Finite Group Databasebeta

← C3×#91784 #13087993

Subgroups — C3×#91784 #13087993

Order 1440.

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

normal subgroups only

This group has 402 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
1C2×C3×D60C212yesmaximal, complemented
2C2×C3×D60C211yesmaximal, characteristic, complemented
3C2×C3×C4×D15C211yesmaximal, characteristic, complemented
4C32×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#6714C212yesmaximal, complemented
6#91784C311yesmaximal, characteristic, direct product factor
7C3×#4041—31nomaximal
8C22×C3×D15C2212yes—
9C22×C3×D15C2211yescharacteristic
10C2×C32×C4×C5C2212yes—
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C3×D60—24no—
14C3×D60—22no—
15C3×C4×D15—22no—
16C3×#895—51nomaximal, Hall
17C2×D60C2×C312yescomplemented
18C2×D60C2×C311yescharacteristic, complemented
19C2×C4×D15C2×C311yescharacteristic, complemented
20C2×C3×D20—32no—
21C2×C3×D20—31no—
22C2×C3×C4×D5—31no—
23C3×C5×C4⋊C4—21no—
24C3×C5×C4⋊C4D311yescharacteristic, complemented
25C3×C5×C4⋊C4C2×C311yescharacteristic, complemented
26#6714C2×C312yescomplemented
27C3×#685—32no—
28C22×C32×C5C2311yescharacteristic
29C2×C3×D15—21no—
30C2×C3×D15—21no—
31C2×C3×D15—22no—
32C2×C3×D15—22no—
33C2×C3×D15—22no—
34C2×C3×D15D412yescomplemented
35C32×C4×C5—22no—
36C32×C4×C5D412yescomplemented
37C3×Dic15—21no—
38#4041—31noHall
39C2×C3×D12—52no—
40C2×C3×D12—51no—
41C2×C3×C4×D3—51no—
42C32×C4⋊C4D511yescharacteristic, complemented
43C3×(C2×D3)⋊C4—52no—
44C22×D15C22×C312yes—
45C22×D15C22×C311yescharacteristic
46C22×C3×D5—31no—
47C22×C3×D5—32no—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5C2×D312yes—
51C2×C3×C4×C5C2×D311yescharacteristic
52C2×C3×C4×C5C22×C312yes—
53C2×C3×C4×C5C22×C311yescharacteristic
54C2×Dic15C22×C311yescharacteristic
55D60—24no—
56D60—22no—
57C4×D15—22no—
58C2×C3×Dic5—31no—
59C3×D20—64no—
60C3×D20—62no—
61C3×C4×D5—62no—
62C3×#121—151no—
63#895—51no—
64C2×C32×C5C2×D411yescharacteristic
65C2×C32×C5C2×D411yescharacteristic
66C2×C32×C5#4111yescharacteristic
67C3×D15—22no—
68C3×D15—42no—
69C2×D20—32no—
70C2×D20—31no—
71C2×C4×D5—31no—
72C5×C4⋊C4C3×D311yescharacteristic, complemented
73#685—32no—
74C22×C3×D3—51no—
75C22×C3×D3—52no—
76C2×C32×C4C2×D512yes—
77C2×C32×C4C2×D511yescharacteristic
78C2×C3×Dic3—51no—
79C3×D12—104no—
80C3×D12—102no—
81C3×C4×D3—102no—
82C22×C3×C5—21no—
83C22×C3×C5C22×D311yescharacteristic
84C22×C3×C5C23×C311yescharacteristic
85C2×D15—21no—
86C2×D15—21no—
87C2×D15—22no—
88C2×D15—22no—
89C2×D15—22no—
90C2×D15C3×D412yescomplemented
91C2×C3×D5—32no—
92C2×C3×D5—61no—
93C2×C3×D5—61no—
94C2×C3×D5—62no—
95C2×C3×D5—62no—
96C2×C3×D5—62no—
97C3×C4×C5—22no—
98C3×C4×C5—22no—
99C3×C4×C5—22no—
100C3×C4×C5—42no—
101C3×C4×C5D1212yescomplemented
102C3×C4×C5C3×D412yescomplemented
103Dic15—21no—
104C3×Dic5—61no—
105C2×C3×D4—152no—
106C2×C3×D4—151no—
107C22×C3×C4—151no—
108C2×D12—52no—
109C2×D12—51no—
110C2×C4×D3—51no—
111C3×C4⋊C4—21no—
112C3×C4⋊C4C3×D511yescharacteristic, complemented
113C3×C4⋊C4D1511yescharacteristic, complemented
114C3×C22⋊C4—152no—
115(C2×D3)⋊C4—52no—
116C32×C5#12111yescharacteristic, complemented, Hall
117C22×D5—31no—
118C22×D5—32no—
119C2×C4×C5C2×C3×D312yes—
120C2×C4×C5C2×C3×D311yescharacteristic
121C2×Dic5—31no—
122D20—64no—
123D20—62no—
124C4×D5—62no—
125C22×C32C22×D511yescharacteristic
126C2×C3×D3—52no—
127C2×C3×D3—101no—
128C2×C3×D3—101no—
129C2×C3×D3—102no—
130C2×C3×D3—102no—
131C2×C3×D3—102no—
132C32×C4—22no—
133C32×C4D2012yescomplemented
134C3×Dic3—101no—
135#121—151noSylow
136C2×C3×C5—21no—
137C2×C3×C5—21no—
138C2×C3×C5—21no—
139C2×C3×C5C2×D1211yescharacteristic
140C2×C3×C5D3×D411yescharacteristic
141C2×C3×C5#23911yescharacteristic
142C2×C3×C5C2×C3×D411yescharacteristic
143C2×C3×C5C2×C3×D411yescharacteristic
