Finite Group Databasebeta

← #14430713

Subgroups — #14430713

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#237C211yesmaximal, characteristic
2D3×#4016C211yesmaximal, characteristic, complemented
3#11751110C211yesmaximal, characteristic, complemented
4C3×#65298C211yesmaximal, characteristic, complemented
5#11749088C211yesmaximal, characteristic, complemented
6#11749087C211yesmaximal, characteristic, complemented
7#11748955C211yesmaximal, characteristic
8#11748955C211yesmaximal, characteristic
9#11747396C211yesmaximal, characteristic, complemented
10#11747393C211yesmaximal, characteristic, complemented
11#11747191C211yesmaximal, characteristic, complemented
12#11747190C211yesmaximal, characteristic, complemented
13#11747011C211yesmaximal, characteristic, complemented
14#11746965C211yesmaximal, characteristic, complemented
15#11746926C211yesmaximal, characteristic, complemented
16#10614240—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×D4×Dic3C2211yescharacteristic
21C4×C5×#67—21no—
22C2×C4×C5×Dic3—21no—
23C5×#892C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C5×#67⋊C4—21no—
26C5×#877—21no—
27C42×C5×D3C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C3×#4016C2211yescharacteristic
30D3×C4⋊Dic5C2211yescharacteristic
31D3×C4⋊Dic5C2211yescharacteristic
32D3×#683—21no—
33D3×#683—21no—
34#91381C2211yescharacteristic
35#91381C2211yescharacteristic
36#91379—21no—
37#91379—21no—
38C2×#6650C2211yescharacteristic
39C2×#6650C2211yescharacteristic
40#91116C2211yescharacteristic
41#91116C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3940C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50#90989C2211yescharacteristic
51#90988C2211yescharacteristic
52#90986C2211yescharacteristic
53#90985C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56#90973C2211yescharacteristic
57#90973C2211yescharacteristic
58#90972C2211yescharacteristic
59#90972C2211yescharacteristic
60#81167—51nomaximal, Hall
61C4×C5×#41—31no—
62C2×#4016—31no—
63#65521—31no—
64#65521—31no—
65#65311—31no—
66#65311—31no—
67#65311—31no—
68#65311—31no—
69#65298—31no—
70#65298—31no—
71#65298—31no—
72#65298D311yescharacteristic, complemented
73#65284—31no—
74#65284—31no—
75#65213—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×C5×#67—21no—
79C22×C5×Dic3—21no—
80C22×C5×Dic3—21no—
81C5×#237—22no—
82C5×#237Q814yes—
83C2×C4×C5×D3D411yescharacteristic
84C2×C4×C5×D3D411yescharacteristic
85C2×C4×C5×D3C2311yescharacteristic
86C2×C5×Dic6C2311yescharacteristic
87C2×D3×Dic5—21no—
88C2×D3×Dic5—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95#6712—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C4×C5×Dic3—21no—
104C4×C5×Dic3—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3D411yescharacteristic
107C4×C5×Dic3D411yescharacteristic
108C4×C5×Dic3C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×#683—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6668—21no—
120#6668—21no—
121#6650—22no—
122#6650—22no—
123D3×#125—51no—
124C4×#237D511yescharacteristic
125C3×#478—51no—
126#5063—51no—
127#5009—51no—
128#4881—51no—
129#4877—51no—
130#4861—51no—
131#4857—51no—
132#4837—51no—
133#4829—51no—
134#4771—51no—
135#4771—51no—
136#4766—51no—
137#4763—51no—
138C2×C5×#41—31no—
139C4×C5×Q8—31no—
140C4×C5×Q8—31no—
141C4×C5×D4—31no—
142C4×C5×D4—61no—
143C4×C5×D4—61no—
144C4×C5×D4C2×D311yescharacteristic
145C5×#117—31no—
146C5×#117—61no—
