Finite Group Databasebeta

← #14430734

Subgroups — #14430734

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#11754444C211yesmaximal, characteristic
2C2×#91384C211yesmaximal, characteristic, complemented
3#11751219C211yesmaximal, characteristic, complemented
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic
6#11748470C211yesmaximal, characteristic, complemented
7#11748368C211yesmaximal, characteristic
8#11747878C212yesmaximal, complemented
9#11747877C212yesmaximal, complemented
10#11747805C212yesmaximal, complemented
11#11747804C212yesmaximal, complemented
12#10610972—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91559—21no—
21#91559—21no—
22C2×Dic3⋊Dic5—21no—
23C2×#6668—21no—
24#91434C2211yescharacteristic
25#91434C2211yescharacteristic
26C4×D5×Dic3—21no—
27#91384—21no—
28#91384—21no—
29#91384C2212yes—
30#91384C2212yes—
31#91357—21no—
32#91331C2211yescharacteristic
33#91331C2211yescharacteristic
34#91098C2212yes—
35#91098C2212yes—
36C5×#818C2212yes—
37C5×#817C2212yes—
38C3×#3953C2212yes—
39C3×#3948C2212yes—
40#90989C2212yes—
41#90986C2212yes—
42#90970C2212yes—
43#90964C2212yes—
44#78871—51nomaximal, Hall
45#65856—31no—
46C2×#4036—31no—
47C5×#428—31no—
48#65422D311yescharacteristic
49#65407—31no—
50#65284—31no—
51#65255—31no—
52#65180—32no—
53#65166—32no—
54#65160—32no—
55#65146—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15D411yescharacteristic
58C22×Dic15D411yescharacteristic
59C22×C5×Dic3—21no—
60C2×C3×C22⋊D5—21no—
61C22×C3×Dic5—21no—
62C3×#709—22no—
63C3×#709Q814yes—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×D5×Dic3—21no—
68C2×D5×Dic3—21no—
69C3×C5×M16—22no—
70C2×C3×C5×C8C2312yes—
71C4×Dic15D411yescharacteristic
72C4×Dic15D411yescharacteristic
73C4×Dic15C2311yescharacteristic
74C4×Dic15C2311yescharacteristic
75#6710—22no—
76C2×C3⋊#168C2312yes—
77C5×#217—21no—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C5×C4⋊Dic3C2312yes—
82C4×C5×Dic3—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85Dic3⋊Dic5—22no—
86Dic3⋊Dic5—22no—
87#6668—22no—
88#6668—22no—
89#6668—21no—
90#6668—21no—
91#6665—21no—
92#6665—21no—
93Dic3×Dic5—21no—
94Dic3×Dic5—21no—
95Dic3×#41—51no—
96C2×#890—51no—
97C3×#417—51no—
98#5232—51no—
99#5121D511yescharacteristic, complemented
100#5118—51no—
101#4964—51no—
102#4799—52no—
103#4796—52no—
104#4766—52no—
105#4763—52no—
106C2×#709C2×D311yescharacteristic
107C2×C5×M16C2×D311yescharacteristic
108C5×#117—31no—
109C2×C5×C4⋊C4—31no—
110C2×C4⋊Dic5—61no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—61no—
113C2×C4×Dic5—31no—
114C2×#681—31no—
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#3953C2×D312yes—
130#3948C2×D312yes—
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×C3×D5—21no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×Q812yes—
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—41no—
145C2×Dic15—41no—
146C2×Dic15C2×D411yescharacteristic
147C2×Dic15C2×D411yescharacteristic
148C2×Dic15C2×D411yescharacteristic
149C2×Dic15C2×D411yescharacteristic
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—42no—
154C3×C22⋊D5—24no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—42no—
158C3×D20—21no—
159C3×D20C2×Q812yes—
160C3×C4×D5—24no—
161C3×Dic10—21no—
162C3×Dic10C2×Q812yes—
163D5×Dic3—42no—
164D5×Dic3—42no—
165C3×C5×C8—22no—
166C3⋊#168—22no—
167C2×C3×#41—51no—
168C2×C3×M16C2×D511yescharacteristic
169C2×C3×C4⋊C4—51no—
170Q8×Dic3—51no—
171Q8×Dic3—51no—
172D4×Dic3—51no—
173D4×Dic3—51no—
174D4×Dic3—101no—
