Finite Group Databasebeta

← #10617417⋊C3 #14512551

Subgroups — #10617417⋊C3 #14512551

Order 1920.

262 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#66266⋊C3C212yesmaximal
2D5×#131⋊C3C211yesmaximal, characteristic
3#10617417C311yesmaximal, characteristic, complemented, Hall
4D5×#41⋊C3C2211yescharacteristic
5AGL(1,𝔽5)×SL(2,𝔽3)—22no—
6C5×#131⋊C3C411yescharacteristic, complemented
7C3×#3994—41nomaximal
8#4094⋊C3C411yescharacteristic, complemented
9#2913⋊C3—51nomaximal, Hall
10#66266C2×C312yes—
11D5×#131C2×C311yescharacteristic
12#65727—32no—
13#65721—31no—
14C2×#3994—31no—
15C5×#41⋊C3C2×C411yescharacteristic
16C3×C4⋊AGL(1,𝔽5)—42no—
17D5×SL(2,𝔽3)D411yescharacteristic
18C5⋊(#41⋊C3)Q811yescharacteristic
19C3×C8×D5—41no—
20C2×#131⋊C3—51no—
21#520⋊C3—52no—
22D5×#41C22×C311yescharacteristic
23Q8×AGL(1,𝔽5)—22no—
24D4×AGL(1,𝔽5)—62no—
25#4130—32no—
26C2×C4⋊AGL(1,𝔽5)—32no—
27C5×#131C3×C411yescharacteristic, complemented
28#4094C3×C411yescharacteristic, complemented
29#4053—31no—
30D5×M16—31no—
31#4047—31no—
32C2×C8×D5—31no—
33#3994—32no—
34#3994—31no—
35#3994A411yescharacteristic
36#3993—32no—
37#2913—51noSylow
38C2×C3×AGL(1,𝔽5)—82no—
39C3×C4×D5—41no—
40C5×SL(2,𝔽3)C4⋊C411yescharacteristic
41C3×C5×C8—41no—
42C3×#168—41no—
43C2×#41⋊C3—51no—
44#131⋊C3—51no—
45#131⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
46C4×SL(2,𝔽3)—102no—
47C3×#107—201no—
48C22×AGL(1,𝔽5)—62no—
49C5×#41C2×C3×C411yescharacteristic
50#713C3×Q811yescharacteristic
51Q8×D5C3×D411yescharacteristic
52#711—31no—
53D4×D5—31no—
54#709—31no—
55C2×C4×D5—31no—
56C22⋊AGL(1,𝔽5)—62no—
57C4⋊AGL(1,𝔽5)—32no—
58C4⋊AGL(1,𝔽5)—62no—
59C4⋊AGL(1,𝔽5)C2×A412yes—
60C4×AGL(1,𝔽5)—62no—
61C5×M16—31no—
62C2×C5×C8—31no—
63#681—31no—
64C2×#168—31no—
65#676—32no—
66C8×D5—31no—
67C8×D5—31no—
68C8×D5—31no—
69C8×D5C2×A411yescharacteristic
70C2×#131—51no—
71#520—52no—
72#428—152no—
73#427—151no—
74C2×#107—151no—
75C2×C3×D5—41no—
76C3×AGL(1,𝔽5)—162no—
77C3×C4×C5—41no—
78C3×Dic5—41no—
79#41⋊C3—51no—
80#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
81C2×SL(2,𝔽3)—51no—
82C2×C3×C8—201no—
83C3×C4⋊C4—202no—
84C22×D5—31no—
85C2×AGL(1,𝔽5)—22no—
86C2×AGL(1,𝔽5)—62no—
87C2×AGL(1,𝔽5)—242no—
88C5×Q8C3×C4⋊C411yescharacteristic
89C5×D4—31no—
90C2×C4×C5—31no—
91C22⋊D5—32no—
92C2×Dic5—31no—
93D20—31no—
94C4×D5—31no—
95C4×D5—31no—
96C4×D5—31no—
97C4×D5C22×A411yescharacteristic
98Dic10—31no—
99C5×C8—31no—
100C5×C8C4×A411yescharacteristic
101#168—31no—
102#168C4×A411yescharacteristic
103C2×#41—51no—
104#131—51no—
105#131—151no—
106#131—151no—
