Finite Group Databasebeta

← C3×#10602721 #14289587

Subgroups — C3×#10602721 #14289587

Order 1920.

436 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 114 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×#555C211yesmaximal, characteristic
2C3×#65381C211yesmaximal, characteristic, complemented
3C3×#65297C212yesmaximal, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C212yesmaximal, complemented
6#10602721C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#121—22no—
10C3×C4×C5×D4C2212yes—
11C3×C5×#117—22no—
12C2×C3×#689—22no—
13C3×#4015C2211yescharacteristic
14C3×#3964—22no—
15C3×#3940—22no—
16C3×C4⋊#168C2212yes—
17C3×C4×#168C2211yescharacteristic
18C3×#1634—51nomaximal, Hall
19C5×#555C2×C311yescharacteristic
20#65381C2×C311yescharacteristic, complemented
21#65297C2×C312yescomplemented
22#64766C2×C311yescharacteristic, complemented
23D4⋊#168C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×C3×Dic10—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C5×C22⋊C4—24no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35C3×#689—44no—
36C3×C4⋊Dic5—22no—
37C2×C3×#168—21no—
38C2×C3×#168—22no—
39C3×#555D511yescharacteristic
40C3×#494—51no—
41C3×#476—52no—
42C3×#333—51no—
43C3×D4⋊C8—52no—
44C5×C4⋊Q8C22×C311yescharacteristic
45C5×#124—22no—
46C5×#121—22no—
47C4×C5×D4C22×C312yes—
48C5×#117—22no—
49C2×#689—22no—
50#4015C22×C311yescharacteristic
51#3964—22no—
52#3940—22no—
53C4⋊#168C22×C312yes—
54C4×#168C22×C311yescharacteristic
55#1634—51noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—22no—
59C3×C5×D4—22no—
60C3×C5×D4—82no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×C3×Dic5—41no—
68C3×Dic10—42no—
69C3×#168—22no—
70C3×#168—42no—
71C2×C3×Q16—102no—
72C3×C4⋊Q8—51no—
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×#124—22no—
75C3×#121—22no—
76C3×C4×D4C2×D512yes—
77C3×#117—22no—
78C3×#106—102no—
79C3×C4⋊C8—52no—
80C3×#102—102no—
81C3×C4×C8—51no—
82C2×C5×Q8C3×D412yes—
83C2×C5×D4—22no—
84C2×C5×D4C3×D412yes—
85C22×C4×C5—22no—
86C2×Dic10—21no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4C3×D412yes—
89C5×C22⋊C4—24no—
90C5×C22⋊C4—22no—
91C42×C5—22no—
92C42×C5C23×C311yescharacteristic
93#689—44no—
94C4⋊Dic5—22no—
95C2×#168—21no—
96C2×#168—22no—
97#555C3×D511yescharacteristic
98#494—51no—
99#476—52no—
100#333—51no—
101D4⋊C8—52no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5#12011yescharacteristic
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5—42no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111C3×Dic5—81no—
112C2×C3×Q8—101no—
113C2×C3×Q8C22⋊D512yes—
114C2×C3×D4—22no—
115C2×C3×D4C22⋊D512yes—
116C22×C3×C4—22no—
117C3×Q16—204no—
118C2×C3×C8—101no—
119C2×C3×C8—102no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—102no—
122C3×C4⋊C4C22⋊D512yes—
123C3×C22⋊C4—24no—
124C3×C22⋊C4—22no—
125C3×C42—22no—
126C3×C42C22×D511yescharacteristic
127C23×C5—22no—
128C5×Q8—42no—
129C5×D4—22no—
130C5×D4—22no—
131C5×D4—82no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5C2×C3×D411yescharacteristic
137C2×C4×C5C2×C3×D412yes—
138C2×Dic5—41no—
139Dic10—42no—
140#168—22no—
141#168—42no—
142C2×Q16—102no—
143C4⋊Q8—51no—
144C4⋊Q8C2×C3×D511yescharacteristic
145#124—22no—
146#121—22no—
147C4×D4C2×C3×D512yes—
148#117—22no—
149#106—102no—
150C4⋊C8—52no—
151#102—102no—
152C4×C8—51no—
153C2×C3×C5—82no—
154C2×C3×C5#45212yes—
155C2×C3×C5#45311yescharacteristic
156C23×C3—22no—
157C3×Q8—42no—
158C3×Q8—202no—
159C3×D4—22no—
160C3×D4—22no—
161C3×D4—82no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—201no—
167C2×C3×C4C2×C22⋊D511yescharacteristic
168C2×C3×C4C2×C22⋊D512yes—
169C3×C8—102no—
170C3×C8—202no—
171C22×C5—42no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5C3×#12011yescharacteristic
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—42no—
178C4×C5C3×#13512yes—
179C4×C5C3×#13712yes—
180Dic5—81no—
181C2×Q8—101no—
182C2×Q8C3×C22⋊D512yes—
183C2×D4—22no—
184C2×D4C3×C22⋊D512yes—
185C22×C4—22no—
186Q16—204no—
187C2×C8—101no—
188C2×C8—102no—
189C4⋊C4—22no—
190C4⋊C4—102no—
191C4⋊C4C3×C22⋊D512yes—
192C22⋊C4—24no—
193C22⋊C4—22no—
194C42—22no—
195C42C22×C3×D511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3#409911yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—42no—
204C3×C4—401no—
205C3×C4#409612yes—
206C3×C4#409712yes—
207C2×C5—82no—
208C2×C5C3×#45212yes—
209C2×C5C3×#45311yescharacteristic
210C23—22no—
211Q8—42no—
212Q8—202no—
213D4—22no—
214D4—22no—
215D4—82no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—201no—
221C2×C4C2×C3×C22⋊D511yescharacteristic
222C2×C4C2×C3×C22⋊D512yes—
223C8—102no—
224C8—202no—
225C2×C3—82no—
226C2×C3#6552812yes—
227C2×C3#6553011yescharacteristic
228C5C3×#163411yescharacteristic, complemented, Sylow
229C22—42no—
230C22—42no—
231C22—42no—
232C22C3×#409911yescharacteristic
233C4—21no—
234C4—42no—
235C4—42no—
236C4—401no—
237C4C3×#409612yes—
238C4C3×#409712yes—
239C3#1060272111yescharacteristic, direct product factor, Sylow
240C2—82no—
241C2C3×#6552812yes—
242C2C3×#6553011yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
Fitting, prime radicalC3×C5×#555C2
socleC22×C3×C5#120
hypercenterC3×#555D5
hypocenterC5C3×#1634
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#555

Complements

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

NH ≅ G/Ntype
2. C3×#65381C2semidirect
3. C3×#65297C2semidirect
4. C3×#64766C2semidirect
5. C3×D4⋊#168C2semidirect
6. #10602721C3direct (N × H)
20. #65381C2×C3semidirect
21. #65297C2×C3semidirect
22. #64766C2×C3semidirect
23. D4⋊#168C2×C3semidirect
196. C3×C5#1634semidirect
228. C5C3×#1634semidirect
239. C3#10602721direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5552
C3×#653812
C3×#652972
C3×#647662
C3×D4⋊#1682
#106027213
C3×#16345