Finite Group Databasebeta

← #11756708

Subgroups — #11756708

Order 960.

158 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 26 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#91901C211yesmaximal, characteristic
2A4×#170C211yesmaximal, characteristic, complemented
3A4⋊#170C211yesmaximal, characteristic, complemented
4#65692—31nomaximal, Hall
5C2×C5⋊S4C411yescharacteristic
6A4×Dic5C2211yescharacteristic
7C5×SL(2,ℤ/4)C411yescharacteristic
8#6738—41nomaximal
9C8×S4—51nomaximal, Hall
10C22×#170D311yescharacteristic, complemented
11C2×D5⋊C8—31no—
12#4027—31no—
13C22⋊#170—31no—
14#4004—31no—
15#4003—31no—
16C4×#170—31no—
17C2×C5×A4C2×C411yescharacteristic
18C5⋊S4C812yescomplemented
19#1200—41no—
20C3⋊#170—41no—
21C3×#170—41no—
22C4×S4—51no—
23C8×A4—51no—
24A4⋊C8—51no—
25C2×C22⋊D5—31no—
26C22×Dic5C2×D311yescharacteristic
27C2×C4×D5—31no—
28C2×#170—31no—
29C2×#170—31no—
30C2×#170—31no—
31C2×#170—31no—
32D5⋊C8—61no—
33D5⋊C8—61no—
34C5×C22⋊C4—31no—
35#685—31no—
36#683—31no—
37C4×Dic5—31no—
38C8×D4—151noSylow
39C2×D15—41no—
40C5×A4C2×C811yescharacteristic, complemented
41C3×Dic5—41no—
42C5×Dic3—41no—
43C2×S4—51no—
44C4×A4—51no—
45SL(2,ℤ/4)AGL(1,𝔽5)11yescharacteristic
46D3×C8—201no—
47C23×C5C4×D311yescharacteristic
48C22×D5—31no—
49C2×C4×C5—31no—
50C2×C4×C5—31no—
51C22⋊D5—32no—
52C22⋊D5—32no—
53C2×Dic5—31no—
54C2×Dic5—31no—
55C2×Dic5—31no—
56C4×D5—61no—
57C4×D5—61no—
58#170—31no—
59#170—61no—
60#170—61no—
61#170S411yescharacteristic, complemented
62C22×C8—51no—
63C22×C8—151no—
64C4×D4—151no—
65C4⋊C8—151no—
66C22⋊C8—151no—
67C22⋊C8—151no—
68C4×C8—151no—
69C2×C3×C5—41no—
70D15—42no—
71C2×A4C2×AGL(1,𝔽5)11yescharacteristic
72S4—52no—
73C4×D3—201no—
74C3×C8—201no—
75C3⋊C8—201no—
76C22×C5—31no—
77C22×C5—31no—
78C22×C5D3×C811yescharacteristic, complemented
79C2×D5—32no—
80C2×D5—61no—
81C2×D5—61no—
82C4×C5—61no—
83C4×C5—61no—
84Dic5—32no—
85Dic5—31no—
86Dic5C2×S411yescharacteristic
87C2×D4—151no—
88C22×C4—51no—
89C22×C4—151no—
90C2×C8—151no—
91C2×C8—151no—
92C2×C8—151no—
93C2×C8—151no—
94C2×C8—301no—
95C2×C8—301no—
96C4⋊C4—151no—
97C22⋊C4—31no—
98C22⋊C4—151no—
99C42—151no—
100C3×C5—41noHall
101C2×D3—201no—
102A4D5⋊C811yescharacteristic, complemented
103C3×C4—201no—
104Dic3—41no—
105C2×C5—31no—
106C2×C5—31no—
107C2×C5C4×S411yescharacteristic
108D5—62no—
109C23—151no—
110C23D3×AGL(1,𝔽5)11yescharacteristic
111D4—152no—
112D4—152no—
113C2×C4—31no—
114C2×C4—31no—
115C2×C4—151no—
116C2×C4—151no—
117C2×C4—151no—
118C2×C4—301no—
119C2×C4—301no—
120C8—51no—
121C8—151no—
122C8—301no—
123C8—301no—
124C2×C3—41no—
125D3—202no—
126C5C8×S411yescharacteristic, complemented, Sylow
127C22—31no—
128C22—31no—
129C22—152no—
130C22—301no—
131C22—301no—
132C22#673811yescharacteristic, complemented
133C4—51no—
134C4—61no—
135C4—61no—
136C4—152no—
137C4—151no—
138C3—41noSylow
139C2—31no—
140C2—31no—
141C2—302no—
142C2AGL(1,𝔽5)×S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽5)×S4
commutator, hypocenterC5×A4C2×C8
Fitting, socleC23×C5C4×D3
prime radicalC2×C5⋊S4C4
cosocleA4×Dic5C22
LCSG ▷ C5×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. A4×#170C2semidirect
3. A4⋊#170C2semidirect
10. C22×#170D3semidirect
18. C5⋊S4C8semidirect
40. C5×A4C2×C8semidirect
61. #170S4semidirect
78. C22×C5D3×C8semidirect
102. A4D5⋊C8semidirect
126. C5C8×S4semidirect
132. C22#6738semidirect

Maximal subgroups

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

subgroupindex
#919012
A4×#1702
A4⋊#1702
#656923
#67384
C8×S45