Finite Group Databasebeta

← C3×#10599167 #14291146

Subgroups — C3×#10599167 #14291146

Order 1920.

392 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 90 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×#66034C211yesmaximal, characteristic
2C3×#65358C211yesmaximal, characteristic, complemented
3C3×#65003C212yesmaximal, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C3×#64684C212yesmaximal, complemented
6#10599167C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#125C2211yescharacteristic
8C3×#4042—22no—
9C3×#4041—22no—
10C3×#4040—22no—
11C3×#4021C2212yes—
12C3×#4015C2211yescharacteristic
13C3×C5×#97C2212yes—
14C3×#3953—22no—
15C3×#3948—22no—
16C3×#3942—22no—
17C3×#3935C2211yescharacteristic
18C3×#1662—51nomaximal, Hall
19#66034C2×C311yescharacteristic
20#65358C2×C311yescharacteristic, complemented
21#65003C2×C312yescomplemented
22C5×#330C2×C311yescharacteristic, complemented
23#64684C2×C312yescomplemented
24C2×C3×D20—22no—
25C2×C3×D20D412yes—
26C2×C3×C4×D5—22no—
27C2×C3×Dic10—21no—
28C2×C3×Dic10D412yes—
29C2×C3×C5×C8—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5C2311yescharacteristic
33C3×#685—22no—
34C3×#685—22no—
35C3×#685—22no—
36C3×C4⋊Dic5—22no—
37C3×#683—22no—
38C2×C3×#168—21no—
39C3×#562—51no—
40C3×#491—51no—
41C3×#489—52no—
42C3×#330D511yescharacteristic, complemented
43C3×#329—52no—
44C5×#125C22×C311yescharacteristic
45#4042—22no—
46#4041—22no—
47#4040—22no—
48#4021C22×C312yes—
49#4015C22×C311yescharacteristic
50C5×#97C22×C312yes—
51#3953—22no—
52#3948—22no—
53#3942—22no—
54#3935C22×C311yescharacteristic
55#1662—51noSylow
56C22×C3×D5—22no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×C3×Dic5—22no—
61C2×C3×Dic5—41no—
62C3×D20—42no—
63C3×D20—82no—
64C3×C4×D5—82no—
65C3×Dic10—42no—
66C3×Dic10—42no—
67C3×C5×C8—42no—
68C3×#168—41no—
69C3×C4⋊Q8—51no—
70C3×#125C2×D511yescharacteristic
71C3×#124—52no—
72C3×#123—102no—
73C3×C22⋊Q8—102no—
74C3×#121—102no—
75C3×#103—102no—
76C3×#103—102no—
77C3×#102—102no—
78C3×#97—51no—
79C3×#97C2×D512yes—
80C2×D20—22no—
81C2×D20C3×D412yes—
82C2×C4×D5—22no—
83C2×Dic10—21no—
84C2×Dic10C3×D412yes—
85C2×C5×C8—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4C3×D412yes—
88C42×C5C23×C311yescharacteristic
89#685—22no—
90#685—22no—
91#685—22no—
92C4⋊Dic5—22no—
93#683—22no—
94C2×#168—21no—
95#562—51no—
96#491—51no—
97#489—52no—
98#330C3×D511yescharacteristic, complemented
99#329—52no—
100C22×C3×C5#12011yescharacteristic
101C2×C3×D5—42no—
102C2×C3×D5—42no—
103C2×C3×D5—42no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×Dic5—42no—
108C3×Dic5—81no—
109C2×C3×Q8—52no—
110C2×C3×Q8—101no—
111C2×C3×D4—52no—
112C2×C3×D4—102no—
113C22×C3×C4—102no—
114C2×C3×C8—22no—
115C2×C3×C8—101no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—102no—
118C3×C4⋊C4—102no—
119C3×C4⋊C4D2012yes—
120C3×C22⋊C4—102no—
121C3×C22⋊C4—102no—
122C3×C22⋊C4—102no—
123C3×C42C22×D511yescharacteristic
124C22×D5—22no—
125C2×C4×C5—22no—
126C2×C4×C5C2×C3×D411yescharacteristic
127C2×C4×C5C2×C3×D412yes—
128C2×Dic5—22no—
129C2×Dic5—41no—
130D20—42no—
131D20—82no—
132C4×D5—82no—
133Dic10—42no—
134Dic10—42no—
135C5×C8—42no—
136#168—41no—
137C4⋊Q8—51no—
138#125C2×C3×D511yescharacteristic
139#124—52no—
140#123—102no—
141C22⋊Q8—102no—
142#121—102no—
143#103—102no—
144#103—102no—
145#102—102no—
146#97—51no—
147#97C2×C3×D512yes—
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150C3×D5—82no—
151C23×C3—102no—
152C3×Q8—202no—
153C3×Q8—202no—
154C3×D4—202no—
155C3×D4—402no—
156C2×C3×C4—22no—
157C2×C3×C4—102no—
158C2×C3×C4—201no—
159C2×C3×C4—402no—
160C2×C3×C4C2×D2011yescharacteristic
161C2×C3×C4D4×D512yes—
162C3×C8—42no—
163C3×C8—201no—
164C22×C5C3×#12011yescharacteristic
165C2×D5—42no—
166C2×D5—42no—
167C2×D5—42no—
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171Dic5—42no—
172Dic5—81no—
173C2×Q8—52no—
174C2×Q8—101no—
175C2×D4—52no—
176C2×D4—102no—
177C22×C4—102no—
178C2×C8—22no—
179C2×C8—101no—
180C4⋊C4—22no—
181C4⋊C4—102no—
182C4⋊C4—102no—
183C4⋊C4C3×D2012yes—
184C22⋊C4—102no—
185C22⋊C4—102no—
186C22⋊C4—102no—
187C42C22×C3×D511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3—202no—
190C22×C3—202no—
191C22×C3—202no—
192C22×C3#402811yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—202no—
197C3×C4—401no—
198C2×C5C3×#45411yescharacteristic
199C2×C5C3×#45512yes—
200D5—82no—
201C23—102no—
202Q8—202no—
203Q8—202no—
204D4—202no—
205D4—402no—
206C2×C4—22no—
207C2×C4—102no—
208C2×C4—201no—
209C2×C4—402no—
210C2×C4C2×C3×D2011yescharacteristic
211C2×C4C3×D4×D512yes—
212C8—42no—
213C8—201no—
214C2×C3—402no—
215C2×C3#6504211yescharacteristic
216C2×C3#6511412yes—
217C5C3×#166211yescharacteristic, complemented, Sylow
218C22—202no—
219C22—202no—
220C22—202no—
221C22C3×#402811yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—202no—
226C4—401no—
227C3#1059916711yescharacteristic, direct product factor, Sylow
228C2—402no—
229C2C3×#6504211yescharacteristic
230C2C3×#6511412yes—
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#330C2
socleC22×C3×C5#120
prime radicalC3×#66034C2
hypercenterC3×#330D5
hypocenterC5C3×#1662
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
2. C3×#65358C2semidirect
3. C3×#65003C2semidirect
4. C3×C5×#330C2semidirect
5. C3×#64684C2semidirect
6. #10599167C3direct (N × H)
20. #65358C2×C3semidirect
21. #65003C2×C3semidirect
22. C5×#330C2×C3semidirect
23. #64684C2×C3semidirect
42. C3×#330D5semidirect
98. #330C3×D5semidirect
188. C3×C5#1662semidirect
217. C5C3×#1662semidirect
227. C3#10599167direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660342
C3×#653582
C3×#650032
C3×C5×#3302
C3×#646842
#105991673
C3×#16625