Subgroups — C₁₉×#8452 #18014411

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#555	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₁₉×#555	—	2	2	no	—
7	C₁₉×#555	—	2	4	no	—
8	C₁₉×#555	C₄	1	4	yes	complemented
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#124	—	2	2	no	—
11	C₂×C₁₉×#121	—	2	2	no	—
12	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×#117	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₉×#103	—	2	2	no	—
16	C₂×C₁₉×#102	—	2	2	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#384	C₂²	1	1	yes	characteristic
19	C₁₉×#340	—	2	2	no	—
20	C₁₉×#333	—	2	2	no	—
21	C₁₉×D₄⋊C₈	—	2	4	no	—
22	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	D₄	1	2	yes	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	—	2	2	no	—
29	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
31	C₁₉×#124	—	2	8	no	—
32	C₁₉×#124	—	2	8	no	—
33	C₁₉×#121	—	2	8	no	—
34	C₁₉×#121	—	2	8	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
38	C₄×D₄×C₁₉	D₄	1	4	yes	—
39	C₁₉×#117	—	2	8	no	—
40	C₁₉×#117	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄²×C₁₉	—	2	2	no	—
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×C₄⋊C₈	—	2	2	no	—
50	C₁₉×C₄⋊C₈	—	2	2	no	—
51	C₁₉×#103	—	4	4	no	—
52	C₁₉×#102	—	4	4	no	—
53	C₄×C₈×C₁₉	—	2	2	no	—
54	C₂⁴×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	4	2	no	—
57	C₂×Q₈×C₁₉	—	4	2	no	—
58	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₂×D₄×C₁₉	—	2	8	no	—
60	C₂×D₄×C₁₉	—	2	2	no	—
61	C₂×D₄×C₁₉	—	2	2	no	—
62	C₂×D₄×C₁₉	—	2	2	no	—
63	C₂×D₄×C₁₉	—	2	2	no	—
64	C₂×D₄×C₁₉	—	2	2	no	—
65	C₂×D₄×C₁₉	—	8	2	no	—
66	C₂×D₄×C₁₉	—	8	2	no	—
67	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₉	—	2	2	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	—	4	1	no	—
82	C₂×C₈×C₁₉	—	4	2	no	—
83	C₂×C₈×C₁₉	—	4	2	no	—
84	C₂×C₈×C₁₉	—	4	2	no	—
85	C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	4	2	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
92	C₂²⋊C₄×C₁₉	—	2	16	no	—
93	C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₄²×C₁₉	—	2	8	no	—
96	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₂×D₄	1	2	yes	—
99	#8452	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	—	2	4	no	—
101	C₂³×C₁₉	—	4	2	no	—
102	C₂³×C₁₉	—	4	2	no	—
103	C₂³×C₁₉	—	4	2	no	—
104	C₂³×C₁₉	—	4	2	no	—
105	C₂³×C₁₉	—	4	2	no	—
106	C₂³×C₁₉	—	4	2	no	—
107	C₂³×C₁₉	#120	1	1	yes	characteristic
108	Q₈×C₁₉	—	4	4	no	—
109	Q₈×C₁₉	—	8	2	no	—
110	D₄×C₁₉	—	2	4	no	—
111	D₄×C₁₉	—	2	4	no	—
112	D₄×C₁₉	—	4	2	no	—
113	D₄×C₁₉	—	4	2	no	—
114	D₄×C₁₉	—	8	8	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	4	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	4	no	—
124	C₂×C₄×C₁₉	—	4	4	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	8	2	no	—
128	C₂×C₄×C₁₉	—	8	1	no	—
129	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#120	1	2	yes	—
133	C₂×C₄×C₁₉	#135	1	2	yes	—
134	C₂×C₄×C₁₉	#135	1	2	yes	—
135	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₉	#137	1	2	yes	—
137	C₈×C₁₉	—	4	2	no	—
138	C₈×C₁₉	—	8	2	no	—
139	C₂×#555	C₂×C₁₉	1	1	yes	characteristic
140	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
141	#1802	C₂×C₁₉	1	2	yes	complemented
142	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
143	C₂×D₄⋊C₈	C₂×C₁₉	1	2	yes	complemented
144	C₂²×C₁₉	—	4	4	no	—
145	C₂²×C₁₉	—	4	4	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	—	8	2	no	—
148	C₂²×C₁₉	—	8	2	no	—
149	C₂²×C₁₉	—	8	2	no	—
150	C₂²×C₁₉	—	8	2	no	—
151	C₂²×C₁₉	#379	1	1	yes	characteristic
152	C₂²×C₁₉	#449	1	2	yes	—
153	C₂²×C₁₉	#452	1	2	yes	—
154	C₂²×C₁₉	#453	1	1	yes	characteristic
155	C₂²×C₁₉	#455	1	1	yes	characteristic
156	C₄×C₁₉	—	2	1	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	4	4	no	—
159	C₄×C₁₉	—	4	4	no	—
160	C₄×C₁₉	—	16	1	no	—
161	C₄×C₁₉	#416	1	2	yes	—
162	C₄×C₁₉	#417	1	2	yes	—
163	C₄×C₁₉	#449	1	2	yes	—
164	C₄×C₁₉	#452	1	2	yes	—
165	#555	—	2	2	no	—
166	#555	—	2	4	no	—
167	#555	C₄×C₁₉	1	4	yes	complemented
168	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
169	C₂×#124	—	2	2	no	—
170	C₂×#121	—	2	2	no	—
171	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
172	C₂×#117	—	2	2	no	—
173	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
