Finite Group Databasebeta

← #14512472

Subgroups — #14512472

Order 1920.

250 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 40 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
1#11756726C212yesmaximal
2D5×#131⋊C3C211yesmaximal, characteristic
3#10604782—31nomaximal, Hall
4D5×#41⋊C3C2211yescharacteristic
5#91886—22no—
6C5×#131⋊C3C411yescharacteristic, complemented
7#91223—41nomaximal
8#4094⋊C3C411yescharacteristic, complemented
9#73126—51nomaximal, Hall
10D5×#131D311yescharacteristic
11#65793—32no—
12D5⋊#108—31no—
13C2×#3994—31no—
14#64899—32no—
15C5×#41⋊C3C2×C411yescharacteristic
16C4⋊ΓL(1,𝔽16)—42no—
17D5×SL(2,𝔽3)D411yescharacteristic
18C5⋊(#41⋊C3)Q811yescharacteristic
19C3×C8×D5—41no—
20C2×#131⋊C3—51no—
21#5426—52no—
22D5×#41C2×D311yescharacteristic
23C2×C4⋊AGL(1,𝔽5)—32no—
24D5⋊M16—32no—
25C5×#131Dic311yescharacteristic, complemented
26#4094Dic311yescharacteristic, complemented
27#4053—31no—
28D5×M16—31no—
29#4047—31no—
30C2×C8×D5—31no—
31#4009—62no—
32#4007—62no—
33#3996—61no—
34#3995—61no—
35#3994—61no—
36#3994—61no—
37#1816—151noSylow
38C2×ΓL(1,𝔽16)—82no—
39C3×C4×D5—41no—
40C5×SL(2,𝔽3)C4⋊C411yescharacteristic
41C3×C5×C8—41no—
42C3×#168—41no—
43C2×#41⋊C3—51no—
44#131⋊C3—51no—
45#131⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
46#859—102no—
47#818—201no—
48C22×AGL(1,𝔽5)—62no—
49C5×#41C2×Dic311yescharacteristic
50#713Dic611yescharacteristic
51Q8×D5D1211yescharacteristic
52#711—31no—
53D4×D5—31no—
54#709—31no—
55C2×C4×D5—31no—
56#704—62no—
57C4⋊AGL(1,𝔽5)—62no—
58C4⋊AGL(1,𝔽5)—62no—
59#700—62no—
60D5⋊C8—62no—
61C5×M16—31no—
62C2×C5×C8—31no—
63#681—31no—
64C2×#168—31no—
65#676—61no—
66C8×D5—31no—
67C8×D5—31no—
68C8×D5—31no—
69C8×D5S411yescharacteristic
70C2×#131—51no—
71C2×#108—151no—
72C2×#107—151no—
73#417—152no—
74#343—152no—
75C2×C3×D5—41no—
76ΓL(1,𝔽16)—162no—
77C3×C4×C5—41no—
78C3×Dic5—41no—
79#41⋊C3—51no—
80#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
81C2×SL(2,𝔽3)—51no—
82C2×C3×C8—201no—
83C4⋊Dic3—202no—
84C22×D5—31no—
85C2×AGL(1,𝔽5)—122no—
86C2×AGL(1,𝔽5)—242no—
87C5×Q8C4⋊Dic311yescharacteristic
88C5×D4—31no—
89C2×C4×C5—31no—
90C22⋊D5—61no—
91C2×Dic5—31no—
92D20—31no—
93C4×D5—31no—
94C4×D5—31no—
95C4×D5—31no—
96C4×D5C2×S411yescharacteristic
97Dic10—31no—
98#170—122no—
99C5×C8—31no—
100C5×C8SL(2,ℤ/4)11yescharacteristic
101#168—31no—
102#168SL(2,ℤ/4)11yescharacteristic
103C2×#41—51no—
104#131—51no—
105#131—151no—
106#131—151no—
