Finite Group Databasebeta

← #14291197

Subgroups — #14291197

Order 1920.

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

normal subgroups only

This group has 344 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
2C3×#65358C211yesmaximal, characteristic
3#11746952C212yesmaximal
4C5×#4543C211yesmaximal, characteristic
5#11745851C212yesmaximal
6#10599170—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91779—22no—
9#91778—22no—
10#91778—22no—
11#91759C2212yes—
12C3×#4015C2211yescharacteristic
13C5×#803C2212yes—
14C3×#3942—22no—
15C3×#3935C2211yescharacteristic
16#90990—22no—
17#90987—22no—
18#71252—51nomaximal, Hall
19C5⋊#564—31no—
20#65358D311yescharacteristic
21#64991—32no—
22C5×#330—31no—
23#64685—32no—
24C2×C3×Dic10—21no—
25C3×C5×C4⋊C4—22no—
26C3×C5×C4⋊C4D412yes—
27C3×C42×C5C2311yescharacteristic
28C4⋊Dic15—22no—
29C4⋊Dic15D412yes—
30C4⋊Dic15D412yes—
31#6712—22no—
32#6712—22no—
33#6712—22no—
34#6712—22no—
35C4×Dic15—22no—
36C2×C5×C3⋊C8—22no—
37C3×C4⋊Dic5—22no—
38C2×C3×#168—21no—
39C3⋊#564—51no—
40C3×#491—51no—
41#5081—52no—
42#4543D511yescharacteristic
43#4465—52no—
44C5×#125C2×D311yescharacteristic
45#4036—62no—
46#4035—62no—
47#4035—62no—
48#4016—32no—
49#4015C2×D311yescharacteristic
50C5×#97—32no—
51#3950—62no—
52#3949—62no—
53#3942—22no—
54#3935C2×D311yescharacteristic
55#1663—151noSylow
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5C2×D411yescharacteristic
58C2×C3×C4×C5C2×D412yes—
59C2×Dic15—22no—
60C2×Dic15—22no—
61C2×C3×Dic5—41no—
62C3×Dic10—42no—
63C3×#168—41no—
64C5×C3⋊C8—24no—
65C3×C4⋊Q8—51no—
66C3×#125C2×D511yescharacteristic
67#890—102no—
68#889—102no—
69#889—102no—
70#870—52no—
71C3×#103—102no—
72C3×#97—51no—
73#808—102no—
74#807—102no—
75#803C2×D512yes—
76C2×Dic10—21no—
77C2×C5×C8—62no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4#6712yes—
80C42×C5C22×D311yescharacteristic
81C4⋊Dic5—22no—
82C4⋊Dic5—32no—
83C4⋊Dic5—32no—
84C4⋊Dic5—62no—
85#683—62no—
86#683—62no—
87#683—62no—
88#683—62no—
89C4×Dic5—62no—
90C2×#168—21no—
91#564—151no—
92#501—152no—
93#491—51no—
94#330—31no—
95#330—152no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100Dic15—42no—
101Dic15—42no—
102C3×Dic5—81no—
103C2×C3×Q8—101no—
104C2×C3×C8—101no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—102no—
107C3×C4⋊C4D2012yes—
108C3×C42C22×D511yescharacteristic
109C4⋊Dic3—52no—
110C4⋊Dic3—52no—
111C4⋊Dic3—102no—
112Dic3⋊C4—102no—
113Dic3⋊C4—102no—
114Dic3⋊C4—102no—
115Dic3⋊C4—102no—
116C4×Dic3—102no—
117C2×C3⋊C8—22no—
118C2×C4×C5—22no—
119C2×C4×C5D3×D412yes—
120C2×C4×C5C2×#6711yescharacteristic
121C2×Dic5—41no—
122C2×Dic5—62no—
123C2×Dic5—62no—
124Dic10—42no—
125C5×C8—64no—
126#168—41no—
127C4⋊Q8—51no—
128#125—152no—
129#125—302no—
130#125—302no—
131#125—302no—
132#125D3×D511yescharacteristic
133#107—302no—
134#106—302no—
135#103—102no—
136#97—32no—
137#97—51no—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C3×Q8—202no—
141C2×C3×C4—22no—
142C2×C3×C4—201no—
143C2×C3×C4C2×D2011yescharacteristic
144C2×C3×C4D4×D512yes—
145C2×Dic3—102no—
146C2×Dic3—102no—
147C3×C8—201no—
148C3⋊C8—24no—
149C22×C5#93711yescharacteristic
150C4×C5—22no—
151C4×C5—21no—
152C4×C5—42no—
153Dic5—81no—
154Dic5—122no—
155Dic5—122no—
156C2×Q8—101no—
157C2×C8—62no—
158C2×C8—101no—
159C4⋊C4—22no—
160C4⋊C4—102no—
161C4⋊C4—152no—
162C4⋊C4—152no—
163C4⋊C4—302no—
164C4⋊C4—302no—
165C4⋊C4—302no—
166C4⋊C4—302no—
167C4⋊C4—302no—
168C4⋊C4#120212yes—
169C42—302no—
170C42C2×D3×D511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#402811yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—401no—
177Dic3—202no—
178Dic3—202no—
179C2×C5#506211yescharacteristic
180C2×C5#520512yes—
181Q8—202no—
182C2×C4—22no—
183C2×C4—201no—
184C2×C4—302no—
185C2×C4—302no—
186C2×C4C2×#120211yescharacteristic
187C2×C4#679012yes—
188C8—64no—
189C8—201no—
190C2×C3#6504211yescharacteristic
191C2×C3#6511512yes—
192C5#7125211yescharacteristic, complemented, Sylow
193C22#9157211yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—401no—
198C4—602no—
199C4—602no—
200C3#1059917011yescharacteristic, complemented, Sylow
201C2#1174938811yescharacteristic
202C2#1174942412yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socle, prime radicalC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1663
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
171. C3×C5#1663semidirect
192. C5#71252semidirect
200. C3#10599170semidirect

Maximal subgroups

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

subgroupindex
#117564452
C3×#653582
#117469522
C5×#45432
#117458512
#105991703
#712525