Finite Group Databasebeta

← C3×#91530 #13086676

Subgroups — C3×#91530 #13086676

Order 1440.

274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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×#6719C211yesmaximal, characteristic
2C3×C5×#217C211yesmaximal, characteristic
3C32×C22⋊Dic5C211yesmaximal, characteristic
4C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
5C3×#6669C211yesmaximal, characteristic, complemented
6C3×#6668C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic5C211yesmaximal, characteristic, complemented
8C3×#4025—31nomaximal
9#91530C311yesmaximal, characteristic, direct product factor
10C23×C32×C5C2211yescharacteristic
11C2×C3×Dic15C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C2×C3×C5×Dic3C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17C3×#879—51nomaximal, Hall
18C3×C5×C22⋊C4—31no—
19#6719C2×C311yescharacteristic
20C5×#217C2×C311yescharacteristic
21C3×C22⋊Dic5—21no—
22C3×C22⋊Dic5—31no—
23C3×C22⋊Dic5D311yescharacteristic
24C3×C22⋊Dic5C2×C311yescharacteristic
25C3×C4⋊Dic5—31no—
26C3×#683—31no—
27C3×#683—31no—
28C3×C4×Dic5—31no—
29Dic3⋊Dic5C2×C311yescharacteristic, complemented
30#6669C2×C311yescharacteristic, complemented
31#6668C2×C311yescharacteristic, complemented
32Dic3×Dic5C2×C311yescharacteristic, complemented
33C22×C32×C5—21no—
34C22×C32×C5—21no—
35C22×C32×C5—21no—
36C22×C32×C5C2311yescharacteristic
37C3×Dic15—21no—
38C3×Dic15—21no—
39C3×C5×Dic3—21no—
40C3×C5×Dic3—21no—
41C32×Dic5—21no—
42C32×Dic5—21no—
43#4025—31noHall
44C32×C22⋊C4—51no—
45C3×#217—51no—
46C3×#217D511yescharacteristic
47C3×C4⋊Dic3—51no—
48C3×Dic3⋊C4—51no—
49C3×Dic3⋊C4—51no—
50C3×C4×Dic3—51no—
51C23×C3×C5—21no—
52C23×C3×C5C2×D311yescharacteristic
53C23×C3×C5C22×C311yescharacteristic
54C2×C3×C4×C5—31no—
55C2×C3×C4×C5—31no—
56C2×Dic15C22×C311yescharacteristic
57C2×Dic15C22×C311yescharacteristic
58C2×C5×Dic3C22×C311yescharacteristic
59C2×C5×Dic3C22×C311yescharacteristic
60C2×C3×Dic5—21no—
61C2×C3×Dic5—21no—
62C2×C3×Dic5—31no—
63C2×C3×Dic5—31no—
64C2×C3×Dic5C2×D311yescharacteristic
65C2×C3×Dic5C2×D311yescharacteristic
66C2×C3×Dic5C22×C311yescharacteristic
67C2×C3×Dic5C22×C311yescharacteristic
68C3×#126—151no—
69#879—51no—
70C2×C32×C5—41no—
71C2×C32×C5#4111yescharacteristic
72C2×C32×C5#4111yescharacteristic
73C2×C32×C5#4111yescharacteristic
74C5×C22⋊C4—31no—
75C22⋊Dic5—31no—
76C22⋊Dic5C3×D311yescharacteristic
77C4⋊Dic5—31no—
78#683—31no—
79#683—31no—
80C4×Dic5—31no—
81C23×C32C2×D511yescharacteristic
82C2×C32×C4—51no—
83C2×C32×C4—51no—
84C2×C3×Dic3—51no—
85C2×C3×Dic3—51no—
86C2×C3×Dic3C2×D511yescharacteristic
87C2×C3×Dic3C2×D511yescharacteristic
88C22×C3×C5—22no—
89C22×C3×C5—21no—
90C22×C3×C5—21no—
91C22×C3×C5—21no—
92C22×C3×C5—21no—
93C22×C3×C5—21no—
94C22×C3×C5—21no—
95C22×C3×C5—21no—
96C22×C3×C5—41no—
97C22×C3×C5—41no—
98C22×C3×C5C22×D311yescharacteristic
99C22×C3×C5C23×C311yescharacteristic
100C3×C4×C5—61no—
101C3×C4×C5—61no—
102Dic15—21no—
103Dic15—21no—
104C3×Dic5—21no—
105C3×Dic5—21no—
106C3×Dic5—21no—
107C3×Dic5—21no—
108C3×Dic5—41no—
109C3×Dic5—41no—
110C3×Dic5—61no—
111C3×Dic5—61no—
112C5×Dic3—21no—
113C5×Dic3—21no—
114C3×C4⋊C4—151no—
115C3×C4⋊C4—151no—
116C3×C4⋊C4—151no—
117C3×C22⋊C4—31no—
118C3×C22⋊C4—51no—
119C3×C22⋊C4—51no—
120C3×C22⋊C4—101no—
121C3×C22⋊C4—151no—
122C3×C42—151no—
123#217—51no—
124#217C3×D511yescharacteristic
125C4⋊Dic3—51no—
126Dic3⋊C4—51no—
127Dic3⋊C4—51no—
128C4×Dic3—51no—
129C32×C5#12611yescharacteristic, complemented, Hall
130C23×C5C2×C3×D311yescharacteristic
131C2×C4×C5—31no—
132C2×C4×C5—31no—
133C2×Dic5—31no—
134C2×Dic5—31no—
135C2×Dic5C2×C3×D311yescharacteristic
136C2×Dic5C2×C3×D311yescharacteristic
