Finite Group Databasebeta

← #14435567

Subgroups — #14435567

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#542C211yesmaximal, characteristic, complemented
2#11756280C211yesmaximal, characteristic, complemented
3#11751188C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751158C211yesmaximal, characteristic, complemented
6#11751158C211yesmaximal, characteristic, complemented
7#11751147C211yesmaximal, characteristic, complemented
8#11751146C211yesmaximal, characteristic, complemented
9#11751137C211yesmaximal, characteristic
10#11751136C211yesmaximal, characteristic, complemented
11#11751127C211yesmaximal, characteristic, complemented
12C4×#6717C211yesmaximal, characteristic, complemented
13#11751115C211yesmaximal, characteristic, complemented
14C4×#6715C211yesmaximal, characteristic, complemented
15#11751101C211yesmaximal, characteristic, complemented
16#10615191—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic, complemented
19C3×C5×#126—21no—
20C3×C5×#124—21no—
21C3×C5×#124C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic
26C3×C4×C5×Q8C2211yescharacteristic, complemented
27C3×C4×C5×D4C2211yescharacteristic, complemented
28C3×C5×#117C2211yescharacteristic
29C2×#6717C2211yescharacteristic
30C2×#6717C2211yescharacteristic
31C2×#6715C2211yescharacteristic
32C2×#6715C2211yescharacteristic
33#91815C2211yescharacteristic
34#91782—21no—
35#91782—21no—
36C22⋊C4×D15—21no—
37C22⋊C4×D15—21no—
38C4×D60C2211yescharacteristic
39C4×D60C2211yescharacteristic
40C4×D60C2211yescharacteristic
41C4×D60C2211yescharacteristic
42#91119C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91116C2211yescharacteristic, complemented
45#91116C2211yescharacteristic, complemented
46#91114C2211yescharacteristic
47#91114C2211yescharacteristic
48#91093C2211yescharacteristic
49#91093C2211yescharacteristic
50#91093C2211yescharacteristic
51#91093C2211yescharacteristic
52#91092C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54#91091C2211yescharacteristic, complemented
55#91091C2211yescharacteristic, complemented
56C4⋊(C3⋊#168)C2211yescharacteristic, complemented
57C4⋊(C3⋊#168)C2211yescharacteristic, complemented
58#91087C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#83460—51nomaximal, Hall
61C5×#542D311yescharacteristic, complemented
62#65855—31no—
63#65376—31no—
64#65373—31no—
65#65346—31no—
66#65346—31no—
67#65335—31no—
68#65334—31no—
69#65325—31no—
70#65324—31no—
71#65315—31no—
72C4×#688—31no—
73#65303—31no—
74C4×#686—31no—
75#65289—31no—
76C23×D15—21no—
77C2×C3×C5×Q8—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×D60—21no—
84C2×D60—22no—
85C2×D60—22no—
86C2×D60C2311yescharacteristic
87C2×D60C2311yescharacteristic
88C2×C4×D15—21no—
89C2×C4×D15—21no—
90C2×C4×D15—21no—
91C2×C4×D15—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4D411yescharacteristic
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C5×C22⋊C4D411yescharacteristic
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C42×C5—21no—
107C3×C42×C5C2311yescharacteristic
108C3×C42×C5C2311yescharacteristic
109#6719—21no—
110#6717—22no—
111#6717—22no—
112#6715—22no—
113#6715—22no—
114#6714—21no—
115#6714—21no—
116#6714—21no—
117#6714—21no—
118C4⋊Dic15C2311yescharacteristic
119C4⋊Dic15C2311yescharacteristic
120C4×Dic15—21no—
