Finite Group Databasebeta

← C3×#10599284 #14289056

Subgroups — C3×#10599284 #14289056

Order 1920.

480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#66068C211yesmaximal, characteristic, complemented
2C3×#65374C211yesmaximal, characteristic, complemented
3C3×#65132C212yesmaximal, complemented
4C3×C5×#333C211yesmaximal, characteristic, complemented
5C3×#64703C212yesmaximal, complemented
6#10599284C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×#4093—22no—
9C2×C3×#688—22no—
10C2×C3×D40—22no—
11C3×#4041—22no—
12C3×#4038—22no—
13C3×#4020C2211yescharacteristic
14C3×C4×D20C2212yes—
15C3×C5×C4⋊C8C2212yes—
16C3×#3953—22no—
17C3×C4×#168C2211yescharacteristic
18C3×#1624—51nomaximal, Hall
19#66068C2×C311yescharacteristic, complemented
20#65374C2×C311yescharacteristic, complemented
21#65132C2×C312yescomplemented
22C5×#333C2×C311yescharacteristic, complemented
23#64703C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×D20—21no—
26C2×C3×D20—22no—
27C2×C3×D20—22no—
28C2×C3×D20D412yes—
29C2×C3×C4×D5—22no—
30C2×C3×C5×C8—22no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C3×#688—44no—
34C3×#685—24no—
35C3×#685—22no—
36C3×C4⋊Dic5D412yes—
37C3×C4×Dic5—22no—
38C2×C3×#168—21no—
39C3×D40—44no—
40C3×#555—51no—
41C3×#492—51no—
42C3×#459—52no—
43C3×#333D511yescharacteristic, complemented
44C3×D4⋊C8—52no—
45C5×C4⋊Q8C22×C311yescharacteristic
46#4093—22no—
47C2×#688—22no—
48C2×D40—22no—
49#4041—22no—
50#4038—22no—
51#4020C22×C311yescharacteristic
52C4×D20C22×C312yes—
53C5×C4⋊C8C22×C312yes—
54#3953—22no—
55C4×#168C22×C311yescharacteristic
56#1624—51noSylow
57C22×C3×D5—22no—
58C22×C3×D5—41no—
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×C3×Dic5—22no—
64C3×D20—22no—
65C3×D20—22no—
66C3×D20—42no—
67C3×D20—42no—
68C3×D20—42no—
69C3×D20—82no—
70C3×C4×D5—42no—
71C3×C4×D5—42no—
72C3×C5×C8—42no—
73C3×#168—22no—
74C2×C3×SD16—102no—
75C2×C3×D8—102no—
76C3×C4⋊Q8C2×D511yescharacteristic
77C3×#127—51no—
78C3×#124—102no—
79C3×#121—102no—
80C3×C4×D4—52no—
81C3×#117—102no—
82C3×C4⋊C8C2×D512yes—
83C3×#102—102no—
84C3×C4×C8—51no—
85C2×C5×Q8C3×D412yes—
86C2×D20—22no—
87C2×D20—21no—
88C2×D20—22no—
89C2×D20C3×D412yes—
90C2×C4×D5—22no—
91C2×C5×C8—22no—
92C5×C4⋊C4—22no—
93C42×C5C23×C311yescharacteristic
94#688—44no—
95#685—24no—
96#685—22no—
97C4⋊Dic5C3×D412yes—
98C4×Dic5—22no—
99C2×#168—21no—
100D40—44no—
101#555—51no—
102#492—51no—
103#459—52no—
104#333C3×D511yescharacteristic, complemented
105D4⋊C8—52no—
106C22×C3×C5#12011yescharacteristic
107C2×C3×D5—42no—
108C2×C3×D5—42no—
109C2×C3×D5—42no—
110C2×C3×D5—82no—
111C2×C3×D5—81no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116C3×Dic5—42no—
117C2×C3×Q8D2012yes—
118C2×C3×D4—52no—
119C2×C3×D4—102no—
120C2×C3×D4—101no—
121C2×C3×D4—102no—
122C22×C3×C4—102no—
123C3×SD16—204no—
124C3×D8—204no—
125C2×C3×C8—22no—
126C2×C3×C8—101no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—52no—
129C3×C22⋊C4—104no—
130C3×C22⋊C4—102no—
131C3×C42—102no—
132C3×C42C22×D511yescharacteristic
133C22×D5—22no—
134C22×D5—41no—
135C5×Q8—42no—
136C2×C4×C5—22no—
