Finite Group Databasebeta

← #14430733

Subgroups — #14430733

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
1#11754414C211yesmaximal, characteristic
2C2×#91388C211yesmaximal, characteristic, complemented
3#11751234C211yesmaximal, characteristic
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65407C211yesmaximal, characteristic, complemented
6#11748460C211yesmaximal, characteristic, complemented
7#11748394C211yesmaximal, characteristic
8#11747858C212yesmaximal, complemented
9#11747852C212yesmaximal, complemented
10#11747780C212yesmaximal, complemented
11#11747773C212yesmaximal, complemented
12#10610972—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C5×#926C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91552—21no—
21#91552—21no—
22C2×Dic3⋊Dic5—21no—
23C2×#6669—21no—
24#91418C2211yescharacteristic
25#91418C2211yescharacteristic
26C4×#1200—21no—
27#91388—21no—
28#91388—21no—
29#91388C2212yes—
30#91388C2212yes—
31#91386—21no—
32#91333C2211yescharacteristic
33#91333C2211yescharacteristic
34#91105C2212yes—
35#91100C2212yes—
36C5×#818C2212yes—
37C5×#817C2212yes—
38C3×#3946C2212yes—
39C3×#3946C2212yes—
40#90988C2212yes—
41#90985C2212yes—
42#90975C2212yes—
43#90969C2212yes—
44#79061—51nomaximal, Hall
45#65856—31no—
46C2×#4036—31no—
47C5×#428—31no—
48#65422—31no—
49#65407D311yescharacteristic, complemented
50#65284—31no—
51#65255—31no—
52#65180—32no—
53#65166—32no—
54#65160—32no—
55#65146—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817Q814yes—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×#1200—21no—
68C2×#1200—21no—
69C3×C5×M16—22no—
70C2×C3×C5×C8C2312yes—
71C4⋊Dic15—21no—
72C4⋊Dic15C2312yes—
73C5×#217—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C4×C5×Dic3—21no—
79C3×C4×Dic5D411yescharacteristic
80C3×C4×Dic5D411yescharacteristic
81C3×C4×Dic5C2311yescharacteristic
82C3×C4×Dic5C2311yescharacteristic
83C3×#681—22no—
84C2×C3×#168C2312yes—
85Dic3⋊Dic5—22no—
86Dic3⋊Dic5—22no—
87#6669—22no—
88#6669—22no—
89#6669—21no—
90#6669—21no—
91#6667—21no—
92#6667—21no—
93Dic3×Dic5—21no—
94Dic3×Dic5—21no—
95C4×#235—51no—
96C2×#870—51no—
97C3×#423—51no—
98#5133—51no—
99#5133—51no—
100#5121—51no—
101#5121D511yescharacteristic, complemented
102#4847—52no—
103#4847—52no—
104#4829—52no—
105#4829—52no—
106C2×#709—31no—
107C2×C5×M16C2×D311yescharacteristic
108C5×#117—31no—
109C2×C5×C4⋊C4—31no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—61no—
112C2×#683—61no—
113C2×C4×Dic5C2×D311yescharacteristic
114C2×#681C2×D311yescharacteristic
115#4039—31no—
116#4039—31no—
117#4036—32no—
118#4036—32no—
119#4036—61no—
120#4036—61no—
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#3946C2×D312yes—
132#3946C2×D312yes—
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×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×Q812yes—
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—24no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—42no—
148D60—21no—
149D60C2×Q812yes—
150C4×D15—24no—
151Dic30—21no—
152Dic30C2×Q812yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—42no—
157C2×C3×Dic5—41no—
158C2×C3×Dic5—41no—
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163#1200—42no—
164#1200—42no—
165C3×C5×C8—22no—
166C3×#168—22no—
167C2×#235—51no—
168C2×C3×M16—51no—
169C2×C3×M16C2×D511yescharacteristic
