Finite Group Databasebeta

← C3×#10598599 #14277990

Subgroups — C3×#10598599 #14277990

Order 1920.

228 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 52 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×#65154C211yesmaximal, characteristic
2C3×#64895C211yesmaximal, characteristic, complemented
3C3×#64891C211yesmaximal, characteristic, complemented
4#10598599C311yesmaximal, characteristic, direct product factor, Hall
5C3×#4130—21no—
6C2×C3×D40C411yescharacteristic, complemented
7C2×C3×#676C2211yescharacteristic
8C3×#4041—21no—
9C3×#3998—21no—
10C3×C5×#106C411yescharacteristic, complemented
11C3×#3941—21no—
12C3×#1339—51nomaximal, Hall
13#65154C2×C311yescharacteristic
14#64895C2×C311yescharacteristic, complemented
15#64891C2×C311yescharacteristic, complemented
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×C4×D5D411yescharacteristic
19C3×C22⋊AGL(1,𝔽5)—41no—
20C3×C4⋊AGL(1,𝔽5)—41no—
21C3×C4×AGL(1,𝔽5)—22no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×C5×C4⋊C4—21no—
24C3×#685—41no—
25C2×C3×#168D411yescharacteristic
26C3×D40—41no—
27C3×#676—41no—
28C3×#674—41no—
29C3×#469—51no—
30C3×#349—51no—
31C3×H(3,ℤ/4)—51no—
32#4130—21no—
33C2×D40C3×C411yescharacteristic, complemented
34C2×#676C22×C311yescharacteristic
35#4041—21no—
36#3998—21no—
37C5×#106C3×C411yescharacteristic, complemented
38#3941—21no—
39#1339—51noSylow
40C22×C3×D5—41no—
41C22×C3×D5D811yescharacteristic
42C2×C3×AGL(1,𝔽5)—42no—
43C2×C3×C4×C5—41no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×Dic5SD1611yescharacteristic
46C3×D20—41no—
47C3×D20—41no—
48C3×D20—82no—
49C3×C4×D5—21no—
50C3×C4×D5—21no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×D8—51no—
54C2×C3×M16—51no—
55C3×#121—101no—
56C3×#117—101no—
57C3×M32—101no—
58C3×#106AGL(1,𝔽5)11yescharacteristic, complemented
59C3×#102—101no—
60C2×D20—21no—
61C2×D20—41no—
62C2×C4×D5C3×D411yescharacteristic
63C22⋊AGL(1,𝔽5)—41no—
64C4⋊AGL(1,𝔽5)—41no—
65C4×AGL(1,𝔽5)—22no—
66C2×C5×C8C2×C3×C411yescharacteristic
67C5×C4⋊C4—21no—
68#685—41no—
69C2×#168C3×D411yescharacteristic
70D40—41no—
71#676—41no—
72#674—41no—
73#469—51no—
74#349—51no—
75H(3,ℤ/4)—51no—
76C22×C3×C5#10211yescharacteristic
77C2×C3×D5—21no—
78C2×C3×D5—41no—
79C2×C3×D5—81no—
80C2×C3×D5—81no—
81C2×C3×D5—81no—
82C3×AGL(1,𝔽5)—82no—
83C3×C4×C5—81no—
84C3×C4×C5#9911yescharacteristic
85C3×C4×C5#10411yescharacteristic
86C3×Dic5—21no—
87C2×C3×D4—101no—
88C2×C3×D4—201no—
89C22×C3×C4—51no—
90C3×D8—201no—
91C3×M16—201no—
92C2×C3×C8—51no—
93C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
94C3×C4⋊C4—21no—
95C3×C4⋊C4—201no—
96C3×C22⋊C4—201no—
97C3×C22⋊C4—201no—
98C3×C42—102no—
99C3×C16—201no—
100C22×D5—41no—
101C22×D5C3×D811yescharacteristic
102C2×AGL(1,𝔽5)—42no—
103C2×C4×C5—41no—
104C2×C4×C5C3×C22⋊C411yescharacteristic
105C2×Dic5C3×SD1611yescharacteristic
106D20—41no—
107D20—41no—
108D20—82no—
109C4×D5—21no—
110C4×D5—21no—
