Finite Group Databasebeta

← C5×#1444⋊C3 #14510669

Subgroups — C5×#1444⋊C3 #14510669

Order 1920.

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

normal subgroups only

This group has 266 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
1C2×C5×#95⋊C3C211yesmaximal, characteristic
2C5×#1444C311yesmaximal, characteristic, complemented, Hall
3C2×C4×C5×A4—41nomaximal
4C5×#95⋊C3C411yescharacteristic, complemented
5#1444⋊C3C511yesmaximal, characteristic, direct product factor, Hall
6C22×C5×C4⋊C4—31no—
7C2×C5×#95—31no—
8C2×C5×#95C2×C311yescharacteristic
9C22×C5×A4—41no—
10C4×C5×A4—42no—
11C2×#95⋊C3C2×C511yescharacteristic
12C23×C4×C5—31no—
13C23×C4×C5—31no—
14C23×C4×C5A411yescharacteristic
15C2×C5×C4⋊C4—62no—
16C2×C5×C4⋊C4—64no—
17C5×#95—31no—
18C5×#95—62no—
19C5×#95C3×C411yescharacteristic, complemented
20#1444C3×C511yescharacteristic, complemented, Sylow
21C2×C5×A4—41no—
22C2×C5×A4—41no—
23C2×C5×A4—41no—
24C2×C3×C4×C5—161no—
25C2×C4×A4—41no—
26#95⋊C3C4×C511yescharacteristic, complemented
27C24×C5C2×A411yescharacteristic
28C22×C4×C5—32no—
29C22×C4×C5—32no—
30C22×C4×C5—31no—
31C22×C4×C5—31no—
32C22×C4×C5—32no—
33C22×C4×C5—61no—
34C22×C4×C5—62no—
35C22×C4×C5—62no—
36C22×C4×C5—62no—
37C22×C4×C5—62no—
38C22×C4×C5—61no—
39C22×C4×C5—61no—
40C22×C4×C5—61no—
41C22×C4×C5SL(2,𝔽3)12yes—
42C5×C4⋊C4—68no—
43C22×C4⋊C4—31no—
44C2×#95—31no—
45C2×#95C2×C3×C511yescharacteristic
46C22×C3×C5—161no—
47C5×A4—41no—
48C3×C4×C5—162no—
49C22×A4—41no—
50C4×A4—42no—
51C23×C5—31no—
52C23×C5—31no—
53C23×C5—31no—
54C23×C5—31no—
55C23×C5C4×A411yescharacteristic
56C23×C5C2×SL(2,𝔽3)11yescharacteristic
57C23×C5#41⋊C311yescharacteristic
58C2×C4×C5—32no—
59C2×C4×C5—32no—
60C2×C4×C5—41no—
61C2×C4×C5—62no—
62C2×C4×C5—62no—
63C2×C4×C5—62no—
64C2×C4×C5—62no—
65C2×C4×C5—64no—
66C2×C4×C5—62no—
67C2×C4×C5—64no—
68C2×C4×C5—62no—
69C2×C4×C5—121no—
70C2×C4×C5—121no—
71C2×C4×C5—122no—
72C2×C4×C5—121no—
73C23×C4—31no—
74C23×C4—31no—
75C23×C4C5×A411yescharacteristic
76C2×C4⋊C4—62no—
77C2×C4⋊C4—64no—
78#95—31no—
79#95—62no—
80#95C3×C4×C511yescharacteristic, complemented
81C2×C3×C5—161no—
82C2×C3×C5—161no—
83C2×C3×C5—161no—
84C2×A4—41no—
85C2×A4—41no—
86C2×A4—41no—
87C2×C3×C4—161no—
88C22×C5—31no—
89C22×C5—31no—
90C22×C5—31no—
91C22×C5—32no—
92C22×C5—31no—
93C22×C5—31no—
94C22×C5—31no—
95C22×C5—31no—
96C22×C5—31no—
97C22×C5—31no—
98C22×C5C4×SL(2,𝔽3)11yescharacteristic
99C22×C5#127⋊C311yescharacteristic
100C4×C5—42no—
101C4×C5—62no—
102C4×C5—62no—
103C4×C5—122no—
104C24C2×C5×A411yescharacteristic
105C22×C4—32no—
106C22×C4—32no—
107C22×C4—31no—
108C22×C4—31no—
109C22×C4—32no—
110C22×C4—61no—
111C22×C4—62no—
112C22×C4—62no—
113C22×C4—61no—
114C22×C4—62no—
115C22×C4—62no—
116C22×C4—61no—
117C22×C4—61no—
118C22×C4C5×SL(2,𝔽3)12yes—
119C4⋊C4—68no—
120C3×C5—161noHall
121C22×C3—161no—
122A4—41no—
123C3×C4—162no—
124C2×C5—31no—
125C2×C5—31no—
126C2×C5—31no—
127C2×C5—31no—
128C2×C5#384⋊C311yescharacteristic
129C2×C5#392⋊C311yescharacteristic
130C2×C5#399⋊C311yescharacteristic
131C23—31no—
132C23—31no—
133C23—31no—
134C23—31no—
135C23C4×C5×A411yescharacteristic
136C23C2×C5×SL(2,𝔽3)11yescharacteristic
137C23C5×#41⋊C311yescharacteristic
138C2×C4—32no—
139C2×C4—32no—
140C2×C4—41no—
141C2×C4—62no—
142C2×C4—62no—
143C2×C4—62no—
144C2×C4—62no—
145C2×C4—64no—
146C2×C4—62no—
147C2×C4—64no—
148C2×C4—62no—
149C2×C4—121no—
150C2×C4—121no—
151C2×C4—122no—
152C2×C4—121no—
153C2×C3—161no—
154C2×C3—161no—
155C2×C3—161no—
156C5#1444⋊C311yescharacteristic, direct product factor, Sylow
157C22—31no—
158C22—31no—
159C22—31no—
160C22—32no—
161C22—31no—
162C22—31no—
163C22—31no—
164C22—31no—
165C22—31no—
166C22—31no—
167C22C4×C5×SL(2,𝔽3)11yescharacteristic
168C22C5×#127⋊C311yescharacteristic
169C4—42no—
170C4—62no—
171C4—62no—
172C4—122no—
173C3—161noSylow
174C2—31no—
175C2—31no—
176C2—31no—
177C2—31no—
178C2C5×#384⋊C311yescharacteristic
179C2C5×#392⋊C311yescharacteristic
180C2C5×#399⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22×C5#127⋊C3
commutator, hypocenter#95C3×C4×C5
FrattiniC24C2×C5×A4
FittingC5×#1444C3
socleC24×C5C2×A4
prime radicalC2×C5×#95⋊C3C2
cosocleC2×#95C2×C3×C5
LCSG ▷ #95
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
2. C5×#1444C3semidirect
4. C5×#95⋊C3C4semidirect
5. #1444⋊C3C5direct (N × H)
19. C5×#95C3×C4semidirect
20. #1444C3×C5semidirect
26. #95⋊C3C4×C5semidirect
80. #95C3×C4×C5semidirect
156. C5#1444⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#95⋊C32
C5×#14443
C2×C4×C5×A44
#1444⋊C35