Finite Group Databasebeta

← #14314908

Subgroups — #14314908

Order 1920.

256 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 76 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
1Dic3×#681C211yesmaximal, characteristic
2#11746783C211yesmaximal, characteristic
3C3×#64912C211yesmaximal, characteristic
4#11746565C212yesmaximal, complemented
5#11746544C212yesmaximal, complemented
6#10604155—31nomaximal, Hall
7C2×#6710C411yescharacteristic
8C2×C4×C5×Dic3C411yescharacteristic
9C2×C3×#681C2211yescharacteristic
10#91227C2212yes—
11C3×#3998C2212yes—
12#90953C411yescharacteristic
13#90953C2211yescharacteristic
14Dic3×#168C411yescharacteristic
15Dic3×#168C2211yescharacteristic
16#69114—51nomaximal, Hall
17C4×#681—31no—
18#64912—31no—
19#64912D311yescharacteristic
20#64861—32no—
21#64860—32no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C22×C5×Dic3—21no—
24#6710—22no—
25C2×C3⋊#168C2×C411yescharacteristic
26C2×C3⋊#168C2×C411yescharacteristic
27C4×C5×Dic3—21no—
28C4×C5×Dic3C2×C411yescharacteristic
29C4×C5×Dic3C2×C411yescharacteristic
30C3×#681—22no—
31C2×C3×#168C2×C411yescharacteristic
32C2×C3×#168C2311yescharacteristic
33C3⋊#674—22no—
34C3×#674—22no—
35Dic3×M16—51no—
36C3×#349—51no—
37#4553—51no—
38#4512—52no—
39#4511—52no—
40C2×C42×C5—31no—
41C2×#681—31no—
42C2×#681C2×D311yescharacteristic
43#3998—32no—
44#3998C2×D312yes—
45#3935—31no—
46#3935—31no—
47C4×#168—31no—
48C4×#168—31no—
49#2165—151noSylow
50C23×C3×C5M1611yescharacteristic
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5M1611yescharacteristic
54C2×C3×C4×C5C22×C411yescharacteristic
55C2×C5×Dic3—21no—
56C2×C5×Dic3—21no—
57C2×C5×Dic3—42no—
58C3⋊#168—21no—
59C3⋊#168M1612yes—
60C3×#168—21no—
61C3×#168#4112yes—
62C2×C3×M16—51no—
63C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
64C2×#208—51no—
65C3×M32—52no—
66#815—51no—
67#815—51no—
68C8×Dic3—51no—
69C8×Dic3—51no—
70#812—52no—
71C22×C4×C5—61no—
72C22×C4×C5C4×D311yescharacteristic
73C42×C5—31no—
74C42×C5—31no—
75C42×C5—61no—
76#681—22no—
77#681—62no—
78C2×#168—31no—
79C2×#168—31no—
80C2×#168C4×D311yescharacteristic
81C2×#168C22×D311yescharacteristic
82#674—22no—
83#674—62no—
84C4×M16—151no—
85#364—152no—
86#349—51no—
87#349—151no—
88#347—152no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×M1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5#11711yescharacteristic
94C3×C4×C5C2×M1611yescharacteristic
95C5×Dic3—22no—
96C5×Dic3—41no—
97C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
98C22×Dic3—21no—
99C3×M16—102no—
100C2×C3×C8—51no—
101C2×C3×C8—51no—
102C4×Dic3—21no—
103C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
104C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
105#208—102no—
106C2×C3⋊C8—51no—
107C2×C3⋊C8—51no—
108C3×C16—102no—
109C3⋊C16—102no—
110C23×C5ΓL(1,𝔽25)11yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—61no—
114C2×C4×C5—61no—
115C2×C4×C5—122no—
116C2×C4×C5ΓL(1,𝔽25)11yescharacteristic
117C2×C4×C5C2×C4×D311yescharacteristic
118#168—21no—
119#168—32no—
120#168—61no—
121#168#23712yes—
122C2×M16—51no—
123C2×M16—151no—
124C2×C42—31no—
125M32—52no—
126M32—152no—
127#97—151no—
128#97—151no—
129C4×C8—151no—
130C4×C8—151no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#43211yescharacteristic
134C23×C3#70411yescharacteristic
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4#70411yescharacteristic
138C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
139C2×Dic3—21no—
140C2×Dic3—21no—
141C2×Dic3—42no—
142C3×C8—52no—
143C3×C8—101no—
144C3⋊C8—52no—
145C3⋊C8—101no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
149C4×C5—21no—
150C4×C5—62no—
151C4×C5—121no—
152C4×C5#87711yescharacteristic
153C4×C5D3×M1611yescharacteristic
154C22×C4—61no—
155C22×C4D3×AGL(1,𝔽5)11yescharacteristic
156M16—102no—
157M16—302no—
158C2×C8—51no—
159C2×C8—51no—
160C2×C8—151no—
161C2×C8—151no—
162C42—31no—
163C42—31no—
164C42—61no—
165C16—102no—
166C16—302no—
167C3×C5#216511yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#70411yescharacteristic
171C3×C4—21no—
172C3×C4D5⋊M1611yescharacteristic
173C3×C4#413011yescharacteristic
174Dic3—22no—
175Dic3—41no—
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#471911yescharacteristic
179C23#673911yescharacteristic
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—122no—
185C2×C4#673911yescharacteristic
186C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
187C8—52no—
188C8—101no—
189C8—152no—
190C8—301no—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6575711yescharacteristic
194C5#6911411yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#673911yescharacteristic
198C4—21no—
199C4—62no—
200C4—121no—
201C4#9192311yescharacteristic
202C4#9193111yescharacteristic
203C3#1060415511yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1175199711yescharacteristic
subgroupG/H
centerC4#91923
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5#432
prime radicalC23×C3×C5M16
cosocleC2×C3×#168C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2165
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746565C2semidirect
5. #11746544C2semidirect
167. C3×C5#2165semidirect
194. C5#69114semidirect
203. C3#10604155semidirect

Maximal subgroups

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

subgroupindex
Dic3×#6812
#117467832
C3×#649122
#117465652
#117465442
#106041553
#691145