Subgroups — C₁₉×#14289 #18020248

Order 4864.

1414 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	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#383	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1445	C₂	1	2	yes	maximal
5	C₁₉×#1445	C₂	1	2	yes	maximal
6	C₁₉×#1441	C₂	1	4	yes	maximal
7	C₁₉×#1436	C₂	1	4	yes	maximal
8	C₂×C₁₉×#125	—	2	4	no	—
9	C₂×C₁₉×#125	—	2	4	no	—
10	C₂×C₁₉×#125	C₄	1	8	yes	complemented
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#383	—	2	4	no	—
19	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₂×C₁₉×#95	C₂²	1	8	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
27	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₁₉×#125	—	2	32	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₉	—	2	4	no	—
49	C₂×C₄²×C₁₉	—	4	4	no	—
50	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₁₉	D₄	1	4	yes	—
52	C₂×C₄²×C₁₉	D₄	1	4	yes	—
53	C₁₉×#95	—	2	4	no	—
54	C₁₉×#95	—	2	4	no	—
55	C₁₉×#95	—	2	4	no	—
56	C₁₉×#95	—	2	4	no	—
57	C₁₉×#95	—	2	16	no	—
58	C₁₉×#95	—	4	8	no	—
59	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	—	2	4	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	—	2	8	no	—
71	C₂²×C₄×C₁₉	—	2	8	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	2	8	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	8	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	#41	1	8	yes	—
92	C₄⋊C₄×C₁₉	—	2	16	no	—
93	C₄⋊C₄×C₁₉	—	2	8	no	—
94	C₄⋊C₄×C₁₉	—	2	16	no	—
95	C₄⋊C₄×C₁₉	—	2	16	no	—
96	C₄⋊C₄×C₁₉	—	2	8	no	—
97	C₄²×C₁₉	—	4	8	no	—
98	C₄²×C₁₉	C₂²⋊C₄	1	16	yes	—
99	#14289	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
101	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
102	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
103	C₂³×C₁₉	C₂×#41	1	4	yes	—
104	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
105	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
106	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
107	C₂×C₄×C₁₉	—	2	4	no	—
108	C₂×C₄×C₁₉	—	2	4	no	—
109	C₂×C₄×C₁₉	—	2	4	no	—
110	C₂×C₄×C₁₉	—	2	4	no	—
111	C₂×C₄×C₁₉	—	2	4	no	—
112	C₂×C₄×C₁₉	—	2	2	no	—
113	C₂×C₄×C₁₉	—	2	4	no	—
114	C₂×C₄×C₁₉	—	2	4	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	4	no	—
117	C₂×C₄×C₁₉	—	2	4	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	2	8	no	—
120	C₂×C₄×C₁₉	—	2	8	no	—
121	C₂×C₄×C₁₉	—	2	8	no	—
122	C₂×C₄×C₁₉	—	2	16	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	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	4	8	no	—
131	C₂×C₄×C₁₉	—	4	4	no	—
132	C₂×C₄×C₁₉	—	4	4	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	—	4	8	no	—
135	C₂×C₄×C₁₉	—	4	8	no	—
136	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
137	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic
140	C₂×#383	C₂×C₁₉	1	1	yes	characteristic
141	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
142	#1445	C₂×C₁₉	1	2	yes	—
143	#1445	C₂×C₁₉	1	2	yes	—
144	#1441	C₂×C₁₉	1	4	yes	—
145	#1436	C₂×C₁₉	1	4	yes	—
146	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₁₉	C₄×#41	1	2	yes	—
148	C₂²×C₁₉	#519	1	2	yes	—
149	C₂²×C₁₉	#520	1	2	yes	—
150	C₂²×C₁₉	#525	1	2	yes	—
151	C₂²×C₁₉	#532	1	2	yes	—
152	C₂²×C₁₉	#535	1	1	yes	characteristic
153	C₂²×C₁₉	#536	1	2	yes	—
154	C₂²×C₁₉	#536	1	2	yes	—
155	C₂²×C₁₉	#536	1	1	yes	characteristic
156	C₂²×C₁₉	#537	1	2	yes	—
157	C₂²×C₁₉	#539	1	8	yes	—
158	C₂²×C₁₉	#541	1	8	yes	—
159	C₄×C₁₉	—	2	4	no	—
160	C₄×C₁₉	—	2	4	no	—
161	C₄×C₁₉	—	2	4	no	—
162	C₄×C₁₉	—	4	4	no	—
163	C₄×C₁₉	—	4	8	no	—
164	C₄×C₁₉	—	4	4	no	—
165	C₄×C₁₉	—	8	4	no	—
166	C₂×#125	—	2	4	no	—
167	C₂×#125	—	2	4	no	—
