Finite Group Databasebeta

← C3×#65954 #11755631

Subgroups — C3×#65954 #11755631

Order 960.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#121C211yesmaximal, characteristic, complemented
2C3×#4086C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4C3×#4085C211yesmaximal, characteristic, complemented
5C3×#4084C211yesmaximal, characteristic, complemented
6C3×#4083C211yesmaximal, characteristic, complemented
7C3×#4083C211yesmaximal, characteristic, complemented
8C3×#4076C211yesmaximal, characteristic, complemented
9C3×#4075C211yesmaximal, characteristic, complemented
10C3×#4044C211yesmaximal, characteristic, complemented
11C3×#4040C211yesmaximal, characteristic, complemented
12C3×#4032C211yesmaximal, characteristic, complemented
13C3×#4030C211yesmaximal, characteristic, complemented
14C3×#4028C211yesmaximal, characteristic, complemented
15C3×#4025C211yesmaximal, characteristic, complemented
16#65954C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×D5C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C2×C3×C5×D4C2211yescharacteristic, complemented
21C22×C3×C4×C5C2211yescharacteristic, complemented
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×C22⋊D5C2211yescharacteristic
26C2×C3×C22⋊D5C2211yescharacteristic
27C2×C3×C22⋊D5C2211yescharacteristic, complemented
28C2×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×Dic5C2211yescharacteristic, complemented
30C2×C3×D20C2211yescharacteristic
31C2×C3×D20C2211yescharacteristic
32C2×C3×C4×D5C2211yescharacteristic, complemented
33C3×C5×C4⋊C4C2211yescharacteristic, complemented
34C3×C5×C22⋊C4C2211yescharacteristic
35C3×C5×C22⋊C4C2211yescharacteristic, complemented
36C3×C22⋊Dic5C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38C3×C22⋊Dic5C2211yescharacteristic, complemented
39C3×#685C2211yescharacteristic
40C3×#685C2211yescharacteristic
41C3×#685C2211yescharacteristic
42C3×#685C2211yescharacteristic
43C3×#685C2211yescharacteristic
44C3×#685C2211yescharacteristic
45C3×#685C2211yescharacteristic, complemented
46C3×C4⋊Dic5C2211yescharacteristic, complemented
47C3×C4⋊Dic5C2211yescharacteristic, complemented
48C3×#683C2211yescharacteristic, complemented
49C3×#683C2211yescharacteristic, complemented
50C3×#683C2211yescharacteristic, complemented
51C3×C4×Dic5C2211yescharacteristic, complemented
52C3×#560—51nomaximal, Hall
53C5×#121C2×C311yescharacteristic, complemented
54#4086C2×C311yescharacteristic, complemented
55#4085C2×C311yescharacteristic, complemented
56#4085C2×C311yescharacteristic, complemented
57#4084C2×C311yescharacteristic, complemented
58#4083C2×C311yescharacteristic, complemented
59#4083C2×C311yescharacteristic, complemented
60#4076C2×C311yescharacteristic, complemented
61#4075C2×C311yescharacteristic, complemented
62#4044C2×C311yescharacteristic, complemented
63#4040C2×C311yescharacteristic, complemented
64#4032C2×C311yescharacteristic, complemented
65#4030C2×C311yescharacteristic, complemented
66#4028C2×C311yescharacteristic, complemented
67#4025C2×C311yescharacteristic, complemented
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C23×C3×C5C2311yescharacteristic
71C22×C3×D5—41no—
72C22×C3×D5—41no—
73C22×C3×D5—41no—
74C22×C3×D5C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
76C22×C3×D5C2311yescharacteristic
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2311yescharacteristic
82C2×C3×C4×C5C2311yescharacteristic
83C2×C3×C4×C5C2311yescharacteristic
84C2×C3×C4×C5C2311yescharacteristic
85C3×C22⋊D5—41no—
86C3×C22⋊D5—41no—
87C3×C22⋊D5—41no—
