Finite Group Databasebeta

← #14430957

Subgroups — #14430957

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752646C211yesmaximal, characteristic
2#11752516C211yesmaximal, characteristic
3#11750930C211yesmaximal, characteristic, complemented
4C5×#4851C211yesmaximal, characteristic, complemented
5C3×#65128C211yesmaximal, characteristic
6#11748122C211yesmaximal, characteristic
7#11747860C211yesmaximal, characteristic, complemented
8#11747852C211yesmaximal, characteristic, complemented
9#11747846C211yesmaximal, characteristic, complemented
10#11747844C211yesmaximal, characteristic, complemented
11#11747671C211yesmaximal, characteristic
12#11747618C211yesmaximal, characteristic
13D5×#816C211yesmaximal, characteristic
14#11746965C211yesmaximal, characteristic, complemented
15#11746963C211yesmaximal, characteristic, complemented
16#10612744—31nomaximal, Hall
17C2×D5×Dic6C2211yescharacteristic
18#91759C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C2×C3×#676C2211yescharacteristic
23C2×C3×C8×D5C2211yescharacteristic
24C3×#4018C2211yescharacteristic
25#91468C2211yescharacteristic
26#91430—21no—
27#91421—21no—
28D5×C4⋊Dic3C2211yescharacteristic
29#91394—21no—
30#91393—21no—
31#91388C2211yescharacteristic
32#91358C2211yescharacteristic
33#91358C2211yescharacteristic
34#91335—21no—
35#91333C2211yescharacteristic
36Dic5×Dic6C2211yescharacteristic
37#91329—21no—
38#91325—21no—
39#91324—21no—
40C3×C5×C4⋊C8C2211yescharacteristic
41#91102C2211yescharacteristic
42#91101C2211yescharacteristic
43#91100C2211yescharacteristic
44#91100C2211yescharacteristic
45C5×#817C2211yescharacteristic
46C5×#817C2211yescharacteristic
47C5×#816C2211yescharacteristic
48C5×#816C2211yescharacteristic
49C3×#3946C2211yescharacteristic
50C3×#3946C2211yescharacteristic
51C3×C4⋊#168C2211yescharacteristic
52#90988C2211yescharacteristic
53#90988C2211yescharacteristic
54#90988C2211yescharacteristic
55#90985C2211yescharacteristic
56#90975C2211yescharacteristic
57#90975C2211yescharacteristic
58#90973C2211yescharacteristic
59#90973C2211yescharacteristic
60#79101—51nomaximal, Hall
61#66063—31no—
62#65906—31no—
63C5×#475—31no—
64#65380—31no—
65#65311—31no—
66#65150—31no—
67#65149—31no—
68#65146—31no—
69#65143—31no—
70#65128D311yescharacteristic
71#65118—31no—
72#65091—31no—
73D5×#103—31no—
74#65088—31no—
75#65083—31no—
76C2×Dic30C2311yescharacteristic
77C2×C5×Dic6—21no—
78C2×C5×Dic6C2311yescharacteristic
79C2×C3×C4×D5C2311yescharacteristic
80C2×#1204—21no—
81C2×#1204—21no—
82C2×D5×Dic3—21no—
83C2×D5×Dic3—21no—
84D5×Dic6—22no—
85D5×Dic6Q814yescomplemented
86C2×C3×C5×C8C2311yescharacteristic
87C2×C3×C5×C8C2311yescharacteristic
88C3×C42×C5C2311yescharacteristic
89C4⋊Dic15C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91C4⋊Dic15C2311yescharacteristic
92#6712—21no—
93#6712—21no—
94#6712—21no—
95C4×Dic15—21no—
96C5×C4⋊Dic3—21no—
97C5×C4⋊Dic3C2311yescharacteristic
98C5×C4⋊Dic3C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C4×C5×Dic3—21no—
102C3×#685D411yescharacteristic
103C3×#685D411yescharacteristic
104C3×#683D411yescharacteristic
105C3×#683D411yescharacteristic
106C3×C4×Dic5C2311yescharacteristic
107C2×C3×#168C2311yescharacteristic
108C2×C3×#168C2311yescharacteristic
109C3×#676—22no—
110C3×C8×D5—22no—