111C5×C8—21no—
112#168—21no—
113C2×D8—51no—
114C2×M16—51no—
115#121—101no—
116#117—101no—
117M32—101no—
118#106C3×AGL(1,𝔽5)11yescharacteristic, complemented
119#102—101no—
120C2×C3×C5—21no—
121C2×C3×C5#32711yescharacteristic
122C3×D5—41no—
123C3×D5—161no—
124C23×C3—51no—
125C23×C3—201no—
126C3×D4—201no—
127C3×D4—201no—
128C3×D4—402no—
129C2×C3×C4—41no—
130C2×C3×C4—51no—
131C2×C3×C4—101no—
132C2×C3×C4—101no—
133C2×C3×C4—202no—
134C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
135C3×C8—21no—
136C3×C8—101no—
137C22×C5C3×#10211yescharacteristic
138C2×D5—21no—
139C2×D5—41no—
140C2×D5—81no—
141C2×D5—81no—
142C2×D5—81no—
143AGL(1,𝔽5)—82no—
144C4×C5—81no—
145C4×C5C3×#9911yescharacteristic
146C4×C5C3×#10411yescharacteristic
147Dic5—21no—
148C2×D4—101no—
149C2×D4—201no—
150C22×C4—51no—
151D8—201no—
152M16—201no—
153C2×C8—51no—
154C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—201no—
157C22⋊C4—201no—
158C22⋊C4—201no—
159C42—102no—
160C16—201no—
161C3×C5#133911yescharacteristic, complemented, Hall
162C22×C3—101no—
163C22×C3—201no—
164C22×C3—401no—
165C22×C3—401no—
166C22×C3—401no—
167C22×C3#400711yescharacteristic
168C3×C4—81no—
169C3×C4—101no—
170C3×C4—402no—
171C3×C4#399911yescharacteristic
172C3×C4#401011yescharacteristic
173C2×C5—21no—
174C2×C5C3×#32711yescharacteristic
175D5—41no—
176D5—161no—
177C23—51no—
178C23—201no—
179D4—201no—
180D4—201no—
181D4—402no—
182C2×C4—41no—
183C2×C4—51no—
184C2×C4—101no—
185C2×C4—101no—
186C2×C4—202no—
187C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
188C8—21no—
189C8—101no—
190C2×C3—21no—
191C2×C3—201no—
192C2×C3—801no—
193C2×C3#6486811yescharacteristic
194C5C3×#133911yescharacteristic, complemented, Sylow
195C22—101no—
196C22—201no—
197C22—401no—
198C22—401no—
199C22—401no—
200C22C3×#400711yescharacteristic
201C4—81no—
202C4—101no—
203C4—402no—
204C4C3×#399911yescharacteristic
205C4C3×#401011yescharacteristic
206C3#1059859911yescharacteristic, direct product factor, Sylow
207C2—21no—
208C2—201no—
209C2—801no—
210C2C3×#6486811yescharacteristic
subgroupG/H
centerC2×C3#64868
commutatorC2×C5×C8C2×C3×C4
FrattiniC2×C8C2×C3×AGL(1,𝔽5)
FittingC3×C5×#106C4
socleC2×C3×C5#327
prime radicalC3×#65154C2
cosocleC2×#676C22×C3
hypercenterC3×#106AGL(1,𝔽5)
hypocenterC5C3×#1339
LCSG ▷ C2×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#106

Complements

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

NH ≅ G/Ntype
2. C3×#64895C2semidirect
3. C3×#64891C2semidirect
4. #10598599C3direct (N × H)
6. C2×C3×D40C4semidirect
10. C3×C5×#106C4semidirect
14. #64895C2×C3semidirect
15. #64891C2×C3semidirect
33. C2×D40C3×C4semidirect
37. C5×#106C3×C4semidirect
58. C3×#106AGL(1,𝔽5)semidirect
118. #106C3×AGL(1,𝔽5)semidirect
161. C3×C5#1339semidirect
194. C5C3×#1339semidirect
206. C3#10598599direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#651542
C3×#648952
C3×#648912
#105985993
C3×#13395