Finite Group Databasebeta

← C3×#10597948 #14278331

Subgroups — C3×#10597948 #14278331

Order 1920.

280 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 70 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×#65268C211yesmaximal, characteristic
2C3×C5×#324C211yesmaximal, characteristic
3C3×#64750C211yesmaximal, characteristic
4#10597948C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×Dic10C411yescharacteristic
6C2×C3×C5×C4⋊C4C2211yescharacteristic
7C2×C3×#683—21no—
8C2×C3×#681—21no—
9C3×C5×C22⋊C8—21no—
10C3×#3963—21no—
11C3×#3963C411yescharacteristic
12C3×#1354—51nomaximal, Hall
13#65268C2×C311yescharacteristic
14C5×#324C2×C311yescharacteristic
15#64750C2×C311yescharacteristic
16C22×C3×C4×C5C2×C411yescharacteristic
17C22×C3×C4×C5D411yescharacteristic
18C22×C3×C4×C5D411yescharacteristic
19C22×C3×Dic5—21no—
20C22×C3×Dic5—21no—
21C2×C3×Dic10—41no—
22C2×C3×Dic10—42no—
23C2×C3×C5×C8—41no—
24C3×C5×C4⋊C4—41no—
25C3×#683—42no—
26C3×#681—22no—
27C3×#681—41no—
28C2×C3×#168—41no—
29C3×#395—51no—
30C3×#343—51no—
31C3×#324D511yescharacteristic
32C22×Dic10C3×C411yescharacteristic
33C2×C5×C4⋊C4C22×C311yescharacteristic
34C2×#683—21no—
35C2×#681—21no—
36C5×C22⋊C8—21no—
37#3963—21no—
38#3963C3×C411yescharacteristic
39#1354—51noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—41no—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5SD1611yescharacteristic
48C2×C3×C4×C5Q1611yescharacteristic
49C2×C3×Dic5—22no—
50C2×C3×Dic5—22no—
51C2×C3×Dic5—41no—
52C2×C3×Dic5—41no—
53C2×C3×Dic5—41no—
54C2×C3×Dic5—41no—
55C3×Dic10—42no—
56C3×Dic10—42no—
57C3×C5×C8—81no—
58C3×#168—42no—
59C22×C3×Q8—51no—
60C2×C3×M16—101no—
61C2×C3×C4⋊C4—101no—
62C2×C3×C4⋊C4C2×D511yescharacteristic
63C3×C22⋊C8—21no—
64C3×#95—51no—
65C3×#95—101no—
66C22×C4×C5C2×C3×C411yescharacteristic
67C22×C4×C5C3×D411yescharacteristic
68C22×C4×C5C3×D411yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C2×Dic10—41no—
72C2×Dic10—42no—
73C2×C5×C8—41no—
74C5×C4⋊C4—41no—
75#683—42no—
76#681—22no—
77#681—41no—
78C2×#168—41no—
79#395—51no—
80#343—51no—
81#324C3×D511yescharacteristic
82C22×C3×C5—21no—
83C22×C3×C5—21no—
84C22×C3×C5#9911yescharacteristic
85C22×C3×C5#10311yescharacteristic
86C22×C3×C5#10411yescharacteristic
87C3×C4×C5—21no—
88C3×C4×C5—21no—
89C3×C4×C5—41no—
90C3×C4×C5—41no—
91C3×Dic5—42no—
92C3×Dic5—42no—
93C2×C3×Q8—201no—
94C2×C3×Q8—202no—
95C22×C3×C4—101no—
96C22×C3×C4—101no—
97C22×C3×C4C4×D511yescharacteristic
98C22×C3×C4D2011yescharacteristic
99C22×C3×C4C22⋊D511yescharacteristic
100C3×M16—102no—
101C3×M16—201no—
102C2×C3×C8—41no—
103C2×C3×C8—201no—
104C3×C4⋊C4—41no—
105C3×C4⋊C4—202no—
106C23×C5C3×C22⋊C411yescharacteristic
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—41no—
112C2×C4×C5—41no—
113C2×C4×C5C3×SD1611yescharacteristic
114C2×C4×C5C3×Q1611yescharacteristic
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5—41no—
118C2×Dic5—41no—
119C2×Dic5—41no—
120C2×Dic5—41no—
121Dic10—42no—
122Dic10—42no—
123C5×C8—81no—