168	C₂×#125	C₄×C₁₉	1	8	yes	complemented
169	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
172	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
173	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
175	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
176	#383	—	2	4	no	—
177	C₄×C₄⋊C₄	—	2	4	no	—
178	C₂×#95	C₂²×C₁₉	1	2	yes	—
179	C₂×#95	C₂²×C₁₉	1	8	yes	—
180	C₂×#95	C₂²×C₁₉	1	2	yes	—
181	C₂×#95	C₂²×C₁₉	1	2	yes	—
182	C₂×#95	C₂²×C₁₉	1	2	yes	—
183	C₂×#95	C₂²×C₁₉	1	8	yes	—
184	C₂×C₁₉	#2297	1	1	yes	characteristic
185	C₂×C₁₉	#2310	1	1	yes	characteristic
186	C₂×C₁₉	#2311	1	1	yes	characteristic
187	C₂×C₁₉	#2336	1	4	yes	—
188	C₂×C₁₉	#2633	1	2	yes	—
189	C₂×C₁₉	#2634	1	2	yes	—
190	C₂×C₁₉	#2664	1	4	yes	—
191	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
192	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
193	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
194	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
195	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
198	#125	—	2	32	no	—
199	C₂×C₄⋊C₄	—	2	4	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	8	no	—
209	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
213	C₂×C₄²	—	2	4	no	—
214	C₂×C₄²	—	4	4	no	—
215	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
216	C₂×C₄²	D₄×C₁₉	1	4	yes	—
217	C₂×C₄²	D₄×C₁₉	1	4	yes	—
218	#95	—	2	4	no	—
219	#95	—	2	4	no	—
220	#95	—	2	4	no	—
221	#95	—	2	4	no	—
222	#95	—	2	16	no	—
223	#95	—	4	8	no	—
224	C₁₉	#14289	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	8	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
257	C₂²×C₄	#41×C₁₉	1	8	yes	—
258	C₄⋊C₄	—	2	16	no	—
259	C₄⋊C₄	—	2	8	no	—
260	C₄⋊C₄	—	2	16	no	—
261	C₄⋊C₄	—	2	16	no	—
262	C₄⋊C₄	—	2	8	no	—
263	C₄²	—	4	8	no	—
264	C₄²	C₂²⋊C₄×C₁₉	1	16	yes	—
265	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
266	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
267	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
268	C₂³	C₂×#41×C₁₉	1	4	yes	—
269	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
270	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
271	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	16	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	8	no	—
300	C₂×C₄	—	4	8	no	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
302	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
304	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
305	C₂²	C₄×#41×C₁₉	1	2	yes	—
306	C₂²	C₁₉×#519	1	2	yes	—
307	C₂²	C₁₉×#520	1	2	yes	—
308	C₂²	C₁₉×#525	1	2	yes	—
309	C₂²	C₁₉×#532	1	2	yes	—
310	C₂²	C₁₉×#535	1	1	yes	characteristic
311	C₂²	C₁₉×#536	1	2	yes	—
312	C₂²	C₁₉×#536	1	2	yes	—
313	C₂²	C₁₉×#536	1	1	yes	characteristic
314	C₂²	C₁₉×#537	1	2	yes	—
315	C₂²	C₁₉×#539	1	8	yes	—
316	C₂²	C₁₉×#541	1	8	yes	—
317	C₄	—	2	4	no	—
318	C₄	—	2	4	no	—
319	C₄	—	2	4	no	—
320	C₄	—	4	4	no	—
321	C₄	—	4	4	no	—
322	C₄	—	4	8	no	—
323	C₄	—	8	4	no	—
324	C₂	C₁₉×#2297	1	1	yes	characteristic
325	C₂	C₁₉×#2310	1	1	yes	characteristic
326	C₂	C₁₉×#2311	1	1	yes	characteristic
327	C₂	C₁₉×#2336	1	4	yes	—
328	C₂	C₁₉×#2633	1	2	yes	—
329	C₂	C₁₉×#2634	1	2	yes	—
330	C₂	C₁₉×#2664	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₂×C₁₉×#125	C₄	semidirect
99. #14289	C₁₉	direct (N × H)
168. C₂×#125	C₄×C₁₉	semidirect
224. C₁₉	#14289	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#125	2
C₂×C₁₉×#383	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1445	2
C₁₉×#1441	2
C₁₉×#1436	2
#14289	19

Subgroups — C19×#14289 #18020248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14289 #18020248