Finite Group Databasebeta

← #14277690

Subgroups — #14277690

Order 1920.

268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C3×#65265C211yesmaximal, characteristic
2#11746784C212yesmaximal
3#10598711—31nomaximal, Hall
4C2×C3×C5×C4⋊C4C411yescharacteristic
5C2×C3×C4⋊Dic5C2211yescharacteristic
6C2×C3×#683—22no—
7C2×C3×C4×Dic5C411yescharacteristic
8#91241—22no—
9#67635—51nomaximal, Hall
10#65265D311yescharacteristic
11#64913—32no—
12C22×C3×C4×C5—21no—
13C22×C3×C4×C5C2×C411yescharacteristic
14C22×C3×Dic5—21no—
15C22×C3×Dic5D412yes—
16C2×C3⋊#170—42no—
17C3×C5×C4⋊C4—41no—
18C3×C4⋊Dic5—41no—
19C3×#683—44no—
20C3×C4×Dic5—21no—
21C3×C4×Dic5C812yescomplemented
22C3×#384—51no—
23#4528—52no—
24C2×C5×C4⋊C4Dic311yescharacteristic
25C2×C4⋊Dic5C2×D311yescharacteristic
26C2×#683—22no—
27C2×C4×Dic5Dic311yescharacteristic
28C22⋊#170—62no—
29#1325—151noSylow
30C23×C3×C5C22⋊C411yescharacteristic
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—42no—
34C2×C3×C4×C5—41no—
35C2×C3×C4×C5C2×C811yescharacteristic
36C2×C3×C4×C5M1611yescharacteristic
37C2×C3×Dic5—22no—
38C2×C3×Dic5—22no—
39C2×C3×Dic5—22no—
40C2×C3×Dic5—22no—
41C2×C3×Dic5—42no—
42C3⋊#170—82no—
43C2×C3×C4⋊C4—51no—
44C2×C3×C4⋊C4—102no—
45C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
46C2×C3×C42—51no—
47#830—102no—
48C22×C4×C5—21no—
49C22×C4×C5C2×Dic311yescharacteristic
50C22×Dic5—21no—
51C22×Dic5#6712yes—
52C2×#170—122no—
53C5×C4⋊C4—41no—
54C4⋊Dic5—41no—
55#683—44no—
56C4×Dic5—21no—
57C4×Dic5C3⋊C812yescomplemented
58#384—51no—
59#324—152no—
60C22×C3×C5—21no—
61C22×C3×C5—21no—
62C22×C3×C5C22⋊C811yescharacteristic
63C22×C3×C5#9911yescharacteristic
64C22×C3×C5#10111yescharacteristic
65C3×C4×C5—21no—
66C3×C4×C5—21no—
67C3×C4×C5—81no—
68C3×Dic5—24no—
69C3×Dic5—42no—
70C22×C3×C4—21no—
71C22×C3×C4—52no—
72C22×C3×C4—101no—
73C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
74C3×C4⋊C4—41no—
75C3×C4⋊C4—201no—
76C3×C4⋊C4—204no—
77C3×C42—52no—
78C3×C42—101no—
79C2×C3⋊C8—202no—
80C23×C5#21711yescharacteristic
81C2×C4×C5—21no—
82C2×C4×C5—21no—
83C2×C4×C5—42no—
84C2×C4×C5—41no—
85C2×C4×C5C2×C3⋊C811yescharacteristic
86C2×C4×C5#20811yescharacteristic
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—42no—
92#170—242no—
93C2×C4⋊C4—51no—
94C2×C4⋊C4—102no—
95C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
96C2×C42—51no—
97C22⋊C8—302no—
98C2×C3×C5—21no—
99C2×C3×C5—21no—
100C2×C3×C5#32411yescharacteristic
101C2×C3×C5#35311yescharacteristic
102C2×C3×C5#35611yescharacteristic
103C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—42no—
107C2×C3×C4—41no—
108C2×C3×C4—102no—
109C2×C3×C4—102no—
110C2×C3×C4—102no—
111C2×C3×C4—102no—
112C2×C3×C4—202no—
113C2×C3×C4D5⋊C811yescharacteristic
114C2×C3×C4#70011yescharacteristic
115C3⋊C8—402no—
116C22×C5—21no—
117C22×C5—21no—
118C22×C5#83011yescharacteristic
119C22×C5#83411yescharacteristic
120C22×C5#83611yescharacteristic
121C4×C5—21no—
122C4×C5—21no—
123C4×C5—81no—
124Dic5—24no—
125Dic5—42no—
126C22×C4—21no—
127C22×C4—52no—
128C22×C4—101no—
129C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
130C2×C8—602no—
131C4⋊C4—41no—
132C4⋊C4—201no—
133C4⋊C4—204no—
134C42—52no—
135C42—101no—
136C3×C5#132511yescharacteristic, complemented, Hall
137C22×C3—21no—
138C22×C3—21no—
139C22×C3#400311yescharacteristic
140C22×C3#400511yescharacteristic
141C22×C3#401111yescharacteristic
142C3×C4—21no—
143C3×C4—21no—
144C3×C4—81no—
145C3×C4—104no—
146C3×C4—202no—
147C2×C5—21no—
148C2×C5—21no—
149C2×C5#452811yescharacteristic
150C2×C5#454511yescharacteristic
151C2×C5#454811yescharacteristic
152C23#676311yescharacteristic
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—102no—
158C2×C4—102no—
159C2×C4—102no—
160C2×C4—102no—
161C2×C4—202no—
162C2×C4D5⋊(C3⋊C8)11yescharacteristic
163C2×C4#675811yescharacteristic
164C8—1202no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3#6491411yescharacteristic
168C2×C3#6492211yescharacteristic
169C2×C3#6492911yescharacteristic
170C5#6763511yescharacteristic, complemented, Sylow
171C22—21no—
172C22—21no—
173C22#9123211yescharacteristic
174C22#9123411yescharacteristic
175C22#9124011yescharacteristic
176C4—21no—
177C4—21no—
178C4—81no—
179C4—104no—
180C4—202no—
181C3#1059871111yescharacteristic, complemented, Sylow
182C2—21no—
183C2—21no—
184C2#1174678511yescharacteristic
185C2#1174679311yescharacteristic
186C2#1174680011yescharacteristic
subgroupG/H
centerC22#91240
commutatorC2×C3×C4×C5C2×C8
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C4⋊Dic5C22
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1325
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
21. C3×C4×Dic5C8semidirect
57. C4×Dic5C3⋊C8semidirect
136. C3×C5#1325semidirect
170. C5#67635semidirect
181. C3#10598711semidirect

Maximal subgroups

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

subgroupindex
C3×#652652
#117467842
#105987113
#676355