Finite Group Databasebeta

← #14430209

Subgroups — #14430209

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic, complemented
2C4×#6817C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4#11751192C211yesmaximal, characteristic, complemented
5#11751188C211yesmaximal, characteristic, complemented
6#11751185C211yesmaximal, characteristic, complemented
7#11751167C212yesmaximal, complemented
8#11751164C212yesmaximal, complemented
9#11751103C212yesmaximal
10#11751099C212yesmaximal, complemented
11C2×C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
12#10615080—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16C3×C5×#125C2212yes—
17C3×C5×C22⋊Q8—21no—
18C3×C5×C22⋊Q8—21no—
19C3×C4×C5×Q8—21no—
20C3×C4×C5×Q8—21no—
21C3×C5×#117C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C4×#1220—21no—
24C4×#1220—21no—
25#91815C2211yescharacteristic
26C22×C3⋊#168C2212yes—
27C4×D60C2211yescharacteristic
28C4×D60C2211yescharacteristic
29#91761—21no—
30C42×D15—21no—
31C4×Dic30C2211yescharacteristic
32C4×Dic30C2211yescharacteristic
33#91094C2212yes—
34#91094C2212yes—
35#91093C2212yes—
36#91093C2212yes—
37#91092C2212yes—
38#91092C2212yes—
39#91091C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42C4⋊(C3⋊#168)C2211yescharacteristic
43C4⋊(C3⋊#168)C2212yes—
44#83349—51nomaximal, Hall
45C5×#533D311yescharacteristic, complemented
46C4×#709—31no—
47#65383—31no—
48#65380—31no—
49#65376—31no—
50#65373—31no—
51#65355—32no—
52#65352—32no—
53#65291—32no—
54#65287—32no—
55C2×C4⋊#168—31no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8—21no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—21no—
62#6817—22no—
63#6817Q814yescomplemented
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×C4×D15—21no—
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C3×C5×C4⋊C4—22no—
70C3×C5×C4⋊C4—22no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4C2312yes—
74C3×C5×C4⋊C4C2312yes—
75C3×C5×C22⋊C4—22no—
76C3×C42×C5—22no—
77C3×C42×C5D411yescharacteristic
78C3×C42×C5D411yescharacteristic
79C3×C42×C5C2311yescharacteristic
80C3×C42×C5C2311yescharacteristic
81#6719—21no—
82#6714—21no—
83#6714—21no—
84C4⋊Dic15C2311yescharacteristic
85C4⋊Dic15C2311yescharacteristic
86#6712—21no—
87#6712—21no—
88C4×Dic15—21no—
89C4×Dic15—21no—
90C4×Dic15—21no—
91C2×C3⋊#168—24no—
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2312yes—
94C3×#533D511yescharacteristic, complemented
95C4×#235—51no—
96#5094—51no—
97#5091—51no—
98#5087—51no—
99#5084—51no—
100#5066—52no—
101#5063—52no—
102#5002—52no—
103#4998—52no—
104C2×C4⋊(C3⋊C8)—51no—
105C2×#709—31no—
106C5×C4⋊Q8C2×D311yescharacteristic
107C5×C4⋊Q8C2×D311yescharacteristic
108C5×#125C2×D312yes—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C4×C5×Q8—21no—
112C4×C5×Q8—21no—
113C5×#117C2×D312yes—
114C2×C42×C5C2×D311yescharacteristic
115C4×C22⋊D5—61no—
116C4×C22⋊D5—61no—
117#4072—31no—
118C22×#168—32no—
119C4×D20—31no—
120C4×D20—31no—
121#4018—61no—
122C42×D5—61no—
123C4×Dic10—31no—
124C4×Dic10—31no—
125#3942—32no—
126#3942—32no—
127#3941—32no—
128#3941—32no—
129#3940—32no—
130#3940—32no—
131#3939—32no—
132#3939—32no—
133C4⋊#168—32no—
134C4⋊#168—31no—
135C4⋊#168—31no—
136#3076—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C3×C5×Q8—42no—
140C3×C5×Q8—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—41no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×Q812yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153#1220—24no—
154C2×Dic15—21no—
155C2×Dic15—21no—
156C2×Dic15—21no—
157D60—21no—
158D60C2×Q812yes—
159C4×D15—24no—
160C4×D15—42no—
161C4×D15—42no—
162Dic30—21no—
163Dic30C2×Q812yes—
164C3⋊#168—22no—
165C3⋊#168—22no—
166C2×#235—51no—
167C3×C4⋊Q8C2×D511yescharacteristic
168C3×C4⋊Q8C2×D511yescharacteristic
169C3×#125C2×D512yes—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—21no—
172C3×C4×Q8—21no—
173C3×C4×Q8—21no—
174C3×#117C2×D512yes—
