Finite Group Databasebeta

← A42×Dic5 #72277489

Subgroups — A42×Dic5 #72277489

Order 2880.

406 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×A42C211yesmaximal, characteristic
2Dic5×C22⋊A4C312yesmaximal, complemented
3C22×A4×Dic5C312yesmaximal, complemented
4C5×A42C411yescharacteristic, complemented
5C3×A4×Dic5—42nomaximal
6C4×A42—51nomaximal, Hall
7C2×C5×C22⋊A4C2×C312yes—
8C23×C5×A4C2×C312yes—
9C2×A4×Dic5—32no—
10C2×A4×Dic5—32no—
11C2×C3×C5×A4—42no—
12C24×Dic5C3211yescharacteristic, complemented, Hall
13C2×A42D511yescharacteristic
14C5×C22⋊A4C3×C412yescomplemented
15C22×C5×A4—32no—
16C22×C5×A4—32no—
17C22×C5×A4C3×C412yescomplemented
18C22×C3×Dic5—42no—
19A4×Dic5—32no—
20A4×Dic5—44no—
21A4×Dic5—122no—
22A4×Dic5A412yesdirect product factor
23C4×C22⋊A4—52no—
24C22×C4×A4—52no—
25C3×C5×A4—42no—
26C32×Dic5—161no—
27C25×C5C2×C3211yescharacteristic
28C23×Dic5—32no—
29C23×Dic5—32no—
30C23×Dic5—91no—
31C23×Dic5—91no—
32A42Dic511yescharacteristic, direct product factor
33C3×C4×A4—202no—
34C23×C3×C5—42no—
35C2×C5×A4—32no—
36C2×C5×A4—32no—
37C2×C5×A4—44no—
38C2×C5×A4—122no—
39C2×C5×A4C2×A412yes—
40C2×C3×Dic5—122no—
41C2×C3×Dic5—122no—
42C2×C22⋊A4C3×D512yes—
43C23×A4C3×D512yes—
44C2×C4×A4—152no—
45C2×C4×A4—152no—
46C2×C32×C5—161no—
47C24×C5—32no—
48C24×C5—32no—
49C24×C5—91no—
50C24×C5—91no—
51C24×C5C32×C411yescharacteristic, complemented
52C22×Dic5—32no—
53C22×Dic5—32no—
54C22×Dic5—91no—
55C22×Dic5—92no—
56C22×Dic5—92no—
57C22×Dic5—92no—
58C22×Dic5—92no—
59C22×Dic5—94no—
60C22×Dic5—91no—
61C22×Dic5C3×A412yescomplemented
62C2×C3×A4—42no—
63C24×C4—51noSylow
64C22×C3×C5—42no—
65C22×C3×C5—122no—
66C22×C3×C5—122no—
67C5×A4—44no—
68C5×A4—122no—
69C5×A4C4×A412yescomplemented
70C3×Dic5—42no—
71C3×Dic5—122no—
72C3×Dic5—162no—
73C22⋊A4C3×Dic512yescomplemented
74C22×A4—32no—
75C22×A4—32no—
76C22×A4C3×Dic512yescomplemented
77C22×C3×C4—202no—
78C4×A4—52no—
79C4×A4—152no—
80C4×A4—204no—
81C4×A4—602no—
82C32×C5—161noHall
83C23×C5—32no—
84C23×C5—32no—
85C23×C5—32no—
86C23×C5—91no—
87C23×C5—91no—
88C23×C5—92no—
89C23×C5—92no—
90C23×C5—92no—
91C23×C5—92no—
92C23×C5—91no—
93C23×C5—94no—
94C23×C5C2×C3×A412yes—
95C2×Dic5—32no—
96C2×Dic5—32no—
97C2×Dic5—91no—
98C2×Dic5—92no—
99C2×Dic5—94no—
100C2×Dic5—91no—
101C2×Dic5—92no—
102C2×Dic5—92no—
103C3×A4—42no—
104C32×C4—801no—
105C25C32×D511yescharacteristic
106C23×C4—152no—
107C23×C4—152no—
108C23×C4—451no—
109C23×C4—451no—
110C2×C3×C5—42no—
111C2×C3×C5—122no—
112C2×C3×C5—122no—
113C2×C3×C5—162no—
114C23×C3—42no—
115C2×A4—32no—
116C2×A4—32no—