170C2×C3×C42—51no—
171C4×#67—101no—
172C4×#67—101no—
173#926C2×D511yescharacteristic
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3C2×D511yescharacteristic
176C2×Dic3⋊C4—101no—
177C2×Dic3⋊C4—101no—
178C4×D12—51no—
179C4×D12—51no—
180#872—101no—
181C42×D3—101no—
182#870—52no—
183#870—52no—
184#870—101no—
185#870—101no—
186C4×Dic6—51no—
187C4×Dic6—51no—
188C3×C4⋊C8—52no—
189C3×C4⋊C8—52no—
190#821—52no—
191#821—52no—
192#818—52no—
193#818C2×D512yes—
194#817—52no—
195#817C2×D512yes—
196#816—52no—
197#816—52no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201C22×Dic5—61no—
202C22×Dic5D1211yescharacteristic
203C22×Dic5D1211yescharacteristic
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—22no—
212C2×C5×C8C22×D312yes—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4—31no—
216C5×C4⋊C4—61no—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219#685—61no—
220#685—61no—
221C4⋊Dic5—32no—
222C4⋊Dic5—61no—
223C4⋊Dic5—62no—
224C4⋊Dic5—62no—
225#683—61no—
226#683—61no—
227#683—62no—
228#683—62no—
229C4×Dic5—61no—
230C4×Dic5—61no—
231C4×Dic5D1211yescharacteristic
232C4×Dic5D1211yescharacteristic
233C4×Dic5C22×D311yescharacteristic
234C4×Dic5C22×D311yescharacteristic
235#681—22no—
236C2×#168C22×D312yes—
237C2×#125—151no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—31no—
244#428—151no—
245#423—51no—
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×C5C22⋊Q812yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—22no—
259Dic15—42no—
260C3×Dic5—21no—
261C3×Dic5—21no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C5×Dic3—42no—
267C22×C3×C4—51no—
268C22×C3×C4—51no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C22×Dic3—21no—
272C22×Dic3—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×M16—22no—
281C3×M16—102no—
282C2×C3×C8—52no—
283C2×C3×C8C22×D512yes—
284C3×C42—51no—
285C3×C42—51no—
286C3×C42—51no—
287C3×C42—51no—
288#217—21no—
289(C2×D3)⋊C4—101no—
290(C2×D3)⋊C4—101no—
291C4⋊Dic3—21no—
292C4⋊Dic3—52no—
293C4⋊Dic3—101no—
294C4⋊Dic3C22×D512yes—
295C4⋊Dic3C22×D511yescharacteristic
296C4⋊Dic3C22×D511yescharacteristic
297Dic3⋊C4—101no—
298Dic3⋊C4—101no—
299Dic3⋊C4—102no—
300Dic3⋊C4—102no—
301Dic3⋊C4—102no—
302Dic3⋊C4—102no—
303C4×Dic3—21no—
304C4×Dic3—101no—
305C4×Dic3—101no—
306C23×C5C2×D1211yescharacteristic
307C22×D5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—62no—
311C2×C4×C5—122no—
312C2×C4×C5C2×D1211yescharacteristic
313C2×C4×C5#23712yes—
314C2×C4×C5D3×Q812yes—
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—64no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—61no—
320C2×Dic5—62no—
321C2×Dic5—122no—
322C2×Dic5C2×D1211yescharacteristic
323C2×Dic5C2×D1211yescharacteristic
324C2×Dic5C2×D1211yescharacteristic
325C2×Dic5C2×D1211yescharacteristic
326D20—32no—
327D20—61no—
328C4×D5—64no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—22no—
334#168—22no—
335C2×#41—151no—
336C2×M16—51no—
337C2×M16D3×D511yescharacteristic
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
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—31no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—51no—
355C2×C42—301no—
356#107—32no—
357#107—152no—
358#106—32no—
359#106—152no—
360C4⋊C8—52no—
361C4⋊C8—52no—
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—51no—