88C3×C22⋊D5—41no—
89C3×C22⋊D5—41no—
90C3×C22⋊D5—41no—
91C3×C22⋊D5—41no—
92C2×C3×Dic5—41no—
93C2×C3×Dic5C2311yescharacteristic
94C2×C3×Dic5C2311yescharacteristic
95C2×C3×Dic5C2311yescharacteristic
96C2×C3×Dic5C2311yescharacteristic
97C2×C3×Dic5C2311yescharacteristic
98C3×D20—41no—
99C3×D20—41no—
100C3×C4×D5—41no—
101C3×#127—51no—
102C3×#126—51no—
103C3×#126—51no—
104C3×#123—51no—
105C3×#123—51no—
106C3×#123—51no—
107C3×#121—51no—
108C3×#121—51no—
109C3×#121—51no—
110C3×#121—51no—
111C3×#121—51no—
112C3×#121D511yescharacteristic, complemented
113C3×#120—51no—
114C3×#120—51no—
115C3×#120—51no—
116C23×D5C22×C311yescharacteristic
117C2×C5×D4C22×C311yescharacteristic
118C2×C5×D4C22×C311yescharacteristic
119C2×C5×D4C22×C311yescharacteristic, complemented
120C22×C4×C5C22×C311yescharacteristic, complemented
121C2×C22⋊D5C22×C311yescharacteristic
122C2×C22⋊D5C22×C311yescharacteristic
123C2×C22⋊D5C22×C311yescharacteristic
124C2×C22⋊D5C22×C311yescharacteristic
125C2×C22⋊D5C22×C311yescharacteristic
126C2×C22⋊D5C22×C311yescharacteristic, complemented
127C2×C22⋊D5C22×C311yescharacteristic, complemented
128C22×Dic5C22×C311yescharacteristic, complemented
129C2×D20C22×C311yescharacteristic
130C2×D20C22×C311yescharacteristic
131C2×C4×D5C22×C311yescharacteristic, complemented
132C5×C4⋊C4C22×C311yescharacteristic, complemented
133C5×C22⋊C4C22×C311yescharacteristic
134C5×C22⋊C4C22×C311yescharacteristic, complemented
135C22⋊Dic5C22×C311yescharacteristic
136C22⋊Dic5C22×C311yescharacteristic
137C22⋊Dic5C22×C311yescharacteristic, complemented
138#685C22×C311yescharacteristic
139#685C22×C311yescharacteristic
140#685C22×C311yescharacteristic
141#685C22×C311yescharacteristic
142#685C22×C311yescharacteristic
143#685C22×C311yescharacteristic
144#685C22×C311yescharacteristic, complemented
145C4⋊Dic5C22×C311yescharacteristic, complemented
146C4⋊Dic5C22×C311yescharacteristic, complemented
147#683C22×C311yescharacteristic, complemented
148#683C22×C311yescharacteristic, complemented
149#683C22×C311yescharacteristic, complemented
150C4×Dic5C22×C311yescharacteristic, complemented
151#560—51noSylow
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5C2411yescharacteristic
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—44no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×Dic5—21no—
177C3×Dic5—21no—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C24×C3—51no—
182C2×C3×D4—51no—
183C2×C3×D4—51no—
184C2×C3×D4—51no—
185C2×C3×D4—51no—
186C2×C3×D4—51no—
187C2×C3×D4—51no—
188C2×C3×D4—51no—
189C2×C3×D4—51no—
190C2×C3×D4—51no—
191C2×C3×D4C2×D511yescharacteristic
192C2×C3×D4C2×D511yescharacteristic
193C2×C3×D4C2×D511yescharacteristic, complemented
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4C2×D511yescharacteristic, complemented
197C3×C4⋊C4—51no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—51no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4C2×D511yescharacteristic, complemented
203C3×C22⋊C4—51no—
204C3×C22⋊C4—51no—
205C3×C22⋊C4—51no—
206C3×C22⋊C4—51no—
207C3×C22⋊C4—51no—
208C3×C22⋊C4—51no—
209C3×C22⋊C4—51no—
210C3×C22⋊C4—51no—
211C3×C22⋊C4—51no—
212C3×C22⋊C4—51no—
213C3×C22⋊C4C2×D511yescharacteristic
214C3×C22⋊C4C2×D511yescharacteristic, complemented
215C3×C42—51no—
216C23×C5C23×C311yescharacteristic
217C23×C5C23×C311yescharacteristic
218C23×C5C23×C311yescharacteristic
219C22×D5—41no—
220C22×D5—41no—
221C22×D5—41no—
222C22×D5C23×C311yescharacteristic
223C22×D5C23×C311yescharacteristic
224C22×D5C23×C311yescharacteristic
225C5×D4—41no—
226C5×D4—41no—
