Finite Group Databasebeta

← #14291177

Subgroups — #14291177

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
2C3×C5×#491C211yesmaximal, characteristic
3#11751182C212yesmaximal
4#11746364C211yesmaximal, characteristic
5#11746286C212yesmaximal
6#10602045—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9#91779—22no—
10#91778—22no—
11#91778—22no—
12#91759C2212yes—
13C3×C5×#103—22no—
14C3×C5×#97C2211yescharacteristic
15#91092—22no—
16#91091—22no—
17#91087C2212yes—
18#71252—51nomaximal, Hall
19C5⋊#564—31no—
20C5×#491D311yescharacteristic
21#65369—32no—
22#64763—31no—
23#64685—32no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×C8—21no—
26C3×C5×C4⋊C4—22no—
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×#491D511yescharacteristic
41#5081—52no—
42#4543—51no—
43#4465—52no—
44C5×C4⋊Q8C2×D311yescharacteristic
45C5×#125C2×D311yescharacteristic
46#4036—62no—
47#4035—62no—
48#4035—62no—
49#4016—32no—
50C5×#103—22no—
51C5×#97C2×D311yescharacteristic
52#3940—62no—
53#3939—62no—
54#3935—32no—
55#1663—151noSylow
56C3×C5×Q8—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—41no—
59C2×C3×C4×C5C2×D412yes—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×Dic15—22no—
62C2×Dic15—22no—
63C3×C5×C8—41no—
64C3⋊#168—24no—
65C3×C4⋊Q8C2×D511yescharacteristic
66C3×#125C2×D511yescharacteristic
67#890—102no—
68#889—102no—
69#889—102no—
70#870—52no—
71C3×#103—22no—
72C3×#97C2×D511yescharacteristic
73#808—102no—
74#807—102no—
75#803—52no—
76C2×C5×Q8—21no—
77C2×C5×C8—21no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4#6712yes—
81C42×C5C22×D311yescharacteristic
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—62no—
91#564—151no—
92#501—152no—
93#491D1511yescharacteristic
94#330—151no—
95#330—152no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100C3×C4×C5—81no—
101Dic15—42no—
102Dic15—42no—
103C2×C3×Q8—21no—
104C2×C3×C8—21no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4C22⋊D512yes—
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—102no—
118C5×Q8—42no—
119C2×C4×C5—22no—
120C2×C4×C5—41no—
121C2×C4×C5D3×D412yes—
122C2×C4×C5C2×#6711yescharacteristic
123C2×Dic5—62no—
124C2×Dic5—62no—
125C5×C8—41no—
126#168—64no—
127C4⋊Q8C2×D1511yescharacteristic
128#125—152no—
129#125—302no—
130#125—302no—
131#125—302no—
132#125C2×D1511yescharacteristic
133#107—302no—
134#106—302no—
135#103—22no—
136#97—152no—
137#97C2×D1511yescharacteristic
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C3×Q8—42no—
141C2×C3×C4—22no—
142C2×C3×C4—41no—
143C2×C3×C4D4×D512yes—
144C2×C3×C4C2×C22⋊D511yescharacteristic
145C2×Dic3—102no—
146C2×Dic3—102no—
147C3×C8—41no—
148C3⋊C8—104no—
149C22×C5#93711yescharacteristic
150C4×C5—22no—
151C4×C5—21no—
152C4×C5—42no—
153C4×C5—81no—
154Dic5—122no—
155Dic5—122no—
156C2×Q8—21no—
157C2×C8—21no—
158C2×C8—302no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—152no—
162C4⋊C4—152no—
163C4⋊C4—302no—
164C4⋊C4—302no—
165C4⋊C4—302no—
166C4⋊C4—302no—
167C4⋊C4—302no—
168C4⋊C4#122012yes—
169C42—302no—
170C42C22×D1511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#408311yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—81no—
177Dic3—202no—
178Dic3—202no—
179C2×C5#506211yescharacteristic
180C2×C5#520512yes—
181Q8—42no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—302no—
185C2×C4—302no—
186C2×C4D4×D1512yes—
187C2×C4C2×#122011yescharacteristic
188C8—41no—
189C8—304no—
190C2×C3#6535111yescharacteristic
191C2×C3#6549412yes—
192C5#7125211yescharacteristic, complemented, Sylow
193C22#9182611yescharacteristic
194C4—22no—
195C4—21no—
196C4—42no—
197C4—81no—
198C4—602no—
199C4—602no—
200C3#1060204511yescharacteristic, complemented, Sylow
201C2#1175116311yescharacteristic
202C2#1175130612yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#491C2
socle, prime radicalC22×C3×C5#120
hypercenter#491D15
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
171. C3×C5#1663semidirect
192. C5#71252semidirect
200. C3#10602045semidirect

Maximal subgroups

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

subgroupindex
#117564452
C3×C5×#4912
#117511822
#117463642
#117462862
#106020453
#712525