Finite Group Databasebeta

← C3×#91838 #13088046

Subgroups — C3×#91838 #13088046

Order 1440.

312 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C32×C5×#41C211yesmaximal, characteristic, complemented
2C2×C3×D60C211yesmaximal, characteristic, complemented
3C3×#6717C212yesmaximal, complemented
4C3×#6715C212yesmaximal, complemented
5C3×#6710C211yesmaximal, characteristic, complemented
6#91838C311yesmaximal, characteristic, direct product factor
7C3×#4095—31nomaximal
8C22×C3×D15—21no—
9C32×C5×Q8C2211yescharacteristic, complemented
10C32×C5×D4—21no—
11C32×C5×D4C2211yescharacteristic, complemented
12C2×C32×C4×C5—21no—
13C2×C32×C4×C5C2211yescharacteristic
14C3×D60—21no—
15C3×D60C2212yes—
16C3×C3⋊#168C2212yescomplemented
17C3×#949—51nomaximal, Hall
18C3×C5×#41—21no—
19C3×C5×#41D311yescharacteristic, complemented
20C3×C5×#41C2×C311yescharacteristic, complemented
21C2×D60C2×C311yescharacteristic, complemented
22C2×C3×D20—31no—
23#6717C2×C312yescomplemented
24#6715C2×C312yescomplemented
25#6710C2×C311yescharacteristic, complemented
26C3×#688—32no—
27C3×#686—32no—
28C3×#681—31no—
29C22×C32×C5—21no—
30C22×C32×C5D411yescharacteristic
31C2×C3×D15—22no—
32C2×C3×D15—42no—
33C32×C4×C5—21no—
34C32×C4×C5D411yescharacteristic
35C32×C4×C5C2311yescharacteristic
36#4095—31noHall
37C32×#41D511yescharacteristic, complemented
38C2×C3×D12—51no—
39C3×#215—52no—
40C3×#213—52no—
41C3×#208—51no—
42C22×D15—21no—
43C22×C3×D5—61no—
44C3×C5×Q8—21no—
45C3×C5×Q8C2×D311yescharacteristic, complemented
46C3×C5×Q8C22×C311yescharacteristic, complemented
47C3×C5×D4—22no—
48C3×C5×D4—21no—
49C3×C5×D4—21no—
50C3×C5×D4—21no—
51C3×C5×D4C2×D311yescharacteristic, complemented
52C3×C5×D4C22×C311yescharacteristic, complemented
53C2×C3×C4×C5—22no—
54C2×C3×C4×C5—21no—
55C2×C3×C4×C5—21no—
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5C2×D311yescharacteristic
58C2×C3×C4×C5C22×C311yescharacteristic
59D60—21no—
60D60C22×C312yes—
61C3×D20—32no—
62C3×D20—61no—
63C3⋊#168C22×C312yescomplemented
64C3×#168—32no—
65C3×AGL(1,ℤ/8)—151no—
66#949—51no—
67C2×C32×C5—21no—
68C2×C32×C5—41no—
69C2×C32×C5C2×D411yescharacteristic
70C3×D15—42no—
71C5×#41C3×D311yescharacteristic, complemented
72C2×D20—31no—
73#688—32no—
74#686—32no—
75#681—31no—
76C22×C3×D3—101no—
77C32×Q8C2×D511yescharacteristic, complemented
78C32×D4—21no—
79C32×D4C2×D511yescharacteristic, complemented
80C2×C32×C4—21no—
81C2×C32×C4C2×D511yescharacteristic
82C3×D12—52no—
83C3×D12—101no—
84C3×C3⋊C8—52no—
85C22×C3×C5—22no—
86C22×C3×C5—21no—
87C22×C3×C5—21no—
88C22×C3×C5—21no—
89C22×C3×C5#6711yescharacteristic
90C22×C3×C5C3×D411yescharacteristic
91C2×D15—22no—
92C2×D15—42no—
93C2×C3×D5—62no—
94C2×C3×D5—122no—
95C3×C4×C5—22no—
96C3×C4×C5—21no—
97C3×C4×C5—21no—
98C3×C4×C5—21no—
99C3×C4×C5—21no—
100C3×C4×C5#6711yescharacteristic
101C3×C4×C5C3×D411yescharacteristic
102C3×C4×C5C22×D311yescharacteristic
103C3×C4×C5C23×C311yescharacteristic
104C3×#41—21no—
105C3×#41C3×D511yescharacteristic, complemented
106C3×#41D1511yescharacteristic, complemented
107C2×C3×D4—151no—
108C2×D12—51no—
109C3×SD16—152no—
110C3×D8—152no—
111C3×M16—151no—
112#215—52no—
113#213—52no—
114#208—51no—
115C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
116C22×D5—61no—
117C5×Q8C2×C3×D311yescharacteristic, complemented
118C5×D4—21no—
119C5×D4C2×C3×D311yescharacteristic, complemented
120C2×C4×C5—21no—
121C2×C4×C5C2×C3×D311yescharacteristic
122D20—32no—
123D20—61no—
124#168—32no—
125C22×C32—21no—
126C22×C32C22⋊D511yescharacteristic
127C2×C3×D3—102no—
128C2×C3×D3—202no—
129C32×C4—21no—
130C32×C4C22⋊D511yescharacteristic
131C32×C4C22×D511yescharacteristic
132AGL(1,ℤ/8)—151noSylow
133C2×C3×C5—21no—
134C2×C3×C5—21no—
135C2×C3×C5—21no—
136C2×C3×C5—41no—
137C2×C3×C5—42no—
138C2×C3×C5—41no—
139C2×C3×C5—41no—
140C2×C3×C5C2×#6711yescharacteristic
141C2×C3×C5C2×C3×D411yescharacteristic
142D15—42no—
143C3×D5—122no—