147C2×C42×C5—31no—
148C2×C42×C5—61no—
149C2×C4⋊Dic5—31no—
150C2×C4⋊Dic5—31no—
151C2×#683—61no—
152C2×#683—61no—
153C2×#681—31no—
154C2×#681—31no—
155#4016—31no—
156#4016—31no—
157#4016—31no—
158#4016—61no—
159#4016—61no—
160#4016C2×D311yescharacteristic
161#3967—31no—
162#3967—31no—
163#3967—31no—
164#3967—31no—
165#3964—31no—
166#3964—31no—
167#3964C2×D311yescharacteristic
168#3964C2×D311yescharacteristic
169#3940—31no—
170#3940—31no—
171#3940—31no—
172#3940C2×D311yescharacteristic
173#3939—31no—
174#3939—31no—
175#3939—31no—
176#3939C2×D311yescharacteristic
177C4⋊#168—31no—
178C4⋊#168—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3080—151noSylow
182C23×C3×C5—21no—
183C22×C5×D3C2×D411yescharacteristic
184C3×C5×D4—21no—
185C3×C5×D4C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—42no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15—21no—
193C5×#67—24no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—24no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—42no—
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C4×C5×D3—41no—
202C4×C5×D3—41no—
203C4×C5×D3C2×Q812yes—
204C4×C5×D3#4112yes—
205C5×Dic6—21no—
206C5×Dic6C2×Q812yes—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209D3×Dic5—42no—
210D3×Dic5—42no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C3×#168—21no—
214C3×#168—21no—
215C2×#237C2×D511yescharacteristic
216C3×#125—51no—
217C3×C4×D4C2×D511yescharacteristic
218D4×Dic3C2×D511yescharacteristic
219C4×#67—21no—
220C2×C4×Dic3—21no—
221C2×ΓL(1,𝔽25)—51no—
222C2×ΓL(1,𝔽25)—51no—
223#892C2×D511yescharacteristic
224D3×C4⋊C4—51no—
225D3×C4⋊C4—51no—
226D3×C4⋊C4—101no—
227D3×C4⋊C4—101no—
228#890—51no—
229#890—51no—
230#889—101no—
231#889—101no—
232#887C2×D511yescharacteristic
233#67⋊C4—21no—
234#877—21no—
235C42×D3C2×D511yescharacteristic
236#870—51no—
237C4×Dic6C2×D511yescharacteristic
238C3×#107—51no—
239C3×#106—51no—
240C3×C4⋊C8—51no—
241C3×#102—51no—
242C3×#102—51no—
243#832—51no—
244#832—51no—
245#818—51no—
246#817—51no—
247#816—51no—
248#816—51no—
249Dic3⋊C8—51no—
250Dic3⋊C8—51no—
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C5×#41—34no—
259C5×#41—62no—
260C2×C5×Q8—31no—
261C2×C5×D4—61no—
262C2×C5×D4C22×D311yescharacteristic
263C22×C4×C5—21no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—61no—
268C22×C4×C5—61no—
269C22×Dic5—61no—
270C22×Dic5—61no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—61no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4C22×D311yescharacteristic
275C5×C22⋊C4—21no—
276C5×C22⋊C4—61no—
277C5×C22⋊C4—61no—
278C42×C5—31no—
279C42×C5—31no—
280C42×C5—31no—
281C42×C5—61no—
282C42×C5—61no—
283C42×C5—61no—
284C42×C5C22×D311yescharacteristic
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—61no—
288C4⋊Dic5—61no—
289C4⋊Dic5C22×D311yescharacteristic
290C4⋊Dic5C22×D311yescharacteristic
291#683—21no—
292#683—21no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#681—62no—
300#681—62no—
301C2×#168—31no—
302C2×#168—31no—
303C2×#168C22×D311yescharacteristic
304C2×#168C22×D311yescharacteristic
305C2×#125—151no—
306C4×#41—31no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—51no—
312#478—151no—
313#478—151no—
314#478—151no—
315#428—151no—
316#428—151no—
317#423—151no—
318#417—151no—
319#417—151no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5C22×D411yescharacteristic
324C2×C5×D3—21no—
325C2×C5×D3—21no—
