Finite Group Databasebeta

← #10617530⋊C3 #14512577

Subgroups — #10617530⋊C3 #14512577

Order 1920.

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

normal subgroups only

This group has 200 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×#4094⋊C3C211yesmaximal, characteristic
2#65791⋊C3C212yesmaximal, complemented
3#10617530C311yesmaximal, characteristic, complemented, Hall
4C2×C5×#41⋊C3C411yescharacteristic
5C3×#3998—41nomaximal
6#4094⋊C3C411yescharacteristic
7#4094⋊C3C2211yescharacteristic
8#3407⋊C3—51nomaximal, Hall
9C2×#4094C2×C311yescharacteristic
10#65791—32no—
11#65791C2×C312yescomplemented
12C2×#3998—31no—
13C2×#3998—31no—
14C5×#41⋊C3C811yescharacteristic
15C5×#41⋊C3C2×C411yescharacteristic
16C2×C5×SL(2,𝔽3)C811yescharacteristic
17C2×C3×#168—41no—
18C3×#674—42no—
19C2×#131⋊C3—51no—
20#504⋊C3—52no—
21C2×C5×#41C3×C411yescharacteristic
22#4094—31no—
23#4094—31no—
24#4094C3×C411yescharacteristic
25#4094C22×C311yescharacteristic
26C2×#681—31no—
27C22×#168—31no—
28#3998—31no—
29#3998—32no—
30#3998—32no—
31#3998A411yescharacteristic
32C2×#674—32no—
33C2×#674—32no—
34#3407—51noSylow
35C2×C3×C4×C5—41no—
36C5×SL(2,𝔽3)C2×C811yescharacteristic
37C3×#168—41no—
38C3×#168—41no—
39C2×#41⋊C3AGL(1,𝔽5)11yescharacteristic
40#131⋊C3—51no—
41#131⋊C3—51no—
42C3×M32—201no—
43C5×#41—31no—
44C5×#41—31no—
45C5×#41C3×C811yescharacteristic
46C5×#41C2×C3×C411yescharacteristic
47C2×C5×Q8C3×C811yescharacteristic
48C2×C5×D4—31no—
49C22×C4×C5—31no—
50#681—32no—
51#681—31no—
52#681—31no—
53C2×#168—31no—
54C2×#168—31no—
55C2×#168—31no—
56C2×#168—31no—
57C2×#168—31no—
58C2×#168C2×A411yescharacteristic
59#674—32no—
60#674C2×A412yes—
61C2×#131—51no—
62#504—52no—
63#504—152no—
64C2×M32—151no—
65C2×M32—151no—
66C22×C3×C5—41no—
67C3×C4×C5—41no—
68C3×C4×C5—41no—
69#41⋊C3#17011yescharacteristic
70#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
71C2×SL(2,𝔽3)#17011yescharacteristic
72C2×C3×C8—201no—
73C3×C16—202no—
74C23×C5—31no—
75C5×Q8—31no—
76C5×Q8C2×C3×C811yescharacteristic
77C5×D4—31no—
78C5×D4—31no—
79C5×D4—32no—
80C2×C4×C5—31no—
81C2×C4×C5—31no—
82C2×C4×C5—31no—
83C2×C4×C5—31no—
84C2×C4×C5—31no—
85C2×C4×C5C4×A411yescharacteristic
86#168—31no—
87#168—31no—
88#168C4×A411yescharacteristic
89#168C22×A411yescharacteristic
90C2×#41C3×AGL(1,𝔽5)11yescharacteristic
91#131—51no—
92#131—51no—
93#131—151no—
94#131—151no—
95C2×M16—151no—
96C22×C8—151no—
97M32—51no—
98M32—152no—
99M32—151no—
100M32—152no—
101C2×C16—152no—
102C2×C16—152no—
103C2×C3×C5—41no—
104C2×C3×C5—81no—
105C2×C3×C4—41no—
106SL(2,𝔽3)C2×#17011yescharacteristic
107C3×C8—201no—
108C3×C8—201no—
109C22×C5—31no—
110C22×C5—31no—
111C22×C5—121no—
112C22×C5C8×A411yescharacteristic
113C4×C5—31no—
114C4×C5—31no—
115C4×C5C8×A411yescharacteristic
116C4×C5C2×C4×A411yescharacteristic
117#41—31no—
118#41—31no—
119#41C3×#17011yescharacteristic
120#41C2×C3×AGL(1,𝔽5)11yescharacteristic
121C2×Q8C3×#17011yescharacteristic
122C2×D4—31no—
123C22×C4—31no—
124M16—152no—
125M16—151no—
126M16—151no—
127C2×C8—51no—
128C2×C8—151no—
129C2×C8—151no—
130C2×C8—151no—
131C2×C8—151no—
132C2×C8—151no—
133C16—52no—
134C16—152no—
135C3×C5—41noHall
136C22×C3—41no—
137C3×C4—41no—
138C3×C4—41no—
139C2×C5—21no—
140C2×C5—61no—
141C2×C5—61no—
142C2×C5C2×C8×A411yescharacteristic
143C23—31no—
144Q8—31no—
145Q8C2×C3×#17011yescharacteristic
146D4—31no—
147D4—31no—
148D4—32no—
149C2×C4—31no—
150C2×C4—31no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—31no—
154C2×C4A4×AGL(1,𝔽5)11yescharacteristic
155C8—51no—
156C8—51no—
157C8—151no—
158C8—151no—
159C2×C3—41no—
160C2×C3—81no—
161C5#3407⋊C311yescharacteristic, complemented, Sylow
162C22—31no—
163C22—31no—
164C22—121no—
165C22A4×#17011yescharacteristic
166C4—31no—
167C4—31no—
168C4A4×#17011yescharacteristic
169C4C2×A4×AGL(1,𝔽5)11yescharacteristic
170C3—41noSylow
171C2—21no—
172C2—61no—
173C2—61no—
174C2C2×A4×#17011yescharacteristic
subgroupG/H
center, FrattiniC4C2×A4×AGL(1,𝔽5)
commutator, hypocenterC5×Q8C2×C3×C8
FittingC2×C5×#41C3×C4
socleC2×C5C2×C8×A4
prime radicalC2×C5×#41⋊C3C4
cosocle#4094C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
LCSG ▷ C5×Q8
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #65791⋊C3C2semidirect
3. #10617530C3semidirect
11. #65791C2×C3semidirect
161. C5#3407⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#4094⋊C32
#65791⋊C32
#106175303
C3×#39984
#3407⋊C35