Finite Group Databasebeta

← C3×#10613186 #14435428

Subgroups — C3×#10613186 #14435428

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65958C211yesmaximal, characteristic
2C2×C3×#4033C211yesmaximal, characteristic, complemented
3C3×C5×#484C211yesmaximal, characteristic, complemented
4C3×#65339C211yesmaximal, characteristic, complemented
5C3×#65257C211yesmaximal, characteristic
6C3×#65178C212yesmaximal, complemented
7C3×#65166C212yesmaximal, complemented
8C3×#65087C212yesmaximal, complemented
9C3×#65078C212yesmaximal, complemented
10C3×#65027C211yesmaximal, characteristic
11C3×#65008C211yesmaximal, characteristic, complemented
12#10613186C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×Dic10C2211yescharacteristic
14C3×C5×C22⋊Q8C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C3×#4093C2211yescharacteristic
17C3×Q8×Dic5C2211yescharacteristic
18C2×C3×#689C2212yes—
19C3×#4076C2211yescharacteristic
20C2×C3×#683—21no—
21C2×C3×C4×Dic5—21no—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×#677C2212yes—
24C3×#4044—21no—
25C3×#4039C2211yescharacteristic
26C3×#4038—21no—
27C3×#4036C2211yescharacteristic
28C3×#4033—21no—
29C3×#4033—21no—
30C3×#4033C2212yes—
31C3×#4033C2212yes—
32C3×#4032—21no—
33C3×#4027—21no—
34C3×C5×#107C2212yes—
35C3×C5×#103C2212yes—
36C3×C5×C22⋊C8C2211yescharacteristic
37C3×C22⋊#168C2211yescharacteristic
38C3×#3948C2212yes—
39C3×#3947C2212yes—
40C3×#3946C2212yes—
41C3×#3942C2212yes—
42C3×#3941C2212yes—
43C3×#3940C2212yes—
44C3×#3117—51nomaximal, Hall
45#65958C2×C311yescharacteristic
46C2×#4033C2×C311yescharacteristic, complemented
47C5×#484C2×C311yescharacteristic, complemented
48#65339C2×C311yescharacteristic, complemented
49#65257C2×C311yescharacteristic
50#65178C2×C312yescomplemented
51#65166C2×C312yescomplemented
52#65087C2×C312yescomplemented
53#65078C2×C312yescomplemented
54#65027C2×C311yescharacteristic
55#65008C2×C311yescharacteristic, complemented
56C2×C3×C5×Q8C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×C3×C22⋊D5—21no—
60C22×C3×Dic5—21no—
61C22×C3×Dic5D411yescharacteristic
62C22×C3×Dic5D411yescharacteristic
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10C2312yes—
68C2×C3×C5×C8C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×#689—24no—
75C3×#685—21no—
76C3×#685—21no—
77C3×#685—21no—
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—21no—
83C3×#683—22no—
84C3×#683—22no—
85C3×C4×Dic5—21no—
86C3×C4×Dic5—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5C2311yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92C2×C3×#168C2312yes—
93C3×#677—24no—
94C3×#529—51no—
95C2×C3×C4×Q8—51no—
96C3×#484D511yescharacteristic, complemented
97C3×#481—51no—
98C3×#479—52no—
99C3×#464—52no—
100C3×#451—51no—
101C3×#448—51no—
102C3×#441—52no—
103C3×#440—52no—
104C3×#432—51no—
105C22×Dic10C22×C311yescharacteristic
106C5×C22⋊Q8C22×C311yescharacteristic
107C2×C5×C4⋊C4C22×C311yescharacteristic
108#4093C22×C311yescharacteristic
109Q8×Dic5C22×C311yescharacteristic
110C2×#689C22×C312yes—
111#4076C22×C311yescharacteristic
112C2×#683—21no—
113C2×C4×Dic5—21no—
114C2×C4×Dic5C22×C311yescharacteristic
115C2×#677C22×C312yes—
116#4044—21no—
117#4039C22×C311yescharacteristic
118#4038—21no—
119#4036C22×C311yescharacteristic
120#4033—21no—
121#4033—21no—
122#4033C22×C312yes—
123#4033C22×C312yes—
124#4032—21no—
125#4027—21no—
126C5×#107C22×C312yes—
127C5×#103C22×C312yes—
128C5×C22⋊C8C22×C311yescharacteristic
129C22⋊#168C22×C311yescharacteristic
130#3948C22×C312yes—
131#3947C22×C312yes—
132#3946C22×C312yes—
133#3942C22×C312yes—
134#3941C22×C312yes—
135#3940C22×C312yes—
136#3117—51noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C3×C22⋊D5—42no—
148C2×C3×Dic5—24no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—41no—
153C2×C3×Dic5C2×D411yescharacteristic
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C3×D20—22no—
158C3×C4×D5—42no—
159C3×Dic10—24no—