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2311yescharacteristic
125C3×#542D511yescharacteristic, complemented
126#5521—51no—
127#5087—51no—
128#5084—51no—
129#5057—51no—
130#5057—51no—
131#5046—51no—
132#5045—51no—
133#5036—51no—
134#5035—51no—
135#5026—51no—
136C4×#215—51no—
137#5014—51no—
138C4×#213—51no—
139#5000—51no—
140C22×D20—31no—
141C5×C4⋊Q8C2×D311yescharacteristic, complemented
142C5×#126—21no—
143C5×#124—21no—
144C5×#124C2×D311yescharacteristic, complemented
145C5×#123—21no—
146C5×C22⋊Q8—21no—
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×#121C2×D311yescharacteristic
149C4×C5×Q8C2×D311yescharacteristic, complemented
150C4×C5×D4C2×D311yescharacteristic, complemented
151C5×#117C2×D311yescharacteristic
152C2×#688—31no—
153C2×#688—31no—
154C2×#686—31no—
155C2×#686—31no—
156#4072—31no—
157#4039—61no—
158#4039—61no—
159D5×C22⋊C4—61no—
160D5×C22⋊C4—61no—
161C4×D20—31no—
162C4×D20—31no—
163C4×D20—31no—
164C4×D20—31no—
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3941—31no—
172#3941—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#3118—151noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—24no—
189C22×D15—81no—
190C22×D15—81no—
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C3×C5×Q8—81no—
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4—81no—
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—81no—
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209C2×Dic15—21no—
210C2×Dic15—21no—
211D60—24no—
212D60—21no—
213D60—21no—
214D60#4112yes—
215D60#4112yes—
216C4×D15—81no—
217C4×D15—81no—
218C4×D15—81no—
219C4×D15—81no—
220C3⋊#168—21no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3⋊#168—21no—
224C22×D12—51no—
225C3×C4⋊Q8C2×D511yescharacteristic, complemented
226C3×#126—21no—
227C3×#124—21no—
228C3×#124C2×D511yescharacteristic, complemented
229C3×#123—21no—
230C3×C22⋊Q8—21no—
231C3×C22⋊Q8C2×D511yescharacteristic
232C3×#121C2×D511yescharacteristic
233C3×C4×Q8C2×D511yescharacteristic, complemented
234C3×C4×D4C2×D511yescharacteristic, complemented
235C3×#117C2×D511yescharacteristic
236C2×#215—51no—
237C2×#215—51no—
238C2×#213—51no—
239C2×#213—51no—
240#926—51no—
241#893—101no—
242#893—101no—
243D3×C22⋊C4—101no—
244D3×C22⋊C4—101no—
245C4×D12—51no—
246C4×D12—51no—
247C4×D12—51no—
248C4×D12—51no—
249#835—51no—
250#835—51no—
251#832—51no—
252#832—51no—
253#830—51no—
254#830—51no—
255#809—51no—
256#809—51no—
257#809—51no—
258#809—51no—
259#808—51no—
260#808—51no—
261#807—51no—
262#807—51no—
263C4⋊(C3⋊C8)—51no—
264C4⋊(C3⋊C8)—51no—
265#803—51no—
266C4×C3⋊C8—51no—
267C23×D5—61no—
268C2×C5×Q8—21no—
269C2×C5×Q8C22×D311yescharacteristic
270C2×C5×D4—21no—
271C2×C5×D4C22×D311yescharacteristic
272C22×C4×C5—21no—
273C22×C4×C5C22×D311yescharacteristic
274C2×D20—31no—
275C2×D20—31no—
276C2×D20—62no—
277C2×D20—62no—
278C2×D20—61no—
279C2×C4×D5—61no—
280C2×C4×D5—61no—
281C2×C4×D5—61no—
282C2×C4×D5—61no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4#6711yescharacteristic
287C5×C4⋊C4#6711yescharacteristic
288C5×C4⋊C4C22×D311yescharacteristic
289C5×C4⋊C4C22×D311yescharacteristic
290C5×C22⋊C4—21no—
291C5×C22⋊C4—21no—
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4#6711yescharacteristic
296C5×C22⋊C4#6711yescharacteristic
297C42×C5—21no—
298C42×C5C22×D311yescharacteristic
