Finite Group Databasebeta

← #11747752

Subgroups — #11747752

Order 960.

248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×C3×D40C211yesmaximal, characteristic
2#91434C211yesmaximal, characteristic, complemented
3#91368C211yesmaximal, characteristic, complemented
4C2×#6655C211yesmaximal, characteristic, complemented
5#91098C211yesmaximal, characteristic, complemented
6C5×#816C211yesmaximal, characteristic, complemented
7#90964C211yesmaximal, characteristic, complemented
8#65108—31nomaximal, Hall
9C2×C5×Dic6C2211yescharacteristic
10C2×C3×D20C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C2×D5×Dic3—21no—
13C2×C3×C5×C8C2211yescharacteristic
14C4×Dic15C2211yescharacteristic
15C2×C3⋊#168C2211yescharacteristic
16C5×C4⋊Dic3C2211yescharacteristic
17C3×D40—22no—
18#6665—21no—
19#6665—21no—
20#6665—21no—
21#6655—22no—
22#5153—51nomaximal, Hall
23#4093—31no—
24C2×#688—31no—
25C2×D40D311yescharacteristic
26#4039—31no—
27C5×#103—31no—
28#3946—31no—
29#3941—31no—
30C22×C3×D5—21no—
31C22×C3×D5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15D411yescharacteristic
34C2×Dic15D411yescharacteristic
35C2×C5×Dic3—21no—
36C2×C5×Dic3—21no—
37C5×Dic6—21no—
38C5×Dic6—21no—
39C3×D20—21no—
40C3×D20—21no—
41C3×D20—21no—
42C3×D20D412yes—
43D5×Dic3—42no—
44C3×C5×C8—21no—
45C3⋊#168—21no—
46C2×C3×D8—51no—
47#936—51no—
48D4×Dic3—51no—
49C2×#214—51no—
50#832—51no—
51#816D511yescharacteristic, complemented
52Dic3⋊C8—51no—
53C2×C5×Q8—31no—
54C2×D20C2×D311yescharacteristic
55C2×D20C2×D311yescharacteristic
56C2×C4×D5—61no—
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4—31no—
59#688—62no—
60#685—61no—
61#685—61no—
62#685—61no—
63C4×Dic5—31no—
64C2×#168—31no—
65D40—22no—
66#463—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C3×D5—22no—
69C2×C3×D5—41no—
70C2×C3×D5—41no—
71C2×C3×D5—41no—
72C2×C3×D5—41no—
73C2×C3×D5—41no—
74C3×C4×C5C2×D411yescharacteristic
75C3×C4×C5#4111yescharacteristic
76Dic15—21no—
77Dic15—21no—
78C5×Dic3—41no—
79C5×Dic3—41no—
80C2×C3×D4—51no—
81C2×C3×D4—51no—
82C22×Dic3—101no—
83C2×Dic6C2×D511yescharacteristic
84C3×D8—102no—
85C2×C3×C8C2×D511yescharacteristic
86#217—101no—
87#217—101no—
88#217—101no—
89#214—102no—
90C4⋊Dic3C2×D511yescharacteristic
91C4×Dic3—51no—
92C2×C3⋊C8—51no—
93C22×D5—21no—
94C22×D5—21no—
95C5×Q8—61no—
96C5×Q8—61no—
97C2×C4×C5—61no—
98C2×C4×C5—61no—
99C2×C4×C5C22×D311yescharacteristic
100C2×Dic5—31no—
101C2×Dic5—31no—
102D20—21no—
103D20—21no—
104D20—21no—
105D20#6712yes—
106C4×D5—122no—
107C5×C8—21no—
108#168—61no—
109C2×SD16—151no—
110C2×D8—51no—
111#124—151no—
112C4×D4—151no—
113C4⋊C8—151no—
114#103—31no—
115#102—151no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5#13511yescharacteristic
118C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
119C3×D5—42no—
120C3×D5—81no—
121C23×C3—101no—
122C23×C3—101no—
123C3×D4—52no—
124C3×D4—101no—
125C3×D4—101no—
126C3×D4—101no—
127C2×C3×C4C22×D511yescharacteristic
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3—51no—
131C2×Dic3—51no—
132C2×Dic3—202no—
133Dic6—21no—
134Dic6—21no—
135C3×C8—21no—
136C3⋊C8—101no—
137C22×C5D3×D411yescharacteristic
138C2×D5—22no—
139C2×D5—41no—
140C2×D5—41no—
141C2×D5—41no—
142C2×D5—41no—
143C2×D5—41no—
144C4×C5—121no—
145C4×C5—121no—
146C4×C5#23711yescharacteristic
147C4×C5C2×#6711yescharacteristic
148Dic5—61no—
149Dic5—61no—
150C2×Q8—31no—
151C2×D4—51no—
152C2×D4—51no—
153C22×C4—301no—
154SD16—302no—
155D8—102no—
156C2×C8—151no—
157C2×C8D3×D511yescharacteristic
158C4⋊C4—31no—
159C22⋊C4—301no—
160C22⋊C4—301no—
161C22⋊C4—301no—
162C42—151no—
163C3×C5#46311yescharacteristic, complemented, Hall
164C22×C3—102no—
165C22×C3—201no—
166C22×C3—201no—
167C22×C3—201no—
168C22×C3—201no—
169C22×C3—201no—
170C22×C3D4×D511yescharacteristic
171C3×C4#70911yescharacteristic
172C3×C4D4×D511yescharacteristic
173Dic3—41no—
174Dic3—41no—
175Dic3—101no—
176Dic3—101no—
177C2×C5#91111yescharacteristic
178C2×C5#91211yescharacteristic
179C2×C5#93911yescharacteristic
180D5—42no—
181D5—81no—
182C23—101no—
183C23—101no—
184Q8—61no—
185Q8—61no—
186D4—52no—
187D4—101no—
188D4—101no—
189D4—101no—
190C2×C4—61no—
191C2×C4—61no—
192C2×C4—151no—
193C2×C4—151no—
194C2×C4—602no—
195C2×C4C2×D3×D511yescharacteristic
196C8—21no—
197C8—301no—
198C2×C3—202no—
199C2×C3—401no—
200C2×C3#403011yescharacteristic
201C2×C3#406011yescharacteristic
202C2×C3#406511yescharacteristic
203C5#515311yescharacteristic, complemented, Sylow
204C22—102no—
205C22—201no—
206C22—201no—
207C22—201no—
208C22—201no—
209C22—201no—
210C22#677711yescharacteristic
211C4—121no—
212C4—121no—
213C4—301no—
214C4—301no—
215C4#676511yescharacteristic
216C4D5×#6711yescharacteristic
217C3#6510811yescharacteristic, complemented, Sylow
218C2—202no—
219C2—401no—
220C2#9125811yescharacteristic
221C2#9127711yescharacteristic
222C2#9140811yescharacteristic
subgroupG/H
centerC22#6777
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D40C2
hypercenterC2×C8D3×D5
hypocenterC3×C5#463
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #91434C2semidirect
3. #91368C2semidirect
4. C2×#6655C2semidirect
5. #91098C2semidirect
6. C5×#816C2semidirect
7. #90964C2semidirect
51. #816D5semidirect
163. C3×C5#463semidirect
203. C5#5153semidirect
217. C3#65108semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D402
#914342
#913682
C2×#66552
#910982
C5×#8162
#909642
#651083
#51535