Finite Group Databasebeta

← C3×#10598032 #14279433

Subgroups — C3×#10598032 #14279433

Order 1920.

240 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 46 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×#65362C211yesmaximal, characteristic
2C3×C5×#353C211yesmaximal, characteristic, complemented
3C3×#64765C211yesmaximal, characteristic, complemented
4#10598032C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#127C2211yescharacteristic
6C2×C3×#686—21no—
7C2×C3×#686—21no—
8C3×#4020C411yescharacteristic, complemented
9C3×C5×#99—21no—
10C3×#3966—21no—
11C3×C4×#168C411yescharacteristic, complemented
12C3×#1408—51nomaximal, Hall
13#65362C2×C311yescharacteristic
14C5×#353C2×C311yescharacteristic, complemented
15#64765C2×C311yescharacteristic, complemented
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×C3×D20—21no—
20C2×C3×D20—41no—
21C3×C5×C22⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C3×C22⋊Dic5—41no—
24C3×#686—42no—
25C3×#686—42no—
26C2×C3×#168—21no—
27C3×#493—51no—
28C3×#353—51no—
29C3×#353D511yescharacteristic, complemented
30C5×#127C22×C311yescharacteristic
31C2×#686—21no—
32C2×#686—21no—
33#4020C3×C411yescharacteristic, complemented
34C5×#99—21no—
35#3966—21no—
36C4×#168C3×C411yescharacteristic, complemented
37#1408—51noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C22×C3×D5—41no—
41C3×C5×D4—41no—
42C3×C5×D4—41no—
43C3×C5×D4—82no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—81no—
46C2×C3×C4×C5C22⋊C411yescharacteristic
47C2×C3×Dic5—81no—
48C3×D20—41no—
49C3×D20—41no—
50C3×D20—82no—
51C3×#168—22no—
52C2×C3×D8—101no—
53C2×C3×D8—101no—
54C3×#127—51no—
55C3×#127C2×D511yescharacteristic
56C3×#99—21no—
57C3×#99—101no—
58C3×C4×C8—51no—
59C2×C5×D4—41no—
60C2×C5×D4C3×D411yescharacteristic
61C2×C5×D4C3×D411yescharacteristic
62C2×D20—21no—
63C2×D20—41no—
64C5×C22⋊C4—41no—
65C42×C5C2×C3×C411yescharacteristic
66C22⋊Dic5—41no—
67#686—42no—
68#686—42no—
69C2×#168—21no—
70#493—51no—
71#353—51no—
72#353C3×D511yescharacteristic, complemented
73C22×C3×C5—41no—
74C22×C3×C5—41no—
75C22×C3×C5—81no—
76C22×C3×C5—81no—
77C22×C3×C5#9911yescharacteristic
78C2×C3×D5—82no—
79C2×C3×D5—81no—
80C3×C4×C5—22no—
81C3×C4×C5—21no—
82C3×C4×C5—161no—
83C3×Dic5—161no—
84C2×C3×D4—41no—
85C2×C3×D4—101no—
86C2×C3×D4—201no—
87C2×C3×D4D2011yescharacteristic
88C2×C3×D4C22⋊D511yescharacteristic
89C3×D8—202no—
90C3×D8—202no—
91C2×C3×C8—101no—
92C3×C22⋊C4—41no—
93C3×C22⋊C4—201no—
94C3×C42C4×D511yescharacteristic
95C23×C5—21no—
96C23×C5—21no—
97C22×D5—41no—
98C5×D4—41no—
99C5×D4—41no—
100C5×D4—82no—
101C2×C4×C5—21no—
102C2×C4×C5—81no—
103C2×C4×C5C3×C22⋊C411yescharacteristic
104C2×Dic5—81no—
105D20—41no—
106D20—41no—
107D20—82no—
108#168—22no—
109C2×D8—101no—
