Finite Group Databasebeta

← AGL(1,𝔽5)×#95⋊C3 #14511594

Subgroups — AGL(1,𝔽5)×#95⋊C3 #14511594

Order 1920.

314 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 28 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
1D5×#95⋊C3C211yesmaximal, characteristic
2AGL(1,𝔽5)×#95C311yesmaximal, characteristic, complemented, Hall
3C2×A4×AGL(1,𝔽5)—41nomaximal
4C5×#95⋊C3C411yescharacteristic, complemented
5C4×#95⋊C3—51nomaximal, Hall
6C22×C4×AGL(1,𝔽5)—31no—
7C2×(C2×AGL(1,𝔽5))⋊C4—31no—
8D5×#95C2×C311yescharacteristic
9C2×D5×A4—41no—
10A4×AGL(1,𝔽5)—42no—
11C2×#95⋊C3—51no—
12C23×AGL(1,𝔽5)—31no—
13C23×AGL(1,𝔽5)A411yescharacteristic
14C22×C4×D5—31no—
15C2×C4×AGL(1,𝔽5)—32no—
16C2×C4×AGL(1,𝔽5)—32no—
17C2×C4×AGL(1,𝔽5)—64no—
18(C2×AGL(1,𝔽5))⋊C4—34no—
19C5×#95C3×C411yescharacteristic, complemented
20#3963—31no—
21C4×#95—51noSylow
22C2×C5×A4—41no—
23C2×C3×AGL(1,𝔽5)—161no—
24D5×A4—41no—
25D5×A4—41no—
26C2×C4×A4—201no—
27#95⋊C3AGL(1,𝔽5)11yescharacteristic, direct product factor
28C23×D5C2×A411yescharacteristic
29C22×AGL(1,𝔽5)—31no—
30C22×AGL(1,𝔽5)—31no—
31C22×AGL(1,𝔽5)—32no—
32C22×AGL(1,𝔽5)—32no—
33C22×AGL(1,𝔽5)—34no—
34C22×AGL(1,𝔽5)—62no—
35C22×AGL(1,𝔽5)—61no—
36C22×AGL(1,𝔽5)—61no—
37C22×AGL(1,𝔽5)SL(2,𝔽3)12yes—
38C22×C4×C5—31no—
39C22×Dic5—31no—
40C2×C4×D5—32no—
41C2×C4×D5—32no—
42C2×C4×D5—62no—
43C2×C4×D5—62no—
44C4×AGL(1,𝔽5)—64no—
45C4×AGL(1,𝔽5)—64no—
46C22×C42—151no—
47C2×#95—51no—
48C2×#95—151no—
49C2×C3×D5—161no—
50C5×A4—41no—
51C3×AGL(1,𝔽5)—162no—
52C22×A4—201no—
53C4×A4—202no—
54C23×C5C4×A411yescharacteristic
55C22×D5—31no—
56C22×D5—31no—
57C22×D5—31no—
58C22×D5—31no—
59C22×D5C2×SL(2,𝔽3)11yescharacteristic
60C22×D5#41⋊C311yescharacteristic
61C2×AGL(1,𝔽5)—32no—
62C2×AGL(1,𝔽5)—31no—
63C2×AGL(1,𝔽5)—32no—
64C2×AGL(1,𝔽5)—32no—
65C2×AGL(1,𝔽5)—32no—
66C2×AGL(1,𝔽5)—34no—
67C2×AGL(1,𝔽5)—62no—
68C2×AGL(1,𝔽5)—64no—
69C2×AGL(1,𝔽5)—62no—
70C2×AGL(1,𝔽5)—64no—
71C2×AGL(1,𝔽5)C42⋊C311yescharacteristic
72C2×C4×C5—32no—
73C2×C4×C5—62no—
74C2×Dic5—32no—
75C2×Dic5—62no—
76C4×D5—62no—
77C4×D5—64no—
78C4×D5—62no—
79C23×C4—51no—
80C23×C4—151no—
81C23×C4—151no—
82C2×C42—152no—
83C2×C42—152no—
84C2×C42—304no—
85#95—151no—
86#95—154no—
87#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
88C2×C3×C5—161no—
89C3×D5—161no—
90C3×D5—161no—
91C2×A4—41no—
92C2×A4—201no—
93C2×A4—201no—
94C2×C3×C4—801no—
95C22×C5—31no—
