Finite Group Databasebeta

← #14436119

Subgroups — #14436119

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×#5625C211yesmaximal, characteristic, complemented
2#11754509C211yesmaximal, characteristic
3#11751145C211yesmaximal, characteristic, complemented
4C3×#65336C211yesmaximal, characteristic
5#11749256C211yesmaximal, characteristic, complemented
6#11749251C211yesmaximal, characteristic, complemented
7Dic3×#688C211yesmaximal, characteristic, complemented
8#11749227C211yesmaximal, characteristic, complemented
9#11748528C211yesmaximal, characteristic
10#11748447C211yesmaximal, characteristic, complemented
11#11748330C211yesmaximal, characteristic, complemented
12#11747296C211yesmaximal, characteristic, complemented
13#11747266C211yesmaximal, characteristic, complemented
14#11747249C211yesmaximal, characteristic, complemented
15#11747222C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C5×Q8×Dic3C2211yescharacteristic
21C5×#944C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C5×#924C2211yescharacteristic
24C5×#890—21no—
25C5×#890C2211yescharacteristic
26C5×#889—21no—
27C5×#887C2211yescharacteristic
28C5×#879—21no—
29C5×#879—21no—
30C2×C3×#689C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32#91559—21no—
33#91559—21no—
34Dic3×D20C2211yescharacteristic
35Dic3×D20C2211yescharacteristic
36D5×C4⋊Dic3—21no—
37#91358—21no—
38Dic3×Dic10C2211yescharacteristic
39Dic3×Dic10C2211yescharacteristic
40C2×#6661C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91119C2211yescharacteristic
43#91119C2211yescharacteristic
44#91114C2211yescharacteristic
45#91091C2211yescharacteristic
46#91091C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50#90985C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90973C2211yescharacteristic
55#90973C2211yescharacteristic
56#90970C2211yescharacteristic
57#90964C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80216—51nomaximal, Hall
61C5×#541—31no—
62#65857—31no—
63#65379—31no—
64#65372—31no—
65#65355—31no—
66#65352—31no—
67#65336—31no—
68#65336D311yescharacteristic
69#65333—31no—
70#65332—31no—
71#65319—31no—
72C4×#689—31no—
73#65315—31no—
74C4×#688—31no—
75#65289—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—21no—
79C2×C5×Dic6C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C3×#709—22no—
82C3×#709—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×Dic10C2311yescharacteristic
86C2×D5×Dic3—21no—
87C2×D5×Dic3—21no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C4⋊Dic15—21no—
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C5×#217—21no—
97C5×#217D411yescharacteristic
98C5×#217D411yescharacteristic
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3D411yescharacteristic
102C5×C4⋊Dic3D411yescharacteristic
103C5×C4⋊Dic3C2311yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C4×C5×Dic3—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C3×#689—22no—
114C3×#688—22no—
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117#6668—21no—
118#6668—21no—
119#6665—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6661—22no—
124#6655—22no—
125#5827—51no—
126#5625D511yescharacteristic, complemented
127C3×#452—51no—
128#5239—51no—
129#5184—51no—
130#5182—51no—
131#5162—51no—
132Dic3×SD16—51no—
133#5044—51no—
134#4799—51no—
135#4790—51no—
136#4763—51no—
137#4757—51no—
138#4721—51no—
139#4720—51no—
140C2×#709C2×D311yescharacteristic
141C5×C4⋊Q8—31no—
142C5×#126—61no—
143C5×#126—61no—
144C5×#125—31no—
145C5×#125—61no—
146C5×#125—61no—
147C5×C22⋊Q8—31no—
148C5×C22⋊Q8C2×D311yescharacteristic
149C4×C5×Q8—31no—
150C4×C5×Q8—31no—
151C5×#117—31no—
152C2×#689—31no—
153C2×#689C2×D311yescharacteristic
154C2×#688—31no—
155C2×#688C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157#4038—61no—
158D5×C4⋊C4—61no—
159#4027—61no—
160#4027—61no—
161C4×D20—31no—
162C4×D20—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3967—31no—
168#3967—31no—
169C22⋊#168—31no—
170C22⋊#168C2×D311yescharacteristic
171#3942—31no—
172#3942C2×D311yescharacteristic
173#3941—31no—
174#3941C2×D311yescharacteristic
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—81no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C5×Dic6—21no—
204C5×Dic6—21no—
205C3×C22⋊D5—24no—
206C2×C3×Dic5—21no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—24no—
210C3×Dic10—21no—
211C3×Dic10#4112yes—
212D5×Dic3—81no—
213D5×Dic3—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×C3×#41—51no—
219C2×C3×Q16—51no—
220C2×C3×SD16—51no—
221C3×C22⋊Q8C2×D511yescharacteristic
222Q8×Dic3—51no—
223Q8×Dic3—51no—
224Q8×Dic3C2×D511yescharacteristic
225#944C2×D511yescharacteristic
226C2×#216—51no—
227D4×Dic3—51no—
228D4×Dic3—51no—
229D4×Dic3—101no—
230D4×Dic3—101no—
231C2×#214—51no—
232#926—101no—
233#926C2×D511yescharacteristic
234C2×C4⋊Dic3—51no—
235C2×C4⋊Dic3—101no—
236#924C2×D511yescharacteristic
237#890—21no—
238#890C2×D511yescharacteristic
239#889—21no—
240#887C2×D511yescharacteristic
241#879—21no—
242#879—21no—
243C3×#103—51no—
244C3×#102—51no—
245C3×C22⋊C8—51no—
246#835—51no—
247#835—51no—
248#835—51no—
249#832—51no—
250#830—51no—
251#817—51no—
252#817—51no—
253#816—51no—
254#816—51no—
255#815—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258C8×Dic3—51no—
259#807—51no—
260#807—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—21no—
265C22×Dic5—61no—
266#709—22no—
267#709—22no—
268C2×D20C22×D311yescharacteristic
269C2×C4×D5—21no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4—61no—
