Finite Group Databasebeta

← #14291159

Subgroups — #14291159

Order 1920.

392 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#66034C211yesmaximal, characteristic
2#11751170C211yesmaximal, characteristic, complemented
3#11746893C212yesmaximal, complemented
4C5×#4543C211yesmaximal, characteristic, complemented
5#11745846C212yesmaximal, complemented
6#10599167—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91758C2211yescharacteristic
9C3×#4042—22no—
10C3×#4041—22no—
11C3×#4040—22no—
12C3×#4021C2212yes—
13#91094—22no—
14#91087C2211yescharacteristic
15C5×#803C2212yes—
16#90971—22no—
17#90965—22no—
18#71954—51nomaximal, Hall
19#66034D311yescharacteristic
20#65358—31no—
21#65003—32no—
22C5×#330—31no—
23#64684—32no—
24C2×Dic30—21no—
25C2×C3×D20—22no—
26C2×C3×D20D412yes—
27C2×C3×C4×D5—22no—
28C2×C3×Dic10D412yes—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C42×C5C2311yescharacteristic
32C4⋊Dic15—22no—
33C2×C3⋊#168—21no—
34C2×C5×C3⋊C8—22no—
35C3×#685—22no—
36C3×#685—22no—
37C3×#685—22no—
38C3×#683—22no—
39C3×#562—51no—
40#5069—51no—
41#5055—52no—
42#4543D511yescharacteristic, complemented
43#4540—52no—
44C5×#125C2×D311yescharacteristic
45#4042—22no—
46#4041—22no—
47#4040—22no—
48#4021C2×D312yes—
49#4015—31no—
50C5×#97—32no—
51#3953—62no—
52#3948—62no—
53#3942—62no—
54#3935—31no—
55#1662—151noSylow
56C22×C3×D5—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—41no—
61Dic30—42no—
62C2×C3×Dic5—22no—
63C3×D20—42no—
64C3×D20—82no—
65C3×C4×D5—82no—
66C3×Dic10—42no—
67C3⋊#168—41no—
68C5×C3⋊C8—42no—
69C3×#125C2×D511yescharacteristic
70C3×#124—52no—
71C3×#123—102no—
72C3×C22⋊Q8—102no—
73C3×#121—102no—
74#869—51no—
75#835—102no—
76#832—102no—
77#810—102no—
78#803—51no—
79#803C2×D512yes—
80C2×D20—22no—
81C2×D20#6712yes—
82C2×C4×D5—22no—
83C2×Dic10—61no—
84C2×Dic10#6712yes—
85C2×C5×C8—62no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4#6712yes—
88C42×C5C22×D311yescharacteristic
89#685—22no—
90#685—22no—
91#685—22no—
92C4⋊Dic5—62no—
93#683—22no—
94C2×#168—61no—
95#562—51no—
96#491—151no—
97#489—152no—
98#330—31no—
99#329—152no—
100C22×C3×C5#12011yescharacteristic
101C2×C3×D5—42no—
102C2×C3×D5—42no—
103C2×C3×D5—42no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107Dic15—81no—
108C3×Dic5—42no—
109C2×C3×Q8—52no—
110C2×C3×D4—52no—
111C2×C3×D4—102no—
112C22×C3×C4—102no—
113C2×Dic6—101no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—102no—
116C3×C4⋊C4D2012yes—
117C3×C22⋊C4—102no—
118C3×C22⋊C4—102no—
119C3×C22⋊C4—102no—
120C3×C42C22×D511yescharacteristic
121C4⋊Dic3—102no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8—101no—
124C22×D5—22no—
125C2×C4×C5—22no—
126C2×C4×C5C2×#6711yescharacteristic
127C2×C4×C5C2×#6712yes—
128C2×Dic5—22no—
129C2×Dic5—121no—
130D20—42no—
131D20—82no—
132C4×D5—82no—
133Dic10—42no—
134Dic10—122no—
135C5×C8—122no—
136#168—121no—
137C4⋊Q8—151no—
138#125D3×D511yescharacteristic
139#124—52no—
140#123—102no—
141C22⋊Q8—102no—
142#121—102no—
143#103—302no—
144#103—302no—
145#102—302no—
146#97—32no—
147#97—151no—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150C3×D5—82no—
151C23×C3—102no—
152C3×Q8—202no—
153C3×D4—202no—
154C3×D4—402no—
155C2×C3×C4—22no—
156C2×C3×C4—102no—
157C2×C3×C4—402no—
158C2×C3×C4C2×D2011yescharacteristic
159C2×C3×C4D4×D512yes—
160C2×Dic3—201no—
161Dic6—202no—
162C3⋊C8—42no—
163C3⋊C8—201no—
164C22×C5#95311yescharacteristic
165C2×D5—42no—
166C2×D5—42no—
167C2×D5—42no—
168C4×C5—22no—
169C4×C5—21no—
170C4×C5—42no—
171Dic5—42no—
172Dic5—241no—
173C2×Q8—52no—
174C2×Q8—301no—
175C2×D4—52no—
176C2×D4—102no—
177C22×C4—102no—
178C2×C8—62no—
179C2×C8—301no—
180C4⋊C4—22no—
181C4⋊C4—102no—
182C4⋊C4—302no—
183C4⋊C4#120212yes—
184C22⋊C4—102no—
185C22⋊C4—102no—
186C22⋊C4—102no—
187C42C2×D3×D511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3—202no—
190C22×C3—202no—
191C22×C3—202no—
192C22×C3#402811yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—202no—
197Dic3—401no—
198C2×C5#524212yes—
199C2×C5#524511yescharacteristic
200D5—82no—
201C23—102no—
202Q8—202no—
203Q8—602no—
204D4—202no—
205D4—402no—
206C2×C4—22no—
207C2×C4—102no—
208C2×C4—402no—
209C2×C4—601no—
210C2×C4C2×#120211yescharacteristic
211C2×C4D5×#6712yes—
212C8—122no—
213C8—601no—
214C2×C3—402no—
215C2×C3#6504211yescharacteristic
216C2×C3#6511412yes—
217C5#7195411yescharacteristic, complemented, Sylow
218C22—202no—
219C22—202no—
220C22—202no—
221C22#9156411yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—202no—
226C4—1201no—
227C3#1059916711yescharacteristic, complemented, Sylow
228C2—402no—
229C2#1174938411yescharacteristic
230C2#1174946312yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC3×#66034C2
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. #11751170C2semidirect
3. #11746893C2semidirect
4. C5×#4543C2semidirect
5. #11745846C2semidirect
42. #4543D5semidirect
188. C3×C5#1662semidirect
217. C5#71954semidirect
227. C3#10599167semidirect

Maximal subgroups

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

subgroupindex
C3×#660342
#117511702
#117468932
C5×#45432
#117458462
#105991673
#719545