Finite Group Databasebeta

← C3×#10598811 #14278011

Subgroups — C3×#10598811 #14278011

Order 1920.

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

normal subgroups only

This group has 208 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×#65478C211yesmaximal, characteristic
2C3×#64895C211yesmaximal, characteristic
3C3×#64891C211yesmaximal, characteristic
4#10598811C311yesmaximal, characteristic, direct product factor, Hall
5C3×#4130—21no—
6C2×C3×C5×Q16C411yescharacteristic, complemented
7C3×#4092—21no—
8C2×C3×#676C2211yescharacteristic
9C3×#3998—21no—
10C3×#3967—21no—
11C3×#3949C411yescharacteristic, complemented
12C3×#1340—51nomaximal, Hall
13#65478C2×C311yescharacteristic
14#64895C2×C311yescharacteristic
15#64891C2×C311yescharacteristic
16C2×C3×C5×Q8—21no—
17C2×C3×C4×D5D411yescharacteristic
18C3×C22⋊AGL(1,𝔽5)—41no—
19C3×C4⋊AGL(1,𝔽5)—41no—
20C3×C4×AGL(1,𝔽5)—22no—
21C3×C5×Q16—41no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×#685—41no—
24C3×C4⋊Dic5—21no—
25C3×#683—41no—
26C2×C3×#168D411yescharacteristic
27C3×#676—41no—
28C3×#674—41no—
29C3×#470—51no—
30C3×#349—51no—
31C3×H(3,ℤ/4)—51no—
32#4130—21no—
33C2×C5×Q16C3×C411yescharacteristic, complemented
34#4092—21no—
35C2×#676C22×C311yescharacteristic
36#3998—21no—
37#3967—21no—
38#3949C3×C411yescharacteristic, complemented
39#1340—51noSylow
40C22×C3×D5D811yescharacteristic
41C2×C3×AGL(1,𝔽5)—42no—
42C3×C5×Q8—41no—
43C3×C5×Q8—41no—
44C2×C3×C4×C5—41no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×C3×Dic5—41no—
47C2×C3×Dic5SD1611yescharacteristic
48C3×C4×D5—21no—
49C3×C4×D5—21no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×Q16AGL(1,𝔽5)11yescharacteristic, complemented
53C2×C3×M16—51no—
54C3×C22⋊Q8—101no—
55C3×#117—101no—
56C3×M32—101no—
57C3×#106—51no—
58C3×#103—101no—
59C2×C5×Q8—21no—
60C2×C4×D5C3×D411yescharacteristic
61C22⋊AGL(1,𝔽5)—41no—
62C4⋊AGL(1,𝔽5)—41no—
63C4×AGL(1,𝔽5)—22no—
64C5×Q16—41no—
65C2×C5×C8C2×C3×C411yescharacteristic
66#685—41no—
67C4⋊Dic5—21no—
68#683—41no—
69C2×#168C3×D411yescharacteristic
70#676—41no—
71#674—41no—
72#470—51no—
73#349—51no—
74H(3,ℤ/4)—51no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—41no—
78C3×AGL(1,𝔽5)—82no—
79C3×C4×C5—81no—
80C3×C4×C5#9911yescharacteristic
81C3×C4×C5#10411yescharacteristic
82C3×Dic5—21no—
83C3×Dic5—81no—
84C2×C3×Q8—21no—
85C22×C3×C4—51no—
86C3×Q16—41no—
87C3×M16—201no—
88C2×C3×C8—51no—
89C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
90C3×C4⋊C4—101no—
91C3×C4⋊C4—201no—
92C3×C4⋊C4—201no—
93C3×C22⋊C4—201no—
94C3×C22⋊C4—201no—
95C3×C42—102no—
96C3×C16—201no—
97C22×D5C3×D811yescharacteristic
98C2×AGL(1,𝔽5)—42no—
99C5×Q8—41no—
100C5×Q8—41no—
101C2×C4×C5—41no—
102C2×C4×C5C3×C22⋊C411yescharacteristic
103C2×Dic5—41no—
