Finite Group Databasebeta

← #14291147

Subgroups — #14291147

Order 1920.

392 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 75 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
1#11756459C211yesmaximal, characteristic
2#11751170C211yesmaximal, characteristic, complemented
3#11750815C212yesmaximal, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5#11746285C212yesmaximal, complemented
6#10599167—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91785—22no—
9#91784—22no—
10#91783—22no—
11#91764C2212yes—
12#91758C2211yescharacteristic
13C3×C5×#97C2212yes—
14#91105—22no—
15#91100—22no—
16#91094—22no—
17#91087C2211yescharacteristic
18#68374—51nomaximal, Hall
19#66034—31no—
20#65358—31no—
21#65003—32no—
22C5×#330D311yescharacteristic, complemented
23#64684—32no—
24C2×D60—22no—
25C2×D60D412yes—
26C2×C4×D15—22no—
27C2×Dic30—21no—
28C2×Dic30D412yes—
29C2×C3×C5×C8—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5C2311yescharacteristic
33#6714—22no—
34#6714—22no—
35#6714—22no—
36C4⋊Dic15—22no—
37#6712—22no—
38C2×C3⋊#168—21no—
39#5700—51no—
40#5069—51no—
41#4714—52no—
42C3×#330D511yescharacteristic, complemented
43#4464—52no—
44C5×#125C2×D311yescharacteristic
45#4042—62no—
46#4041—62no—
47#4040—62no—
48#4021—32no—
49#4015—31no—
50C5×#97C2×D312yes—
51#3953—62no—
52#3948—62no—
53#3942—62no—
54#3935—31no—
55#1662—151noSylow
56C22×D15—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—22no—
61C2×Dic15—41no—
62D60—42no—
63D60—82no—
64C4×D15—82no—
65Dic30—42no—
66Dic30—42no—
67C3×C5×C8—42no—
68C3⋊#168—41no—
69C3×#125C2×D511yescharacteristic
70#896—102no—
71#895—102no—
72#894—102no—
73#875—52no—
74#869—51no—
75C3×#97C2×D512yes—
76#821—102no—
77#816—102no—
78#810—102no—
79#803—51no—
80C2×D20—32no—
81C2×D20—62no—
82C2×C4×D5—62no—
83C2×Dic10—32no—
84C2×Dic10—61no—
85C2×C5×C8—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4D1212yes—
88C42×C5C22×D311yescharacteristic
89#685—62no—
90#685—62no—
91#685—62no—
92C4⋊Dic5—62no—
93#683—62no—
94C2×#168—61no—
95#562—151no—
96#491—151no—
97#489—152no—
98#330D1511yescharacteristic, complemented
99#329—152no—
100C22×C3×C5#12011yescharacteristic
101C2×D15—42no—
102C2×D15—42no—
103C2×D15—42no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107Dic15—42no—
108Dic15—81no—
109C2×D12—52no—
110C2×D12—102no—
111C2×C4×D3—102no—
112C2×Dic6—52no—
113C2×Dic6—101no—
114C2×C3×C8—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4D2012yes—
117C3×C42C22×D511yescharacteristic
118(C2×D3)⋊C4—102no—
119(C2×D3)⋊C4—102no—
120(C2×D3)⋊C4—102no—
121C4⋊Dic3—102no—
122Dic3⋊C4—102no—
123C2×C3⋊C8—101no—
124C22×D5—62no—
125C2×C4×C5—22no—
126C2×C4×C5C2×D1211yescharacteristic
127C2×C4×C5D3×D412yes—
128C2×Dic5—62no—
129C2×Dic5—121no—
130D20—122no—
131D20—242no—
132C4×D5—242no—
133Dic10—122no—
134Dic10—122no—
135C5×C8—42no—
136#168—121no—
137C4⋊Q8—151no—
138#125C2×D1511yescharacteristic
139#124—152no—
140#123—302no—
141C22⋊Q8—302no—
142#121—302no—
143#103—302no—
144#103—302no—
145#102—302no—
146#97—151no—
147#97C2×D1512yes—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150D15—82no—
151C22×D3—102no—
152C2×C3×C4—22no—
153C2×C3×C4C2×D2011yescharacteristic
154C2×C3×C4D4×D512yes—
155C2×Dic3—102no—
156C2×Dic3—201no—
157D12—202no—
158D12—402no—
159C4×D3—402no—
160Dic6—202no—
161Dic6—202no—
162C3×C8—42no—
163C3⋊C8—201no—
164C22×C5#88211yescharacteristic
165C2×D5—122no—
166C2×D5—122no—
167C2×D5—122no—
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171Dic5—122no—
172Dic5—241no—
173C2×Q8—152no—
174C2×Q8—301no—
175C2×D4—152no—
176C2×D4—302no—
177C22×C4—302no—
178C2×C8—22no—
179C2×C8—301no—
180C4⋊C4—22no—
181C4⋊C4—302no—
182C4⋊C4—302no—
183C4⋊C4D6012yes—
184C22⋊C4—302no—
185C22⋊C4—302no—
186C22⋊C4—302no—
187C42C22×D1511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3#402811yescharacteristic
190C2×D3—202no—
191C2×D3—202no—
192C2×D3—202no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196Dic3—202no—
197Dic3—401no—
198C2×C5#475311yescharacteristic
199C2×C5#482512yes—
200D5—242no—
201C23—302no—
202Q8—602no—
203Q8—602no—
204D4—602no—
205D4—1202no—
206C2×C4—22no—
207C2×C4—302no—
208C2×C4—601no—
209C2×C4—1202no—
210C2×C4C2×D6011yescharacteristic
211C2×C4D4×D1512yes—
212C8—42no—
213C8—601no—
214C2×C3#6504211yescharacteristic
215C2×C3#6511412yes—
216D3—402no—
217C5#6837411yescharacteristic, complemented, Sylow
218C22—602no—
219C22—602no—
220C22—602no—
221C22#9177111yescharacteristic
222C4—22no—
223C4—21no—
224C4—42no—
225C4—602no—
226C4—1201no—
227C3#1059916711yescharacteristic, complemented, Sylow
228C2—1202no—
229C2#1175085411yescharacteristic
230C2#1175092612yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5#120
prime radical#11756459C2
hypercenter#330D15
hypocenterC3×C5#1662
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11751170C2semidirect
3. #11750815C2semidirect
4. C3×C5×#330C2semidirect
5. #11746285C2semidirect
22. C5×#330D3semidirect
42. C3×#330D5semidirect
98. #330D15semidirect
188. C3×C5#1662semidirect
217. C5#68374semidirect
227. C3#10599167semidirect

Maximal subgroups

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

subgroupindex
#117564592
#117511702
#117508152
C3×C5×#3302
#117462852
#105991673
#683745