Finite Group Databasebeta

← #13085886

Subgroups — #13085886

Order 1440.

358 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 88 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×D5×C3⋊Dic3C211yesmaximal, characteristic
2#10623832C211yesmaximal, characteristic, complemented
3Dic3×Dic15C212yesmaximal, complemented
4C5×#3724C211yesmaximal, characteristic, complemented
5C3×#6665C212yesmaximal
6#91394—32nomaximal
7C22×C32×D5C2211yescharacteristic
8C2×C3⋊Dic15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×Dic15C2212yes—
11C2×C3×C5×Dic3C2212yes—
12D5×C3⋊Dic3C414yescomplemented
13#63957—51nomaximal, Hall
14C2×D5×Dic3—32no—
15C2×D5×Dic3—61no—
16C4×Dic15—32no—
17C5×Dic3⋊C4—32no—
18C3×#685—32no—
19Dic3⋊Dic5—32no—
20#6665D312yes—
21Dic3×Dic5—32no—
22C22×C32×C5C2311yescharacteristic
23C2×C32×D5—21no—
24C2×C32×D5—21no—
25C2×C32×D5C2×C412yes—
26C3⋊Dic15C2×C412yes—
27C5×C3⋊Dic3C2×C412yes—
28C3×Dic15—22no—
29C3×C5×Dic3—22no—
30#4038—91noHall
31C22×C3⋊Dic3—51no—
32C3×#217—52no—
33#3724—51no—
34#3724D511yescharacteristic, complemented
35Dic32—52no—
36C22×C3×D5—21no—
37C22×C3×D5C2×D312yes—
38C2×C3×C4×C5—32no—
39C2×Dic15—32no—
40C2×Dic15—61no—
41C2×Dic15C2×D312yes—
42C2×C5×Dic3—32no—
43C2×C5×Dic3—61no—
44C2×C5×Dic3C2×D312yes—
45C2×C3×Dic5—32no—
46D5×Dic3—38no—
47D5×Dic3—64no—
48#877—152no—
49C2×C32×C5C22×C411yescharacteristic
50C2×C32×C5#4111yescharacteristic
51C2×C32×C5#4111yescharacteristic
52C32×D5—22no—
53C2×C4×D5—91no—
54C5×C4⋊C4—91no—
55#685—32no—
56C4⋊Dic5—91no—
57C4×Dic5—92no—
58C23×C32—51no—
59C2×C3⋊Dic3—51no—
60C2×C3⋊Dic3—54no—
61C2×C3⋊Dic3C2×D511yescharacteristic
62C2×C3×Dic3—52no—
63C2×C3×Dic3C2×D512yes—
64C22×C3×C5—21no—
65C22×C3×C5C22×D312yes—
66C2×C3×D5—22no—
67C2×C3×D5—22no—
68C2×C3×D5—22no—
69C2×C3×D5—22no—
70C2×C3×D5—22no—
71C2×C3×D5C4×D314yes—
72C3×C4×C5—62no—
73Dic15—22no—
74Dic15—34no—
75Dic15—62no—
76C3×Dic5—62no—
77C5×Dic3—22no—
78C5×Dic3—34no—
79C5×Dic3—62no—
80C22×Dic3—152no—
81C22×Dic3—301no—
82C3×C22⋊C4—152no—
83#217—52no—
84Dic3⋊C4—32no—
85Dic3⋊C4—152no—
86C4×Dic3—152no—
87C4×Dic3—152no—
88C32×C5#11711yescharacteristic, complemented, Hall
89C22×D5D3211yescharacteristic
90C2×C4×C5—32no—
91C2×C4×C5—91no—
92C2×Dic5—32no—
93C2×Dic5—91no—
94C4×D5—94no—
95C22×C32—52no—
96C22×C32—101no—
97C22×C32—101no—
98C22×C32C22×D511yescharacteristic
99C3⋊Dic3—52no—
100C3⋊Dic3C4×D512yes—
101C3×Dic3—22no—
102C3×Dic3—102no—
103#117—451noSylow
104C2×C3×C5—21no—
105C2×C3×C5—21no—
106C2×C3×C5—21no—
107C2×C3×C5C2×C4×D312yes—
108C2×C3×C5#23712yes—
109C2×C3×C5#23712yes—
110C3×D5—24no—
111C3×D5—24no—
112C23×C3—52no—
113C23×C3—101no—
114C2×C3×C4—32no—
115C2×C3×C4—152no—
116C2×Dic3—32no—
117C2×Dic3—52no—
118C2×Dic3—61no—
119C2×Dic3—158no—
120C2×Dic3—152no—
121C2×Dic3—304no—
122C2×Dic3—301no—
123C2×Dic3D3×D512yes—
124C22×C5C2×D3211yescharacteristic
125C2×D5—21no—
126C2×D5—21no—
127C2×D5#62412yes—
128C4×C5—62no—
129C4×C5—92no—
130Dic5—62no—
131Dic5—92no—
132C2×C32—102no—
133C2×C32C2×C4×D511yescharacteristic
134C2×C32#71111yescharacteristic
135C2×C32#71311yescharacteristic
136C22×C4—451no—
137C4⋊C4—91no—
138C4⋊C4—451no—
139C22⋊C4—152no—
140C42—452no—
141C3×C5—21no—
142C3×C5#87712yescomplemented
143C22×C3—21no—
144C22×C3—54no—
145C22×C3—102no—
146C22×C3—102no—
147C22×C3—102no—
148C22×C3—102no—
149C22×C3—102no—
150C22×C3C2×D3×D512yes—
151C3×C4—62no—
152C3×C4—302no—
153Dic3—22no—
154Dic3—34no—
155Dic3—62no—
156Dic3—102no—
157Dic3—154no—
158Dic3—302no—
159C2×C5#380511yescharacteristic
160C2×C5#380511yescharacteristic
161C2×C5C2×#62411yescharacteristic
162D5—22no—
163C32#403811yescharacteristic, complemented, Sylow
164C23—51no—
165C2×C4—32no—
166C2×C4—91no—
167C2×C4—152no—
168C2×C4—454no—
169C2×C4—451no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—104no—
174C2×C3—104no—
175C2×C3#676612yes—
176C2×C3C4×D3×D512yes—
177C2×C3#678012yes—
178C5#6395711yescharacteristic, complemented, Sylow
179C22—52no—
180C22—101no—
181C22—101no—
182C22D32×D511yescharacteristic
183C4—62no—
184C4—92no—
185C4—302no—
186C4—452no—
187C3—21no—
188C3#9139412yescomplemented
189C2—102no—
190C2D5×#62411yescharacteristic
191C2#1062404611yescharacteristic
192C2#1062404711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C32×D5C22
hypocenterC32×C5#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #10623832C2semidirect
3. Dic3×Dic15C2semidirect
4. C5×#3724C2semidirect
12. D5×C3⋊Dic3C4semidirect
34. #3724D5semidirect
88. C32×C5#117semidirect
142. C3×C5#877semidirect
163. C32#4038semidirect
178. C5#63957semidirect
188. C3#91394semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C3⋊Dic32
#106238322
Dic3×Dic152
C5×#37242
C3×#66652
#913943
#639575