Finite Group Databasebeta

← C3×#65517 #11750125

Subgroups — C3×#65517 #11750125

Order 960.

296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C22×C3×C5×Q8C211yesmaximal, characteristic
2C2×C3×#689C212yesmaximal, complemented
3C3×#4070C211yesmaximal, characteristic
4C3×#3967C212yesmaximal, complemented
5C3×C22⋊#168C211yesmaximal, characteristic
6#65517C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q8—24no—
8C2×C3×C5×Q8—21no—
9C2×C3×C5×Q8C2212yes—
10C22×C3×C4×C5—21no—
11C22×C3×C4×C5C2211yescharacteristic
12C2×C3×Dic10C2211yescharacteristic
13C3×C22⋊Dic5—21no—
14C3×#689—24no—
15C3×C4⋊Dic5C2211yescharacteristic
16C3×#683—21no—
17C2×C3×#168C2212yes—
18C3×#451—51nomaximal, Hall
19C22×C5×Q8C2×C311yescharacteristic
20C2×#689C2×C312yescomplemented
21#4070C2×C311yescharacteristic
22#3967C2×C312yescomplemented
23C22⋊#168C2×C311yescharacteristic
24C23×C3×C5D411yescharacteristic
25C3×C5×Q8—24no—
26C3×C5×Q8—22no—
27C3×C5×Q8D414yes—
28C2×C3×C4×C5—24no—
29C2×C3×C4×C5—22no—
30C2×C3×C4×C5—22no—
31C2×C3×C4×C5D411yescharacteristic
32C2×C3×C4×C5C2311yescharacteristic
33C2×C3×Dic5—21no—
34C2×C3×Dic5—21no—
35C3×Dic10—22no—
36C3×#168—22no—
37C22×C3×Q8D511yescharacteristic
38C2×C3×Q16—52no—
39C3×C22⋊Q8—51no—
40C3×#103—52no—
41C3×C22⋊C8—51no—
42C2×C5×Q8—24no—
43C2×C5×Q8—21no—
44C2×C5×Q8C22×C312yes—
45C22×C4×C5—21no—
46C22×C4×C5C22×C311yescharacteristic
47C2×Dic10C22×C311yescharacteristic
48C22⋊Dic5—21no—
49#689—24no—
50C4⋊Dic5C22×C311yescharacteristic
51#683—21no—
52C2×#168C22×C312yes—
53#451—51noSylow
54C22×C3×C5—21no—
55C22×C3×C5—21no—
56C22×C3×C5Q1612yescomplemented
57C22×C3×C5C2×D411yescharacteristic
58C3×C4×C5—24no—
59C3×C4×C5—21no—
60C3×C4×C5C2×D412yes—
61C3×Dic5—41no—
62C3×Dic5—41no—
63C2×C3×Q8—24no—
64C2×C3×Q8—21no—
65C2×C3×Q8—51no—
66C2×C3×Q8C2×D512yes—
67C22×C3×C4—21no—
68C22×C3×C4C2×D511yescharacteristic
69C3×Q16—104no—
70C2×C3×C8—52no—
71C3×C4⋊C4—51no—
72C3×C4⋊C4—101no—
73C3×C22⋊C4—101no—
74C23×C5C3×D411yescharacteristic
75C5×Q8—24no—
76C5×Q8—22no—
77C5×Q8C3×D414yes—
78C2×C4×C5—24no—
79C2×C4×C5—22no—
80C2×C4×C5—22no—
81C2×C4×C5C3×D411yescharacteristic
82C2×C4×C5C23×C311yescharacteristic
83C2×Dic5—21no—
84C2×Dic5—21no—
85Dic10—22no—
86#168—22no—
87C22×Q8C3×D511yescharacteristic
88C2×Q16—52no—
89C22⋊Q8—51no—
90#103—52no—
91C22⋊C8—51no—
92C2×C3×C5—22no—
93C2×C3×C5#12011yescharacteristic
94C2×C3×C5C2×Q1611yescharacteristic
95C2×C3×C5#13711yescharacteristic
96C23×C3C22⋊D511yescharacteristic
97C3×Q8—24no—
98C3×Q8—22no—
99C3×Q8—102no—
100C3×Q8C22⋊D514yes—
101C2×C3×C4—24no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×C3×C4—101no—
105C2×C3×C4—101no—
106C2×C3×C4C22⋊D511yescharacteristic
107C2×C3×C4C22×D511yescharacteristic
108C3×C8—102no—
109C22×C5—21no—
110C22×C5—21no—
111C22×C5C3×Q1612yescomplemented
112C22×C5C2×C3×D411yescharacteristic
113C4×C5—24no—
114C4×C5—21no—
115C4×C5C2×C3×D412yes—
116Dic5—41no—
117Dic5—41no—
118C2×Q8—24no—
119C2×Q8—21no—
120C2×Q8—51no—
121C2×Q8C2×C3×D512yes—
122C22×C4—21no—
123C22×C4C2×C3×D511yescharacteristic
124Q16—104no—
125C2×C8—52no—
126C4⋊C4—51no—
127C4⋊C4—101no—
128C22⋊C4—101no—
129C3×C5#45111yescharacteristic, complemented, Hall
130C22×C3—21no—
131C22×C3—21no—
132C22×C3#68912yescomplemented
133C22×C3C2×C22⋊D511yescharacteristic
134C3×C4—24no—
135C3×C4—21no—
136C3×C4—201no—
137C3×C4—201no—
138C3×C4C2×C22⋊D512yes—
139C2×C5—22no—
140C2×C5C3×#12011yescharacteristic
141C2×C5C2×C3×Q1611yescharacteristic
142C2×C5C3×#13711yescharacteristic
143C23C3×C22⋊D511yescharacteristic
144Q8—24no—
145Q8—22no—
146Q8—102no—
147Q8C3×C22⋊D514yes—
148C2×C4—24no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—101no—
152C2×C4—101no—
153C2×C4C3×C22⋊D511yescharacteristic
154C2×C4C22×C3×D511yescharacteristic
155C8—102no—
156C2×C3—22no—
157C2×C3#408811yescharacteristic
158C2×C3C2×#68911yescharacteristic
159C2×C3#409911yescharacteristic
160C5C3×#45111yescharacteristic, complemented, Sylow
161C22—21no—
162C22—21no—
163C22C3×#68912yescomplemented
164C22C2×C3×C22⋊D511yescharacteristic
165C4—24no—
166C4—21no—
167C4—201no—
168C4—201no—
169C4C2×C3×C22⋊D512yes—
170C3#6551711yescharacteristic, direct product factor, Sylow
171C2—22no—
172C2C3×#408811yescharacteristic
173C2C2×C3×#68911yescharacteristic
174C2C3×#409911yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊D5
commutator, cosocleC2×C4×C5C23×C3
FrattiniC2×C4C22×C3×D5
FittingC22×C3×C5×Q8C2
socleC22×C3×C5C2×D4
prime radicalC23×C3×C5D4
hypercenterC22×C3×Q8D5
hypocenterC5C3×#451
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#689C2semidirect
4. C3×#3967C2semidirect
6. #65517C3direct (N × H)
20. C2×#689C2×C3semidirect
22. #3967C2×C3semidirect
56. C22×C3×C5Q16semidirect
111. C22×C5C3×Q16semidirect
129. C3×C5#451semidirect
132. C22×C3#689semidirect
160. C5C3×#451semidirect
163. C22C3×#689semidirect
170. C3#65517direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×Q82
C2×C3×#6892
C3×#40702
C3×#39672
C3×C22⋊#1682
#655173
C3×#4515