Finite Group Databasebeta

← #10617186⋊C3 #14512525

Subgroups — #10617186⋊C3 #14512525

Order 1920.

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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×#4133⋊C3C212yesmaximal
2C4×C5⋊(#41⋊C3)C211yesmaximal, characteristic
3#10617186C311yesmaximal, characteristic, complemented, Hall
4C2×C5⋊(#41⋊C3)C2211yescharacteristic
5#4133⋊C3—22no—
6C4×C5×SL(2,𝔽3)C411yescharacteristic
7C3×#4004—41nomaximal
8Dic5×SL(2,𝔽3)C411yescharacteristic
9C4⋊(#131⋊C3)—51nomaximal, Hall
10C2×#4133C2×C312yes—
11C4×#713C2×C311yescharacteristic
12#65708—32no—
13#65682—31no—
14D5⋊(C4⋊C8)—31no—
15C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
16C2×C3×#170—42no—
17C5⋊(#41⋊C3)D411yescharacteristic
18C5⋊(#41⋊C3)Q811yescharacteristic
19C3×C4×Dic5—41no—
20C2×#131⋊C3—52no—
21C4×#41⋊C3—51no—
22C2×#713C22×C311yescharacteristic
23#4133—22no—
24#4133—62no—
25C2×#700—32no—
26C2×D5⋊C8—32no—
27C4×C5×Q8C3×C411yescharacteristic
28Q8×Dic5C3×C411yescharacteristic
29#4039—31no—
30#4038—31no—
31C4×D20—31no—
32C42×D5—31no—
33#4004—32no—
34#4004—31no—
35#4004A411yescharacteristic
36C4⋊#170—32no—
37#2906—51noSylow
38C2×C3×C4×C5—41no—
39C2×C3×Dic5—41no—
40C2×C3×Dic5—41no—
41C5×SL(2,𝔽3)C4⋊C411yescharacteristic
42C3×#170—82no—
43C2×#41⋊C3—51no—
44#131⋊C3—102no—
45C4×SL(2,𝔽3)—51no—
46C4×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
47C3×C4⋊C8—201no—
48C2×C5×Q8C2×C3×C411yescharacteristic
49#713—31no—
50#713—31no—
51#713C3×D411yescharacteristic
52#713C3×Q811yescharacteristic
53C2×D20—31no—
54C2×C4×D5—31no—
55C2×C4×D5—31no—
56C2×C4×D5—31no—
57C2×#170—32no—
58C2×#170C2×A412yes—
59#700—62no—
60#700—62no—
61D5⋊C8—62no—
62D5⋊C8—62no—
63C5×C4⋊C4—31no—
64C42×C5—31no—
65#685—32no—
66C4⋊Dic5—31no—
67C4×Dic5—31no—
68C4×Dic5—31no—
69C4×Dic5C2×A411yescharacteristic
70C2×#131—52no—
71C4×#41—51no—
72#424—152no—
73#423—151no—
74C2×C4⋊C8—151no—
75C22×C3×C5—41no—
76C3×C4×C5—81no—
77C3×Dic5—42no—
78C3×Dic5—41no—
79C3×Dic5—41no—
80#41⋊C3—51no—
81#41⋊C3—51no—
82C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
83C2×C3×C8—202no—
84C3×C42—201no—
85C22×D5—31no—
86C5×Q8—31no—
87C5×Q8C3×C4⋊C411yescharacteristic
88C2×C4×C5—31no—
89C2×C4×C5—31no—
90C2×C4×C5C4×A411yescharacteristic
91C2×Dic5—31no—
92C2×Dic5C4×A411yescharacteristic
93C2×Dic5C22×A411yescharacteristic
94D20—31no—
95D20—31no—
96D20—32no—
97C4×D5—31no—
98C4×D5—31no—
99C4×D5—31no—
100C4×D5—31no—
101C4×D5—62no—
102C4×D5—121no—
103#170—22no—
104#170—62no—
105C2×#41—51no—
106#131—102no—
107#131—302no—
108C2×M16—152no—
