Finite Group Databasebeta

← #13086110

Subgroups — #13086110

Order 1440.

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

normal subgroups only

This group has 366 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×#67155C211yesmaximal, characteristic, complemented
2C2×#67140C211yesmaximal, characteristic
3#10623813C212yesmaximal, complemented
4C5×#3722C211yesmaximal, characteristic, complemented
5C3×Dic3⋊Dic5C212yesmaximal, complemented
6#91427—32nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C22×C5×C3⋊D3C2211yescharacteristic
9C2×C3×Dic15C2212yes—
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67155—22no—
13#67140—22no—
14#63897—51nomaximal, Hall
15C2×#1203—32no—
16C2×#1203—61no—
17C2×D3×Dic5—32no—
18#6714—32no—
19C5×(C2×D3)⋊C4—32no—
20C3×C4⋊Dic5—32no—
21Dic3⋊Dic5D312yescomplemented
22#6667—32no—
23C22×C32×C5C2311yescharacteristic
24C2×C3⋊D15—21no—
25C2×C3⋊D15—22no—
26C2×C5×C3⋊D3—22no—
27C2×C5×C3⋊D3D412yes—
28C3×Dic15—22no—
29C3×C5×Dic3—22no—
30C32×Dic5—21no—
31#4032—91noHall
32C2×C4⋊(C3⋊D3)—51no—
33C2×#624—51no—
34C3×Dic3⋊C4—52no—
35#3722—52no—
36#3722D511yescharacteristic, complemented
37C22×D15—32no—
38C22×D15—61no—
39C22×C5×D3—32no—
40C22×C5×D3—61no—
41C2×C3×C4×C5—32no—
42C2×Dic15C2×D312yes—
43C2×C5×Dic3C2×D312yes—
44C2×C3×Dic5—21no—
45C2×C3×Dic5—32no—
46C2×C3×Dic5C2×D312yes—
47#1203—64no—
48#1203—64no—
49D3×Dic5—64no—
50#894—152no—
51C2×C32×C5C2×D411yescharacteristic
52C2×C32×C5#4112yes—
53C3⋊D15—41no—
54C5×C3⋊D3—22no—
55C2×C22⋊D5—91no—
56C22×Dic5—91no—
57C5×C22⋊C4—91no—
58#685—92no—
59C4⋊Dic5—32no—
60C22×C3⋊D3—51no—
61C22×C3⋊D3C2×D511yescharacteristic
62C2×C32×C4—51no—
63C4⋊(C3⋊D3)—102no—
64C2×C3×Dic3—52no—
65C2×C3×Dic3C2×D512yes—
66#624—102no—
67C22×C3×C5—21no—
68C22×C3×C5C22×D312yes—
69C2×D15—62no—
70C2×D15—62no—
71C2×D15—62no—
72C2×D15—62no—
73C2×D15—122no—
74C2×C5×D3—34no—
75C2×C5×D3—62no—
76C2×C5×D3—62no—
77C2×C5×D3—62no—
78C2×C5×D3—122no—
79C3×C4×C5—62no—
80Dic15—22no—
81C3×Dic5—22no—
82C3×Dic5—22no—
83C3×Dic5—62no—
84C5×Dic3—22no—
85C2×D12—152no—
86C2×D12—301no—
87C2×C4×D3—152no—
88C3×C4⋊C4—152no—
89(C2×D3)⋊C4—32no—
90(C2×D3)⋊C4—152no—
91(C2×D3)⋊C4—152no—
92Dic3⋊C4—52no—
93C32×C5#12311yescharacteristic, complemented, Hall
94C23×C5—91no—
95C22×D5—91no—
96C2×C4×C5—32no—
97C22⋊D5—182no—
98C2×Dic5—32no—
99C2×Dic5—182no—
100C2×Dic5D3211yescharacteristic
101C22×C32C22×D511yescharacteristic
102C2×C3⋊D3—22no—
103C2×C3⋊D3—101no—
104C2×C3⋊D3—102no—
105C2×C3⋊D3D2012yes—
106C32×C4—101no—
107C3×Dic3—22no—
108C3×Dic3—102no—
109#123—451noSylow
110C2×C3×C5—22no—
111C2×C3×C5—21no—
112C2×C3×C5#23512yes—
113C2×C3×C5D3×D412yes—
114C2×C3×C5#23912yes—
115D15—122no—
116D15—122no—
117C5×D3—64no—
118C5×D3—122no—
119C22×D3—32no—
120C22×D3—61no—
121C22×D3—152no—
122C22×D3—301no—
123C2×C3×C4—32no—
124C2×C3×C4—52no—
125C2×C3×C4—101no—
126C2×C3×C4—152no—
127C2×Dic3—52no—
128C2×Dic3D3×D512yes—
129D12—304no—
130D12—304no—
131C4×D3—304no—
132C22×C5—92no—
133C22×C5—182no—
134C22×C5C2×D3211yescharacteristic
135C2×D5—182no—
136C2×D5—181no—
137C4×C5—62no—
138Dic5—21no—
139Dic5—62no—
140C2×C32C2×D2011yescharacteristic
141C2×C32#71112yes—
142C3⋊D3—22no—
143C3⋊D3—201no—
144C2×D4—451no—
145C22×C4—451no—
146C4⋊C4—152no—
147C22⋊C4—91no—
148C22⋊C4—452no—
149C3×C5—21no—
150C3×C5#89412yescomplemented
151C22×C3—21no—
152C22×C3C2×D3×D512yes—
153C2×D3—34no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—122no—
158C2×D3—302no—
159C2×D3—302no—
160C2×D3—302no—
161C2×D3—302no—
162C2×D3—602no—
163C3×C4—62no—
164C3×C4—102no—
165C3×C4—102no—
166C3×C4—302no—
167Dic3—22no—
168Dic3—102no—
169C2×C5—182no—
170C2×C5#379912yes—
171C2×C5#381111yescharacteristic
172D5—361no—
173C32#403211yescharacteristic, complemented, Sylow
174C23—91no—
175C23—451no—
176D4—902no—
177C2×C4—32no—
178C2×C4—51no—
179C2×C4—152no—
180C2×C4—902no—
181C2×C3—21no—
182C2×C3—22no—
183C2×C3#676812yes—
184C2×C3D3×D2012yes—
185C2×C3#678212yes—
186D3—64no—
187D3—122no—
188D3—602no—
189D3—602no—
190C5#6389711yescharacteristic, complemented, Sylow
191C22—92no—
192C22—182no—
193C22—901no—
194C22—902no—
195C22D32×D511yescharacteristic
196C4—62no—
197C4—101no—
198C4—302no—
199C3—21no—
200C3#9142712yescomplemented
201C2—182no—
202C2—1801no—
203C2#1062403111yescharacteristic
204C2#1062405112yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67140C2
hypocenterC32×C5#123
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67155C2semidirect
3. #10623813C2semidirect
4. C5×#3722C2semidirect
5. C3×Dic3⋊Dic5C2semidirect
21. Dic3⋊Dic5D3semidirect
36. #3722D5semidirect
93. C32×C5#123semidirect
150. C3×C5#894semidirect
173. C32#4032semidirect
190. C5#63897semidirect
200. C3#91427semidirect

Maximal subgroups

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

subgroupindex
C2×#671552
C2×#671402
#106238132
C5×#37222
C3×Dic3⋊Dic52
#914273
#638975