Finite Group Databasebeta

← #14436077

Subgroups — #14436077

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
1C3×C5×#541C211yesmaximal, characteristic, complemented
2#11756282C211yesmaximal, characteristic
3#11751191C211yesmaximal, characteristic, complemented
4#11751184C211yesmaximal, characteristic, complemented
5#11751167C211yesmaximal, characteristic, complemented
6#11751164C211yesmaximal, characteristic, complemented
7#11751148C211yesmaximal, characteristic
8#11751148C211yesmaximal, characteristic
9#11751145C211yesmaximal, characteristic, complemented
10#11751144C211yesmaximal, characteristic, complemented
11#11751131C211yesmaximal, characteristic, complemented
12C4×#6718C211yesmaximal, characteristic, complemented
13#11751127C211yesmaximal, characteristic, complemented
14C4×#6717C211yesmaximal, characteristic, complemented
15#11751101C211yesmaximal, characteristic, complemented
16#10615177—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#126—21no—
21C3×C5×#125—21no—
22C3×C5×#125—21no—
23C3×C5×#125C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×C22⋊Q8C2211yescharacteristic
26C3×C4×C5×Q8C2211yescharacteristic
27C3×C4×C5×Q8C2211yescharacteristic
28C3×C5×#117C2211yescharacteristic
29C2×#6718C2211yescharacteristic
30C2×#6718C2211yescharacteristic
31C2×#6717C2211yescharacteristic
32C2×#6717C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic
34#91781—21no—
35C4⋊C4×D15—21no—
36#91770—21no—
37#91770—21no—
38C4×D60C2211yescharacteristic
39C4×D60C2211yescharacteristic
40C4×Dic30C2211yescharacteristic
41C4×Dic30C2211yescharacteristic
42#91119C2211yescharacteristic
43#91119C2211yescharacteristic
44#91119C2211yescharacteristic
45#91119C2211yescharacteristic
46#91114C2211yescharacteristic
47#91114C2211yescharacteristic
48#91094C2211yescharacteristic
49#91094C2211yescharacteristic
50#91093C2211yescharacteristic
51#91093C2211yescharacteristic
52#91092C2211yescharacteristic
53#91092C2211yescharacteristic
54#91091C2211yescharacteristic
55#91091C2211yescharacteristic
56C4⋊(C3⋊#168)C2211yescharacteristic
57C4⋊(C3⋊#168)C2211yescharacteristic
58#91087C2211yescharacteristic
59C4×C3⋊#168C2211yescharacteristic
60#83446—51nomaximal, Hall
61C5×#541D311yescharacteristic, complemented
62#65857—31no—
63#65379—31no—
64#65372—31no—
65#65355—31no—
66#65352—31no—
67#65336—31no—
68#65336—31no—
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
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C22×Dic15—21no—
81#6817—22no—
82#6817—22no—
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C4×D15—21no—
86C2×C4×D15—21no—
87C2×Dic30C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C42×C5—21no—
105C3×C42×C5—21no—
106C3×C42×C5C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108#6718—22no—
109#6718—22no—
110#6717—22no—
111#6717—22no—
112#6714—21no—
113#6714—21no—
114C4⋊Dic15—21no—
115C4⋊Dic15C2311yescharacteristic
116C4⋊Dic15C2311yescharacteristic
117#6712—21no—
118#6712—21no—
119C4×Dic15—21no—
120C4×Dic15—21no—
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2311yescharacteristic
125C3×#541D511yescharacteristic, complemented
126#5523—51no—
127#5090—51no—
128#5083—51no—
129#5066—51no—
130#5063—51no—
131#5047—51no—
132#5047—51no—
133#5044—51no—
134#5043—51no—
135#5030—51no—
136C4×#216—51no—
137#5026—51no—
138C4×#215—51no—
139#5000—51no—
140C2×#709—31no—
141C5×C4⋊Q8C2×D311yescharacteristic
142C5×#126—21no—
143C5×#126—21no—
144C5×#125—21no—
145C5×#125—21no—
146C5×#125C2×D311yescharacteristic
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×C22⋊Q8C2×D311yescharacteristic
149C4×C5×Q8C2×D311yescharacteristic
150C4×C5×Q8C2×D311yescharacteristic
151C5×#117C2×D311yescharacteristic
152C2×#689—31no—
153C2×#689—31no—
154C2×#688—31no—
155C2×#688—31no—
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⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941—31no—
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×D15—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202#1220—24no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—81no—
