Subgroups — C₂×C₁₉×#1444 #18019802

Order 4864.

3550 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	3	yes	maximal
2	C₂²×C₁₉×#95	C₂	1	3	yes	maximal
3	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1444	C₂	1	8	yes	maximal, direct product factor
5	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	—
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	—
8	C₂²×C₄⋊C₄×C₁₉	—	2	24	no	—
9	C₂²×C₄⋊C₄×C₁₉	—	2	12	no	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	12	yes	—
11	C₂×C₁₉×#95	—	2	12	no	—
12	C₂×C₁₉×#95	C₄	1	8	yes	complemented
13	C₂×C₁₉×#95	C₂²	1	12	yes	—
14	C₂×C₁₉×#95	C₂²	1	4	yes	—
15	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	—	2	12	no	—
17	C₂³×C₄×C₁₉	—	2	12	no	—
18	C₂³×C₄×C₁₉	—	2	6	no	—
19	C₂³×C₄×C₁₉	—	2	6	no	—
20	C₂³×C₄×C₁₉	—	2	12	no	—
21	C₂³×C₄×C₁₉	—	2	12	no	—
22	C₂³×C₄×C₁₉	—	2	6	no	—
23	C₂³×C₄×C₁₉	—	2	6	no	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	12	yes	—
25	C₂³×C₄×C₁₉	D₄	1	12	yes	—
26	C₂³×C₄×C₁₉	D₄	1	12	yes	—
27	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
28	C₂³×C₄×C₁₉	Q₈	1	12	yes	—
29	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
32	C₂×C₄⋊C₄×C₁₉	—	2	96	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	48	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	24	no	—
35	C₁₉×#95	—	2	24	no	—
36	C₁₉×#95	C₂×C₄	1	16	yes	complemented
37	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
38	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
39	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
40	C₂⁴×C₁₉	C₂×Q₈	1	6	yes	—
41	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
42	C₂⁴×C₁₉	#41	1	6	yes	—
43	C₂⁴×C₁₉	#41	1	2	yes	—
44	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	48	no	—
46	C₂²×C₄×C₁₉	—	2	24	no	—
47	C₂²×C₄×C₁₉	—	2	48	no	—
48	C₂²×C₄×C₁₉	—	2	24	no	—
49	C₂²×C₄×C₁₉	—	2	12	no	—
50	C₂²×C₄×C₁₉	—	2	12	no	—
51	C₂²×C₄×C₁₉	—	2	48	no	—
52	C₂²×C₄×C₁₉	—	2	24	no	—
53	C₂²×C₄×C₁₉	—	2	24	no	—
54	C₂²×C₄×C₁₉	—	2	12	no	—
55	C₂²×C₄×C₁₉	—	2	12	no	—
56	C₂²×C₄×C₁₉	—	2	6	no	—
57	C₂²×C₄×C₁₉	—	2	6	no	—
58	C₂²×C₄×C₁₉	—	2	6	no	—
59	C₂²×C₄×C₁₉	—	2	6	no	—
60	C₂²×C₄×C₁₉	—	4	12	no	—
61	C₂²×C₄×C₁₉	—	4	24	no	—
62	C₂²×C₄×C₁₉	—	4	12	no	—
63	C₂²×C₄×C₁₉	—	4	12	no	—
64	C₂²×C₄×C₁₉	—	4	4	no	—
65	C₂²×C₄×C₁₉	C₄⋊C₄	1	48	yes	complemented
66	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
67	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
68	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
69	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₁₉	C₂×Q₈	1	12	yes	—
71	C₄⋊C₄×C₁₉	—	2	96	no	—
72	C₂×#1444	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂³×C₁₉	C₂×C₄⋊C₄	1	12	yes	—
74	C₂³×C₁₉	C₄×D₄	1	12	yes	—
75	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
76	C₂³×C₁₉	#120	1	12	yes	—
77	C₂³×C₁₉	#121	1	12	yes	—
78	C₂³×C₁₉	C₂²⋊Q₈	1	24	yes	—
79	C₂³×C₁₉	C₂²⋊Q₈	1	12	yes	—
80	C₂³×C₁₉	#123	1	12	yes	—
81	C₂³×C₁₉	#125	1	12	yes	—
82	C₂³×C₁₉	#127	1	4	yes	—
83	C₂³×C₁₉	C₄⋊Q₈	1	12	yes	—
84	C₂³×C₁₉	C₄⋊Q₈	1	12	yes	—
85	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
86	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
87	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
88	C₂³×C₁₉	C₂²×Q₈	1	3	yes	—
89	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
90	C₂³×C₁₉	C₂×#41	1	3	yes	—
91	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
92	C₂×C₄×C₁₉	—	2	24	no	—
93	C₂×C₄×C₁₉	—	2	12	no	—
94	C₂×C₄×C₁₉	—	2	24	no	—
95	C₂×C₄×C₁₉	—	2	12	no	—
96	C₂×C₄×C₁₉	—	2	96	no	—
