Finite Group Databasebeta

← #14458595

Subgroups — #14458595

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#552C211yesmaximal, characteristic, complemented
2#11756309C211yesmaximal, characteristic
3#11751169C211yesmaximal, characteristic, complemented
4#11751167C211yesmaximal, characteristic, complemented
5#11751152C211yesmaximal, characteristic, complemented
6#11751149C211yesmaximal, characteristic, complemented
7#11751148C211yesmaximal, characteristic, complemented
8#11751147C211yesmaximal, characteristic, complemented
9#11751129C211yesmaximal, characteristic, complemented
10C4×#6717C211yesmaximal, characteristic, complemented
11D4×C3⋊#168C211yesmaximal, characteristic, complemented
12#11751104C211yesmaximal, characteristic, complemented
13#11751103C211yesmaximal, characteristic, complemented
14#11751072C211yesmaximal, characteristic, complemented
15C2×#91093C211yesmaximal, characteristic, complemented
16#10615329—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#125—21no—
21C3×C5×#125C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26C3×C4×C5×D4C2211yescharacteristic
27C3×C5×#117—21no—
28C3×C5×#117C2211yescharacteristic, complemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×#6718C2211yescharacteristic, complemented
31C2×#6717C2211yescharacteristic
32C2×#6717C2211yescharacteristic
33#91826—21no—
34#91819C2211yescharacteristic
35#91813C2211yescharacteristic
36C22×C3⋊#168C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic, complemented
38#91783—21no—
39#91773—21no—
40C22⋊C4×D15—21no—
41#91764C2211yescharacteristic
42C4×D60C2211yescharacteristic
43#91119C2211yescharacteristic, complemented
44#91114C2211yescharacteristic
45#91114C2211yescharacteristic, complemented
46#91094C2211yescharacteristic, complemented
47#91094C2211yescharacteristic, complemented
48#91094C2211yescharacteristic, complemented
49#91093C2211yescharacteristic
50#91093C2211yescharacteristic
51#91093C2211yescharacteristic
52#91093C2211yescharacteristic
53#91093C2211yescharacteristic
54#91093C2211yescharacteristic
55#91092C2211yescharacteristic, complemented
56#91092C2211yescharacteristic, complemented
57#91091C2211yescharacteristic, complemented
58C4⋊(C3⋊#168)C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#83598—51nomaximal, Hall
61C5×#552D311yescharacteristic, complemented
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65340—31no—
66#65337—31no—
67#65336—31no—
68#65335—31no—
69#65317—31no—
70C4×#688—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65260—31no—
75C2×#3941—31no—
76C23×D15—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4D411yescharacteristic
79C22×C3×C4×C5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84#6817—22no—
85#6817—41no—
86C2×D60—22no—
87C2×D60—21no—
88C2×D60—41no—
89C2×D60C2311yescharacteristic
90C2×D60C2311yescharacteristic
91C2×C4×D15—21no—
92C2×C4×D15—21no—
93C2×Dic30C2311yescharacteristic
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4D411yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4—21no—
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C5×C22⋊C4D411yescharacteristic
109C3×C42×C5—21no—
110C3×C42×C5—21no—
111C3×C42×C5C2311yescharacteristic
112#6719—21no—
113#6718—41no—
114#6717—22no—
115#6717—41no—
116#6714—21no—
117#6714—21no—
118#6714—21no—
119#6714—21no—
120C4⋊Dic15C2311yescharacteristic
121#6712—21no—
122C2×C3⋊#168—41no—
123C2×C3⋊#168—41no—
124C2×C3⋊#168C2311yescharacteristic
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C3×#552D511yescharacteristic, complemented
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5051—51no—
133#5048—51no—
134#5047—51no—
135#5046—51no—
136#5028—51no—
137C4×#215—51no—
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4971—51no—
142C2×#809—51no—
