Finite Group Databasebeta

← #14331240

Subgroups — #14331240

Order 1920.

848 conjugacy classes of subgroups; only the 375 normal subgroups are shown.

normal subgroups only

This group has 848 conjugacy classes of subgroups — too many to draw. Only its 375 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×C3×C5×C4⋊Q8C211yesmaximal, characteristic
2#11751330C214yesmaximal
3#11751081C218yesmaximal
4#11751038C212yesmaximal
5#10614962—31nomaximal, Hall
6C22×C3×C5×Q8C2212yes—
7C3×C5×C4⋊Q8C418yescomplemented
8C2×C3×C5×C4⋊C4C2214yes—
9C2×C3×C42×C5C2211yescharacteristic
10C2×C4⋊Dic15C2214yes—
11C2×C4×Dic15C2214yes—
12#91115C2214yes—
13#91115C2218yes—
14#91115C2218yes—
15#83231—51nomaximal, Hall
16C2×C5×C4⋊Q8D311yescharacteristic
17#65519—34no—
18#65270—38no—
19#65226—32no—
20C2×C3×C5×Q8—42no—
21C2×C3×C5×Q8—42no—
22C2×C3×C5×Q8C2×C418yes—
23C22×C3×C4×C5C2314yes—
24C22×C3×C4×C5C2312yes—
25C22×C3×C4×C5C2311yescharacteristic
26C22×Dic15C2318yes—
27C3×C5×C4⋊C4C2×C4116yes—
28C3×C42×C5C2×C414yes—
29C4⋊Dic15—44no—
30C4×Dic15—44no—
31C2×C3×C4⋊Q8D511yescharacteristic
32#5229—54no—
33#4980—58no—
34#4937—52no—
35C22×C5×Q8C2×D312yes—
36C5×C4⋊Q8Dic318yescomplemented
37C2×C5×C4⋊C4C2×D314yes—
38C2×C42×C5C2×D311yescharacteristic
39C2×C4⋊Dic5—34no—
40C2×C4×Dic5—34no—
41#3963—34no—
42#3963—38no—
43#3963—38no—
44#2381—151noSylow
45C23×C3×C5C2411yescharacteristic
46C3×C5×Q8—48no—
47C2×C3×C4×C5—24no—
48C2×C3×C4×C5—24no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5—24no—
51C2×C3×C4×C5C22×C414yes—
52C2×C3×C4×C5C22×C412yes—
53C2×C3×C4×C5C22×C418yes—
54C2×Dic15—28no—
55C2×Dic15—216no—
56C22×C3×Q8C2×D512yes—
57C3×C4⋊Q8Dic518yescomplemented
58C2×C3×C4⋊C4C2×D514yes—
59C2×C3×C42C2×D511yescharacteristic
60C2×C4⋊Dic3—54no—
61C2×C4×Dic3—54no—
62C3⋊#95—54no—
63C3⋊#95—58no—
64C3⋊#95—58no—
65C2×C5×Q8—42no—
66C2×C5×Q8—42no—
67C2×C5×Q8C2×Dic318yes—
68C22×C4×C5C22×D312yes—
69C22×C4×C5C22×D311yescharacteristic
70C22×C4×C5C22×D314yes—
71C22×Dic5—38no—
72C5×C4⋊C4C2×Dic3116yes—
73C42×C5C2×Dic314yes—
74C4⋊Dic5—124no—
75C4×Dic5—124no—
76C2×C4⋊Q8D1511yescharacteristic
77#391—154no—
78#387—158no—
79#383—152no—
80C22×C3×C5C23×C411yescharacteristic
81C22×C3×C5H(5,𝔽2)12yes—
82C22×C3×C52−1+414yes—
83C3×C4×C5—28no—
84C3×C4×C5—22no—
85C3×C4×C5—24no—
86Dic15—48no—
87C2×C3×Q8—42no—
88C2×C3×Q8—42no—
89C2×C3×Q8C2×Dic518yes—
90C22×C3×C4C22×D512yes—
91C22×C3×C4C22×D511yescharacteristic
92C22×C3×C4C22×D514yes—
93C22×Dic3—58no—
94C3×C4⋊C4C2×Dic5116yes—
95C3×C42C2×Dic514yes—
