Finite Group Databasebeta

← #13085918

Subgroups — #13085918

Order 1440.

406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 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×#67157C211yesmaximal, characteristic
2C2×C3×#1200C212yesmaximal, complemented
3#10623811C212yesmaximal, complemented
4C5×#3724C211yesmaximal, characteristic, complemented
5Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#91444—32nomaximal
7C22×C3×D15C2212yes—
8C2×C3⋊Dic15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67157C414yescomplemented
13C3×#1200—24no—
14C4×#625—51nomaximal, Hall
15C2×C3×C4×D5—32no—
16C2×#1202—32no—
17C2×#1200D312yescomplemented
18#6714—32no—
19C5×Dic3⋊C4—32no—
20#6665—32no—
21Dic3×Dic5—32no—
22Dic3×Dic5—61no—
23C22×C32×C5C2311yescharacteristic
24C2×C3×D15—22no—
25C2×C3×D15—22no—
26C2×C3×D15C2×C414yescomplemented
27C3⋊Dic15—21no—
28C5×C3⋊Dic3C2×C412yescomplemented
29C3×C5×Dic3—22no—
30C32×Dic5D412yescomplemented
31#4039—91noHall
32C2×C3×C4×D3—52no—
33C2×#625—51no—
34C4×C3⋊Dic3—51no—
35#3724D511yescharacteristic, complemented
36(C2×D3)⋊Dic3—52no—
37C22×D15C2×D312yes—
38C22×C3×D5—32no—
39C2×C3×C4×C5—32no—
40C2×Dic15—32no—
41C2×Dic15—61no—
42C2×C5×Dic3—32no—
43C2×C5×Dic3—61no—
44C2×C5×Dic3C2×D312yes—
45C2×C3×Dic5—21no—
46C2×C3×Dic5C2×D312yes—
47C3×C4×D5—64no—
48#1202—38no—
49#1200—24no—
50C4×#67—152no—
51C2×C32×C5C22×C411yescharacteristic
52C2×C32×C5C2×D411yescharacteristic
53C2×C32×C5#4111yescharacteristic
54C3×D15—24no—
55C2×D20—91no—
56C2×C4×D5—32no—
57C5×C4⋊C4—91no—
58#685—92no—
59C4×Dic5—91no—
60C22×C3×D3—52no—
61C2×C32×C4—51no—
62C2×C3⋊Dic3—51no—
63C2×C3⋊Dic3C2×D511yescharacteristic
64C2×C3×Dic3C2×D512yes—
65C3×C4×D3—104no—
66#625—54no—
67C22×C3×C5—21no—
68C22×C3×C5C22×D312yes—
69C2×D15—22no—
70C2×D15—22no—
71C2×D15C4×D314yescomplemented
72C2×C3×D5—34no—
73C2×C3×D5—62no—
74C2×C3×D5—62no—
75C3×C4×C5—62no—
76Dic15—62no—
77Dic15—62no—
78C3×Dic5—22no—
79C3×Dic5#6714yescomplemented
80C5×Dic3—22no—
81C5×Dic3—34no—
82C5×Dic3—62no—
83C22×C3×C4—152no—
84C2×#67—152no—
85C2×C4×D3—52no—
86#217—152no—
87(C2×D3)⋊C4—152no—
88Dic3⋊C4—32no—
89C4×Dic3—152no—
90C4×Dic3—301no—
91C32×C5C4×D411yescharacteristic, complemented, Hall
92C22×D5—32no—
93C2×C4×C5—32no—
94C2×C4×C5—91no—
95C2×Dic5—91no—
96C2×Dic5D3211yescharacteristic
97D20—94no—
98C4×D5—64no—
99C22×C32C22×D511yescharacteristic
100C2×C3×D3—54no—
101C2×C3×D3—102no—
102C2×C3×D3—102no—
103C32×C4—52no—
104C3⋊Dic3—101no—
105C3⋊Dic3C4×D512yescomplemented
106C3×Dic3—22no—
107C4×D4—451noSylow
108C2×C3×C5—21no—
109C2×C3×C5—21no—
110C2×C3×C5—21no—
111C2×C3×C5C2×C4×D312yes—
112C2×C3×C5#23512yes—
113C2×C3×C5C2×#6712yes—
114D15—24no—
115C3×D5—64no—
116C23×C3—152no—
117C22×D3—52no—
118C2×C3×C4—32no—
119C2×C3×C4—52no—
120C2×C3×C4—101no—
121C2×C3×C4—304no—
122#67—158no—
123C2×Dic3—32no—
124C2×Dic3—61no—
125C2×Dic3—152no—
126C2×Dic3—301no—
127C2×Dic3D3×D512yes—
128C4×D3—104no—
129C22×C5C2×D3211yescharacteristic
130C2×D5—34no—
131C2×D5—62no—
132C2×D5—62no—
133C4×C5—62no—
134C4×C5—92no—
135Dic5—181no—
136Dic5#62512yescomplemented
137C2×C32C2×C4×D511yescharacteristic
138C2×C32D4×D511yescharacteristic
139C2×C32#71311yescharacteristic
140C3×D3—104no—
141C2×D4—451no—
142C22×C4—152no—
143C4⋊C4—91no—
144C22⋊C4—452no—
145C42—451no—
146C3×C5—21no—
147C3×C5C4×#6712yescomplemented
148C22×C3—21no—
149C22×C3—154no—
150C22×C3—302no—
151C22×C3—302no—
152C22×C3C2×D3×D512yes—
153C2×D3—54no—
154C2×D3—102no—
155C2×D3—102no—
156C3×C4—54no—
157C3×C4—62no—
158C3×C4—102no—
159Dic3—22no—
160Dic3—34no—
161Dic3—62no—
162Dic3—302no—
163Dic3—302no—
164C2×C5#379811yescharacteristic
165C2×C5C4×D3211yescharacteristic
166C2×C5C2×#62511yescharacteristic
167D5—64no—
168C32#403911yescharacteristic, complemented, Sylow
169C23—152no—
170D4—454no—
171C2×C4—32no—
172C2×C4—51no—
173C2×C4—91no—
174C2×C4—304no—
175C2×C4—451no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—304no—
180C2×C3#677312yes—
181C2×C3C4×D3×D512yes—
182C2×C3D5×#6712yes—
183D3—104no—
184C5C4×#62511yescharacteristic, complemented, Sylow
185C22—154no—
186C22—302no—
187C22—302no—
188C22D32×D511yescharacteristic
189C4—52no—
190C4—62no—
191C4—92no—
192C4—901no—
193C3—21no—
194C3#9144412yescomplemented
195C2—304no—
196C2#1062402211yescharacteristic
197C2D5×#62511yescharacteristic
198C2#1062405211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67157C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3×#1200C2semidirect
3. #10623811C2semidirect
4. C5×#3724C2semidirect
5. Dic5×C3⋊Dic3C2semidirect
12. #67157C4semidirect
17. C2×#1200D3semidirect
26. C2×C3×D15C2×C4semidirect
28. C5×C3⋊Dic3C2×C4semidirect
30. C32×Dic5D4semidirect
35. #3724D5semidirect
71. C2×D15C4×D3semidirect
79. C3×Dic5#67semidirect
91. C32×C5C4×D4semidirect
105. C3⋊Dic3C4×D5semidirect
136. Dic5#625semidirect
147. C3×C5C4×#67semidirect
168. C32#4039semidirect
184. C5C4×#625semidirect
194. C3#91444semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×C3×#12002
#106238112
C5×#37242
Dic5×C3⋊Dic32
#914443
C4×#6255