96C22×C5—31no—
97C22×C5C4×SL(2,𝔽3)11yescharacteristic
98C2×D5—32no—
99C2×D5—31no—
100C2×D5—31no—
101C2×D5—31no—
102C2×D5—31no—
103C2×D5—31no—
104C2×D5—31no—
105C2×D5—31no—
106C2×D5C2×C42⋊C311yescharacteristic
107AGL(1,𝔽5)—32no—
108AGL(1,𝔽5)—64no—
109AGL(1,𝔽5)#95⋊C312yesdirect product factor
110C4×C5—62no—
111Dic5—62no—
112C24—51no—
113C22×C4—31no—
114C22×C4—52no—
115C22×C4—152no—
116C22×C4—152no—
117C22×C4—151no—
118C22×C4—151no—
119C22×C4—152no—
120C22×C4—154no—
121C22×C4—152no—
122C22×C4—151no—
123C22×C4—302no—
124C22×C4—302no—
125C22×C4—301no—
126C22×C4—302no—
127C22×C4—301no—
128C42—304no—
129C42—304no—
130C3×C5—161noHall
131C22×C3—801no—
132A4—41no—
133C3×C4—802no—
134C2×C5—31no—
135C2×C5—31no—
136C2×C5C4×C42⋊C311yescharacteristic
137D5—31no—
138D5—31no—
139D5C2×#95⋊C311yescharacteristic
140D5#376⋊C311yescharacteristic
141C23—51no—
142C23—51no—
143C23—151no—
144C23—151no—
145C23—151no—
146C23—151no—
147C23A4×AGL(1,𝔽5)11yescharacteristic
148C2×C4—32no—
149C2×C4—51no—
150C2×C4—62no—
151C2×C4—152no—
152C2×C4—152no—
153C2×C4—151no—
154C2×C4—152no—
155C2×C4—152no—
156C2×C4—152no—
157C2×C4—154no—
158C2×C4—302no—
159C2×C4—302no—
160C2×C4—304no—
161C2×C4—302no—
162C2×C4—302no—
163C2×C4—302no—
164C2×C4—304no—
165C2×C4—304no—
166C2×C3—161no—
167C2×C3—801no—
168C2×C3—801no—
169C5C4×#95⋊C311yescharacteristic, complemented, Sylow
170C22—31no—
171C22—31no—
172C22—51no—
173C22—151no—
174C22—151no—
175C22—151no—
176C22—151no—
177C22—151no—
178C22—151no—
179C22—152no—
180C22—151no—
181C22AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic
182C4—52no—
183C4—62no—
184C4—152no—
185C4—302no—
186C4—304no—
187C3—161noSylow
188C2—31no—
189C2—31no—
190C2—51no—
191C2—51no—
192C2—151no—
193C2—151no—
194C2AGL(1,𝔽5)×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×C42⋊C3
commutator, Fitting, hypocenterC5×#95C3×C4
FrattiniC23A4×AGL(1,𝔽5)
socleC23×C5C4×A4
prime radicalD5×#95⋊C3C2
cosocleD5×#95C2×C3
LCSG ▷ C5×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. AGL(1,𝔽5)×#95C3semidirect
4. C5×#95⋊C3C4semidirect
19. C5×#95C3×C4semidirect
27. #95⋊C3AGL(1,𝔽5)direct (N × H)
87. #95C3×AGL(1,𝔽5)semidirect
109. AGL(1,𝔽5)#95⋊C3direct (N × H)
169. C5C4×#95⋊C3semidirect

Maximal subgroups

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

subgroupindex
D5×#95⋊C32
AGL(1,𝔽5)×#953
C2×A4×AGL(1,𝔽5)4
C4×#95⋊C35