175C2×C3×C42C2×D511yescharacteristic
176C4×#67—101no—
177C4×#67—101no—
178#926—51no—
179C22×C3⋊C8—52no—
180C4×D12—51no—
181C4×D12—51no—
182#872—101no—
183C42×D3—101no—
184C4×Dic6—51no—
185C4×Dic6—51no—
186#810—52no—
187#810—52no—
188#809—52no—
189#809—52no—
190#808—52no—
191#808—52no—
192#807—52no—
193#807—52no—
194C4⋊(C3⋊C8)—52no—
195C4⋊(C3⋊C8)—51no—
196C4⋊(C3⋊C8)—51no—
197C2×C5×Q8—21no—
198C2×C5×Q8—21no—
199C22×C4×C5#6711yescharacteristic
200C22×C4×C5#6711yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—61no—
203#709—34no—
204#709—62no—
205C2×D20—31no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×C4⋊C4—22no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4C22×D312yes—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—22no—
217C42×C5—22no—
218C42×C5#6711yescharacteristic
219C42×C5#6711yescharacteristic
220C42×C5C22×D311yescharacteristic
221C42×C5C22×D311yescharacteristic
222C22⋊Dic5—61no—
223#685—61no—
224#685—61no—
225C4⋊Dic5—31no—
226C4⋊Dic5—31no—
227#683—61no—
228#683—61no—
229C4×Dic5—61no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C2×#168—32no—
233C2×#168—32no—
234C2×#168—64no—
235#533D1511yescharacteristic, complemented
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475—151no—
242#474—151no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C22⋊Q812yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—22no—
251C2×D15—41no—
252C2×D15—41no—
253C3×C4×C5—21no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5—42no—
257C3×C4×C5—42no—
258C3×C4×C5C22⋊Q812yes—
259C3×C4×C5#13512yes—
260C3×C4×C5C22×Q811yescharacteristic
261C3×C4×C5C2×#4111yescharacteristic
262Dic15—22no—
263Dic15—41no—
264Dic15—41no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C22×C3×C4C22⋊D511yescharacteristic
268C22×C3×C4C22⋊D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271#235—54no—
272#235—102no—
273C2×D12—51no—
274C2×C4×D3—101no—
275C2×C4×D3—101no—
276C2×C4×D3—101no—
277C2×Dic6—51no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4C22×D512yes—
283C3×C4⋊C4C22×D512yes—
284C3×C22⋊C4—22no—
285C3×C42—22no—
286C3×C42C22⋊D511yescharacteristic
287C3×C42C22⋊D511yescharacteristic
288C3×C42C22×D511yescharacteristic
289C3×C42C22×D511yescharacteristic
290#217—101no—
291(C2×D3)⋊C4—101no—
292(C2×D3)⋊C4—101no—
293C4⋊Dic3—51no—
294C4⋊Dic3—51no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—52no—
302C2×C3⋊C8—104no—
303C23×C5C2×#6711yescharacteristic
304C22×D5—61no—
305C5×Q8—42no—
306C5×Q8—42no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—41no—
311C2×C4×C5D3×Q812yes—
312C2×C4×C5#23912yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C2×#6711yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C22⋊D5—64no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323D20—32no—
324D20—61no—
325C4×D5—64no—
326C4×D5—122no—
327C4×D5—122no—
328Dic10—32no—
329Dic10—61no—
330#168—62no—
331#168—62no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8C2×D1511yescharacteristic
335C4⋊Q8C2×D1511yescharacteristic
336#125C2×D1512yes—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—151no—
342C4×Q8—151no—
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—151no—
348#117—301no—
349#117C2×D1512yes—
350C2×C42—301no—
351C2×C42C2×D1511yescharacteristic
352#107—152no—
353#107—152no—
354#106—152no—
355#106—152no—
356C4⋊C8—151no—
357C4⋊C8—151no—
358C4⋊C8—152no—
359#103—152no—
360#103—152no—
361#102—152no—
362#102—152no—
363C2×C3×C5—22no—
364C2×C3×C5C2×C22⋊Q811yescharacteristic
365C2×C3×C5C2×#13511yescharacteristic
366C2×C3×C5#57511yescharacteristic
367D15—42no—
368C23×C3C2×C22⋊D511yescharacteristic
369C22×D3—101no—
370C3×Q8—42no—
371C3×Q8—42no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—41no—
376C2×C3×C4Q8×D512yes—
377C2×C3×C4#71312yes—
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C2×C22⋊D511yescharacteristic
381C2×C3×C4C2×C22⋊D511yescharacteristic