96C4⋊Dic3—204no—
97C4×Dic3—204no—
98C23×C5C23×D311yescharacteristic
99C5×Q8—48no—
100C2×C4×C5—24no—
101C2×C4×C5—24no—
102C2×C4×C5—22no—
103C2×C4×C5—24no—
104C2×C4×C5C22×Dic314yes—
105C2×C4×C5C22×Dic312yes—
106C2×C4×C5C22×Dic318yes—
107C2×Dic5—68no—
108C2×Dic5—616no—
109C22×Q8C2×D1512yes—
110C4⋊Q8Dic1518yescomplemented
111C2×C4⋊C4—154no—
112C2×C4⋊C4C2×D1514yes—
113C2×C42—154no—
114C2×C42C2×D1511yescharacteristic
115#95—158no—
116#95—154no—
117#95—158no—
118C2×C3×C5#51811yescharacteristic
119C2×C3×C5#51912yes—
120C2×C3×C5#56314yes—
121C23×C3C23×D511yescharacteristic
122C3×Q8—48no—
123C2×C3×C4—24no—
124C2×C3×C4—24no—
125C2×C3×C4—22no—
126C2×C3×C4—24no—
127C2×C3×C4C22×Dic514yes—
128C2×C3×C4C22×Dic512yes—
129C2×C3×C4C22×Dic518yes—
130C2×Dic3—108no—
131C2×Dic3—1016no—
132C22×C5#100412yes—
133C22×C5#100714yes—
134C22×C5C23×Dic311yescharacteristic
135C4×C5—28no—
136C4×C5—22no—
137C4×C5—24no—
138Dic5—128no—
139C2×Q8—42no—
140C2×Q8—42no—
141C2×Q8C2×Dic1518yes—
142C22×C4—158no—
143C22×C4C22×D1512yes—
144C22×C4C22×D1511yescharacteristic
145C22×C4C22×D1514yes—
146C4⋊C4—604no—
147C4⋊C4C2×Dic15116yes—
148C42—604no—
149C42C2×Dic1514yes—
150C3×C5#238111yescharacteristic, complemented, Hall
151C22×C3#414412yes—
152C22×C3#414714yes—
153C22×C3C23×Dic511yescharacteristic
154C3×C4—28no—
155C3×C4—22no—
156C3×C4—24no—
157Dic3—208no—
158C2×C5#573514yes—
159C2×C5#579811yescharacteristic
160C2×C5#581212yes—
161C23C23×D1511yescharacteristic
162Q8—48no—
163C2×C4—24no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—308no—
168C2×C4—3016no—
169C2×C4C22×Dic1514yes—
170C2×C4C22×Dic1512yes—
171C2×C4C22×Dic1518yes—
172C2×C3#6606914yes—
173C2×C3#6613211yescharacteristic
174C2×C3#6614612yes—
175C5#8323111yescharacteristic, complemented, Sylow
176C22#9209512yes—
177C22#9209814yes—
178C22C23×Dic1511yescharacteristic
179C4—22no—
180C4—28no—
181C4—24no—
182C4—608no—
183C3#1061496211yescharacteristic, complemented, Sylow
184C2#1175649414yes—
185C2#1175655711yescharacteristic
186C2#1175657112yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊Q8C2
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC2×C4⋊Q8D15
hypocenterC3×C5#2381
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
7. C3×C5×C4⋊Q8C4semidirect
36. C5×C4⋊Q8Dic3semidirect
57. C3×C4⋊Q8Dic5semidirect
110. C4⋊Q8Dic15semidirect
150. C3×C5#2381semidirect
175. C5#83231semidirect
183. C3#10614962semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C4⋊Q82
#117513302
#117510812
#117510382
#106149623
#832315