Finite Group Databasebeta

← C3×#10602745 #14290905

Subgroups — C3×#10602745 #14290905

Order 1920.

460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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×C5×#562C211yesmaximal, characteristic, complemented
2C3×#65356C211yesmaximal, characteristic, complemented
3C3×#65347C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64760C212yesmaximal, complemented
6#10602745C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#125C2211yescharacteristic
8C3×C5×#124C2212yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#121—22no—
12C2×C3×#688—22no—
13C2×C3×#686—22no—
14C3×#4020C2211yescharacteristic
15C3×#3941—22no—
16C3×#3935C2212yes—
17C3×#3935C2211yescharacteristic
18C3×#1656—51nomaximal, Hall
19C5×#562C2×C311yescharacteristic, complemented
20#65356C2×C311yescharacteristic, complemented
21#65347C2×C312yescomplemented
22#64763C2×C311yescharacteristic, complemented
23#64760C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×C3×D20—22no—
29C2×C3×D20—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4D412yes—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37C3×#688—44no—
38C3×#686—44no—
39C2×C3×#168—22no—
40C2×C3×#168—21no—
41C3×#562D511yescharacteristic, complemented
42C3×#496—52no—
43C3×#490—51no—
44C3×#330—51no—
45C3×#329—52no—
46C5×#125C22×C311yescharacteristic
47C5×#124C22×C312yes—
48C5×#123—22no—
49C5×C22⋊Q8—22no—
50C5×#121—22no—
51C2×#688—22no—
52C2×#686—22no—
53#4020C22×C311yescharacteristic
54#3941—22no—
55#3935C22×C312yes—
56#3935C22×C311yescharacteristic
57#1656—51noSylow
58C23×C3×C5—22no—
59C22×C3×D5—41no—
60C3×C5×Q8—42no—
61C3×C5×D4—42no—
62C3×C5×D4—82no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—82no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×C3×C4×C5C2×D412yes—
68C3×D20—42no—
69C3×D20—42no—
70C3×D20—42no—
71C3×#168—24no—
72C3×#168—41no—
73C2×C3×SD16—102no—
74C2×C3×D8—102no—
75C3×#127—51no—
76C3×#125C2×D511yescharacteristic
77C3×#124C2×D512yes—
78C3×#123—22no—
79C3×C22⋊Q8—22no—
80C3×#121—22no—
81C3×#102—102no—
82C3×#97—51no—
83C3×#97—52no—
84C2×C5×Q8C3×D412yes—
85C2×C5×D4—22no—
86C2×C5×D4C3×D412yes—
87C22×C4×C5—22no—
88C2×D20—21no—
89C2×D20—22no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4C3×D412yes—
93C5×C22⋊C4—22no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—22no—
96C42×C5C23×C311yescharacteristic
97#688—44no—
98#686—44no—
99C2×#168—22no—
100C2×#168—21no—
101#562C3×D511yescharacteristic, complemented
102#496—52no—
103#490—51no—
104#330—51no—
105#329—52no—
106C22×C3×C5—42no—
107C22×C3×C5—42no—
108C22×C3×C5—42no—
109C22×C3×C5#12011yescharacteristic
110C2×C3×D5—82no—
111C2×C3×D5—81no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C3×C4×C5—42no—
116C2×C3×Q8C22⋊D512yes—
117C2×C3×D4—22no—
118C2×C3×D4—101no—
119C2×C3×D4—102no—
120C2×C3×D4C22⋊D512yes—
121C22×C3×C4—22no—
122C3×SD16—204no—
123C3×D8—204no—
124C2×C3×C8—102no—
125C2×C3×C8—101no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4C22⋊D512yes—
129C3×C22⋊C4—22no—
130C3×C22⋊C4—22no—
131C3×C22⋊C4—22no—
132C3×C42C22×D511yescharacteristic
133C23×C5—22no—
134C22×D5—41no—