107#131ΓL(1,𝔽16)11yescharacteristic, complemented
108C2×M16—151no—
109C2×M16—152no—
110C22×C8—151no—
111C2×C4⋊C4—152no—
112#108—301no—
113#108—301no—
114#107—301no—
115#107—301no—
116#103—302no—
117#102—302no—
118C2×C3×C5—41no—
119C3×D5—41no—
120C3×D5—41no—
121C2×C3×C4—201no—
122C2×Dic3—402no—
123SL(2,𝔽3)C4⋊AGL(1,𝔽5)11yescharacteristic
124C3×C8—41no—
125C3×C8—201no—
126C22×C5—31no—
127C2×D5—31no—
128C2×D5—61no—
129C2×D5—61no—
130C2×D5C4⋊S411yescharacteristic
131AGL(1,𝔽5)—242no—
132C4×C5—31no—
133C4×C5C2×SL(2,ℤ/4)11yescharacteristic
134Dic5—31no—
135Dic5A4⋊Q811yescharacteristic
136#41—51no—
137#41—151no—
138#41—151no—
139#41C2×ΓL(1,𝔽16)11yescharacteristic
140C2×Q8—51no—
141C2×D4—151no—
142C22×C4—151no—
143C22×C4—302no—
144M16—31no—
145M16—151no—
146M16—301no—
147M16—302no—
148M16—302no—
149C2×C8—31no—
150C2×C8—51no—
151C2×C8—151no—
152C2×C8—151no—
153C2×C8—151no—
154C2×C8—151no—
155C2×C8—302no—
156C4⋊C4—302no—
157C4⋊C4—302no—
158C3×C5—41noHall
159C22×C3—201no—
160C3×C4—41no—
161C3×C4—201no—
162Dic3—802no—
163C2×C5—61no—
164C2×C5C4⋊SL(2,ℤ/4)11yescharacteristic
165D5—61no—
166D5#540311yescharacteristic
167D5#540711yescharacteristic
168C23—151no—
169Q8—151no—
170Q8C4⋊ΓL(1,𝔽16)11yescharacteristic
171D4—31no—
172D4—151no—
173D4—301no—
174C2×C4—31no—
175C2×C4—51no—
176C2×C4—151no—
177C2×C4—151no—
178C2×C4—151no—
179C2×C4—151no—
180C2×C4—602no—
181C2×C4—1202no—
182C8—31no—
183C8—51no—
184C8—151no—
185C8—602no—
186C8A4⋊AGL(1,𝔽5)11yescharacteristic
187C2×C3—41no—
188C2×C3—201no—
189C2×C3—201no—
190C5#7312611yescharacteristic, complemented, Sylow
191C22—31no—
192C22—51no—
193C22—151no—
194C22—301no—
195C22—301no—
196C4—31no—
197C4—51no—
198C4—151no—
199C4—1202no—
200C4C2×A4⋊AGL(1,𝔽5)11yescharacteristic
201C3—41noSylow
202C2—51no—
203C2—51no—
204C2—61no—
205C2—301no—
206C2C4⋊(A4⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C4⋊(A4⋊AGL(1,𝔽5))
commutatorC5×#41⋊C3C2×C4
FrattiniC4C2×A4⋊AGL(1,𝔽5)
FittingC5×#131Dic3
socleC2×C5C4⋊SL(2,ℤ/4)
prime radical, cosocleD5×#41⋊C3C22
hypercenterC8A4⋊AGL(1,𝔽5)
hypocenterC5×SL(2,𝔽3)C4⋊C4
LCSG ▷ C5×#41⋊C3 ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
6. C5×#131⋊C3C4semidirect
8. #4094⋊C3C4semidirect
25. C5×#131Dic3semidirect
26. #4094Dic3semidirect
45. #131⋊C3AGL(1,𝔽5)semidirect
107. #131ΓL(1,𝔽16)semidirect
190. C5#73126semidirect

Maximal subgroups

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

subgroupindex
#117567262
D5×#131⋊C32
#106047823
#912234
#731265