Finite Group Databasebeta

← #14291183

Subgroups — #14291183

Order 1920.

344 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C3×C5×#564C211yesmaximal, characteristic
2#11751170C211yesmaximal, characteristic
3#11751165C212yesmaximal
4#11746364C211yesmaximal, characteristic
5#11746364C212yesmaximal
6#10602754—31nomaximal, Hall
7C3×C5×#125—22no—
8C3×C5×#125—22no—
9C3×C5×#125—22no—
10C3×C5×#125C2211yescharacteristic
11C3×C5×#125C2212yes—
12#91758C2211yescharacteristic
13#91094—22no—
14#91092—22no—
15#91091—22no—
16#91087C2211yescharacteristic
17#91087C2212yes—
18#71961—51nomaximal, Hall
19C5×#564D311yescharacteristic
20#65358—31no—
21#65354—32no—
22#64763—32no—
23#64763—31no—
24C2×Dic30—21no—
25C3×C5×C4⋊C4—22no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C5×C4⋊C4D412yes—
33C3×C5×C4⋊C4D412yes—
34C3×C42×C5—22no—
35C3×C42×C5C2311yescharacteristic
36C4⋊Dic15—22no—
37C2×C3⋊#168—22no—
38C2×C3⋊#168—21no—
39C3×#564D511yescharacteristic
40#5069—51no—
41#5064—52no—
42#4543—51no—
43#4543—52no—
44C5×#125—22no—
45C5×#125—22no—
46C5×#125—22no—
47C5×#125C2×D312yes—
48C5×#125C2×D311yescharacteristic
49#4015—31no—
50#3942—62no—
51#3940—62no—
52#3939—62no—
53#3935—32no—
54#3935—31no—
55#1663—151noSylow
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C2×D412yes—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×Dic15—41no—
62Dic30—42no—
63C3⋊#168—24no—
64C3⋊#168—41no—
65C3×#125—22no—
66C3×#125—22no—
67C3×#125—22no—
68C3×#125C2×D512yes—
69C3×#125C2×D511yescharacteristic
70#869—51no—
71#810—102no—
72#808—102no—
73#807—102no—
74#803—52no—
75#803—51no—
76C2×Dic10—61no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4—22no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4#6712yes—
84C5×C4⋊C4#6712yes—
85C5×C4⋊C4#6712yes—
86C42×C5—22no—
87C42×C5C22×D311yescharacteristic
88C4⋊Dic5—62no—
89C2×#168—62no—
90C2×#168—61no—
91#564D1511yescharacteristic
92#501—152no—
93#491—151no—
94#330—152no—
95#330—151no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100C3×C4×C5—42no—
101C3×C4×C5—42no—
102Dic15—81no—
103C2×Dic6—101no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4C22⋊D512yes—
111C3×C4⋊C4C22⋊D512yes—
112C3×C4⋊C4C22⋊D512yes—
113C3×C42—22no—
114C3×C42C22×D511yescharacteristic
115C4⋊Dic3—102no—
116C2×C3⋊C8—102no—
117C2×C3⋊C8—101no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5C2×#6712yes—
122C2×C4×C5C2×#6711yescharacteristic
123C2×Dic5—121no—
124Dic10—122no—
125#168—64no—
126#168—121no—
127C4⋊Q8—151no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125C2×D1511yescharacteristic
132#125C2×D1512yes—
133#107—302no—
134#106—302no—
135#103—302no—
136#97—151no—
137#97—152no—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4C2×C22⋊D512yes—
144C2×C3×C4C2×C22⋊D511yescharacteristic
145C2×Dic3—201no—
146Dic6—202no—
147C3⋊C8—104no—
148C3⋊C8—201no—
149C22×C5#95311yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—42no—
154C4×C5—42no—
155Dic5—241no—
156C2×Q8—301no—
157C2×C8—302no—
158C2×C8—301no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C4⋊C4—302no—
166C4⋊C4#122012yes—
167C4⋊C4#122012yes—
168C4⋊C4#122012yes—
169C42—22no—
170C42C22×D1511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#409911yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—42no—
177C3×C4—42no—
178Dic3—401no—
179C2×C5#524511yescharacteristic
180C2×C5#524612yes—
181Q8—602no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—601no—
186C2×C4C2×#122012yes—
187C2×C4C2×#122011yescharacteristic
188C8—304no—
189C8—601no—
190C2×C3#6553411yescharacteristic
191C2×C3#6553512yes—
192C5#7196111yescharacteristic, complemented, Sylow
193C22#9184211yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—42no—
199C4—1201no—
200C3#1060275411yescharacteristic, complemented, Sylow
201C2#1175134611yescharacteristic
202C2#1175134712yes—
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#564C2
socle, prime radicalC22×C3×C5#120
hypercenter#564D15
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
171. C3×C5#1663semidirect
192. C5#71961semidirect
200. C3#10602754semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5642
#117511702
#117511652
#117463642
#106027543
#719615