Subgroups — #14572293

Order 2432.

402 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926605	C₂	1	4	yes	maximal, complemented
2	#11926601	C₂	1	2	yes	maximal, complemented
3	#11926597	C₂	1	2	yes	maximal, complemented
4	#11926571	C₂	1	2	yes	maximal, complemented
5	#11926508	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	#11926500	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₄	1	1	yes	characteristic
11	C₁₉×#117	C₄	1	1	yes	characteristic
12	C₁₉×#117	C₄	1	2	yes	—
13	C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₁₉×#117	C₂²	1	2	yes	—
15	C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₂×#64520	C₂²	1	2	yes	—
21	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
22	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
24	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
26	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
27	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	complemented
28	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	complemented
29	#10597260	C₂²	1	4	yes	complemented
30	C₄×C₁₉⋊C₈	C₂²	1	4	yes	complemented
31	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₄²×C₁₉	C₂×C₄	1	2	yes	—
52	C₄²×C₁₉	C₂×C₄	1	2	yes	—
53	C₄²×C₁₉	C₂³	1	2	yes	—
54	C₄²×C₁₉	C₂³	1	2	yes	—
55	#64520	—	2	4	no	—
56	C₂×C₁₉⋊C₈	—	2	4	no	—
57	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
58	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
59	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	—	4	1	no	—
63	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#41	1	4	yes	—
81	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
82	C₁₉⋊C₈	—	2	2	no	—
83	C₁₉⋊C₈	—	2	2	no	—
84	C₁₉⋊C₈	—	2	4	no	—
85	#2924	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	—	2	1	no	—
93	C₂²×C₁₉	—	4	4	no	—
94	C₂²×C₁₉	#117	1	2	yes	—
95	C₂²×C₁₉	#131	1	2	yes	—
96	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
97	C₄×C₁₉	—	2	1	no	—
98	C₄×C₁₉	—	2	1	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	#117	1	2	yes	—
104	C₄×C₁₉	C₂×#41	1	2	yes	—
105	C₂×#117	D₁₉	1	1	yes	characteristic
106	#433	—	19	4	no	—
107	#432	—	19	2	no	—
108	#431	—	19	2	no	—
109	#424	—	19	2	no	—
110	#407	—	19	1	no	—
111	C₂×C₂²⋊C₈	—	19	1	no	—
112	#405	—	19	2	no	—
113	C₂×C₁₉	—	2	2	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	—	4	1	no	—
116	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
117	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
118	C₂×C₁₉	#568	1	1	yes	characteristic
119	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
120	C₂×M₁₆	—	19	2	no	—
121	C₂²×C₈	—	19	2	no	—
122	#117	Dic₁₉	1	1	yes	characteristic
123	#117	Dic₁₉	1	1	yes	characteristic
124	#117	Dic₁₉	1	2	yes	—
125	#117	C₂×D₁₉	1	1	yes	characteristic
126	#117	C₂×D₁₉	1	1	yes	characteristic
127	#117	C₂×D₁₉	1	2	yes	—
128	C₂×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
129	C₂×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
130	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
131	C₂×C₄²	C₂×D₁₉	1	2	yes	—
132	C₄⋊C₈	—	19	4	no	—
133	C₄⋊C₈	—	19	4	no	—
134	C₂²⋊C₈	—	19	1	no	—
135	C₂²⋊C₈	—	19	1	no	—
136	C₂²⋊C₈	—	19	2	no	—
137	C₂²⋊C₈	—	19	2	no	—
138	C₂²⋊C₈	—	19	2	no	—
139	#97	—	19	4	no	—
140	C₄×C₈	—	19	4	no	—
141	C₁₉	#2924	1	1	yes	characteristic, complemented, Sylow
142	C₂⁴	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
145	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
147	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
149	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
152	M₁₆	—	38	4	no	—
153	C₂×C₈	—	19	2	no	—
154	C₂×C₈	—	19	4	no	—
155	C₂×C₈	—	19	2	no	—
156	C₂×C₈	—	38	4	no	—
157	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
158	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
159	C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
160	C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
161	C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
162	C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
163	C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
164	C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
165	C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
166	C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
167	C₄²	C₂×Dic₁₉	1	2	yes	—
168	C₄²	C₂×Dic₁₉	1	2	yes	—
169	C₄²	C₂²×D₁₉	1	2	yes	—
170	C₄²	C₂²×D₁₉	1	2	yes	—
171	C₂³	—	2	2	no	—
172	C₂³	—	2	2	no	—
173	C₂³	—	4	1	no	—
174	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
175	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
176	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	#64541	1	4	yes	—
185	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
186	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
187	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
188	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
189	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
190	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
191	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
192	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
193	C₈	—	38	2	no	—
194	C₈	—	38	2	no	—
195	C₈	—	38	4	no	—
196	C₂²	—	2	1	no	—
197	C₂²	—	2	1	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	4	4	no	—
204	C₂²	#10597372	1	2	yes	—
205	C₂²	#10597394	1	2	yes	—
206	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
207	C₄	—	2	2	no	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	2	2	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	#10597372	1	2	yes	—
214	C₄	C₂×#64541	1	2	yes	—
215	C₂	—	2	2	no	—
216	C₂	—	2	2	no	—
217	C₂	—	4	1	no	—
218	C₂	C₂×#10597372	1	1	yes	characteristic
219	C₂	C₂×#10597394	1	1	yes	characteristic
220	C₂	#11927311	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₂×C₁₉×#117	C₂
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#2924
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #11926605	C₂	semidirect
2. #11926601	C₂	semidirect
3. #11926597	C₂	semidirect
4. #11926571	C₂	semidirect
7. #11926500	C₂	semidirect
27. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
28. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
29. #10597260	C₂²	semidirect
30. C₄×C₁₉⋊C₈	C₂²	semidirect
141. C₁₉	#2924	semidirect

Maximal subgroups

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

subgroup	index
#11926605	2
#11926601	2
#11926597	2
#11926571	2
#11926508	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
#11926500	2
C₂×C₁₉×#117	2
#2924	19