Finite Group Databasebeta

← #10603804⋊C3 #14511595

Subgroups — #10603804⋊C3 #14511595

Order 1920.

266 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 25 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
2#10603804C311yesmaximal, characteristic, complemented, Hall
3C2×A4×AGL(1,𝔽5)—41nomaximal
4C5×#95⋊C3C411yescharacteristic, complemented
5#1444⋊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)—62no—
16C2×C4⋊AGL(1,𝔽5)—64no—
17(C2×AGL(1,𝔽5))⋊C4—62no—
18C5×#95C3×C411yescharacteristic, complemented
19#3963—31no—
20#1444—51noSylow
21C2×C5×A4—41no—
22C2×C3×AGL(1,𝔽5)—161no—
23D5×A4—41no—
24D5×A4—41no—
25C2×C4×A4—201no—
26#95⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
27C23×D5C2×A411yescharacteristic
28C22×AGL(1,𝔽5)—32no—
29C22×AGL(1,𝔽5)—61no—
30C22×AGL(1,𝔽5)—62no—
31C22×AGL(1,𝔽5)—62no—
32C22×AGL(1,𝔽5)—61no—
33C22×AGL(1,𝔽5)—61no—
34C22×AGL(1,𝔽5)—61no—
35C22×AGL(1,𝔽5)SL(2,𝔽3)12yes—
36C22×C4×C5—31no—
37C22×Dic5—31no—
38C2×C4×D5—32no—
39C2×C4×D5—32no—
40C2×C4×D5—62no—
41C2×C4×D5—62no—
42C4⋊AGL(1,𝔽5)—68no—
43C22×C4⋊C4—151no—
44C2×#95—51no—
45C2×#95—151no—
46C2×C3×D5—161no—
47C5×A4—41no—
48C3×AGL(1,𝔽5)—162no—
49C22×A4—201no—
50C4×A4—202no—
51C23×C5C4×A411yescharacteristic
52C22×D5—31no—
53C22×D5—31no—
54C22×D5—31no—
55C22×D5—31no—
56C22×D5C2×SL(2,𝔽3)11yescharacteristic
57C22×D5#41⋊C311yescharacteristic
58C2×AGL(1,𝔽5)—41no—
59C2×AGL(1,𝔽5)—62no—
60C2×AGL(1,𝔽5)—64no—
61C2×AGL(1,𝔽5)—62no—
62C2×AGL(1,𝔽5)—121no—
63C2×AGL(1,𝔽5)—121no—
64C2×AGL(1,𝔽5)—122no—
65C2×AGL(1,𝔽5)—121no—
66C2×C4×C5—32no—
67C2×C4×C5—62no—
68C2×Dic5—32no—
69C2×Dic5—62no—
70C4×D5—62no—
71C4×D5—64no—
72C4×D5—62no—
73C23×C4—51no—
74C23×C4—151no—
75C23×C4—151no—
76C2×C4⋊C4—302no—
77C2×C4⋊C4—304no—
78#95—151no—
79#95—302no—
80#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
81C2×C3×C5—161no—
82C3×D5—161no—
83C3×D5—161no—
84C2×A4—41no—
85C2×A4—201no—
86C2×A4—201no—
87C2×C3×C4—801no—
88C22×C5—31no—
89C22×C5—31no—
90C22×C5C4×SL(2,𝔽3)11yescharacteristic
91C2×D5—32no—
92C2×D5—31no—
93C2×D5—31no—
94C2×D5—31no—
95C2×D5—31no—
96C2×D5—31no—
97C2×D5—31no—
98C2×D5—31no—
99C2×D5#127⋊C311yescharacteristic
100AGL(1,𝔽5)—42no—
101AGL(1,𝔽5)—122no—
102C4×C5—62no—
103Dic5—62no—
104C24—51no—
105C22×C4—31no—
106C22×C4—52no—
107C22×C4—152no—
108C22×C4—152no—
109C22×C4—151no—
110C22×C4—152no—
111C22×C4—302no—
112C22×C4—302no—
113C22×C4—301no—
114C22×C4—301no—
115C22×C4—301no—
116C22×C4—302no—
117C22×C4—302no—
118C22×C4—301no—
119C4⋊C4—308no—
120C3×C5—161noHall
121C22×C3—801no—
122A4—41no—
123C3×C4—802no—
124C2×C5—31no—
125C2×C5—31no—
126C2×C5#384⋊C311yescharacteristic
127D5—31no—
128D5—31no—
129D5#392⋊C311yescharacteristic
130D5#399⋊C311yescharacteristic
131C23—51no—
132C23—51no—
133C23—151no—
134C23—151no—
135C23—151no—
136C23—151no—
137C23A4×AGL(1,𝔽5)11yescharacteristic
138C2×C4—32no—
139C2×C4—62no—
140C2×C4—152no—
141C2×C4—201no—
142C2×C4—302no—
143C2×C4—302no—
144C2×C4—304no—
145C2×C4—302no—
146C2×C4—302no—
147C2×C4—304no—
148C2×C4—302no—
149C2×C4—601no—
150C2×C4—601no—
151C2×C4—601no—
152C2×C4—602no—
153C2×C3—161no—
154C2×C3—801no—
155C2×C3—801no—
156C5#1444⋊C311yescharacteristic, complemented, Sylow
157C22—31no—
158C22—31no—
159C22—51no—
160C22—151no—
161C22—151no—
162C22—151no—
163C22—151no—
164C22—151no—
165C22—151no—
166C22—152no—
167C22—151no—
168C22AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic
169C4—62no—
170C4—202no—
171C4—302no—
172C4—602no—
173C3—161noSylow
174C2—31no—
175C2—31no—
176C2—51no—
177C2—51no—
178C2—151no—
179C2—151no—
180C2#65688⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#65688⋊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. #10603804C3semidirect
4. C5×#95⋊C3C4semidirect
18. C5×#95C3×C4semidirect
26. #95⋊C3AGL(1,𝔽5)semidirect
80. #95C3×AGL(1,𝔽5)semidirect
156. C5#1444⋊C3semidirect

Maximal subgroups

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

subgroupindex
D5×#95⋊C32
#106038043
C2×A4×AGL(1,𝔽5)4
#1444⋊C35