Finite Group Databasebeta

← C3×#10599263 #14292175

Subgroups — C3×#10599263 #14292175

Order 1920.

332 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65379C211yesmaximal, characteristic, complemented
2C3×#65377C211yesmaximal, characteristic
3C3×#65137C211yesmaximal, characteristic
4C3×#65119C211yesmaximal, characteristic, complemented
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7C3×#64699C211yesmaximal, characteristic, complemented
8#10599263C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×C3×#689—21no—
11C2×C3×#677—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×#3967—21no—
17C3×#3953—21no—
18C3×#3946—21no—
19C3×C8×Dic5—21no—
20C3×#3941—21no—
21C3×#3941—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1682—51nomaximal, Hall
25#65379C2×C311yescharacteristic, complemented
26#65377C2×C311yescharacteristic
27#65137C2×C311yescharacteristic
28#65119C2×C311yescharacteristic, complemented
29C5×#332C2×C311yescharacteristic, complemented
30#64705C2×C311yescharacteristic
31#64699C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×Dic10D411yescharacteristic
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C3×#689—42no—
43C3×C4⋊Dic5D411yescharacteristic
44C3×#683—21no—
45C3×C4×Dic5—21no—
46C2×C3×#168—21no—
47C2×C3×#168D411yescharacteristic
48C2×C3×#168D411yescharacteristic
49C3×#677—42no—
50C3×#486—51no—
51C3×#462—51no—
52C3×#460—51no—
53C3×C8×Q8—51no—
54C3×#335—51no—
55C3×#332D511yescharacteristic, complemented
56C3×#331—51no—
57C5×C4⋊Q8C22×C311yescharacteristic
58C2×#689—21no—
59C2×#677—21no—
60#4020C22×C311yescharacteristic
61C4×Dic10C22×C311yescharacteristic
62C5×C4⋊C8C22×C311yescharacteristic
63C5×C4⋊C8C22×C311yescharacteristic
64#3967—21no—
65#3953—21no—
66#3946—21no—
67C8×Dic5—21no—
68#3941—21no—
69#3941—21no—
70C4⋊#168C22×C311yescharacteristic
71C4×#168C22×C311yescharacteristic
72#1682—51noSylow
73C22×C3×D5—41no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×C3×Dic5—21no—
81C2×C3×Dic5—21no—
82C3×D20—41no—
83C3×D20—41no—
84C3×D20—41no—
85C3×D20—41no—
86C3×D20—81no—
87C3×Dic10—21no—
88C3×Dic10D812yes—
89C3×C5×C8—41no—
90C3×C5×C8—41no—
91C3×#168—21no—
92C3×#168—21no—
93C3×#168—41no—
94C2×C3×Q16—101no—
95C2×C3×SD16—101no—
96C3×C4⋊Q8C2×D511yescharacteristic
97C3×#127—51no—
98C3×C4×Q8—51no—
99C3×C4⋊C8—51no—
100C3×C4⋊C8—101no—
101C3×C4⋊C8C2×D511yescharacteristic
102C3×C4⋊C8C2×D511yescharacteristic
103C3×#103—101no—
104C3×#102—101no—
105C3×#102—101no—
106C3×#102—101no—
107C3×C4×C8—51no—
108C3×C4×C8—101no—
109C2×C5×Q8—21no—
110C2×D20—21no—
111C2×D20—21no—
112C2×D20—21no—
113C2×Dic10C3×D411yescharacteristic
114C2×C5×C8—21no—
115C2×C5×C8—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C42×C5C23×C311yescharacteristic
119#689—42no—
120C4⋊Dic5C3×D411yescharacteristic
121#683—21no—
122C4×Dic5—21no—
123C2×#168—21no—
124C2×#168C3×D411yescharacteristic
125C2×#168C3×D411yescharacteristic
126#677—42no—
127#486—51no—
128#462—51no—
129#460—51no—
130C8×Q8—51no—
131#335—51no—
132#332C3×D511yescharacteristic, complemented
133#331—51no—
134C22×C3×C5#12111yescharacteristic
135C2×C3×D5—81no—
136C2×C3×D5—81no—
137C2×C3×D5—81no—
138C3×C4×C5—21no—
139C3×C4×C5—81no—
140C3×C4×C5C2×D811yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5#13511yescharacteristic
143C3×C4×C5#13711yescharacteristic
144C3×Dic5—22no—
145C3×Dic5—41no—
146C2×C3×Q8—21no—
147C2×C3×Q8—51no—
148C2×C3×D4—101no—
149C2×C3×D4—101no—
150C2×C3×D4—101no—
151C3×Q16—202no—
152C3×SD16—202no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—51no—
156C2×C3×C8—51no—
157C2×C3×C8—101no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—51no—
161C3×C4⋊C4—101no—
162C3×C42—101no—
163C3×C42C22×D511yescharacteristic
164C22×D5—41no—
165C5×Q8—41no—
166C5×Q8—41no—
167C2×C4×C5—41no—
168C2×C4×C5C2×C3×D411yescharacteristic
169C2×C4×C5C2×C3×D411yescharacteristic