207D60—21no—
208D60#4112yes—
209C4×D15—24no—
210C4×D15—81no—
211C4×D15—81no—
212Dic30—21no—
213Dic30#4112yes—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C2×#235—51no—
219C3×C4⋊Q8C2×D511yescharacteristic
220C3×#126—21no—
221C3×#126—21no—
222C3×#125—21no—
223C3×#125—21no—
224C3×#125C2×D511yescharacteristic
225C3×C22⋊Q8C2×D511yescharacteristic
226C3×C22⋊Q8C2×D511yescharacteristic
227C3×C4×Q8C2×D511yescharacteristic
228C3×C4×Q8C2×D511yescharacteristic
229C3×#117C2×D511yescharacteristic
230C2×#216—51no—
231C2×#216—51no—
232C2×#215—51no—
233C2×#215—51no—
234C2×C4⋊Dic3—51no—
235#892—101no—
236D3×C4⋊C4—101no—
237#67⋊C4—101no—
238#67⋊C4—101no—
239C4×D12—51no—
240C4×D12—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#835—51no—
246#835—51no—
247#830—51no—
248#830—51no—
249#810—51no—
250#810—51no—
251#809—51no—
252#809—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8C22×D311yescharacteristic
262C2×C5×Q8C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—61no—
265C22×Dic5—61no—
266#709—62no—
267#709—62no—
268C2×D20—31no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10—31no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4#6711yescharacteristic
282C5×C4⋊C4#6711yescharacteristic
283C5×C4⋊C4C22×D311yescharacteristic
284C5×C4⋊C4C22×D311yescharacteristic
285C5×C22⋊C4—21no—
286C5×C22⋊C4—21no—
287C5×C22⋊C4#6711yescharacteristic
288C5×C22⋊C4#6711yescharacteristic
289C42×C5—21no—
290C42×C5—21no—
291C42×C5C22×D311yescharacteristic
292C42×C5C22×D311yescharacteristic
293#689—62no—
294#689—62no—
295#688—62no—
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×#168—31no—
309C2×#168—31no—
310#541D1511yescharacteristic, complemented
311#520—151no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
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×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5—41no—
341C3×C4×C5C2×#4111yescharacteristic
342C3×C4×C5C2×#4111yescharacteristic
343Dic15—22no—
344Dic15—41no—
345Dic15—41no—
346C2×C3×Q8C22×D511yescharacteristic
347C2×C3×Q8C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—101no—
350C22×Dic3—101no—
351#235—102no—
352#235—102no—
353C2×D12—51no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×Dic6—51no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4C22⋊D511yescharacteristic
367C3×C4⋊C4C22⋊D511yescharacteristic
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C4⋊C4C22×D511yescharacteristic
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4C22⋊D511yescharacteristic
373C3×C22⋊C4C22⋊D511yescharacteristic
374C3×C42—21no—
375C3×C42—21no—
376C3×C42C22×D511yescharacteristic
377C3×C42C22×D511yescharacteristic
378#216—102no—
379#216—102no—
380#215—102no—
381#215—102no—
382(C2×D3)⋊C4—101no—
383(C2×D3)⋊C4—101no—
384C4⋊Dic3—51no—
385C4⋊Dic3—51no—
386C4⋊Dic3—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5C2×#6711yescharacteristic
396C22×D5—61no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5C2×#6711yescharacteristic
408C2×C4×C5C2×#6711yescharacteristic
409C2×C4×C5C2×#6711yescharacteristic
410C2×C4×C5C2×#6711yescharacteristic
411C2×C4×C5C2×#6711yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C22⋊D5—64no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—241no—
418D20—32no—
419D20—61no—
420C4×D5—64no—
421C4×D5—241no—
422C4×D5—241no—
423Dic10—32no—
424Dic10—61no—
425#168—61no—
426#168—61no—
427#168—61no—
428#168—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8C2×D1511yescharacteristic
435#126—21no—
436#126—21no—
437#125—21no—
438#125—21no—
439#125C2×D1511yescharacteristic
440C22⋊Q8C2×D1511yescharacteristic
441C22⋊Q8C2×D1511yescharacteristic
442C4×Q8—151no—
443C4×Q8—151no—
444C4×Q8C2×D1511yescharacteristic
445C4×Q8C2×D1511yescharacteristic
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—301no—
451#117C2×D1511yescharacteristic
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—151no—
