Finite Group Databasebeta

← C3×#10601765 #14287958

Subgroups — C3×#10601765 #14287958

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65939C211yesmaximal, characteristic
2C3×C5×#448C211yesmaximal, characteristic, complemented
3C3×#65520C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic, complemented
7C3×#64688C211yesmaximal, characteristic, complemented
8#10601765C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic, complemented
10C2×C3×D4×D5—21no—
11C2×C3×C5×SD16—21no—
12C3×C5×#121C2211yescharacteristic
13C2×C3×#688—21no—
14C3×#4085—21no—
15C3×#4083—21no—
16C3×#4076C2211yescharacteristic
17C2×C3×#685—21no—
18C2×C3×#685C2211yescharacteristic
19C3×#4040—21no—
20C3×#4029—21no—
21C3×#4028—21no—
22C3×C5×#103—21no—
23C3×C5×C22⋊C8C2211yescharacteristic, complemented
24C3×#3967—21no—
25C3×#3963—21no—
26C3×#3963C2211yescharacteristic, complemented
27C3×C22⋊#168C2211yescharacteristic, complemented
28C3×#1601—51nomaximal, Hall
29#65939C2×C311yescharacteristic
30C5×#448C2×C311yescharacteristic, complemented
31#65520C2×C311yescharacteristic, complemented
32#65516C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic, complemented
35#64688C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C23×C3×D5D411yescharacteristic
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—42no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C22⋊D5—21no—
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—21no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5D411yescharacteristic
50C3×D4×D5—42no—
51C3×D4×D5—42no—
52C2×C3×D20—21no—
53C2×C3×D20D411yescharacteristic
54C2×C3×C4×D5—21no—
55C3×C5×SD16—42no—
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4D411yescharacteristic
58C3×C5×C22⋊C4—21no—
59C3×C22⋊Dic5—21no—
60C3×#688—42no—
61C3×#685—21no—
62C3×#685—21no—
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—42no—
66C3×C4⋊Dic5D411yescharacteristic
67C3×#683—21no—
68C2×C3×#168—21no—
69C3×#534—51no—
70C3×#448—51no—
71C3×#448D511yescharacteristic, complemented
72C3×#393—51no—
73C3×#327—51no—
74C3×#327—51no—
75C3×#323—51no—
76C22×C5×Q8C22×C311yescharacteristic, complemented
77C2×D4×D5—21no—
78C2×C5×SD16—21no—
79C5×#121C22×C311yescharacteristic
80C2×#688—21no—
81#4085—21no—
82#4083—21no—
83#4076C22×C311yescharacteristic
84C2×#685—21no—
85C2×#685C22×C311yescharacteristic
86#4040—21no—
87#4029—21no—
88#4028—21no—
89C5×#103—21no—
90C5×C22⋊C8C22×C311yescharacteristic, complemented
91#3967—21no—
92#3963—21no—
93#3963C22×C311yescharacteristic, complemented
94C22⋊#168C22×C311yescharacteristic, complemented
95#1601—51noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—42no—
102C22×C3×D5—41no—
103C22×C3×D5—41no—
104C22×C3×D5—81no—
105C22×C3×D5—81no—
106C22×C3×D5SD1612yescomplemented
107C3×C5×Q8—22no—
108C3×C5×Q8—22no—
109C3×C5×Q8—41no—
110C3×C5×Q8—41no—
111C3×C5×D4—41no—
112C3×C5×D4—41no—
113C3×C5×D4—41no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C3×C22⋊D5—42no—
122C3×C22⋊D5—41no—
123C3×C22⋊D5—41no—
124C3×C22⋊D5—81no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5—41no—
131C3×D20—41no—
132C3×D20—42no—
133C3×C4×D5—42no—
134C3×C5×C8—41no—
135C3×#168—41no—
136C22×C3×Q8C2×D511yescharacteristic, complemented
137C22×C3×D4—101no—
138C2×C3×SD16—21no—
139C2×C3×SD16—101no—
140C3×#123—101no—
141C3×#123—101no—
142C3×#121—51no—
143C3×#121—101no—
144C3×#121C2×D511yescharacteristic
145C3×#120—101no—
146C3×#120—101no—
147C2×C3×C22⋊C4—51no—
148C2×C3×C22⋊C4—101no—
149C3×#103—21no—
150C3×#103—101no—
151C3×C22⋊C8—51no—
152C3×C22⋊C8C2×D511yescharacteristic, complemented
153C3×#95—51no—
154C3×#95—101no—
155C23×D5—21no—
156C23×D5C3×D411yescharacteristic
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—42no—
160C2×C5×D4—21no—
161C2×C5×D4C3×D411yescharacteristic
162C22×C4×C5—21no—
163C22×C4×C5C23×C311yescharacteristic
164C2×C22⋊D5—21no—
165C2×C22⋊D5—21no—
166C2×C22⋊D5—21no—
167C22×Dic5—21no—
168C22×Dic5C3×D411yescharacteristic
169D4×D5—42no—