174	C₂×#103	—	2	2	no	—
175	C₂×#102	—	2	2	no	—
176	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
177	#384	C₂²×C₁₉	1	1	yes	characteristic
178	#340	—	2	2	no	—
179	#333	—	2	2	no	—
180	D₄⋊C₈	—	2	4	no	—
181	C₂×C₁₉	—	8	4	no	—
182	C₂×C₁₉	#1624	1	1	yes	characteristic
183	C₂×C₁₉	#1634	1	1	yes	characteristic
184	C₂×C₁₉	#1646	1	2	yes	—
185	C₂×C₁₉	#1788	1	2	yes	—
186	C₂×C₁₉	#1792	1	1	yes	characteristic
187	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
188	C₂²×D₄	—	2	2	no	—
189	C₂²×D₄	D₄×C₁₉	1	2	yes	—
190	C₂³×C₄	—	2	2	no	—
191	C₂²×C₈	—	2	1	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₄⋊Q₈	—	2	2	no	—
194	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
195	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
196	#124	—	2	8	no	—
197	#124	—	2	8	no	—
198	#121	—	2	8	no	—
199	#121	—	2	8	no	—
200	C₄×D₄	—	2	2	no	—
201	C₄×D₄	—	2	2	no	—
202	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
203	C₄×D₄	D₄×C₁₉	1	4	yes	—
204	#117	—	2	8	no	—
205	#117	—	2	8	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
210	C₂×C₂²⋊C₄	—	2	4	no	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	#103	—	4	4	no	—
217	#102	—	4	4	no	—
218	C₄×C₈	—	2	2	no	—
219	C₁₉	#8452	1	1	yes	characteristic, direct product factor, Sylow
220	C₂⁴	—	2	2	no	—
221	C₂×Q₈	—	2	2	no	—
222	C₂×Q₈	—	4	2	no	—
223	C₂×Q₈	—	4	2	no	—
224	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
225	C₂×D₄	—	2	8	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	—	2	2	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	8	2	no	—
232	C₂×D₄	—	8	2	no	—
233	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	—	4	1	no	—
243	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	4	1	no	—
247	C₂×C₈	—	4	1	no	—
248	C₂×C₈	—	4	2	no	—
249	C₂×C₈	—	4	2	no	—
250	C₂×C₈	—	4	2	no	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
258	C₂²⋊C₄	—	2	16	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₄²	—	2	8	no	—
262	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
263	C₄²	C₂×D₄×C₁₉	1	2	yes	—
264	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂³	—	2	4	no	—
266	C₂³	—	4	2	no	—
267	C₂³	—	4	2	no	—
268	C₂³	—	4	2	no	—
269	C₂³	—	4	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	—	4	2	no	—
272	C₂³	C₁₉×#120	1	1	yes	characteristic
273	Q₈	—	4	4	no	—
274	Q₈	—	8	2	no	—
275	D₄	—	2	4	no	—
276	D₄	—	2	4	no	—
277	D₄	—	4	2	no	—
278	D₄	—	4	2	no	—
279	D₄	—	8	8	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	8	2	no	—
293	C₂×C₄	—	8	1	no	—
294	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
296	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
297	C₂×C₄	C₁₉×#120	1	2	yes	—
298	C₂×C₄	C₁₉×#135	1	2	yes	—
299	C₂×C₄	C₁₉×#135	1	2	yes	—
300	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
301	C₂×C₄	C₁₉×#137	1	2	yes	—
302	C₈	—	4	2	no	—
303	C₈	—	8	2	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	4	4	no	—
307	C₂²	—	8	2	no	—
308	C₂²	—	8	2	no	—
309	C₂²	—	8	2	no	—
310	C₂²	—	8	2	no	—
311	C₂²	C₁₉×#379	1	1	yes	characteristic
312	C₂²	C₁₉×#449	1	2	yes	—
313	C₂²	C₁₉×#452	1	2	yes	—
314	C₂²	C₁₉×#453	1	1	yes	characteristic
315	C₂²	C₁₉×#455	1	1	yes	characteristic
316	C₄	—	2	1	no	—
317	C₄	—	2	1	no	—
318	C₄	—	4	4	no	—
319	C₄	—	4	4	no	—
320	C₄	—	16	1	no	—
321	C₄	C₁₉×#416	1	2	yes	—
322	C₄	C₁₉×#417	1	2	yes	—
323	C₄	C₁₉×#449	1	2	yes	—
324	C₄	C₁₉×#452	1	2	yes	—
325	C₂	—	8	4	no	—
326	C₂	C₁₉×#1624	1	1	yes	characteristic
327	C₂	C₁₉×#1634	1	1	yes	characteristic
328	C₂	C₁₉×#1646	1	2	yes	—
329	C₂	C₁₉×#1788	1	2	yes	—
330	C₂	C₁₉×#1792	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#555	C₂
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
2. C₁₉×#1956	C₂	semidirect
3. C₁₉×#1802	C₂	semidirect
4. C₂×C₁₉×#333	C₂	semidirect
5. C₂×C₁₉×D₄⋊C₈	C₂	semidirect
8. C₁₉×#555	C₄	semidirect
99. #8452	C₁₉	direct (N × H)
140. #1956	C₂×C₁₉	semidirect
141. #1802	C₂×C₁₉	semidirect
142. C₂×#333	C₂×C₁₉	semidirect
143. C₂×D₄⋊C₈	C₂×C₁₉	semidirect
167. #555	C₄×C₁₉	semidirect
219. C₁₉	#8452	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#555	2
C₁₉×#1956	2
C₁₉×#1802	2
C₂×C₁₉×#333	2
C₂×C₁₉×D₄⋊C₈	2
#8452	19

Subgroups — C19×#8452 #18014411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8452 #18014411