170C2×C4×C5C3×#4111yescharacteristic
171C2×Dic5—21no—
172C2×Dic5—21no—
173D20—41no—
174D20—41no—
175D20—41no—
176D20—41no—
177D20—81no—
178Dic10—21no—
179Dic10C3×D812yes—
180C5×C8—41no—
181C5×C8—41no—
182#168—21no—
183#168—21no—
184#168—41no—
185C2×Q16—101no—
186C2×SD16—101no—
187C4⋊Q8C2×C3×D511yescharacteristic
188#127—51no—
189C4×Q8—51no—
190C4⋊C8—51no—
191C4⋊C8—101no—
192C4⋊C8C2×C3×D511yescharacteristic
193C4⋊C8C2×C3×D511yescharacteristic
194#103—101no—
195#102—101no—
196#102—101no—
197#102—101no—
198C4×C8—51no—
199C4×C8—101no—
200C2×C3×C5#46411yescharacteristic
201C2×C3×C5#46611yescharacteristic
202C2×C3×C5#47111yescharacteristic
203C3×D5—161no—
204C23×C3—201no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—52no—
208C3×Q8—101no—
209C3×D4—201no—
210C3×D4—201no—
211C3×D4—201no—
212C3×D4—201no—
213C3×D4—401no—
214C2×C3×C4—41no—
215C2×C3×C4—101no—
216C2×C3×C4—101no—
217C2×C3×C4#70911yescharacteristic
218C2×C3×C4D4×D511yescharacteristic
219C2×C3×C4D4×D511yescharacteristic
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—101no—
223C3×C8—101no—
224C3×C8—201no—
225C22×C5C3×#12111yescharacteristic
226C2×D5—81no—
227C2×D5—81no—
228C2×D5—81no—
229C4×C5—21no—
230C4×C5—81no—
231C4×C5C2×C3×D811yescharacteristic
232C4×C5C3×#13511yescharacteristic
233C4×C5C3×#13511yescharacteristic
234C4×C5C3×#13711yescharacteristic
235Dic5—22no—
236Dic5—41no—
237C2×Q8—21no—
238C2×Q8—51no—
239C2×D4—101no—
240C2×D4—101no—
241C2×D4—101no—
242Q16—202no—
243SD16—202no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—51no—
247C2×C8—51no—
248C2×C8—101no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—51no—
252C4⋊C4—101no—
253C42—101no—
254C42C22×C3×D511yescharacteristic
255C3×C5#168211yescharacteristic, complemented, Hall
256C22×C3—401no—
257C22×C3—401no—
258C22×C3—401no—
259C22×C3#403011yescharacteristic
260C3×C4—21no—
261C3×C4—81no—
262C3×C4—102no—
263C3×C4—201no—
264C3×C4D5×D811yescharacteristic
265C3×C4#406211yescharacteristic
266C3×C4#406211yescharacteristic
267C3×C4#406411yescharacteristic
268C2×C5C3×#46411yescharacteristic
269C2×C5C3×#46611yescharacteristic
270C2×C5C3×#47111yescharacteristic
271D5—161no—
272C23—201no—
273Q8—41no—
274Q8—41no—
275Q8—52no—
276Q8—101no—
277D4—201no—
278D4—201no—
279D4—201no—
280D4—201no—
281D4—401no—
282C2×C4—41no—
283C2×C4—101no—
284C2×C4—101no—
285C2×C4C3×#70911yescharacteristic
286C2×C4C3×D4×D511yescharacteristic
287C2×C4C3×D4×D511yescharacteristic
288C8—41no—
289C8—41no—
290C8—101no—
291C8—101no—
292C8—201no—
293C2×C3—801no—
294C2×C3#6504311yescharacteristic
295C2×C3#6506411yescharacteristic
296C2×C3#6508711yescharacteristic
297C5C3×#168211yescharacteristic, complemented, Sylow
298C22—401no—
299C22—401no—
300C22—401no—
301C22C3×#403011yescharacteristic
302C4—21no—
303C4—81no—
304C4—102no—
305C4—201no—
306C4C3×D5×D811yescharacteristic
307C4C3×#406211yescharacteristic
308C4C3×#406211yescharacteristic
309C4C3×#406411yescharacteristic
310C3#1059926311yescharacteristic, direct product factor, Sylow
311C2—801no—
312C2C3×#6504311yescharacteristic
313C2C3×#6506411yescharacteristic
314C2C3×#6508711yescharacteristic
subgroupG/H
centerC22×C3#4030
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radicalC3×#4020C22
hypercenterC3×#332D5
hypocenterC5C3×#1682
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#65379C2semidirect
4. C3×#65119C2semidirect
5. C3×C5×#332C2semidirect
7. C3×#64699C2semidirect
8. #10599263C3direct (N × H)
25. #65379C2×C3semidirect
28. #65119C2×C3semidirect
29. C5×#332C2×C3semidirect
31. #64699C2×C3semidirect
55. C3×#332D5semidirect
132. #332C3×D5semidirect
255. C3×C5#1682semidirect
297. C5C3×#1682semidirect
310. C3#10599263direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653792
C3×#653772
C3×#651372
C3×#651192
C3×C5×#3322
C3×#647052
C3×#646992
#105992633
C3×#16825