Finite Group Databasebeta

← #13086128

Subgroups — #13086128

Order 1440.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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×#627C211yesmaximal, characteristic, complemented
2C2×#67139C211yesmaximal, characteristic
3#10623828C211yesmaximal, characteristic, complemented
4#10623813C212yesmaximal, complemented
5C3×#6665C212yesmaximal, complemented
6#91455—32nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C22×C32×D5C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×Dic15C2212yes—
11C2×C3×C5×Dic3C2212yes—
12C5×#627—22no—
13#67139—22no—
14#63953—51nomaximal, Hall
15C2×C5×Dic6—32no—
16C2×#1202—32no—
17C2×#1202—61no—
18#6714—32no—
19C3×#685—32no—
20#6667—32no—
21#6665D312yescomplemented
22Dic3×Dic5—32no—
23C22×C32×C5C2311yescharacteristic
24C2×C3⋊D15—21no—
25C2×C3⋊D15—22no—
26C2×C32×D5—21no—
27C2×C32×D5—22no—
28C5×C3⋊Dic3D412yes—
29C3×Dic15—22no—
30C3×C5×Dic3—22no—
31#4093—91noHall
32C2×#638—51no—
33C2×#627D511yescharacteristic, complemented
34C3×#217—52no—
35#3722—52no—
36Dic32—51no—
37C22×D15—32no—
38C22×D15—61no—
39C22×C3×D5—21no—
40C22×C3×D5C2×D312yes—
41C2×C3×C4×C5—32no—
42C2×Dic15C2×D312yes—
43C2×C5×Dic3—32no—
44C2×C5×Dic3—61no—
45C2×C5×Dic3C2×D312yes—
46C5×Dic6—64no—
47C2×C3×Dic5—32no—
48#1202—64no—
49#1202—64no—
50#885—152no—
51C2×C32×C5C2×D411yescharacteristic
52C2×C32×C5#4112yes—
53C3⋊D15—41no—
54C32×D5—41no—
55C2×C5×Q8—91no—
56C2×D20—91no—
57#685—32no—
58#685—92no—
59C4×Dic5—91no—
60C23×C32—51no—
61C22×C3⋊D3—51no—
62#638—102no—
63C2×C3⋊Dic3C2×D511yescharacteristic
64C2×C3×Dic3—52no—
65C2×C3×Dic3C2×D512yes—
66#627—22no—
67C22×C3×C5—21no—
68C22×C3×C5C22×D312yes—
69C2×D15—62no—
70C2×D15—62no—
71C2×D15—62no—
72C2×D15—62no—
73C2×D15—122no—
74C2×C3×D5—22no—
75C2×C3×D5—22no—
76C2×C3×D5—22no—
77C2×C3×D5—22no—
78C2×C3×D5—42no—
79C3×C4×C5—62no—
80Dic15—22no—
81C3×Dic5—62no—
82C5×Dic3—22no—
83C5×Dic3—34no—
84C5×Dic3—62no—
85C2×#67—152no—
86C2×#67—301no—
87C2×Dic6—32no—
88C3×C22⋊C4—152no—
89#217—52no—
90(C2×D3)⋊C4—152no—
91(C2×D3)⋊C4—152no—
92C4×Dic3—152no—
93C32×C5#12411yescharacteristic, complemented, Hall
94C22×D5—91no—
95C22×D5D3211yescharacteristic
96C5×Q8—182no—
97C2×C4×C5—32no—
98C2×C4×C5—91no—
99C2×Dic5—32no—
100D20—182no—
101C22×C32—101no—
102C22×C32—102no—
103C22×C32C22×D511yescharacteristic
104C2×C3⋊D3—101no—
105C2×C3⋊D3—102no—
106C3⋊Dic3C22⋊D512yes—
107C3×Dic3—22no—
108C3×Dic3—102no—
109#124—451noSylow
110C2×C3×C5—22no—
111C2×C3×C5—21no—
112C2×C3×C5#23512yes—
113C2×C3×C5D3×D412yes—
114C2×C3×C5#23712yes—
115D15—122no—
116D15—122no—
117C3×D5—42no—
118C3×D5—42no—
119C23×C3—52no—
120C23×C3—101no—
121C22×D3—152no—
122C22×D3—301no—
123C2×C3×C4—32no—
124C2×C3×C4—152no—
125#67—304no—
126#67—304no—
127C2×Dic3—32no—
128C2×Dic3—52no—
129C2×Dic3—61no—
130C2×Dic3D3×D512yes—
131Dic6—64no—
132C22×C5C2×D3211yescharacteristic
133C2×D5—22no—
134C2×D5—21no—
135C2×D5—182no—
136C2×D5—181no—
137C4×C5—62no—
138C4×C5—92no—
139Dic5—62no—
140C2×C32—201no—
141C2×C32#71312yes—
142C2×C32C2×C22⋊D511yescharacteristic
143C3⋊D3—201no—
144C2×Q8—91no—
145C2×D4—451no—
146C22⋊C4—152no—
147C22⋊C4—452no—
148C42—451no—
149C3×C5—21no—
150C3×C5#88512yescomplemented
151C22×C3—21no—
152C22×C3—102no—
153C22×C3—102no—
154C22×C3—102no—
155C22×C3—102no—
156C22×C3—202no—
157C22×C3C2×D3×D512yes—
158C2×D3—302no—
159C2×D3—302no—
160C2×D3—302no—
161C2×D3—302no—
162C2×D3—602no—
163C3×C4—62no—
164C3×C4—302no—
165Dic3—22no—
166Dic3—34no—
167Dic3—62no—
168Dic3—102no—
169C2×C5#380412yes—
170C2×C5#381111yescharacteristic
171D5—41no—
172D5—361no—
173C32#409311yescharacteristic, complemented, Sylow
174C23—51no—
175C23—451no—
176Q8—182no—
177D4—902no—
178C2×C4—32no—
179C2×C4—91no—
180C2×C4—152no—
181C2×C3—21no—
182C2×C3—22no—
183C2×C3—202no—
184C2×C3—202no—
185C2×C3#676612yes—
186C2×C3#677312yes—
187C2×C3D3×C22⋊D512yes—
188D3—602no—
189D3—602no—
190C5#6395311yescharacteristic, complemented, Sylow
191C22—101no—
192C22—102no—
193C22—901no—
194C22—902no—
195C22D32×D511yescharacteristic
196C4—62no—
197C4—92no—
198C4—302no—
199C3—21no—
200C3#9145512yescomplemented
201C2—201no—
202C2—1801no—
203C2#1062402911yescharacteristic
204C2#1062404412yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67139C2
hypocenterC32×C5#124
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C5×#627C2semidirect
3. #10623828C2semidirect
4. #10623813C2semidirect
5. C3×#6665C2semidirect
21. #6665D3semidirect
33. C2×#627D5semidirect
93. C32×C5#124semidirect
150. C3×C5#885semidirect
173. C32#4093semidirect
190. C5#63953semidirect
200. C3#91455semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6272
C2×#671392
#106238282
#106238132
C3×#66652
#914553
#639535