Finite Group Databasebeta

← C3×#10599556 #14308906

Subgroups — C3×#10599556 #14308906

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65853C211yesmaximal, characteristic, complemented
2C3×#65420C211yesmaximal, characteristic
3C3×#65290C211yesmaximal, characteristic
4C3×#65228C211yesmaximal, characteristic
5C3×C5×#339C211yesmaximal, characteristic, complemented
6C3×#64774C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599556C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×C3×#685—22no—
14C3×#4072C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4036—21no—
18C3×#4034—21no—
19C3×#4024—22no—
20C3×#4016—21no—
21C3×#4015—21no—
22C3×#3953—21no—
23C3×#3953—21no—
24C3×#3941—21no—
25C3×#3941—21no—
26C3×#2027—51nomaximal, Hall
27#65853C2×C311yescharacteristic, complemented
28#65420C2×C311yescharacteristic
29#65290C2×C311yescharacteristic
30#65228C2×C311yescharacteristic
31C5×#339C2×C311yescharacteristic, complemented
32#64774C2×C311yescharacteristic, complemented
33#64743C2×C311yescharacteristic, complemented
34C23×C3×D5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5D412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20Q812yescomplemented
44C2×C3×Dic10—22no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5—21no—
53C3×C42×C5—21no—
54C3×C22⋊Dic5—21no—
55C3×#685—44no—
56C3×C4⋊Dic5—22no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4⋊Dic5D411yescharacteristic
61C3×#683—22no—
62C3×#683—22no—
63C3×C4×Dic5—21no—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67C3×#544—51no—
68C3×#418—51no—
69C3×#418—51no—
70C3×#390—51no—
71C3×#343—51no—
72C3×#339—51no—
73C3×#339D511yescharacteristic, complemented
74C22×D20C22×C311yescharacteristic
75C2×C5×M16C22×C311yescharacteristic
76C5×#117C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78C2×#685—22no—
79#4072C22×C311yescharacteristic
80C2×C4⋊Dic5C22×C311yescharacteristic
81C2×#681C22×C311yescharacteristic
82#4036—21no—
83#4034—21no—
84#4024—22no—
85#4016—21no—
86#4015—21no—
87#3953—21no—
88#3953—21no—
89#3941—21no—
90#3941—21no—
91#2027—51noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C3×D5—22no—
94C22×C3×D5—42no—
95C22×C3×D5—42no—
96C22×C3×D5—41no—
97C22×C3×D5—41no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—42no—
113C3×D20—22no—
114C3×D20—22no—
115C3×D20—41no—
116C3×D20—41no—
117C3×Dic10—82no—
118C3×C5×C8—41no—
119C3×#168—41no—
120C22×C3×D4—51no—
121C2×C3×M16—51no—
122C2×C3×M16C2×D511yescharacteristic
123C3×C4⋊Q8—101no—
124C3×C4⋊Q8—101no—
125C3×#125—101no—
126C3×#125—101no—
127C3×C22⋊Q8—102no—
128C3×#117—51no—
129C3×#117C2×D511yescharacteristic
130C2×C3×C4⋊C4—51no—
131C2×C3×C22⋊C4—102no—
132C2×C3×C42C2×D511yescharacteristic
133C3×#102—101no—
134C3×#102—101no—
135C3×#102—101no—
136C3×#102—101no—
137C23×D5—21no—
138C22×C4×C5—21no—
139C22×C4×C5C23×C311yescharacteristic
140C22×Dic5C3×D412yes—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20C3×Q812yescomplemented
147C2×Dic10—22no—
148C5×M16—21no—
149C5×M16—21no—
150C2×C5×C8—21no—
151C5×C4⋊C4C3×D411yescharacteristic
152C5×C4⋊C4C3×D411yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5—21no—
155C42×C5—21no—
156C42×C5—21no—
157C22⋊Dic5—21no—
158#685—44no—
159C4⋊Dic5—22no—
160C4⋊Dic5—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5C3×D411yescharacteristic
