Finite Group Databasebeta

← C3×#10602097 #14289581

Subgroups — C3×#10602097 #14289581

Order 1920.

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

normal subgroups only

This group has 436 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
2C3×C5×#494C211yesmaximal, characteristic, complemented
3C3×#65373C212yesmaximal, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×#64679C212yesmaximal, complemented
6#10602097C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4093—22no—
11C3×#4041—22no—
12C3×#4038—22no—
13C3×C4×D20C2212yes—
14C3×C4×C5×C8C2211yescharacteristic
15C3×#3941—22no—
16C3×#3940—22no—
17C3×C4⋊#168C2212yes—
18C3×#1634—51nomaximal, Hall
19#66068C2×C311yescharacteristic
20C5×#494C2×C311yescharacteristic, complemented
21#65373C2×C312yescomplemented
22#64766C2×C311yescharacteristic, complemented
23#64679C2×C312yescomplemented
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×C3×D20—22no—
27C2×C3×D20D412yes—
28C2×C3×C4×D5—22no—
29C3×C5×Q16—44no—
30C2×C3×C5×C8—21no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34C3×#685—24no—
35C3×#685—22no—
36C3×C4⋊Dic5D412yes—
37C3×C4×Dic5—22no—
38C2×C3×#168—22no—
39C3×#555—51no—
40C3×#494D511yescharacteristic, complemented
41C3×#476—52no—
42C3×#333—51no—
43C3×D4⋊C8—52no—
44C2×C5×Q16—22no—
45C5×C4⋊Q8C22×C311yescharacteristic
46C5×C4⋊Q8C22×C311yescharacteristic
47#4093—22no—
48#4041—22no—
49#4038—22no—
50C4×D20C22×C312yes—
51C4×C5×C8C22×C311yescharacteristic
52#3941—22no—
53#3940—22no—
54C4⋊#168C22×C312yes—
55#1634—51noSylow
56C22×C3×D5—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5—41no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×C3×Dic5—22no—
64C3×D20—22no—
65C3×D20—22no—
66C3×D20—82no—
67C3×C4×D5—42no—
68C3×C4×D5—42no—
69C3×C5×C8—22no—
70C3×#168—42no—
71C2×C3×Q16—22no—
72C3×C4⋊Q8C2×D511yescharacteristic
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×#124—102no—
75C3×#121—102no—
76C3×C4×D4—52no—
77C3×#117—102no—
78C3×#106—102no—
79C3×C4⋊C8—52no—
80C3×#102—102no—
81C3×C4×C8C2×D511yescharacteristic
82C2×C5×Q8—21no—
83C2×C5×Q8C3×D412yes—
84C2×D20—22no—
85C2×D20C3×D412yes—
86C2×C4×D5—22no—
87C5×Q16—44no—
88C2×C5×C8—21no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—22no—
91C42×C5C23×C311yescharacteristic
92#685—24no—
93#685—22no—
94C4⋊Dic5C3×D412yes—
95C4×Dic5—22no—
96C2×#168—22no—
97#555—51no—
98#494C3×D511yescharacteristic, complemented
99#476—52no—
100#333—51no—
101D4⋊C8—52no—
102C22×C3×C5#12011yescharacteristic
103C2×C3×D5—42no—
104C2×C3×D5—42no—
105C2×C3×D5—42no—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5—81no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111C3×Dic5—42no—
112C2×C3×Q8—21no—
113C2×C3×Q8C22⋊D512yes—
114C2×C3×D4—52no—
115C2×C3×D4—102no—
116C22×C3×C4—102no—
117C3×Q16—44no—
118C2×C3×C8—21no—
119C2×C3×C8—102no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—22no—
122C3×C4⋊C4—52no—
123C3×C22⋊C4—104no—
124C3×C22⋊C4—102no—
125C3×C42—102no—
126C3×C42C22×D511yescharacteristic