97	C₂×C₄×C₁₉	—	2	24	no	—
98	C₂×C₄×C₁₉	—	2	12	no	—
99	C₂×C₄×C₁₉	—	2	12	no	—
100	C₂×C₄×C₁₉	—	4	6	no	—
101	C₂×C₄×C₁₉	—	4	12	no	—
102	C₂×C₄×C₁₉	—	4	6	no	—
103	C₂×C₄×C₁₉	—	4	6	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	48	no	—
106	C₂×C₄×C₁₉	—	4	16	no	—
107	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	24	yes	complemented
108	C₂³×C₄⋊C₄	C₂×C₁₉	1	3	yes	—
109	C₂²×#95	C₂×C₁₉	1	3	yes	—
110	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
111	#1444	C₂×C₁₉	1	8	yes	direct product factor
112	C₂²×C₁₉	#384	1	8	yes	—
113	C₂²×C₁₉	#385	1	24	yes	—
114	C₂²×C₁₉	#389	1	24	yes	—
115	C₂²×C₁₉	#392	1	8	yes	—
116	C₂²×C₁₉	#395	1	24	yes	—
117	C₂²×C₁₉	#398	1	24	yes	—
118	C₂²×C₁₉	#399	1	8	yes	—
119	C₂²×C₁₉	C₂²×C₄⋊C₄	1	3	yes	—
120	C₂²×C₁₉	C₂×C₄×D₄	1	3	yes	—
121	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
122	C₂²×C₁₉	C₂×#120	1	3	yes	—
123	C₂²×C₁₉	C₂×#121	1	3	yes	—
124	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	6	yes	—
125	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	3	yes	—
126	C₂²×C₁₉	C₂×#123	1	3	yes	—
127	C₂²×C₁₉	C₂×#125	1	3	yes	—
128	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
129	C₂²×C₁₉	C₂×C₄⋊Q₈	1	3	yes	—
130	C₂²×C₁₉	C₂×C₄⋊Q₈	1	3	yes	—
131	C₄×C₁₉	—	2	24	no	—
132	C₄×C₁₉	—	4	12	no	—
133	C₄×C₁₉	—	4	4	no	—
134	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	—
135	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
136	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	—
137	C₂²×C₄⋊C₄	—	2	24	no	—
138	C₂²×C₄⋊C₄	—	2	12	no	—
139	C₂²×C₄⋊C₄	C₂²×C₁₉	1	12	yes	—
140	C₂×#95	—	2	12	no	—
141	C₂×#95	C₄×C₁₉	1	8	yes	complemented
142	C₂×#95	C₂²×C₁₉	1	12	yes	—
143	C₂×#95	C₂²×C₁₉	1	4	yes	—
144	C₂×C₁₉	#1444	1	16	yes	direct product factor
145	C₂×C₁₉	C₂×#384	1	1	yes	characteristic
146	C₂×C₁₉	C₂×#385	1	3	yes	—
147	C₂×C₁₉	C₂×#389	1	3	yes	—
148	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
149	C₂×C₁₉	C₂×#395	1	3	yes	—
150	C₂×C₁₉	C₂×#398	1	3	yes	—
151	C₂×C₁₉	C₂×#399	1	1	yes	characteristic
152	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
153	C₂³×C₄	—	2	12	no	—
154	C₂³×C₄	—	2	12	no	—
155	C₂³×C₄	—	2	12	no	—
156	C₂³×C₄	—	2	12	no	—
157	C₂³×C₄	—	2	6	no	—
158	C₂³×C₄	—	2	6	no	—
159	C₂³×C₄	—	2	6	no	—
160	C₂³×C₄	—	2	6	no	—
161	C₂³×C₄	C₂×C₄×C₁₉	1	12	yes	—
162	C₂³×C₄	D₄×C₁₉	1	12	yes	—
163	C₂³×C₄	D₄×C₁₉	1	12	yes	—
164	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
165	C₂³×C₄	Q₈×C₁₉	1	12	yes	—
166	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
167	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
168	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
169	C₂×C₄⋊C₄	—	2	96	no	—
170	C₂×C₄⋊C₄	—	2	48	no	—
171	C₂×C₄⋊C₄	—	2	24	no	—
172	#95	—	2	24	no	—
173	#95	C₂×C₄×C₁₉	1	16	yes	complemented
174	C₁₉	C₂×#1444	1	1	yes	characteristic, direct product factor, Sylow
175	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
176	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
177	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
178	C₂⁴	C₂×Q₈×C₁₉	1	6	yes	—
179	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
180	C₂⁴	#41×C₁₉	1	6	yes	—
181	C₂⁴	#41×C₁₉	1	2	yes	—
182	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
183	C₂²×C₄	—	2	48	no	—
184	C₂²×C₄	—	2	24	no	—
185	C₂²×C₄	—	2	48	no	—
186	C₂²×C₄	—	2	24	no	—
187	C₂²×C₄	—	2	12	no	—
188	C₂²×C₄	—	2	12	no	—
189	C₂²×C₄	—	2	48	no	—
190	C₂²×C₄	—	2	24	no	—
191	C₂²×C₄	—	2	24	no	—
192	C₂²×C₄	—	2	6	no	—
193	C₂²×C₄	—	2	6	no	—
194	C₂²×C₄	—	2	12	no	—
195	C₂²×C₄	—	2	12	no	—