284C5×C4⋊C4C22×D311yescharacteristic
285C5×C22⋊C4—21no—
286C5×C22⋊C4—31no—
287C5×C22⋊C4—31no—
288C5×C22⋊C4—61no—
289C42×C5—31no—
290C42×C5—31no—
291C42×C5—61no—
292C42×C5—61no—
293#689—22no—
294#689—62no—
295#688—22no—
296#688—62no—
297#685—61no—
298#685—61no—
299C4⋊Dic5—31no—
300C4⋊Dic5—31no—
301C4⋊Dic5—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—31no—
311#520—151no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—51no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—41no—
338Dic15—41no—
339C3×Dic5—22no—
340C5×Dic3—21no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×D4—51no—
351C2×C3×D4—101no—
352C22×C3×C4—101no—
353C22×C3×C4C22×D511yescharacteristic
354C22×Dic3—101no—
355C22×Dic3—101no—
356C22×Dic3—101no—
357C2×Dic6C22×D511yescharacteristic
358C3×Q16—102no—
359C3×SD16—102no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4C22×D511yescharacteristic
364C3×C22⋊C4—21no—
365#217—21no—
366#217—101no—
367#217—101no—
368#217C22⋊D511yescharacteristic
369#217C22⋊D511yescharacteristic
370#216—102no—
371#214—102no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378C4⋊Dic3—101no—
379C4⋊Dic3C22⋊D511yescharacteristic
380C4⋊Dic3C22⋊D511yescharacteristic
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3C22×D511yescharacteristic
392C4×Dic3C22×D511yescharacteristic
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5D3×D411yescharacteristic
396C22×D5—21no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—61no—
400C5×Q8—61no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—24no—
414C2×Dic5—21no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—241no—
418D20—21no—
419D20#23712yes—
420C4×D5—24no—
421C4×D5—241no—
422C4×D5—241no—
423Dic10—21no—
424Dic10#23712yes—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41—51no—
430C2×Q16—51no—
431C2×Q16—151no—
432C2×SD16—51no—
433C2×SD16—151no—
434C4⋊Q8—31no—
435#126—61no—
436#126—61no—
437#125—31no—
438#125—61no—
439#125—61no—
440C22⋊Q8—31no—
441C22⋊Q8D3×D511yescharacteristic
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—31no—
451#117—301no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—51no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—51no—
467#102—151no—
468C22⋊C8—51no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—42no—
477C23×C3—101no—
478C23×C3C2×C22⋊D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—52no—
482C3×Q8—101no—
483C3×D4—52no—
484C3×D4—104no—
485C3×D4—101no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—104no—
491C2×C3×C4—101no—
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—401no—
499C2×Dic3—401no—
500C2×Dic3—401no—
501C2×Dic3C2×C22⋊D511yescharacteristic
502C2×Dic3C2×C22⋊D511yescharacteristic
503C2×Dic3C2×C22⋊D511yescharacteristic
504C2×Dic3C2×C22⋊D511yescharacteristic
505Dic6—21no—
506Dic6—21no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—61no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—61no—
525C4×C5—121no—
526C4×C5—121no—
527C4×C5C2×#23711yescharacteristic
528C4×C5C2×#23711yescharacteristic
529Dic5—22no—
530Dic5—121no—
531Dic5—121no—
532#41—102no—
533#41—102no—
534C2×Q8—31no—
535C2×Q8—51no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—101no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—102no—
545Q16—302no—
546SD16—102no—
547SD16—302no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—151no—
564C4⋊C4—151no—
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—31no—
577C42—61no—
578C42—61no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—102no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C22×C22⋊D511yescharacteristic
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—102no—
593C3×C4D5×#4111yescharacteristic
594C3×C4D5×#4111yescharacteristic
595Dic3—21no—
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#558611yescharacteristic
605C2×C5#577011yescharacteristic
606C2×C5#577911yescharacteristic
607D5—42no—
608C23—101no—
609C23D3×C22⋊D511yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—52no—
613Q8—61no—
614Q8—61no—
615Q8—101no—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—104no—
630C2×C4—101no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—1201no—
634C2×C4—1201no—
635C2×C4—1201no—
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—202no—
644C2×C3#6616211yescharacteristic
645C2×C3#6617111yescharacteristic
646C2×C3#6617211yescharacteristic
647C5#8021611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—61no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—102no—
663C4—121no—
664C4—121no—
665C4—601no—
666C4—601no—
667C4D5×#23711yescharacteristic
668C4D5×#23711yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—202no—
672C2#1175480111yescharacteristic
673C2#1175511411yescharacteristic
674C2#1175532611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5625C2semidirect
3. #11751145C2semidirect
5. #11749256C2semidirect
6. #11749251C2semidirect
7. Dic3×#688C2semidirect
8. #11749227C2semidirect
10. #11748447C2semidirect
11. #11748330C2semidirect
12. #11747296C2semidirect
13. #11747266C2semidirect
14. #11747249C2semidirect
15. #11747222C2semidirect
126. #5625D5semidirect
581. C3×C5#3120semidirect
647. C5#80216semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C5×#56252
#117545092
#117511452
C3×#653362
#117492562
#117492512
Dic3×#6882
#117492272
#117485282
#117484472
#117483302
#117472962
#117472662
#117472492
#117472222
#106151773
#802165