127C22×D5—22no—
128C5×Q8—42no—
129C5×Q8—42no—
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5C2×C3×D412yes—
133C2×C4×C5C2×C3×D411yescharacteristic
134C2×Dic5—22no—
135D20—22no—
136D20—22no—
137D20—82no—
138C4×D5—42no—
139C4×D5—42no—
140C5×C8—22no—
141#168—42no—
142C2×Q16—22no—
143C4⋊Q8C2×C3×D511yescharacteristic
144C4⋊Q8C2×C3×D511yescharacteristic
145#124—102no—
146#121—102no—
147C4×D4—52no—
148#117—102no—
149#106—102no—
150C4⋊C8—52no—
151#102—102no—
152C4×C8C2×C3×D511yescharacteristic
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C3×D5—82no—
156C23×C3—102no—
157C3×Q8—42no—
158C3×Q8—42no—
159C3×D4—102no—
160C3×D4—102no—
161C3×D4—402no—
162C2×C3×C4—22no—
163C2×C3×C4—41no—
164C2×C3×C4—102no—
165C2×C3×C4—202no—
166C2×C3×C4—202no—
167C2×C3×C4D4×D512yes—
168C2×C3×C4C2×C22⋊D511yescharacteristic
169C3×C8—22no—
170C3×C8—202no—
171C22×C5C3×#12011yescharacteristic
172C2×D5—42no—
173C2×D5—42no—
174C2×D5—42no—
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—81no—
178C4×C5C3×#13512yes—
179C4×C5C3×#13712yes—
180Dic5—42no—
181C2×Q8—21no—
182C2×Q8C3×C22⋊D512yes—
183C2×D4—52no—
184C2×D4—102no—
185C22×C4—102no—
186Q16—44no—
187C2×C8—21no—
188C2×C8—102no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—52no—
192C22⋊C4—104no—
193C22⋊C4—102no—
194C42—102no—
195C42C22×C3×D511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3—202no—
198C22×C3—202no—
199C22×C3—202no—
200C22×C3#408311yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—81no—
204C3×C4—202no—
205C3×C4#406412yes—
206C3×C4#406512yes—
207C2×C5C3×#45212yes—
208C2×C5C3×#45311yescharacteristic
209D5—82no—
210C23—102no—
211Q8—42no—
212Q8—42no—
213D4—102no—
214D4—102no—
215D4—402no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—102no—
219C2×C4—202no—
220C2×C4—202no—
221C2×C4C3×D4×D512yes—
222C2×C4C2×C3×C22⋊D511yescharacteristic
223C8—22no—
224C8—202no—
225C2×C3—402no—
226C2×C3#6536611yescharacteristic
227C2×C3#6547612yes—
228C5C3×#163411yescharacteristic, complemented, Sylow
229C22—202no—
230C22—202no—
231C22—202no—
232C22C3×#408311yescharacteristic
233C4—21no—
234C4—42no—
235C4—81no—
236C4—202no—
237C4C3×#406412yes—
238C4C3×#406512yes—
239C3#1060209711yescharacteristic, direct product factor, Sylow
240C2—402no—
241C2C3×#6536611yescharacteristic
242C2C3×#6547612yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#494C2
socleC22×C3×C5#120
prime radicalC3×#66068C2
hypercenterC3×#494D5
hypocenterC5C3×#1634
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
2. C3×C5×#494C2semidirect
3. C3×#65373C2semidirect
4. C3×#64766C2semidirect
5. C3×#64679C2semidirect
6. #10602097C3direct (N × H)
20. C5×#494C2×C3semidirect
21. #65373C2×C3semidirect
22. #64766C2×C3semidirect
23. #64679C2×C3semidirect
40. C3×#494D5semidirect
98. #494C3×D5semidirect
196. C3×C5#1634semidirect
228. C5C3×#1634semidirect
239. C3#10602097direct (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×C5×#4942
C3×#653732
C3×#647662
C3×#646792
#106020973
C3×#16345