Finite Group Databasebeta

← #10614293⋊C3 #14512237

Subgroups — #10614293⋊C3 #14512237

Order 1920.

262 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C5×#520⋊C3C211yesmaximal, characteristic
2#66161⋊C3C211yesmaximal, characteristic
3C2×#4094⋊C3C211yesmaximal, characteristic
4#10614293C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6C4×C5×SL(2,𝔽3)—21no—
7#4094⋊C3C412yescomplemented
8Dic5×SL(2,𝔽3)—21no—
9C3×#3939—41nomaximal
10#2913⋊C3—51nomaximal, Hall
11C5×#520C2×C311yescharacteristic
12#66161C2×C311yescharacteristic
13C2×#4094C2×C311yescharacteristic
14#65287—31no—
15#65284—31no—
16#65253—31no—
17C2×#3939—31no—
18C5×#41⋊C3C2×C411yescharacteristic
19C5×#41⋊C3Q811yescharacteristic
20C2×C5×SL(2,𝔽3)D411yescharacteristic
21C3×C5×C4⋊C4—41no—
22C3×C4⋊Dic5—41no—
23C2×C3×#168—41no—
24C2×#131⋊C3—51no—
25#520⋊C3—51no—
26#520⋊C3D511yescharacteristic
27C2×C5×#41C22×C311yescharacteristic
28C4×C5×Q8—21no—
29C4×C5×D4—61no—
30C5×#117—31no—
31C2×C5×C4⋊C4—31no—
32#4094—32no—
33#4094C3×C412yescomplemented
34Q8×Dic5—21no—
35D4×Dic5—61no—
36#4072—31no—
37C2×C4⋊Dic5—31no—
38C2×#681—31no—
39C22×#168—31no—
40#3940—31no—
41#3940—31no—
42#3939—32no—
43#3939—31no—
44#3939A411yescharacteristic
45#2913—51noSylow
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5—81no—
48C2×C3×Dic5—81no—
49C5×SL(2,𝔽3)C4⋊C411yescharacteristic
50C3×#168—42no—
51C2×#41⋊C3C2×D511yescharacteristic
52#131⋊C3—52no—
53C4×SL(2,𝔽3)—21no—
54C4×SL(2,𝔽3)—101no—
55C3×#107—201no—
56C5×#41—31no—
57C5×#41—31no—
58C5×#41C2×C3×C411yescharacteristic
59C5×#41C3×Q811yescharacteristic
60C2×C5×Q8C3×D411yescharacteristic
61C2×C5×D4—31no—
62C22×C4×C5—31no—
63C22×C4×C5—61no—
64C22×Dic5—61no—
65C5×C4⋊C4—31no—
66C5×C4⋊C4—61no—
67C5×C4⋊C4C2×A411yescharacteristic
68C5×C22⋊C4—61no—
69C42×C5—61no—
70C22⋊Dic5—61no—
71C4⋊Dic5—31no—
72C4⋊Dic5—61no—
73C4⋊Dic5C2×A411yescharacteristic
74C4×Dic5—61no—
75#681—32no—
76#681—32no—
77C2×#168—31no—
78C2×#168—32no—
79C2×#168—32no—
80C2×#168C2×A411yescharacteristic
81C2×#131—51no—
82#520—51no—
83#520C3×D511yescharacteristic
84#428—151no—
85#428—151no—
86#427—151no—
87C2×#107—151no—
88C22×C3×C5—41no—
89C3×C4×C5—41no—
90C3×C4×C5—41no—
91C3×C4×C5—161no—
92C3×Dic5—161no—
93#41⋊C3Dic1011yescharacteristic
94#41⋊C3C4×D511yescharacteristic
95C2×SL(2,𝔽3)C22⋊D511yescharacteristic
96C2×C3×C8—201no—
97C3×C4⋊C4—41no—
98C3×C4⋊C4—201no—
99C23×C5—31no—
100C5×Q8—31no—
101C5×Q8C3×C4⋊C411yescharacteristic
102C5×D4—31no—
103C5×D4—31no—
104C5×D4—32no—
105C2×C4×C5—21no—
106C2×C4×C5—31no—
107C2×C4×C5—31no—
108C2×C4×C5—31no—
109C2×C4×C5—31no—
110C2×C4×C5—31no—
111C2×C4×C5—61no—
112C2×C4×C5—241no—
113C2×C4×C5C22×A411yescharacteristic
114C2×Dic5—21no—
115C2×Dic5—61no—
116C2×Dic5—241no—
