Subgroups — #18088243

Order 4864.

626 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563374	C₂	1	2	yes	maximal
2	C₂×#11926309	C₂	1	2	yes	maximal
3	C₂×C₁₉⋊#338	C₂	1	2	yes	maximal
4	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	C₂²	1	4	yes	—
6	#11926313	—	2	4	no	—
7	#11926309	—	2	4	no	—
8	C₁₉⋊#338	C₄	1	8	yes	complemented
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₁₉×#405	—	2	4	no	—
13	C₂×C₁₉×#97	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
15	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂×M₁₆×C₁₉	—	2	2	no	—
18	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	4	yes	—
25	C₁₉×#117	—	2	2	no	—
26	C₁₉×#117	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
28	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×#64520	—	2	4	no	—
31	C₂×#64520	—	2	4	no	—
32	C₂×#64520	—	2	4	no	—
33	C₂×#64520	—	2	4	no	—
34	C₂×#64520	—	2	4	no	—
35	C₂×#64520	C₂×C₄	1	8	yes	—
36	C₂²×C₁₉⋊C₈	—	2	4	no	—
37	C₁₉×#97	—	2	4	no	—
38	C₄×C₈×C₁₉	—	2	4	no	—
39	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₁₉	#41	1	2	yes	—
46	C₂²×C₄×C₁₉	#41	1	2	yes	—
47	C₂²×C₄×C₁₉	#41	1	2	yes	—
48	C₂²×C₄×C₁₉	#41	1	2	yes	—
49	M₁₆×C₁₉	—	2	8	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	1	no	—
52	C₂×C₈×C₁₉	—	2	1	no	—
53	C₂×C₈×C₁₉	—	2	1	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	8	no	—
57	C₂×C₈×C₁₉	C₄²	1	4	yes	—
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	#64520	—	2	8	no	—
65	#64520	—	2	8	no	—
66	#64520	—	4	4	no	—
67	#64520	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	2	8	no	—
69	C₂×C₁₉⋊C₈	—	4	4	no	—
70	C₂×C₁₉⋊C₈	—	4	4	no	—
71	#10815	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	—	4	2	no	—
73	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
75	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
76	C₂³×C₁₉	#125	1	2	yes	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#117	1	4	yes	—
82	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
88	C₂×C₄×C₁₉	#121	1	2	yes	—
89	C₂×C₄×C₁₉	#123	1	4	yes	—
90	C₂×C₄×C₁₉	#124	1	2	yes	—
91	C₂×C₄×C₁₉	#126	1	4	yes	—
92	C₈×C₁₉	—	2	4	no	—
93	C₈×C₁₉	—	2	2	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₁₉⋊C₈	—	4	8	no	—
96	C₂×#405	D₁₉	1	1	yes	characteristic
97	#1742	—	19	2	no	—
98	C₂×#341	—	19	2	no	—
99	C₂×#338	—	19	2	no	—
100	C₂²×C₁₉	—	2	2	no	—
101	C₂²×C₁₉	—	2	4	no	—
102	C₂²×C₁₉	—	4	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₁₉	#380	1	1	yes	characteristic
106	C₂²×C₁₉	#382	1	1	yes	characteristic
107	C₂²×C₁₉	#387	1	4	yes	—
108	C₄×C₁₉	—	4	4	no	—
109	C₄×C₁₉	#376	1	1	yes	characteristic
110	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
111	C₄×C₁₉	#381	1	1	yes	characteristic
112	C₄×C₁₉	#383	1	1	yes	characteristic
113	C₄×C₁₉	#388	1	4	yes	—
114	C₂²×M₁₆	—	19	4	no	—
115	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
116	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
117	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
118	#405	—	2	4	no	—
119	C₂×#97	Dic₁₉	1	2	yes	—
120	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
121	#343	—	38	4	no	—
122	#341	—	38	4	no	—
123	#338	—	19	8	no	—
124	C₂×C₁₉	—	2	1	no	—
125	C₂×C₁₉	—	2	1	no	—
126	C₂×C₁₉	—	2	4	no	—
127	C₂×C₁₉	#1434	1	1	yes	characteristic
128	C₂×C₁₉	#1813	1	2	yes	—
129	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
130	C₂×M₁₆	—	2	2	no	—
131	C₂×M₁₆	—	2	2	no	—
