Finite Group Databasebeta

← #13089400

Subgroups — #13089400

Order 1440.

622 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×C5×#634C211yesmaximal, characteristic, complemented
2C3×#6817C212yesmaximal, complemented
3#10624229C214yesmaximal, complemented
4#10624221C214yesmaximal, complemented
5#10624219C214yesmaximal, complemented
6#92000—32nomaximal
7C2×C32×C4×C5C2211yescharacteristic
8C2×C5×C3⋊Dic3C2212yes—
9C5×#634C2214yes—
10C3×#1220C2214yes—
11C3×D60C2212yes—
12C3×C4×D15C2214yes—
13C3×Dic30C2212yes—
14#67158C2214yes—
15#67157C2214yes—
16#67154C2218yes—
17#64298—51nomaximal, Hall
18#6817D312yescomplemented
19C2×C5×Dic6—32no—
20C2×C5×Dic6—61no—
21C3×#709—32no—
22#6779—38no—
23#6773—34no—
24D15⋊Q8—34no—
25#6766—34no—
26D5×Dic6—34no—
27C22×C32×C5C2311yescharacteristic
28C2×C3×D15C2314yes—
29C32×C4×C5C2312yes—
30C5×C3⋊Dic3C2314yes—
31C3×Dic15C2314yes—
32#4147—91noHall
33C2×#634D511yescharacteristic, complemented
34C3×#235—52no—
35#3805—54no—
36#3795—54no—
37D3×Dic6—54no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5C2×D312yes—
40#1220C2×D314yes—
41D60C2×D312yes—
42C4×D15C2×D314yes—
43Dic30C2×D312yes—
44C2×C5×Dic3—34no—
45C2×C5×Dic3—62no—
46C5×Dic6—34no—
47C5×Dic6—34no—
48C5×Dic6—64no—
49C3×C22⋊D5—34no—
50C3×D20—32no—
51C3×C4×D5—34no—
52C3×Dic10—32no—
53#1204—38no—
54#1202—38no—
55#1200—38no—
56D5×Dic3—38no—
57#1010—152no—
58C2×C32×C5—21no—
59C2×C32×C5C2411yescharacteristic
60C3×D15—24no—
61C2×C5×Q8—91no—
62#713—94no—
63Q8×D5—94no—
64#709—32no—
65#709—94no—
66C2×C32×C4C2×D511yescharacteristic
67C2×C3⋊Dic3C2×D512yes—
68#634C2×D514yes—
69C3×#67—54no—
70C3×D12—52no—
71C3×C4×D3—54no—
72C3×Dic6—52no—
73#627—54no—
74#625—54no—
75D3×Dic3—58no—
76C22×C3×C5—21no—
77C22×C3×C5C22×D312yes—
78C2×D15C22×D314yes—
79C2×C3×D5—34no—
80C3×C4×C5—22no—
81C3×C4×C5C22×D312yes—
82C3×C4×C5C22×D312yes—
83Dic15C22×D314yes—
84C3×Dic5—34no—
85C5×Dic3—38no—
86C5×Dic3—64no—
87C3×#41—152no—
88D3×Q8—154no—
89#237—154no—
90#237—158no—
91#235—52no—
92#235—154no—
93C2×Dic6—32no—
94C2×Dic6—61no—
95C2×Dic6—154no—
96C32×C52−1+411yescharacteristic, complemented, Hall
97C5×Q8—94no—
98C2×C4×C5—92no—
99C2×C4×C5D3211yescharacteristic
100C22⋊D5—34no—
101D20—32no—
102D20—94no—
103C4×D5—34no—
104C4×D5—98no—
105Dic10—32no—
106Dic10—94no—
107C22×C32C22×D511yescharacteristic
108C2×C3×D3—54no—
109C32×C4C22×D512yes—
110C3⋊Dic3C22×D514yes—
111C3×Dic3—54no—
1122−1+4—451noSylow
113C2×C3×C5—22no—
114C2×C3×C5—22no—
115C2×C3×C5—21no—
116C2×C3×C5C23×D312yes—
117D15—24no—
118C3×D5—64no—
119C3×Q8—152no—
120C3×D4—154no—
121C3×D4—152no—
122C2×C3×C4—21no—
123C2×C3×C4—154no—
124C2×C3×C4D3×D512yes—
125#67—54no—
126#67—158no—
127C2×Dic3—34no—
128C2×Dic3—62no—
129C2×Dic3—158no—
130D12—52no—
131C4×D3—54no—
132C4×D3—158no—
133Dic6—34no—
134Dic6—34no—
135Dic6—52no—
136Dic6—64no—
137Dic6—158no—
138C22×C5C2×D3211yescharacteristic
139C2×D5—34no—
140C4×C5—94no—
141C4×C5C2×D3212yes—
142Dic5—34no—
143C2×C32—21no—
144C2×C32C23×D511yescharacteristic
145C3×D3—104no—
146#41—152no—
147#41—454no—
148#41—454no—
149C2×Q8—91no—
150C2×Q8—454no—
151C3×C5—21no—
152C3×C5#101012yescomplemented
153C22×C3—21no—
154C22×C3—154no—
155C22×C3C2×D3×D512yes—
156C2×D3—54no—
157C3×C4—22no—
158C3×C4—154no—
159C3×C4C2×D3×D512yes—
160C3×C4C2×D3×D512yes—
161Dic3—38no—
162Dic3—54no—
163Dic3—64no—
164C2×C5—21no—
165C2×C5C22×D3211yescharacteristic
166D5—64no—
167C32#414711yescharacteristic, complemented, Sylow
168Q8—94no—
169Q8—152no—
170Q8—454no—
171D4—154no—
172D4—152no—
173D4—454no—
174C2×C4—92no—
175C2×C4—154no—
176C2×C4—458no—
177C2×C4(C3⋊D3)⋊D511yescharacteristic
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—21no—
181C2×C3—304no—
182C2×C3C22×D3×D512yes—
183D3—104no—
184C5#6429811yescharacteristic, complemented, Sylow
185C22—154no—
186C22C2×(C3⋊D3)⋊D511yescharacteristic
187C4—94no—
188C4—154no—
189C4C2×(C3⋊D3)⋊D512yes—
190C3—21no—
191C3#9200012yescomplemented
192C2—21no—
193C2—304no—
194C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×(C3⋊D3)⋊D5
commutator, socle, cosocleC2×C32×C5C24
FittingC2×C32×C4×C5C22
hypercenterC2×C4(C3⋊D3)⋊D5
hypocenterC32×C52−1+4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#634C2semidirect
2. C3×#6817C2semidirect
3. #10624229C2semidirect
4. #10624221C2semidirect
5. #10624219C2semidirect
18. #6817D3semidirect
33. C2×#634D5semidirect
96. C32×C52−1+4semidirect
152. C3×C5#1010semidirect
167. C32#4147semidirect
184. C5#64298semidirect
191. C3#92000semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6342
C3×#68172
#106242292
#106242212
#106242192
#920003
#642985