196	C₂²×C₄	—	2	6	no	—
197	C₂²×C₄	—	2	6	no	—
198	C₂²×C₄	—	4	12	no	—
199	C₂²×C₄	—	4	24	no	—
200	C₂²×C₄	—	4	12	no	—
201	C₂²×C₄	—	4	12	no	—
202	C₂²×C₄	—	4	4	no	—
203	C₂²×C₄	C₄⋊C₄×C₁₉	1	48	yes	complemented
204	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
205	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
206	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
207	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
208	C₂²×C₄	C₂×Q₈×C₁₉	1	12	yes	—
209	C₄⋊C₄	—	2	96	no	—
210	C₂³	C₂×C₄⋊C₄×C₁₉	1	12	yes	—
211	C₂³	C₄×D₄×C₁₉	1	12	yes	—
212	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
213	C₂³	C₁₉×#120	1	12	yes	—
214	C₂³	C₁₉×#121	1	12	yes	—
215	C₂³	C₁₉×C₂²⋊Q₈	1	24	yes	—
216	C₂³	C₁₉×C₂²⋊Q₈	1	12	yes	—
217	C₂³	C₁₉×#123	1	12	yes	—
218	C₂³	C₁₉×#125	1	12	yes	—
219	C₂³	C₁₉×#127	1	4	yes	—
220	C₂³	C₁₉×C₄⋊Q₈	1	12	yes	—
221	C₂³	C₁₉×C₄⋊Q₈	1	12	yes	—
222	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
223	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
224	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
225	C₂³	C₂²×Q₈×C₁₉	1	3	yes	—
226	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
227	C₂³	C₂×#41×C₁₉	1	3	yes	—
228	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
229	C₂×C₄	—	2	96	no	—
230	C₂×C₄	—	2	24	no	—
231	C₂×C₄	—	2	12	no	—
232	C₂×C₄	—	2	24	no	—
233	C₂×C₄	—	2	12	no	—
234	C₂×C₄	—	2	24	no	—
235	C₂×C₄	—	2	12	no	—
236	C₂×C₄	—	2	12	no	—
237	C₂×C₄	—	4	48	no	—
238	C₂×C₄	—	4	16	no	—
239	C₂×C₄	—	4	6	no	—
240	C₂×C₄	—	4	12	no	—
241	C₂×C₄	—	4	6	no	—
242	C₂×C₄	—	4	6	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	24	yes	complemented
245	C₂²	C₁₉×#384	1	8	yes	—
246	C₂²	C₁₉×#385	1	24	yes	—
247	C₂²	C₁₉×#389	1	24	yes	—
248	C₂²	C₁₉×#392	1	8	yes	—
249	C₂²	C₁₉×#395	1	24	yes	—
250	C₂²	C₁₉×#398	1	24	yes	—
251	C₂²	C₁₉×#399	1	8	yes	—
252	C₂²	C₂²×C₄⋊C₄×C₁₉	1	3	yes	—
253	C₂²	C₂×C₄×D₄×C₁₉	1	3	yes	—
254	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
255	C₂²	C₂×C₁₉×#120	1	3	yes	—
256	C₂²	C₂×C₁₉×#121	1	3	yes	—
257	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	6	yes	—
258	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	3	yes	—
259	C₂²	C₂×C₁₉×#123	1	3	yes	—
260	C₂²	C₂×C₁₉×#125	1	3	yes	—
261	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
262	C₂²	C₂×C₁₉×C₄⋊Q₈	1	3	yes	—
263	C₂²	C₂×C₁₉×C₄⋊Q₈	1	3	yes	—
264	C₄	—	2	24	no	—
265	C₄	—	4	12	no	—
266	C₄	—	4	4	no	—
267	C₂	C₁₉×#1444	1	16	yes	direct product factor
268	C₂	C₂×C₁₉×#384	1	1	yes	characteristic
269	C₂	C₂×C₁₉×#385	1	3	yes	—
270	C₂	C₂×C₁₉×#389	1	3	yes	—
271	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
272	C₂	C₂×C₁₉×#395	1	3	yes	—
273	C₂	C₂×C₁₉×#398	1	3	yes	—
274	C₂	C₂×C₁₉×#399	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₁₉	C₂³
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1444	C₂	direct (N × H)
12. C₂×C₁₉×#95	C₄	semidirect
36. C₁₉×#95	C₂×C₄	semidirect
65. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
72. C₂×#1444	C₁₉	direct (N × H)
107. C₂×C₄×C₁₉	C₂×C₄⋊C₄	semidirect
111. #1444	C₂×C₁₉	direct (N × H)
141. C₂×#95	C₄×C₁₉	semidirect
144. C₂×C₁₉	#1444	direct (N × H)
173. #95	C₂×C₄×C₁₉	semidirect
174. C₁₉	C₂×#1444	direct (N × H)
203. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect
244. C₂×C₄	C₂×C₄⋊C₄×C₁₉	semidirect
267. C₂	C₁₉×#1444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₁₉×#1444	2
C₂×#1444	19

Subgroups — C2×C19×#1444 #18019802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1444 #18019802