Subgroups — C₁₉×#8896 #18014855

Order 4864.

498 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
9	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#106	—	2	1	no	—
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#103	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#389	—	2	2	no	—
16	C₁₉×#389	—	2	1	no	—
17	C₁₉×#384	—	2	1	no	—
18	C₁₉×#384	C₂²	1	1	yes	characteristic
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#340	—	2	1	no	—
23	C₁₉×#340	—	2	1	no	—
24	C₁₉×#340	—	2	2	no	—
25	C₁₉×Q₈⋊C₈	C₄	1	4	yes	complemented
26	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₄×Q₈×C₁₉	—	2	1	no	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	4	2	no	—
33	C₄×Q₈×C₁₉	—	4	2	no	—
34	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×Q₈×C₁₉	Q₈	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	2	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×#106	—	4	2	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₉×#103	—	4	2	no	—
58	C₄×C₈×C₁₉	—	2	1	no	—
59	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
66	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
67	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	4	1	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	—	4	1	no	—
82	C₂×C₈×C₁₉	—	4	1	no	—
83	C₂×C₈×C₁₉	—	4	1	no	—
84	C₂×C₈×C₁₉	—	4	1	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₄⋊C₄×C₁₉	—	4	2	no	—
93	C₄⋊C₄×C₁₉	—	4	4	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	8	2	no	—
104	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
105	C₄⋊C₄×C₁₉	Q₁₆	1	2	yes	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	4	4	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	#8896	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	#120	1	1	yes	characteristic
117	Q₈×C₁₉	—	2	2	no	—
118	Q₈×C₁₉	—	2	2	no	—
119	Q₈×C₁₉	—	2	2	no	—
120	Q₈×C₁₉	#106	1	4	yes	complemented
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
155	C₈×C₁₉	—	4	2	no	—
156	C₈×C₁₉	—	4	2	no	—
157	C₈×C₁₉	—	8	1	no	—
158	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
159	#1948	C₂×C₁₉	1	1	yes	characteristic
160	#1834	C₂×C₁₉	1	1	yes	characteristic
161	#1803	C₂×C₁₉	1	1	yes	characteristic
162	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic
163	#1296	C₂×C₁₉	1	1	yes	characteristic
164	#1279	C₂×C₁₉	1	1	yes	characteristic
165	C₂²×C₁₉	#385	1	1	yes	characteristic
166	C₂²×C₁₉	#448	1	1	yes	characteristic
167	C₂²×C₁₉	#449	1	1	yes	characteristic
168	C₂²×C₁₉	#450	1	1	yes	characteristic
169	C₂²×C₁₉	#451	1	1	yes	characteristic
170	C₂²×C₁₉	#454	1	1	yes	characteristic
171	C₂²×C₁₉	#455	1	1	yes	characteristic
172	C₄×C₁₉	—	2	4	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	4	2	no	—
176	C₄×C₁₉	—	4	2	no	—
177	C₄×C₁₉	—	8	1	no	—
178	C₄×C₁₉	—	8	2	no	—
179	C₄×C₁₉	—	16	1	no	—
180	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
181	C₄×C₁₉	#428	1	1	yes	characteristic
182	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
183	C₄×C₁₉	#440	1	1	yes	characteristic
184	C₄×C₁₉	#477	1	1	yes	characteristic
185	C₄×C₁₉	#479	1	1	yes	characteristic
186	C₄×C₁₉	#481	1	1	yes	characteristic
187	C₄×C₁₉	#483	1	1	yes	characteristic
188	C₂×C₄×Q₈	—	2	1	no	—
189	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
190	C₂×#106	—	2	1	no	—
191	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×#103	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
195	#389	—	2	1	no	—
196	#389	—	2	2	no	—
197	#384	—	2	1	no	—
198	#384	C₂²×C₁₉	1	1	yes	characteristic
199	#384	C₂²×C₁₉	1	1	yes	characteristic
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
202	#340	—	2	1	no	—
203	#340	—	2	2	no	—
204	#340	—	2	1	no	—
205	Q₈⋊C₈	C₄×C₁₉	1	4	yes	complemented
206	C₂×C₁₉	#1626	1	1	yes	characteristic
207	C₂×C₁₉	#1637	1	1	yes	characteristic
