Finite Group Databasebeta

← #10604988⋊C3 #14511604

Subgroups — #10604988⋊C3 #14511604

Order 1920.

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

normal subgroups only

This group has 322 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×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic
2#10604988C311yesmaximal, characteristic, complemented, Hall
3C2×A4×AGL(1,𝔽5)—41nomaximal
4C5×C22⋊SL(2,𝔽3)C411yescharacteristic, complemented
5#1446⋊C3—51nomaximal, Hall
6C22×Q8×D5C2×C311yescharacteristic
7C2×(C2×AGL(1,𝔽5))⋊C4—31no—
8C2×(C2×AGL(1,𝔽5))⋊C4—31no—
9C2×D5×A4—41no—
10A4×AGL(1,𝔽5)—42no—
11D5×SL(2,𝔽3)—82no—
12C2×C22⋊SL(2,𝔽3)—51no—
13C23×AGL(1,𝔽5)—31no—
14C23×AGL(1,𝔽5)A411yescharacteristic
15C22×C5×Q8C3×C411yescharacteristic, complemented
16C2×Q8×D5—62no—
17C2×Q8×D5—62no—
18C22×C4×D5—31no—
19C22×Dic10—31no—
20(C2×AGL(1,𝔽5))⋊C4—62no—
21(C2×AGL(1,𝔽5))⋊C4—62no—
22#1446—51noSylow
23C2×C5×A4—41no—
24C2×C3×AGL(1,𝔽5)—161no—
25D5×A4—41no—
26D5×A4—41no—
27C5×SL(2,𝔽3)—82no—
28C22⋊SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic, complemented
29C2×C4×A4—201no—
30C23×D5C2×A411yescharacteristic
31C22×AGL(1,𝔽5)—32no—
32C22×AGL(1,𝔽5)—61no—
33C22×AGL(1,𝔽5)—62no—
34C22×AGL(1,𝔽5)—61no—
35C22×AGL(1,𝔽5)—62no—
36C22×AGL(1,𝔽5)—61no—
37C22×AGL(1,𝔽5)—61no—
38C22×AGL(1,𝔽5)SL(2,𝔽3)12yescomplemented
39C2×C5×Q8—62no—
40C22×C4×C5—31no—
41C22×Dic5—31no—
42Q8×D5—22no—
43Q8×D5—62no—
44Q8×D5—64no—
45Q8×D5—62no—
46Q8×D5—62no—
47C2×C4×D5—32no—
48C2×C4×D5—32no—
49C2×C4×D5—62no—
50C2×C4×D5—62no—
51C2×Dic10—64no—
52C2×Dic10—62no—
53C23×Q8—51no—
54C2×#95—151no—
55C2×#95—151no—
56C2×C3×D5—161no—
57C5×A4—41no—
58C3×AGL(1,𝔽5)—162no—
59C22×A4—201no—
60C2×SL(2,𝔽3)—402no—
61C4×A4—202no—
62C23×C5C4×A411yescharacteristic
63C22×D5—31no—
64C22×D5—31no—
65C22×D5—31no—
66C22×D5—31no—
67C22×D5C2×SL(2,𝔽3)11yescharacteristic
68C22×D5#41⋊C311yescharacteristic
69C2×AGL(1,𝔽5)—41no—
70C2×AGL(1,𝔽5)—62no—
71C2×AGL(1,𝔽5)—64no—
72C2×AGL(1,𝔽5)—62no—
73C2×AGL(1,𝔽5)—121no—
74C2×AGL(1,𝔽5)—121no—
75C2×AGL(1,𝔽5)—121no—
76C2×AGL(1,𝔽5)—122no—
77C5×Q8—22no—
78C5×Q8—62no—
79C2×C4×C5—32no—
80C2×C4×C5—62no—
81C2×Dic5—32no—
82C2×Dic5—62no—
83C4×D5—64no—
84C4×D5—62no—
85C4×D5—62no—
86Dic10—64no—
87Dic10—62no—
88Dic10—62no—
89C22×Q8—151no—
90C22×Q8—302no—
91C22×Q8—302no—
92C22×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
93C23×C4—51no—
94C23×C4—151no—
95C23×C4—151no—
96#95—302no—
97#95—302no—
98C2×C3×C5—161no—
99C3×D5—161no—
100C3×D5—161no—
101C2×A4—41no—
102C2×A4—201no—