110C2×D8—101no—
111#127—51no—
112#127C2×C3×D511yescharacteristic
113#99—21no—
114#99—101no—
115C4×C8—51no—
116C2×C3×C5—21no—
117C2×C3×C5—81no—
118C2×C3×C5—81no—
119C2×C3×C5#35311yescharacteristic
120C3×D5—161no—
121C23×C3—21no—
122C23×C3—21no—
123C23×C3—201no—
124C3×D4—41no—
125C3×D4—41no—
126C3×D4—82no—
127C3×D4—201no—
128C3×D4—201no—
129C3×D4—402no—
130C2×C3×C4—21no—
131C2×C3×C4—81no—
132C2×C3×C4—401no—
133C2×C3×C4#68511yescharacteristic
134C3×C8—102no—
135C22×C5—41no—
136C22×C5—41no—
137C22×C5—81no—
138C22×C5—81no—
139C22×C5C3×#9911yescharacteristic
140C2×D5—82no—
141C2×D5—81no—
142C4×C5—22no—
143C4×C5—21no—
144C4×C5—161no—
145Dic5—161no—
146C2×D4—41no—
147C2×D4—101no—
148C2×D4—201no—
149C2×D4C3×D2011yescharacteristic
150C2×D4C3×C22⋊D511yescharacteristic
151D8—202no—
152D8—202no—
153C2×C8—101no—
154C22⋊C4—41no—
155C22⋊C4—201no—
156C42C3×C4×D511yescharacteristic
157C3×C5#140811yescharacteristic, complemented, Hall
158C22×C3—41no—
159C22×C3—41no—
160C22×C3—81no—
161C22×C3—81no—
162C22×C3—402no—
163C22×C3—401no—
164C22×C3#393811yescharacteristic
165C3×C4—22no—
166C3×C4—21no—
167C3×C4—161no—
168C3×C4—801no—
169C2×C5—21no—
170C2×C5—81no—
171C2×C5—81no—
172C2×C5C3×#35311yescharacteristic
173D5—161no—
174C23—21no—
175C23—21no—
176C23—201no—
177D4—41no—
178D4—41no—
179D4—82no—
180D4—201no—
181D4—201no—
182D4—402no—
183C2×C4—21no—
184C2×C4—81no—
185C2×C4—401no—
186C2×C4C3×#68511yescharacteristic
187C8—102no—
188C2×C3—21no—
189C2×C3—81no—
190C2×C3—81no—
191C2×C3—801no—
192C2×C3#6469411yescharacteristic
193C5C3×#140811yescharacteristic, complemented, Sylow
194C22—41no—
195C22—41no—
196C22—81no—
197C22—81no—
198C22—402no—
199C22—401no—
200C22C3×#393811yescharacteristic
201C4—22no—
202C4—21no—
203C4—161no—
204C4—801no—
205C3#1059803211yescharacteristic, direct product factor, Sylow
206C2—21no—
207C2—81no—
208C2—81no—
209C2—801no—
210C2C3×#6469411yescharacteristic
subgroupG/H
centerC2×C3#64694
commutatorC42×C5C2×C3×C4
Frattini#127C2×C3×D5
FittingC3×C5×#353C2
socleC2×C3×C5#353
prime radicalC3×#65362C2
cosocleC5×#127C22×C3
hypercenterC3×#353D5
hypocenterC5C3×#1408
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#127 ◁ C3×#353

Complements

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

NH ≅ G/Ntype
2. C3×C5×#353C2semidirect
3. C3×#64765C2semidirect
4. #10598032C3direct (N × H)
8. C3×#4020C4semidirect
11. C3×C4×#168C4semidirect
14. C5×#353C2×C3semidirect
15. #64765C2×C3semidirect
29. C3×#353D5semidirect
33. #4020C3×C4semidirect
36. C4×#168C3×C4semidirect
72. #353C3×D5semidirect
157. C3×C5#1408semidirect
193. C5C3×#1408semidirect
205. C3#10598032direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653622
C3×C5×#3532
C3×#647652
#105980323
C3×#14085