Finite Group Databasebeta

← #14430718

Subgroups — #14430718

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4036C211yesmaximal, characteristic, complemented
2#11754414C211yesmaximal, characteristic
3#11751067C211yesmaximal, characteristic
4C5×#4964C211yesmaximal, characteristic, complemented
5#11748470C211yesmaximal, characteristic, complemented
6#11748431C211yesmaximal, characteristic, complemented
7#11748413C211yesmaximal, characteristic
8#11747288C212yesmaximal, complemented
9#11747286C212yesmaximal, complemented
10#11747244C212yesmaximal, complemented
11#11747242C212yesmaximal, complemented
12#10610972—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×C4⋊Dic5—21no—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#683—21no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×#4036—21no—
23C3×#4036—21no—
24C3×#4036C2212yes—
25C3×#4036C2212yes—
26#91552—21no—
27#91552—21no—
28#91418C2211yescharacteristic
29#91418C2211yescharacteristic
30C4×#1200—21no—
31#91386—21no—
32#91333C2211yescharacteristic
33#91333C2211yescharacteristic
34#91094C2212yes—
35#91093C2212yes—
36C5×#808C2212yes—
37C5×#807C2212yes—
38#90989C2212yes—
39#90986C2212yes—
40#90982C2212yes—
41#90982C2212yes—
42#90974C2212yes—
43#90968C2212yes—
44#83017—51nomaximal, Hall
45#65856—31no—
46C2×#4036D311yescharacteristic, complemented
47C5×#428—31no—
48#65422—31no—
49#65407—31no—
50#65284—31no—
51#65255—31no—
52#65180—32no—
53#65166—32no—
54#65160—32no—
55#65146—32no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817Q814yes—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C3×Dic5—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×#1200—21no—
68C2×#1200—21no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71#6710—22no—
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×C4⋊Dic3C2311yescharacteristic
76C4×C5×Dic3—21no—
77C5×#208—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5C2312yes—
83C3×#683—22no—
84C3×#683—22no—
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5C2311yescharacteristic
88C3×C4×Dic5C2311yescharacteristic
89#6669—21no—
90#6669—21no—
91#6667—21no—
92#6667—21no—
93Dic3×Dic5—21no—
94Dic3×Dic5—21no—
95C2×C3×#125—51no—
96C4×#235—51no—
97#5066—52no—
98#5066—52no—
99#5063—52no—
100#5063—52no—
101#4966—51no—
102#4966—51no—
103#4964—51no—
104#4964D511yescharacteristic, complemented
105#4924—51no—
106C2×#709—31no—
107C2×C5×M16—31no—
108C5×#117—31no—
109C2×C5×C4⋊C4C2×D311yescharacteristic
110C2×C4⋊Dic5—21no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—21no—
113C2×C4×Dic5C2×D311yescharacteristic
114C2×#681—31no—
115#4039—31no—
116#4039—31no—
117#4036—21no—
118#4036—21no—
119#4036C2×D312yes—
120#4036C2×D312yes—
121#4033—31no—
122#4033—31no—
123#4027—61no—
124#4027—61no—
125#4018—61no—
126C42×D5—61no—
127C5×#107—32no—
128C5×#106—32no—
129#3953—32no—
130#3948—32no—
131#3946—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3939—32no—
137#3080—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—42no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×Q812yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148D60—21no—
149D60C2×Q812yes—
150C4×D15—24no—
151Dic30—21no—
152Dic30C2×Q812yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5—41no—
158C2×C3×Dic5—42no—
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163#1200—42no—
164#1200—42no—
165C3⋊#168—22no—
166C5×C3⋊C8—22no—
167C2×#235—51no—
168C3×#125—52no—
169C3×#125—52no—
170C3×#125—101no—
171C3×#125—101no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C4⋊C4—101no—
174C2×C3×C4⋊C4—101no—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176C2×C3×C42—51no—