163C4⋊Dic5C3×D411yescharacteristic
164#683—22no—
165#683—22no—
166C4×Dic5—21no—
167#681—21no—
168#681—21no—
169C2×#168—21no—
170#544—51no—
171#418—51no—
172#418—51no—
173#390—51no—
174#343—51no—
175#339—51no—
176#339C3×D511yescharacteristic, complemented
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5#12011yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#12411yescharacteristic
182C2×C3×D5—44no—
183C2×C3×D5—42no—
184C2×C3×D5—82no—
185C2×C3×D5—81no—
186C2×C3×D5—81no—
187C3×C4×C5—42no—
188C3×C4×C5—41no—
189C3×C4×C5—41no—
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12411yescharacteristic
193C3×C4×C5#12411yescharacteristic
194C3×Dic5—41no—
195C3×Dic5—42no—
196C3×Dic5—41no—
197C24×C3—101no—
198C2×C3×Q8—102no—
199C2×C3×D4—52no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C2×C3×D4—101no—
205C22×C3×C4—21no—
206C22×C3×C4—52no—
207C22×C3×C4C22×D511yescharacteristic
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—101no—
211C3×M16—101no—
212C2×C3×C8—21no—
213C2×C3×C8—101no—
214C3×C4⋊C4—51no—
215C3×C4⋊C4—51no—
216C3×C4⋊C4—102no—
217C3×C4⋊C4—102no—
218C3×C4⋊C4—102no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4D2011yescharacteristic
222C3×C4⋊C4D2011yescharacteristic
223C3×C22⋊C4—21no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—204no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—101no—
230C23×C5C2×C3×D411yescharacteristic
231C22×D5—22no—
232C22×D5—42no—
233C22×D5—42no—
234C22×D5—41no—
235C22×D5—41no—
236C2×C4×C5—22no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5C2×C3×D411yescharacteristic
242C2×C4×C5C2×C3×D411yescharacteristic
243C2×C4×C5C2×C3×Q811yescharacteristic
244C2×C4×C5C3×#4111yescharacteristic
245C2×C4×C5C3×#4111yescharacteristic
246C2×C4×C5C3×#4111yescharacteristic
247C2×Dic5—21no—
248C2×Dic5—21no—
249C2×Dic5—22no—
250C2×Dic5—42no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255Dic10—82no—
256C5×C8—41no—
257#168—41no—
258C22×D4—51no—
259C2×M16—51no—
260C2×M16C2×C3×D511yescharacteristic
261C4⋊Q8—101no—
262C4⋊Q8—101no—
263#125—101no—
264#125—101no—
265C22⋊Q8—102no—
266#117—51no—
267#117C2×C3×D511yescharacteristic
268C2×C4⋊C4—51no—
269C2×C22⋊C4—102no—
270C2×C42C2×C3×D511yescharacteristic
271#102—101no—
272#102—101no—
273#102—101no—
274#102—101no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5#39311yescharacteristic
278C2×C3×C5#45311yescharacteristic
279C2×C3×C5#45411yescharacteristic
280C3×D5—82no—
281C23×C3—102no—
282C23×C3—202no—
283C23×C3—202no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3D4×D511yescharacteristic
287C3×Q8—402no—
288C3×D4—102no—
289C3×D4—102no—
290C3×D4—201no—
291C3×D4—201no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—102no—
300C2×C3×C4—202no—
301C2×C3×C4C2×D2011yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4#70911yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4Q8×D511yescharacteristic
307C3×C8—41no—
308C3×C8—201no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5C3×#12011yescharacteristic
312C22×C5C3×C22⋊Q811yescharacteristic
313C22×C5C3×#12411yescharacteristic
314C2×D5—44no—
315C2×D5—42no—
316C2×D5—82no—
317C2×D5—81no—
318C2×D5—81no—
319C4×C5—42no—
320C4×C5—41no—
321C4×C5—41no—
322C4×C5C3×C22⋊Q811yescharacteristic
323C4×C5C3×C22⋊Q811yescharacteristic
324C4×C5C3×#12411yescharacteristic