382C2×C3×C4C2×C22⋊D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—104no—
385C2×Dic3—101no—
386C2×Dic3—101no—
387C2×Dic3—101no—
388D12—52no—
389D12—101no—
390C4×D3—104no—
391C4×D3—202no—
392C4×D3—202no—
393Dic6—52no—
394Dic6—101no—
395C3⋊C8—102no—
396C3⋊C8—102no—
397C22×C5—21no—
398C22×C5—21no—
399C22×C5#94612yes—
400C22×C5C22×#6711yescharacteristic
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C4×C5—21no—
405C4×C5—21no—
406C4×C5—21no—
407C4×C5—42no—
408C4×C5—42no—
409C4×C5#94612yes—
410C4×C5#95012yes—
411C4×C5C2×D3×Q811yescharacteristic
412C4×C5C2×#23911yescharacteristic
413Dic5—62no—
414Dic5—121no—
415Dic5—121no—
416#41—154no—
417#41—302no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—151no—
421C2×D4—151no—
422C2×D4—301no—
423C22×C4—301no—
424C22×C4—301no—
425C22×C4—301no—
426C22×C4#122011yescharacteristic
427C22×C4#122011yescharacteristic
428C22×C4C22×D1511yescharacteristic
429C2×C8—152no—
430C2×C8—152no—
431C2×C8—304no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—151no—
437C4⋊C4—151no—
438C4⋊C4—301no—
439C4⋊C4—301no—
440C4⋊C4C22×D1512yes—
441C4⋊C4C22×D1512yes—
442C22⋊C4—22no—
443C22⋊C4—301no—
444C22⋊C4—301no—
445C22⋊C4—301no—
446C42—22no—
447C42—301no—
448C42—301no—
449C42—301no—
450C42#122011yescharacteristic
451C42#122011yescharacteristic
452C42C22×D1511yescharacteristic
453C42C22×D1511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3#409212yes—
458C22×C3C22×C22⋊D511yescharacteristic
459C2×D3—102no—
460C2×D3—201no—
461C2×D3—201no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4#409212yes—
468C3×C4#409612yes—
469C3×C4C2×Q8×D511yescharacteristic
470C3×C4C2×#71311yescharacteristic
471Dic3—102no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—22no—
475C2×C5C2×#94611yescharacteristic
476C2×C5C2×#95011yescharacteristic
477C2×C5#582211yescharacteristic
478D5—122no—
479C23—301no—
480C23C2×#122011yescharacteristic
481Q8—42no—
482Q8—42no—
483Q8—152no—
484Q8—301no—
485D4—152no—
486D4—304no—
487D4—301no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—301no—
493C2×C4—304no—
494C2×C4—301no—
495C2×C4—301no—
496C2×C4—602no—
497C2×C4—602no—
498C2×C4Q8×D1512yes—
499C2×C4#682112yes—
500C2×C4C2×#122011yescharacteristic
501C2×C4C2×#122011yescharacteristic
502C2×C4C2×#122011yescharacteristic
503C2×C4C2×#122011yescharacteristic
504C2×C4C2×#122011yescharacteristic
505C2×C4C23×D1511yescharacteristic
506C8—302no—
507C8—302no—
508C2×C3—22no—
509C2×C3C2×#409211yescharacteristic
510C2×C3C2×#409611yescharacteristic
511C2×C3#6615611yescharacteristic
512D3—202no—
513C5#8334911yescharacteristic, complemented, Sylow
514C22—21no—
515C22—21no—
516C22—302no—
517C22—601no—
518C22—601no—
519C22#9183512yes—
520C22C22×#122011yescharacteristic
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—302no—
527C4—601no—
528C4—601no—
529C4#9183512yes—
530C4#9183912yes—
531C4C2×Q8×D1511yescharacteristic
532C4C2×#682111yescharacteristic
533C3#1061508011yescharacteristic, complemented, Sylow
534C2—22no—
535C2—602no—
536C2C2×#9183511yescharacteristic
537C2C2×#9183911yescharacteristic
538C2#1175658111yescharacteristic
subgroupG/H
centerC2×C4C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#533C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#533D15
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×C5×#533C2semidirect
3. #11751195C2semidirect
4. #11751192C2semidirect
5. #11751188C2semidirect
6. #11751185C2semidirect
7. #11751167C2semidirect
8. #11751164C2semidirect
10. #11751099C2semidirect
11. C2×C4⋊(C3⋊#168)C2semidirect
45. C5×#533D3semidirect
63. #6817Q8semidirect
94. C3×#533D5semidirect
235. #533D15semidirect
454. C3×C5#3076semidirect
513. C5#83349semidirect
533. C3#10615080semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5332
C4×#68172
#117511952
#117511922
#117511882
#117511852
#117511672
#117511642
#117511032
#117510992
C2×C4⋊(C3⋊#168)2
#106150803
#833495