Finite Group Databasebeta

← C3×#10598740 #14279539

Subgroups — C3×#10598740 #14279539

Order 1920.

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

normal subgroups only

This group has 168 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
1C3×#65357C211yesmaximal, characteristic
2C3×#64856C211yesmaximal, characteristic
3C3×#64854C211yesmaximal, characteristic
4#10598740C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#125C411yescharacteristic, complemented
6C3×#4021C2211yescharacteristic
7C3×#4005—21no—
8C3×#3999—21no—
9C3×#3942—21no—
10C3×#3941—21no—
11C3×C4×#168C411yescharacteristic, complemented
12C3×#1414—51nomaximal, Hall
13#65357C2×C311yescharacteristic
14#64856C2×C311yescharacteristic
15#64854C2×C311yescharacteristic
16C2×C3×D20D411yescharacteristic
17C2×C3×Dic10D411yescharacteristic
18C3×C22⋊AGL(1,𝔽5)—41no—
19C3×#704—41no—
20C3×C5×C4⋊C4—21no—
21C3×C5×C4⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C3×#685—41no—
24C2×C3×#168—21no—
25C3×#488—51no—
26C3×#355—51no—
27C3×#354—51no—
28C5×#125C3×C411yescharacteristic, complemented
29#4021C22×C311yescharacteristic
30#4005—21no—
31#3999—21no—
32#3942—21no—
33#3941—21no—
34C4×#168C3×C411yescharacteristic, complemented
35#1414—51noSylow
36C22×C3×D5—21no—
37C2×C3×AGL(1,𝔽5)—81no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—41no—
40C2×C3×C4×C5C22⋊C411yescharacteristic
41C2×C3×Dic5—21no—
42C3×D20—41no—
43C3×Dic10—41no—
44C3×#170—81no—
45C3×#168—41no—
46C3×#125AGL(1,𝔽5)11yescharacteristic, complemented
47C3×#124—51no—
48C3×#103—101no—
49C3×#102—101no—
50C3×#101—101no—
51C3×#99—101no—
52C3×C4×C8—51no—
53C2×D20C3×D411yescharacteristic
54C2×Dic10C3×D411yescharacteristic
55C22⋊AGL(1,𝔽5)—41no—
56#704—41no—
57C5×C4⋊C4—21no—
58C5×C4⋊C4—41no—
59C42×C5C2×C3×C411yescharacteristic
60#685—41no—
61C2×#168—21no—
62#488—51no—
63#355—51no—
64#354—51no—
65C22×C3×C5#9911yescharacteristic
66C2×C3×D5—41no—
67C2×C3×D5—81no—
68C3×AGL(1,𝔽5)—161no—
69C3×C4×C5—21no—
70C3×C4×C5—41no—
71C3×C4×C5—81no—
72C3×Dic5—41no—
73C2×C3×Q8—51no—
74C2×C3×D4—51no—
75C3×M16—201no—
76C2×C3×C8—101no—
77C3×C4⋊C4—21no—
78C3×C4⋊C4—41no—
79C3×C22⋊C4—201no—
80C3×C22⋊C4—201no—
81C3×C42C2×AGL(1,𝔽5)11yescharacteristic
82C22×D5—21no—
83C2×AGL(1,𝔽5)—81no—
84C2×C4×C5—21no—
85C2×C4×C5—41no—
86C2×C4×C5C3×C22⋊C411yescharacteristic
87C2×Dic5—21no—
88D20—41no—
89Dic10—41no—
90#170—81no—
91#168—41no—
92#125C3×AGL(1,𝔽5)11yescharacteristic, complemented
93#124—51no—
94#103—101no—
95#102—101no—
96#101—101no—
97#99—101no—
98C4×C8—51no—
99C2×C3×C5—21no—
100C2×C3×C5#35411yescharacteristic
101C3×D5—81no—
102C23×C3—101no—
103C3×Q8—201no—
104C3×D4—201no—
105C2×C3×C4—21no—
106C2×C3×C4—41no—
107C2×C3×C4—101no—
108C2×C3×C4—401no—
109C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
110C3×C8—201no—
111C3×C8—401no—
112C22×C5C3×#9911yescharacteristic
113C2×D5—41no—
114C2×D5—81no—
115AGL(1,𝔽5)—161no—
116C4×C5—21no—
117C4×C5—41no—
118C4×C5—81no—
119Dic5—41no—
120C2×Q8—51no—
121C2×D4—51no—
122M16—201no—
123C2×C8—101no—
124C4⋊C4—21no—
125C4⋊C4—41no—
126C22⋊C4—201no—
127C22⋊C4—201no—
128C42C2×C3×AGL(1,𝔽5)11yescharacteristic
129C3×C5#141411yescharacteristic, complemented, Hall
130C22×C3—201no—
131C22×C3—401no—
132C22×C3#401111yescharacteristic
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—81no—
136C3×C4—201no—
137C3×C4—801no—
138C2×C5—21no—
139C2×C5C3×#35411yescharacteristic
140D5—81no—
141C23—101no—
142Q8—201no—
143D4—201no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—101no—
147C2×C4—401no—
148C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
149C8—201no—
150C8—401no—
151C2×C3—21no—
152C2×C3—401no—
153C2×C3#6492811yescharacteristic
154C5C3×#141411yescharacteristic, complemented, Sylow
155C22—201no—
156C22—401no—
157C22C3×#401111yescharacteristic
158C4—21no—
159C4—41no—
160C4—81no—
161C4—201no—
162C4—801no—
163C3#1059874011yescharacteristic, direct product factor, Sylow
164C2—21no—
165C2—401no—
166C2C3×#6492811yescharacteristic
subgroupG/H
centerC2×C3#64928
commutatorC42×C5C2×C3×C4
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×#125C4
socleC2×C3×C5#354
prime radicalC2×C3×D20D4
cosocle#4021C22×C3
hypercenterC3×#125AGL(1,𝔽5)
hypocenterC5C3×#1414
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
4. #10598740C3direct (N × H)
5. C3×C5×#125C4semidirect
11. C3×C4×#168C4semidirect
28. C5×#125C3×C4semidirect
34. C4×#168C3×C4semidirect
46. C3×#125AGL(1,𝔽5)semidirect
92. #125C3×AGL(1,𝔽5)semidirect
129. C3×C5#1414semidirect
154. C5C3×#1414semidirect
163. C3#10598740direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653572
C3×#648562
C3×#648542
#105987403
C3×#14145