170D4×D5—42no—
171C2×D20—21no—
172C2×D20C3×D411yescharacteristic
173C2×C4×D5—21no—
174C5×SD16—42no—
175C2×C5×C8—21no—
176C5×C4⋊C4C3×D411yescharacteristic
177C5×C22⋊C4—21no—
178C22⋊Dic5—21no—
179#688—42no—
180#685—21no—
181#685—21no—
182#685—21no—
183#685—21no—
184#685—42no—
185C4⋊Dic5C3×D411yescharacteristic
186#683—21no—
187C2×#168—21no—
188#534—51no—
189#448—51no—
190#448C3×D511yescharacteristic, complemented
191#393—51no—
192#327—51no—
193#327—51no—
194#323—51no—
195C22×C3×C5—21no—
196C22×C3×C5—21no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5#12011yescharacteristic
201C22×C3×C5C2×SD1611yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C2×C3×D5—22no—
204C2×C3×D5—41no—
205C2×C3×D5—41no—
206C2×C3×D5—42no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C2×C3×D5—81no—
211C2×C3×D5—84no—
212C3×C4×C5—21no—
213C3×C4×C5—21no—
214C3×C4×C5—41no—
215C3×C4×C5—42no—
216C3×Dic5—41no—
217C3×Dic5—41no—
218C3×Dic5—81no—
219C24×C3—51no—
220C24×C3—101no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—42no—
224C2×C3×D4—21no—
225C2×C3×D4—51no—
226C2×C3×D4—101no—
227C2×C3×D4—101no—
228C2×C3×D4—101no—
229C2×C3×D4—101no—
230C2×C3×D4—202no—
231C2×C3×D4—202no—
232C2×C3×D4C22⋊D511yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—51no—
235C22×C3×C4—101no—
236C22×C3×C4—101no—
237C22×C3×C4C22×D511yescharacteristic
238C3×SD16—42no—
239C3×SD16—202no—
240C2×C3×C8—21no—
241C2×C3×C8—101no—
242C3×C4⋊C4—51no—
243C3×C4⋊C4—101no—
244C3×C4⋊C4C22⋊D511yescharacteristic
245C3×C22⋊C4—21no—
246C3×C22⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250C3×C22⋊C4—101no—
251C3×C22⋊C4—202no—
252C23×C5—21no—
253C23×C5C2×C3×D411yescharacteristic
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—42no—
258C22×D5—41no—
259C22×D5—41no—
260C22×D5—81no—
261C22×D5—81no—
262C22×D5C3×SD1612yescomplemented
263C5×Q8—22no—
264C5×Q8—22no—
265C5×Q8—41no—
266C5×Q8—41no—
267C5×D4—41no—
268C5×D4—41no—
269C5×D4—41no—
270C2×C4×C5—22no—
271C2×C4×C5—21no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5C2×C3×D411yescharacteristic
276C2×C4×C5C2×C3×D411yescharacteristic
277C22⋊D5—42no—
278C22⋊D5—41no—
279C22⋊D5—41no—
280C22⋊D5—81no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287D20—41no—
288D20—42no—
289C4×D5—42no—
290C5×C8—41no—
291#168—41no—
292C22×Q8C2×C3×D511yescharacteristic, complemented
293C22×D4—101no—
294C2×SD16—21no—
295C2×SD16—101no—
296#123—101no—
297#123—101no—
298#121—51no—
299#121—101no—
300#121C2×C3×D511yescharacteristic
301#120—101no—
302#120—101no—
303C2×C22⋊C4—51no—
304C2×C22⋊C4—101no—
305#103—21no—
306#103—101no—
307C22⋊C8—51no—
308C22⋊C8C2×C3×D511yescharacteristic, complemented
309#95—51no—
310#95—101no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—81no—
314C2×C3×C5#45011yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5B(4,𝔽2)11yescharacteristic
317C3×D5—42no—
318C3×D5—81no—
319C23×C3—21no—
320C23×C3—52no—
321C23×C3—101no—
322C23×C3—101no—
323C23×C3—101no—
324C23×C3—201no—
325C23×C3—201no—
326C23×C3—202no—
327C23×C3—401no—
328C23×C3—401no—
329C23×C3D4×D511yescharacteristic
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×D4—41no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—201no—
338C3×D4—202no—
339C3×D4—202no—
340C3×D4—201no—
341C3×D4—201no—
342C3×D4—401no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—202no—
351C2×C3×C4—201no—
352C2×C3×C4—201no—
353C2×C3×C4—201no—
354C2×C3×C4—201no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4C2×C22⋊D511yescharacteristic
357C3×C8—41no—
358C3×C8—201no—
359C22×C5—21no—
360C22×C5—21no—
361C22×C5—41no—
362C22×C5—41no—
363C22×C5—41no—
364C22×C5C3×#12011yescharacteristic
365C22×C5C2×C3×SD1611yescharacteristic
366C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
367C2×D5—22no—
368C2×D5—41no—
369C2×D5—41no—
370C2×D5—42no—
371C2×D5—41no—
372C2×D5—41no—
373C2×D5—41no—
374C2×D5—81no—
375C2×D5—84no—
376C4×C5—21no—
377C4×C5—21no—
378C4×C5—41no—
379C4×C5—42no—
380Dic5—41no—
381Dic5—41no—