143C2×#709—31no—
144C22×D20—31no—
145C5×#126—21no—
146C5×#125—21no—
147C5×#125C2×D311yescharacteristic, complemented
148C5×#123—21no—
149C5×C22⋊Q8C2×D311yescharacteristic
150C5×C22⋊Q8C2×D311yescharacteristic, complemented
151C4×C5×Q8C2×D311yescharacteristic, complemented
152C4×C5×D4C2×D311yescharacteristic
153C5×#117—21no—
154C5×#117C2×D311yescharacteristic, complemented
155C2×C5×C4⋊C4C2×D311yescharacteristic
156C2×#689—31no—
157C2×#688—31no—
158C2×#688—31no—
159#4083—61no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3967—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941—31no—
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×D4—22no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211#1220—42no—
212#1220—81no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215D60—21no—
216D60—21no—
217D60—21no—
218D60—42no—
219D60#4112yes—
220C4×D15—42no—
221C4×D15—81no—
222Dic30—21no—
223Dic30—21no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C2×#235—51no—
229C22×D12—51no—
230C3×#126—21no—
231C3×#125—21no—
232C3×#125C2×D511yescharacteristic, complemented
233C3×#123—21no—
234C3×C22⋊Q8C2×D511yescharacteristic
235C3×C22⋊Q8C2×D511yescharacteristic, complemented
236C3×C4×Q8C2×D511yescharacteristic, complemented
237C3×C4×D4C2×D511yescharacteristic
238C3×#117—21no—
239C3×#117C2×D511yescharacteristic, complemented
240C2×C3×C4⋊C4C2×D511yescharacteristic
241C2×#216—51no—
242C2×#215—51no—
243C2×#215—51no—
244#937—101no—
245#930—51no—
246#924—51no—
247C22×C3⋊C8—51no—
248C22×C3⋊C8—51no—
249#894—101no—
250#884—101no—
251D3×C22⋊C4—101no—
252#875—51no—
253C4×D12—51no—
254#835—51no—
255#830—51no—
256#830—51no—
257#810—51no—
258#810—51no—
259#810—51no—
260#809—51no—
261#809—51no—
262#809—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#808—51no—
267#808—51no—
268#807—51no—
269C4⋊(C3⋊C8)—51no—
270C4×C3⋊C8—51no—
271C23×D5—61no—
272C2×C5×Q8C22×D311yescharacteristic
273C2×C5×D4#6711yescharacteristic
274C22×C4×C5—21no—
275C22×C4×C5C22×D311yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C2×C22⋊D5—61no—
278C2×C22⋊D5—61no—
279#709—62no—
280#709—121no—
281C2×D20—31no—
282C2×D20—31no—
283C2×D20—62no—
284C2×D20—61no—
285C2×D20—121no—
286C2×C4×D5—61no—
287C2×C4×D5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—21no—
292C5×C4⋊C4—21no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4#6711yescharacteristic
296C5×C4⋊C4C22×D311yescharacteristic
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4#6711yescharacteristic
303C5×C22⋊C4#6711yescharacteristic
304C42×C5—21no—
305C42×C5—21no—
306C42×C5C22×D311yescharacteristic
307C22⋊Dic5—61no—
308#689—121no—
309#688—62no—
310#688—121no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316#683—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—31no—
320C2×#168—31no—
321C2×#168—121no—
322C2×#168—121no—
323#552D1511yescharacteristic, complemented
324#546—151no—
325#488—151no—
326#483—151no—
327#482—151no—
328#478—151no—
329#467—151no—
330#465—151no—
331#464—151no—
332#452—151no—
333#450—151no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×D15—84no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5—41no—
357C3×C4×C5—41no—
358C3×C4×C5—41no—
359C3×C4×C5—41no—
360C3×C4×C5C2×#4111yescharacteristic
361C3×C4×C5H(5,𝔽2)11yescharacteristic
362Dic15—41no—
363Dic15—41no—
364C23×D3—101no—
365C2×C3×Q8C22×D511yescharacteristic
366C2×C3×D4C22⋊D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4C22×D511yescharacteristic
369C22×C3×C4C22×D511yescharacteristic
370C2×#67—101no—
371C2×#67—101no—
372#235—102no—
373#235—201no—
374C2×D12—51no—
375C2×D12—51no—
376C2×D12—102no—
377C2×D12—101no—
378C2×D12—201no—
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×Dic6—51no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4C22⋊D511yescharacteristic