132	C₂×M₁₆	—	19	8	no	—
133	C₂×M₁₆	—	38	4	no	—
134	C₂×M₁₆	—	38	4	no	—
135	C₂×M₁₆	—	38	4	no	—
136	C₂×M₁₆	—	38	4	no	—
137	C₂×M₁₆	—	38	4	no	—
138	C₂×M₁₆	C₄×D₁₉	1	4	yes	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	38	4	no	—
142	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
143	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
144	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂²×C₈	C₂²⋊D₁₉	1	4	yes	—
146	#117	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
149	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
150	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
151	#97	—	2	4	no	—
152	C₄×C₈	—	2	4	no	—
153	C₁₉	#10815	1	1	yes	characteristic, complemented, Sylow
154	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
155	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
156	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
157	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
158	C₂²×C₄	#64541	1	2	yes	—
159	C₂²×C₄	#64541	1	2	yes	—
160	C₂²×C₄	#64541	1	2	yes	—
161	C₂²×C₄	#64541	1	2	yes	—
162	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
163	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
164	M₁₆	—	2	8	no	—
165	M₁₆	—	38	8	no	—
166	M₁₆	—	38	8	no	—
167	M₁₆	—	76	4	no	—
168	M₁₆	—	76	4	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	8	no	—
176	C₂×C₈	—	38	8	no	—
177	C₂×C₈	—	76	4	no	—
178	C₂×C₈	—	76	4	no	—
179	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
180	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
181	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
182	C₄⋊C₄	—	2	4	no	—
183	C₂²⋊C₄	—	2	4	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₂³	—	4	2	no	—
187	C₂³	C₄×Dic₃₈	1	2	yes	—
188	C₂³	#10597316	1	2	yes	—
189	C₂³	#10597370	1	2	yes	—
190	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	#10597318	1	4	yes	—
194	C₂×C₄	C₄×D₇₆	1	2	yes	—
195	C₂×C₄	#10597321	1	2	yes	—
196	C₂×C₄	#10597322	1	4	yes	—
197	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
198	C₂×C₄	#10597372	1	1	yes	characteristic
199	C₂×C₄	#10597372	1	1	yes	characteristic
200	C₂×C₄	#10597372	1	1	yes	characteristic
201	C₂×C₄	#10597372	1	1	yes	characteristic
202	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
203	C₂×C₄	#10597375	1	4	yes	—
204	C₂×C₄	#10597376	1	2	yes	—
205	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
206	C₈	—	2	4	no	—
207	C₈	—	2	2	no	—
208	C₈	—	2	2	no	—
209	C₈	—	76	8	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
215	C₂²	#11926404	1	1	yes	characteristic
216	C₂²	#11926410	1	1	yes	characteristic
217	C₂²	#11926428	1	4	yes	—
218	C₄	—	4	4	no	—
219	C₄	#11926390	1	1	yes	characteristic
220	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
221	C₄	#11926407	1	1	yes	characteristic
222	C₄	#11926412	1	1	yes	characteristic
223	C₄	#11926435	1	4	yes	—
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	—	2	4	no	—
227	C₂	#14561862	1	1	yes	characteristic
228	C₂	#14563685	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#405	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#405	D₁₉
hypocenter	C₁₉	#10815
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
8. C₁₉⋊#338	C₄	semidirect
153. C₁₉	#10815	semidirect

Maximal subgroups

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

subgroup	index
#14563374	2
C₂×#11926309	2
C₂×C₁₉⋊#338	2
C₂×C₁₉×#405	2
#10815	19