135C5×Q8—42no—
136C5×D4—42no—
137C5×D4—82no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—82no—
141C2×C4×C5C2×C3×D411yescharacteristic
142C2×C4×C5C2×C3×D412yes—
143D20—42no—
144D20—42no—
145D20—42no—
146#168—24no—
147#168—41no—
148C2×SD16—102no—
149C2×D8—102no—
150#127—51no—
151#125C2×C3×D511yescharacteristic
152#124C2×C3×D512yes—
153#123—22no—
154C22⋊Q8—22no—
155#121—22no—
156#102—102no—
157#97—51no—
158#97—52no—
159C2×C3×C5—82no—
160C2×C3×C5#45312yes—
161C2×C3×C5#45411yescharacteristic
162C3×D5—161no—
163C23×C3—22no—
164C23×C3—201no—
165C3×Q8—42no—
166C3×D4—42no—
167C3×D4—82no—
168C3×D4—202no—
169C3×D4—202no—
170C3×D4—202no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—82no—
174C2×C3×C4C2×C22⋊D511yescharacteristic
175C2×C3×C4C2×C22⋊D512yes—
176C3×C8—104no—
177C3×C8—201no—
178C22×C5—42no—
179C22×C5—42no—
180C22×C5—42no—
181C22×C5C3×#12011yescharacteristic
182C2×D5—82no—
183C2×D5—81no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—42no—
187C4×C5—42no—
188C2×Q8C3×C22⋊D512yes—
189C2×D4—22no—
190C2×D4—101no—
191C2×D4—102no—
192C2×D4C3×C22⋊D512yes—
193C22×C4—22no—
194SD16—204no—
195D8—204no—
196C2×C8—102no—
197C2×C8—101no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4C3×C22⋊D512yes—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C42C22×C3×D511yescharacteristic
205C3×C5#165611yescharacteristic, complemented, Hall
206C22×C3—42no—
207C22×C3—42no—
208C22×C3—42no—
209C22×C3—402no—
210C22×C3—401no—
211C22×C3#409911yescharacteristic
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—42no—
215C3×C4—42no—
216C2×C5—82no—
217C2×C5C3×#45312yes—
218C2×C5C3×#45411yescharacteristic
219D5—161no—
220C23—22no—
221C23—201no—
222Q8—42no—
223D4—42no—
224D4—82no—
225D4—202no—
226D4—202no—
227D4—202no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—82no—
231C2×C4C2×C3×C22⋊D511yescharacteristic
232C2×C4C2×C3×C22⋊D512yes—
233C8—104no—
234C8—201no—
235C2×C3—82no—
236C2×C3—801no—
237C2×C3#6553012yes—
238C2×C3#6553411yescharacteristic
239C5C3×#165611yescharacteristic, complemented, Sylow
240C22—42no—
241C22—42no—
242C22—42no—
243C22—402no—
244C22—401no—
245C22C3×#409911yescharacteristic
246C4—22no—
247C4—21no—
248C4—42no—
249C4—42no—
250C3#1060274511yescharacteristic, direct product factor, Sylow
251C2—82no—
252C2—801no—
253C2C3×#6553012yes—
254C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#562C2
socleC22×C3×C5#120
hypercenterC3×#562D5
hypocenterC5C3×#1656
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#562

Complements

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

NH ≅ G/Ntype
1. C3×C5×#562C2semidirect
2. C3×#65356C2semidirect
3. C3×#65347C2semidirect
4. C3×#64763C2semidirect
5. C3×#64760C2semidirect
6. #10602745C3direct (N × H)
19. C5×#562C2×C3semidirect
20. #65356C2×C3semidirect
21. #65347C2×C3semidirect
22. #64763C2×C3semidirect
23. #64760C2×C3semidirect
41. C3×#562D5semidirect
101. #562C3×D5semidirect
205. C3×C5#1656semidirect
239. C5C3×#1656semidirect
250. C3#10602745direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5622
C3×#653562
C3×#653472
C3×#647632
C3×#647602
#106027453
C3×#16565