Finite Group Databasebeta

← C3×#10599718 #14303599

Subgroups — C3×#10599718 #14303599

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65411C211yesmaximal, characteristic
2C3×#65408C211yesmaximal, characteristic
3C3×#65395C211yesmaximal, characteristic
4C3×C5×#341C211yesmaximal, characteristic
5C3×#64775C211yesmaximal, characteristic
6C3×#64775C211yesmaximal, characteristic
7C3×#64770C211yesmaximal, characteristic
8#10599718C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×M16C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C3×#4072C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C3×#3950C411yescharacteristic, complemented
17C3×#3950C411yescharacteristic, complemented
18C3×#3949C411yescharacteristic, complemented
19C3×#3949C411yescharacteristic, complemented
20C3×#3947—21no—
21C3×#3946—21no—
22C3×#3946—21no—
23C3×C8×Dic5—21no—
24C3×#1922—51nomaximal, Hall
25#65411C2×C311yescharacteristic
26#65408C2×C311yescharacteristic
27#65395C2×C311yescharacteristic
28C5×#341C2×C311yescharacteristic
29#64775C2×C311yescharacteristic
30#64775C2×C311yescharacteristic
31#64770C2×C311yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C22×C3×Dic5—21no—
34C3×C5×M16—21no—
35C3×C5×M16—21no—
36C3×C5×M16—21no—
37C3×C5×M16Q812yes—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8C2×C411yescharacteristic
43C2×C3×C5×C8C2×C411yescharacteristic
44C3×C22⋊Dic5—21no—
45C3×C22⋊Dic5—21no—
46C3×C4⋊Dic5C2×C411yescharacteristic
47C3×C4⋊Dic5C2×C411yescharacteristic
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×C4×Dic5—21no—
51C3×C4×Dic5—21no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168D411yescharacteristic
57C2×C3×#168D411yescharacteristic
58C3×#427—51no—
59C3×#424—51no—
60C3×#405—51no—
61C3×#341D511yescharacteristic
62C3×#339—51no—
63C3×#339—51no—
64C3×#336—51no—
65C2×C5×M16C22×C311yescharacteristic
66C2×C5×M16C22×C311yescharacteristic
67C22×C5×C8C22×C311yescharacteristic
68#4072C22×C311yescharacteristic
69#4072C22×C311yescharacteristic
70C2×C4×Dic5C22×C311yescharacteristic
71C22×#168C22×C311yescharacteristic
72#3950C3×C411yescharacteristic, complemented
73#3950C3×C411yescharacteristic, complemented
74#3949C3×C411yescharacteristic, complemented
75#3949C3×C411yescharacteristic, complemented
76#3947—21no—
77#3946—21no—
78#3946—21no—
79C8×Dic5—21no—
80#1922—51noSylow
81C23×C3×C5#4111yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×Q811yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—41no—
94C2×C3×Dic5—41no—
95C3×C5×C8—21no—
96C3×C5×C8—21no—
97C3×C5×C8—22no—
98C3×C5×C8—41no—
99C3×#168—21no—
100C3×#168—21no—
101C2×C3×M16C2×D511yescharacteristic
102C2×C3×M16C2×D511yescharacteristic
103C22×C3×C8—51no—
104C22×C3×C8C2×D511yescharacteristic
105C3×#117—51no—
106C3×#117—51no—
107C2×C3×C42—51no—
108C3×#107—51no—
109C3×#107—51no—
110C3×#106—51no—
111C3×#106—51no—
112C3×C4⋊C8—101no—
113C3×C4⋊C8—101no—
114C3×#97—101no—
115C3×C4×C8—101no—
116C22×C4×C5C23×C311yescharacteristic
117C22×Dic5—21no—
118C5×M16—21no—
119C5×M16—21no—
120C5×M16—21no—
121C5×M16C3×Q812yes—
122C2×C5×C8—21no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8C2×C3×C411yescharacteristic
127C2×C5×C8C2×C3×C411yescharacteristic
128C22⋊Dic5—21no—
129C22⋊Dic5—21no—
130C4⋊Dic5C2×C3×C411yescharacteristic
131C4⋊Dic5C2×C3×C411yescharacteristic
132C4⋊Dic5C2×C3×C411yescharacteristic
133C4⋊Dic5C2×C3×C411yescharacteristic
134C4×Dic5—21no—
135C4×Dic5—21no—
136C4×Dic5—21no—
137C4×Dic5—21no—
138C2×#168—21no—
139C2×#168—21no—
140C2×#168C3×D411yescharacteristic
141C2×#168C3×D411yescharacteristic
142#427—51no—
143#424—51no—
144#405—51no—
145#341C3×D511yescharacteristic
146#339—51no—
147#339—51no—
148#336—51no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C4×D411yescharacteristic
152C22×C3×C5#12511yescharacteristic
153C22×C3×C5#12611yescharacteristic
154C3×C4×C5#11711yescharacteristic
155C3×C4×C5C4×Q811yescharacteristic
156C3×C4×C5C22⋊Q811yescharacteristic
157C3×C4×C5#12311yescharacteristic
158C3×Dic5—42no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C22×C3×C4—101no—
164C22×C3×C4C22×D511yescharacteristic
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—21no—
168C3×M16Dic1012yes—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—51no—
174C2×C3×C8—51no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8C4×D511yescharacteristic
178C2×C3×C8C4×D511yescharacteristic
179C3×C4⋊C4—51no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C42—101no—
186C3×C42—101no—
187C3×C42—101no—
188C3×C42—101no—
