Finite Group Databasebeta

← C3×#10602690 #14308978

Subgroups — C3×#10602690 #14308978

Order 1920.

932 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 142 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×#543C211yesmaximal, characteristic, complemented
2C3×#65244C213yesmaximal
3C3×#64746C213yesmaximal, complemented
4#10602690C311yesmaximal, characteristic, direct product factor, Hall
5C24×C3×D5C2211yescharacteristic
6C3×C5×C22⋊Q8—26no—
7C2×C3×C5×C22⋊C4C2213yes—
8C2×C3×C22⋊Dic5C2213yes—
9C2×C3×#685—26no—
10C3×#2029—51nomaximal, Hall
11C5×#543C2×C311yescharacteristic, complemented
12#65244C2×C313yes—
13#64746C2×C313yescomplemented
14C24×C3×C5C2311yescharacteristic
15C23×C3×D5—23no—
16C23×C3×D5—23no—
17C23×C3×D5—44no—
18C23×C3×D5Q812yescomplemented
19C2×C3×C5×Q8—22no—
20C22×C3×C4×C5D416yes—
21C22×C3×Dic5—23no—
22C3×C5×C4⋊C4—26no—
23C3×C5×C22⋊C4—26no—
24C3×C22⋊Dic5—26no—
25C3×#685—412no—
26C3×#543D511yescharacteristic, complemented
27C3×#379—53no—
28C3×#342—53no—
29C24×D5C22×C311yescharacteristic
30C5×C22⋊Q8—26no—
31C2×C5×C22⋊C4C22×C313yes—
32C2×C22⋊Dic5C22×C313yes—
33C2×#685—26no—
34#2029—51noSylow
35C23×C3×C5—42no—
36C23×C3×C5C2×D413yes—
37C23×C3×C5C2×Q811yescharacteristic
38C23×C3×C5#4113yes—
39C22×C3×D5—212no—
40C22×C3×D5—26no—
41C22×C3×D5—44no—
42C22×C3×D5—412no—
43C22×C3×D5—46no—
44C22×C3×D5—41no—
45C22×C3×D5—43no—
46C3×C5×Q8—82no—
47C2×C3×C4×C5—26no—
48C2×C3×C4×C5—46no—
49C2×C3×Dic5—46no—
50C2×C3×Dic5—43no—
51C25×C3—51no—
52C3×C22⋊Q8—26no—
53C2×C3×C22⋊C4—53no—
54C2×C3×C22⋊C4—106no—
55C2×C3×C22⋊C4C2×D513yes—
56C24×C5C23×C311yescharacteristic
57C23×D5—23no—
58C23×D5—23no—
59C23×D5—44no—
60C23×D5C3×Q812yescomplemented
61C2×C5×Q8—22no—
62C22×C4×C5C3×D416yes—
63C22×Dic5—23no—
64C5×C4⋊C4—26no—
65C5×C22⋊C4—26no—
66C22⋊Dic5—26no—
67#685—412no—
68#543C3×D511yescharacteristic, complemented
69#379—53no—
70#342—53no—
71C22×C3×C5—26no—
72C22×C3×C5—41no—
73C22×C3×C5—43no—
74C22×C3×C5#12011yescharacteristic
75C22×C3×C5C22⋊Q813yes—
76C22×C3×C5#12413yes—
77C2×C3×D5—212no—
78C2×C3×D5—412no—
79C2×C3×D5—46no—
80C2×C3×D5—42no—
81C2×C3×D5—44no—
82C3×C4×C5—46no—
83C3×Dic5—83no—
84C24×C3—52no—
85C24×C3—103no—
86C24×C3—103no—
87C24×C3—204no—
88C24×C3C22×D511yescharacteristic
89C2×C3×Q8—22no—
90C22×C3×C4—103no—
91C22×C3×C4C22⋊D516yes—
92C3×C4⋊C4—26no—
93C3×C22⋊C4—26no—
94C3×C22⋊C4—106no—
95C3×C22⋊C4—2012no—
96C23×C5—42no—
97C23×C5C2×C3×D413yes—
98C23×C5C2×C3×Q811yescharacteristic
99C23×C5C3×#4113yes—
100C22×D5—212no—
101C22×D5—26no—
102C22×D5—44no—
103C22×D5—412no—
104C22×D5—46no—
105C22×D5—41no—
106C22×D5—43no—
107C5×Q8—82no—
108C2×C4×C5—26no—
109C2×C4×C5—46no—
110C2×Dic5—46no—
111C2×Dic5—43no—
112C25—51no—
113C22⋊Q8—26no—
114C2×C22⋊C4—53no—
115C2×C22⋊C4—106no—
