Finite Group Databasebeta

← #11749330

Subgroups — #11749330

Order 960.

180 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 60 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×#4090C211yesmaximal, characteristic
2#91388C211yesmaximal, characteristic
3#91119C211yesmaximal, characteristic
4C5×#835C211yesmaximal, characteristic
5#90971C211yesmaximal, characteristic
6#90970C211yesmaximal, characteristic
7#90952C211yesmaximal, characteristic
8#65086—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×Dic10C2211yescharacteristic
11C4⋊Dic15C2211yescharacteristic
12C2×C3⋊#168C2211yescharacteristic
13C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊C8C2211yescharacteristic
15C3×#683—21no—
16C3×#683—21no—
17C3×C4×Dic5C2211yescharacteristic
18Dic3⋊Dic5—21no—
19#6669—21no—
20#5082—51nomaximal, Hall
21#4090D311yescharacteristic
22#4036—31no—
23C5×#103—31no—
24#3967—31no—
25#3948—31no—
26#3947—31no—
27#3942—31no—
28C3×C5×Q8—21no—
29C3×C5×Q8—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×C5×Dic3—21no—
34C2×C3×Dic5—21no—
35C2×C3×Dic5D411yescharacteristic
36C2×C3×Dic5D411yescharacteristic
37C3×Dic10—21no—
38C3×Dic10—21no—
39C3⋊#168—21no—
40C5×C3⋊C8—21no—
41C3×C4⋊Q8—51no—
42#870—51no—
43#835—51no—
44#835—51no—
45#835—51no—
46#835D511yescharacteristic
47#803—51no—
48C2×C5×Q8C2×D311yescharacteristic
49C2×Dic10C2×D311yescharacteristic
50C2×C5×C8—31no—
51C5×C4⋊C4—31no—
52C4⋊Dic5—31no—
53C4⋊Dic5—61no—
54#683—21no—
55#683—21no—
56#683—61no—
57C4×Dic5C2×D311yescharacteristic
58C2×#168—31no—
59#491—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C3×C4×C5—41no—
62C3×C4×C5#4111yescharacteristic
63C3×C4×C5#4111yescharacteristic
64Dic15—41no—
65C3×Dic5—21no—
66C3×Dic5—21no—
67C3×Dic5—41no—
68C5×Dic3—41no—
69C2×C3×Q8—51no—
70C2×C3×Q8C2×D511yescharacteristic
71C3×C4⋊C4—101no—
72C3×C4⋊C4—101no—
73C3×C42—51no—
74C4⋊Dic3—51no—
75C4⋊Dic3C2×D511yescharacteristic
76Dic3⋊C4—101no—
77Dic3⋊C4—101no—
78C2×C3⋊C8—51no—
79C2×C3⋊C8C2×D511yescharacteristic
80C5×Q8—21no—
81C5×Q8—21no—
82C2×C4×C5—21no—
83C2×C4×C5—61no—
84C2×C4×C5C22×D311yescharacteristic
85C2×Dic5—21no—
86C2×Dic5—61no—
87C2×Dic5#6711yescharacteristic
88C2×Dic5#6711yescharacteristic
89Dic10—21no—
90Dic10—21no—
91C5×C8—61no—
92#168—61no—
93C4⋊Q8—51no—
94#125—151no—
95#103—31no—
96#103—151no—
97#103—151no—
98#103—151no—
99#97—151no—
100C2×C3×C5#12411yescharacteristic
101C2×C3×C5#13711yescharacteristic
102C2×C3×C5#13711yescharacteristic
103C3×Q8—21no—
104C3×Q8—21no—
105C3×Q8—101no—
106C3×Q8—101no—
107C2×C3×C4—21no—
108C2×C3×C4—51no—
109C2×C3×C4—51no—
110C2×C3×C4—101no—
111C2×C3×C4C22×D511yescharacteristic
112C2×Dic3—21no—
113C2×Dic3—101no—
114C3⋊C8—21no—
115C3⋊C8—101no—
116C22×C5C2×#6711yescharacteristic
117C4×C5—41no—
118C4×C5—121no—
119C4×C5#23711yescharacteristic
120C4×C5#23711yescharacteristic
121Dic5—21no—
122Dic5—21no—
123Dic5—41no—
124Dic5—121no—
125C2×Q8—51no—
126C2×Q8D3×D511yescharacteristic
127C2×C8—31no—
128C2×C8—151no—
129C4⋊C4—31no—
130C4⋊C4—101no—
131C4⋊C4—101no—
132C4⋊C4—151no—
133C4⋊C4—301no—
134C4⋊C4—301no—
135C42—51no—
136C3×C5#49111yescharacteristic, complemented, Hall
137C22×C3D4×D511yescharacteristic
138C3×C4—41no—
139C3×C4—101no—
140C3×C4—101no—
141C3×C4—201no—
142C3×C4#70911yescharacteristic
143C3×C4#71111yescharacteristic
144Dic3—41no—
145Dic3—201no—
146C2×C5#93611yescharacteristic
147C2×C5#94211yescharacteristic
148C2×C5#94211yescharacteristic
149Q8—21no—
150Q8—21no—
151Q8—101no—
152Q8—101no—
153C2×C4—21no—
154C2×C4—51no—
155C2×C4—51no—
156C2×C4—61no—
157C2×C4—101no—
158C2×C4—301no—
159C2×C4C2×D3×D511yescharacteristic
160C8—61no—
161C8—301no—
162C2×C3#403111yescharacteristic
163C2×C3#406111yescharacteristic
164C2×C3#406411yescharacteristic
165C5#508211yescharacteristic, complemented, Sylow
166C22D5×#6711yescharacteristic
167C4—41no—
168C4—101no—
169C4—101no—
170C4—121no—
171C4—201no—
172C4—601no—
173C4#677911yescharacteristic
174C4#678011yescharacteristic
175C3#6508611yescharacteristic, complemented, Sylow
176C2#9151311yescharacteristic
177C2#9151511yescharacteristic
178C2#9153411yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socle, prime radicalC22×C3×C5C2×D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#491
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
136. C3×C5#491semidirect
165. C5#5082semidirect
175. C3#65086semidirect

Maximal subgroups

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

subgroupindex
C3×#40902
#913882
#911192
C5×#8352
#909712
#909702
#909522
#650863
#50825