Finite Group Databasebeta

← #14436167

Subgroups — #14436167

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5546C211yesmaximal, characteristic
2#11752479C211yesmaximal, characteristic, complemented
3#11751110C211yesmaximal, characteristic, complemented
4C3×#65308C211yesmaximal, characteristic, complemented
5#11749059C211yesmaximal, characteristic
6#11749059C211yesmaximal, characteristic
7#11749010C211yesmaximal, characteristic, complemented
8Dic3×#687C211yesmaximal, characteristic, complemented
9#11747349C211yesmaximal, characteristic, complemented
10#11747348C211yesmaximal, characteristic, complemented
11#11747267C211yesmaximal, characteristic, complemented
12#11747266C211yesmaximal, characteristic, complemented
13#11747099C211yesmaximal, characteristic, complemented
14#11746965C211yesmaximal, characteristic, complemented
15#11746854C211yesmaximal, characteristic, complemented
16#10614306—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×D4×Dic3C2211yescharacteristic
21C4×C5×#67—21no—
22C2×C5×Dic3⋊C4—21no—
23C5×D3×C4⋊C4C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C5×#67⋊C4—21no—
26C5×#877—21no—
27C5×#872C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic
31C3×#4015C2211yescharacteristic
32#91369C2211yescharacteristic
33#91369C2211yescharacteristic
34#91341—21no—
35#91341—21no—
36#91339—21no—
37#91339—21no—
38Dic3×Dic10C2211yescharacteristic
39Dic3×Dic10C2211yescharacteristic
40C2×#6661C2211yescharacteristic
41C2×#6661C2211yescharacteristic
42#91116C2211yescharacteristic
43#91116C2211yescharacteristic
44#91092C2211yescharacteristic
45#91091C2211yescharacteristic
46C4⋊(C3⋊#168)C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50#90988C2211yescharacteristic
51#90985C2211yescharacteristic
52#90973C2211yescharacteristic
53#90973C2211yescharacteristic
54#90970C2211yescharacteristic
55#90970C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80412—51nomaximal, Hall
61C5×#520—31no—
62#65852—31no—
63#65528—31no—
64#65528—31no—
65#65320—31no—
66#65319—31no—
67C4×#689—31no—
68#65311—31no—
69#65308D311yescharacteristic, complemented
70#65307—31no—
71C4×#687—31no—
72#65298—31no—
73#65289—31no—
74#65260—31no—
75#65259—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×#237—22no—
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3C2311yescharacteristic
85C2×C5×Dic6C2311yescharacteristic
86C2×C3×Dic10C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C22⋊C4—21no—
90C3×C42×C5C2311yescharacteristic
91C4⋊Dic15C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94#6712—21no—
95C2×C3⋊#168C2311yescharacteristic
96C2×C3⋊#168C2311yescharacteristic
97C5×#217—21no—
98C5×(C2×D3)⋊C4D411yescharacteristic
99C5×(C2×D3)⋊C4D411yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4D411yescharacteristic
105C5×Dic3⋊C4D411yescharacteristic
106C4×C5×Dic3—21no—
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C3×#687—22no—
110C3×#687—22no—
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119(C2×D3)⋊Dic5—21no—
120(C2×D3)⋊Dic5—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6661—22no—
124#6661—22no—
125#5731—51no—
126#5546D511yescharacteristic
127C3×#461—51no—
128#5173—51no—
129#5173—51no—
130#5164—51no—
131Dic3×SD16—51no—
132#5090—51no—
133#5009—51no—
134#4840—51no—
135#4829—51no—
136#4811—51no—
137#4805—51no—
138#4790—51no—
139#4789—51no—
140C2×C5×#41—31no—
141C4×C5×Q8—31no—
142C4×C5×Q8—31no—
143C4×C5×D4—31no—
144C4×C5×D4—61no—
145C4×C5×D4—61no—
146C4×C5×D4C2×D311yescharacteristic
147C5×#117—31no—
148C5×#117—61no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—61no—
151C2×#689—31no—
152C2×#689—31no—
153C2×#687C2×D311yescharacteristic
154C2×#687C2×D311yescharacteristic
155#4070—31no—
156#4070—31no—
157#4035—61no—
158#4035—61no—
159#4025—61no—
160#4025—61no—
161#4016—31no—
162#4015C2×D311yescharacteristic
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3942C2×D311yescharacteristic
174#3942C2×D311yescharacteristic
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C23×C3×C5—21no—
185C22×C5×D3C2×D411yescharacteristic
186C3×C5×D4—21no—
187C3×C5×D4#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—81no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195C5×#67—24no—
