Finite Group Databasebeta

← C3×#91835 #13088043

Subgroups — C3×#91835 #13088043

Order 1440.

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

normal subgroups only

This group has 334 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×C32×C5×Q8C211yesmaximal, characteristic, complemented
2C2×C3×C4×D15C211yesmaximal, characteristic
3C3×#6714C212yesmaximal
4C3×C4⋊Dic15C211yesmaximal, characteristic, complemented
5C3×#6712C212yesmaximal, complemented
6#91835C311yesmaximal, characteristic, direct product factor
7C3×#4092—31nomaximal
8C22×C3×D15C2211yescharacteristic
9C32×C5×Q8—22no—
10C2×C32×C4×C5C2212yes—
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C2×C3×Dic15C2212yes—
14C3×C4×D15—22no—
15C3×#946—51nomaximal, Hall
16C2×C3×C5×Q8—21no—
17C2×C3×C5×Q8D311yescharacteristic, complemented
18C2×C3×C5×Q8C2×C311yescharacteristic, complemented
19C2×C4×D15C2×C311yescharacteristic
20C2×C3×C4×D5—31no—
21#6714C2×C312yes—
22C4⋊Dic15C2×C311yescharacteristic, complemented
23#6712C2×C312yescomplemented
24C3×#685—32no—
25C3×C4⋊Dic5—31no—
26C3×#683—32no—
27C22×C32×C5C2311yescharacteristic
28C2×C3×D15—21no—
29C2×C3×D15—21no—
30C2×C3×D15Q812yescomplemented
31C32×C4×C5—22no—
32C32×C4×C5D412yes—
33C3×Dic15—21no—
34C3×Dic15—22no—
35#4092—31noHall
36C2×C32×Q8D511yescharacteristic, complemented
37C2×C3×C4×D3—51no—
38C3×(C2×D3)⋊C4—52no—
39C3×C4⋊Dic3—51no—
40C3×Dic3⋊C4—52no—
41C22×D15C22×C311yescharacteristic
42C22×C3×D5—31no—
43C3×C5×Q8—24no—
44C3×C5×Q8—22no—
45C3×C5×Q8—22no—
46C2×C3×C4×C5—22no—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5C2×D312yes—
49C2×C3×C4×C5C2×D311yescharacteristic
50C2×C3×C4×C5C22×C312yes—
51C2×C3×C4×C5C22×C311yescharacteristic
52C2×Dic15C22×C311yescharacteristic
53C2×Dic15C22×C312yes—
54C4×D15—22no—
55C2×C3×Dic5—31no—
56C2×C3×Dic5—32no—
57C3×C4×D5—62no—
58C3×C22⋊Q8—151no—
59#946—51no—
60C2×C32×C5C2×D411yescharacteristic
61C2×C32×C5C2×Q811yescharacteristic
62C2×C32×C5#4111yescharacteristic
63C3×D15—22no—
64C2×C5×Q8C3×D311yescharacteristic, complemented
65C2×C4×D5—31no—
66#685—32no—
67C4⋊Dic5—31no—
68#683—32no—
69C22×C3×D3—51no—
70C32×Q8—22no—
71C2×C32×C4C2×D512yes—
72C2×C32×C4C2×D511yescharacteristic
73C2×C3×Dic3—51no—
74C2×C3×Dic3—52no—
75C3×C4×D3—102no—
76C22×C3×C5—21no—
77C22×C3×C5C22×D311yescharacteristic
78C22×C3×C5C23×C311yescharacteristic
79C2×D15—21no—
80C2×D15—21no—
81C2×D15C3×Q812yescomplemented
82C2×C3×D5—32no—
83C2×C3×D5—61no—
84C2×C3×D5—61no—
85C3×C4×C5—24no—
86C3×C4×C5—22no—
87C3×C4×C5—22no—
88C3×C4×C5—22no—
89C3×C4×C5#6712yes—
90C3×C4×C5C3×D412yes—
91Dic15—21no—
92Dic15—22no—
93C3×Dic5—62no—
94C3×Dic5—61no—
95C2×C3×Q8—21no—
96C2×C3×Q8C3×D511yescharacteristic, complemented
97C2×C3×Q8D1511yescharacteristic, complemented
98C22×C3×C4—151no—
99C2×C4×D3—51no—
100C3×C4⋊C4—152no—
101C3×C4⋊C4—151no—
102C3×C22⋊C4—152no—
103(C2×D3)⋊C4—52no—
104C4⋊Dic3—51no—
105Dic3⋊C4—52no—
106C32×C5C22⋊Q811yescharacteristic, complemented, Hall
107C22×D5—31no—
108C5×Q8—22no—
109C2×C4×C5C2×C3×D312yes—
110C2×C4×C5C2×C3×D311yescharacteristic
111C2×Dic5—31no—
112C2×Dic5—32no—
113C4×D5—62no—
114C22×C32C22×D511yescharacteristic
115C2×C3×D3—52no—
116C2×C3×D3—101no—
117C2×C3×D3—101no—
118C32×C4—22no—
119C32×C4C22⋊D512yes—
120C3×Dic3—102no—
121C3×Dic3—101no—
122C22⋊Q8—151noSylow
123C2×C3×C5—21no—
124C2×C3×C5—21no—
125C2×C3×C5—21no—
126C2×C3×C5D3×Q811yescharacteristic