104C2×Dic5C3×SD1611yescharacteristic
105C4×D5—21no—
106C4×D5—21no—
107C5×C8—21no—
108#168—21no—
109C2×Q16C3×AGL(1,𝔽5)11yescharacteristic, complemented
110C2×M16—51no—
111C22⋊Q8—101no—
112#117—101no—
113M32—101no—
114#106—51no—
115#103—101no—
116C2×C3×C5—21no—
117C2×C3×C5#32711yescharacteristic
118C3×D5—41no—
119C23×C3—51no—
120C3×Q8—41no—
121C3×Q8—41no—
122C2×C3×C4—41no—
123C2×C3×C4—51no—
124C2×C3×C4—101no—
125C2×C3×C4—101no—
126C2×C3×C4—202no—
127C2×C3×C4—201no—
128C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
129C3×C8—21no—
130C3×C8—101no—
131C22×C5C3×#10211yescharacteristic
132C2×D5—21no—
133C2×D5—41no—
134AGL(1,𝔽5)—82no—
135C4×C5—81no—
136C4×C5C3×#9911yescharacteristic
137C4×C5C3×#10411yescharacteristic
138Dic5—21no—
139Dic5—81no—
140C2×Q8—21no—
141C22×C4—51no—
142Q16—41no—
143M16—201no—
144C2×C8—51no—
145C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
146C4⋊C4—101no—
147C4⋊C4—201no—
148C4⋊C4—201no—
149C22⋊C4—201no—
150C22⋊C4—201no—
151C42—102no—
152C16—201no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—101no—
155C22×C3—201no—
156C22×C3#400711yescharacteristic
157C3×C4—81no—
158C3×C4—101no—
159C3×C4—401no—
160C3×C4—402no—
161C3×C4#400811yescharacteristic
162C3×C4#401111yescharacteristic
163C2×C5—21no—
164C2×C5C3×#32711yescharacteristic
165D5—41no—
166C23—51no—
167Q8—41no—
168Q8—41no—
169C2×C4—41no—
170C2×C4—51no—
171C2×C4—101no—
172C2×C4—101no—
173C2×C4—202no—
174C2×C4—201no—
175C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
176C8—21no—
177C8—101no—
178C2×C3—21no—
179C2×C3—201no—
180C2×C3#6492011yescharacteristic
181C5C3×#134011yescharacteristic, complemented, Sylow
182C22—101no—
183C22—201no—
184C22C3×#400711yescharacteristic
185C4—81no—
186C4—101no—
187C4—401no—
188C4—402no—
189C4C3×#400811yescharacteristic
190C4C3×#401111yescharacteristic
191C3#1059881111yescharacteristic, direct product factor, Sylow
192C2—21no—
193C2—201no—
194C2C3×#6492011yescharacteristic
subgroupG/H
centerC2×C3#64920
commutatorC2×C5×C8C2×C3×C4
FrattiniC2×C8C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×Q16C4
socleC2×C3×C5#327
prime radicalC22×C3×D5D8
cosocleC2×#676C22×C3
hypercenterC2×C3×Q16AGL(1,𝔽5)
hypocenterC5C3×#1340
LCSG ▷ C2×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×Q16

Complements

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

NH ≅ G/Ntype
4. #10598811C3direct (N × H)
6. C2×C3×C5×Q16C4semidirect
11. C3×#3949C4semidirect
33. C2×C5×Q16C3×C4semidirect
38. #3949C3×C4semidirect
52. C2×C3×Q16AGL(1,𝔽5)semidirect
109. C2×Q16C3×AGL(1,𝔽5)semidirect
153. C3×C5#1340semidirect
181. C5C3×#1340semidirect
191. C3#10598811direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#654782
C3×#648952
C3×#648912
#105988113
C3×#13405