326C2×C5×D3C22⋊Q812yes—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5—41no—
330C3×C4×C5C22×Q811yescharacteristic
331C3×C4×C5C2×#4111yescharacteristic
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—41no—
335C3×Dic5—41no—
336C5×Dic3—22no—
337C5×Dic3—21no—
338C5×Dic3—21no—
339C5×Dic3—41no—
340C5×Dic3C22⋊Q812yes—
341C2×C3×D4C22×D511yescharacteristic
342C22×C3×C4—21no—
343C2×#67—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346#237—22no—
347#237Dic1014yes—
348C2×C4×D3—101no—
349C2×C4×D3—101no—
350C2×C4×D3C22⋊D511yescharacteristic
351C2×C4×D3C22⋊D511yescharacteristic
352C2×C4×D3C22×D511yescharacteristic
353C2×Dic6C22×D511yescharacteristic
354C2×C3×C8—51no—
355C2×C3×C8—51no—
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4C22×D511yescharacteristic
361C3×C22⋊C4—21no—
362C3×C42C22×D511yescharacteristic
363#217—21no—
364(C2×D3)⋊C4—21no—
365C4⋊Dic3—51no—
366C4⋊Dic3—51no—
367C4⋊Dic3—101no—
368C4⋊Dic3—101no—
369C4⋊Dic3C22×D511yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3C22⋊D511yescharacteristic
382C4×Dic3C22⋊D511yescharacteristic
383C4×Dic3C22×D511yescharacteristic
384C2×C3⋊C8—51no—
385C2×C3⋊C8—51no—
386ΓL(1,𝔽25)—102no—
387ΓL(1,𝔽25)—102no—
388C23×C5—21no—
389C23×C5—31no—
390C5×Q8—32no—
391C5×Q8—61no—
392C5×D4—21no—
393C5×D4—64no—
394C5×D4D3×Q812yes—
395C2×C4×C5—21no—
396C2×C4×C5—31no—
397C2×C4×C5—32no—
398C2×C4×C5—32no—
399C2×C4×C5—31no—
400C2×C4×C5—31no—
401C2×C4×C5—42no—
402C2×C4×C5—64no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—121no—
406C2×C4×C5—121no—
407C2×C4×C5—122no—
408C2×C4×C5D3×D411yescharacteristic
409C2×C4×C5D3×D411yescharacteristic
410C2×C4×C5C23×D311yescharacteristic
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—122no—
416C2×Dic5—122no—
417#168—21no—
418#168—21no—
419#168—61no—
420#168—61no—
421C2×#41—31no—
422C2×M16—151no—
423C2×M16—151no—
424#125—51no—
425#125—151no—
426#125—151no—
427#125—151no—
428#125—301no—
429#125—301no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×D4—31no—
433C4×D4—61no—
434C4×D4—61no—
435C4×D4D3×D511yescharacteristic
436#117—31no—
437#117—61no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—301no—
441C2×C4⋊C4—301no—
442C2×C42—31no—
443C2×C42—61no—
444#107—51no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—51no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—51no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460#102—51no—
461#102—51no—
462#102—151no—
463#102—151no—
464C2×C3×C5—42no—
465C2×C3×C5C2×C22⋊Q811yescharacteristic
466C2×C3×C5#57511yescharacteristic
467C2×C3×C5#57511yescharacteristic
468C5×D3—22no—
469C23×C3—21no—
470C22×D3C2×C22⋊D511yescharacteristic
471C3×D4—21no—
472C3×D4C2×Dic1012yes—
473C2×C3×C4—21no—
474C2×C3×C4—42no—
475C2×C3×C4—101no—
476C2×C3×C4—101no—
477C2×C3×C4C2×C22⋊D511yescharacteristic
478C2×C3×C4C2×C22⋊D511yescharacteristic
479C2×C3×C4C23×D511yescharacteristic
480#67—24no—
481C2×Dic3—21no—
482C2×Dic3—24no—
483C2×Dic3—21no—
484C2×Dic3—42no—
485C2×Dic3—101no—
486C2×Dic3—101no—
487C2×Dic3C2×C22⋊D511yescharacteristic
488C2×Dic3C2×C22⋊D511yescharacteristic
489C2×Dic3C2×C22⋊D511yescharacteristic
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—202no—
493C4×D3—202no—
494C4×D3C2×Dic1012yes—
495C4×D3#70912yes—
496Dic6—21no—
497Dic6C2×Dic1012yes—
498C3×C8—101no—
499C3×C8—101no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5—22no—
503C22×C5—32no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—61no—