189C23×C5C3×#4111yescharacteristic
190C2×C4×C5C22×C3×C411yescharacteristic
191C2×C4×C5C2×C3×D411yescharacteristic
192C2×C4×C5C2×C3×Q811yescharacteristic
193C2×C4×C5C3×#4111yescharacteristic
194C2×C4×C5C3×#4111yescharacteristic
195C2×C4×C5C3×#4111yescharacteristic
196C2×Dic5—22no—
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—41no—
202C2×Dic5—41no—
203C5×C8—21no—
204C5×C8—21no—
205C5×C8—22no—
206C5×C8—41no—
207#168—21no—
208#168—21no—
209C2×M16C2×C3×D511yescharacteristic
210C2×M16C2×C3×D511yescharacteristic
211C22×C8—51no—
212C22×C8C2×C3×D511yescharacteristic
213#117—51no—
214#117—51no—
215C2×C42—51no—
216#107—51no—
217#107—51no—
218#106—51no—
219#106—51no—
220C4⋊C8—101no—
221C4⋊C8—101no—
222#97—101no—
223C4×C8—101no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5#38711yescharacteristic
227C2×C3×C5#44311yescharacteristic
228C2×C3×C5#44411yescharacteristic
229C23×C3#71311yescharacteristic
230C2×C3×C4—102no—
231C2×C3×C4—101no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—201no—
236C2×C3×C4—201no—
237C2×C3×C4C2×Dic1011yescharacteristic
238C2×C3×C4C2×C4×D511yescharacteristic
239C2×C3×C4#70911yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4#71111yescharacteristic
242C2×C3×C4#71111yescharacteristic
243C3×C8—21no—
244C3×C8—21no—
245C3×C8—22no—
246C3×C8—41no—
247C3×C8—101no—
248C3×C8—101no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C3×C4×D411yescharacteristic
252C22×C5C3×#12511yescharacteristic
253C22×C5C3×#12611yescharacteristic
254C4×C5C3×#11711yescharacteristic
255C4×C5C3×C4×Q811yescharacteristic
256C4×C5C3×C22⋊Q811yescharacteristic
257C4×C5C3×#12311yescharacteristic
258Dic5—42no—
259Dic5—41no—
260Dic5—41no—
261Dic5—41no—
262Dic5—41no—
263C22×C4—101no—
264C22×C4C22×C3×D511yescharacteristic
265M16—21no—
266M16—21no—
267M16—21no—
268M16C3×Dic1012yes—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—51no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C3×C4×D511yescharacteristic
278C2×C8C3×C4×D511yescharacteristic
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4—51no—
282C4⋊C4—51no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C42—101no—
286C42—101no—
287C42—101no—
288C42—101no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3#403611yescharacteristic
293C22×C3#403911yescharacteristic
294C22×C3#404411yescharacteristic
295C3×C4—202no—
296C3×C4—201no—
297C3×C4—201no—
298C3×C4—201no—
299C3×C4—201no—
300C3×C4C4×Dic1011yescharacteristic
301C3×C4#402311yescharacteristic
302C3×C4#402411yescharacteristic
303C3×C4#402911yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5C3×#38711yescharacteristic
307C2×C5C3×#44311yescharacteristic
308C2×C5C3×#44411yescharacteristic
309C23C3×#71311yescharacteristic
310C2×C4—102no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4C2×C3×Dic1011yescharacteristic
318C2×C4C2×C3×C4×D511yescharacteristic
319C2×C4C3×#70911yescharacteristic
320C2×C4C3×D4×D511yescharacteristic
321C2×C4C3×#71111yescharacteristic
322C2×C4C3×#71111yescharacteristic
323C8—21no—
324C8—21no—
325C8—22no—
326C8—41no—
327C8—101no—
328C8—101no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3#6494311yescharacteristic
332C2×C3#6518311yescharacteristic
333C2×C3#6518411yescharacteristic
334C5C3×#192211yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22C3×#403611yescharacteristic
338C22C3×#403911yescharacteristic
339C22C3×#404411yescharacteristic
340C4—202no—
341C4—201no—
342C4—201no—
343C4—201no—
344C4—201no—
345C4C3×C4×Dic1011yescharacteristic
346C4C3×#402311yescharacteristic
347C4C3×#402411yescharacteristic
348C4C3×#402911yescharacteristic
349C3#1059971811yescharacteristic, direct product factor, Sylow
350C2—21no—
351C2—21no—
352C2C3×#6494311yescharacteristic
353C2C3×#6518311yescharacteristic
354C2C3×#6518411yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#341C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC3×#341D5
hypocenterC5C3×#1922
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#341

Complements

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

NH ≅ G/Ntype
8. #10599718C3direct (N × H)
16. C3×#3950C4semidirect
17. C3×#3950C4semidirect
18. C3×#3949C4semidirect
19. C3×#3949C4semidirect
72. #3950C3×C4semidirect
73. #3950C3×C4semidirect
74. #3949C3×C4semidirect
75. #3949C3×C4semidirect
289. C3×C5#1922semidirect
334. C5C3×#1922semidirect
349. C3#10599718direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#654112
C3×#654082
C3×#653952
C3×C5×#3412
C3×#647752
C3×#647702
#105997183
C3×#19225