461#103—151no—
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—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476D15—42no—
477C23×C3C2×C22⋊D511yescharacteristic
478C22×D3—101no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4C2×C22⋊D511yescharacteristic
490C2×C3×C4C2×C22⋊D511yescharacteristic
491C2×C3×C4C2×C22⋊D511yescharacteristic
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C2×C22⋊D511yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495#67—104no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—401no—
500D12—52no—
501D12—101no—
502C4×D3—104no—
503C4×D3—401no—
504C4×D3—401no—
505Dic6—52no—
506Dic6—101no—
507C3⋊C8—101no—
508C3⋊C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×#6711yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—41no—
524C4×C5—41no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5D3×#4111yescharacteristic
528C4×C5D3×#4111yescharacteristic
529Dic5—62no—
530Dic5—121no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—151no—
535C2×Q8C22×D1511yescharacteristic
536C2×Q8C22×D1511yescharacteristic
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—301no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C22×D1511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—151no—
549C2×C8—151no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—151no—
561C4⋊C4—151no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4#122011yescharacteristic
566C4⋊C4#122011yescharacteristic
567C4⋊C4C22×D1511yescharacteristic
568C4⋊C4C22×D1511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4#122011yescharacteristic
574C22⋊C4#122011yescharacteristic
575C42—21no—
576C42—21no—
577C42—301no—
578C42—301no—
579C42C22×D1511yescharacteristic
580C42C22×D1511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C22×C22⋊D511yescharacteristic
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4D5×#4111yescharacteristic
599C3×C4D5×#4111yescharacteristic
600Dic3—102no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#582811yescharacteristic
605C2×C5#583711yescharacteristic
606C2×C5#583811yescharacteristic
607D5—122no—
608C23—301no—
609C23C2×#122011yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—152no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—304no—
626C2×C4—301no—
627C2×C4—301no—
628C2×C4—301no—
629C2×C4—1201no—
630C2×C4—1201no—
631C2×C4—1201no—
632C2×C4C2×#122011yescharacteristic
633C2×C4C2×#122011yescharacteristic
634C2×C4C2×#122011yescharacteristic
635C2×C4C2×#122011yescharacteristic
636C2×C4C2×#122011yescharacteristic
637C2×C4C23×D1511yescharacteristic
638C8—301no—
639C8—301no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3#6616211yescharacteristic
644C2×C3#6617111yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—202no—
647C5#8344611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C22×#122011yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—302no—
665C4—601no—
666C4—601no—
667C4#41×D1511yescharacteristic
668C4#41×D1511yescharacteristic
669C3#1061517711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175658711yescharacteristic
673C2#1175659611yescharacteristic
674C2#1175659711yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#541C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#541D15
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C3×C5×#541C2semidirect
3. #11751191C2semidirect
4. #11751184C2semidirect
5. #11751167C2semidirect
6. #11751164C2semidirect
9. #11751145C2semidirect
10. #11751144C2semidirect
11. #11751131C2semidirect
12. C4×#6718C2semidirect
13. #11751127C2semidirect
14. C4×#6717C2semidirect
15. #11751101C2semidirect
61. C5×#541D3semidirect
125. C3×#541D5semidirect
310. #541D15semidirect
581. C3×C5#3120semidirect
647. C5#83446semidirect
669. C3#10615177semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5412
#117562822
#117511912
#117511842
#117511672
#117511642
#117511482
#117511452
#117511442
#117511312
C4×#67182
#117511272
C4×#67172
#117511012
#106151773
#834465