Finite Group Databasebeta

← #14512442

Subgroups — #14512442

Order 1920.

218 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 38 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⋊C3)C211yesmaximal, characteristic
2SL(2,𝔽3)⋊#170C212yesmaximal, complemented
3#10604440—31nomaximal, Hall
4C2×C5⋊(#41⋊C3)C411yescharacteristic
5C4×C5×SL(2,𝔽3)C411yescharacteristic
6#91231—41nomaximal
7Dic5×SL(2,𝔽3)C2211yescharacteristic
8#73069—51nomaximal, Hall
9C4×#713D311yescharacteristic
10#65683—31no—
11#65680—31no—
12Q8⋊#170—32no—
13#64871—32no—
14C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
15C2×C3⋊#170—42no—
16C5⋊(#41⋊C3)—21no—
17C3×C4×Dic5—41no—
18C4×#41⋊C3—51no—
19SL(2,𝔽3)⋊C8—52no—
20C2×#713Dic311yescharacteristic
21C4×C5×Q8Dic311yescharacteristic
22Q8×Dic5C2×D311yescharacteristic
23#4039—31no—
24#4038—31no—
25C4×D20—31no—
26C42×D5—31no—
27#4003—61no—
28#4003—61no—
29#4002—61no—
30C4⋊#170—32no—
31C4⋊#170—61no—
32C4×#170—32no—
33#1488—151noSylow
34C2×C3×C4×C5—41no—
35C2×C3×Dic5—41no—
36C2×C3×Dic5—41no—
37C5×SL(2,𝔽3)M1611yescharacteristic
38C3⋊#170—44no—
39C2×#41⋊C3—51no—
40C4×SL(2,𝔽3)—51no—
41C4×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
42#803—201no—
43C2×C5×Q8C2×Dic311yescharacteristic
44#713—21no—
45#713—61no—
46C2×D20—31no—
47C2×C4×D5—31no—
48C2×C4×D5—31no—
49C2×C4×D5—31no—
50C2×#170—62no—
51C2×#170—62no—
52C5×C4⋊C4—31no—
53C42×C5—31no—
54#685—61no—
55C4⋊Dic5—31no—
56C4×Dic5—31no—
57C4×Dic5—31no—
58C4×Dic5S411yescharacteristic
59C4×#41—51no—
60#432—151no—
61#431—151no—
62Q8⋊C8—152no—
63D4⋊C8—152no—
64C22×C3×C5—41no—
65C3×C4×C5—81no—
66C3×Dic5—42no—
67C3×Dic5—81no—
68#41⋊C3—101no—
69C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
70C3×C42—201no—
71C2×C3⋊C8—202no—
72C22×D5—31no—
73C5×Q8—31no—
74C5×Q8#20811yescharacteristic
75C2×C4×C5—31no—
76C2×C4×C5—31no—
77C2×C4×C5SL(2,ℤ/4)11yescharacteristic
78C2×Dic5—31no—
79C2×Dic5SL(2,ℤ/4)11yescharacteristic
80C2×Dic5C2×S411yescharacteristic
81D20—32no—
82D20—61no—
83C4×D5—61no—
84C4×D5—61no—
85C4×D5—62no—
86C4×D5—121no—
87#170—122no—
88#170—122no—
89C2×#41—51no—
90C4×Q8—51no—
91C4×Q8ΓL(1,𝔽16)11yescharacteristic
92C4×D4—151no—
93C4×D4—151no—
94#117—151no—
95C2×C42—151no—
96C4⋊C8—152no—
97C4⋊C8—301no—
98C22⋊C8—301no—
99C22⋊C8—301no—
100#97—301no—
101C4×C8—152no—
102C2×C3×C5—41no—
103C2×C3×C5—41no—
104C2×C3×C5—41no—
105C2×C3×C4—41no—
106C2×C3×C4—201no—
107C2×C3×C4—201no—
108SL(2,𝔽3)#70011yescharacteristic
109C3⋊C8—204no—
110C22×C5C2×SL(2,ℤ/4)11yescharacteristic
111C2×D5—61no—
112C2×D5—61no—
113C2×D5—61no—
114C4×C5—21no—
115C4×C5—31no—
116C4×C5—31no—
117C4×C5—61no—
118Dic5—21no—
119Dic5—61no—
120Dic5#98512yes—
121#41—101no—
122#41—301no—
123C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
124C2×D4—151no—
125C22×C4—151no—
126C22×C4—151no—
127C22×C4—151no—
128C2×C8—302no—
129C2×C8—302no—
130C4⋊C4—31no—
131C4⋊C4—151no—
132C22⋊C4—301no—
133C42—31no—
134C42—51no—
135C42—151no—
136C42—151no—
137C3×C5—41noHall
138C22×C3—41no—
139C3×C4—81no—
140C3×C4—202no—
141C3×C4—401no—
142C2×C5#540911yescharacteristic
143C2×C5#542311yescharacteristic
144C2×C5#542411yescharacteristic
145D5—121no—
146C23—151no—
147Q8—31no—
148Q8#675811yescharacteristic
149D4—152no—
150D4—301no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—51no—
154C2×C4—51no—
155C2×C4—151no—
156C2×C4—301no—
157C2×C4—301no—
158C2×C4—302no—
159C2×C4—601no—
160C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
161C8—602no—
162C8—602no—
163C2×C3—41no—
164C2×C3—41no—
165C2×C3—41no—
166C5#7306911yescharacteristic, complemented, Sylow
167C22—301no—
168C22—301no—
169C22—301no—
170C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
171C4—21no—
172C4—31no—
173C4—31no—
174C4—52no—
175C4—61no—
176C4—101no—
177C4—301no—
178C3—41noSylow
179C2—601no—
180C2#1175671611yescharacteristic
181C2#1175672011yescharacteristic
182C2#1175672511yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutatorC2×C5×SL(2,𝔽3)C2×C4
FittingC4×C5×Q8Dic3
socleC22×C5C2×SL(2,ℤ/4)
prime radicalC2×C5⋊(#41⋊C3)C4
cosocleDic5×SL(2,𝔽3)C22
hypercenterC2×C4A4⋊AGL(1,𝔽5)
hypocenterC5×SL(2,𝔽3)M16
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. SL(2,𝔽3)⋊#170C2semidirect
166. C5#73069semidirect

Maximal subgroups

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

subgroupindex
C4×C5⋊(#41⋊C3)2
SL(2,𝔽3)⋊#1702
#106044403
#912314
#730695