107#131C3×AGL(1,𝔽5)11yescharacteristic, complemented
108C2×M16—151no—
109C22×C8—151no—
110C4×Q8—102no—
111C4×D4—302no—
112#117—152no—
113C2×C4⋊C4—152no—
114#107—51no—
115#107—151no—
116#107—152no—
117#106—152no—
118C2×C3×C5—41no—
119C3×D5—41no—
120C3×D5—41no—
121C2×C3×C4—201no—
122C2×C3×C4—402no—
123SL(2,𝔽3)C4⋊AGL(1,𝔽5)11yescharacteristic
124C3×C8—41no—
125C3×C8—201no—
126C22×C5—31no—
127C2×D5—31no—
128C2×D5—61no—
129C2×D5—61no—
130C2×D5D4×A411yescharacteristic
131AGL(1,𝔽5)—42no—
132AGL(1,𝔽5)—122no—
133C4×C5—31no—
134C4×C5C2×C4×A411yescharacteristic
135Dic5—31no—
136Dic5Q8×A411yescharacteristic
137#41—51no—
138#41—151no—
139#41—151no—
140#41C2×C3×AGL(1,𝔽5)11yescharacteristic
141C2×Q8—51no—
142C2×D4—151no—
143C22×C4—151no—
144C22×C4—302no—
145M16—31no—
146M16—152no—
147M16—151no—
148C2×C8—31no—
149C2×C8—51no—
150C2×C8—151no—
151C2×C8—151no—
152C2×C8—151no—
153C2×C8—151no—
154C4⋊C4—52no—
155C4⋊C4—152no—
156C4⋊C4—302no—
157C22⋊C4—302no—
158C42—302no—
159C3×C5—41noHall
160C22×C3—201no—
161C3×C4—41no—
162C3×C4—201no—
163C3×C4—802no—
164C2×C5—61no—
165C2×C5A4×C4⋊C411yescharacteristic
166D5—61no—
167D5#576⋊C311yescharacteristic
168D5#578⋊C311yescharacteristic
169C23—151no—
170Q8—151no—
171Q8C3×C4⋊AGL(1,𝔽5)11yescharacteristic
172D4—31no—
173D4—151no—
174D4—152no—
175C2×C4—31no—
176C2×C4—51no—
177C2×C4—102no—
178C2×C4—151no—
179C2×C4—151no—
180C2×C4—151no—
181C2×C4—151no—
182C2×C4—302no—
183C2×C4—1202no—
184C8—31no—
185C8—51no—
186C8—151no—
187C8A4×AGL(1,𝔽5)11yescharacteristic
188C2×C3—41no—
189C2×C3—201no—
190C2×C3—201no—
191C5#2913⋊C311yescharacteristic, complemented, Sylow
192C22—31no—
193C22—51no—
194C22—151no—
195C22—301no—
196C22—301no—
197C4—31no—
198C4—51no—
199C4—151no—
200C4—202no—
201C4—602no—
202C4C2×A4×AGL(1,𝔽5)11yescharacteristic
203C3—41noSylow
204C2—51no—
205C2—51no—
206C2—61no—
207C2—301no—
208C2A4×C4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2A4×C4⋊AGL(1,𝔽5)
commutatorC5×#41C2×C3×C4
FrattiniC4C2×A4×AGL(1,𝔽5)
FittingC5×#131C3×C4
socleC2×C5A4×C4⋊C4
prime radicalD5×#41⋊C3C22
cosocleD5×#41C22×C3
hypercenterC8A4×AGL(1,𝔽5)
hypocenterC5×Q8C3×C4⋊C4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
3. #10617417C3semidirect
6. C5×#131⋊C3C4semidirect
8. #4094⋊C3C4semidirect
27. C5×#131C3×C4semidirect
28. #4094C3×C4semidirect
45. #131⋊C3AGL(1,𝔽5)semidirect
107. #131C3×AGL(1,𝔽5)semidirect
191. C5#2913⋊C3semidirect

Maximal subgroups

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

subgroupindex
#66266⋊C32
D5×#131⋊C32
#106174173
C3×#39944
#2913⋊C35