Finite Group Databasebeta

← #14513741

Subgroups — #14513741

Order 1920.

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

normal subgroups only

This group has 390 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2#11752145C212yesmaximal
3#11752108C214yesmaximal, complemented
4#10614240—31nomaximal, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#91759—41nomaximal
7C4×C5×SL(2,𝔽3)C2212yes—
8#91184C2214yes—
9#85339—51nomaximal, Hall
10C4×C5×#41D311yescharacteristic
11C2×#4016—31no—
12#65521—32no—
13#65311—34no—
14#65298—34no—
15#65284—32no—
16#65213—31no—
17C5×#41⋊C3Q812yes—
18C2×C5×SL(2,𝔽3)C2311yescharacteristic
19C3×C42×C5—41no—
20C4⋊Dic15—42no—
21#6712—44no—
22C4×#41⋊C3D511yescharacteristic
23#5426—52no—
24#5389—54no—
25C2×C5×#41C2×D311yescharacteristic
26C4×C5×Q8C2×D312yes—
27C4×C5×D4—32no—
28C5×#117—31no—
29C2×C42×C5—31no—
30C2×C4⋊Dic5—32no—
31C2×#683—62no—
32C2×#681—32no—
33#4016—34no—
34#4016—61no—
35#4016—61no—
36#3967—34no—
37#3964—34no—
38#3940—34no—
39#3939—34no—
40C4⋊#168—34no—
41#3080—151noSylow
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5—42no—
44C2×Dic15—44no—
45C5×SL(2,𝔽3)C2×Q811yescharacteristic
46C2×#41⋊C3C2×D511yescharacteristic
47#870—201no—
48C4×SL(2,𝔽3)C2×D512yes—
49#859—54no—
50C5×#41—32no—
51C5×#41Dic612yes—
52C2×C5×Q8C22×D311yescharacteristic
53C2×C5×D4—31no—
54C22×C4×C5—31no—
55C22×C4×C5—32no—
56C22×Dic5—62no—
57C5×C4⋊C4—32no—
58C5×C22⋊C4—61no—
59C42×C5—31no—
60C42×C5—32no—
61C42×C5S411yescharacteristic
62C4⋊Dic5—34no—
63C4⋊Dic5—62no—
64#683—64no—
65#683—64no—
66#681—64no—
67C2×#168—34no—
68C2×#125—151no—
69C4×#41D1511yescharacteristic
70#479—154no—
71#478—154no—
72#428—152no—
73#423—151no—
74#417—152no—
75C22×C3×C5—41no—
76C3×C4×C5—42no—
77C3×C4×C5—82no—
78Dic15—84no—
79#41⋊C3Dic1012yes—
80C2×SL(2,𝔽3)C22×D511yescharacteristic
81C3×C42—41no—
82C4⋊Dic3—202no—
83Dic3⋊C4—204no—
84C23×C5—31no—
85C5×Q8—31no—
86C5×Q8C2×Dic611yescharacteristic
87C5×D4—32no—
88C5×D4—61no—
89C2×C4×C5—31no—
90C2×C4×C5—32no—
91C2×C4×C5—32no—
92C2×C4×C5—32no—
93C2×C4×C5—122no—
94C2×C4×C5C2×S412yes—
95C2×C4×C5C2×S411yescharacteristic
96C2×Dic5—64no—
97C2×Dic5—124no—
98#168—64no—
99C2×#41C2×D1511yescharacteristic
100C2×M16—152no—
101#125—154no—
102#125—301no—
103#125—301no—
104C4×Q8C2×D1512yes—
105C4×D4—32no—
106#117—31no—
107C2×C4⋊C4—152no—
108C2×C4⋊C4—302no—
109C2×C42—31no—
110#107—154no—
111#106—154no—
112C4⋊C8—154no—
113#103—154no—
114#102—154no—
115C2×C3×C5—41no—
116C2×C3×C5—42no—
117C2×C3×C4—41no—
118C2×C3×C4—42no—
119C2×Dic3—204no—
120SL(2,𝔽3)C2×Dic1011yescharacteristic
121C22×C5—32no—
122C22×C5—62no—
123C22×C5C22×S411yescharacteristic
124C4×C5—22no—
125C4×C5—31no—
126C4×C5—31no—
127C4×C5—62no—
128C4×C5A4⋊Q812yes—
129Dic5—124no—
130#41—32no—
131#41Dic3012yes—
132C2×Q8C22×D1511yescharacteristic
133C2×D4—31no—
134C22×C4—31no—
135C22×C4—32no—
136C22×C4—302no—
137M16—304no—
138C2×C8—154no—
139C4⋊C4—32no—
140C4⋊C4—154no—
141C4⋊C4—304no—
142C4⋊C4—302no—
143C4⋊C4—304no—
144C22⋊C4—61no—
145C42—32no—
146C42—31no—
147C42C5⋊S411yescharacteristic
148C3×C5—41noHall
149C22×C3—41no—
150C3×C4—42no—
151C3×C4—82no—
152Dic3—404no—
153C2×C5—62no—
154C2×C5C2×A4⋊Q811yescharacteristic
155C2×C5#592312yes—
156C23—31no—
157Q8—31no—
158Q8C2×Dic3011yescharacteristic
159D4—32no—
160D4—61no—
161C2×C4—31no—
162C2×C4—32no—
163C2×C4—32no—
164C2×C4—32no—
165C2×C4—122no—
166C2×C4—304no—
167C2×C4—604no—
168C2×C4C2×C5⋊S412yes—
169C2×C4C2×C5⋊S411yescharacteristic
170C8—304no—
171C2×C3—41no—
172C2×C3—42no—
173C5#8533911yescharacteristic, complemented, Sylow
174C22—32no—
175C22—62no—
176C22C22×C5⋊S411yescharacteristic
177C4—22no—
178C4—31no—
179C4—31no—
180C4—62no—
181C4—604no—
182C4#9194812yes—
183C3—41noSylow
184C2—62no—
185C2C2×#9194811yescharacteristic
186C2#1175690712yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11752108C2semidirect
173. C5#85339semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#117521452
#117521082
#106142403
#917594
#853395