Finite Group Databasebeta

← #14290990

Subgroups — #14290990

Order 1920.

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

normal subgroups only

This group has 364 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#11756445C211yesmaximal, characteristic, complemented
2C3×#65356C211yesmaximal, characteristic
3#11746892C212yesmaximal
4C5×#4543C211yesmaximal, characteristic, complemented
5#11745851C212yesmaximal, complemented
6#10599168—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91779—22no—
9#91778—22no—
10#91778—22no—
11#91759C2212yes—
12C3×#4020C2211yescharacteristic
13C5×#803C2212yes—
14C3×#3941—22no—
15C3×#3935C2211yescharacteristic
16#90965—22no—
17#90965—22no—
18#71250—51nomaximal, Hall
19C5⋊#564—31no—
20#65356D311yescharacteristic
21#65002—32no—
22C5×#330—31no—
23#64685—32no—
24C2×C3×D20—22no—
25C2×C3×D20—21no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4D412yes—
28C3×C42×C5C2311yescharacteristic
29C4⋊Dic15—22no—
30C4⋊Dic15D412yes—
31C4⋊Dic15D412yes—
32#6712—22no—
33#6712—22no—
34#6712—22no—
35#6712—22no—
36C4×Dic15—22no—
37C2×C5×C3⋊C8—22no—
38C2×C3×#168—21no—
39C3⋊#564—51no—
40C3×#490—51no—
41#5071—52no—
42#4543D511yescharacteristic, complemented
43#4465—52no—
44C5×#125C2×D311yescharacteristic
45#4036—62no—
46#4035—62no—
47#4035—62no—
48#4020C2×D311yescharacteristic
49#4016—32no—
50C5×#97—32no—
51#3953—62no—
52#3953—62no—
53#3941—22no—
54#3935C2×D311yescharacteristic
55#1658—151noSylow
56C22×C3×D5—41no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—22no—
61C2×Dic15—22no—
62C3×D20—44no—
63C3×D20—42no—
64C3×#168—41no—
65C5×C3⋊C8—42no—
66C3×#127—51no—
67C3×#125C2×D511yescharacteristic
68#890—102no—
69#889—102no—
70#889—102no—
71#870—52no—
72C3×#102—102no—
73C3×#97—51no—
74#832—102no—
75#832—102no—
76#803C2×D512yes—
77C2×D20—22no—
78C2×D20—21no—
79C2×C5×C8—62no—
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—21no—
92#564—151no—
93#490—51no—
94#490—152no—
95#330—31no—
96#330—152no—
97C22×C3×C5#12011yescharacteristic
98C2×C3×D5—81no—
99C2×C3×D5—82no—
100C3×C4×C5—22no—
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103Dic15—42no—
104Dic15—42no—
105C2×C3×D4—101no—
106C2×C3×D4—102no—
107C2×C3×C8—101no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4D2012yes—
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—22no—
120C22×D5—41no—
121C2×C4×C5—22no—
122C2×C4×C5D3×D412yes—
123C2×C4×C5C2×#6711yescharacteristic
124C2×Dic5—62no—
125C2×Dic5—62no—
126D20—44no—
127D20—42no—
128C5×C8—122no—
129#168—41no—
130#127—51no—
131#125—152no—
132#125—302no—
133#125—302no—
134#125—302no—
135#125D3×D511yescharacteristic
136#102—102no—
137#102—302no—
138#102—302no—
139#97—32no—
140#97—51no—
141C2×C3×C5#45411yescharacteristic
142C2×C3×C5#45412yes—
143C3×D5—161no—
144C23×C3—201no—
145C3×D4—202no—
146C3×D4—204no—
147C2×C3×C4—22no—
148C2×C3×C4C2×D2011yescharacteristic
149C2×C3×C4D4×D512yes—
150C2×Dic3—102no—
151C2×Dic3—102no—
152C3×C8—201no—
153C3⋊C8—42no—
154C22×C5#93711yescharacteristic
155C2×D5—82no—
156C2×D5—81no—
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—42no—
160Dic5—122no—
161Dic5—122no—
162C2×D4—101no—
163C2×D4—102no—
164C2×C8—62no—
165C2×C8—101no—
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#120212yes—
175C42—302no—
176C42C2×D3×D511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3—401no—
179C22×C3—402no—
180C22×C3#402811yescharacteristic
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184Dic3—202no—
185Dic3—202no—
186C2×C5#506211yescharacteristic
187C2×C5#520112yes—
188D5—161no—
189C23—201no—
190D4—202no—
191D4—204no—
192C2×C4—22no—
193C2×C4—302no—
194C2×C4—302no—
195C2×C4C2×#120211yescharacteristic
196C2×C4#679012yes—
197C8—122no—
198C8—201no—
199C2×C3—801no—
200C2×C3#6504211yescharacteristic
201C2×C3#6511612yes—
202C5#7125011yescharacteristic, complemented, Sylow
203C22—401no—
204C22—402no—
205C22#9157211yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—602no—
210C4—602no—
211C3#1059916811yescharacteristic, complemented, Sylow
212C2—801no—
213C2#1174938811yescharacteristic
214C2#1174946012yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenter#125D3×D5
hypocenterC3×C5#1658
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
1. #11756445C2semidirect
4. C5×#4543C2semidirect
5. #11745851C2semidirect
42. #4543D5semidirect
177. C3×C5#1658semidirect
202. C5#71250semidirect
211. C3#10599168semidirect

Maximal subgroups

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

subgroupindex
#117564452
C3×#653562
#117468922
C5×#45432
#117458512
#105991683
#712505