Finite Group Databasebeta

← #11747977

Subgroups — #11747977

Order 960.

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

normal subgroups only

This group has 260 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
1C2×C5×#204C211yesmaximal, characteristic, complemented
2C2×C3×#677C211yesmaximal, characteristic, complemented
3#91370C211yesmaximal, characteristic, complemented
4#91368C211yesmaximal, characteristic, complemented
5C2×#6661C211yesmaximal, characteristic, complemented
6C2×#6652C211yesmaximal, characteristic
7C8×Dic15C211yesmaximal, characteristic, complemented
8#65457—31nomaximal, Hall
9C2×C5×D12C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C2×C3×Dic10C2211yescharacteristic
13C2×C3×C5×C8C2211yescharacteristic
14C4×Dic15C2211yescharacteristic
15C2×C3⋊#168C2211yescharacteristic
16C5×#204—22no—
17C3×#677—22no—
18(C2×D3)⋊Dic5—22no—
19#6665—22no—
20#6661—22no—
21#6652—22no—
22#5168—51nomaximal, Hall
23C2×C5×SD16—31no—
24#4093—31no—
25C2×#689—31no—
26#4082—31no—
27C2×#686—31no—
28C2×#677D311yescharacteristic, complemented
29C8×Dic5—31no—
30C22×C5×D3—21no—
31C22×C3×D5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15D412yes—
34C2×C5×Dic3—21no—
35C5×D12—21no—
36C5×D12—21no—
37C5×Dic6—21no—
38C5×Dic6—21no—
39C2×C3×Dic5—21no—
40C3×D20—21no—
41C3×D20—21no—
42C3×Dic10—21no—
43C3×Dic10—21no—
44C3×C5×C8D412yes—
45C3⋊#168D412yes—
46C2×C3×SD16—51no—
47#947—51no—
48C2×#216—51no—
49#936—51no—
50C2×#213—51no—
51C2×#204D511yescharacteristic, complemented
52C8×Dic3—51no—
53C2×C5×Q8—31no—
54C2×C5×D4—31no—
55C2×D20C2×D311yescharacteristic
56C2×Dic10C2×D311yescharacteristic
57C5×SD16—62no—
58C2×C5×C8C2×D311yescharacteristic
59C22⋊Dic5—62no—
60#689—62no—
61#686—62no—
62#685—62no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—22no—
66#495—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C5×D3—41no—
69C2×C5×D3—42no—
70C2×C3×D5—41no—
71C2×C3×D5—42no—
72C3×C4×C5C2×D411yescharacteristic
73C3×C4×C5C2×D411yescharacteristic
74Dic15—22no—
75C3×Dic5—41no—
76C5×Dic3—41no—
77C2×C3×Q8—51no—
78C2×C3×D4—51no—
79C2×D12C2×D511yescharacteristic
80C2×Dic6C2×D511yescharacteristic
81C3×SD16—102no—
82C2×C3×C8C2×D511yescharacteristic
83#217—102no—
84#216—102no—
85#213—102no—
86(C2×D3)⋊C4—102no—
87C4×Dic3—51no—
88C2×C3⋊C8—51no—
89#204—22no—
90C23×C5—61no—
91C22×D5—21no—
92C5×Q8—61no—
93C5×Q8—61no—
94C5×D4—61no—
95C5×D4—61no—
96C2×C4×C5—61no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—21no—
99C2×Dic5—32no—
100D20—21no—
101D20—21no—
102Dic10—21no—
103Dic10—21no—
104C5×C8#6712yes—
105#168—32no—
106C2×Q16—151no—
107C2×SD16—31no—
108C2×SD16—51no—
109C2×D8—151no—
110#124—151no—
111#124—151no—
112C4×C8—151no—
113C2×C3×C5#12711yescharacteristic
114C2×C3×C5#13512yes—
115C3×D5—81no—
116C5×D3—81no—
117C23×C3—101no—
118C22×D3—21no—
119C3×Q8—101no—
120C3×Q8—101no—
121C3×D4—101no—
122C3×D4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22×D511yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—52no—
127D12—21no—
128D12—21no—
129Dic6—21no—
130Dic6—21no—
131C3×C8C22⋊D512yes—
132C3⋊C8—52no—
133C22×C5—122no—
134C22×C5—121no—
135C22×C5D3×D411yescharacteristic
136C2×D5—42no—
137C2×D5—41no—
138C4×C5—121no—
139C4×C5D3×D411yescharacteristic
140C4×C5C2×#6711yescharacteristic
141Dic5—41no—
142Dic5—62no—
143C2×Q8—31no—
144C2×Q8—51no—
145C2×D4—31no—
146C2×D4—51no—
147Q16—302no—
148SD16—62no—
149SD16—102no—
150D8—302no—
151C2×C8—151no—
152C2×C8D3×D511yescharacteristic
153C22⋊C4—302no—
154C22⋊C4—302no—
155C42—151no—
156C3×C5#49511yescharacteristic, complemented, Hall
157C22×C3—202no—
158C22×C3—201no—
159C22×C3D4×D511yescharacteristic
160C2×D3—42no—
161C2×D3—41no—
162C3×C4—201no—
163C3×C4D4×D511yescharacteristic
164C3×C4C2×C22⋊D511yescharacteristic
165Dic3—41no—
166Dic3—102no—
167C2×C5—241no—
168C2×C5#91612yes—
169C2×C5#94011yescharacteristic
170D5—81no—
171C23—61no—
172C23—101no—
173Q8—61no—
174Q8—61no—
175Q8—101no—
176Q8—101no—
177D4—61no—
178D4—61no—
179D4—101no—
180D4—101no—
181C2×C4—61no—
182C2×C4—101no—
183C2×C4—152no—
184C2×C4C2×D3×D511yescharacteristic
185C8—152no—
186C8#120112yes—
187C2×C3—401no—
188C2×C3#406212yes—
189C2×C3#408611yescharacteristic
190D3—81no—
191C5#516811yescharacteristic, complemented, Sylow
192C22—121no—
193C22—122no—
194C22—201no—
195C22—202no—
196C22#677711yescharacteristic
197C4—121no—
198C4—201no—
199C4—302no—
200C4#677711yescharacteristic
201C4C2×#120111yescharacteristic
202C3#6545711yescharacteristic, complemented, Sylow
203C2—241no—
204C2—401no—
205C2#9127612yes—
206C2#9146311yescharacteristic
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#495
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×C5×#204C2semidirect
2. C2×C3×#677C2semidirect
3. #91370C2semidirect
4. #91368C2semidirect
5. C2×#6661C2semidirect
7. C8×Dic15C2semidirect
28. C2×#677D3semidirect
51. C2×#204D5semidirect
156. C3×C5#495semidirect
191. C5#5168semidirect
202. C3#65457semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#2042
C2×C3×#6772
#913702
#913682
C2×#66612
C2×#66522
C8×Dic152
#654573
#51685