Finite Group Databasebeta

← #10603803⋊C3 #14511596

Subgroups — #10603803⋊C3 #14511596

Order 1920.

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

normal subgroups only

This group has 222 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#10603803C311yesmaximal, characteristic, complemented, Hall
3C2×A4×AGL(1,𝔽5)—41nomaximal
4C5×#95⋊C3C411yescharacteristic, complemented
5#1443⋊C3—51nomaximal, Hall
6C2×(C2×AGL(1,𝔽5))⋊C4—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—
15(C2×AGL(1,𝔽5))⋊C4—62no—
16(C2×AGL(1,𝔽5))⋊C4—62no—
17C5×#95C3×C411yescharacteristic, complemented
18#3963—31no—
19#1443—51noSylow
20C2×C5×A4—41no—
21C2×C3×AGL(1,𝔽5)—161no—
22D5×A4—41no—
23D5×A4—41no—
24C2×C4×A4—201no—
25#95⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
26C23×D5C2×A411yescharacteristic
27C22×AGL(1,𝔽5)—32no—
28C22×AGL(1,𝔽5)—61no—
29C22×AGL(1,𝔽5)—61no—
30C22×AGL(1,𝔽5)—61no—
31C22×AGL(1,𝔽5)—61no—
32C22×AGL(1,𝔽5)—61no—
33C22×AGL(1,𝔽5)—61no—
34C22×AGL(1,𝔽5)—61no—
35C22×AGL(1,𝔽5)—61no—
36C22×AGL(1,𝔽5)SL(2,𝔽3)12yes—
37C22×C4×C5—31no—
38C22×Dic5—31no—
39C2×C4×D5—61no—
40C2×C4×D5—61no—
41C2×C4×D5—61no—
42C2×C4×D5—61no—
43C2×C4×D5—61no—
44C2×C4×D5—61no—
45C2×#95—51no—
46C2×#95—151no—
47C2×#95—151no—
48C2×C3×D5—161no—
49C5×A4—41no—
50C3×AGL(1,𝔽5)—162no—
51C22×A4—201no—
52C4×A4—202no—
53C23×C5C4×A411yescharacteristic
54C22×D5—31no—
55C22×D5—31no—
56C22×D5—31no—
57C22×D5—31no—
58C22×D5C2×SL(2,𝔽3)11yescharacteristic
59C22×D5#41⋊C311yescharacteristic
60C2×AGL(1,𝔽5)—41no—
61C2×AGL(1,𝔽5)—62no—
62C2×AGL(1,𝔽5)—62no—
63C2×AGL(1,𝔽5)—62no—
64C2×AGL(1,𝔽5)—62no—
65C2×AGL(1,𝔽5)—121no—
66C2×AGL(1,𝔽5)—121no—
67C2×AGL(1,𝔽5)—121no—
68C2×AGL(1,𝔽5)—121no—
69C2×AGL(1,𝔽5)—121no—
70C2×C4×C5—61no—
71C2×C4×C5—61no—
72C2×C4×C5—61no—
73C2×Dic5—61no—
74C2×Dic5—61no—
75C2×Dic5—61no—
76C4×D5—121no—
77C4×D5—121no—
78C4×D5—121no—
79C4×D5—121no—
80C23×C4—51no—
81C23×C4—151no—
82C23×C4—151no—
83#95—151no—
84#95—302no—
85#95—302no—
86#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
87C2×C3×C5—161no—
88C3×D5—161no—
89C3×D5—161no—
90C2×A4—41no—
91C2×A4—201no—
92C2×A4—201no—
93C2×C3×C4—801no—
94C22×C5—31no—
95C22×C5—31no—
96C22×C5C4×SL(2,𝔽3)11yescharacteristic
97C2×D5—31no—
98C2×D5—31no—
99C2×D5—31no—
100C2×D5—31no—
101C2×D5—31no—
102C2×D5—31no—
103C2×D5—31no—
104C2×D5—31no—
105C2×D5—31no—
106C2×D5#126⋊C311yescharacteristic
107AGL(1,𝔽5)—42no—
108AGL(1,𝔽5)—122no—
109C4×C5—121no—
110Dic5—121no—
111C24—51no—
112C22×C4—31no—
113C22×C4—52no—
114C22×C4—152no—
115C22×C4—151no—
116C22×C4—301no—
117C22×C4—301no—
118C22×C4—301no—
119C22×C4—301no—
120C22×C4—301no—
121C22×C4—301no—
122C22×C4—301no—
123C22×C4—301no—
124C22×C4—301no—
125C22×C4—301no—
126C22×C4—301no—
127C22×C4—301no—
128C22×C4—301no—
129C22×C4—301no—
130C3×C5—161noHall
131C22×C3—801no—
132A4—41no—
133C3×C4—802no—
134C2×C5—31no—
135C2×C5—31no—
136C2×C5#383⋊C311yescharacteristic
137D5—31no—
138D5—31no—
139D5#396⋊C311yescharacteristic
140D5#401⋊C311yescharacteristic
141C23—51no—
142C23—51no—
143C23—151no—
144C23—151no—
145C23—151no—
146C23—151no—
147C23A4×AGL(1,𝔽5)11yescharacteristic
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—61no—
151C2×C4—201no—
152C2×C4—302no—
153C2×C4—301no—
154C2×C4—301no—
155C2×C4—301no—
156C2×C4—302no—
157C2×C4—302no—
158C2×C4—302no—
159C2×C4—601no—
160C2×C4—601no—
161C2×C4—601no—
162C2×C4—601no—
163C2×C4—601no—
164C2×C4—601no—
165C2×C4—601no—
166C2×C4—601no—
167C2×C4—601no—
168C2×C3—161no—
169C2×C3—801no—
170C2×C3—801no—
171C5#1443⋊C311yescharacteristic, complemented, Sylow
172C22—31no—
173C22—31no—
174C22—51no—
175C22—151no—
176C22—151no—
177C22—151no—
178C22—151no—
179C22—151no—
180C22—151no—
181C22—151no—
182C22—151no—
183C22—151no—
184C22AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic
185C4—121no—
186C4—202no—
187C4—601no—
188C4—602no—
189C3—161noSylow
190C2—31no—
191C2—31no—
192C2—51no—
193C2—51no—
194C2—151no—
195C2—151no—
196C2#65690⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#65690⋊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. #10603803C3semidirect
4. C5×#95⋊C3C4semidirect
17. C5×#95C3×C4semidirect
25. #95⋊C3AGL(1,𝔽5)semidirect
86. #95C3×AGL(1,𝔽5)semidirect
171. C5#1443⋊C3semidirect

Maximal subgroups

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

subgroupindex
D5×#95⋊C32
#106038033
C2×A4×AGL(1,𝔽5)4
#1443⋊C35