Subgroups — #18076188

Order 4864.

310 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563321	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14561479	C₂	1	2	yes	maximal
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	C₂×#10597272	C₄	1	1	yes	characteristic
9	C₂×#10597272	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926297	—	2	1	no	—
14	#11926295	—	2	1	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#335	—	2	1	no	—
18	C₁₉×#334	—	2	1	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₂²⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	—	2	2	no	—
29	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
30	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
32	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
33	C₁₉⋊#95	—	2	1	no	—
34	C₁₉⋊#95	—	2	1	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	#10597272	—	2	2	no	—
37	#10597272	C₈	1	4	yes	complemented
38	C₈×Dic₁₉	—	2	2	no	—
39	C₈×Dic₁₉	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	#10597260	—	2	1	no	—
42	#10597260	—	2	1	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂²×Dic₁₉	—	2	1	no	—
48	C₂²×Dic₁₉	—	2	1	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	1	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
57	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₁₉	#41	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	1	yes	characteristic
62	C₄×Dic₁₉	—	2	1	no	—
63	C₄×Dic₁₉	—	2	1	no	—
64	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
65	C₄×Dic₁₉	M₁₆	1	2	yes	—
66	C₂×C₁₉⋊C₈	—	2	1	no	—
67	C₂×C₁₉⋊C₈	—	2	1	no	—
68	C₂×C₁₉⋊C₈	—	2	1	no	—
69	C₂×C₁₉⋊C₈	—	2	1	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
72	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
73	#8781	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	#117	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
87	C₂×Dic₁₉	—	2	2	no	—
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	—	4	1	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₈×C₁₉	—	2	1	no	—
94	C₈×C₁₉	—	2	1	no	—
95	C₈×C₁₉	—	8	2	no	—
96	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
97	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
98	C₁₉⋊C₈	—	2	2	no	—
99	C₁₉⋊C₈	—	2	2	no	—
100	C₁₉⋊C₈	—	8	2	no	—
101	#1726	—	19	1	no	—
102	#1564	—	19	1	no	—
103	#1564	D₁₉	1	1	yes	characteristic
104	#1281	—	19	2	no	—
105	#1274	—	19	2	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	#382	1	1	yes	characteristic
109	C₂²×C₁₉	#431	1	1	yes	characteristic
110	C₂²×C₁₉	#432	1	1	yes	characteristic
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
116	C₄×C₁₉	#423	1	1	yes	characteristic
117	C₄×C₁₉	#431	1	1	yes	characteristic
118	C₄×C₁₉	#432	1	1	yes	characteristic
119	Dic₁₉	—	4	2	no	—
120	Dic₁₉	—	4	2	no	—
121	#431	—	19	2	no	—
122	#431	C₂×D₁₉	1	2	yes	—
123	C₂×#97	—	19	1	no	—
124	C₂×#97	—	19	1	no	—
125	C₂×#97	—	19	1	no	—
126	C₂×C₄×C₈	—	19	1	no	—
127	C₂×C₄×C₈	—	19	1	no	—
128	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
129	#376	—	19	1	no	—
130	#335	—	2	1	no	—
131	#335	—	38	1	no	—
132	#334	—	2	1	no	—
133	#334	—	38	1	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	#1831	1	1	yes	characteristic
137	C₂×C₁₉	#1833	1	1	yes	characteristic
138	C₂×C₁₉	#1833	1	1	yes	characteristic
139	C₂²×C₈	—	19	1	no	—
140	C₂²×C₈	—	19	1	no	—
141	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
143	C₂×C₄²	—	19	1	no	—
144	C₂×C₄²	—	19	1	no	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₂²⋊C₈	—	2	2	no	—
149	C₂²⋊C₈	—	38	2	no	—
150	#97	—	19	4	no	—
151	#97	—	38	2	no	—
152	#97	—	38	1	no	—
153	#97	—	38	1	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	38	2	no	—
156	C₄×C₈	—	38	2	no	—
157	C₄×C₈	—	38	2	no	—
158	C₄×C₈	Dic₃₈	1	1	yes	characteristic
159	C₄×C₈	Dic₃₈	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
161	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
162	#95	—	38	1	no	—
163	#95	—	38	1	no	—
164	C₁₉	#8781	1	1	yes	characteristic, complemented, Sylow
165	C₂²×C₄	—	38	1	no	—
166	C₂²×C₄	—	38	1	no	—
167	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
168	C₂²×C₄	#64543	1	1	yes	characteristic
169	C₂²×C₄	#64545	1	1	yes	characteristic
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	19	2	no	—
174	C₂×C₈	—	19	2	no	—
175	C₂×C₈	—	38	1	no	—
176	C₂×C₈	—	38	1	no	—
177	C₂×C₈	—	38	1	no	—
178	C₂×C₈	—	38	1	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	C₈×D₁₉	1	2	yes	—
181	C₂×C₈	#64515	1	2	yes	—
182	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
183	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
184	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
185	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
186	C₄²	—	19	2	no	—
187	C₄²	—	19	2	no	—
188	C₄²	—	38	1	no	—
189	C₄²	—	38	1	no	—
190	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
191	C₄²	#64543	1	1	yes	characteristic
192	C₄²	#64545	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
194	C₂³	#10597338	1	1	yes	characteristic
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	38	2	no	—
198	C₂×C₄	—	38	2	no	—
199	C₂×C₄	—	76	1	no	—
200	C₂×C₄	—	76	1	no	—
201	C₂×C₄	—	76	1	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	#10597336	1	1	yes	characteristic
204	C₂×C₄	#10597336	1	1	yes	characteristic
205	C₂×C₄	#10597338	1	1	yes	characteristic
206	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
207	C₂×C₄	C₂×#64515	1	1	yes	characteristic
208	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
209	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
210	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
211	C₂×C₄	#10597382	1	1	yes	characteristic
212	C₂×C₄	#10597393	1	1	yes	characteristic
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	—	8	2	no	—
216	C₈	—	38	2	no	—
217	C₈	—	38	2	no	—
218	C₈	—	152	2	no	—
219	C₈	Dic₁₉⋊C₈	1	2	yes	—
220	C₈	Dic₁₉⋊C₈	1	2	yes	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	#11926409	1	1	yes	characteristic
224	C₂²	#11926596	1	1	yes	characteristic
225	C₂²	#11926600	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	76	2	no	—
231	C₄	—	76	2	no	—
232	C₄	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
233	C₄	#11926567	1	1	yes	characteristic
234	C₄	#11926596	1	1	yes	characteristic
235	C₄	#11926600	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#14563751	1	1	yes	characteristic
239	C₂	#14563758	1	1	yes	characteristic
240	C₂	#14563760	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597338
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8781
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
37. #10597272	C₈	semidirect
164. C₁₉	#8781	semidirect

Maximal subgroups

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

subgroup	index
#14563321	2
#14562383	2
#14561479	2
#14561463	2
C₁₉×#1564	2
#8781	19