38	1	no	—
216	C₈×Q₈	—	38	1	no	—
217	C₄×Q₁₆	—	2	1	no	—
218	C₄×Q₁₆	—	2	1	no	—
219	#431	C₂×D₁₉	1	1	yes	characteristic
220	#423	—	19	1	no	—
221	#423	—	38	1	no	—
222	C₂×#103	—	38	1	no	—
223	C₄×M₁₆	—	19	1	no	—
224	C₄×M₁₆	—	38	1	no	—
225	C₂×C₄×C₈	—	19	1	no	—
226	C₄×C₄⋊C₄	—	19	1	no	—
227	#340	—	38	1	no	—
228	#339	—	38	1	no	—
229	#339	—	38	1	no	—
230	Q₈⋊C₈	—	38	2	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	#1871	1	1	yes	characteristic
234	C₂×C₁₉	#1878	1	1	yes	characteristic
235	C₂×C₁₉	#1881	1	1	yes	characteristic
236	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×M₁₆	—	19	1	no	—
240	C₂×M₁₆	—	19	1	no	—
241	C₂×M₁₆	—	38	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
245	#125	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
253	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
254	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
256	#117	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	38	1	no	—
259	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	38	1	no	—
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	#107	—	2	1	no	—
264	#107	—	2	1	no	—
265	C₄⋊C₈	—	19	2	no	—
266	C₄⋊C₈	—	38	2	no	—
267	C₄⋊C₈	—	38	2	no	—
268	C₄⋊C₈	—	38	1	no	—
269	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
270	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
271	#103	—	2	1	no	—
272	#103	—	2	1	no	—
273	#103	—	2	1	no	—
274	#103	—	2	1	no	—
275	#103	—	38	4	no	—
276	C₂²⋊C₈	—	2	1	no	—
277	#97	—	38	2	no	—
278	#97	—	38	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	38	2	no	—
281	C₄×C₈	—	38	1	no	—
282	C₄×C₈	—	38	1	no	—
283	C₄×C₈	—	38	1	no	—
284	#95	—	38	1	no	—
285	C₁₉	#8990	1	1	yes	characteristic, complemented, Sylow
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
292	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	#64543	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	M₁₆	—	19	2	no	—
302	M₁₆	—	38	1	no	—
303	M₁₆	—	38	1	no	—
304	M₁₆	—	38	1	no	—
305	M₁₆	—	76	1	no	—
306	M₁₆	—	76	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	38	1	no	—
310	C₂×C₈	—	38	2	no	—
311	C₂×C₈	—	38	2	no	—
312	C₂×C₈	—	38	1	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	—	76	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	38	2	no	—
327	C₄⋊C₄	—	76	1	no	—
328	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
329	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂²⋊C₄	—	4	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	76	1	no	—
337	C₄²	—	76	1	no	—
338	C₄²	D₄×D₁₉	1	1	yes	characteristic
339	C₄²	#64543	1	1	yes	characteristic
340	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
342	C₂³	#10597385	1	1	yes	characteristic
343	Q₈	—	2	1	no	—
344	Q₈	—	2	1	no	—
345	Q₈	—	2	1	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	#10597294	1	2	yes	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	76	2	no	—
363	C₂×C₄	—	152	1	no	—
364	C₂×C₄	—	152	1	no	—
365	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
366	C₂×C₄	#10597364	1	1	yes	characteristic
367	C₂×C₄	#10597364	1	1	yes	characteristic
368	C₂×C₄	#10597365	1	1	yes	characteristic
369	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
370	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
371	C₂×C₄	#10597381	1	1	yes	characteristic
372	C₂×C₄	#10597383	1	1	yes	characteristic
373	C₂×C₄	#10597385	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
375	C₈	—	4	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	38	2	no	—
378	C₈	—	76	2	no	—
379	C₈	—	76	1	no	—
380	C₈	—	76	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	#11926424	1	1	yes	characteristic
384	C₂²	#11926752	1	1	yes	characteristic
385	C₂²	#11926768	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	—	152	2	no	—
396	C₄	C₂×#10597294	1	1	yes	characteristic
397	C₄	#11926561	1	1	yes	characteristic
398	C₄	Q₁₆×Dic₁₉	1	1	yes	characteristic
399	C₄	#11926651	1	1	yes	characteristic
400	C₄	#11926698	1	1	yes	characteristic
401	C₄	#11926705	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#14563938	1	1	yes	characteristic
405	C₂	#14563978	1	1	yes	characteristic
406	C₂	#14563999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3104	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3104	D₁₉
hypocenter	C₁₉	#8990
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3104

Complements

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

N	H ≅ G/N	type
25. C₁₉×#477	C₄	semidirect
26. C₁₉×#477	C₄	semidirect
27. C₁₉×#462	C₄	semidirect
28. C₁₉×#462	C₄	semidirect
131. #64520	Q₁₆	semidirect
209. #477	Dic₁₉	semidirect
210. #477	Dic₁₉	semidirect
211. #462	Dic₁₉	semidirect
212. #462	Dic₁₉	semidirect
285. C₁₉	#8990	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#64520	2
#14564580	2
C₄×#10597292	2
#14562090	2
#14561537	2
#14561471	2
C₁₉×#3104	2
#8990	19