Finite Group Databasebeta

← #13086200

Subgroups — #13086200

Order 1440.

302 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 84 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×#67153C212yesmaximal
2#10623832C211yesmaximal, characteristic
3C5×#3724C211yesmaximal, characteristic
4Dic5×C3⋊Dic3C211yesmaximal, characteristic
5C3×#6668C212yesmaximal
6#91328—32nomaximal
7C2×C3⋊Dic15C2211yescharacteristic
8C2×C5×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic15C2212yes—
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67153—24no—
13#63919—51nomaximal, Hall
14C2×Dic30—32no—
15C2×#1204—32no—
16C5×Dic3⋊C4—32no—
17C3×#683—32no—
18Dic3⋊Dic5—32no—
19#6668D312yes—
20Dic3×Dic5—32no—
21Dic3×Dic5—61no—
22C22×C32×C5C2311yescharacteristic
23C3⋊Dic15D412yes—
24C5×C3⋊Dic3Q812yescomplemented
25C3×Dic15—22no—
26C3×C5×Dic3—22no—
27C32×Dic5Q812yescomplemented
28#4034—91noHall
29C2×#627—52no—
30C4×C3⋊Dic3—51no—
31C3×C4⋊Dic3—52no—
32#3724—51no—
33#3724D511yescharacteristic
34C2×C3×C4×C5—32no—
35C2×Dic15—32no—
36C2×Dic15—61no—
37C2×Dic15C2×D312yes—
38Dic30—64no—
39C2×C5×Dic3—32no—
40C2×C5×Dic3—61no—
41C2×C5×Dic3C2×D312yes—
42C2×C3×Dic5—21no—
43C2×C3×Dic5—32no—
44C2×C3×Dic5C2×D312yes—
45#1204—64no—
46#888—152no—
47C2×C32×C5C2×D411yescharacteristic
48C2×C32×C5C2×Q811yescharacteristic
49C2×C32×C5C2×Q811yescharacteristic
50C2×Dic10—92no—
51C5×C4⋊C4—91no—
52C4⋊Dic5—91no—
53#683—32no—
54C4×Dic5—91no—
55C2×C32×C4—51no—
56C2×C3⋊Dic3—51no—
57C2×C3⋊Dic3C2×D511yescharacteristic
58C2×C3×Dic3—52no—
59C2×C3×Dic3C2×D512yes—
60#627—104no—
61C22×C3×C5—21no—
62C22×C3×C5C22×D312yes—
63C3×C4×C5—62no—
64Dic15—22no—
65Dic15—34no—
66Dic15—62no—
67C3×Dic5—22no—
68C3×Dic5—62no—
69C3×Dic5Dic614yescomplemented
70C5×Dic3—22no—
71C5×Dic3—34no—
72C5×Dic3—62no—
73C2×Dic6—152no—
74C2×Dic6—152no—
75C3×C4⋊C4—152no—
76C4⋊Dic3—52no—
77Dic3⋊C4—32no—
78Dic3⋊C4—152no—
79C4×Dic3—152no—
80C4×Dic3—301no—
81C32×C5C4⋊Q811yescharacteristic, complemented, Hall
82C2×C4×C5—32no—
83C2×C4×C5—91no—
84C2×Dic5—32no—
85C2×Dic5—91no—
86C2×Dic5D3211yescharacteristic
87Dic10—184no—
88C22×C32C22×D511yescharacteristic
89C32×C4—52no—
90C3⋊Dic3—52no—
91C3⋊Dic3Dic1012yescomplemented
92C3×Dic3—22no—
93C3×Dic3—102no—
94C4⋊Q8—451noSylow
95C2×C3×C5—21no—
96C2×C3×C5—21no—
97C2×C3×C5—21no—
98C2×C3×C5C2×Dic612yes—
99C2×C3×C5D3×D412yes—
100C2×C3×C5D3×Q812yes—
101C2×C3×C4—32no—
102C2×C3×C4—52no—
103C2×C3×C4—101no—
104C2×C3×C4—152no—
105C2×Dic3—32no—
106C2×Dic3—52no—
107C2×Dic3—61no—
108C2×Dic3—152no—
109C2×Dic3—301no—
110C2×Dic3D3×D512yes—
111Dic6—304no—
112Dic6—304no—
113C22×C5C2×D3211yescharacteristic
114C4×C5—62no—
115C4×C5—92no—
116Dic5—62no—
117Dic5—92no—
118Dic5#62712yescomplemented
119C2×C32C2×Dic1011yescharacteristic
120C2×C32D4×D511yescharacteristic
121C2×C32Q8×D511yescharacteristic
122C2×Q8—452no—
123C4⋊C4—91no—
124C4⋊C4—152no—
125C4⋊C4—451no—
126C42—451no—
127C3×C5—21no—
128C3×C5#88812yescomplemented
129C22×C3—21no—
130C22×C3C2×D3×D512yes—
131C3×C4—54no—
132C3×C4—62no—
133C3×C4—102no—
134C3×C4—302no—
135Dic3—22no—
136Dic3—34no—
137Dic3—62no—
138Dic3—102no—
139Dic3—154no—
140Dic3—302no—
141C2×C5#379711yescharacteristic
142C2×C5#380211yescharacteristic
143C2×C5C2×#62711yescharacteristic
144C32#403411yescharacteristic, complemented, Sylow
145Q8—904no—
146C2×C4—32no—
147C2×C4—51no—
148C2×C4—91no—
149C2×C4—152no—
150C2×C4—451no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—21no—
154C2×C3D5×Dic612yes—
155C2×C3D3×Dic1012yes—
156C2×C3#679012yes—
157C5#6391911yescharacteristic, complemented, Sylow
158C22D32×D511yescharacteristic
159C4—52no—
160C4—62no—
161C4—92no—
162C4—302no—
163C4—452no—
164C3—21no—
165C3#9132812yescomplemented
166C2#1062403511yescharacteristic
167C2D5×#62711yescharacteristic
168C2#1062403911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, prime radical, cosocleC22×C32×C5C23
hypocenterC32×C5C4⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
24. C5×C3⋊Dic3Q8semidirect
27. C32×Dic5Q8semidirect
69. C3×Dic5Dic6semidirect
81. C32×C5C4⋊Q8semidirect
91. C3⋊Dic3Dic10semidirect
118. Dic5#627semidirect
128. C3×C5#888semidirect
144. C32#4034semidirect
157. C5#63919semidirect
165. C3#91328semidirect

Maximal subgroups

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

subgroupindex
C2×#671532
#106238322
C5×#37242
Dic5×C3⋊Dic32
C3×#66682
#913283
#639195