Finite Group Databasebeta

← C3×#10599487 #14300231

Subgroups — C3×#10599487 #14300231

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4047C211yesmaximal, characteristic
2C3×#65402C211yesmaximal, characteristic
3C2×C3×#3951C211yesmaximal, characteristic, complemented
4C3×#65391C211yesmaximal, characteristic, complemented
5C2×C3×#3937C211yesmaximal, characteristic
6C3×C5×#336C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599487C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4047—22no—
17C3×#4047—22no—
18C2×C3×#676—21no—
19C2×C3×C8×D5—21no—
20C3×#3953C411yescharacteristic, complemented
21C3×#3953C411yescharacteristic, complemented
22C3×#3951—22no—
23C3×#3948C411yescharacteristic, complemented
24C3×#3948C411yescharacteristic, complemented
25C3×#3946—21no—
26C3×#3946—21no—
27C3×#3937—22no—
28C3×#1866—51nomaximal, Hall
29C2×#4047C2×C311yescharacteristic
30#65402C2×C311yescharacteristic
31C2×#3951C2×C311yescharacteristic, complemented
32#65391C2×C311yescharacteristic, complemented
33C2×#3937C2×C311yescharacteristic
34C5×#336C2×C311yescharacteristic, complemented
35#64743C2×C311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C22⋊D5—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709D412yes—
42C3×#709Q812yes—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×Dic10C2×C411yescharacteristic
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8C2×C411yescharacteristic
51C2×C3×C5×C8C2×C411yescharacteristic
52C2×C3×C5×C8D411yescharacteristic
53C2×C3×C5×C8D411yescharacteristic
54C3×C42×C5—21no—
55C3×C42×C5—21no—
56C3×C22⋊Dic5—21no—
57C3×C4⋊Dic5C2×C411yescharacteristic
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×C4×Dic5—21no—
60C3×#681—21no—
61C3×#681—21no—
62C3×#681—21no—
63C3×#681D412yes—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C3×#676—24no—
67C3×C8×D5—24no—
68C2×C3×#131—51no—
69C2×C3×#108—51no—
70C3×#424—51no—
71C2×C3×#104—51no—
72C3×#416—51no—
73C3×#339—51no—
74C3×#336D511yescharacteristic, complemented
75C2×#709C22×C311yescharacteristic
76C22×C5×C8C22×C311yescharacteristic
77C22×C5×C8C22×C311yescharacteristic
78C2×C42×C5C22×C311yescharacteristic
79#4072C22×C311yescharacteristic
80C2×#681C22×C311yescharacteristic
81C2×#681C22×C311yescharacteristic
82#4047—22no—
83#4047—22no—
84C2×#676—21no—
85C2×C8×D5—21no—
86#3953C3×C411yescharacteristic, complemented
87#3953C3×C411yescharacteristic, complemented
88#3951—22no—
89#3948C3×C411yescharacteristic, complemented
90#3948C3×C411yescharacteristic, complemented
91#3946—21no—
92#3946—21no—
93#3937—22no—
94#1866—51noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C3×D5—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C3×C22⋊D5—22no—
107C3×C22⋊D5—22no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C3×D20—21no—
112C3×D20C4⋊C412yes—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×Dic10—21no—
116C3×Dic10C4⋊C412yes—
117C3×C5×C8—21no—
118C3×C5×C8—21no—
119C3×C5×C8—21no—
120C3×C5×C8—21no—
121C3×#168—22no—
122C3×#168—41no—
123C2×C3×#41—51no—
124C3×#131—102no—
125C3×#131—102no—
126C2×C3×M16—51no—
127C2×C3×M16—51no—
128C2×C3×M16—101no—
129C22×C3×C8—101no—
130C22×C3×C8C2×D511yescharacteristic
131C22×C3×C8C2×D511yescharacteristic
132C3×#117—51no—
133C2×C3×C42C2×D511yescharacteristic
134C3×#108—102no—
135C3×C4⋊C8—101no—
136C3×C4⋊C8—101no—
137C3×#104—102no—
138C3×#103—51no—
139C3×#103—51no—
140C3×#102—51no—
141C3×#102—51no—
142C22×C4×C5—21no—
