Finite Group Databasebeta

← C3×#10602044 #14291137

Subgroups — C3×#10602044 #14291137

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×C5×#491C211yesmaximal, characteristic, complemented
3C3×#65378C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64684C212yesmaximal, complemented
6#10602044C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9C3×#4042—22no—
10C3×#4041—22no—
11C3×#4040—22no—
12C3×#4021C2212yes—
13C3×C5×#103—22no—
14C3×C5×#97C2211yescharacteristic
15C3×#3942—22no—
16C3×#3941—22no—
17C3×#3935C2212yes—
18C3×#1662—51nomaximal, Hall
19#66034C2×C311yescharacteristic
20C5×#491C2×C311yescharacteristic, complemented
21#65378C2×C312yescomplemented
22#64763C2×C311yescharacteristic, complemented
23#64684C2×C312yescomplemented
24C2×C3×C5×Q8—21no—
25C2×C3×D20—22no—
26C2×C3×D20D412yes—
27C2×C3×C4×D5—22no—
28C2×C3×Dic10D412yes—
29C2×C3×C5×C8—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4D412yes—
33C3×C42×C5C2311yescharacteristic
34C3×#685—22no—
35C3×#685—22no—
36C3×#685—22no—
37C3×#683—22no—
38C2×C3×#168—22no—
39C3×#562—51no—
40C3×#491D511yescharacteristic, complemented
41C3×#489—52no—
42C3×#330—51no—
43C3×#329—52no—
44C5×C4⋊Q8C22×C311yescharacteristic
45C5×#125C22×C311yescharacteristic
46#4042—22no—
47#4041—22no—
48#4040—22no—
49#4021C22×C312yes—
50C5×#103—22no—
51C5×#97C22×C311yescharacteristic
52#3942—22no—
53#3941—22no—
54#3935C22×C312yes—
55#1662—51noSylow
56C22×C3×D5—22no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5C2×D412yes—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×Dic5—22no—
63C3×D20—42no—
64C3×D20—82no—
65C3×C4×D5—82no—
66C3×Dic10—42no—
67C3×C5×C8—41no—
68C3×#168—42no—
69C3×C4⋊Q8C2×D511yescharacteristic
70C3×#125C2×D511yescharacteristic
71C3×#124—52no—
72C3×#123—102no—
73C3×C22⋊Q8—102no—
74C3×#121—102no—
75C3×#103—22no—
76C3×#103—102no—
77C3×#102—102no—
78C3×#97—52no—
79C3×#97C2×D511yescharacteristic
80C2×C5×Q8—21no—
81C2×D20—22no—
82C2×D20C3×D412yes—
83C2×C4×D5—22no—
84C2×Dic10C3×D412yes—
85C2×C5×C8—21no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4C3×D412yes—
89C42×C5C23×C311yescharacteristic
90#685—22no—
91#685—22no—
92#685—22no—
93#683—22no—
94C2×#168—22no—
95#562—51no—
96#491C3×D511yescharacteristic, complemented
97#489—52no—
98#330—51no—
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×C4×C5—81no—
108C3×Dic5—42no—
109C2×C3×Q8—21no—
110C2×C3×Q8—52no—
111C2×C3×D4—52no—
112C2×C3×D4—102no—
113C22×C3×C4—102no—
114C2×C3×C8—21no—
115C2×C3×C8—102no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—102no—
119C3×C4⋊C4C22⋊D512yes—
120C3×C22⋊C4—102no—
121C3×C22⋊C4—102no—
122C3×C22⋊C4—102no—
123C3×C42C22×D511yescharacteristic
124C22×D5—22no—
125C5×Q8—42no—
126C2×C4×C5—22no—
127C2×C4×C5—41no—
128C2×C4×C5C2×C3×D412yes—
129C2×C4×C5C2×C3×D411yescharacteristic
130C2×Dic5—22no—
131D20—42no—
132D20—82no—
133C4×D5—82no—
134Dic10—42no—
135C5×C8—41no—
136#168—42no—
137C4⋊Q8C2×C3×D511yescharacteristic
138#125C2×C3×D511yescharacteristic
139#124—52no—
140#123—102no—
141C22⋊Q8—102no—
142#121—102no—
143#103—22no—
144#103—102no—
145#102—102no—
146#97—52no—
147#97C2×C3×D511yescharacteristic
148C2×C3×C5#45411yescharacteristic
149C2×C3×C5#45512yes—
150C3×D5—82no—
151C23×C3—102no—
152C3×Q8—42no—
153C3×Q8—202no—
154C3×D4—202no—
155C3×D4—402no—
156C2×C3×C4—22no—
157C2×C3×C4—41no—
158C2×C3×C4—102no—
159C2×C3×C4—402no—
160C2×C3×C4D4×D512yes—
161C2×C3×C4C2×C22⋊D511yescharacteristic
162C3×C8—41no—
163C3×C8—202no—
164C22×C5C3×#12011yescharacteristic
165C2×D5—42no—
166C2×D5—42no—
167C2×D5—42no—
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171C4×C5—81no—
172Dic5—42no—
173C2×Q8—21no—
174C2×Q8—52no—
175C2×D4—52no—
176C2×D4—102no—
177C22×C4—102no—
178C2×C8—21no—
179C2×C8—102no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—102no—
183C4⋊C4C3×C22⋊D512yes—
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#408311yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—81no—
197C3×C4—202no—
198C2×C5C3×#45411yescharacteristic
199C2×C5C3×#45512yes—
200D5—82no—
201C23—102no—
202Q8—42no—
203Q8—202no—
204D4—202no—
205D4—402no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—102no—
209C2×C4—402no—
210C2×C4C3×D4×D512yes—
211C2×C4C2×C3×C22⋊D511yescharacteristic
212C8—41no—
213C8—202no—
214C2×C3—402no—
215C2×C3#6535111yescharacteristic
216C2×C3#6549112yes—
217C5C3×#166211yescharacteristic, complemented, Sylow
218C22—202no—
219C22—202no—
220C22—202no—
221C22C3×#408311yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—81no—
226C4—202no—
227C3#1060204411yescharacteristic, direct product factor, Sylow
228C2—402no—
229C2C3×#6535111yescharacteristic
230C2C3×#6549112yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#491C2
socleC22×C3×C5#120
prime radicalC3×#66034C2
hypercenterC3×#491D5
hypocenterC5C3×#1662
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#491

Complements

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

NH ≅ G/Ntype
2. C3×C5×#491C2semidirect
3. C3×#65378C2semidirect
4. C3×#64763C2semidirect
5. C3×#64684C2semidirect
6. #10602044C3direct (N × H)
20. C5×#491C2×C3semidirect
21. #65378C2×C3semidirect
22. #64763C2×C3semidirect
23. #64684C2×C3semidirect
40. C3×#491D5semidirect
96. #491C3×D5semidirect
188. C3×C5#1662semidirect
217. C5C3×#1662semidirect
227. C3#10602044direct (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×C5×#4912
C3×#653782
C3×#647632
C3×#646842
#106020443
C3×#16625