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5—21no—
113#6669—21no—
114#6669—21no—
115#6668—21no—
116#6668—21no—
117#6665—21no—
118#6665—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#5519—51no—
124#5516—51no—
125C3×#424—51no—
126#5121—51no—
127#5120—51no—
128#5106—51no—
129C2×#816—51no—
130#4851—51no—
131#4851D511yescharacteristic, complemented
132#4850—51no—
133#4850—51no—
134#4829—51no—
135#4829—51no—
136#4829—51no—
137#4829—51no—
138C2×Q8×D5—31no—
139C5×C4⋊Q8—31no—
140C4×C5×Q8—31no—
141#4092—61no—
142Q8×Dic5—31no—
143#4090—61no—
144C2×#676C2×D311yescharacteristic
145C2×C8×D5C2×D311yescharacteristic
146#4042—61no—
147#4038—31no—
148#4038—31no—
149#4038—61no—
150D5×C4⋊C4—31no—
151#4036—31no—
152#4035—61no—
153#4034—31no—
154#4033—31no—
155#4033—61no—
156#4018—61no—
157#4018C2×D311yescharacteristic
158#4016—31no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#106—31no—
162C5×#106—31no—
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946C2×D311yescharacteristic
173#3946C2×D311yescharacteristic
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168C2×D311yescharacteristic
181#3082—151noSylow
182C22×C3×D5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C5×Dic6—21no—
197C5×Dic6—81no—
198C5×Dic6C2×Q812yes—
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C3×C4×D5C2×Q812yes—
203C3×C4×D5#4112yes—
204#1204—24no—
205#1204—81no—
206D5×Dic3—24no—
207D5×Dic3—81no—
208C3×C5×C8—21no—
209C3×C5×C8—21no—
210C3×#168—21no—
211C3×#168—21no—
212C22×Dic6—51no—
213C2×C3×M16—51no—
214C22×C3×C8—51no—
215C3×#117—51no—
216#926—51no—
217#926—51no—
218C2×C4⋊Dic3—51no—
219#890—101no—
220#888—101no—
221#887—101no—
222#887—101no—
223#878—101no—
224#878—101no—
225#877—101no—
226#877—101no—
227#870—51no—
228#870—51no—
229#869—51no—
230#869C2×D511yescharacteristic
231C4×Dic6—51no—
232C4×Dic6—51no—
233C4×Dic6—51no—
234C4×Dic6C2×D511yescharacteristic
235C3×C4⋊C8—51no—
236C3×C4⋊C8—51no—
237C3×C4⋊C8—51no—
238C3×C4⋊C8C2×D511yescharacteristic
239#818—51no—
240#818—51no—
241#818—51no—
242#818—51no—
243#817—51no—
244#817—51no—
245#817C2×D511yescharacteristic
246#817C2×D511yescharacteristic
247#816—51no—
248#816—51no—
249#816—51no—
250#816—51no—
251#816—51no—
252#816—51no—
253#816C2×D511yescharacteristic
254#816C2×D511yescharacteristic
255C2×C5×Q8—31no—
256C2×C5×Q8—61no—
257Q8×D5—34no—
258Q8×D5—62no—
259C2×C4×D5—61no—
260C2×C4×D5—61no—
261C2×C4×D5C22×D311yescharacteristic
262C2×Dic10—31no—
263C2×Dic10—61no—
264C2×Dic10—61no—
265C2×C5×C8C22×D311yescharacteristic
266C2×C5×C8C22×D311yescharacteristic
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—61no—
271C5×C4⋊C4—61no—
272C42×C5—61no—
273C42×C5C22×D311yescharacteristic
274#685—61no—
275#685—61no—
276#685D1211yescharacteristic
277#685D1211yescharacteristic
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283#683—61no—
284#683—61no—
285#683—61no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683D1211yescharacteristic
291#683D1211yescharacteristic
292C4×Dic5—61no—
293C4×Dic5—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5C22×D311yescharacteristic
298C2×#168C22×D311yescharacteristic
299C2×#168C22×D311yescharacteristic
300#676—22no—
301C8×D5—22no—
302#544—151no—
303#519—151no—
304#479—151no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—151no—
309#477—151no—
