Finite Group Databasebeta

← #14290978

Subgroups — #14290978

Order 1920.

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

normal subgroups only

This group has 364 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#11756445C211yesmaximal, characteristic, complemented
2C3×C5×#490C211yesmaximal, characteristic
3#11751172C212yesmaximal
4#11746364C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10602043—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9#91779—22no—
10#91778—22no—
11#91778—22no—
12#91759C2212yes—
13C3×C5×#102—22no—
14C3×C5×#97C2211yescharacteristic
15#91116—22no—
16#91116—22no—
17#91087C2212yes—
18#71250—51nomaximal, Hall
19C5⋊#564—31no—
20C5×#490D311yescharacteristic
21#65360—32no—
22#64763—31no—
23#64685—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4—21no—
26C2×C3×C5×C8—21no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4D412yes—
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15D412yes—
32C4⋊Dic15D412yes—
33#6712—22no—
34#6712—22no—
35#6712—22no—
36#6712—22no—
37C4×Dic15—22no—
38C2×C3⋊#168—22no—
39C3⋊#564—51no—
40C3×#490D511yescharacteristic
41#5071—52no—
42#4543—51no—
43#4465—52no—
44C5×#127C2×D311yescharacteristic
45C5×#125C2×D311yescharacteristic
46#4036—62no—
47#4035—62no—
48#4035—62no—
49#4016—32no—
50C5×#102—22no—
51C5×#97C2×D311yescharacteristic
52#3964—62no—
53#3964—62no—
54#3935—32no—
55#1658—151noSylow
56C23×C3×C5—41no—
57C3×C5×D4—44no—
58C3×C5×D4—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D412yes—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×Dic15—22no—
63C2×Dic15—22no—
64C3×C5×C8—41no—
65C3⋊#168—42no—
66C3×#127C2×D511yescharacteristic
67C3×#125C2×D511yescharacteristic
68#890—102no—
69#889—102no—
70#889—102no—
71#870—52no—
72C3×#102—22no—
73C3×#97C2×D511yescharacteristic
74#832—102no—
75#832—102no—
76#803—52no—
77C2×C5×D4—22no—
78C2×C5×D4—21no—
79C2×C5×C8—21no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4#6712yes—
82C42×C5C22×D311yescharacteristic
83C4⋊Dic5—32no—
84C4⋊Dic5—32no—
85C4⋊Dic5—62no—
86#683—62no—
87#683—62no—
88#683—62no—
89#683—62no—
90C4×Dic5—62no—
91C2×#168—62no—
92#564—151no—
93#490—152no—
94#490D1511yescharacteristic
95#330—151no—
96#330—152no—
97C22×C3×C5—81no—
98C22×C3×C5—82no—
99C22×C3×C5#12011yescharacteristic
100C3×C4×C5—22no—
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103Dic15—42no—
104Dic15—42no—
105C2×C3×D4—22no—
106C2×C3×D4—21no—
107C2×C3×C8—21no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4C22⋊D512yes—
110C3×C42C22×D511yescharacteristic
111C4⋊Dic3—52no—
112C4⋊Dic3—52no—
113C4⋊Dic3—102no—
114Dic3⋊C4—102no—
115Dic3⋊C4—102no—
116Dic3⋊C4—102no—
117Dic3⋊C4—102no—
118C4×Dic3—102no—
119C2×C3⋊C8—102no—
120C23×C5—41no—
121C5×D4—44no—
122C5×D4—42no—
123C2×C4×C5—22no—
124C2×C4×C5D3×D412yes—
125C2×C4×C5C2×#6711yescharacteristic
126C2×Dic5—62no—
127C2×Dic5—62no—
128C5×C8—41no—
129#168—122no—
130#127C2×D1511yescharacteristic
131#125—152no—
132#125—302no—
133#125—302no—
134#125—302no—
135#125C2×D1511yescharacteristic
136#102—22no—
137#102—302no—
138#102—302no—
139#97—152no—
140#97C2×D1511yescharacteristic
141C2×C3×C5—161no—
142C2×C3×C5#45411yescharacteristic
143C2×C3×C5#45412yes—
144C23×C3—41no—
145C3×D4—42no—
146C3×D4—44no—
147C2×C3×C4—22no—
148C2×C3×C4D4×D512yes—
149C2×C3×C4C2×C22⋊D511yescharacteristic
150C2×Dic3—102no—
151C2×Dic3—102no—
152C3×C8—41no—
153C3⋊C8—202no—
154C22×C5—82no—
155C22×C5—81no—
156C22×C5#93711yescharacteristic
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—42no—
160Dic5—122no—
161Dic5—122no—
162C2×D4—22no—
163C2×D4—21no—
164C2×C8—21no—
165C2×C8—302no—
166C4⋊C4—22no—
167C4⋊C4—152no—
168C4⋊C4—152no—
169C4⋊C4—302no—
170C4⋊C4—302no—
171C4⋊C4—302no—
172C4⋊C4—302no—
173C4⋊C4—302no—
174C4⋊C4#122012yes—
175C42—302no—
176C42C22×D1511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3—81no—
179C22×C3—82no—
180C22×C3#408311yescharacteristic
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184Dic3—202no—
185Dic3—202no—
186C2×C5—161no—
187C2×C5#506211yescharacteristic
188C2×C5#520112yes—
189C23—41no—
190D4—44no—
191D4—42no—
192C2×C4—22no—
193C2×C4—302no—
194C2×C4—302no—
195C2×C4D4×D1512yes—
196C2×C4C2×#122011yescharacteristic
197C8—41no—
198C8—602no—
199C2×C3—161no—
200C2×C3#6535111yescharacteristic
201C2×C3#6549012yes—
202C5#7125011yescharacteristic, complemented, Sylow
203C22—82no—
204C22—81no—
205C22#9182611yescharacteristic
206C4—22no—
207C4—21no—
208C4—42no—
209C4—602no—
210C4—602no—
211C3#1060204311yescharacteristic, complemented, Sylow
212C2—161no—
213C2#1175116311yescharacteristic
214C2#1175130212yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#490C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenter#490D15
hypocenterC3×C5#1658
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #11756445C2semidirect
4. #11746364C2semidirect
5. #11746286C2semidirect
177. C3×C5#1658semidirect
202. C5#71250semidirect
211. C3#10602043semidirect

Maximal subgroups

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

subgroupindex
#117564452
C3×C5×#4902
#117511722
#117463642
#117462862
#106020433
#712505