Finite Group Databasebeta

← #11756442

Subgroups — #11756442

Order 960.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#124C211yesmaximal, characteristic, complemented
2#91836C212yesmaximal, complemented
3#91826C212yesmaximal, complemented
4#91774C214yesmaximal, complemented
5#91771C214yesmaximal, complemented
6#91764C212yesmaximal, complemented
7#66017—31nomaximal, Hall
8C23×D15C2212yescomplemented
9C2×C3×C5×Q8C2211yescharacteristic, complemented
10C2×C3×C5×D4C2211yescharacteristic
11C2×#1220C2214yes—
12C2×D60C2212yes—
13C2×D60C2212yes—
14C2×Dic30C2212yescomplemented
15C3×C5×C22⋊C4C2214yescomplemented
16C3×C42×C5C2211yescharacteristic, complemented
17#6719C2212yescomplemented
18#6714C2214yescomplemented
19#6714C2214yescomplemented
20#6714C2214yescomplemented
21C4×Dic15C2212yescomplemented
22#5683—51nomaximal, Hall
23C5×#124D311yescharacteristic, complemented
24#4093—32no—
25#4083—32no—
26#4031—34no—
27#4028—34no—
28#4021—32no—
29C23×C3×C5C2312yes—
30C22×D15—42no—
31C22×D15—44no—
32C22×D15C2314yes—
33C3×C5×Q8—41no—
34C3×C5×D4—41no—
35C2×C3×C4×C5C2312yes—
36C2×C3×C4×C5C2311yescharacteristic
37C2×C3×C4×C5C2312yes—
38#1220—44no—
39C2×Dic15C2314yes—
40D60—42no—
41D60—42no—
42Dic30—42no—
43C3×#124D511yescharacteristic, complemented
44#947—52no—
45#937—52no—
46#885—54no—
47#882—54no—
48#875—52no—
49C23×D5—32no—
50C2×C5×Q8C2×D311yescharacteristic, complemented
51C2×C5×D4C2×D311yescharacteristic
52C2×C22⋊D5—34no—
53C2×D20—32no—
54C2×D20—32no—
55C2×Dic10—32no—
56C5×C22⋊C4C2×D314yescomplemented
57C42×C5C2×D311yescharacteristic, complemented
58C22⋊Dic5—32no—
59#685—34no—
60#685—34no—
61#685—34no—
62C4×Dic5—32no—
63H(3,𝔽4)—151noSylow
64C22×C3×C5—24no—
65C22×C3×C5—22no—
66C22×C3×C5C2411yescharacteristic
67C2×D15—24no—
68C2×D15—24no—
69C2×D15—24no—
70C2×D15—48no—
71C3×C4×C5—22no—
72C3×C4×C5—22no—
73C3×C4×C5—21no—
74Dic15—24no—
75C23×D3—52no—
76C2×C3×Q8C2×D511yescharacteristic, complemented
77C2×C3×D4C2×D511yescharacteristic
78C2×#67—54no—
79C2×D12—52no—
80C2×D12—52no—
81C2×Dic6—52no—
82C3×C22⋊C4C2×D514yescomplemented
83C3×C42C2×D511yescharacteristic, complemented
84#217—52no—
85(C2×D3)⋊C4—54no—
86(C2×D3)⋊C4—54no—
87(C2×D3)⋊C4—54no—
88C4×Dic3—52no—
89C23×C5C22×D312yes—
90C22×D5—34no—
91C22×D5—122no—
92C22×D5—124no—
93C5×Q8—41no—
94C5×D4—41no—
95C2×C4×C5C22×D312yes—
96C2×C4×C5C22×D311yescharacteristic
97C2×C4×C5C22×D312yes—
98C22⋊D5—124no—
99C2×Dic5—34no—
100D20—122no—
101D20—122no—
102Dic10—122no—
103#124—152no—
104#124—154no—
105#124—152no—
106#124D1511yescharacteristic, complemented
107#120—152no—
108#120—154no—
109C2×C3×C5—42no—
110C2×C3×C5H(5,𝔽2)11yescharacteristic
111C2×C3×C5H(5,𝔽2)12yes—
112D15—44no—
113C23×C3C22×D512yes—
114C22×D3—54no—
115C22×D3—202no—
116C22×D3—204no—