310#475—31no—
311#475—151no—
312#428—151no—
313#427—151no—
314#424—51no—
315#419—151no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C3×D5—21no—
319C2×C3×D5—21no—
320C2×C3×D5C22⋊Q812yes—
321C3×C4×C5—21no—
322C3×C4×C5—21no—
323C3×C4×C5C22×Q811yescharacteristic
324C3×C4×C5C2×#4111yescharacteristic
325Dic15—22no—
326Dic15—41no—
327Dic15—41no—
328Dic15—41no—
329C3×Dic5—21no—
330C3×Dic5—21no—
331C3×Dic5C22⋊Q812yes—
332C5×Dic3—22no—
333C5×Dic3—41no—
334C5×Dic3—41no—
335C5×Dic3—41no—
336C22×C3×C4—51no—
337C22×Dic3—101no—
338C22×Dic3—101no—
339C2×Dic6—21no—
340C2×Dic6—51no—
341C2×Dic6—54no—
342C2×Dic6—102no—
343C2×Dic6—101no—
344C2×Dic6—101no—
345C2×Dic6C22×D511yescharacteristic
346C3×M16—102no—
347C2×C3×C8—51no—
348C2×C3×C8—51no—
349C2×C3×C8—102no—
350C2×C3×C8C22×D511yescharacteristic
351C2×C3×C8C22×D511yescharacteristic
352C3×C4⋊C4—51no—
353C3×C4⋊C4—51no—
354C3×C22⋊C4—51no—
355C3×C22⋊C4—51no—
356C3×C42—51no—
357C3×C42C22×D511yescharacteristic
358#217—101no—
359#217—101no—
360C4⋊Dic3—21no—
361C4⋊Dic3—51no—
362C4⋊Dic3—51no—
363C4⋊Dic3—51no—
364C4⋊Dic3—101no—
365C4⋊Dic3—101no—
366C4⋊Dic3C22×D511yescharacteristic
367C4⋊Dic3C22×D511yescharacteristic
368C4⋊Dic3C22×D511yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377C4×Dic3—21no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3—101no—
382C4×Dic3—101no—
383C22×D5C2×D1211yescharacteristic
384C5×Q8—32no—
385C5×Q8—61no—
386C5×Q8—241no—
387C2×C4×C5—61no—
388C2×C4×C5—61no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
391C2×C4×C5C2×D1211yescharacteristic
392C2×C4×C5C2×D1211yescharacteristic
393C2×C4×C5C23×D311yescharacteristic
394C2×Dic5—61no—
395C2×Dic5—61no—
396C2×Dic5—61no—
397C2×Dic5—61no—
398C2×Dic5C2×D1211yescharacteristic
399C2×Dic5C2×D1211yescharacteristic
400C2×Dic5C2×D1211yescharacteristic
401C4×D5—64no—
402C4×D5—241no—
403C4×D5#23712yes—
404C4×D5D3×Q812yes—
405Dic10—32no—
406Dic10—61no—
407Dic10—64no—
408Dic10—241no—
409C5×C8—21no—
410C5×C8—21no—
411#168—21no—
412#168—21no—
413C22×Q8—151no—
414C2×M16—51no—
415C22×C8—51no—
416C4⋊Q8—31no—
417C4⋊Q8—151no—
418C4⋊Q8—301no—
419#125—151no—
420#125—151no—
421#125—301no—
422C22⋊Q8—301no—
423C22⋊Q8—301no—
424C4×Q8—31no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—51no—
431#117—151no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—151no—
436#107—151no—
437#107—151no—
438#107—151no—
439#107—151no—
440#106—31no—
441#106—31no—
442#106—151no—
443#106—151no—
444C4⋊C8—51no—
445C4⋊C8—51no—
446C4⋊C8—51no—
447C4⋊C8D3×D511yescharacteristic
448#103—31no—
449#103—31no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103—151no—
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C3×D5—22no—
460C23×C3—51no—
461C2×C3×C4—51no—
462C2×C3×C4—52no—
463C2×C3×C4—52no—
464C2×C3×C4—51no—
465C2×C3×C4—51no—
466C2×C3×C4D4×D511yescharacteristic
467C2×C3×C4D4×D511yescharacteristic
468C2×C3×C4C23×D511yescharacteristic
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—104no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C2×Dic3—401no—
479Dic6—21no—
480Dic6—52no—
481Dic6—81no—
482Dic6—104no—
483Dic6—101no—
484Dic6—401no—
485Dic6Q8×D512yes—
486C3×C8—21no—
487C3×C8—21no—
488C3×C8—101no—
489C3×C8—101no—
490C22×C5C22×D1211yescharacteristic
491C2×D5—21no—
492C2×D5—21no—
493C2×D5#89712yes—
494C4×C5—21no—