116C2×C22⋊C4C2×C3×D513yes—
117C2×C3×C5—23no—
118C2×C3×C5—23no—
119C2×C3×C5#39311yescharacteristic
120C2×C3×C5B(4,𝔽2)12yes—
121C3×D5—44no—
122C23×C3—42no—
123C23×C3—1012no—
124C23×C3—106no—
125C23×C3—206no—
126C23×C3—204no—
127C23×C3—2012no—
128C23×C3—201no—
129C23×C3—203no—
130C23×C3Q8×D511yescharacteristic
131C23×C3#71313yes—
132C23×C3C2×C22⋊D513yes—
133C3×Q8—82no—
134C2×C3×C4—26no—
135C2×C3×C4—46no—
136C2×C3×C4—206no—
137C2×C3×C4—203no—
138C22×C5—26no—
139C22×C5—41no—
140C22×C5—43no—
141C22×C5C3×#12011yescharacteristic
142C22×C5C3×C22⋊Q813yes—
143C22×C5C3×#12413yes—
144C2×D5—212no—
145C2×D5—412no—
146C2×D5—46no—
147C2×D5—42no—
148C2×D5—44no—
149C4×C5—46no—
150Dic5—83no—
151C24—52no—
152C24—103no—
153C24—103no—
154C24—204no—
155C24C22×C3×D511yescharacteristic
156C2×Q8—22no—
157C22×C4—103no—
158C22×C4C3×C22⋊D516yes—
159C4⋊C4—26no—
160C22⋊C4—26no—
161C22⋊C4—106no—
162C22⋊C4—2012no—
163C3×C5#202911yescharacteristic, complemented, Hall
164C22×C3—26no—
165C22×C3—41no—
166C22×C3—43no—
167C22×C3—1012no—
168C22×C3—2012no—
169C22×C3—206no—
170C22×C3—202no—
171C22×C3—204no—
172C22×C3#409213yes—
173C22×C3#409313yes—
174C22×C3#409911yescharacteristic
175C3×C4—46no—
176C3×C4—403no—
177C2×C5—23no—
178C2×C5—23no—
179C2×C5C3×#39311yescharacteristic
180C2×C5C3×B(4,𝔽2)12yes—
181D5—44no—
182C23—42no—
183C23—1012no—
184C23—106no—
185C23—206no—
186C23—204no—
187C23—2012no—
188C23—203no—
189C23—201no—
190C23C3×Q8×D511yescharacteristic
191C23C3×#71313yes—
192C23C2×C3×C22⋊D513yes—
193Q8—82no—
194C2×C4—26no—
195C2×C4—46no—
196C2×C4—206no—
197C2×C4—203no—
198C2×C3—23no—
199C2×C3—23no—
200C2×C3—204no—
201C2×C3#6552011yescharacteristic
202C2×C3#6553312yes—
203C5C3×#202911yescharacteristic, complemented, Sylow
204C22—26no—
205C22—41no—
206C22—43no—
207C22—1012no—
208C22—2012no—
209C22—206no—
210C22—202no—
211C22—204no—
212C22C3×#409213yes—
213C22C3×#409313yes—
214C22C3×#409911yescharacteristic
215C4—46no—
216C4—403no—
217C3#1060269011yescharacteristic, direct product factor, Sylow
218C2—23no—
219C2—23no—
220C2—204no—
221C2C3×#6552011yescharacteristic
222C2C3×#6553312yes—
subgroupG/H
centerC22×C3#4099
commutator, cosocleC24×C5C23×C3
FrattiniC24C22×C3×D5
FittingC3×C5×#543C2
socleC22×C3×C5#120
prime radicalC24×C3×D5C22
hypercenterC3×#543D5
hypocenterC5C3×#2029
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
1. C3×C5×#543C2semidirect
3. C3×#64746C2semidirect
4. #10602690C3direct (N × H)
11. C5×#543C2×C3semidirect
13. #64746C2×C3semidirect
18. C23×C3×D5Q8semidirect
26. C3×#543D5semidirect
60. C23×D5C3×Q8semidirect
68. #543C3×D5semidirect
163. C3×C5#2029semidirect
203. C5C3×#2029semidirect
217. C3#10602690direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5432
C3×#652442
C3×#647462
#106026903
C3×#20295