Finite Group Databasebeta

← #14277675

Subgroups — #14277675

Order 1920.

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

normal subgroups only

This group has 236 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×#65266C211yesmaximal, characteristic
2#11746784C212yesmaximal
3#10598710—31nomaximal, Hall
4C2×C3×C5×C4⋊C4C411yescharacteristic
5C2×C3×C4⋊Dic5C2211yescharacteristic
6C2×C3×C4×Dic5C411yescharacteristic
7#91241—22no—
8C3×#3963—22no—
9#67632—51nomaximal, Hall
10#65266D311yescharacteristic
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×C4×Dic5—21no—
20C3×C4×Dic5C812yescomplemented
21C3×#382—51no—
22#4528—52no—
23C2×C5×C4⋊C4Dic311yescharacteristic
24C2×C4⋊Dic5C2×D311yescharacteristic
25C2×C4×Dic5Dic311yescharacteristic
26C22⋊#170—62no—
27#3963—22no—
28#1324—151noSylow
29C23×C3×C5C22⋊C411yescharacteristic
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5—42no—
33C2×C3×C4×C5—41no—
34C2×C3×C4×C5C2×C811yescharacteristic
35C2×C3×C4×C5M1611yescharacteristic
36C2×C3×Dic5—22no—
37C2×C3×Dic5—22no—
38C2×C3×Dic5—41no—
39C2×C3×Dic5—41no—
40C2×C3×Dic5—42no—
41C3⋊#170—82no—
42C2×C3×C4⋊C4—51no—
43C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
44C2×C3×C42—51no—
45C3×#95—102no—
46#830—102no—
47C22×C4×C5—21no—
48C22×C4×C5C2×Dic311yescharacteristic
49C22×Dic5—21no—
50C22×Dic5#6712yes—
51C2×#170—122no—
52C5×C4⋊C4—41no—
53C4⋊Dic5—41no—
54C4×Dic5—21no—
55C4×Dic5C3⋊C812yescomplemented
56#382—51no—
57#324—152no—
58C22×C3×C5—21no—
59C22×C3×C5—21no—
60C22×C3×C5C22⋊C811yescharacteristic
61C22×C3×C5#9911yescharacteristic
62C22×C3×C5#10111yescharacteristic
63C3×C4×C5—21no—
64C3×C4×C5—21no—
65C3×C4×C5—81no—
66C3×Dic5—42no—
67C3×Dic5—42no—
68C22×C3×C4—21no—
69C22×C3×C4—52no—
70C22×C3×C4—101no—
71C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
72C3×C4⋊C4—41no—
73C3×C4⋊C4—201no—
74C3×C42—52no—
75C3×C42—101no—
76C2×C3⋊C8—202no—
77C23×C5#21711yescharacteristic
78C2×C4×C5—21no—
79C2×C4×C5—21no—
80C2×C4×C5—42no—
81C2×C4×C5—41no—
82C2×C4×C5C2×C3⋊C811yescharacteristic
83C2×C4×C5#20811yescharacteristic
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—41no—
87C2×Dic5—41no—
88C2×Dic5—42no—
89#170—242no—
90C2×C4⋊C4—51no—
91C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
92C2×C42—51no—
93C22⋊C8—302no—
94#95—102no—
95C2×C3×C5—21no—
96C2×C3×C5—21no—
97C2×C3×C5#32411yescharacteristic
98C2×C3×C5#35411yescharacteristic
99C2×C3×C5#35511yescharacteristic
100C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—42no—
104C2×C3×C4—41no—
105C2×C3×C4—102no—
106C2×C3×C4—102no—
107C2×C3×C4—201no—
108C2×C3×C4—201no—
109C2×C3×C4—202no—
110C2×C3×C4D5⋊C811yescharacteristic
111C2×C3×C4#70011yescharacteristic
112C3⋊C8—402no—
113C22×C5—21no—
114C22×C5—21no—
115C22×C5#83011yescharacteristic
116C22×C5#83411yescharacteristic
117C22×C5#83611yescharacteristic
118C4×C5—21no—
119C4×C5—21no—
120C4×C5—81no—
121Dic5—42no—
122Dic5—42no—
123C22×C4—21no—
124C22×C4—52no—
125C22×C4—101no—
126C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
127C2×C8—602no—
128C4⋊C4—41no—
129C4⋊C4—201no—
130C42—52no—
131C42—101no—
132C3×C5#132411yescharacteristic, complemented, Hall
133C22×C3—21no—
134C22×C3—21no—
135C22×C3#400311yescharacteristic
136C22×C3#400511yescharacteristic
137C22×C3#401111yescharacteristic
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—81no—
141C3×C4—202no—
142C3×C4—202no—
143C2×C5—21no—
144C2×C5—21no—
145C2×C5#452811yescharacteristic
146C2×C5#454111yescharacteristic
147C2×C5#454211yescharacteristic
148C23#676311yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—102no—
154C2×C4—102no—
155C2×C4—201no—
156C2×C4—201no—
157C2×C4—202no—
158C2×C4D5⋊(C3⋊C8)11yescharacteristic
159C2×C4#675811yescharacteristic
160C8—1202no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3#6491411yescharacteristic
164C2×C3#6492311yescharacteristic
165C2×C3#6492811yescharacteristic
166C5#6763211yescharacteristic, complemented, Sylow
167C22—21no—
168C22—21no—
169C22#9123211yescharacteristic
170C22#9123411yescharacteristic
171C22#9124011yescharacteristic
172C4—21no—
173C4—21no—
174C4—81no—
175C4—202no—
176C4—202no—
177C3#1059871011yescharacteristic, complemented, Sylow
178C2—21no—
179C2—21no—
180C2#1174678511yescharacteristic
181C2#1174679411yescharacteristic
182C2#1174679911yescharacteristic
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#1324
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
20. C3×C4×Dic5C8semidirect
55. C4×Dic5C3⋊C8semidirect
132. C3×C5#1324semidirect
166. C5#67632semidirect
177. C3#10598710semidirect

Maximal subgroups

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

subgroupindex
C3×#652662
#117467842
#105987103
#676325