Finite Group Databasebeta

← #14512403

Subgroups — #14512403

Order 1920.

170 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 30 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#11751615C211yesmaximal, characteristic
2#65791⋊C3C211yesmaximal, characteristic, complemented
3#11751558C211yesmaximal, characteristic, complemented
4#10604862—31nomaximal, Hall
5C5×#985C411yescharacteristic
6#4094⋊C3C2211yescharacteristic
7#91185C411yescharacteristic
8#91165—41nomaximal
9#73039—51nomaximal, Hall
10#65791—31no—
11#65791D311yescharacteristic, complemented
12#65485—31no—
13#64932—31no—
14#64932—31no—
15#64889—31no—
16#64886—31no—
17C5×#41⋊C3C2×C411yescharacteristic
18C5×GL(2,𝔽3)C811yescharacteristic
19C5×#226C811yescharacteristic
20D3×#168—41no—
21C3⋊#674—41no—
22C3×#674—41no—
23#5404—51no—
24#504⋊C3—51no—
25#4628—51no—
26C5×#135—31no—
27#4094—31no—
28#4094C2×D311yescharacteristic
29#3998—31no—
30#3998—31no—
31#3998—61no—
32C2×#674—31no—
33C2×#674—31no—
34C2×#674—61no—
35#3969—31no—
36#3969—31no—
37#3951—31no—
38C8×Dic5—31no—
39#2171—151noSylow
40C4×C5×D3—41no—
41C5×SL(2,𝔽3)C2×C811yescharacteristic
42C3⋊#168—41no—
43C3×#168—41no—
44#985AGL(1,𝔽5)11yescharacteristic
45#131⋊C3—51no—
46GU(2,𝔽3)—51no—
47#798—201no—
48C5×#41—31no—
49C5×#41C4×D311yescharacteristic
50C5×Q16—31no—
51C5×SD16—31no—
52C5×SD16—31no—
53C5×D8—31no—
54C2×C5×C8—31no—
55C4×Dic5—31no—
56#681—31no—
57#681—31no—
58#681—61no—
59C2×#168—31no—
60C2×#168—61no—
61#674—31no—
62#674—61no—
63#674—61no—
64#674S411yescharacteristic
65#504—51no—
66#504—151no—
67#443—151no—
68#364—151no—
69#350—151no—
70#350—151no—
71#346—151no—
72C2×C5×D3—41no—
73C3×C4×C5—41no—
74C5×Dic3—41no—
75#41⋊C3C2×AGL(1,𝔽5)11yescharacteristic
76GL(2,𝔽3)#17011yescharacteristic
77#226#17011yescharacteristic
78D3×C8—201no—
79C3×C16—201no—
80C3⋊C16—201no—
81C5×Q8—31no—
82C5×Q8D3×C811yescharacteristic
83C5×D4—31no—
84C5×D4—31no—
85C5×D4—61no—
86C2×C4×C5—31no—
87C2×C4×C5—61no—
88C2×Dic5—61no—
89C5×C8—31no—
90C5×C8—31no—
91#168—31no—
92#168—61no—
93#168C2×S411yescharacteristic
94#135—31no—
95#131—51no—
96#131—151no—
97M32—151no—
98M32—151no—
99M32—301no—
100C2×C16—151no—
101C2×C16—151no—
102C2×C16—301no—
103#108—151no—
104#104—151no—
105#104—151no—
106C4×C8—151no—
107C2×C3×C5—41no—
108C5×D3—81no—
109C4×D3—41no—
110SL(2,𝔽3)C2×#17011yescharacteristic
111C3×C8—201no—
112C3⋊C8—201no—
113C22×C5—31no—
114C22×C5—61no—
115C4×C5—31no—
116C4×C5—61no—
117C4×C5C4×S411yescharacteristic
118Dic5—121no—
119#41—31no—
120#41D3×AGL(1,𝔽5)11yescharacteristic
121Q16—31no—
122SD16—31no—
123SD16—31no—
124D8—31no—
125M16—151no—
126M16—151no—
127M16—301no—
128C2×C8—31no—
129C2×C8—151no—
130C2×C8—301no—
131C42—151no—
132C16—51no—
133C16—151no—
134C16—301no—
135C16—301no—
136C3×C5—41noHall
137C2×D3—41no—
138C3×C4—41no—
139Dic3—41no—
140C2×C5—61no—
141C2×C5—121no—
142C2×C5C8×S411yescharacteristic
143Q8—31no—
144Q8D3×#17011yescharacteristic
145D4—31no—
146D4—31no—
147D4—61no—
148C2×C4—31no—
149C2×C4—61no—
150C2×C4—301no—
151C8—31no—
152C8—31no—
153C8—51no—
154C8—151no—
155C8—301no—
156C2×C3—41no—
157D3—81no—
158C5#7303911yescharacteristic, complemented, Sylow
159C22—31no—
160C22—61no—
161C4—31no—
162C4—61no—
163C4—601no—
164C4AGL(1,𝔽5)×S411yescharacteristic
165C3—41noSylow
166C2—61no—
167C2—121no—
168C2S4×#17011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4AGL(1,𝔽5)×S4
commutator, hypocenterC5×SL(2,𝔽3)C2×C8
FittingC5×#41C4×D3
socleC2×C5C8×S4
prime radicalC5×#985C4
cosocle#4094⋊C3C22
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #65791⋊C3C2semidirect
3. #11751558C2semidirect
11. #65791D3semidirect
158. C5#73039semidirect

Maximal subgroups

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

subgroupindex
#117516152
#65791⋊C32
#117515582
#106048623
#911654
#730395