143C22×C4×C5C23×C311yescharacteristic
144C2×C22⋊D5—21no—
145#709—21no—
146#709—21no—
147#709C3×D412yes—
148#709C3×Q812yes—
149C2×D20C2×C3×C411yescharacteristic
150C2×C4×D5—21no—
151C2×Dic10C2×C3×C411yescharacteristic
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C2×C5×C8—21no—
156C2×C5×C8C2×C3×C411yescharacteristic
157C2×C5×C8C2×C3×C411yescharacteristic
158C2×C5×C8C3×D411yescharacteristic
159C2×C5×C8C3×D411yescharacteristic
160C42×C5—21no—
161C42×C5—21no—
162C22⋊Dic5—21no—
163C4⋊Dic5C2×C3×C411yescharacteristic
164C4⋊Dic5C2×C3×C411yescharacteristic
165C4×Dic5—21no—
166#681—21no—
167#681—21no—
168#681—21no—
169#681C3×D412yes—
170C2×#168—21no—
171C2×#168—21no—
172#676—24no—
173C8×D5—24no—
174C2×#131—51no—
175C2×#108—51no—
176#424—51no—
177C2×#104—51no—
178#416—51no—
179#339—51no—
180#336C3×D511yescharacteristic, complemented
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—42no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×Dic5—22no—
195C3×Dic5—41no—
196C3×Dic5—41no—
197C3×#41—52no—
198C3×#41—52no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—21no—
205C22×C3×C4—101no—
206C22×C3×C4C22×D511yescharacteristic
207C3×M16—52no—
208C3×M16—104no—
209C3×M16—101no—
210C3×M16—101no—
211C3×M16—101no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—104no—
217C2×C3×C8—101no—
218C2×C3×C8—101no—
219C2×C3×C8C4×D511yescharacteristic
220C2×C3×C8C4×D511yescharacteristic
221C2×C3×C8D2011yescharacteristic
222C2×C3×C8D2011yescharacteristic
223C3×C4⋊C4—51no—
224C3×C4⋊C4—51no—
225C3×C22⋊C4—101no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—101no—
229C23×C5C3×#4111yescharacteristic
230C22×D5—21no—
231C2×C4×C5—22no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5C22×C3×C411yescharacteristic
235C2×C4×C5C2×C3×D411yescharacteristic
236C2×C4×C5C2×C3×D411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C2×C4×C5C2×C3×Q811yescharacteristic
239C2×C4×C5C3×#4111yescharacteristic
240C22⋊D5—22no—
241C22⋊D5—22no—
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—21no—
245D20—21no—
246D20C3×C4⋊C412yes—
247C4×D5—22no—
248C4×D5—22no—
249Dic10—21no—
250Dic10C3×C4⋊C412yes—
251C5×C8—21no—
252C5×C8—21no—
253C5×C8—21no—
254C5×C8—21no—
255#168—22no—
256#168—41no—
257C2×#41—51no—
258#131—102no—
259#131—102no—
260C2×M16—51no—
261C2×M16—51no—
262C2×M16—101no—
263C22×C8—101no—
264C22×C8C2×C3×D511yescharacteristic
265C22×C8C2×C3×D511yescharacteristic
266#117—51no—
267C2×C42C2×C3×D511yescharacteristic
268#108—102no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—102no—
272#103—51no—
273#103—51no—
274#102—51no—
275#102—51no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#44311yescharacteristic
280C2×C3×C5#44411yescharacteristic
281C3×D5—42no—
282C23×C3—101no—
283C23×C3#70911yescharacteristic
284C3×Q8—52no—
285C3×Q8—101no—
286C3×D4—52no—
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—101no—
290C2×C3×C4—22no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—101no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4Q8×D511yescharacteristic
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—21no—
307C3×C8—21no—
308C3×C8—102no—
309C3×C8—201no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5C3×C4×D411yescharacteristic
313C22×C5C3×C22⋊Q811yescharacteristic
314C22×C5C3×#12311yescharacteristic
315C2×D5—22no—
316C2×D5—41no—
317C2×D5—41no—
318C4×C5—42no—
319C4×C5C2×C3×C4⋊C411yescharacteristic
320C4×C5C3×C4×D411yescharacteristic
321C4×C5C3×#12011yescharacteristic