175D4×Dic3—101no—
176#926—101no—
177#926C2×D511yescharacteristic
178C2×C4⋊Dic3—101no—
179C2×C4⋊Dic3C2×D511yescharacteristic
180C2×Dic3⋊C4—101no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—101no—
183C2×#208—51no—
184#890—52no—
185#890—52no—
186#890—101no—
187#890—101no—
188C3×#103—52no—
189C3×#102—52no—
190#835—52no—
191#832—52no—
192#818C2×D512yes—
193#817C2×D512yes—
194Dic3⋊C8—52no—
195Dic3⋊C8—52no—
196#808—52no—
197#807—52no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201C22×Dic5—21no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204#709—22no—
205#709Dic614yes—
206C2×D20C22×D311yescharacteristic
207C2×C4×D5—21no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C2×Dic10C22×D311yescharacteristic
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—21no—
222C4⋊Dic5—62no—
223C4⋊Dic5—62no—
224C4⋊Dic5C22×D312yes—
225#683—61no—
226#683—61no—
227#683—62no—
228#683—62no—
229C4×Dic5—31no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—31no—
233C4×Dic5—61no—
234C4×Dic5—61no—
235#681—62no—
236C2×#168—32no—
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—151no—
246#417—51no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×C3×D5—22no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C3×C4×C5C22⋊Q812yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—21no—
259Dic15—21no—
260Dic15—21no—
261Dic15—21no—
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C5×Dic3—42no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C22×C3×C4—101no—
273C22×C3×C4—101no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—21no—
276C22×Dic3—51no—
277C22×Dic3—51no—
278C22×Dic3—101no—
279C22×Dic3—101no—
280C3×M16—22no—
281C2×C3×C8C22×D512yes—
282C3×C4⋊C4—52no—
283C3×C4⋊C4—101no—
284#217—21no—
285#217—101no—
286#217—101no—
287C4⋊Dic3—21no—
288C4⋊Dic3—102no—
289C4⋊Dic3—102no—
290C4⋊Dic3—101no—
291C4⋊Dic3—101no—
292C4⋊Dic3C22×D511yescharacteristic
293C4⋊Dic3C22×D511yescharacteristic
294C4⋊Dic3C22×D512yes—
295Dic3⋊C4—102no—
296Dic3⋊C4—102no—
297C4×Dic3—21no—
298C4×Dic3—51no—
299C4×Dic3—51no—
300C4×Dic3—51no—
301C4×Dic3—51no—
302C4×Dic3—101no—
303C4×Dic3—101no—
304#208—102no—
305C2×C3⋊C8—52no—
306C23×C5D3×D411yescharacteristic
307C22×D5—21no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—62no—
311C2×C4×C5—122no—
312C2×C4×C5C2×Dic612yes—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5#23712yes—
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—24no—
317C2×Dic5—21no—
318C2×Dic5—22no—
319C2×Dic5—31no—
320C2×Dic5—31no—
321C2×Dic5—31no—
322C2×Dic5—31no—
323C2×Dic5—42no—
324C2×Dic5—121no—
325C2×Dic5—121no—
326D20—21no—
327D20C2×Dic612yes—
328C4×D5—24no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—21no—
332Dic10C2×Dic612yes—
333C5×C8—22no—
334#168—62no—
335C2×#41—51no—
336C2×M16—151no—
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—51no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—151no—
355C2×C42—301no—
356#107—32no—
357#107—152no—
358#106—32no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—52no—
363#103—152no—
364#102—52no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C3×D5—42no—
371C23×C3—101no—
372C23×C3D4×D511yescharacteristic
373C3×Q8—52no—
374C3×Q8—101no—
375C3×D4—52no—
376C3×D4—104no—
377C3×D4—101no—
378C2×C3×C4—101no—
379C2×C3×C4—104no—
380C2×C3×C4—102no—
381C2×C3×C4—202no—
382C2×C3×C4#70912yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4Q8×D512yes—
385C2×C3×C4C23×D511yescharacteristic
