Finite Group Databasebeta

← #11751346

Subgroups — #11751346

Order 960.

292 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C3×C5×2−1+4C211yesmaximal, characteristic, complemented
2#91838C212yesmaximal, complemented
3#91836C211yesmaximal, characteristic, complemented
4#91121C212yesmaximal, complemented
5#91120C211yesmaximal, characteristic, complemented
6#65534—31nomaximal, Hall
7C3×C5×#41—22no—
8C3×C5×#41—22no—
9C3×C5×#41C2212yes—
10C2×C3×C5×Q8—22no—
11C2×C3×C5×Q8C2211yescharacteristic
12C2×D60C2211yescharacteristic
13#6717—22no—
14#6715—22no—
15#6714—22no—
16C4×Dic15C2211yescharacteristic
17#6710C2212yes—
18#5245—51nomaximal, Hall
19C5×2−1+4D311yescharacteristic, complemented
20#4095—32no—
21#4093—31no—
22#3969—32no—
23#3968—31no—
24C22×D15—21no—
25C3×C5×Q8—22no—
26C3×C5×Q8—22no—
27C3×C5×Q8D412yes—
28C3×C5×D4—22no—
29C3×C5×D4—22no—
30C3×C5×D4D412yes—
31C2×C3×C4×C5—24no—
32C2×C3×C4×C5—22no—
33C2×C3×C4×C5D412yes—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36D60—22no—
37C3⋊#168—22no—
38C3×2−1+4D511yescharacteristic, complemented
39#949—52no—
40#947—51no—
41#837—52no—
42#836—51no—
43C5×#41—22no—
44C5×#41—22no—
45C5×#41C2×D312yes—
46C2×C5×Q8—22no—
47C2×C5×Q8C2×D311yescharacteristic
48C2×D20—31no—
49#688—62no—
50#686—62no—
51#685—62no—
52C4×Dic5—31no—
53#681—32no—
54#454—151noSylow
55C22×C3×C5—22no—
56C22×C3×C5C2×D411yescharacteristic
57C2×D15—42no—
58C2×D15—41no—
59C3×C4×C5—22no—
60C3×C4×C5—22no—
61C3×C4×C5C2×D412yes—
62Dic15—41no—
63C3×#41—22no—
64C3×#41—22no—
65C3×#41C2×D512yes—
66C2×C3×Q8—22no—
67C2×C3×Q8C2×D511yescharacteristic
68C2×D12—51no—
69#215—102no—
70#213—102no—
71(C2×D3)⋊C4—102no—
72C4×Dic3—51no—
73#208—52no—
74C22×D5—61no—
75C5×Q8—22no—
76C5×Q8—22no—
77C5×Q8#6712yes—
78C5×D4—22no—
79C5×D4—22no—
80C5×D4#6712yes—
81C2×C4×C5—24no—
82C2×C4×C5—22no—
83C2×C4×C5#6712yes—
84C2×C4×C5C22×D311yescharacteristic
85C2×Dic5—61no—
86D20—62no—
87#168—62no—
882−1+4D1511yescharacteristic, complemented
89AGL(1,ℤ/8)—152no—
90#124—151no—
91#104—152no—
92#101—151no—
93C2×C3×C5—21no—
94C2×C3×C5—42no—
95C2×C3×C5#12011yescharacteristic
96D15—81no—
97C22×D3—101no—
98C3×Q8—22no—
99C3×Q8—22no—
100C3×Q8C22⋊D512yes—
101C3×D4—22no—
102C3×D4—22no—
103C3×D4C22⋊D512yes—
104C2×C3×C4—24no—
105C2×C3×C4—22no—
106C2×C3×C4C22⋊D512yes—
107C2×C3×C4C22×D511yescharacteristic
108C2×Dic3—101no—
109D12—102no—
110C3⋊C8—102no—
111C22×C5—22no—
112C22×C5C2×#6711yescharacteristic
113C2×D5—122no—
114C2×D5—121no—
115C4×C5—22no—
116C4×C5—22no—
117C4×C5C2×#6712yes—
118Dic5—121no—
119#41—22no—
120#41—22no—
121#41C2×D1512yes—
122C2×Q8—22no—
123C2×Q8C2×D1511yescharacteristic
124C2×D4—151no—
125SD16—302no—
126D8—302no—
127M16—152no—
128C22⋊C4—302no—
129C42—151no—
130C3×C5#45411yescharacteristic, complemented, Hall
131C22×C3—22no—
132C22×C3C2×C22⋊D511yescharacteristic
133C2×D3—202no—
134C2×D3—201no—
135C3×C4—22no—
136C3×C4—22no—
137C3×C4C2×C22⋊D512yes—
138Dic3—201no—
139C2×C5—21no—
140C2×C5—42no—
141C2×C5#95311yescharacteristic
142D5—241no—
143C23—301no—
144Q8—22no—
145Q8—22no—
146Q8#122012yes—
147D4—22no—
148D4—22no—
149D4—302no—
150D4#122012yes—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—301no—
154C2×C4#122012yes—
155C2×C4C22×D1511yescharacteristic
156C8—302no—
157C2×C3—21no—
158C2×C3—42no—
159C2×C3#409911yescharacteristic
160D3—401no—
161C5#524511yescharacteristic, complemented, Sylow
162C22—22no—
163C22—602no—
164C22—601no—
165C22C2×#122011yescharacteristic
166C4—22no—
167C4—22no—
168C4—601no—
169C4C2×#122012yes—
170C3#6553411yescharacteristic, complemented, Sylow
171C2—21no—
172C2—42no—
173C2—1201no—
174C2#9184211yescharacteristic
subgroupG/H
centerC2#91842
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×2−1+4C2
socleC2×C3×C5#120
hypercenter2−1+4D15
hypocenterC3×C5#454
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. C3×C5×2−1+4C2semidirect
2. #91838C2semidirect
3. #91836C2semidirect
4. #91121C2semidirect
5. #91120C2semidirect
19. C5×2−1+4D3semidirect
38. C3×2−1+4D5semidirect
88. 2−1+4D15semidirect
130. C3×C5#454semidirect
161. C5#5245semidirect
170. C3#65534semidirect

Maximal subgroups

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

subgroupindex
C3×C5×2−1+42
#918382
#918362
#911212
#911202
#655343
#52455