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C4⋊C4C22×D511yescharacteristic
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4C22⋊D511yescharacteristic
396C3×C22⋊C4C22⋊D511yescharacteristic
397C3×C42—21no—
398C3×C42—21no—
399C3×C42C22×D511yescharacteristic
400#217—101no—
401#216—201no—
402#215—102no—
403#215—201no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409Dic3⋊C4—101no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—201no—
415C2×C3⋊C8—201no—
416C23×C5C2×#6711yescharacteristic
417C23×C5C2×#6711yescharacteristic
418C22×D5—61no—
419C22×D5—61no—
420C22×D5—122no—
421C22×D5—122no—
422C22×D5—241no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—22no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—42no—
435C2×C4×C5C2×#6711yescharacteristic
436C2×C4×C5C2×#6711yescharacteristic
437C2×C4×C5C2×#6711yescharacteristic
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—122no—
441C22⋊D5—241no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444D20—32no—
445D20—61no—
446D20—61no—
447D20—61no—
448D20—122no—
449C4×D5—122no—
450C4×D5—241no—
451Dic10—61no—
452Dic10—61no—
453#168—61no—
454#168—61no—
455#168—61no—
456#168—61no—
457C2×#41—151no—
458C22×D4—151no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—21no—
465#125—21no—
466#125C2×D1511yescharacteristic, complemented
467#124—151no—
468#123—21no—
469#123—301no—
470C22⋊Q8—151no—
471C22⋊Q8C2×D1511yescharacteristic
472C22⋊Q8C2×D1511yescharacteristic, complemented
473#121—151no—
474#121—301no—
475#120—301no—
476C4×Q8C2×D1511yescharacteristic, complemented
477C4×D4—151no—
478C4×D4C2×D1511yescharacteristic
479#117—21no—
480#117C2×D1511yescharacteristic, complemented
481C2×C4⋊C4C2×D1511yescharacteristic
482C2×C22⋊C4—301no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—151no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—151no—
492#102—151no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505D15—42no—
506D15—81no—
507C23×C3C2×C22⋊D511yescharacteristic
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—101no—
510C22×D3—101no—
511C22×D3—202no—
512C22×D3—202no—
513C22×D3—401no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×D4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—42no—
526C2×C3×C4C2×C22⋊D511yescharacteristic
527C2×C3×C4C2×C22⋊D511yescharacteristic
528C2×C3×C4C2×C22⋊D511yescharacteristic
529C2×C3×C4C2×C22⋊D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531#67—202no—
532#67—401no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535D12—52no—
536D12—101no—
537D12—101no—
538D12—101no—
539D12—202no—
540C4×D3—202no—
541C4×D3—401no—
542Dic6—101no—
543Dic6—101no—
544C3⋊C8—101no—
545C3⋊C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5#95012yes—
554C22×C5C22×#6711yescharacteristic
555C2×D5—62no—
556C2×D5—121no—
557C2×D5—121no—
558C2×D5—121no—
559C2×D5—121no—
560C2×D5—121no—
561C2×D5—244no—
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—41no—
567C4×C5—41no—
568C4×C5—41no—
569C4×C5—41no—
570C4×C5D3×#4111yescharacteristic
571C4×C5#100911yescharacteristic
572Dic5—121no—
573Dic5—121no—
574C24—301no—
575#41—302no—
576#41—601no—
577C2×Q8—151no—
578C2×Q8C22×D1511yescharacteristic
579C2×D4—151no—
580C2×D4—151no—
581C2×D4—302no—
582C2×D4—301no—
583C2×D4—301no—
584C2×D4—301no—
585C2×D4—601no—
586C2×D4#122011yescharacteristic
587C22×C4—21no—
588C22×C4—301no—
589C22×C4—301no—
590C22×C4C22×D1511yescharacteristic
591C22×C4C22×D1511yescharacteristic
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—151no—
596C2×C8—151no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—151no—
608C4⋊C4—301no—
609C4⋊C4#122011yescharacteristic
610C4⋊C4C22×D1511yescharacteristic
611C4⋊C4C22×D1511yescharacteristic
612C4⋊C4C22×D1511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—301no—