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—42no—
390C2×Dic3—51no—
391C2×Dic3—51no—
392C2×Dic3—51no—
393C2×Dic3—51no—
394C2×Dic3—202no—
395C2×Dic3—202no—
396C2×Dic3—201no—
397C2×Dic3—201no—
398C3×C8—22no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5#87812yes—
403C22×C5C2×D3×D411yescharacteristic
404C2×D5—22no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—121no—
408C4×C5—121no—
409C4×C5—122no—
410C4×C5#87812yes—
411C4×C5C22×Dic611yescharacteristic
412C4×C5C2×#23711yescharacteristic
413Dic5—22no—
414Dic5—42no—
415Dic5—61no—
416Dic5—61no—
417Dic5—61no—
418Dic5—61no—
419#41—54no—
420#41—102no—
421C2×Q8—51no—
422C2×D4—51no—
423C2×D4—101no—
424C22×C4—61no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—151no—
428C22×C4—151no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—22no—
433M16—302no—
434C2×C8—152no—
435C2×C8C2×D3×D512yes—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—31no—
439C4⋊C4—52no—
440C4⋊C4—61no—
441C4⋊C4—101no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C4⋊C4—301no—
448C22⋊C4—61no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—61no—
452C42—151no—
453C42—151no—
454C42—151no—
455C42—151no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—102no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3#404212yes—
465C22×C3C2×D4×D511yescharacteristic
466C3×C4—102no—
467C3×C4—202no—
468C3×C4#404212yes—
469C3×C4C2×#70911yescharacteristic
470C3×C4C2×Q8×D511yescharacteristic
471Dic3—42no—
472Dic3—41no—
473Dic3—41no—
474Dic3—101no—
475Dic3—101no—
476Dic3—101no—
477Dic3—101no—
478C2×C5—22no—
479C2×C5C2×#87811yescharacteristic
480C2×C5#577311yescharacteristic
481C2×C5#577711yescharacteristic
482D5—42no—
483C23—101no—
484C23#677711yescharacteristic
485Q8—52no—
486Q8—101no—
487D4—52no—
488D4—104no—
489D4—101no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—101no—
494C2×C4—104no—
495C2×C4—102no—
496C2×C4—122no—
497C2×C4—151no—
498C2×C4—151no—
499C2×C4—151no—
500C2×C4—151no—
501C2×C4—202no—
502C2×C4—602no—
503C2×C4—602no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4D5×Dic612yes—
507C2×C4#677711yescharacteristic
508C2×C4#677912yes—
509C2×C4C22×D3×D511yescharacteristic
510C8—22no—
511C8—302no—
512C2×C3—22no—
513C2×C3—202no—
514C2×C3C2×#404211yescharacteristic
515C2×C3#6610711yescharacteristic
516C2×C3#6611111yescharacteristic
517C5#7887111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—102no—
521C22—201no—
522C22—201no—
523C22#9143012yes—
524C22C2×#677711yescharacteristic
525C4—102no—
526C4—122no—
527C4—121no—
528C4—121no—
529C4—202no—
530C4—301no—
531C4—301no—
532C4—301no—
533C4—301no—
534C4#9143012yes—
535C4C2×D5×Dic611yescharacteristic
536C4C2×#677911yescharacteristic
537C3#1061097211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—202no—
540C2#1175403511yescharacteristic
541C2#1175403611yescharacteristic
542C2C2×#9143011yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
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×#91384C2semidirect
3. #11751219C2semidirect
4. C5×#5121C2semidirect
6. #11748470C2semidirect
8. #11747878C2semidirect
9. #11747877C2semidirect
10. #11747805C2semidirect
11. #11747804C2semidirect
99. #5121D5semidirect
458. C3×C5#3080semidirect
517. C5#78871semidirect
537. C3#10610972semidirect

Maximal subgroups

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

subgroupindex
#117544442
C2×#913842
#117512192
C5×#51212
C3×#654222
#117484702
#117483682
#117478782
#117478772
#117478052
#117478042
#106109723
#788715