177C4×#67—101no—
178C4×#67—101no—
179#926C2×D511yescharacteristic
180C2×#208—51no—
181C2×#208C2×D511yescharacteristic
182C4×D12—51no—
183C4×D12—51no—
184#872—101no—
185C42×D3—101no—
186C4×Dic6—51no—
187C4×Dic6—51no—
188#810—52no—
189#810—52no—
190#809—52no—
191#809—52no—
192#808—52no—
193#808C2×D512yes—
194#807—52no—
195#807C2×D512yes—
196C4⋊(C3⋊C8)—52no—
197C4⋊(C3⋊C8)—52no—
198C22×C4×C5—21no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201C22×Dic5—21no—
202C22×Dic5#6711yescharacteristic
203C22×Dic5#6711yescharacteristic
204#709—34no—
205#709—62no—
206C2×D20—31no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C2×Dic10—31no—
211C5×M16—62no—
212C2×C5×C8—32no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4—31no—
216C5×C4⋊C4C22×D312yes—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219#685—61no—
220#685—61no—
221C4⋊Dic5—21no—
222C4⋊Dic5—22no—
223C4⋊Dic5—22no—
224C4⋊Dic5C22×D312yes—
225#683—22no—
226#683—22no—
227#683—61no—
228#683—61no—
229C4×Dic5—61no—
230C4×Dic5—61no—
231C4×Dic5#6711yescharacteristic
232C4×Dic5#6711yescharacteristic
233C4×Dic5C22×D311yescharacteristic
234C4×Dic5C22×D311yescharacteristic
235#681—62no—
236C2×#168—32no—
237C2×#125—51no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—31no—
244#428—151no—
245#423—151no—
246#417—151no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—22no—
253C2×D15—41no—
254C2×D15—41no—
255C3×C4×C5—42no—
256C3×C4×C5C22⋊Q812yes—
257C3×C4×C5C22×Q811yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260C3×Dic5—21no—
261C3×Dic5—21no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—42no—
265C5×Dic3—41no—
266C5×Dic3—41no—
267C22×C3×C4—21no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—101no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—101no—
273#235—54no—
274#235—102no—
275C2×D12—51no—
276C2×C4×D3—101no—
277C2×C4×D3—101no—
278C2×C4×D3—101no—
279C2×Dic6—51no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—52no—
282C3×C4⋊C4—102no—
283C3×C4⋊C4—102no—
284C3×C4⋊C4—102no—
285C3×C4⋊C4—102no—
286C3×C4⋊C4—101no—
287C3×C4⋊C4C22×D512yes—
288C3×C42—51no—
289C3×C42—51no—
290C3×C42—51no—
291C3×C42—51no—
292#217—21no—
293(C2×D3)⋊C4—101no—
294(C2×D3)⋊C4—101no—
295C4⋊Dic3C22×D511yescharacteristic
296C4⋊Dic3C22×D511yescharacteristic
297Dic3⋊C4—101no—
298Dic3⋊C4—101no—
299C4×Dic3—21no—
300C4×Dic3—101no—
301C4×Dic3—101no—
302#208—22no—
303#208—102no—
304C2×C3⋊C8—52no—
305C2×C3⋊C8C22×D512yes—
306C23×C5C2×#6711yescharacteristic
307C22×D5—61no—
308C2×C4×C5—22no—
309C2×C4×C5—42no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5D3×Q812yes—
313C2×C4×C5#23912yes—
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—64no—
317C2×Dic5—22no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—42no—
321C2×Dic5—61no—
322C2×Dic5C2×#6711yescharacteristic
323C2×Dic5C2×#6711yescharacteristic
324C2×Dic5C2×#6711yescharacteristic
325C2×Dic5C2×#6711yescharacteristic
326D20—32no—
327D20—61no—
328C4×D5—64no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—62no—
334#168—62no—
335C2×#41—151no—
336C2×M16—31no—
337C2×M16—151no—
338#125—52no—
339#125—52no—
340#125—101no—
341#125—101no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—151no—
345C4×D4—151no—
346C4×D4—301no—
347C4×D4—301no—
348#117—31no—
349#117—301no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4D3×D511yescharacteristic
354C2×C42—51no—
355C2×C42—301no—
356#107—32no—
357#107—152no—
358#106—32no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—152no—
363#103—152no—
364#102—152no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370D15—42no—
371C23×C3D4×D511yescharacteristic
372C22×D3—101no—
373C2×C3×C4—22no—
