Finite Group Databasebeta

← #11750847

Subgroups — #11750847

Order 960.

304 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 63 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#92095C211yesmaximal, characteristic
2#91825C211yesmaximal, characteristic, complemented
3#91798C212yesmaximal, complemented
4C3×C5×#100C211yesmaximal, characteristic, complemented
5#91109C212yesmaximal, complemented
6#65035—31nomaximal, Hall
7C2×C3×C5×D4C2211yescharacteristic
8C2×#1220—22no—
9#6819—22no—
10D4×D15—22no—
11#6817C2212yes—
12C2×Dic30C2211yescharacteristic, complemented
13C3×C5×M16C2212yescomplemented
14#6719—22no—
15C4×Dic15C2211yescharacteristic, complemented
16Dic60—22no—
17#6706—22no—
18#4746—51nomaximal, Hall
19#4144—31no—
20#4082—31no—
21#4055—32no—
22C5×#100D311yescharacteristic, complemented
23#3957—32no—
24C23×C3×C5D412yes—
25C22×D15—22no—
26C3×C5×D4—22no—
27C2×C3×C4×C5C2311yescharacteristic
28#1220—24no—
29#1220—22no—
30C2×Dic15—22no—
31C2×Dic15—21no—
32C2×Dic15—21no—
33D60D412yes—
34C4×D15—22no—
35Dic30—22no—
36Dic30D412yes—
37C3×C5×C8—22no—
38#1004—51no—
39#936—51no—
40#909—52no—
41C3×#100D511yescharacteristic, complemented
42#825—52no—
43C2×C5×D4C2×D311yescharacteristic
44C2×C22⋊D5—62no—
45#711—62no—
46D4×D5—62no—
47#709—32no—
48C2×Dic10—31no—
49C5×M16C2×D312yescomplemented
50C22⋊Dic5—62no—
51C4×Dic5—31no—
52Dic20—62no—
53#677—62no—
54#455—151noSylow
55C22×C3×C5—22no—
56C22×C3×C5—42no—
57C22×C3×C5C2×D411yescharacteristic
58C2×D15—22no—
59C2×D15—82no—
60C3×C4×C5C2×D412yes—
61Dic15—22no—
62Dic15—41no—
63Dic15—41no—
64C2×C3×D4C2×D511yescharacteristic
65C2×#67—102no—
66#237—102no—
67D3×D4—102no—
68#235—52no—
69C2×Dic6—51no—
70C3×M16C2×D512yescomplemented
71#217—102no—
72C4×Dic3—51no—
73Dic12—102no—
74#204—102no—
75C23×C5D1212yes—
76C22×D5—62no—
77C5×D4—22no—
78C2×C4×C5C22×D311yescharacteristic
79C22⋊D5—64no—
80C22⋊D5—62no—
81C2×Dic5—62no—
82C2×Dic5—61no—
83C2×Dic5—61no—
84D20—32no—
85C4×D5—62no—
86Dic10—32no—
87Dic10—62no—
88C5×C8—22no—
89H(5,𝔽2)—151no—
90#137—152no—
91#124—151no—
92#104—152no—
93#100D1511yescharacteristic, complemented
94C2×C3×C5—21no—
95C2×C3×C5—42no—
96C2×C3×C5#12011yescharacteristic
97D15—42no—
98C23×C3D2012yes—
99C22×D3—102no—
100C3×D4—22no—
101C2×C3×C4C22×D511yescharacteristic
102#67—104no—
103#67—102no—
104C2×Dic3—102no—
105C2×Dic3—101no—
106C2×Dic3—101no—
107D12—52no—
108C4×D3—102no—
109Dic6—52no—
110Dic6—102no—
111C3×C8—22no—
112C22×C5—22no—
113C22×C5—42no—
114C22×C5C2×D1211yescharacteristic
115C2×D5—62no—
116C2×D5—242no—
117C4×C5D3×D412yes—
118Dic5—62no—
119Dic5—121no—
120Dic5—121no—
121#41—152no—
122#41—302no—
123C2×Q8—151no—
124C2×D4—302no—
125C2×D4—302no—
126C2×D4C2×D1511yescharacteristic
127Q16—302no—
128SD16—302no—
129M16C2×D1512yescomplemented
130C22⋊C4—302no—
131C42—151no—
132C3×C5#45511yescharacteristic, complemented, Hall
133C22×C3—22no—
134C22×C3—42no—
135C22×C3C2×D2011yescharacteristic
136C2×D3—102no—
137C2×D3—402no—
138C3×C4D4×D512yes—
139Dic3—102no—
140Dic3—201no—
141Dic3—201no—
142C2×C5—21no—
143C2×C5—42no—
144C2×C5#88211yescharacteristic
145D5—122no—
146C23—302no—
147C23D6012yes—
148Q8—152no—
149Q8—302no—
150D4—22no—
151D4—152no—
152D4—304no—
153D4—302no—
154C2×C4—302no—
155C2×C4—302no—
156C2×C4—301no—
157C2×C4—301no—
158C2×C4C22×D1511yescharacteristic
159C8—22no—
160C2×C3—21no—
161C2×C3—42no—
162C2×C3#402811yescharacteristic
163D3—202no—
164C5#474611yescharacteristic, complemented, Sylow
165C22—22no—
166C22—42no—
167C22—302no—
168C22—1202no—
169C22C2×D6011yescharacteristic
170C4—302no—
171C4—601no—
172C4—601no—
173C4D4×D1512yes—
174C3#6503511yescharacteristic, complemented, Sylow
175C2—21no—
176C2—42no—
177C2—602no—
178C2#9177111yescharacteristic
subgroupG/H
centerC2#91771
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#100C2
socleC2×C3×C5#120
prime radical#92095C2
hypercenter#100D15
hypocenterC3×C5#455
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. #91825C2semidirect
3. #91798C2semidirect
4. C3×C5×#100C2semidirect
5. #91109C2semidirect
12. C2×Dic30C22semidirect
13. C3×C5×M16C22semidirect
15. C4×Dic15C22semidirect
22. C5×#100D3semidirect
41. C3×#100D5semidirect
49. C5×M16C2×D3semidirect
70. C3×M16C2×D5semidirect
93. #100D15semidirect
129. M16C2×D15semidirect
132. C3×C5#455semidirect
164. C5#4746semidirect
174. C3#65035semidirect

Maximal subgroups

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

subgroupindex
#920952
#918252
#917982
C3×C5×#1002
#911092
#650353
#47465