196C2×C5×Dic3—24no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—81no—
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C4×C5×D3—21no—
204C4×C5×D3—21no—
205C4×C5×D3—81no—
206C5×Dic6—21no—
207C5×Dic6#4112yes—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—21no—
213C3×Dic10—21no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#237C2×D511yescharacteristic
219C2×C3×SD16—51no—
220C2×C3×SD16—51no—
221C3×C4⋊Q8—51no—
222C3×C4×D4C2×D511yescharacteristic
223#946—51no—
224#946—51no—
225Q8×Dic3—51no—
226Q8×Dic3—51no—
227C2×#216—51no—
228C2×#216—51no—
229D4×Dic3C2×D511yescharacteristic
230C4×#67—21no—
231C2×Dic3⋊C4—21no—
232#898—101no—
233#898—101no—
234D3×C4⋊C4C2×D511yescharacteristic
235#889—101no—
236#889—101no—
237#887C2×D511yescharacteristic
238#67⋊C4—21no—
239#877—21no—
240#872C2×D511yescharacteristic
241#870—51no—
242C4×Dic6C2×D511yescharacteristic
243C3×C4⋊C8—51no—
244C3×#103—51no—
245C3×#103—51no—
246#835—51no—
247#835—51no—
248#832—51no—
249#832—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252#818—51no—
253#817—51no—
254#816—51no—
255#816—51no—
256#815—51no—
257C8×Dic3—51no—
258#808—51no—
259#807—51no—
260C4⋊(C3⋊C8)—51no—
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8—31no—
264C2×C5×D4—61no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—21no—
267C22×C4×C5—31no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5—61no—
271C2×Dic10C22×D311yescharacteristic
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—21no—
281C5×C22⋊C4—31no—
282C5×C22⋊C4—31no—
283C5×C22⋊C4—61no—
284C42×C5—31no—
285C42×C5—61no—
286C42×C5—61no—
287C42×C5C22×D311yescharacteristic
288C22⋊Dic5—61no—
289C22⋊Dic5—61no—
290#689—62no—
291#689—62no—
292#687—22no—
293#687—22no—
294C4⋊Dic5—21no—
295C4⋊Dic5—21no—
296C4⋊Dic5—31no—
297C4⋊Dic5—31no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168—31no—
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310#541—151no—
311#520—31no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—51no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—22no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—21no—
330C2×C5×D3—21no—
331C2×C5×D3—21no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—41no—
338Dic15—41no—
339C3×Dic5—41no—
340C3×Dic5—41no—
341C5×Dic3—22no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—41no—
346C2×C3×Q8—51no—
347C2×C3×Q8—51no—
348C2×C3×D4C22×D511yescharacteristic
349C22×C3×C4—21no—
350C2×#67—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353#237—22no—
354#237—22no—
355C2×C4×D3—21no—
356C2×C4×D3C22×D511yescharacteristic
357C2×Dic6C22×D511yescharacteristic
358C3×SD16—102no—
359C3×SD16—102no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—21no—
366C3×C42C22×D511yescharacteristic
367#217—21no—
368#216—102no—
369#216—102no—
370(C2×D3)⋊C4—101no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4C22⋊D511yescharacteristic
373(C2×D3)⋊C4C22⋊D511yescharacteristic
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378C4⋊Dic3C22×D511yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4C22⋊D511yescharacteristic
387Dic3⋊C4C22⋊D511yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—101no—
391C4×Dic3—101no—
392C4×Dic3C22×D511yescharacteristic
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5—21no—
396C23×C5—31no—
397C5×Q8—32no—
398C5×Q8—61no—
399C5×D4—21no—
400C5×D4—64no—
401C5×D4#23712yes—
402C2×C4×C5—21no—
403C2×C4×C5—31no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—64no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—81no—
412C2×C4×C5—241no—
413C2×C4×C5—241no—
414C2×C4×C5D3×D411yescharacteristic
415C2×C4×C5D3×D411yescharacteristic
416C2×C4×C5C23×D311yescharacteristic
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421Dic10—21no—
422Dic10—21no—
423Dic10—21no—
424Dic10—21no—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41—31no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—51no—
433C2×SD16—51no—
434C4⋊Q8—51no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—151no—
441C22⋊Q8—151no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—31no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4D3×D511yescharacteristic
