Finite Group Databasebeta

← C3×#10598031 #14279448

Subgroups — C3×#10598031 #14279448

Order 1920.

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

normal subgroups only

This group has 220 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×#65365C211yesmaximal, characteristic
2C3×C5×#353C211yesmaximal, characteristic
3C3×#64765C211yesmaximal, characteristic
4#10598031C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#127C2211yescharacteristic
6C2×C3×#687—21no—
7C2×C3×#687—21no—
8C3×#4015C411yescharacteristic, complemented
9C3×C5×#99—21no—
10C3×#3966—21no—
11C3×C4×#168C411yescharacteristic, complemented
12C3×#1409—51nomaximal, Hall
13#65365C2×C311yescharacteristic
14C5×#353C2×C311yescharacteristic
15#64765C2×C311yescharacteristic
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×C3×Dic10—21no—
20C3×C5×C22⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22C3×C22⋊Dic5—41no—
23C3×#687—42no—
24C3×#687—42no—
25C3×C4⋊Dic5—41no—
26C2×C3×#168—21no—
27C3×#492—51no—
28C3×#353—51no—
29C3×#353D511yescharacteristic
30C5×#127C22×C311yescharacteristic
31C2×#687—21no—
32C2×#687—21no—
33#4015C3×C411yescharacteristic, complemented
34C5×#99—21no—
35#3966—21no—
36C4×#168C3×C411yescharacteristic, complemented
37#1409—51noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C3×C5×D4—41no—
41C3×C5×D4—41no—
42C3×C5×D4—82no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—81no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×C3×Dic5—41no—
47C2×C3×Dic5—81no—
48C3×Dic10—41no—
49C3×Dic10—41no—
50C3×#168—22no—
51C2×C3×SD16—101no—
52C2×C3×SD16—101no—
53C3×C4⋊Q8—51no—
54C3×#127C2×D511yescharacteristic
55C3×#99—21no—
56C3×#99—101no—
57C3×C4×C8—51no—
58C2×C5×D4—41no—
59C2×C5×D4C3×D411yescharacteristic
60C2×C5×D4C3×D411yescharacteristic
61C2×Dic10—21no—
62C5×C22⋊C4—41no—
63C42×C5C2×C3×C411yescharacteristic
64C22⋊Dic5—41no—
65#687—42no—
66#687—42no—
67C4⋊Dic5—41no—
68C2×#168—21no—
69#492—51no—
70#353—51no—
71#353C3×D511yescharacteristic
72C22×C3×C5—41no—
73C22×C3×C5—41no—
74C22×C3×C5—81no—
75C22×C3×C5—81no—
76C22×C3×C5#9911yescharacteristic
77C3×C4×C5—22no—
78C3×C4×C5—21no—
79C3×C4×C5—161no—
80C3×Dic5—81no—
81C3×Dic5—161no—
82C2×C3×Q8—101no—
83C2×C3×D4—41no—
84C2×C3×D4D2011yescharacteristic
85C2×C3×D4C22⋊D511yescharacteristic
86C3×SD16—202no—
87C3×SD16—202no—
88C2×C3×C8—101no—
89C3×C4⋊C4—201no—
90C3×C22⋊C4—41no—
91C3×C22⋊C4—201no—
92C3×C42C4×D511yescharacteristic
93C23×C5—21no—
94C23×C5—21no—
95C5×D4—41no—
96C5×D4—41no—
97C5×D4—82no—
98C2×C4×C5—21no—
99C2×C4×C5—81no—
100C2×C4×C5C3×C22⋊C411yescharacteristic
101C2×Dic5—41no—
102C2×Dic5—81no—
103Dic10—41no—
104Dic10—41no—
105#168—22no—
106C2×SD16—101no—
107C2×SD16—101no—
108C4⋊Q8—51no—
109#127C2×C3×D511yescharacteristic
110#99—21no—
111#99—101no—
112C4×C8—51no—
113C2×C3×C5—21no—
114C2×C3×C5—81no—
115C2×C3×C5—81no—
116C2×C3×C5#35311yescharacteristic
117C23×C3—21no—
118C23×C3—21no—
119C3×Q8—201no—
120C3×Q8—201no—
121C3×D4—41no—
122C3×D4—41no—
123C3×D4—82no—
124C2×C3×C4—21no—
125C2×C3×C4—81no—
126C2×C3×C4—201no—
127C2×C3×C4—401no—
128C2×C3×C4#68511yescharacteristic
129C3×C8—102no—
130C22×C5—41no—
131C22×C5—41no—
132C22×C5—81no—
133C22×C5—81no—
134C22×C5C3×#9911yescharacteristic
135C4×C5—22no—
136C4×C5—21no—
137C4×C5—161no—
138Dic5—81no—
139Dic5—161no—
140C2×Q8—101no—
141C2×D4—41no—
142C2×D4C3×D2011yescharacteristic
143C2×D4C3×C22⋊D511yescharacteristic
144SD16—202no—
145SD16—202no—
146C2×C8—101no—
147C4⋊C4—201no—
148C22⋊C4—41no—
149C22⋊C4—201no—
150C42C3×C4×D511yescharacteristic
151C3×C5#140911yescharacteristic, complemented, Hall
152C22×C3—41no—
153C22×C3—41no—
154C22×C3—81no—
155C22×C3—81no—
156C22×C3#393811yescharacteristic
157C3×C4—22no—
158C3×C4—21no—
159C3×C4—161no—
160C3×C4—401no—
161C3×C4—801no—
162C2×C5—21no—
163C2×C5—81no—
164C2×C5—81no—
165C2×C5C3×#35311yescharacteristic
166C23—21no—
167C23—21no—
168Q8—201no—
169Q8—201no—
170D4—41no—
171D4—41no—
172D4—82no—
173C2×C4—21no—
174C2×C4—81no—
175C2×C4—201no—
176C2×C4—401no—
177C2×C4C3×#68511yescharacteristic
178C8—102no—
179C2×C3—21no—
180C2×C3—81no—
181C2×C3—81no—
182C2×C3#6469411yescharacteristic
183C5C3×#140911yescharacteristic, complemented, Sylow
184C22—41no—
185C22—41no—
186C22—81no—
187C22—81no—
188C22C3×#393811yescharacteristic
189C4—22no—
190C4—21no—
191C4—161no—
192C4—401no—
193C4—801no—
194C3#1059803111yescharacteristic, direct product factor, Sylow
195C2—21no—
196C2—81no—
197C2—81no—
198C2C3×#6469411yescharacteristic
subgroupG/H
centerC2×C3#64694
commutatorC42×C5C2×C3×C4
Frattini#127C2×C3×D5
FittingC3×C5×#353C2
socleC2×C3×C5#353
prime radicalC3×C5×#127C22
cosocleC5×#127C22×C3
hypercenterC3×#353D5
hypocenterC5C3×#1409
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
4. #10598031C3direct (N × H)
8. C3×#4015C4semidirect
11. C3×C4×#168C4semidirect
33. #4015C3×C4semidirect
36. C4×#168C3×C4semidirect
151. C3×C5#1409semidirect
183. C5C3×#1409semidirect
194. C3#10598031direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653652
C3×C5×#3532
C3×#647652
#105980313
C3×#14095