124#168—42no—
125C22×Q8—51no—
126C2×M16—101no—
127C2×C4⋊C4—101no—
128C2×C4⋊C4C2×C3×D511yescharacteristic
129C22⋊C8—21no—
130#95—51no—
131#95—101no—
132C2×C3×C5—21no—
133C2×C3×C5—21no—
134C2×C3×C5#32811yescharacteristic
135C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
136C2×C3×C5#35611yescharacteristic
137C23×C3#68511yescharacteristic
138C3×Q8—202no—
139C3×Q8—202no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4—102no—
147C2×C3×C4—102no—
148C2×C3×C4—201no—
149C2×C3×C4—201no—
150C2×C3×C4—201no—
151C2×C3×C4—201no—
152C2×C3×C4#67711yescharacteristic
153C2×C3×C4Dic2011yescharacteristic
154C3×C8—81no—
155C3×C8—202no—
156C22×C5—21no—
157C22×C5—21no—
158C22×C5C3×#9911yescharacteristic
159C22×C5C3×#10311yescharacteristic
160C22×C5C3×#10411yescharacteristic
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—41no—
164C4×C5—41no—
165Dic5—42no—
166Dic5—42no—
167C2×Q8—201no—
168C2×Q8—202no—
169C22×C4—101no—
170C22×C4—101no—
171C22×C4C3×C4×D511yescharacteristic
172C22×C4C3×D2011yescharacteristic
173C22×C4C3×C22⋊D511yescharacteristic
174M16—102no—
175M16—201no—
176C2×C8—41no—
177C2×C8—201no—
178C4⋊C4—41no—
179C4⋊C4—202no—
180C3×C5#135411yescharacteristic, complemented, Hall
181C22×C3—21no—
182C22×C3—21no—
183C22×C3#393811yescharacteristic
184C22×C3#394811yescharacteristic
185C22×C3#395711yescharacteristic
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—41no—
189C3×C4—41no—
190C3×C4—202no—
191C3×C4—202no—
192C2×C5—21no—
193C2×C5—21no—
194C2×C5C3×#32811yescharacteristic
195C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
196C2×C5C3×#35611yescharacteristic
197C23C3×#68511yescharacteristic
198Q8—202no—
199Q8—202no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—201no—
209C2×C4—201no—
210C2×C4—201no—
211C2×C4—201no—
212C2×C4C3×#67711yescharacteristic
213C2×C4C3×Dic2011yescharacteristic
214C8—81no—
215C8—202no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3#6468711yescharacteristic
219C2×C3#6469111yescharacteristic
220C2×C3#6469811yescharacteristic
221C5C3×#135411yescharacteristic, complemented, Sylow
222C22—21no—
223C22—21no—
224C22C3×#393811yescharacteristic
225C22C3×#394811yescharacteristic
226C22C3×#395711yescharacteristic
227C4—21no—
228C4—21no—
229C4—41no—
230C4—41no—
231C4—202no—
232C4—202no—
233C3#1059794811yescharacteristic, direct product factor, Sylow
234C2—21no—
235C2—21no—
236C2C3×#6468711yescharacteristic
237C2C3×#6469111yescharacteristic
238C2C3×#6469811yescharacteristic
subgroupG/H
centerC22×C3#3938
commutatorC22×C4×C5C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D5
FittingC3×C5×#324C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C5×C4⋊C4C22×C3
hypercenterC3×#324D5
hypocenterC5C3×#1354
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
4. #10597948C3direct (N × H)
180. C3×C5#1354semidirect
221. C5C3×#1354semidirect
233. C3#10597948direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#652682
C3×C5×#3242
C3×#647502
#105979483
C3×#13545