Finite Group Databasebeta

← C3×#10602747 #14291143

Subgroups — C3×#10602747 #14291143

Order 1920.

392 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 98 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×#562C211yesmaximal, characteristic
2C3×#65358C211yesmaximal, characteristic, complemented
3C3×#65344C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64760C212yesmaximal, complemented
6#10602747C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#125C2211yescharacteristic
8C3×C5×#124C2212yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#121—22no—
12C3×#4015C2211yescharacteristic
13C3×#3967—22no—
14C3×#3964—22no—
15C3×#3942—22no—
16C3×#3935C2212yes—
17C3×#3935C2211yescharacteristic
18C3×#1662—51nomaximal, Hall
19C5×#562C2×C311yescharacteristic
20#65358C2×C311yescharacteristic, complemented
21#65344C2×C312yescomplemented
22#64763C2×C311yescharacteristic, complemented
23#64760C2×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⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C5×C22⋊C4—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36C3×C4⋊Dic5—22no—
37C2×C3×#168—21no—
38C2×C3×#168—22no—
39C3×#562D511yescharacteristic
40C3×#491—51no—
41C3×#489—52no—
42C3×#330—51no—
43C3×#329—52no—
44C5×#125C22×C311yescharacteristic
45C5×#124C22×C312yes—
46C5×#123—22no—
47C5×C22⋊Q8—22no—
48C5×#121—22no—
49#4015C22×C311yescharacteristic
50#3967—22no—
51#3964—22no—
52#3942—22no—
53#3935C22×C312yes—
54#3935C22×C311yescharacteristic
55#1662—51noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—42no—
59C3×C5×D4—82no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—82no—
63C2×C3×C4×C5C2×D412yes—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×C3×Dic5—41no—
66C3×Dic10—42no—
67C3×#168—41no—
68C3×#168—42no—
69C3×C4⋊Q8—51no—
70C3×#125C2×D511yescharacteristic
71C3×#124C2×D512yes—
72C3×#123—22no—
73C3×C22⋊Q8—22no—
74C3×#121—22no—
75C3×#103—102no—
76C3×#103—102no—
77C3×#102—102no—
78C3×#97—51no—
79C3×#97—52no—
80C2×C5×Q8C3×D412yes—
81C2×C5×D4—22no—
82C2×C5×D4C3×D412yes—
83C22×C4×C5—22no—
84C2×Dic10—21no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4C3×D412yes—
88C5×C22⋊C4—22no—
89C5×C22⋊C4—22no—
90C5×C22⋊C4—22no—
91C42×C5C23×C311yescharacteristic
92C4⋊Dic5—22no—
93C2×#168—21no—
94C2×#168—22no—
95#562C3×D511yescharacteristic
96#491—51no—
97#489—52no—
98#330—51no—
99#329—52no—
100C22×C3×C5—42no—
101C22×C3×C5—42no—
102C22×C3×C5—42no—
103C22×C3×C5#12011yescharacteristic
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C3×Dic5—81no—
109C2×C3×Q8—101no—
110C2×C3×Q8C22⋊D512yes—
111C2×C3×D4—22no—
112C2×C3×D4C22⋊D512yes—
113C22×C3×C4—22no—
114C2×C3×C8—102no—
115C2×C3×C8—101no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—102no—
119C3×C4⋊C4C22⋊D512yes—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C42C22×D511yescharacteristic
124C23×C5—22no—
125C5×Q8—42no—
126C5×D4—42no—
127C5×D4—82no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—82no—
131C2×C4×C5C2×C3×D412yes—
132C2×C4×C5C2×C3×D411yescharacteristic
133C2×Dic5—41no—
134Dic10—42no—
135#168—41no—
136#168—42no—
137C4⋊Q8—51no—
138#125C2×C3×D511yescharacteristic
139#124C2×C3×D512yes—
140#123—22no—
141C22⋊Q8—22no—
142#121—22no—
143#103—102no—
144#103—102no—
145#102—102no—
146#97—51no—
147#97—52no—
148C2×C3×C5—82no—
149C2×C3×C5#45411yescharacteristic
150C2×C3×C5#45512yes—
151C23×C3—22no—
152C3×Q8—42no—
153C3×Q8—202no—
154C3×D4—42no—
155C3×D4—82no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—82no—
159C2×C3×C4—201no—
160C2×C3×C4C2×C22⋊D511yescharacteristic
161C2×C3×C4C2×C22⋊D512yes—
162C3×C8—202no—
163C3×C8—201no—
164C22×C5—42no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5C3×#12011yescharacteristic
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171C4×C5—42no—
172Dic5—81no—
173C2×Q8—101no—
174C2×Q8C3×C22⋊D512yes—
175C2×D4—22no—
176C2×D4C3×C22⋊D512yes—
177C22×C4—22no—
178C2×C8—102no—
179C2×C8—101no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—102no—
183C4⋊C4C3×C22⋊D512yes—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C42C22×C3×D511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3—42no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3#409911yescharacteristic
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—42no—
196C3×C4—42no—
197C3×C4—401no—
198C2×C5—82no—
199C2×C5C3×#45411yescharacteristic
200C2×C5C3×#45512yes—
201C23—22no—
202Q8—42no—
203Q8—202no—
204D4—42no—
205D4—82no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—201no—
210C2×C4C2×C3×C22⋊D511yescharacteristic
211C2×C4C2×C3×C22⋊D512yes—
212C8—202no—
213C8—201no—
214C2×C3—82no—
215C2×C3#6553112yes—
216C2×C3#6553411yescharacteristic
217C5C3×#166211yescharacteristic, complemented, Sylow
218C22—42no—
219C22—42no—
220C22—42no—
221C22C3×#409911yescharacteristic
222C4—22no—
223C4—21no—
224C4—42no—
225C4—42no—
226C4—401no—
227C3#1060274711yescharacteristic, direct product factor, Sylow
228C2—82no—
229C2C3×#6553112yes—
230C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
Fitting, prime radicalC3×C5×#562C2
socleC22×C3×C5#120
hypercenterC3×#562D5
hypocenterC5C3×#1662
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#562

Complements

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

NH ≅ G/Ntype
2. C3×#65358C2semidirect
3. C3×#65344C2semidirect
4. C3×#64763C2semidirect
5. C3×#64760C2semidirect
6. #10602747C3direct (N × H)
20. #65358C2×C3semidirect
21. #65344C2×C3semidirect
22. #64763C2×C3semidirect
23. #64760C2×C3semidirect
188. C3×C5#1662semidirect
217. C5C3×#1662semidirect
227. C3#10602747direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5622
C3×#653582
C3×#653442
C3×#647632
C3×#647602
#106027473
C3×#16625