507C22×C5—61no—
508C22×C5C2×D3×D411yescharacteristic
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—32no—
512C4×C5—41no—
513C4×C5—61no—
514C4×C5—61no—
515C4×C5—62no—
516C4×C5—121no—
517C4×C5C2×D3×Q811yescharacteristic
518C4×C5D3×#4111yescharacteristic
519Dic5—41no—
520Dic5—41no—
521Dic5—121no—
522Dic5—121no—
523#41—34no—
524#41—62no—
525C2×Q8—31no—
526C2×D4—61no—
527C2×D4C2×D3×D511yescharacteristic
528C22×C4—21no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—301no—
535C22×C4—301no—
536M16—302no—
537M16—302no—
538C2×C8—51no—
539C2×C8—51no—
540C2×C8—151no—
541C2×C8—151no—
542C4⋊C4—31no—
543C4⋊C4—51no—
544C4⋊C4—51no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—151no—
550C4⋊C4—151no—
551C4⋊C4—301no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—61no—
562C22⋊C4—61no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—22no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3C22×C22⋊D511yescharacteristic
575C2×D3—21no—
576C2×D3—21no—
577C2×D3#407012yes—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—41no—
581C3×C4—201no—
582C3×C4—201no—
583C3×C4C22×Dic1011yescharacteristic
584C3×C4C2×#70911yescharacteristic
585Dic3—22no—
586Dic3—21no—
587Dic3—21no—
588Dic3—41no—
589Dic3—201no—
590Dic3—201no—
591Dic3#407012yes—
592C2×C5—42no—
593C2×C5—62no—
594C2×C5D3×C22⋊Q811yescharacteristic
595C2×C5#576811yescharacteristic
596C2×C5#577311yescharacteristic
597C23—21no—
598C23—31no—
599Q8—32no—
600Q8—61no—
601D4—21no—
602D4—64no—
603D4D3×Dic1012yes—
604C2×C4—21no—
605C2×C4—31no—
606C2×C4—32no—
607C2×C4—32no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—42no—
611C2×C4—64no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—121no—
617C2×C4—121no—
618C2×C4—122no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—602no—
622C2×C4—602no—
623C2×C4D3×C22⋊D511yescharacteristic
624C2×C4D3×C22⋊D511yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—101no—
627C8—101no—
628C8—301no—
629C8—301no—
630C2×C3—42no—
631C2×C3C2×#407011yescharacteristic
632C2×C3#6615611yescharacteristic
633C2×C3#6615611yescharacteristic
634D3—22no—
635C5#8116711yescharacteristic, complemented, Sylow
636C22—22no—
637C22—32no—
638C22—41no—
639C22—41no—
640C22—61no—
641C22—61no—
642C22C2×D3×C22⋊D511yescharacteristic
643C4—21no—
644C4—21no—
645C4—32no—
646C4—41no—
647C4—61no—
648C4—62no—
649C4—61no—
650C4—121no—
651C4—201no—
652C4—201no—
653C4—601no—
654C4—601no—
655C4C2×D3×Dic1011yescharacteristic
656C4D3×#70911yescharacteristic
657C3#1061424011yescharacteristic, complemented, Sylow
658C2—42no—
659C2—62no—
660C2D3×#407011yescharacteristic
661C2#1175469611yescharacteristic
662C2#1175532211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#237C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. D3×#4016C2semidirect
3. #11751110C2semidirect
4. C3×#65298C2semidirect
5. #11749088C2semidirect
6. #11749087C2semidirect
9. #11747396C2semidirect
10. #11747393C2semidirect
11. #11747191C2semidirect
12. #11747190C2semidirect
13. #11747011C2semidirect
14. #11746965C2semidirect
15. #11746926C2semidirect
72. #65298D3semidirect
570. C3×C5#3080semidirect
635. C5#81167semidirect
657. C3#10614240semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#2372
D3×#40162
#117511102
C3×#652982
#117490882
#117490872
#117489552
#117473962
#117473932
#117471912
#117471902
#117470112
#117469652
#117469262
#106142403
#811675