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C22×D511yescharacteristic
141C32×C4—101no—
142C32×C4—101no—
143C3×Dic3—21no—
144C3×Dic3—21no—
145C3×Dic3—101no—
146C3×Dic3—101no—
147#126—151noSylow
148C2×C3×C5—21no—
149C2×C3×C5—21no—
150C2×C3×C5—21no—
151C2×C3×C5—42no—
152C2×C3×C5—41no—
153C2×C3×C5—41no—
154C2×C3×C5#23511yescharacteristic
155C2×C3×C5#23711yescharacteristic
156C2×C3×C5#23711yescharacteristic
157C2×C3×C5C3×#4111yescharacteristic
158C2×C3×C5C3×#4111yescharacteristic
159C2×C3×C5C3×#4111yescharacteristic
160C23×C3—21no—
161C23×C3D3×D511yescharacteristic
162C23×C3C2×C3×D511yescharacteristic
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—51no—
166C2×C3×C4—51no—
167C2×C3×C4—51no—
168C2×C3×C4—51no—
169C2×C3×C4—101no—
170C2×C3×C4—101no—
171C2×C3×C4—151no—
172C2×C3×C4—151no—
173C2×Dic3—51no—
174C2×Dic3—51no—
175C2×Dic3C2×C3×D511yescharacteristic
176C2×Dic3C2×C3×D511yescharacteristic
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5C22×C3×D311yescharacteristic
181C4×C5—61no—
182C4×C5—61no—
183Dic5—21no—
184Dic5—21no—
185Dic5—61no—
186Dic5—61no—
187C2×C32—41no—
188C2×C32#70911yescharacteristic
189C2×C32#71111yescharacteristic
190C2×C32#71111yescharacteristic
191C4⋊C4—151no—
192C4⋊C4—151no—
193C4⋊C4—151no—
194C22⋊C4—31no—
195C22⋊C4—51no—
196C22⋊C4—151no—
197C42—151no—
198C3×C5—21no—
199C3×C5#87911yescharacteristic, complemented
200C3×C5C3×#12611yescharacteristic, complemented
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—41no—
210C22×C3—41no—
211C22×C3C2×D3×D511yescharacteristic
212C22×C3C22×C3×D511yescharacteristic
213C3×C4—61no—
214C3×C4—61no—
215C3×C4—101no—
216C3×C4—101no—
217C3×C4—101no—
218C3×C4—101no—
219C3×C4—201no—
220C3×C4—201no—
221C3×C4—301no—
222C3×C4—301no—
223Dic3—21no—
224Dic3—21no—
225Dic3—101no—
226Dic3—101no—
227C2×C5—41no—
228C2×C5C3×#23511yescharacteristic
229C2×C5C3×#23711yescharacteristic
230C2×C5C3×#23711yescharacteristic
231C32#402511yescharacteristic, complemented, Sylow
232C23C3×D3×D511yescharacteristic
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—51no—
236C2×C4—51no—
237C2×C4—151no—
238C2×C4—151no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—42no—
243C2×C3—41no—
244C2×C3—41no—
245C2×C3#677911yescharacteristic
246C2×C3#678011yescharacteristic
247C2×C3#678211yescharacteristic
248C2×C3C3×#70911yescharacteristic
249C2×C3C3×#71111yescharacteristic
250C2×C3C3×#71111yescharacteristic
251C5C3×#87911yescharacteristic, complemented, Sylow
252C22—21no—
253C22—21no—
254C22—21no—
255C22C2×C3×D3×D511yescharacteristic
256C4—61no—
257C4—61no—
258C4—101no—
259C4—101no—
260C4—301no—
261C4—301no—
262C3—21no—
263C3#9153011yescharacteristic, direct product factor
264C3C3×#402511yescharacteristic, complemented
265C2—41no—
266C2C3×#677911yescharacteristic
267C2C3×#678011yescharacteristic
268C2C3×#678211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D5
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C2×C3×D3×D5
Fitting, prime radicalC23×C32×C5C22
socleC22×C32×C5C23
hypercenterC23×C3D3×D5
hypocenterC3×C5C3×#126
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
4. C3×Dic3⋊Dic5C2semidirect
5. C3×#6669C2semidirect
6. C3×#6668C2semidirect
7. C3×Dic3×Dic5C2semidirect
9. #91530C3direct (N × H)
29. Dic3⋊Dic5C2×C3semidirect
30. #6669C2×C3semidirect
31. #6668C2×C3semidirect
32. Dic3×Dic5C2×C3semidirect
129. C32×C5#126semidirect
199. C3×C5#879semidirect
200. C3×C5C3×#126semidirect
231. C32#4025semidirect
251. C5C3×#879semidirect
263. C3#91530direct (N × H)
264. C3C3×#4025semidirect

Maximal subgroups

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

subgroupindex
C3×#67192
C3×C5×#2172
C32×C22⋊Dic52
C3×Dic3⋊Dic52
C3×#66692
C3×#66682
C3×Dic3×Dic52
C3×#40253
#915303
C3×#8795