Subgroups — C₁₉×#8303 #18014262

Order 4864.

1050 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1817	C₂	1	2	yes	maximal
3	C₂×C₁₉×#324	C₂	1	4	yes	maximal
4	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
6	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
7	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₉	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
12	C₁₉×#336	—	2	4	no	—
13	C₁₉×#324	—	2	8	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	2	no	—
16	C₂²×Q₈×C₁₉	—	2	2	no	—
17	C₂²×Q₈×C₁₉	—	2	4	no	—
18	C₂²×Q₈×C₁₉	C₈	1	4	yes	complemented
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	4	no	—
25	C₄×Q₈×C₁₉	—	2	32	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
31	C₂×C₄²×C₁₉	—	2	4	no	—
32	C₂×C₄²×C₁₉	—	2	4	no	—
33	C₂×C₄²×C₁₉	—	2	4	no	—
34	C₂×C₄²×C₁₉	—	2	4	no	—
35	C₂×C₄²×C₁₉	D₄	1	4	yes	—
36	C₁₉×C₂²⋊C₈	—	2	8	no	—
37	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Q₈×C₁₉	—	2	8	no	—
39	C₂×Q₈×C₁₉	—	2	16	no	—
40	C₂×Q₈×C₁₉	—	2	8	no	—
41	C₂×Q₈×C₁₉	—	2	16	no	—
42	C₂×Q₈×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
60	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
61	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
62	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
65	C₂×C₈×C₁₉	—	4	8	no	—
66	C₂×C₈×C₁₉	—	4	4	no	—
67	C₄⋊C₄×C₁₉	—	2	8	no	—
68	C₄⋊C₄×C₁₉	—	2	16	no	—
69	C₄²×C₁₉	—	2	16	no	—
70	C₄²×C₁₉	—	2	8	no	—
71	#8303	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
77	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
79	Q₈×C₁₉	—	2	32	no	—
80	C₂×C₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	2	4	no	—
87	C₂×C₄×C₁₉	—	2	4	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	4	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	4	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	4	4	no	—
98	C₂×C₄×C₁₉	—	4	4	no	—
99	C₂×C₄×C₁₉	C₂²⋊C₈	1	8	yes	—
100	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
101	C₂×C₄×C₁₉	#101	1	4	yes	—
102	C₂×C₄×C₁₉	#120	1	4	yes	—
103	C₈×C₁₉	—	8	4	no	—
104	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
105	#1817	C₂×C₁₉	1	2	yes	—
106	C₂×#324	C₂×C₁₉	1	4	yes	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	4	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	#379	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
114	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
115	C₂²×C₁₉	#407	1	2	yes	—
116	C₂²×C₁₉	#407	1	1	yes	characteristic
117	C₂²×C₁₉	#410	1	2	yes	—
118	C₂²×C₁₉	C₂×#101	1	2	yes	—
119	C₄×C₁₉	—	2	8	no	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	—	2	4	no	—
123	C₄×C₁₉	—	4	4	no	—
124	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic
125	C₂×C₄×Q₈	—	2	8	no	—
126	C₂×C₄×Q₈	—	2	4	no	—
127	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
128	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
129	C₂²×C₄²	C₄×C₁₉	1	2	yes	—
130	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
131	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
132	#336	—	2	4	no	—
133	#324	—	2	8	no	—
134	C₂×C₁₉	—	2	2	no	—
135	C₂×C₁₉	—	2	2	no	—
136	C₂×C₁₉	#1461	1	2	yes	—
137	C₂×C₁₉	#1467	1	2	yes	—
138	C₂×C₁₉	#1779	1	1	yes	characteristic
139	C₂×C₁₉	#1782	1	1	yes	characteristic
140	C₂×C₁₉	#1784	1	1	yes	characteristic
141	C₂²×Q₈	—	2	4	no	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×Q₈	—	2	4	no	—
144	C₂²×Q₈	—	2	2	no	—
145	C₂²×Q₈	C₈×C₁₉	1	4	yes	complemented
146	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
147	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
148	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
149	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
150	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
151	C₂²×C₈	—	2	4	no	—
152	C₄×Q₈	—	2	32	no	—
153	C₂×C₄⋊C₄	—	2	4	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	4	no	—
156	C₂×C₄⋊C₄	—	2	4	no	—
157	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
158	C₂×C₄²	—	2	4	no	—
159	C₂×C₄²	—	2	4	no	—
160	C₂×C₄²	—	2	4	no	—
161	C₂×C₄²	—	2	4	no	—
162	C₂×C₄²	D₄×C₁₉	1	4	yes	—
163	C₂²⋊C₈	—	2	8	no	—
164	C₁₉	#8303	1	1	yes	characteristic, direct product factor, Sylow
165	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
166	C₂×Q₈	—	2	8	no	—
167	C₂×Q₈	—	2	16	no	—
168	C₂×Q₈	—	2	8	no	—
169	C₂×Q₈	—	2	16	no	—
170	C₂×Q₈	—	2	8	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	4	4	no	—
183	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
184	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
185	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
186	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
187	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
188	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	—
189	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
190	C₂²×C₄	M₁₆×C₁₉	1	4	yes	—
191	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
192	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
193	C₂×C₈	—	4	8	no	—
194	C₂×C₈	—	4	4	no	—
195	C₄⋊C₄	—	2	8	no	—
196	C₄⋊C₄	—	2	16	no	—
197	C₄²	—	2	16	no	—
198	C₄²	—	2	8	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	2	no	—
201	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
202	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
203	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
204	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
205	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
206	Q₈	—	2	32	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	4	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	C₁₉×C₂²⋊C₈	1	8	yes	—
227	C₂×C₄	C₁₉×C₂²⋊C₈	1	4	yes	—
228	C₂×C₄	C₁₉×#101	1	4	yes	—
229	C₂×C₄	C₁₉×#120	1	4	yes	—
230	C₈	—	8	4	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	4	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	2	no	—
236	C₂²	C₁₉×#379	1	1	yes	characteristic
237	C₂²	C₂×C₁₉×C₂²⋊C₈	1	2	yes	—
238	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
239	C₂²	C₁₉×#407	1	2	yes	—
240	C₂²	C₁₉×#407	1	1	yes	characteristic
241	C₂²	C₁₉×#410	1	2	yes	—
242	C₂²	C₂×C₁₉×#101	1	2	yes	—
243	C₄	—	2	8	no	—
244	C₄	—	2	4	no	—
245	C₄	—	2	4	no	—
246	C₄	—	2	4	no	—
247	C₄	—	4	4	no	—
248	C₂	—	2	2	no	—
249	C₂	—	2	2	no	—
250	C₂	C₁₉×#1461	1	2	yes	—
251	C₂	C₁₉×#1467	1	2	yes	—
252	C₂	C₁₉×#1779	1	1	yes	characteristic
253	C₂	C₁₉×#1782	1	1	yes	characteristic
254	C₂	C₁₉×#1784	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
18. C₂²×Q₈×C₁₉	C₈	semidirect
71. #8303	C₁₉	direct (N × H)
145. C₂²×Q₈	C₈×C₁₉	semidirect
164. C₁₉	#8303	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×C₄×Q₈×C₁₉	2
C₁₉×#1817	2
C₂×C₁₉×#324	2
#8303	19

Subgroups — C19×#8303 #18014262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8303 #18014262