374C2×C3×C4—51no—
375C2×C3×C4—51no—
376C2×C3×C4—51no—
377C2×C3×C4—201no—
378C2×C3×C4—201no—
379C2×C3×C4#70912yes—
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4Q8×D512yes—
382C2×C3×C4C23×D511yescharacteristic
383#67—104no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—42no—
388C2×Dic3—101no—
389C2×Dic3—102no—
390C2×Dic3—202no—
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#89712yes—
403C22×C5C22×D1211yescharacteristic
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C4×C5—121no—
408C4×C5—121no—
409C4×C5—122no—
410C4×C5#89712yes—
411C4×C5C2×#23711yescharacteristic
412C4×C5C2×D3×Q811yescharacteristic
413Dic5—21no—
414Dic5—21no—
415Dic5—21no—
416Dic5—21no—
417Dic5—62no—
418Dic5—122no—
419#41—154no—
420#41—302no—
421C2×Q8—151no—
422C2×D4—151no—
423C2×D4—301no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—61no—
427C22×C4—301no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—22no—
433M16—102no—
434C2×C8—52no—
435C2×C8C2×D3×D512yes—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—31no—
439C4⋊C4—61no—
440C4⋊C4—152no—
441C4⋊C4—302no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4—301no—
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—101no—
467C3×C4—101no—
468C3×C4—101no—
469C3×C4—101no—
470C3×C4#404212yes—
471C3×C4C2×#70911yescharacteristic
472C3×C4C2×Q8×D511yescharacteristic
473Dic3—41no—
474Dic3—42no—
475Dic3—41no—
476Dic3—102no—
477Dic3—202no—
478C2×C5—22no—
479C2×C5C2×#89711yescharacteristic
480C2×C5#574811yescharacteristic
481C2×C5#574811yescharacteristic
482D5—122no—
483C23—301no—
484C23D5×D1211yescharacteristic
485Q8—152no—
486Q8—301no—
487D4—152no—
488D4—304no—
489D4—301no—
490C2×C4—51no—
491C2×C4—51no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—62no—
497C2×C4—122no—
498C2×C4—201no—
499C2×C4—201no—
500C2×C4—301no—
501C2×C4—304no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4—602no—
505C2×C4—602no—
506C2×C4D15⋊Q812yes—
507C2×C4D5×D1211yescharacteristic
508C2×C4#677912yes—
509C2×C4C22×D3×D511yescharacteristic
510C8—22no—
511C8—102no—
512C2×C3—22no—
513C2×C3C2×#404211yescharacteristic
514C2×C3#6610711yescharacteristic
515C2×C3#6611111yescharacteristic
516D3—202no—
517C5#7906111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—302no—
521C22—601no—
522C22—601no—
523C22#9141912yes—
524C22C2×D5×D1211yescharacteristic
525C4—101no—
526C4—101no—
527C4—101no—
528C4—101no—
529C4—121no—
530C4—122no—
531C4—121no—
532C4—302no—
533C4—602no—
534C4#9141912yes—
535C4C2×D15⋊Q811yescharacteristic
536C4C2×#677911yescharacteristic
537C3#1061097211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—602no—
540C2#1175402111yescharacteristic
541C2#1175402211yescharacteristic
542C2C2×#9141911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91388C2semidirect
4. C5×#5121C2semidirect
5. C3×#65407C2semidirect
6. #11748460C2semidirect
8. #11747858C2semidirect
9. #11747852C2semidirect
10. #11747780C2semidirect
11. #11747773C2semidirect
49. #65407D3semidirect
101. #5121D5semidirect
458. C3×C5#3080semidirect
517. C5#79061semidirect
537. C3#10610972semidirect

Maximal subgroups

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

subgroupindex
#117544142
C2×#913882
#117512342
C5×#51212
C3×#654072
#117484602
#117483942
#117478582
#117478522
#117477802
#117477732
#106109723
#790615