Finite Group Databasebeta

← #13086135

Subgroups — #13086135

Order 1440.

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

normal subgroups only

This group has 334 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×#67157C211yesmaximal, characteristic
2C2×C5×#627C211yesmaximal, characteristic, complemented
3#10623811C212yesmaximal, complemented
4Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#6667C212yesmaximal, complemented
6#91455—32nomaximal
7C22×C3×D15C2212yes—
8C2×C3⋊Dic15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67157—22no—
13C5×#627—22no—
14#63915—51nomaximal, Hall
15C2×C5×Dic6—32no—
16C2×#1202—32no—
17#6714—32no—
18C3×#685—32no—
19#6667D312yescomplemented
20#6665—32no—
21Dic3×Dic5—32no—
22Dic3×Dic5—61no—
23C22×C32×C5C2311yescharacteristic
24C2×C3×D15—22no—
25C2×C3×D15—22no—
26C2×C3×D15—22no—
27C3⋊Dic15—21no—
28C5×C3⋊Dic3D412yes—
29C3×C5×Dic3—22no—
30C32×Dic5—21no—
31#4093—91noHall
32C2×#627D511yescharacteristic, complemented
33C2×#625—51no—
34C4×C3⋊Dic3—51no—
35C3×(C2×D3)⋊C4—52no—
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—
45C5×Dic6—64no—
46C2×C3×Dic5—21no—
47C2×C3×Dic5C2×D312yes—
48#1202—64no—
49#885—152no—
50C2×C32×C5C2×D411yescharacteristic
51C2×C32×C5#4111yescharacteristic
52C2×C32×C5#4111yescharacteristic
53C3×D15—42no—
54C2×C5×Q8—91no—
55C2×D20—91no—
56#685—32no—
57#685—92no—
58C4×Dic5—91no—
59C22×C3×D3—52no—
60C2×C32×C4—51no—
61C2×C3⋊Dic3—51no—
62C2×C3⋊Dic3C2×D511yescharacteristic
63C2×C3×Dic3C2×D512yes—
64#627—22no—
65#625—102no—
66C22×C3×C5—21no—
67C22×C3×C5C22×D312yes—
68C2×D15—22no—
69C2×D15—22no—
70C2×D15—22no—
71C2×C3×D5—62no—
72C2×C3×D5—62no—
73C2×C3×D5—62no—
74C3×C4×C5—62no—
75Dic15—62no—
76Dic15—62no—
77C3×Dic5—22no—
78C3×Dic5—22no—
79C5×Dic3—22no—
80C5×Dic3—34no—
81C5×Dic3—62no—
82C2×#67—152no—
83C2×Dic6—32no—
84C3×C22⋊C4—152no—
85#217—152no—
86(C2×D3)⋊C4—52no—
87(C2×D3)⋊C4—152no—
88C4×Dic3—152no—
89C4×Dic3—301no—
90C32×C5#12411yescharacteristic, complemented, Hall
91C22×D5—32no—
92C5×Q8—182no—
93C2×C4×C5—32no—
94C2×C4×C5—91no—
95C2×Dic5—91no—
96C2×Dic5D3211yescharacteristic
97D20—182no—
98C22×C32C22×D511yescharacteristic
99C2×C3×D3—102no—
100C2×C3×D3—102no—
101C2×C3×D3—102no—
102C32×C4—101no—
103C3⋊Dic3—101no—
104C3⋊Dic3C22⋊D512yes—
105C3×Dic3—22no—
106#124—451noSylow
107C2×C3×C5—21no—
108C2×C3×C5—21no—
109C2×C3×C5—21no—
110C2×C3×C5#23512yes—
111C2×C3×C5D3×D412yes—
112C2×C3×C5#23712yes—
113D15—42no—
114C3×D5—122no—
115C23×C3—152no—
116C22×D3—52no—
117C2×C3×C4—32no—
118C2×C3×C4—52no—
119C2×C3×C4—101no—
120#67—304no—
121C2×Dic3—32no—
122C2×Dic3—61no—
123C2×Dic3—152no—
124C2×Dic3—301no—
125C2×Dic3D3×D512yes—
126Dic6—64no—
127C22×C5C2×D3211yescharacteristic
128C2×D5—62no—
129C2×D5—62no—
130C2×D5—62no—
131C4×C5—62no—
132C4×C5—92no—
133Dic5—21no—
134Dic5—181no—
135C2×C32#71311yescharacteristic
136C2×C32#71311yescharacteristic
137C2×C32C2×C22⋊D511yescharacteristic
138C3×D3—202no—
139C2×Q8—91no—
140C2×D4—451no—
141C22⋊C4—152no—
142C22⋊C4—452no—
143C42—451no—
144C3×C5—21no—
145C3×C5#88512yescomplemented
146C22×C3—21no—
147C22×C3—302no—
148C22×C3—302no—
149C22×C3—302no—
150C22×C3C2×D3×D512yes—
151C2×D3—102no—
152C2×D3—102no—
153C2×D3—102no—
154C3×C4—62no—
155C3×C4—102no—
156C3×C4—102no—
157Dic3—22no—
158Dic3—34no—
159Dic3—62no—
160Dic3—302no—
161Dic3—302no—
162C2×C5#379811yescharacteristic
163C2×C5#380211yescharacteristic
164C2×C5#380511yescharacteristic
165D5—122no—
166C32#409311yescharacteristic, complemented, Sylow
167C23—152no—
168Q8—182no—
169D4—902no—
170C2×C4—32no—
171C2×C4—51no—
172C2×C4—91no—
173C2×C4—451no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—602no—
178C2×C3#676612yes—
179C2×C3#677312yes—
180C2×C3D3×C22⋊D512yes—
181D3—202no—
182C5#6391511yescharacteristic, complemented, Sylow
183C22—302no—
184C22—302no—
185C22—302no—
186C22D32×D511yescharacteristic
187C4—62no—
188C4—92no—
189C4—101no—
190C4—901no—
191C3—21no—
192C3#9145512yescomplemented
193C2—602no—
194C2#1062403411yescharacteristic
195C2#1062404711yescharacteristic
196C2#1062405211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67157C2
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
2. C2×C5×#627C2semidirect
3. #10623811C2semidirect
4. Dic5×C3⋊Dic3C2semidirect
5. C3×#6667C2semidirect
19. #6667D3semidirect
32. C2×#627D5semidirect
90. C32×C5#124semidirect
145. C3×C5#885semidirect
166. C32#4093semidirect
182. C5#63915semidirect
192. C3#91455semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×C5×#6272
#106238112
Dic5×C3⋊Dic32
C3×#66672
#914553
#639155