117#168—32no—
118#168C4×A412yes—
119C2×#41C2×C3×D511yescharacteristic
120#131—52no—
121#131—152no—
122C2×M16—151no—
123C22×C8—151no—
124C4×Q8—21no—
125C4×Q8—101no—
126C4×D4—61no—
127C4×D4—301no—
128#117—31no—
129#117—151no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—151no—
132#107—51no—
133#107—151no—
134#107—152no—
135#106—151no—
136#106—151no—
137C2×C3×C5—41no—
138C2×C3×C5—41no—
139C2×C3×C5—41no—
140C2×C3×C4—41no—
141C2×C3×C4—81no—
142C2×C3×C4—401no—
143SL(2,𝔽3)#68311yescharacteristic
144C3×C8—202no—
145C22×C5—31no—
146C22×C5—31no—
147C22×C5—61no—
148C22×C5—61no—
149C22×C5D4×A411yescharacteristic
150C4×C5—31no—
151C4×C5—31no—
152C4×C5—41no—
153C4×C5—121no—
154C4×C5C2×C4×A411yescharacteristic
155C4×C5Q8×A411yescharacteristic
156Dic5—41no—
157Dic5—121no—
158#41—31no—
159#41—31no—
160#41C3×Dic1011yescharacteristic
161#41C3×C4×D511yescharacteristic
162C2×Q8C3×C22⋊D511yescharacteristic
163C2×D4—31no—
164C22×C4—31no—
165C22×C4—61no—
166C22×C4—301no—
167M16—152no—
168M16—152no—
169C2×C8—51no—
170C2×C8—152no—
171C2×C8—152no—
172C2×C8—151no—
173C4⋊C4—31no—
174C4⋊C4—51no—
175C4⋊C4—61no—
176C4⋊C4—151no—
177C4⋊C4—301no—
178C4⋊C4D5×A411yescharacteristic
179C22⋊C4—61no—
180C22⋊C4—301no—
181C42—61no—
182C42—301no—
183C3×C5—41noHall
184C22×C3—41no—
185C3×C4—41no—
186C3×C4—41no—
187C3×C4—161no—
188C3×C4—801no—
189C2×C5—61no—
190C2×C5—61no—
191C2×C5A4×C4⋊C411yescharacteristic
192C2×C5#576⋊C311yescharacteristic
193C2×C5#578⋊C311yescharacteristic
194C23—31no—
195Q8—31no—
196Q8C3×#68311yescharacteristic
197D4—31no—
198D4—31no—
199D4—32no—
200C2×C4—21no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—61no—
207C2×C4—101no—
208C2×C4—241no—
209C2×C4—301no—
210C2×C4—1201no—
211C2×C4C2×D5×A411yescharacteristic
212C8—52no—
213C8—152no—
214C2×C3—41no—
215C2×C3—41no—
216C2×C3—41no—
217C5#2913⋊C311yescharacteristic, complemented, Sylow
218C22—31no—
219C22—31no—
220C22—61no—
221C22—61no—
222C22A4×C22⋊D511yescharacteristic
223C4—31no—
224C4—31no—
225C4—41no—
226C4—121no—
227C4—201no—
228C4—601no—
229C4A4×Dic1011yescharacteristic
230C4C4×D5×A411yescharacteristic
231C3—41noSylow
232C2—61no—
233C2—61no—
234C2A4×#68311yescharacteristic
235C2#66169⋊C311yescharacteristic
236C2#66172⋊C311yescharacteristic
subgroupG/H
centerC22A4×C22⋊D5
commutatorC5×#41C2×C3×C4
FrattiniC2×C4C2×D5×A4
FittingC5×#520C2×C3
socleC22×C5D4×A4
prime radicalC2×C5×#41⋊C3C22
cosocleC2×C5×#41C22×C3
hypercenterC4⋊C4D5×A4
hypocenterC5×Q8C3×C4⋊C4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10614293C3semidirect
7. #4094⋊C3C4semidirect
33. #4094C3×C4semidirect
217. C5#2913⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×#520⋊C32
#66161⋊C32
C2×#4094⋊C32
#106142933
C3×#39394
#2913⋊C35