160C3×Dic10—22no—
161C3×Dic10#4114yes—
162C3×C5×C8—22no—
163C3×#168—22no—
164C22×C3×Q8—51no—
165C2×C3×Q16—52no—
166C2×C3×SD16—52no—
167C3×#126—101no—
168C3×#125—51no—
169C3×#124—51no—
170C3×#123—101no—
171C3×C22⋊Q8C2×D511yescharacteristic
172C3×#121—51no—
173C3×C4×Q8—51no—
174C3×C4×Q8—52no—
175C3×C4×Q8—52no—
176C3×C4×Q8—101no—
177C3×C4×Q8—101no—
178C3×C4×D4—51no—
179C3×C4×D4—101no—
180C3×#117—101no—
181C2×C3×C4⋊C4—101no—
182C2×C3×C4⋊C4C2×D511yescharacteristic
183C2×C3×C42—51no—
184C2×C3×C42—101no—
185C3×#107C2×D512yes—
186C3×#106—52no—
187C3×C4⋊C8—52no—
188C3×#103—52no—
189C3×#103—52no—
190C3×#103C2×D512yes—
191C3×#102—52no—
192C3×C22⋊C8—51no—
193C3×C22⋊C8C2×D511yescharacteristic
194C3×#97—52no—
195C2×C5×Q8C23×C311yescharacteristic
196C22×C4×C5—21no—
197C22×C4×C5C23×C311yescharacteristic
198C2×C22⋊D5—21no—
199C22×Dic5—21no—
200C22×Dic5C3×D411yescharacteristic
201C22×Dic5C3×D411yescharacteristic
202C2×D20C23×C311yescharacteristic
203C2×C4×D5—21no—
204C2×Dic10—21no—
205C2×Dic10—24no—
206C2×Dic10C23×C312yes—
207C2×C5×C8C23×C312yes—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C23×C312yes—
211C5×C4⋊C4C23×C311yescharacteristic
212C5×C22⋊C4—21no—
213#689—24no—
214#685—21no—
215#685—21no—
216#685—21no—
217#685—21no—
218C4⋊Dic5—21no—
219C4⋊Dic5—21no—
220C4⋊Dic5C23×C311yescharacteristic
221#683—21no—
222#683—22no—
223#683—22no—
224C4×Dic5—21no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5C3×D411yescharacteristic
228C4×Dic5C3×D411yescharacteristic
229C4×Dic5C23×C311yescharacteristic
230C4×Dic5C23×C311yescharacteristic
231C2×#168C23×C312yes—
232#677—24no—
233#529—51no—
234C2×C4×Q8—51no—
235#484C3×D511yescharacteristic, complemented
236#481—51no—
237#479—52no—
238#464—52no—
239#451—51no—
240#448—51no—
241#441—52no—
242#440—52no—
243#432—51no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5—42no—
255C3×C4×C5C2×#4112yes—
256C3×Dic5—24no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—21no—
260C3×Dic5—21no—
261C3×Dic5—41no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C2×C3×Q8C22×D511yescharacteristic
266C2×C3×D4—51no—
267C2×C3×D4—101no—
268C22×C3×C4—21no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—101no—
272C22×C3×C4—101no—
273C22×C3×C4C22×D511yescharacteristic
274C3×Q16—104no—
275C3×SD16—104no—
276C2×C3×C8—52no—
277C2×C3×C8C22×D512yes—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4—102no—
282C3×C4⋊C4—102no—
283C3×C4⋊C4—101no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4—101no—
286C3×C4⋊C4C22×D512yes—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C22⋊C4—101no—
290C3×C22⋊C4—101no—
291C3×C22⋊C4—101no—
292C3×C22⋊C4—101no—
293C3×C42—51no—
294C3×C42—51no—
295C3×C42—51no—
296C3×C42—51no—
297C3×C42—102no—
298C3×C42—102no—
299C3×C42—101no—
300C23×C5C2×C3×D411yescharacteristic
301C22×D5—21no—
302C5×Q8—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—42no—
308C2×C4×C5C2×C3×D411yescharacteristic
309C2×C4×C5C24×C311yescharacteristic
310C22⋊D5—42no—
311C2×Dic5—24no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5—41no—
316C2×Dic5C2×C3×D411yescharacteristic
317C2×Dic5C2×C3×D411yescharacteristic
318C2×Dic5C2×C3×D411yescharacteristic
319C2×Dic5C2×C3×D411yescharacteristic
320D20—22no—
321C4×D5—42no—
322Dic10—24no—
323Dic10—22no—
324Dic10C3×#4114yes—
325C5×C8—22no—
326#168—22no—
327C22×Q8—51no—
328C2×Q16—52no—
329C2×SD16—52no—
330#126—101no—
331#125—51no—
332#124—51no—
333#123—101no—
334C22⋊Q8C2×C3×D511yescharacteristic
335#121—51no—
336C4×Q8—51no—
337C4×Q8—52no—
338C4×Q8—52no—
339C4×Q8—101no—
340C4×Q8—101no—
341C4×D4—51no—
342C4×D4—101no—
343#117—101no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4C2×C3×D511yescharacteristic
346C2×C42—51no—
347C2×C42—101no—
348#107C2×C3×D512yes—
349#106—52no—
350C4⋊C8—52no—
351#103—52no—
352#103—52no—
353#103C2×C3×D512yes—
354#102—52no—
355C22⋊C8—51no—
356C22⋊C8C2×C3×D511yescharacteristic
