Finite Group Databasebeta

← #11747411

Subgroups — #11747411

Order 960.

192 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4033C211yesmaximal, characteristic
2#91468C211yesmaximal, characteristic
3#91092C211yesmaximal, characteristic
4C5×#808C211yesmaximal, characteristic
5#90982C211yesmaximal, characteristic
6#90971C211yesmaximal, characteristic
7#90970C211yesmaximal, characteristic
8#65143—31nomaximal, Hall
9C2×C3×Dic10C2211yescharacteristic
10C2×#1204—21no—
11C3×C5×C4⋊C4C2211yescharacteristic
12C4⋊Dic15C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#683—21no—
17C3×C4×Dic5—21no—
18C3×C4×Dic5C2211yescharacteristic
19#6668—21no—
20#5020—51nomaximal, Hall
21#4034—31no—
22#4033D311yescharacteristic
23C5×#106—31no—
24#3948—31no—
25#3946—31no—
26#3942—31no—
27#3940—31no—
28C2×C3×C4×C5—21no—
29C2×C3×C4×C5C2311yescharacteristic
30C2×Dic15—21no—
31C2×C5×Dic3—21no—
32C2×C3×Dic5—21no—
33C2×C3×Dic5D411yescharacteristic
34C2×C3×Dic5D411yescharacteristic
35C3×Dic10—21no—
36C3×Dic10Q812yescomplemented
37#1204—42no—
38C3⋊#168—21no—
39C5×C3⋊C8—21no—
40C3×C4×Q8—51no—
41#869—51no—
42#835—51no—
43#835—51no—
44#808—51no—
45#808D511yescharacteristic
46C4⋊(C3⋊C8)—51no—
47C2×Dic10—61no—
48C2×Dic10C2×D311yescharacteristic
49C2×C5×C8—31no—
50C5×C4⋊C4—31no—
51C5×C4⋊C4C2×D311yescharacteristic
52C4⋊Dic5—31no—
53#683—21no—
54#683—61no—
55C4×Dic5—21no—
56C4×Dic5C2×D311yescharacteristic
57C2×#168—31no—
58#475—151noSylow
59C22×C3×C5C2×D411yescharacteristic
60C3×C4×C5—41no—
61C3×C4×C5C2×Q811yescharacteristic
62C3×C4×C5#4111yescharacteristic
63Dic15—41no—
64C3×Dic5—22no—
65C3×Dic5—21no—
66C3×Dic5SD1612yes—
67C5×Dic3—41no—
68C2×C3×Q8—51no—
69C2×Dic6—101no—
70C3×C4⋊C4—101no—
71C3×C4⋊C4C2×D511yescharacteristic
72C3×C42—51no—
73C3×C42—101no—
74C4⋊Dic3—51no—
75C4⋊Dic3—101no—
76C4⋊Dic3C2×D511yescharacteristic
77C2×C3⋊C8—51no—
78C2×C3⋊C8C2×D511yescharacteristic
79C2×C4×C5—21no—
80C2×C4×C5—61no—
81C2×C4×C5C22×D311yescharacteristic
82C2×Dic5—21no—
83C2×Dic5—61no—
84C2×Dic5#6711yescharacteristic
85C2×Dic5#6711yescharacteristic
86Dic10—21no—
87Dic10—122no—
88Dic10Dic612yescomplemented
89C5×C8—61no—
90#168—61no—
91C4⋊Q8—151no—
92C4×Q8—51no—
93#106—31no—
94#106—151no—
95C4⋊C8—151no—
96#103—151no—
97#103—151no—
98C2×C3×C5C22⋊Q811yescharacteristic
99C2×C3×C5C2×SD1611yescharacteristic
100C2×C3×C5#13711yescharacteristic
101C3×Q8—52no—
102C3×Q8—101no—
103C2×C3×C4—21no—
104C2×C3×C4—51no—
105C2×C3×C4—51no—
106C2×C3×C4—101no—
107C2×C3×C4C22×D511yescharacteristic
108C2×Dic3—21no—
109C2×Dic3—101no—
110Dic6—202no—
111C3⋊C8—21no—
112C3⋊C8—101no—
113C22×C5C2×#6711yescharacteristic
114C4×C5—41no—
115C4×C5—121no—
116C4×C5C2×Dic611yescharacteristic
117C4×C5#23511yescharacteristic
118Dic5—22no—
119Dic5—21no—
120Dic5—121no—
121Dic5#21512yes—
122C2×Q8—51no—
123C2×Q8—301no—
124C2×C8—31no—
125C2×C8—151no—
126C4⋊C4—31no—
127C4⋊C4—101no—
128C4⋊C4—151no—
129C4⋊C4—301no—
130C4⋊C4D3×D511yescharacteristic
131C42—51no—
132C42—101no—
133C3×C5#47511yescharacteristic, complemented, Hall
134C22×C3D4×D511yescharacteristic
135C3×C4—41no—
136C3×C4—52no—
137C3×C4—102no—
138C3×C4—101no—
139C3×C4#70911yescharacteristic
140C3×C4Q8×D511yescharacteristic
141Dic3—41no—
142Dic3—201no—
143C2×C5#92411yescharacteristic
144C2×C5C2×#21511yescharacteristic
145C2×C5#95111yescharacteristic
146Q8—52no—
147Q8—101no—
148Q8—602no—
149C2×C4—21no—
150C2×C4—51no—
151C2×C4—51no—
152C2×C4—61no—
153C2×C4—101no—
154C2×C4—301no—
155C2×C4C2×D3×D511yescharacteristic
156C8—61no—
157C8—301no—
158C2×C3#404211yescharacteristic
159C2×C3D5×SD1611yescharacteristic
160C2×C3#406111yescharacteristic
161C5#502011yescharacteristic, complemented, Sylow
162C22D5×#6711yescharacteristic
163C4—41no—
164C4—52no—
165C4—101no—
166C4—102no—
167C4—121no—
168C4—601no—
169C4D5×Dic611yescharacteristic
170C4#677111yescharacteristic
171C3#6514311yescharacteristic, complemented, Sylow
172C2#9134911yescharacteristic
173C2#9148411yescharacteristic
174C2D5×#21511yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socle, prime radicalC22×C3×C5C2×D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#475
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C3×Dic10Q8semidirect
88. Dic10Dic6semidirect
133. C3×C5#475semidirect
161. C5#5020semidirect
171. C3#65143semidirect

Maximal subgroups

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

subgroupindex
C3×#40332
#914682
#910922
C5×#8082
#909822
#909712
#909702
#651433
#50205