495C4×C5—21no—
496C4×C5—62no—
497C4×C5—121no—
498C4×C5—121no—
499C4×C5—121no—
500C4×C5C2×#23711yescharacteristic
501C4×C5C2×D3×Q811yescharacteristic
502Dic5—21no—
503Dic5—21no—
504Dic5—62no—
505Dic5—121no—
506Dic5—121no—
507Dic5—121no—
508Dic5#89712yes—
509C2×Q8—31no—
510C2×Q8—61no—
511C2×Q8—154no—
512C2×Q8—151no—
513C2×Q8—301no—
514C2×Q8—301no—
515C2×Q8—302no—
516C22×C4—51no—
517C22×C4—301no—
518C22×C4—301no—
519M16—102no—
520C2×C8—51no—
521C2×C8—51no—
522C2×C8—102no—
523C2×C8C2×D3×D511yescharacteristic
524C2×C8C2×D3×D511yescharacteristic
525C4⋊C4—31no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—51no—
529C4⋊C4—51no—
530C4⋊C4—61no—
531C4⋊C4—61no—
532C4⋊C4—151no—
533C4⋊C4—151no—
534C4⋊C4—151no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4—301no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C22⋊C4—51no—
545C22⋊C4—51no—
546C22⋊C4—301no—
547C22⋊C4—301no—
548C42—51no—
549C42—61no—
550C42—301no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42C2×D3×D511yescharacteristic
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3—52no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3C2×D4×D511yescharacteristic
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—52no—
564C3×C4—101no—
565C3×C4—101no—
566C3×C4C2×Q8×D511yescharacteristic
567C3×C4D5×#4111yescharacteristic
568Dic3—22no—
569Dic3—41no—
570Dic3—41no—
571Dic3—41no—
572Dic3—102no—
573Dic3—201no—
574Dic3—201no—
575Dic3—201no—
576C2×C5C2×#89711yescharacteristic
577C2×C5#575111yescharacteristic
578C2×C5#575311yescharacteristic
579D5—22no—
580C23—51no—
581Q8—32no—
582Q8—61no—
583Q8—152no—
584Q8—241no—
585Q8—304no—
586Q8—301no—
587Q8—1201no—
588C2×C4—51no—
589C2×C4—52no—
590C2×C4—52no—
591C2×C4—51no—
592C2×C4—51no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—304no—
598C2×C4—301no—
599C2×C4—301no—
600C2×C4—301no—
601C2×C4—301no—
602C2×C4—1201no—
603C2×C4D5×D1211yescharacteristic
604C2×C4D5×D1211yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—21no—
608C8—101no—
609C8—101no—
610C2×C3—102no—
611C2×C3D5×C22⋊Q811yescharacteristic
612C2×C3#6609611yescharacteristic
613C2×C3#6611311yescharacteristic
614C5#7910111yescharacteristic, complemented, Sylow
615C22—52no—
616C22—101no—
617C22—101no—
618C22C2×D5×D1211yescharacteristic
619C4—21no—
620C4—21no—
621C4—52no—
622C4—62no—
623C4—101no—
624C4—101no—
625C4—121no—
626C4—121no—
627C4—121no—
628C4—302no—
629C4—601no—
630C4—601no—
631C4—601no—
632C4D5×#23711yescharacteristic
633C4D3×Q8×D511yescharacteristic
634C3#1061274411yescharacteristic, complemented, Sylow
635C2—102no—
636C2D5×#89711yescharacteristic
637C2#1175396011yescharacteristic
638C2#1175404011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11750930C2semidirect
4. C5×#4851C2semidirect
7. #11747860C2semidirect
8. #11747852C2semidirect
9. #11747846C2semidirect
10. #11747844C2semidirect
14. #11746965C2semidirect
15. #11746963C2semidirect
85. D5×Dic6Q8semidirect
131. #4851D5semidirect
556. C3×C5#3082semidirect
614. C5#79101semidirect
634. C3#10612744semidirect

Maximal subgroups

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

subgroupindex
#117526462
#117525162
#117509302
C5×#48512
C3×#651282
#117481222
#117478602
#117478522
#117478462
#117478442
#117476712
#117476182
D5×#8162
#117469652
#117469632
#106127443
#791015