Finite Group Databasebeta

← #14291186

Subgroups — #14291186

Order 1920.

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

normal subgroups only

This group has 344 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
2#11751170C211yesmaximal, characteristic
3#11750803C212yesmaximal
4C3×C5×#330C211yesmaximal, characteristic
5#11746286C212yesmaximal
6#10599170—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91779—22no—
9#91778—22no—
10#91778—22no—
11#91759C2212yes—
12#91758C2211yescharacteristic
13C3×C5×#97C2212yes—
14#91102—22no—
15#91101—22no—
16#91094—22no—
17#91087C2211yescharacteristic
18#68377—51nomaximal, Hall
19C5⋊#564—31no—
20#65358—31no—
21#64991—32no—
22C5×#330D311yescharacteristic
23#64685—32no—
24C2×Dic30—21no—
25C2×C3×C5×C8—22no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4D412yes—
28C3×C42×C5C2311yescharacteristic
29C4⋊Dic15—22no—
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—21no—
39C3⋊#564—51no—
40#5069—51no—
41#4702—52no—
42C3×#330D511yescharacteristic
43#4465—52no—
44C5×#125C2×D311yescharacteristic
45#4036—62no—
46#4035—62no—
47#4035—62no—
48#4016—32no—
49#4015—31no—
50C5×#97C2×D312yes—
51#3950—62no—
52#3949—62no—
53#3942—62no—
54#3935—31no—
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×Dic15—41no—
62Dic30—42no—
63C3×C5×C8—24no—
64C3⋊#168—41no—
65C3×#125C2×D511yescharacteristic
66#890—102no—
67#889—102no—
68#889—102no—
69#870—52no—
70#869—51no—
71C3×#97C2×D512yes—
72#818—102no—
73#817—102no—
74#810—102no—
75#803—51no—
76C2×Dic10—61no—
77C2×C5×C8—22no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4D1212yes—
80C42×C5C22×D311yescharacteristic
81C4⋊Dic5—32no—
82C4⋊Dic5—32no—
83C4⋊Dic5—62no—
84C4⋊Dic5—62no—
85#683—62no—
86#683—62no—
87#683—62no—
88#683—62no—
89C4×Dic5—62no—
90C2×#168—61no—
91#564—151no—
92#501—152no—
93#491—151no—
94#330—152no—
95#330D1511yescharacteristic
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100Dic15—42no—
101Dic15—42no—
102Dic15—81no—
103C2×Dic6—101no—
104C2×C3×C8—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4D2012yes—
107C3×C42C22×D511yescharacteristic
108C4⋊Dic3—52no—
109C4⋊Dic3—52no—
110C4⋊Dic3—102no—
111C4⋊Dic3—102no—
112Dic3⋊C4—102no—
113Dic3⋊C4—102no—
114Dic3⋊C4—102no—
115Dic3⋊C4—102no—
116C4×Dic3—102no—
117C2×C3⋊C8—101no—
118C2×C4×C5—22no—
119C2×C4×C5C2×D1211yescharacteristic
120C2×C4×C5D3×D412yes—
121C2×Dic5—62no—
122C2×Dic5—62no—
123C2×Dic5—121no—
124Dic10—122no—
125C5×C8—24no—
126#168—121no—
127C4⋊Q8—151no—
128#125—152no—
129#125—302no—
130#125—302no—
131#125—302no—
132#125C2×D1511yescharacteristic
133#107—302no—
134#106—302no—
135#103—302no—
136#97—151no—
137#97C2×D1512yes—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C2×C3×C4—22no—
141C2×C3×C4C2×D2011yescharacteristic
142C2×C3×C4D4×D512yes—
143C2×Dic3—102no—
144C2×Dic3—102no—
145C2×Dic3—201no—
146Dic6—202no—
147C3×C8—24no—
148C3⋊C8—201no—
149C22×C5#88211yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153Dic5—122no—
154Dic5—122no—
155Dic5—241no—
156C2×Q8—301no—
157C2×C8—22no—
158C2×C8—301no—
159C4⋊C4—22no—
160C4⋊C4—152no—
161C4⋊C4—152no—
162C4⋊C4—302no—
163C4⋊C4—302no—
164C4⋊C4—302no—
165C4⋊C4—302no—
166C4⋊C4—302no—
167C4⋊C4—302no—
168C4⋊C4D6012yes—
169C42—302no—
170C42C22×D1511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#402811yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176Dic3—202no—
177Dic3—202no—
178Dic3—401no—
179C2×C5#475311yescharacteristic
180C2×C5#482612yes—
181Q8—602no—
182C2×C4—22no—
183C2×C4—302no—
184C2×C4—302no—
185C2×C4—601no—
186C2×C4C2×D6011yescharacteristic
187C2×C4D4×D1512yes—
188C8—24no—
189C8—601no—
190C2×C3#6504211yescharacteristic
191C2×C3#6511512yes—
192C5#6837711yescharacteristic, complemented, Sylow
193C22#9177111yescharacteristic
194C4—22no—
195C4—21no—
196C4—42no—
197C4—602no—
198C4—602no—
199C4—1201no—
200C3#1059917011yescharacteristic, complemented, Sylow
201C2#1175085411yescharacteristic
202C2#1175092712yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#330C2
socle, prime radicalC22×C3×C5#120
hypercenter#330D15
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
171. C3×C5#1663semidirect
192. C5#68377semidirect
200. C3#10599170semidirect

Maximal subgroups

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

subgroupindex
#117564452
#117511702
#117508032
C3×C5×#3302
#117462862
#105991703
#683775