357#97—52no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C3×D5—81no—
363C23×C3—101no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—22no—
366C3×Q8—54no—
367C3×Q8—104no—
368C3×Q8—102no—
369C3×D4—102no—
370C3×D4—202no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—42no—
376C2×C3×C4—51no—
377C2×C3×C4—51no—
378C2×C3×C4—51no—
379C2×C3×C4—51no—
380C2×C3×C4—104no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4—101no—
384C2×C3×C4—202no—
385C2×C3×C4—201no—
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C23×D511yescharacteristic
388C3×C8—22no—
389C3×C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5C3×#13712yes—
393C22×C5C22×C3×D411yescharacteristic
394C2×D5—41no—
395C2×D5—41no—
396C2×D5—41no—
397C4×C5—21no—
398C4×C5—41no—
399C4×C5—42no—
400C4×C5—41no—
401C4×C5C2×C3×#4112yes—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—21no—
406Dic5—24no—
407Dic5—41no—
408C2×Q8—52no—
409C2×Q8—104no—
410C2×Q8—101no—
411C2×Q8C22×C3×D511yescharacteristic
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—21no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4C22×C3×D511yescharacteristic
420Q16—104no—
421SD16—104no—
422C2×C8—52no—
423C2×C8C22×C3×D512yes—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—51no—
427C4⋊C4—102no—
428C4⋊C4—102no—
429C4⋊C4—101no—
430C4⋊C4—101no—
431C4⋊C4—101no—
432C4⋊C4C22×C3×D512yes—
433C4⋊C4C22×C3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—101no—
436C22⋊C4—101no—
437C22⋊C4—101no—
438C22⋊C4—101no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—102no—
444C42—102no—
445C42—101no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3#406412yes—
453C22×C3C2×D4×D511yescharacteristic
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—101no—
461C3×C4—101no—
462C3×C4—104no—
463C3×C4—201no—
464C3×C4D5×#4112yes—
465C2×C5—22no—
466C2×C5C3×#52511yescharacteristic
467C2×C5C2×C3×#13711yescharacteristic
468C2×C5C3×#57511yescharacteristic
469D5—81no—
470C23—101no—
471C23C3×D4×D511yescharacteristic
472Q8—22no—
473Q8—54no—
474Q8—104no—
475Q8—102no—
476D4—102no—
477D4—202no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—104no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—101no—
491C2×C4—202no—
492C2×C4—201no—
493C2×C4C3×D4×D511yescharacteristic
494C2×C4C23×C3×D511yescharacteristic
495C8—22no—
496C8—102no—
497C2×C3—22no—
498C2×C3—401no—
499C2×C3#6599011yescharacteristic
500C2×C3C2×#406411yescharacteristic
501C2×C3#6610711yescharacteristic
502C5C3×#311711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22C3×#406412yes—
509C22C2×C3×D4×D511yescharacteristic
510C4—21no—
511C4—42no—
512C4—41no—
513C4—41no—
514C4—101no—
515C4—101no—
516C4—104no—
517C4—101no—
518C4—101no—
519C4—201no—
520C4C3×D5×#4112yes—
521C3#1061318611yescharacteristic, direct product factor, Sylow
522C2—22no—
523C2—401no—
524C2C3×#6599011yescharacteristic
525C2C2×C3×#406411yescharacteristic
526C2C3×#6610711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#484C2
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC3×#484D5
hypocenterC5C3×#3117
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#484

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4033C2semidirect
3. C3×C5×#484C2semidirect
4. C3×#65339C2semidirect
6. C3×#65178C2semidirect
7. C3×#65166C2semidirect
8. C3×#65087C2semidirect
9. C3×#65078C2semidirect
11. C3×#65008C2semidirect
12. #10613186C3direct (N × H)
46. C2×#4033C2×C3semidirect
47. C5×#484C2×C3semidirect
48. #65339C2×C3semidirect
50. #65178C2×C3semidirect
51. #65166C2×C3semidirect
52. #65087C2×C3semidirect
53. #65078C2×C3semidirect
55. #65008C2×C3semidirect
96. C3×#484D5semidirect
235. #484C3×D5semidirect
446. C3×C5#3117semidirect
502. C5C3×#3117semidirect
521. C3#10613186direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659582
C2×C3×#40332
C3×C5×#4842
C3×#653392
C3×#652572
C3×#651782
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