127C2×C3×C5#23911yescharacteristic
128C2×C3×C5C2×#6711yescharacteristic
129C2×C3×C5C2×C3×D411yescharacteristic
130C2×C3×C5C2×C3×Q811yescharacteristic
131C2×C3×C5C3×#4111yescharacteristic
132D15—22no—
133C3×D5—62no—
134C23×C3—151no—
135C22×D3—51no—
136C3×Q8—24no—
137C3×Q8—22no—
138C3×Q8—22no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—152no—
142C2×C3×C4—151no—
143C2×C3×C4—302no—
144C2×C3×C4C2×C3×D512yes—
145C2×C3×C4C2×C3×D511yescharacteristic
146C2×C3×C4C2×D1512yes—
147C2×C3×C4C2×D1511yescharacteristic
148C2×Dic3—51no—
149C2×Dic3—52no—
150C4×D3—102no—
151C22×C5C22×C3×D311yescharacteristic
152C2×D5—32no—
153C2×D5—61no—
154C2×D5—61no—
155C4×C5—22no—
156C4×C5C3×#6712yes—
157Dic5—62no—
158Dic5—61no—
159C2×C32Q8×D511yescharacteristic
160C2×C32#71311yescharacteristic
161C2×C32C2×C22⋊D511yescharacteristic
162C3×D3—102no—
163C2×Q8C3×D1511yescharacteristic, complemented
164C22×C4—151no—
165C4⋊C4—152no—
166C4⋊C4—151no—
167C22⋊C4—152no—
168C3×C5—21no—
169C3×C5#94611yescharacteristic, complemented
170C3×C5C3×C22⋊Q811yescharacteristic, complemented
171C22×C3—21no—
172C22×C3—152no—
173C22×C3—301no—
174C22×C3—301no—
175C22×C3C22×C3×D511yescharacteristic
176C22×C3C22×D1511yescharacteristic
177C2×D3—52no—
178C2×D3—101no—
179C2×D3—101no—
180C3×C4—24no—
181C3×C4—22no—
182C3×C4—22no—
183C3×C4—22no—
184C3×C4—302no—
185C3×C4—301no—
186C3×C4C3×C22⋊D512yes—
187C3×C4#122012yes—
188Dic3—102no—
189Dic3—101no—
190C2×C5C3×D3×Q811yescharacteristic
191C2×C5C3×#23911yescharacteristic
192C2×C5C2×C3×#6711yescharacteristic
193D5—62no—
194C32#409211yescharacteristic, complemented, Sylow
195C23—151no—
196Q8—22no—
197C2×C4—152no—
198C2×C4—151no—
199C2×C4—302no—
200C2×C4C2×C3×D1512yes—
201C2×C4C2×C3×D1511yescharacteristic
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3—302no—
206C2×C3C3×Q8×D511yescharacteristic
207C2×C3C3×#71311yescharacteristic
208C2×C3C2×C3×C22⋊D511yescharacteristic
209C2×C3Q8×D1511yescharacteristic
210C2×C3#682111yescharacteristic
211C2×C3C2×#122011yescharacteristic
212D3—102no—
213C5C3×#94611yescharacteristic, complemented, Sylow
214C22—152no—
215C22—301no—
216C22—301no—
217C22C22×C3×D1511yescharacteristic
218C4—22no—
219C4—302no—
220C4—301no—
221C4C3×#122012yes—
222C3—21no—
223C3C3×#409211yescharacteristic, complemented
224C3#9183511yescharacteristic, direct product factor
225C2—302no—
226C2C3×Q8×D1511yescharacteristic
227C2C3×#682111yescharacteristic
228C2C2×C3×#122011yescharacteristic
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC2×C32×C5×Q8C2
socleC22×C32×C5C23
prime radicalC22×C3×D15C22
hypercenterC2×C3×Q8D15
hypocenterC3×C5C3×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×Q8C2semidirect
4. C3×C4⋊Dic15C2semidirect
5. C3×#6712C2semidirect
6. #91835C3direct (N × H)
17. C2×C3×C5×Q8D3semidirect
18. C2×C3×C5×Q8C2×C3semidirect
22. C4⋊Dic15C2×C3semidirect
23. #6712C2×C3semidirect
30. C2×C3×D15Q8semidirect
36. C2×C32×Q8D5semidirect
64. C2×C5×Q8C3×D3semidirect
81. C2×D15C3×Q8semidirect
96. C2×C3×Q8C3×D5semidirect
97. C2×C3×Q8D15semidirect
106. C32×C5C22⋊Q8semidirect
163. C2×Q8C3×D15semidirect
169. C3×C5#946semidirect
170. C3×C5C3×C22⋊Q8semidirect
194. C32#4092semidirect
213. C5C3×#946semidirect
223. C3C3×#4092semidirect
224. C3#91835direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×Q82
C2×C3×C4×D152
C3×#67142
C3×C4⋊Dic152
C3×#67122
#918353
C3×#40923
C3×#9465