144C23×C3—301no—
145C22×D3—101no—
146C3×Q8—21no—
147C3×Q8C2×C3×D511yescharacteristic, complemented
148C3×Q8C2×D1511yescharacteristic, complemented
149C3×D4—22no—
150C3×D4—21no—
151C3×D4—21no—
152C3×D4—21no—
153C3×D4—152no—
154C3×D4—301no—
155C3×D4C2×C3×D511yescharacteristic, complemented
156C3×D4C2×D1511yescharacteristic, complemented
157C2×C3×C4—22no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4C2×C3×D511yescharacteristic
162C2×C3×C4C2×D1511yescharacteristic
163D12—52no—
164D12—101no—
165C3×C8—152no—
166C3⋊C8—52no—
167C22×C5—21no—
168C22×C5C3×#6711yescharacteristic
169C2×D5—62no—
170C2×D5—122no—
171C4×C5—21no—
172C4×C5C3×#6711yescharacteristic
173C4×C5C22×C3×D311yescharacteristic
174C2×C32—21no—
175C2×C32—41no—
176C2×C32C2×C22⋊D511yescharacteristic
177C3×D3—202no—
178#41C3×D1511yescharacteristic, complemented
179C2×D4—151no—
180SD16—152no—
181D8—152no—
182M16—151no—
183C3×C5—21no—
184C3×C5#94911yescharacteristic, complemented
185C3×C5C3×AGL(1,ℤ/8)11yescharacteristic, complemented
186C22×C3—22no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—302no—
191C22×C3—602no—
192C22×C3C3×C22⋊D511yescharacteristic
193C22×C3#122011yescharacteristic
194C2×D3—102no—
195C2×D3—202no—
196C3×C4—22no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—21no—
201C3×C4C3×C22⋊D511yescharacteristic
202C3×C4#122011yescharacteristic
203C3×C4C22×C3×D511yescharacteristic
204C3×C4C22×D1511yescharacteristic
205C2×C5—21no—
206C2×C5—41no—
207C2×C5C2×C3×#6711yescharacteristic
208D5—122no—
209C32#409511yescharacteristic, complemented, Sylow
210C23—301no—
211Q8C2×C3×D1511yescharacteristic, complemented
212D4—21no—
213D4—152no—
214D4—301no—
215D4C2×C3×D1511yescharacteristic, complemented
216C2×C4—21no—
217C2×C4C2×C3×D1511yescharacteristic
218C8—152no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—41no—
223C2×C3—42no—
224C2×C3—41no—
225C2×C3—41no—
226C2×C3—602no—
227C2×C3C2×C3×C22⋊D511yescharacteristic
228C2×C3C2×#122011yescharacteristic
229D3—202no—
230C5C3×#94911yescharacteristic, complemented, Sylow
231C22—21no—
232C22—302no—
233C22—602no—
234C22C3×#122011yescharacteristic
235C4—21no—
236C4C3×#122011yescharacteristic
237C4C22×C3×D1511yescharacteristic
238C3—21no—
239C3C3×#409511yescharacteristic, complemented
240C3#9183811yescharacteristic, direct product factor
241C2—21no—
242C2—41no—
243C2—602no—
244C2C2×C3×#122011yescharacteristic
subgroupG/H
centerC2×C3C2×#1220
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C22×C3×D15
FittingC32×C5×#41C2
socleC2×C32×C5C2×D4
hypercenterC3×#41D15
hypocenterC3×C5C3×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
1. C32×C5×#41C2semidirect
2. C2×C3×D60C2semidirect
3. C3×#6717C2semidirect
4. C3×#6715C2semidirect
5. C3×#6710C2semidirect
6. #91838C3direct (N × H)
9. C32×C5×Q8C22semidirect
11. C32×C5×D4C22semidirect
16. C3×C3⋊#168C22semidirect
19. C3×C5×#41D3semidirect
20. C3×C5×#41C2×C3semidirect
21. C2×D60C2×C3semidirect
23. #6717C2×C3semidirect
24. #6715C2×C3semidirect
25. #6710C2×C3semidirect
37. C32×#41D5semidirect
45. C3×C5×Q8C2×D3semidirect
46. C3×C5×Q8C22×C3semidirect
51. C3×C5×D4C2×D3semidirect
52. C3×C5×D4C22×C3semidirect
63. C3⋊#168C22×C3semidirect
71. C5×#41C3×D3semidirect
77. C32×Q8C2×D5semidirect
79. C32×D4C2×D5semidirect
105. C3×#41C3×D5semidirect
106. C3×#41D15semidirect
115. C32×C5AGL(1,ℤ/8)semidirect
117. C5×Q8C2×C3×D3semidirect
119. C5×D4C2×C3×D3semidirect
147. C3×Q8C2×C3×D5semidirect
148. C3×Q8C2×D15semidirect
155. C3×D4C2×C3×D5semidirect
156. C3×D4C2×D15semidirect
178. #41C3×D15semidirect
184. C3×C5#949semidirect
185. C3×C5C3×AGL(1,ℤ/8)semidirect
209. C32#4095semidirect
211. Q8C2×C3×D15semidirect
215. D4C2×C3×D15semidirect
230. C5C3×#949semidirect
239. C3C3×#4095semidirect
240. C3#91838direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×#412
C2×C3×D602
C3×#67172
C3×#67152
C3×#67102
#918383
C3×#40953
C3×#9495