227C5×D4—41no—
228C2×C4×C5—41no—
229C2×C4×C5C23×C311yescharacteristic
230C2×C4×C5C23×C311yescharacteristic
231C2×C4×C5C23×C311yescharacteristic
232C2×C4×C5C23×C311yescharacteristic
233C22⋊D5—41no—
234C22⋊D5—41no—
235C22⋊D5—41no—
236C22⋊D5—41no—
237C22⋊D5—41no—
238C22⋊D5—41no—
239C22⋊D5—41no—
240C2×Dic5—41no—
241C2×Dic5C23×C311yescharacteristic
242C2×Dic5C23×C311yescharacteristic
243C2×Dic5C23×C311yescharacteristic
244C2×Dic5C23×C311yescharacteristic
245C2×Dic5C23×C311yescharacteristic
246D20—41no—
247D20—41no—
248C4×D5—41no—
249#127—51no—
250#126—51no—
251#126—51no—
252#123—51no—
253#123—51no—
254#123—51no—
255#121—51no—
256#121—51no—
257#121—51no—
258#121—51no—
259#121—51no—
260#121C3×D511yescharacteristic, complemented
261#120—51no—
262#120—51no—
263#120—51no—
264C2×C3×C5—41no—
265C2×C3×C5—41no—
266C2×C3×C5—41no—
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268C2×C3×C5H(5,𝔽2)11yescharacteristic
269C2×C3×C5H(5,𝔽2)11yescharacteristic
270C3×D5—41no—
271C3×D5—41no—
272C3×D5—41no—
273C23×C3—51no—
274C23×C3—51no—
275C23×C3—51no—
276C23×C3—201no—
277C23×C3—201no—
278C23×C3—201no—
279C23×C3C22×D511yescharacteristic
280C23×C3C22×D511yescharacteristic
281C23×C3C22×D511yescharacteristic
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—41no—
285C3×D4—201no—
286C3×D4—201no—
287C3×D4—201no—
288C3×D4—201no—
289C3×D4—201no—
290C3×D4—201no—
291C3×D4—201no—
292C3×D4—201no—
293C3×D4—201no—
294C2×C3×C4—41no—
295C2×C3×C4—51no—
296C2×C3×C4—51no—
297C2×C3×C4—51no—
298C2×C3×C4—51no—
299C2×C3×C4—51no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4C22×D511yescharacteristic
303C2×C3×C4C22×D511yescharacteristic
304C2×C3×C4C22×D511yescharacteristic
305C2×C3×C4C22×D511yescharacteristic
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5C24×C311yescharacteristic
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—21no—
324C2×D5—21no—
325C2×D5—44no—
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—21no—
330Dic5—21no—
331Dic5—21no—
332Dic5—21no—
333Dic5—21no—
334Dic5—21no—
335C24—51no—
336C2×D4—51no—
337C2×D4—51no—
338C2×D4—51no—
339C2×D4—51no—
340C2×D4—51no—
341C2×D4—51no—
342C2×D4—51no—
343C2×D4—51no—
344C2×D4—51no—
345C2×D4C2×C3×D511yescharacteristic
346C2×D4C2×C3×D511yescharacteristic
347C2×D4C2×C3×D511yescharacteristic, complemented
348C22×C4—51no—
349C22×C4—51no—
350C22×C4C2×C3×D511yescharacteristic, complemented
351C4⋊C4—51no—
352C4⋊C4—51no—
353C4⋊C4—51no—
354C4⋊C4—51no—
355C4⋊C4—51no—
356C4⋊C4C2×C3×D511yescharacteristic, complemented
357C22⋊C4—51no—
358C22⋊C4—51no—
359C22⋊C4—51no—
360C22⋊C4—51no—
361C22⋊C4—51no—
362C22⋊C4—51no—
363C22⋊C4—51no—
364C22⋊C4—51no—
365C22⋊C4—51no—
366C22⋊C4—51no—
367C22⋊C4C2×C3×D511yescharacteristic
368C22⋊C4C2×C3×D511yescharacteristic, complemented
369C42—51no—
370C3×C5#56011yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—101no—
381C22×C3—101no—
382C22×C3—101no—
383C22×C3—101no—
384C22×C3—101no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3—101no—
388C22×C3—101no—
389C22×C3—204no—
390C22×C3C23×D511yescharacteristic
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—101no—
396C3×C4—101no—
397C3×C4—101no—
398C3×C4—101no—
399C3×C4—101no—
400C2×C5—41no—
401C2×C5—41no—
402C2×C5—41no—
403C2×C5C3×H(5,𝔽2)11yescharacteristic
404C2×C5C3×H(5,𝔽2)11yescharacteristic
405C2×C5C3×H(5,𝔽2)11yescharacteristic
406D5—41no—
407D5—41no—
408D5—41no—
409C23—51no—
410C23—51no—
411C23—51no—
412C23—201no—
413C23—201no—
414C23—201no—
415C23C22×C3×D511yescharacteristic
416C23C22×C3×D511yescharacteristic