374C2×C3×C4—42no—
375C2×C3×C4—51no—
376C2×C3×C4—51no—
377C2×C3×C4—51no—
378C2×C3×C4—51no—
379C2×C3×C4—102no—
380C2×C3×C4—201no—
381C2×C3×C4—201no—
382C2×C3×C4—202no—
383C2×C3×C4#70912yes—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4Q8×D512yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—104no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—101no—
391D12—52no—
392D12—101no—
393C4×D3—104no—
394C4×D3—202no—
395C4×D3—202no—
396Dic6—52no—
397Dic6—101no—
398C3⋊C8—22no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5#94612yes—
403C22×C5C22×#6711yescharacteristic
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C4×C5—42no—
408C4×C5—121no—
409C4×C5—121no—
410C4×C5#94612yes—
411C4×C5C2×D3×Q811yescharacteristic
412C4×C5C2×#23911yescharacteristic
413Dic5—21no—
414Dic5—21no—
415Dic5—21no—
416Dic5—21no—
417Dic5—42no—
418Dic5—62no—
419#41—154no—
420#41—302no—
421C2×Q8—151no—
422C2×D4—151no—
423C2×D4—301no—
424C22×C4—21no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—101no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—62no—
433M16—302no—
434C2×C8—32no—
435C2×C8—152no—
436C4⋊C4—21no—
437C4⋊C4—31no—
438C4⋊C4—31no—
439C4⋊C4—52no—
440C4⋊C4—102no—
441C4⋊C4—102no—
442C4⋊C4—102no—
443C4⋊C4—102no—
444C4⋊C4—101no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4C2×D3×D512yes—
448C22⋊C4—61no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—51no—
452C42—51no—
453C42—51no—
454C42—51no—
455C42—61no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3#404212yes—
462C22×C3C2×D4×D511yescharacteristic
463C2×D3—102no—
464C2×D3—201no—
465C2×D3—201no—
466C3×C4—42no—
467C3×C4—101no—
468C3×C4—101no—
469C3×C4—101no—
470C3×C4—101no—
471C3×C4—202no—
472C3×C4#404212yes—
473C3×C4C2×#70911yescharacteristic
474C3×C4C2×Q8×D511yescharacteristic
475Dic3—41no—
476Dic3—41no—
477Dic3—102no—
478C2×C5—22no—
479C2×C5C2×#94611yescharacteristic
480C2×C5#582211yescharacteristic
481C2×C5#582211yescharacteristic
482D5—122no—
483C23—301no—
484C23D5×#6711yescharacteristic
485Q8—152no—
486Q8—301no—
487D4—152no—
488D4—304no—
489D4—301no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—51no—
495C2×C4—51no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—102no—
499C2×C4—201no—
500C2×C4—201no—
501C2×C4—202no—
502C2×C4—301no—
503C2×C4—304no—
504C2×C4—602no—
505C2×C4—602no—
506C2×C4#676912yes—
507C2×C4D15⋊Q812yes—
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—302no—
512C2×C3—22no—
513C2×C3C2×#404211yescharacteristic
514C2×C3#6610711yescharacteristic
515C2×C3#6611111yescharacteristic
516D3—202no—
517C5#8301711yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—302no—
521C22—601no—
522C22—601no—
523C22#9141112yes—
524C22C2×D5×#6711yescharacteristic
525C4—42no—
526C4—101no—
527C4—101no—
528C4—101no—
529C4—101no—
530C4—121no—
531C4—121no—
532C4—202no—
533C4—302no—
534C4#9141112yes—
535C4C2×#676911yescharacteristic
536C4C2×D15⋊Q811yescharacteristic
537C3#1061097211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—602no—
540C2C2×#9141111yescharacteristic
541C2#1175469011yescharacteristic
542C2#1175508411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4036C2semidirect
4. C5×#4964C2semidirect
5. #11748470C2semidirect
6. #11748431C2semidirect
8. #11747288C2semidirect
9. #11747286C2semidirect
10. #11747244C2semidirect
11. #11747242C2semidirect
46. C2×#4036D3semidirect
104. #4964D5semidirect
458. C3×C5#3080semidirect
517. C5#83017semidirect
537. C3#10610972semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40362
#117544142
#117510672
C5×#49642
#117484702
#117484312
#117484132
#117472882
#117472862
#117472442
#117472422
#106109723
#830175