Finite Group Databasebeta

← #14291155

Subgroups — #14291155

Order 1920.

392 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 72 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
2C5×#5069C211yesmaximal, characteristic, complemented
3#11746914C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745848C212yesmaximal, complemented
6#10602044—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91785—22no—
9#91784—22no—
10#91783—22no—
11#91764C2212yes—
12C5×#869C2211yescharacteristic
13C5×#810—22no—
14C5×#803C2211yescharacteristic
15C3×#3935C2212yes—
16#90975—22no—
17#90969—22no—
18#68374—51nomaximal, Hall
19#66034—31no—
20C5×#491—31no—
21#65378—32no—
22#64763D311yescharacteristic, complemented
23#64684—32no—
24C2×D60—22no—
25C2×D60D412yes—
26C2×C4×D15—22no—
27C2×Dic30D412yes—
28C2×C5×Dic6—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C42×C5C2311yescharacteristic
32#6714—22no—
33#6714—22no—
34#6714—22no—
35#6712—22no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39#5700—51no—
40#5069D511yescharacteristic, complemented
41#4714—52no—
42C3×#330—51no—
43#4464—52no—
44C5×C4⋊Q8—31no—
45C5×#125C2×D311yescharacteristic
46#4042—62no—
47#4041—62no—
48#4040—62no—
49#4021—32no—
50C5×#103—62no—
51C5×#97—31no—
52#3942—62no—
53#3941—62no—
54#3935C2×D312yes—
55#1662—151noSylow
56C22×D15—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×Dic15—22no—
61D60—42no—
62D60—82no—
63C4×D15—82no—
64Dic30—42no—
65C2×C5×Dic3—41no—
66C5×Dic6—42no—
67C3×#168—42no—
68C5×C3⋊C8—41no—
69C3×#125C2×D511yescharacteristic
70#896—102no—
71#895—102no—
72#894—102no—
73#875—52no—
74#869C2×D511yescharacteristic
75C3×#97—52no—
76#821—102no—
77#816—102no—
78#810—22no—
79#803C2×D511yescharacteristic
80C2×C5×Q8—61no—
81C2×D20—32no—
82C2×D20—62no—
83C2×C4×D5—62no—
84C2×Dic10—32no—
85C2×C5×C8—61no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—62no—
88C5×C4⋊C4D1212yes—
89C42×C5C22×D311yescharacteristic
90#685—62no—
91#685—62no—
92#685—62no—
93#683—62no—
94C2×#168—22no—
95#562—151no—
96#491—31no—
97#489—152no—
98#330—51no—
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—
108C5×Dic3—81no—
109C2×D12—52no—
110C2×D12—102no—
111C2×C4×D3—102no—
112C2×Dic6—21no—
113C2×Dic6—52no—
114C2×C3×C8—102no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4C22⋊D512yes—
117C3×C42C22×D511yescharacteristic
118(C2×D3)⋊C4—102no—
119(C2×D3)⋊C4—102no—
120(C2×D3)⋊C4—102no—
121C4⋊Dic3—22no—
122Dic3⋊C4—102no—
123C2×C3⋊C8—21no—
124C22×D5—62no—
125C5×Q8—122no—
126C2×C4×C5—22no—
127C2×C4×C5—121no—
128C2×C4×C5C2×D1211yescharacteristic
129C2×C4×C5D3×D412yes—
130C2×Dic5—62no—
131D20—122no—
132D20—242no—
133C4×D5—242no—
134Dic10—122no—
135C5×C8—121no—
136#168—42no—
137C4⋊Q8—31no—
138#125D3×D511yescharacteristic
139#124—152no—
140#123—302no—
141C22⋊Q8—302no—
142#121—302no—
143#103—62no—
144#103—302no—
145#102—302no—
146#97—31no—
147#97—52no—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150D15—82no—
151C22×D3—102no—
152C2×C3×C4—22no—
153C2×C3×C4D4×D512yes—
154C2×C3×C4C2×C22⋊D511yescharacteristic
155C2×Dic3—41no—
156C2×Dic3—102no—
157D12—202no—
158D12—402no—
159C4×D3—402no—
160Dic6—42no—
161Dic6—202no—
162C3×C8—202no—
163C3⋊C8—41no—
164C22×C5#88211yescharacteristic
165C2×D5—122no—
166C2×D5—122no—
167C2×D5—122no—
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171C4×C5—241no—
172Dic5—122no—
173C2×Q8—61no—
174C2×Q8—152no—
175C2×D4—152no—
176C2×D4—302no—
177C22×C4—302no—
178C2×C8—61no—
179C2×C8—102no—
180C4⋊C4—22no—
181C4⋊C4—62no—
182C4⋊C4—302no—
183C4⋊C4#120312yes—
184C22⋊C4—302no—
185C22⋊C4—302no—
186C22⋊C4—302no—
187C42C2×D3×D511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3#408311yescharacteristic
190C2×D3—202no—
191C2×D3—202no—
192C2×D3—202no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196Dic3—81no—
197Dic3—202no—
198C2×C5#475311yescharacteristic
199C2×C5#482512yes—
200D5—242no—
201C23—302no—
202Q8—122no—
203Q8—602no—
204D4—602no—
205D4—1202no—
206C2×C4—22no—
207C2×C4—121no—
208C2×C4—302no—
209C2×C4—1202no—
210C2×C4C2×#120311yescharacteristic
211C2×C4#679012yes—
212C8—121no—
213C8—202no—
214C2×C3#6535111yescharacteristic
215C2×C3#6549112yes—
216D3—402no—
217C5#6837411yescharacteristic, complemented, Sylow
218C22—602no—
219C22—602no—
220C22—602no—
221C22#9157311yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—241no—
226C4—602no—
227C3#1060204411yescharacteristic, complemented, Sylow
228C2—1202no—
229C2#1174938911yescharacteristic
230C2#1174946812yes—
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radical#11756459C2
hypercenter#125D3×D5
hypocenterC3×C5#1662
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C5×#5069C2semidirect
3. #11746914C2semidirect
4. C3×#64763C2semidirect
5. #11745848C2semidirect
22. #64763D3semidirect
40. #5069D5semidirect
188. C3×C5#1662semidirect
217. C5#68374semidirect
227. C3#10602044semidirect

Maximal subgroups

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

subgroupindex
#117564592
C5×#50692
#117469142
C3×#647632
#117458482
#106020443
#683745