Finite Group Databasebeta

← #11747751

Subgroups — #11747751

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×#677C211yesmaximal, characteristic, complemented
2#91434C211yesmaximal, characteristic, complemented
3#91370C211yesmaximal, characteristic, complemented
4C2×#6652C211yesmaximal, characteristic
5#91098C211yesmaximal, characteristic, complemented
6C5×#821C211yesmaximal, characteristic, complemented
7#90970C211yesmaximal, characteristic, complemented
8#65076—31nomaximal, Hall
9C2×C5×D12C2211yescharacteristic
10C2×C3×D20C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C2×D5×Dic3—21no—
13C2×C3×C5×C8C2211yescharacteristic
14C4×Dic15C2211yescharacteristic
15C2×C3⋊#168C2211yescharacteristic
16C5×C4⋊Dic3C2211yescharacteristic
17C3×#677—22no—
18(C2×D3)⋊Dic5—21no—
19(C2×D3)⋊Dic5—21no—
20#6665—21no—
21#6652—22no—
22#5165—51nomaximal, Hall
23#4082—31no—
24C2×#686—31no—
25C2×#677D311yescharacteristic, complemented
26#4039—31no—
27C5×#102—31no—
28#3946—31no—
29#3942—31no—
30C22×C5×D3—21no—
31C22×C3×D5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15D411yescharacteristic
34C2×Dic15D411yescharacteristic
35C2×C5×Dic3—21no—
36C5×D12—21no—
37C5×D12—21no—
38C2×C3×Dic5—21no—
39C3×D20—21no—
40C3×D20D412yes—
41C3×Dic10—21no—
42C3×Dic10—21no—
43D5×Dic3—42no—
44C3×C5×C8—21no—
45C3⋊#168—21no—
46C2×C3×SD16—51no—
47#947—51no—
48D4×Dic3—51no—
49C2×#213—51no—
50#835—51no—
51#821D511yescharacteristic, complemented
52Dic3⋊C8—51no—
53C2×C5×D4—31no—
54C2×D20C2×D311yescharacteristic
55C2×C4×D5—61no—
56C2×Dic10C2×D311yescharacteristic
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4—31no—
59C22⋊Dic5—61no—
60C22⋊Dic5—61no—
61#686—62no—
62#685—61no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—22no—
66#463—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C5×D3—41no—
69C2×C5×D3—41no—
70C2×C5×D3—41no—
71C2×C3×D5—22no—
72C2×C3×D5—41no—
73C2×C3×D5—41no—
74C3×C4×C5C2×D411yescharacteristic
75C3×C4×C5#4111yescharacteristic
76Dic15—21no—
77Dic15—21no—
78C3×Dic5—41no—
79C5×Dic3—41no—
80C2×C3×Q8—51no—
81C2×C3×D4—51no—
82C22×Dic3—101no—
83C2×D12C2×D511yescharacteristic
84C3×SD16—102no—
85C2×C3×C8C2×D511yescharacteristic
86#217—101no—
87#213—102no—
88(C2×D3)⋊C4—101no—
89(C2×D3)⋊C4—101no—
90C4⋊Dic3C2×D511yescharacteristic
91C4×Dic3—51no—
92C2×C3⋊C8—51no—
93C23×C5—61no—
94C22×D5—21no—
95C5×D4—61no—
96C5×D4—61no—
97C2×C4×C5—61no—
98C2×C4×C5C22×D311yescharacteristic
99C2×Dic5—21no—
100C2×Dic5—31no—
101C2×Dic5—31no—
102D20—21no—
103D20#6712yes—
104C4×D5—122no—
105Dic10—21no—
106Dic10—21no—
107C5×C8—21no—
108#168—61no—
109C2×SD16—51no—
110C2×D8—151no—
111#124—151no—
112C4×D4—151no—
113C4⋊C8—151no—
114#103—151no—
115#102—31no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5#13511yescharacteristic
118C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
119C3×D5—42no—
120C5×D3—81no—
121C23×C3—101no—
122C22×D3—21no—
123C3×Q8—101no—
124C3×Q8—101no—
125C3×D4—52no—
126C3×D4—101no—
127C2×C3×C4—101no—
128C2×C3×C4C22×D511yescharacteristic
129C2×Dic3—21no—
130C2×Dic3—51no—
131C2×Dic3—51no—
132C2×Dic3—202no—
133D12—21no—
134D12—21no—
135C3×C8—21no—
136C3⋊C8—101no—
137C22×C5—121no—
138C22×C5—121no—
139C22×C5—121no—
140C22×C5D3×D411yescharacteristic
141C2×D5—22no—
142C2×D5—41no—
143C2×D5—41no—
144C4×C5—121no—
145C4×C5#23711yescharacteristic
146C4×C5C2×#6711yescharacteristic
147Dic5—41no—
148Dic5—61no—
149Dic5—61no—
150C2×Q8—51no—
151C2×D4—31no—
152C2×D4—51no—
153C22×C4—301no—
154SD16—102no—
155D8—302no—
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×C3D4×D511yescharacteristic
168C2×D3—41no—
169C2×D3—41no—
170C2×D3—41no—
171C3×C4—201no—
172C3×C4#70911yescharacteristic
173C3×C4D4×D511yescharacteristic
174Dic3—41no—
175Dic3—101no—
176Dic3—101no—
177C2×C5—241no—
178C2×C5#91411yescharacteristic
179C2×C5#91611yescharacteristic
180C2×C5#93911yescharacteristic
181D5—42no—
182C23—61no—
183C23—101no—
184Q8—101no—
185Q8—101no—
186D4—52no—
187D4—61no—
188D4—61no—
189D4—101no—
190C2×C4—61no—
191C2×C4—101no—
192C2×C4—151no—
193C2×C4—151no—
194C2×C4—602no—
195C2×C4C2×D3×D511yescharacteristic
196C8—21no—
197C8—301no—
198C2×C3—202no—
199C2×C3#403011yescharacteristic
200C2×C3#405711yescharacteristic
201C2×C3#406211yescharacteristic
202D3—81no—
203C5#516511yescharacteristic, complemented, Sylow
204C22—102no—
205C22—121no—
206C22—121no—
207C22—121no—
208C22—201no—
209C22—201no—
210C22#677711yescharacteristic
211C4—121no—
212C4—201no—
213C4—301no—
214C4—301no—
215C4#676511yescharacteristic
216C4D5×#6711yescharacteristic
217C3#6507611yescharacteristic, complemented, Sylow
218C2—202no—
219C2—241no—
220C2#9125711yescharacteristic
221C2#9127611yescharacteristic
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×#6652C2
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
1. C2×C3×#677C2semidirect
2. #91434C2semidirect
3. #91370C2semidirect
5. #91098C2semidirect
6. C5×#821C2semidirect
7. #90970C2semidirect
25. C2×#677D3semidirect
51. #821D5semidirect
163. C3×C5#463semidirect
203. C5#5165semidirect
217. C3#65076semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#6772
#914342
#913702
C2×#66522
#910982
C5×#8212
#909702
#650763
#51655