450#117—31no—
451#117—61no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—51no—
459C4⋊C8—151no—
460#103—51no—
461#103—51no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—42no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C5×D3—41no—
477C23×C3—21no—
478C22×D3C2×C22⋊D511yescharacteristic
479C3×Q8—101no—
480C3×Q8—101no—
481C3×Q8—101no—
482C3×Q8—101no—
483C3×D4—21no—
484C3×D4#70912yes—
485C2×C3×C4—21no—
486C2×C3×C4—81no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4C2×C22⋊D511yescharacteristic
490C2×C3×C4C2×C22⋊D511yescharacteristic
491C2×C3×C4C23×D511yescharacteristic
492#67—24no—
493C2×Dic3—24no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—81no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3C2×C22⋊D511yescharacteristic
500C2×Dic3C2×C22⋊D511yescharacteristic
501C2×Dic3C2×C22⋊D511yescharacteristic
502C4×D3—21no—
503C4×D3—21no—
504C4×D3—81no—
505Dic6—21no—
506Dic6#70912yes—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—61no—
515C22×C5—61no—
516C22×C5—61no—
517C22×C5C2×D3×D411yescharacteristic
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—41no—
521C4×C5—61no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—62no—
525C4×C5—121no—
526C4×C5C2×#23711yescharacteristic
527C4×C5D3×#4111yescharacteristic
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8—51no—
536C2×Q8—51no—
537C2×D4—61no—
538C2×D4C2×D3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—31no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544Q16—302no—
545Q16—302no—
546SD16—102no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—151no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—61no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—301no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—22no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3C22×C22⋊D511yescharacteristic
586C2×D3—21no—
587C2×D3—21no—
588C2×D3—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—201no—
593C3×C4—201no—
594C3×C4C2×#70911yescharacteristic
595C3×C4C2×#70911yescharacteristic
596Dic3—22no—
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—42no—
604C2×C5—121no—
605C2×C5#560611yescharacteristic
606C2×C5#576211yescharacteristic
607C2×C5#577911yescharacteristic
608C23—21no—
609C23—31no—
610Q8—32no—
611Q8—61no—
612Q8—101no—
613Q8—101no—
614Q8—101no—
615Q8—101no—
616D4—21no—
617D4—64no—
618D4#676512yes—
619C2×C4—21no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—64no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—81no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—241no—
632C2×C4—241no—
633C2×C4—301no—
634C2×C4—301no—
635C2×C4D3×C22⋊D511yescharacteristic
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—42no—
643C2×C3#6612511yescharacteristic
644C2×C3#6617011yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—41no—
647C5#8041211yescharacteristic, complemented, Sylow
648C22—22no—
649C22—41no—
650C22—41no—
651C22—61no—
652C22—61no—
653C22—61no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—21no—
657C4—41no—
658C4—61no—
659C4—61no—
660C4—62no—
661C4—61no—
662C4—121no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#676511yescharacteristic
668C4D3×#70911yescharacteristic
669C3#1061430611yescharacteristic, complemented, Sylow
670C2—42no—
671C2—121no—
672C2#1175434111yescharacteristic
673C2#1175471111yescharacteristic
674C2#1175534111yescharacteristic
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#3120
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. #11752479C2semidirect
3. #11751110C2semidirect
4. C3×#65308C2semidirect
7. #11749010C2semidirect
8. Dic3×#687C2semidirect
9. #11747349C2semidirect
10. #11747348C2semidirect
11. #11747267C2semidirect
12. #11747266C2semidirect
13. #11747099C2semidirect
14. #11746965C2semidirect
15. #11746854C2semidirect
69. #65308D3semidirect
581. C3×C5#3120semidirect
647. C5#80412semidirect
669. C3#10614306semidirect

Maximal subgroups

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

subgroupindex
C5×#55462
#117524792
#117511102
C3×#653082
#117490592
#117490102
Dic3×#6872
#117473492
#117473482
#117472672
#117472662
#117470992
#117469652
#117468542
#106143063
#804125