208	C₂×C₁₉	#1642	1	1	yes	characteristic
209	C₂×C₁₉	#1645	1	1	yes	characteristic
210	C₂×C₁₉	#1853	1	1	yes	characteristic
211	C₂×C₁₉	#1860	1	1	yes	characteristic
212	C₂×C₁₉	#1863	1	1	yes	characteristic
213	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
214	C₂²×C₈	—	2	1	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	4	2	no	—
220	C₄×Q₈	—	4	2	no	—
221	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
222	C₄×Q₈	Q₈×C₁₉	1	2	yes	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
239	#106	—	4	2	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
244	#103	—	4	2	no	—
245	C₄×C₈	—	2	1	no	—
246	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
247	#95	—	2	2	no	—
248	#95	—	2	1	no	—
249	C₁₉	#8896	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×Q₈	—	2	1	no	—
251	C₂×Q₈	—	2	1	no	—
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
254	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	—
255	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	4	1	no	—
268	C₂×C₈	—	4	1	no	—
269	C₂×C₈	—	4	1	no	—
270	C₂×C₈	—	4	1	no	—
271	C₂×C₈	—	4	1	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	8	2	no	—
292	C₄⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
293	C₄⋊C₄	Q₁₆×C₁₉	1	2	yes	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	4	4	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
300	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
301	C₄²	#41×C₁₉	1	1	yes	characteristic
302	C₄²	#41×C₁₉	1	1	yes	characteristic
303	C₂³	C₁₉×#120	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	Q₈	—	2	2	no	—
306	Q₈	—	2	2	no	—
307	Q₈	C₁₉×#106	1	4	yes	complemented
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	8	1	no	—
326	C₂×C₄	—	8	1	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
331	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
332	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
333	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
334	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
335	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
336	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
337	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
338	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
341	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
342	C₈	—	4	2	no	—
343	C₈	—	4	2	no	—
344	C₈	—	8	1	no	—
345	C₂²	C₁₉×#385	1	1	yes	characteristic
346	C₂²	C₁₉×#448	1	1	yes	characteristic
347	C₂²	C₁₉×#449	1	1	yes	characteristic
348	C₂²	C₁₉×#450	1	1	yes	characteristic
349	C₂²	C₁₉×#451	1	1	yes	characteristic
350	C₂²	C₁₉×#454	1	1	yes	characteristic
351	C₂²	C₁₉×#455	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	1	no	—
358	C₄	—	8	2	no	—
359	C₄	—	16	1	no	—
360	C₄	C₂×C₁₉×#106	1	1	yes	characteristic
361	C₄	C₁₉×#428	1	1	yes	characteristic
362	C₄	C₄×Q₁₆×C₁₉	1	1	yes	characteristic
363	C₄	C₁₉×#440	1	1	yes	characteristic
364	C₄	C₁₉×#477	1	1	yes	characteristic
365	C₄	C₁₉×#479	1	1	yes	characteristic
366	C₄	C₁₉×#481	1	1	yes	characteristic
367	C₄	C₁₉×#483	1	1	yes	characteristic
368	C₂	C₁₉×#1626	1	1	yes	characteristic
369	C₂	C₁₉×#1637	1	1	yes	characteristic
370	C₂	C₁₉×#1642	1	1	yes	characteristic
371	C₂	C₁₉×#1645	1	1	yes	characteristic
372	C₂	C₁₉×#1853	1	1	yes	characteristic
373	C₂	C₁₉×#1860	1	1	yes	characteristic
374	C₂	C₁₉×#1863	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₁₉×Q₈⋊C₈	C₄	semidirect
115. #8896	C₁₉	direct (N × H)
120. Q₈×C₁₉	#106	semidirect
205. Q₈⋊C₈	C₄×C₁₉	semidirect
249. C₁₉	#8896	direct (N × H)
307. Q₈	C₁₉×#106	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#1948	2
C₁₉×#1834	2
C₁₉×#1803	2
C₂×C₁₉×Q₈⋊C₈	2
C₁₉×#1296	2
C₁₉×#1279	2
#8896	19

Subgroups — C19×#8896 #18014855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8896 #18014855