Finite Group Databasebeta

← #11749145

Subgroups — #11749145

Order 960.

304 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 64 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×#4144C211yesmaximal, characteristic
2#91825C211yesmaximal, characteristic, complemented
3#91313C212yesmaximal, complemented
4C5×#833C211yesmaximal, characteristic, complemented
5#90976C212yesmaximal, complemented
6#65035—31nomaximal, Hall
7C2×C3×C5×D4C2211yescharacteristic
8C2×Dic30C2211yescharacteristic, complemented
9C2×C3×C22⋊D5—22no—
10C3×#711—22no—
11C3×D4×D5—22no—
12C3×#709C2212yes—
13#6719—22no—
14C4×Dic15C2211yescharacteristic, complemented
15C5×#208C2212yescomplemented
16#6662—22no—
17#6657—22no—
18#5242—51nomaximal, Hall
19#4144D311yescharacteristic
20#4082—31no—
21#4055—32no—
22C5×#100—31no—
23#3957—32no—
24C23×C3×C5D412yes—
25C22×C3×D5—22no—
26C3×C5×D4—22no—
27C2×C3×C4×C5C2311yescharacteristic
28C2×Dic15—21no—
29C2×Dic15—21no—
30Dic30—22no—
31C3×C22⋊D5—24no—
32C3×C22⋊D5—22no—
33C2×C3×Dic5—22no—
34C3×D20D412yes—
35C3×C4×D5—22no—
36C3×Dic10D412yes—
37C5×C3⋊C8—22no—
38C3×H(5,𝔽2)—51no—
39#951—52no—
40#936—51no—
41#837—52no—
42#833D511yescharacteristic, complemented
43C2×C5×D4C2×D311yescharacteristic
44C2×C22⋊D5—22no—
45#711—22no—
46D4×D5—22no—
47#709C2×D312yes—
48C2×Dic10—31no—
49C5×M16—32no—
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×C3×D5—22no—
59C2×C3×D5—82no—
60C3×C4×C5C2×D412yes—
61Dic15—41no—
62Dic15—41no—
63C3×Dic5—22no—
64C3×#41—52no—
65C3×#41—102no—
66C2×C3×D4—102no—
67C2×C3×D4—102no—
68C2×C3×D4C2×D511yescharacteristic
69C2×Dic6—51no—
70#217—102no—
71#216—102no—
72#214—102no—
73C4×Dic3—51no—
74#208C2×D512yescomplemented
75C23×C5#6712yes—
76C22×D5—22no—
77C5×D4—22no—
78C2×C4×C5C22×D311yescharacteristic
79C22⋊D5—24no—
80C22⋊D5—22no—
81C2×Dic5—22no—
82C2×Dic5—61no—
83C2×Dic5—61no—
84D20#6712yes—
85C4×D5—22no—
86Dic10—62no—
87Dic10#6712yes—
88C5×C8—62no—
89H(5,𝔽2)—51no—
90#137—152no—
91#124—151no—
92#104—152no—
93#100—31no—
94C2×C3×C5—21no—
95C2×C3×C5—42no—
96C2×C3×C5#12011yescharacteristic
97C3×D5—42no—
98C23×C3—102no—
99C23×C3D2012yes—
100C3×Q8—52no—
101C3×D4—22no—
102C3×D4—52no—
103C3×D4—104no—
104C3×D4—102no—
105C2×C3×C4—102no—
106C2×C3×C4—102no—
107C2×C3×C4C22×D511yescharacteristic
108C2×Dic3—101no—
109C2×Dic3—101no—
110Dic6—102no—
111C3⋊C8—22no—
112C22×C5—22no—
113C22×C5—42no—
114C22×C5C2×#6711yescharacteristic
115C2×D5—22no—
116C2×D5—82no—
117C4×C5C2×#6712yes—
118Dic5—22no—
119Dic5—121no—
120Dic5—121no—
121#41—52no—
122#41—102no—
123C2×Q8—151no—
124C2×D4—102no—
125C2×D4—102no—
126C2×D4D3×D511yescharacteristic
127Q16—302no—
128SD16—302no—
129M16—32no—
130C22⋊C4—302no—
131C42—151no—
132C3×C5#45511yescharacteristic, complemented, Hall
133C22×C3—22no—
134C22×C3—42no—
135C22×C3—102no—
136C22×C3—402no—
137C22×C3C2×D2011yescharacteristic
138C3×C4—102no—
139C3×C4D4×D512yes—
140Dic3—201no—
141Dic3—201no—
142C2×C5—21no—
143C2×C5—42no—
144C2×C5#95311yescharacteristic
145D5—42no—
146C23—102no—
147C23#120212yes—
148Q8—52no—
149Q8—302no—
150D4—22no—
151D4—52no—
152D4—104no—
153D4—102no—
154C2×C4—102no—
155C2×C4—102no—
156C2×C4—301no—
157C2×C4—301no—
158C2×C4C2×D3×D511yescharacteristic
159C8—62no—
160C2×C3—21no—
161C2×C3—42no—
162C2×C3—202no—
163C2×C3#402811yescharacteristic
164C5#524211yescharacteristic, complemented, Sylow
165C22—22no—
166C22—42no—
167C22—102no—
168C22—402no—
169C22C2×#120211yescharacteristic
170C4—102no—
171C4—601no—
172C4—601no—
173C4D5×#6712yes—
174C3#6503511yescharacteristic, complemented, Sylow
175C2—21no—
176C2—42no—
177C2—202no—
178C2#9156411yescharacteristic
subgroupG/H
centerC2#91564
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×D4C22
socleC2×C3×C5#120
prime radicalC3×#4144C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#455
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #91825C2semidirect
3. #91313C2semidirect
4. C5×#833C2semidirect
5. #90976C2semidirect
8. C2×Dic30C22semidirect
14. C4×Dic15C22semidirect
15. C5×#208C22semidirect
42. #833D5semidirect
74. #208C2×D5semidirect
132. C3×C5#455semidirect
164. C5#5242semidirect
174. C3#65035semidirect

Maximal subgroups

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

subgroupindex
C3×#41442
#918252
#913132
C5×#8332
#909762
#650353
#52425