144C2×C3×C5C3×#4111yescharacteristic
145D15—22no—
146D15—42no—
147C3×D5—62no—
148C3×D5—122no—
149C23×C3—151no—
150C23×C3—152no—
151C22×D3—51no—
152C22×D3—52no—
153C3×D4—304no—
154C3×D4—302no—
155C2×C3×C4—21no—
156C2×C3×C4—22no—
157C2×C3×C4—151no—
158C2×C3×C4—302no—
159C2×C3×C4C2×C3×D512yes—
160C2×C3×C4C2×C3×D511yescharacteristic
161C2×C3×C4C2×D1512yes—
162C2×C3×C4C2×D1511yescharacteristic
163C2×Dic3—51no—
164D12—104no—
165D12—102no—
166C4×D3—102no—
167C22×C5C22×C3×D311yescharacteristic
168C2×D5—32no—
169C2×D5—61no—
170C2×D5—61no—
171C2×D5—62no—
172C2×D5—62no—
173C2×D5—62no—
174C4×C5—22no—
175C4×C5C3×D1212yescomplemented
176Dic5—61no—
177C2×C32C2×D2011yescharacteristic
178C2×C32D4×D511yescharacteristic
179C2×C32#71311yescharacteristic
180C3×D3—102no—
181C3×D3—202no—
182C2×D4—152no—
183C2×D4—151no—
184C22×C4—151no—
185C4⋊C4C3×D1511yescharacteristic, complemented
186C22⋊C4—152no—
187C3×C5—21no—
188C3×C5#89511yescharacteristic, complemented
189C3×C5C3×#12111yescharacteristic, complemented
190C22×C3—21no—
191C22×C3—152no—
192C22×C3—301no—
193C22×C3—301no—
194C22×C3—302no—
195C22×C3—302no—
196C22×C3—302no—
197C22×C3C22×C3×D511yescharacteristic
198C22×C3C22×D1511yescharacteristic
199C2×D3—52no—
200C2×D3—101no—
201C2×D3—101no—
202C2×D3—102no—
203C2×D3—102no—
204C2×D3—102no—
205C3×C4—22no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—42no—
209C3×C4—301no—
210C3×C4C3×D2012yescomplemented
211C3×C4D6012yescomplemented
212Dic3—101no—
213C2×C5C2×C3×D1211yescharacteristic
214C2×C5C3×D3×D411yescharacteristic
215C2×C5C3×#23911yescharacteristic
216D5—62no—
217D5—122no—
218C32#404111yescharacteristic, complemented, Sylow
219C23—151no—
220C23—152no—
221D4—304no—
222D4—302no—
223C2×C4—151no—
224C2×C4—302no—
225C2×C4C2×C3×D1512yes—
226C2×C4C2×C3×D1511yescharacteristic
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—302no—
231C2×C3—602no—
232C2×C3C2×C3×D2011yescharacteristic
233C2×C3C3×D4×D511yescharacteristic
234C2×C3C3×#71311yescharacteristic
235C2×C3C2×D6011yescharacteristic
236C2×C3D4×D1511yescharacteristic
237C2×C3#682111yescharacteristic
238D3—102no—
239D3—202no—
240C5C3×#89511yescharacteristic, complemented, Sylow
241C22—152no—
242C22—301no—
243C22—301no—
244C22—302no—
245C22—302no—
246C22—302no—
247C22C22×C3×D1511yescharacteristic
248C4—22no—
249C4—301no—
250C4C3×D6012yescomplemented
251C3—21no—
252C3C3×#404111yescharacteristic, complemented
253C3#9178411yescharacteristic, direct product factor
254C2—302no—
255C2—602no—
256C2C2×C3×D6011yescharacteristic
257C2C3×D4×D1511yescharacteristic
258C2C3×#682111yescharacteristic
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC32×C5×C4⋊C4C2
socleC22×C32×C5C23
hypercenterC3×C4⋊C4D15
hypocenterC3×C5C3×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D60C2semidirect
2. C2×C3×D60C2semidirect
3. C2×C3×C4×D15C2semidirect
4. C32×C5×C4⋊C4C2semidirect
5. C3×#6714C2semidirect
6. #91784C3direct (N × H)
17. C2×D60C2×C3semidirect
18. C2×D60C2×C3semidirect
19. C2×C4×D15C2×C3semidirect
24. C3×C5×C4⋊C4D3semidirect
25. C3×C5×C4⋊C4C2×C3semidirect
26. #6714C2×C3semidirect
34. C2×C3×D15D4semidirect
36. C32×C4×C5D4semidirect
42. C32×C4⋊C4D5semidirect
72. C5×C4⋊C4C3×D3semidirect
90. C2×D15C3×D4semidirect
101. C3×C4×C5D12semidirect
102. C3×C4×C5C3×D4semidirect
112. C3×C4⋊C4C3×D5semidirect
113. C3×C4⋊C4D15semidirect
116. C32×C5#121semidirect
133. C32×C4D20semidirect
175. C4×C5C3×D12semidirect
185. C4⋊C4C3×D15semidirect
188. C3×C5#895semidirect
189. C3×C5C3×#121semidirect
210. C3×C4C3×D20semidirect
211. C3×C4D60semidirect
218. C32#4041semidirect
240. C5C3×#895semidirect
250. C4C3×D60semidirect
252. C3C3×#4041semidirect
253. C3#91784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D602
C2×C3×C4×D152
C32×C5×C4⋊C42
C3×#67142
#917843
C3×#40413
C3×#8955