417C23C22×C3×D511yescharacteristic
418D4—41no—
419D4—41no—
420D4—41no—
421D4—201no—
422D4—201no—
423D4—201no—
424D4—201no—
425D4—201no—
426D4—201no—
427D4—201no—
428D4—201no—
429D4—201no—
430C2×C4—41no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4C22×C3×D511yescharacteristic
439C2×C4C22×C3×D511yescharacteristic
440C2×C4C22×C3×D511yescharacteristic
441C2×C4C22×C3×D511yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—201no—
446C2×C3—201no—
447C2×C3—201no—
448C2×C3#414411yescharacteristic
449C2×C3#414411yescharacteristic
450C2×C3#414911yescharacteristic
451C5C3×#56011yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—101no—
465C22—101no—
466C22—101no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—204no—
471C22C23×C3×D511yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—101no—
477C4—101no—
478C4—101no—
479C4—101no—
480C4—101no—
481C3#6595411yescharacteristic, direct product factor, Sylow
482C2—41no—
483C2—41no—
484C2—41no—
485C2—201no—
486C2—201no—
487C2—201no—
488C2C3×#414411yescharacteristic
489C2C3×#414411yescharacteristic
490C2C3×#414911yescharacteristic
subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#121C2
socleC22×C3×C5C24
hypercenterC3×#121D5
hypocenterC5C3×#560
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C3×C5×#121C2semidirect
2. C3×#4086C2semidirect
3. C3×#4085C2semidirect
4. C3×#4085C2semidirect
5. C3×#4084C2semidirect
6. C3×#4083C2semidirect
7. C3×#4083C2semidirect
8. C3×#4076C2semidirect
9. C3×#4075C2semidirect
10. C3×#4044C2semidirect
11. C3×#4040C2semidirect
12. C3×#4032C2semidirect
13. C3×#4030C2semidirect
14. C3×#4028C2semidirect
15. C3×#4025C2semidirect
16. #65954C3direct (N × H)
20. C2×C3×C5×D4C22semidirect
21. C22×C3×C4×C5C22semidirect
27. C2×C3×C22⋊D5C22semidirect
28. C2×C3×C22⋊D5C22semidirect
29. C22×C3×Dic5C22semidirect
32. C2×C3×C4×D5C22semidirect
33. C3×C5×C4⋊C4C22semidirect
35. C3×C5×C22⋊C4C22semidirect
38. C3×C22⋊Dic5C22semidirect
45. C3×#685C22semidirect
46. C3×C4⋊Dic5C22semidirect
47. C3×C4⋊Dic5C22semidirect
48. C3×#683C22semidirect
49. C3×#683C22semidirect
50. C3×#683C22semidirect
51. C3×C4×Dic5C22semidirect
53. C5×#121C2×C3semidirect
54. #4086C2×C3semidirect
55. #4085C2×C3semidirect
56. #4085C2×C3semidirect
57. #4084C2×C3semidirect
58. #4083C2×C3semidirect
59. #4083C2×C3semidirect
60. #4076C2×C3semidirect
61. #4075C2×C3semidirect
62. #4044C2×C3semidirect
63. #4040C2×C3semidirect
64. #4032C2×C3semidirect
65. #4030C2×C3semidirect
66. #4028C2×C3semidirect
67. #4025C2×C3semidirect
112. C3×#121D5semidirect
119. C2×C5×D4C22×C3semidirect
120. C22×C4×C5C22×C3semidirect
126. C2×C22⋊D5C22×C3semidirect
127. C2×C22⋊D5C22×C3semidirect
128. C22×Dic5C22×C3semidirect
131. C2×C4×D5C22×C3semidirect
132. C5×C4⋊C4C22×C3semidirect
134. C5×C22⋊C4C22×C3semidirect
137. C22⋊Dic5C22×C3semidirect
144. #685C22×C3semidirect
145. C4⋊Dic5C22×C3semidirect
146. C4⋊Dic5C22×C3semidirect
147. #683C22×C3semidirect
148. #683C22×C3semidirect
149. #683C22×C3semidirect
150. C4×Dic5C22×C3semidirect
193. C2×C3×D4C2×D5semidirect
196. C22×C3×C4C2×D5semidirect
202. C3×C4⋊C4C2×D5semidirect
214. C3×C22⋊C4C2×D5semidirect
260. #121C3×D5semidirect
347. C2×D4C2×C3×D5semidirect
350. C22×C4C2×C3×D5semidirect
356. C4⋊C4C2×C3×D5semidirect
368. C22⋊C4C2×C3×D5semidirect
370. C3×C5#560semidirect
451. C5C3×#560semidirect
481. C3#65954direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#1212
C3×#40862
C3×#40852
C3×#40842
C3×#40832
C3×#40762
C3×#40752
C3×#40442
C3×#40402
C3×#40322
C3×#40302
C3×#40282
C3×#40252
#659543
C3×#5605