117C2×A4—44no—
118C2×A4—122no—
119C2×A4D5×A412yes—
120C2×C3×C4—602no—
121C2×C3×C4—602no—
122C22×C5—32no—
123C22×C5—32no—
124C22×C5—32no—
125C22×C5—91no—
126C22×C5—92no—
127C22×C5—91no—
128C22×C5—92no—
129C22×C5—92no—
130C22×C5—94no—
131C22×C5—92no—
132C22×C5—91no—
133C22×C5C3×C4×A412yescomplemented
134Dic5—32no—
135Dic5—91no—
136Dic5A4211yescharacteristic, direct product factor
137C2×C32—161no—
138C24—32no—
139C24—32no—
140C24—91no—
141C24—91no—
142C24C32×Dic511yescharacteristic, complemented
143C22×C4—52no—
144C22×C4—152no—
145C22×C4—152no—
146C22×C4—451no—
147C22×C4—452no—
148C22×C4—452no—
149C22×C4—452no—
150C22×C4—452no—
151C22×C4—454no—
152C22×C4—451no—
153C3×C5—42no—
154C3×C5—162no—
155C22×C3—42no—
156C22×C3—122no—
157C22×C3—122no—
158A4—44no—
159A4—122no—
160A4A4×Dic512yesdirect product factor
161C3×C4—202no—
162C3×C4—602no—
163C3×C4—802no—
164C2×C5—32no—
165C2×C5—32no—
166C2×C5—91no—
167C2×C5—91no—
168C2×C5C2×A4211yescharacteristic
169C32—161noSylow
170C23—32no—
171C23—32no—
172C23—32no—
173C23—91no—
174C23—91no—
175C23—92no—
176C23—92no—
177C23—92no—
178C23—92no—
179C23—91no—
180C23—94no—
181C23C3×D5×A412yes—
182C2×C4—152no—
183C2×C4—152no—
184C2×C4—451no—
185C2×C4—451no—
186C2×C4—452no—
187C2×C4—454no—
188C2×C4—452no—
189C2×C4—452no—
190C2×C3—42no—
191C2×C3—122no—
192C2×C3—122no—
193C2×C3—162no—
194C5C4×A4211yescharacteristic, complemented, Sylow
195C22—32no—
196C22—32no—
197C22—32no—
198C22—91no—
199C22—92no—
200C22—91no—
201C22—92no—
202C22—92no—
203C22—94no—
204C22—92no—
205C22—91no—
206C22C3×A4×Dic512yescomplemented
207C4—51no—
208C4—152no—
209C4—451no—
210C3—42no—
211C3—162no—
212C2—32no—
213C2—32no—
214C2—91no—
215C2—91no—
216C2D5×A4211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D5×A42
commutator, hypocenterC24×C5C32×C4
Fitting, socle, cosocleC25×C5C2×C32
prime radicalC2×C5×A42C2
LCSG ▷ C24×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic5×C22⋊A4C3semidirect
3. C22×A4×Dic5C3semidirect
4. C5×A42C4semidirect
12. C24×Dic5C32semidirect
14. C5×C22⋊A4C3×C4semidirect
17. C22×C5×A4C3×C4semidirect
22. A4×Dic5A4direct (N × H)
32. A42Dic5direct (N × H)
51. C24×C5C32×C4semidirect
61. C22×Dic5C3×A4semidirect
69. C5×A4C4×A4semidirect
73. C22⋊A4C3×Dic5semidirect
76. C22×A4C3×Dic5semidirect
133. C22×C5C3×C4×A4semidirect
136. Dic5A42direct (N × H)
142. C24C32×Dic5semidirect
160. A4A4×Dic5direct (N × H)
194. C5C4×A42semidirect
206. C22C3×A4×Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C5×A422
Dic5×C22⋊A43
C22×A4×Dic53
C3×A4×Dic54
C4×A425