137C2×C4×C5C2×C3×D411yescharacteristic
138C2×C4×C5C2×C3×D412yes—
139C2×Dic5—22no—
140D20—22no—
141D20—22no—
142D20—42no—
143D20—42no—
144D20—42no—
145D20—82no—
146C4×D5—42no—
147C4×D5—42no—
148C5×C8—42no—
149#168—22no—
150C2×SD16—102no—
151C2×D8—102no—
152C4⋊Q8C2×C3×D511yescharacteristic
153#127—51no—
154#124—102no—
155#121—102no—
156C4×D4—52no—
157#117—102no—
158C4⋊C8C2×C3×D512yes—
159#102—102no—
160C4×C8—51no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163C3×D5—82no—
164C3×D5—161no—
165C23×C3—102no—
166C23×C3—201no—
167C3×Q8—42no—
168C3×D4—102no—
169C3×D4—102no—
170C3×D4—202no—
171C3×D4—202no—
172C3×D4—202no—
173C3×D4—402no—
174C2×C3×C4—22no—
175C2×C3×C4—102no—
176C2×C3×C4—202no—
177C2×C3×C4—202no—
178C2×C3×C4C2×D2011yescharacteristic
179C2×C3×C4D4×D512yes—
180C3×C8—42no—
181C3×C8—102no—
182C22×C5C3×#12011yescharacteristic
183C2×D5—42no—
184C2×D5—42no—
185C2×D5—42no—
186C2×D5—82no—
187C2×D5—81no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5C3×#13512yes—
191C4×C5C3×AGL(1,ℤ/8)12yes—
192Dic5—42no—
193C2×Q8C3×D2012yes—
194C2×D4—52no—
195C2×D4—102no—
196C2×D4—101no—
197C2×D4—102no—
198C22×C4—102no—
199SD16—204no—
200D8—204no—
201C2×C8—22no—
202C2×C8—101no—
203C4⋊C4—22no—
204C4⋊C4—52no—
205C22⋊C4—104no—
206C22⋊C4—102no—
207C42—102no—
208C42C22×C3×D511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—202no—
211C22×C3—202no—
212C22×C3—202no—
213C22×C3—401no—
214C22×C3—402no—
215C22×C3#402811yescharacteristic
216C3×C4—21no—
217C3×C4—42no—
218C3×C4—202no—
219C3×C4#406012yes—
220C3×C4#406512yes—
221C2×C5C3×#44912yes—
222C2×C5C3×#45311yescharacteristic
223D5—82no—
224D5—161no—
225C23—102no—
226C23—201no—
227Q8—42no—
228D4—102no—
229D4—102no—
230D4—202no—
231D4—202no—
232D4—202no—
233D4—402no—
234C2×C4—22no—
235C2×C4—102no—
236C2×C4—202no—
237C2×C4—202no—
238C2×C4C2×C3×D2011yescharacteristic
239C2×C4C3×D4×D512yes—
240C8—42no—
241C8—102no—
242C2×C3—402no—
243C2×C3—801no—
244C2×C3#6503611yescharacteristic
245C2×C3#6510012yes—
246C5C3×#162411yescharacteristic, complemented, Sylow
247C22—202no—
248C22—202no—
249C22—202no—
250C22—401no—
251C22—402no—
252C22C3×#402811yescharacteristic
253C4—21no—
254C4—42no—
255C4—202no—
256C4C3×#406012yes—
257C4C3×#406512yes—
258C3#1059928411yescharacteristic, direct product factor, Sylow
259C2—402no—
260C2—801no—
261C2C3×#6503611yescharacteristic
262C2C3×#6510012yes—
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#333C2
socleC22×C3×C5#120
hypercenterC3×#333D5
hypocenterC5C3×#1624
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
1. C3×#66068C2semidirect
2. C3×#65374C2semidirect
3. C3×#65132C2semidirect
4. C3×C5×#333C2semidirect
5. C3×#64703C2semidirect
6. #10599284C3direct (N × H)
19. #66068C2×C3semidirect
20. #65374C2×C3semidirect
21. #65132C2×C3semidirect
22. C5×#333C2×C3semidirect
23. #64703C2×C3semidirect
43. C3×#333D5semidirect
104. #333C3×D5semidirect
209. C3×C5#1624semidirect
246. C5C3×#1624semidirect
258. C3#10599284direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660682
C3×#653742
C3×#651322
C3×C5×#3332
C3×#647032
#105992843
C3×#16245