322C4×C5C3×C22⋊Q811yescharacteristic
323Dic5—22no—
324Dic5—41no—
325Dic5—41no—
326#41—52no—
327#41—52no—
328#41—101no—
329#41—101no—
330C2×Q8—51no—
331C2×D4—51no—
332C2×D4—101no—
333C22×C4—21no—
334C22×C4—101no—
335C22×C4C22×C3×D511yescharacteristic
336M16—52no—
337M16—104no—
338M16—101no—
339M16—101no—
340M16—101no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—104no—
346C2×C8—101no—
347C2×C8—101no—
348C2×C8C3×C4×D511yescharacteristic
349C2×C8C3×C4×D511yescharacteristic
350C2×C8C3×D2011yescharacteristic
351C2×C8C3×D2011yescharacteristic
352C4⋊C4—51no—
353C4⋊C4—51no—
354C22⋊C4—101no—
355C42—21no—
356C42—21no—
357C42—101no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—102no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3C4×D2011yescharacteristic
365C22×C3#402911yescharacteristic
366C22×C3#404211yescharacteristic
367C3×C4—42no—
368C3×C4—102no—
369C3×C4—201no—
370C3×C4—201no—
371C3×C4#402711yescharacteristic
372C3×C4#402811yescharacteristic
373C3×C4D5×C4⋊C411yescharacteristic
374C3×C4#404311yescharacteristic
375C2×C5—21no—
376C2×C5—21no—
377C2×C5C3×#38511yescharacteristic
378C2×C5C3×#44311yescharacteristic
379C2×C5C3×#44411yescharacteristic
380D5—42no—
381C23—101no—
382C23C3×#70911yescharacteristic
383Q8—52no—
384Q8—101no—
385D4—52no—
386D4—102no—
387D4—102no—
388D4—101no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—101no—
393C2×C4—102no—
394C2×C4—102no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4C2×C3×C4×D511yescharacteristic
398C2×C4C2×C3×D2011yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C2×C4C3×D4×D511yescharacteristic
401C2×C4C3×#71111yescharacteristic
402C2×C4C3×Q8×D511yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8—21no—
407C8—102no—
408C8—201no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—202no—
412C2×C3#6495711yescharacteristic
413C2×C3#6498911yescharacteristic
414C2×C3#6500611yescharacteristic
415C5C3×#186611yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—102no—
419C22—201no—
420C22—201no—
421C22C3×C4×D2011yescharacteristic
422C22C3×#402911yescharacteristic
423C22C3×#404211yescharacteristic
424C4—42no—
425C4—102no—
426C4—201no—
427C4—201no—
428C4C3×#402711yescharacteristic
429C4C3×#402811yescharacteristic
430C4C3×D5×C4⋊C411yescharacteristic
431C4C3×#404311yescharacteristic
432C3#1059948711yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—202no—
436C2C3×#6495711yescharacteristic
437C2C3×#6498911yescharacteristic
438C2C3×#6500611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#336C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#336D5
hypocenterC5C3×#1866
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C8 ◁ C3×#336

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3951C2semidirect
4. C3×#65391C2semidirect
6. C3×C5×#336C2semidirect
7. C3×#64743C2semidirect
8. #10599487C3direct (N × H)
20. C3×#3953C4semidirect
21. C3×#3953C4semidirect
23. C3×#3948C4semidirect
24. C3×#3948C4semidirect
31. C2×#3951C2×C3semidirect
32. #65391C2×C3semidirect
34. C5×#336C2×C3semidirect
35. #64743C2×C3semidirect
74. C3×#336D5semidirect
86. #3953C3×C4semidirect
87. #3953C3×C4semidirect
89. #3948C3×C4semidirect
90. #3948C3×C4semidirect
180. #336C3×D5semidirect
358. C3×C5#1866semidirect
415. C5C3×#1866semidirect
432. C3#10599487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40472
C3×#654022
C2×C3×#39512
C3×#653912
C2×C3×#39372
C3×C5×#3362
C3×#647432
#105994873
C3×#18665