109C22×C8—152no—
110C4×Q8—51no—
111C4×Q8C3×AGL(1,𝔽5)11yescharacteristic
112C4×D4—151no—
113C4×D4—151no—
114#117—151no—
115C2×C42—151no—
116C4⋊C8—51no—
117C4⋊C8—151no—
118C4⋊C8—152no—
119C4⋊C8—152no—
120C2×C3×C5—41no—
121C2×C3×C5—41no—
122C2×C3×C5—41no—
123C2×C3×C4—41no—
124C2×C3×C4—201no—
125C2×C3×C4—201no—
126SL(2,𝔽3)C4⋊AGL(1,𝔽5)11yescharacteristic
127C3×C8—402no—
128C22×C5C2×C4×A411yescharacteristic
129C2×D5—31no—
130C2×D5—31no—
131C2×D5—61no—
132C2×D5—61no—
133C4×C5—21no—
134C4×C5—31no—
135C4×C5—31no—
136C4×C5—61no—
137Dic5—61no—
138Dic5#131⋊C312yescomplemented
139Dic5D4×A411yescharacteristic
140Dic5Q8×A411yescharacteristic
141#41—51no—
142#41—51no—
143#41—151no—
144#41—151no—
145C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
146C2×D4—151no—
147C22×C4—151no—
148C22×C4—151no—
149C22×C4—151no—
150M16—302no—
151M16—302no—
152C2×C8—52no—
153C2×C8—152no—
154C2×C8—302no—
155C2×C8—302no—
156C4⋊C4—31no—
157C4⋊C4—151no—
158C22⋊C4—152no—
159C42—31no—
160C42—51no—
161C42—151no—
162C42—151no—
163C3×C5—41noHall
164C22×C3—41no—
165C3×C4—81no—
166C3×C4—201no—
167C3×C4—202no—
168C3×C4—201no—
169C2×C5A4×C4⋊C411yescharacteristic
170C2×C5C2×#131⋊C311yescharacteristic
171C2×C5#568⋊C311yescharacteristic
172D5—61no—
173D5—61no—
174C23—151no—
175Q8—31no—
176Q8C3×C4⋊AGL(1,𝔽5)11yescharacteristic
177D4—151no—
178D4—151no—
179D4—152no—
180C2×C4—31no—
181C2×C4—31no—
182C2×C4—51no—
183C2×C4—51no—
184C2×C4—151no—
185C2×C4—151no—
186C2×C4—151no—
187C2×C4—151no—
188C2×C4—151no—
189C2×C4—302no—
190C2×C4—601no—
191C2×C4A4×AGL(1,𝔽5)11yescharacteristic
192C8—102no—
193C8—302no—
194C2×C3—41no—
195C2×C3—41no—
196C2×C3—41no—
197C5C4⋊(#131⋊C3)11yescharacteristic, complemented, Sylow
198C22—151no—
199C22—151no—
200C22—301no—
201C22—301no—
202C22C2×A4×AGL(1,𝔽5)11yescharacteristic
203C4—21no—
204C4—31no—
205C4—31no—
206C4—51no—
207C4—51no—
208C4—52no—
209C4—61no—
210C4—301no—
211C3—41noSylow
212C2—301no—
213C2—301no—
214C2A4×C4⋊AGL(1,𝔽5)11yescharacteristic
215C2#66260⋊C311yescharacteristic
216C2D5⋊(#131⋊C3)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4×AGL(1,𝔽5)
commutatorC2×C5×Q8C2×C3×C4
FittingC4×C5×Q8C3×C4
socleC22×C5C2×C4×A4
prime radicalC2×C5⋊(#41⋊C3)C22
cosocleC2×#713C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
hypocenterC5×Q8C3×C4⋊C4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #10617186C3semidirect
138. Dic5#131⋊C3semidirect
197. C5C4⋊(#131⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C2×#4133⋊C32
C4×C5⋊(#41⋊C3)2
#106171863
C3×#40044
C4⋊(#131⋊C3)5