325C4×C5C3×#12411yescharacteristic
326Dic5—41no—
327Dic5—42no—
328Dic5—41no—
329C24—101no—
330C2×Q8—102no—
331C2×D4—52no—
332C2×D4—101no—
333C2×D4—101no—
334C2×D4—101no—
335C2×D4—101no—
336C2×D4—101no—
337C22×C4—21no—
338C22×C4—52no—
339C22×C4C22×C3×D511yescharacteristic
340M16—21no—
341M16—21no—
342M16—101no—
343M16—101no—
344C2×C8—21no—
345C2×C8—101no—
346C4⋊C4—51no—
347C4⋊C4—51no—
348C4⋊C4—102no—
349C4⋊C4—102no—
350C4⋊C4—102no—
351C4⋊C4—101no—
352C4⋊C4—101no—
353C4⋊C4C3×D2011yescharacteristic
354C4⋊C4C3×D2011yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—101no—
357C22⋊C4—204no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—101no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—204no—
366C22×C3—202no—
367C22×C3—402no—
368C22×C3—401no—
369C22×C3—401no—
370C22×C3#402811yescharacteristic
371C22×C3#403111yescharacteristic
372C22×C3#404211yescharacteristic
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—202no—
377C3×C4—201no—
378C3×C4—201no—
379C3×C4#402111yescharacteristic
380C3×C4#403111yescharacteristic
381C3×C4#404211yescharacteristic
382C3×C4#404311yescharacteristic
383C2×C5—21no—
384C2×C5—21no—
385C2×C5C3×#39311yescharacteristic
386C2×C5C3×#45311yescharacteristic
387C2×C5C3×#45411yescharacteristic
388D5—82no—
389C23—102no—
390C23—202no—
391C23—202no—
392C23—201no—
393C23—201no—
394C23C3×D4×D511yescharacteristic
395Q8—402no—
396D4—102no—
397D4—102no—
398D4—201no—
399D4—201no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—101no—
406C2×C4—101no—
407C2×C4—102no—
408C2×C4—202no—
409C2×C4C2×C3×D2011yescharacteristic
410C2×C4C3×#70911yescharacteristic
411C2×C4C3×#70911yescharacteristic
412C2×C4C3×D4×D511yescharacteristic
413C2×C4C3×#71111yescharacteristic
414C2×C4C3×Q8×D511yescharacteristic
415C8—41no—
416C8—201no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—402no—
420C2×C3#6496211yescharacteristic
421C2×C3#6511111yescharacteristic
422C2×C3#6511611yescharacteristic
423C5C3×#202711yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—204no—
427C22—202no—
428C22—402no—
429C22—401no—
430C22—401no—
431C22C3×#402811yescharacteristic
432C22C3×#403111yescharacteristic
433C22C3×#404211yescharacteristic
434C4—42no—
435C4—41no—
436C4—41no—
437C4—202no—
438C4—201no—
439C4—201no—
440C4C3×#402111yescharacteristic
441C4C3×#403111yescharacteristic
442C4C3×#404211yescharacteristic
443C4C3×#404311yescharacteristic
444C3#1059955611yescharacteristic, direct product factor, Sylow
445C2—21no—
446C2—21no—
447C2—402no—
448C2C3×#6496211yescharacteristic
449C2C3×#6511111yescharacteristic
450C2C3×#6511611yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
hypercenterC3×#339D5
hypocenterC5C3×#2027
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
1. C3×#65853C2semidirect
5. C3×C5×#339C2semidirect
6. C3×#64774C2semidirect
7. C3×#64743C2semidirect
8. #10599556C3direct (N × H)
27. #65853C2×C3semidirect
31. C5×#339C2×C3semidirect
32. #64774C2×C3semidirect
33. #64743C2×C3semidirect
43. C2×C3×D20Q8semidirect
73. C3×#339D5semidirect
146. C2×D20C3×Q8semidirect
176. #339C3×D5semidirect
362. C3×C5#2027semidirect
423. C5C3×#2027semidirect
444. C3#10599556direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658532
C3×#654202
C3×#652902
C3×#652282
C3×C5×#3392
C3×#647742
C3×#647432
#105995563
C3×#20275