117C3×Q8—41no—
118C3×D4—41no—
119C2×C3×C4C22×D512yes—
120C2×C3×C4C22×D511yescharacteristic
121C2×C3×C4C22×D512yes—
122#67—204no—
123C2×Dic3—54no—
124D12—202no—
125D12—202no—
126Dic6—202no—
127C22×C5—22no—
128C22×C5—24no—
129C22×C5C23×D311yescharacteristic
130C2×D5—64no—
131C2×D5—64no—
132C2×D5—64no—
133C2×D5—128no—
134C4×C5—22no—
135C4×C5—21no—
136C4×C5—22no—
137Dic5—64no—
138C24—152no—
139C2×Q8—152no—
140C2×Q8C2×D1511yescharacteristic, complemented
141C2×D4—154no—
142C2×D4—152no—
143C2×D4—152no—
144C2×D4C2×D1511yescharacteristic
145C22⋊C4—152no—
146C22⋊C4—154no—
147C22⋊C4—154no—
148C22⋊C4—154no—
149C22⋊C4C2×D1514yescomplemented
150C42—152no—
151C42C2×D1511yescharacteristic, complemented
152C3×C5H(3,𝔽4)11yescharacteristic, complemented, Hall
153C22×C3—22no—
154C22×C3—24no—
155C22×C3C23×D511yescharacteristic
156C2×D3—104no—
157C2×D3—104no—
158C2×D3—104no—
159C2×D3—208no—
160C3×C4—22no—
161C3×C4—21no—
162C3×C4—22no—
163Dic3—104no—
164C2×C5—42no—
165C2×C5#100411yescharacteristic
166C2×C5#100912yes—
167D5—124no—
168C23—154no—
169C23—602no—
170C23—604no—
171C23C22×D1512yes—
172Q8—41no—
173Q8—602no—
174D4—41no—
175D4—602no—
176D4—602no—
177D4—604no—
178C2×C4—154no—
179C2×C4C22×D1512yes—
180C2×C4C22×D1511yescharacteristic
181C2×C4C22×D1512yes—
182C2×C3—42no—
183C2×C3#414411yescharacteristic
184C2×C3#414912yes—
185D3—204no—
186C5#568311yescharacteristic, complemented, Sylow
187C22—22no—
188C22—24no—
189C22—304no—
190C22—304no—
191C22—304no—
192C22—608no—
193C22C23×D1511yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—304no—
198C3#6601711yescharacteristic, complemented, Sylow
199C2—42no—
200C2—604no—
201C2#9209511yescharacteristic
202C2#9210012yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#124C2
hypercenter#124D15
hypocenterC3×C5H(3,𝔽4)
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×C5×#124C2semidirect
2. #91836C2semidirect
3. #91826C2semidirect
4. #91774C2semidirect
5. #91771C2semidirect
6. #91764C2semidirect
8. C23×D15C22semidirect
9. C2×C3×C5×Q8C22semidirect
14. C2×Dic30C22semidirect
15. C3×C5×C22⋊C4C22semidirect
16. C3×C42×C5C22semidirect
17. #6719C22semidirect
18. #6714C22semidirect
19. #6714C22semidirect
20. #6714C22semidirect
21. C4×Dic15C22semidirect
23. C5×#124D3semidirect
43. C3×#124D5semidirect
50. C2×C5×Q8C2×D3semidirect
56. C5×C22⋊C4C2×D3semidirect
57. C42×C5C2×D3semidirect
76. C2×C3×Q8C2×D5semidirect
82. C3×C22⋊C4C2×D5semidirect
83. C3×C42C2×D5semidirect
106. #124D15semidirect
140. C2×Q8C2×D15semidirect
149. C22⋊C4C2×D15semidirect
151. C42C2×D15semidirect
152. C3×C5H(3,𝔽4)semidirect
186. C5#5683semidirect
198. C3#66017semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1242
#918362
#918262
#917742
#917712
#917642
#660173
#56835