382Dic5—81no—
383C24—51no—
384C24—101no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×D4—21no—
389C2×D4—51no—
390C2×D4—101no—
391C2×D4—101no—
392C2×D4—101no—
393C2×D4—101no—
394C2×D4—202no—
395C2×D4—202no—
396C2×D4C3×C22⋊D511yescharacteristic
397C22×C4—21no—
398C22×C4—51no—
399C22×C4—101no—
400C22×C4—101no—
401C22×C4C22×C3×D511yescharacteristic
402SD16—42no—
403SD16—202no—
404C2×C8—21no—
405C2×C8—101no—
406C4⋊C4—51no—
407C4⋊C4—101no—
408C4⋊C4C3×C22⋊D511yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—101no—
411C22⋊C4—101no—
412C22⋊C4—101no—
413C22⋊C4—101no—
414C22⋊C4—101no—
415C22⋊C4—202no—
416C3×C5#160111yescharacteristic, complemented, Hall
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—102no—
423C22×C3—202no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3—201no—
429C22×C3—401no—
430C22×C3—404no—
431C22×C3D5×SD1611yescharacteristic
432C22×C3#406011yescharacteristic
433C22×C3#408311yescharacteristic
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—42no—
437C3×C4—41no—
438C3×C4—201no—
439C3×C4—201no—
440C3×C4—401no—
441C2×C5—21no—
442C2×C5—21no—
443C2×C5—81no—
444C2×C5C3×#45011yescharacteristic
445C2×C5C3×#45511yescharacteristic
446C2×C5C3×B(4,𝔽2)11yescharacteristic
447D5—42no—
448D5—81no—
449C23—21no—
450C23—52no—
451C23—101no—
452C23—101no—
453C23—101no—
454C23—201no—
455C23—201no—
456C23—202no—
457C23—401no—
458C23—401no—
459C23C3×D4×D511yescharacteristic
460Q8—22no—
461Q8—22no—
462Q8—41no—
463Q8—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—201no—
468D4—202no—
469D4—202no—
470D4—201no—
471D4—201no—
472D4—401no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—101no—
479C2×C4—101no—
480C2×C4—202no—
481C2×C4—201no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—201no—
485C2×C4C3×D4×D511yescharacteristic
486C2×C4C2×C3×C22⋊D511yescharacteristic
487C8—41no—
488C8—201no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—81no—
492C2×C3—202no—
493C2×C3—401no—
494C2×C3#6532111yescharacteristic
495C2×C3#6545811yescharacteristic
496C2×C3#6549111yescharacteristic
497C5C3×#160111yescharacteristic, complemented, Sylow
498C22—21no—
499C22—21no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—102no—
504C22—202no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22—201no—
509C22—201no—
510C22—401no—
511C22—404no—
512C22C3×D5×SD1611yescharacteristic
513C22C3×#406011yescharacteristic
514C22C3×#408311yescharacteristic
515C4—21no—
516C4—21no—
517C4—42no—
518C4—41no—
519C4—201no—
520C4—201no—
521C4—401no—
522C3#1060176511yescharacteristic, direct product factor, Sylow
523C2—21no—
524C2—21no—
525C2—81no—
526C2—202no—
527C2—401no—
528C2C3×#6532111yescharacteristic
529C2C3×#6545811yescharacteristic
530C2C3×#6549111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#448C2
socleC22×C3×C5#120
prime radicalC3×#65939C2
hypercenterC3×#448D5
hypocenterC5C3×#1601
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
2. C3×C5×#448C2semidirect
3. C3×#65520C2semidirect
4. C3×#65516C2semidirect
5. C3×#64757C2semidirect
6. C3×#64690C2semidirect
7. C3×#64688C2semidirect
8. #10601765C3direct (N × H)
9. C22×C3×C5×Q8C22semidirect
23. C3×C5×C22⋊C8C22semidirect
26. C3×#3963C22semidirect
27. C3×C22⋊#168C22semidirect
30. C5×#448C2×C3semidirect
31. #65520C2×C3semidirect
32. #65516C2×C3semidirect
33. #64757C2×C3semidirect
34. #64690C2×C3semidirect
35. #64688C2×C3semidirect
71. C3×#448D5semidirect
76. C22×C5×Q8C22×C3semidirect
90. C5×C22⋊C8C22×C3semidirect
93. #3963C22×C3semidirect
94. C22⋊#168C22×C3semidirect
106. C22×C3×D5SD16semidirect
136. C22×C3×Q8C2×D5semidirect
152. C3×C22⋊C8C2×D5semidirect
190. #448C3×D5semidirect
262. C22×D5C3×SD16semidirect
292. C22×Q8C2×C3×D5semidirect
308. C22⋊C8C2×C3×D5semidirect
416. C3×C5#1601semidirect
497. C5C3×#1601semidirect
522. C3#10601765direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659392
C3×C5×#4482
C3×#655202
C3×#655162
C3×#647572
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