Finite Group Databasebeta

← #11747367

Subgroups — #11747367

Order 960.

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

normal subgroups only

This group has 208 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
1C4⋊C4×D15C211yesmaximal, characteristic
2#91390C211yesmaximal, characteristic
3C5×#808C211yesmaximal, characteristic, complemented
4C3×#3942C211yesmaximal, characteristic, complemented
5#90985C211yesmaximal, characteristic, complemented
6#90971C211yesmaximal, characteristic, complemented
7#90957C211yesmaximal, characteristic
8#65151—31nomaximal, Hall
9C2×C4×D15—21no—
10C2×C4×D15C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14#6712—21no—
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C2×C3×#168C2211yescharacteristic
18Dic3⋊Dic5—21no—
19#6667—21no—
20#4805—51nomaximal, Hall
21#4043—31no—
22D5×C4⋊C4—31no—
23C5×#106—31no—
24#3952—31no—
25#3948—31no—
26#3942D311yescharacteristic, complemented
27#3940—31no—
28C22×D15D411yescharacteristic
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C2311yescharacteristic
31C2×Dic15—21no—
32C2×Dic15D411yescharacteristic
33C4×D15—21no—
34C4×D15—21no—
35C4×D15—42no—
36C2×C5×Dic3—21no—
37C2×C3×Dic5—21no—
38C3×Dic10—21no—
39C3×Dic10—21no—
40C3×#168—21no—
41C5×C3⋊C8—21no—
42#946—51no—
43D3×C4⋊C4—51no—
44C3×#103—51no—
45#835—51no—
46(C2×D3)⋊C8—51no—
47#817—51no—
48#808D511yescharacteristic, complemented
49C2×C4×D5—31no—
50C2×C4×D5—61no—
51C2×Dic10C2×D311yescharacteristic
52C2×C5×C8—31no—
53C5×C4⋊C4—31no—
54C5×C4⋊C4C2×D311yescharacteristic
55#685—61no—
56C4⋊Dic5—31no—
57C4⋊Dic5—61no—
58#683—61no—
59C2×#168C2×D311yescharacteristic
60#483—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×D15—21no—
63C2×D15—21no—
64C2×D15SD1612yes—
65C3×C4×C5—41no—
66C3×C4×C5#4111yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—21no—
69Dic15—41no—
70C3×Dic5—41no—
71C5×Dic3—41no—
72C2×C3×Q8—51no—
73C2×C4×D3—51no—
74C2×C4×D3—101no—
75C2×C3×C8—51no—
76C3×C4⋊C4C2×D511yescharacteristic
77(C2×D3)⋊C4—101no—
78C4⋊Dic3—51no—
79C4⋊Dic3C2×D511yescharacteristic
80Dic3⋊C4—101no—
81Dic3⋊C4—101no—
82C2×C3⋊C8C2×D511yescharacteristic
83C22×D5—31no—
84C2×C4×C5—21no—
85C2×C4×C5—61no—
86C2×C4×C5C22×D311yescharacteristic
87C2×Dic5—21no—
88C2×Dic5—31no—
89C2×Dic5—61no—
90C4×D5—61no—
91C4×D5—61no—
92C4×D5—122no—
93Dic10—21no—
94Dic10—21no—
95C5×C8—61no—
96#168—21no—
97C22⋊Q8—151no—
98C2×C4⋊C4—151no—
99#106—31no—
100#106—151no—
101#103—51no—
102#103—151no—
103C22⋊C8—151no—
104C2×C3×C5#12311yescharacteristic
105C2×C3×C5C2×SD1611yescharacteristic
106C2×C3×C5#13711yescharacteristic
107D15—22no—
108C22×D3—51no—
109C3×Q8—101no—
110C3×Q8—101no—
111C2×C3×C4—21no—
112C2×C3×C4—101no—
113C2×C3×C4C22×D511yescharacteristic
114C2×Dic3—21no—
115C2×Dic3—51no—
116C2×Dic3—101no—
117C4×D3—101no—
118C4×D3—101no—
119C4×D3—202no—
120C3×C8—101no—
121C3⋊C8—21no—
122C22×C5D3×D411yescharacteristic
123C2×D5—32no—
124C2×D5—61no—
125C2×D5—61no—
126C4×C5—41no—
127C4×C5—121no—
128C4×C5#23511yescharacteristic
129C4×C5#23711yescharacteristic
130Dic5—41no—
131Dic5—61no—
132Dic5—121no—
133C2×Q8—51no—
134C22×C4—151no—
135C22×C4—301no—
136C2×C8—31no—
137C2×C8—51no—
138C4⋊C4—31no—
139C4⋊C4—151no—
140C4⋊C4—301no—
141C4⋊C4—301no—
142C4⋊C4D3×D511yescharacteristic
143C22⋊C4—301no—
144C3×C5#48311yescharacteristic, complemented, Hall
145C22×C3D4×D511yescharacteristic
146C2×D3—52no—
147C2×D3—101no—
148C2×D3—101no—
149C3×C4—41no—
150C3×C4—201no—
151C3×C4#70911yescharacteristic
152C3×C4#71311yescharacteristic
153Dic3—41no—
154Dic3—101no—
155Dic3—201no—
156C2×C5#88311yescharacteristic
157C2×C5D3×SD1611yescharacteristic
158C2×C5#91811yescharacteristic
159D5—62no—
160C23—151no—
161Q8—101no—
162Q8—101no—
163C2×C4—21no—
164C2×C4—61no—
165C2×C4—101no—
166C2×C4—151no—
167C2×C4—301no—
168C2×C4—301no—
169C2×C4—301no—
170C2×C4—602no—
171C2×C4C2×D3×D511yescharacteristic
172C8—61no—
173C8—101no—
174C2×C3#404011yescharacteristic
175C2×C3D5×SD1611yescharacteristic
176C2×C3#406111yescharacteristic
177D3—102no—
178C5#480511yescharacteristic, complemented, Sylow
179C22—152no—
180C22—301no—
181C22—301no—
182C22#679011yescharacteristic
183C4—41no—
184C4—121no—
185C4—201no—
186C4—301no—
187C4—601no—
188C4#676611yescharacteristic
189C4#677111yescharacteristic
190C3#6515111yescharacteristic, complemented, Sylow
191C2—302no—
192C2#9135411yescharacteristic
193C2#9148711yescharacteristic
194C2#9152411yescharacteristic
subgroupG/H
centerC22#6790
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC22×D15D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#483
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
3. C5×#808C2semidirect
4. C3×#3942C2semidirect
5. #90985C2semidirect
6. #90971C2semidirect
26. #3942D3semidirect
48. #808D5semidirect
144. C3×C5#483semidirect
178. C5#4805semidirect
190. C3#65151semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D152
#913902
C5×#8082
C3×#39422
#909852
#909712
#909572
#651513
#48055