Finite Group Databasebeta

← #10617413⋊C3 #14512547

Subgroups — #10617413⋊C3 #14512547

Order 1920.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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×#131⋊C3C211yesmaximal, characteristic
2#65791⋊C3C212yesmaximal, complemented
3#10617413C311yesmaximal, characteristic, complemented, Hall
4D5×#41⋊C3C411yescharacteristic
5C5×#131⋊C3C411yescharacteristic
6C3×#3990—41nomaximal
7#4094⋊C3C2211yescharacteristic
8#3407⋊C3—51nomaximal, Hall
9D5×#131C2×C311yescharacteristic
10#65791C2×C312yescomplemented
11#65725—32no—
12D5⋊M32—31no—
13C2×#3990—31no—
14C5×#41⋊C3C2×C411yescharacteristic
15D5×SL(2,𝔽3)C811yescharacteristic
16C5⋊(#41⋊C3)C811yescharacteristic
17C3×C8×D5—41no—
18C3×#674—42no—
19C2×#131⋊C3—51no—
20#504⋊C3—52no—
21D5×#41C3×C411yescharacteristic
22C5×#131C3×C411yescharacteristic
23#4094C22×C311yescharacteristic
24#4053—31no—
25D5×M16—31no—
26#4047—31no—
27C2×C8×D5—31no—
28#3998—32no—
29C2×#674—32no—
30#3990—31no—
31#3990—32no—
32#3990A411yescharacteristic
33D5⋊C16—32no—
34#3407—51noSylow
35C3×C4×D5—41no—
36C5×SL(2,𝔽3)C2×C811yescharacteristic
37C3×C5×C8—41no—
38C3×#168—41no—
39C2×#41⋊C3—51no—
40#131⋊C3—51no—
41#131⋊C3AGL(1,𝔽5)11yescharacteristic
42C3×M32—201no—
43C5×#41C2×C3×C411yescharacteristic
44#713C3×C811yescharacteristic
45Q8×D5C3×C811yescharacteristic
46#711—31no—
47D4×D5—31no—
48#709—31no—
49C2×C4×D5—31no—
50C5×M16—31no—
51C2×C5×C8—31no—
52#681—31no—
53C2×#168—31no—
54#676—32no—
55C8×D5—31no—
56C8×D5—31no—
57C8×D5—31no—
58C8×D5C2×A411yescharacteristic
59#674—32no—
60#674C2×A412yes—
61C2×#131—51no—
62#504—52no—
63#504—152no—
64C2×M32—151no—
65C2×M32—151no—
66C2×C3×D5—41no—
67C3×C4×C5—41no—
68C3×Dic5—41no—
69#41⋊C3—51no—
70#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
71C2×SL(2,𝔽3)—51no—
72C2×C3×C8—201no—
73C3×C16—202no—
74C22×D5—31no—
75C5×Q8C2×C3×C811yescharacteristic
76C5×D4—31no—
77C2×C4×C5—31no—
78C22⋊D5—32no—
79C2×Dic5—31no—
80D20—31no—
81C4×D5—31no—
82C4×D5—31no—
83C4×D5—31no—
84C4×D5C4×A411yescharacteristic
85Dic10—31no—
86C5×C8—31no—
87C5×C8C4×A411yescharacteristic
88#168—31no—
89#168C22×A411yescharacteristic
90C2×#41—51no—
91#131—51no—
92#131—151no—
93#131—151no—
94#131C3×AGL(1,𝔽5)11yescharacteristic
95C2×M16—151no—
96C22×C8—151no—
97M32—51no—
98M32—152no—
99M32—151no—
100M32—152no—
101C2×C16—152no—
102C2×C16—152no—
103C2×C3×C5—41no—
104C3×D5—81no—
105C2×C3×C4—201no—
106SL(2,𝔽3)D5⋊C811yescharacteristic
107C3×C8—41no—
108C3×C8—201no—
109C22×C5—31no—
110C2×D5—31no—
111C2×D5—121no—
112C2×D5C8×A411yescharacteristic
113C4×C5—31no—
114C4×C5C2×C4×A411yescharacteristic
115Dic5—31no—
116Dic5C8×A411yescharacteristic
117#41—51no—
118#41—151no—
119#41—151no—
120#41C2×C3×AGL(1,𝔽5)11yescharacteristic
121C2×Q8—51no—
122C2×D4—151no—
123C22×C4—151no—
124M16—31no—
125M16—152no—
126M16—151no—
127C2×C8—31no—
128C2×C8—51no—
129C2×C8—151no—
130C2×C8—151no—
131C2×C8—151no—
132C2×C8—151no—
133C16—52no—
134C16—152no—
135C3×C5—41noHall
136C22×C3—201no—
137C3×C4—41no—
138C3×C4—201no—
139C2×C5—61no—
140C2×C5C2×C8×A411yescharacteristic
141D5—21no—
142D5—61no—
143C23—151no—
144Q8—151no—
145Q8C3×D5⋊C811yescharacteristic
146D4—31no—
147D4—151no—
148D4—152no—
149C2×C4—31no—
150C2×C4—51no—
151C2×C4—151no—
152C2×C4—151no—
153C2×C4—151no—
154C2×C4—151no—
155C8—31no—
156C8—51no—
157C8—151no—
158C8A4×AGL(1,𝔽5)11yescharacteristic
159C2×C3—41no—
160C2×C3—401no—
161C5#3407⋊C311yescharacteristic, complemented, Sylow
162C22—31no—
163C22—51no—
164C22—151no—
165C22—601no—
166C4—31no—
167C4—51no—
168C4—151no—
169C4C2×A4×AGL(1,𝔽5)11yescharacteristic
170C3—41noSylow
171C2—61no—
172C2—101no—
173C2—301no—
174C2A4×D5⋊C811yescharacteristic
subgroupG/H
center, FrattiniC4C2×A4×AGL(1,𝔽5)
commutator, hypocenterC5×Q8C2×C3×C8
FittingC5×#131C3×C4
socleC2×C5C2×C8×A4
prime radicalD5×#41⋊C3C4
cosocle#4094C22×C3
hypercenterC8A4×AGL(1,𝔽5)
LCSG ▷ C5×Q8
UCSC1 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #65791⋊C3C2semidirect
3. #10617413C3semidirect
10. #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
D5×#131⋊C32
#65791⋊C32
#106174133
C3×#39904
#3407⋊C35