617C22⋊C4—301no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4#122011yescharacteristic
622C22⋊C4#122011yescharacteristic
623C42—21no—
624C42—21no—
625C42C22×D1511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3#409612yes—
633C22×C3C22×C22⋊D511yescharacteristic
634C2×D3—102no—
635C2×D3—201no—
636C2×D3—201no—
637C2×D3—201no—
638C2×D3—201no—
639C2×D3—201no—
640C2×D3—404no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4D5×#4111yescharacteristic
650C3×C4#414911yescharacteristic
651Dic3—201no—
652Dic3—201no—
653C2×C5—22no—
654C2×C5—41no—
655C2×C5C2×#95011yescharacteristic
656C2×C5#582911yescharacteristic
657C2×C5#583711yescharacteristic
658D5—122no—
659D5—241no—
660C23—301no—
661C23—301no—
662C23—602no—
663C23—602no—
664C23—1201no—
665C23C2×#122011yescharacteristic
666C23C2×#122011yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—301no—
670Q8—301no—
671D4—22no—
672D4—152no—
673D4—301no—
674D4—301no—
675D4—301no—
676D4—602no—
677D4—602no—
678D4—1201no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—42no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—602no—
691C2×C4—1201no—
692C2×C4C2×#122011yescharacteristic
693C2×C4C2×#122011yescharacteristic
694C2×C4C2×#122011yescharacteristic
695C2×C4C2×#122011yescharacteristic
696C2×C4C23×D1511yescharacteristic
697C8—301no—
698C8—301no—
699C8—301no—
700C8—301no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3C2×#409611yescharacteristic
704C2×C3#6616311yescharacteristic
705C2×C3#6617111yescharacteristic
706D3—202no—
707D3—401no—
708C5#8359811yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—302no—
715C22—601no—
716C22—601no—
717C22—601no—
718C22—601no—
719C22—601no—
720C22—1204no—
721C22#9183912yes—
722C22C22×#122011yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—601no—
732C4—601no—
733C4#41×D1511yescharacteristic
734C4#9210011yescharacteristic
735C3#1061532911yescharacteristic, complemented, Sylow
736C2—22no—
737C2—41no—
738C2—602no—
739C2—1201no—
740C2C2×#9183911yescharacteristic
741C2#1175658811yescharacteristic
742C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#552C2
socleC22×C3×C5C22×D4
prime radical#11756309C2
hypercenter#552D15
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C3×C5×#552C2semidirect
3. #11751169C2semidirect
4. #11751167C2semidirect
5. #11751152C2semidirect
6. #11751149C2semidirect
7. #11751148C2semidirect
8. #11751147C2semidirect
9. #11751129C2semidirect
10. C4×#6717C2semidirect
11. D4×C3⋊#168C2semidirect
12. #11751104C2semidirect
13. #11751103C2semidirect
14. #11751072C2semidirect
15. C2×#91093C2semidirect
21. C3×C5×#125C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
25. C3×C4×C5×Q8C22semidirect
28. C3×C5×#117C22semidirect
30. C2×#6718C22semidirect
37. C22×C3⋊#168C22semidirect
43. #91119C22semidirect
45. #91114C22semidirect
46. #91094C22semidirect
47. #91094C22semidirect
48. #91094C22semidirect
55. #91092C22semidirect
56. #91092C22semidirect
57. #91091C22semidirect
58. C4⋊(C3⋊#168)C22semidirect
59. C4×C3⋊#168C22semidirect
61. C5×#552D3semidirect
128. C3×#552D5semidirect
147. C5×#125C2×D3semidirect
150. C5×C22⋊Q8C2×D3semidirect
151. C4×C5×Q8C2×D3semidirect
154. C5×#117C2×D3semidirect
232. C3×#125C2×D5semidirect
235. C3×C22⋊Q8C2×D5semidirect
236. C3×C4×Q8C2×D5semidirect
239. C3×#117C2×D5semidirect
323. #552D15semidirect
466. #125C2×D15semidirect
472. C22⋊Q8C2×D15semidirect
476. C4×Q8C2×D15semidirect
480. #117C2×D15semidirect
626. C3×C5#3296semidirect
708. C5#83598semidirect
735. C3#10615329semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5522
#117563092
#117511692
#117511672
#117511522
#117511492
#117511482
#117511472
#117511292
C4×#67172
D4×C3⋊#1682
#117511042
#117511032
#117510722
C2×#910932
#106153293
#835985