103C2×A4—201no—
104C2×C3×C4—801no—
105SL(2,𝔽3)—82no—
106C22×C5—31no—
107C22×C5—31no—
108C22×C5C4×SL(2,𝔽3)11yescharacteristic
109C2×D5—32no—
110C2×D5—31no—
111C2×D5—31no—
112C2×D5—31no—
113C2×D5—31no—
114C2×D5—31no—
115C2×D5—31no—
116C2×D5—31no—
117C2×D5#120⋊C311yescharacteristic
118AGL(1,𝔽5)—42no—
119AGL(1,𝔽5)—122no—
120C4×C5—62no—
121Dic5—62no—
122C24—51no—
123C2×Q8—62no—
124C2×Q8—102no—
125C2×Q8—302no—
126C2×Q8—304no—
127C2×Q8—302no—
128C2×Q8—302no—
129C2×Q8—304no—
130C2×Q8—302no—
131C22×C4—31no—
132C22×C4—52no—
133C22×C4—152no—
134C22×C4—152no—
135C22×C4—151no—
136C22×C4—152no—
137C22×C4—302no—
138C22×C4—302no—
139C22×C4—301no—
140C22×C4—301no—
141C22×C4—301no—
142C22×C4—302no—
143C22×C4—302no—
144C22×C4—301no—
145C3×C5—161noHall
146C22×C3—801no—
147A4—41no—
148C3×C4—802no—
149C2×C5—31no—
150C2×C5—31no—
151C2×C5#379⋊C311yescharacteristic
152D5—31no—
153D5—31no—
154D5#393⋊C311yescharacteristic
155D5#395⋊C311yescharacteristic
156C23—51no—
157C23—51no—
158C23—151no—
159C23—151no—
160C23—151no—
161C23—151no—
162C23A4×AGL(1,𝔽5)11yescharacteristic
163Q8—22no—
164Q8—62no—
165Q8—302no—
166Q8—302no—
167Q8—304no—
168C2×C4—32no—
169C2×C4—62no—
170C2×C4—152no—
171C2×C4—201no—
172C2×C4—302no—
173C2×C4—302no—
174C2×C4—304no—
175C2×C4—302no—
176C2×C4—302no—
177C2×C4—302no—
178C2×C4—304no—
179C2×C4—601no—
180C2×C4—601no—
181C2×C4—602no—
182C2×C4—601no—
183C2×C3—161no—
184C2×C3—801no—
185C2×C3—801no—
186C5#1446⋊C311yescharacteristic, complemented, Sylow
187C22—31no—
188C22—31no—
189C22—51no—
190C22—151no—
191C22—151no—
192C22—151no—
193C22—151no—
194C22—151no—
195C22—151no—
196C22—152no—
197C22—151no—
198C22AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic
199C4—62no—
200C4—202no—
201C4—302no—
202C4—602no—
203C3—161noSylow
204C2—31no—
205C2—31no—
206C2—51no—
207C2—51no—
208C2—151no—
209C2—151no—
210C2#65800⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#65800⋊C3
commutator, Fitting, hypocenterC22×C5×Q8C3×C4
FrattiniC23A4×AGL(1,𝔽5)
socleC23×C5C4×A4
prime radicalD5×C22⋊SL(2,𝔽3)C2
cosocleC22×Q8×D5C2×C3
LCSG ▷ C22×C5×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #10604988C3semidirect
4. C5×C22⋊SL(2,𝔽3)C4semidirect
15. C22×C5×Q8C3×C4semidirect
28. C22⋊SL(2,𝔽3)AGL(1,𝔽5)semidirect
38. C22×AGL(1,𝔽5)SL(2,𝔽3)semidirect
92. C22×Q8C3×AGL(1,𝔽5)semidirect
186. C5#1446⋊C3semidirect

Maximal subgroups

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

subgroupindex
D5×C22⋊SL(2,𝔽3)2
#106049883
C2×A4×AGL(1,𝔽5)4
#1446⋊C35