299C42×C5C22×D311yescharacteristic
300C22⋊Dic5—61no—
301#688—62no—
302#688—62no—
303#686—62no—
304#686—62no—
305#685—61no—
306#685—61no—
307#685—61no—
308#685—61no—
309C4⋊Dic5—31no—
310C4⋊Dic5—31no—
311C4×Dic5—61no—
312C2×#168—31no—
313C2×#168—31no—
314C2×#168—31no—
315C2×#168—31no—
316#542D1511yescharacteristic, complemented
317#518—151no—
318#485—151no—
319#482—151no—
320#476—151no—
321#474—151no—
322#463—151no—
323#463—151no—
324#450—151no—
325#447—151no—
326#442—151no—
327#440—151no—
328C4×SD16—151no—
329C4×D8—151no—
330#433—151no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5C22×D411yescharacteristic
338C2×D15—22no—
339C2×D15—22no—
340C2×D15—41no—
341C2×D15—41no—
342C2×D15—41no—
343C2×D15—41no—
344C2×D15—84no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5—41no—
353C3×C4×C5C2×#4111yescharacteristic
354C3×C4×C5C2×#4111yescharacteristic
355Dic15—41no—
356Dic15—41no—
357C23×D3—101no—
358C2×C3×Q8—21no—
359C2×C3×Q8C22×D511yescharacteristic
360C2×C3×D4—21no—
361C2×C3×D4C22×D511yescharacteristic
362C22×C3×C4—21no—
363C22×C3×C4C22×D511yescharacteristic
364C2×D12—51no—
365C2×D12—51no—
366C2×D12—102no—
367C2×D12—102no—
368C2×D12—101no—
369C2×C4×D3—101no—
370C2×C4×D3—101no—
371C2×C4×D3—101no—
372C2×C4×D3—101no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4C22⋊D511yescharacteristic
377C3×C4⋊C4C22⋊D511yescharacteristic
378C3×C4⋊C4C22×D511yescharacteristic
379C3×C4⋊C4C22×D511yescharacteristic
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4C22⋊D511yescharacteristic
386C3×C22⋊C4C22⋊D511yescharacteristic
387C3×C42—21no—
388C3×C42C22×D511yescharacteristic
389C3×C42C22×D511yescharacteristic
390#217—101no—
391#215—102no—
392#215—102no—
393#213—102no—
394#213—102no—
395(C2×D3)⋊C4—101no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399C4⋊Dic3—51no—
400C4⋊Dic3—51no—
401C4×Dic3—101no—
402C2×C3⋊C8—51no—
403C2×C3⋊C8—51no—
404C2×C3⋊C8—51no—
405C2×C3⋊C8—51no—
406C23×C5—21no—
407C23×C5C2×#6711yescharacteristic
408C22×D5—61no—
409C22×D5—61no—
410C22×D5—64no—
411C22×D5—241no—
412C22×D5—241no—
413C5×Q8—21no—
414C5×Q8—21no—
415C5×Q8—81no—
416C5×D4—21no—
417C5×D4—21no—
418C5×D4—81no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—81no—
425C2×C4×C5C2×#6711yescharacteristic
426C2×C4×C5C2×#6711yescharacteristic
427C2×C4×C5C2×#6711yescharacteristic
428C2×C4×C5C2×#6711yescharacteristic
429C2×C4×C5C2×#6711yescharacteristic
430C2×C4×C5C23×D311yescharacteristic
431C2×Dic5—61no—
432C2×Dic5—61no—
433D20—32no—
434D20—32no—
435D20—64no—
436D20—61no—
437D20—61no—
438C4×D5—241no—
439C4×D5—241no—
440C4×D5—241no—
441C4×D5—241no—
442#168—61no—
443#168—61no—
444#168—61no—
445#168—61no—
446C22×D4—151no—
447C2×SD16—151no—
448C2×SD16—151no—
449C2×D8—151no—
450C2×D8—151no—
451C4⋊Q8C2×D1511yescharacteristic, complemented
452#126—21no—
453#124—21no—
454#124C2×D1511yescharacteristic, complemented
455#123—21no—
456C22⋊Q8—21no—
457C22⋊Q8C2×D1511yescharacteristic
458#121C2×D1511yescharacteristic
459C4×Q8C2×D1511yescharacteristic, complemented
460C4×D4—151no—
461C4×D4—151no—
462C4×D4—151no—
463C4×D4—151no—
464C4×D4—301no—
465C4×D4—301no—
466C4×D4C2×D1511yescharacteristic, complemented
467#117—151no—
468#117C2×D1511yescharacteristic
469C2×C22⋊C4—301no—
470C2×C22⋊C4—301no—
471#107—151no—
472#107—151no—
473#106—151no—
474#106—151no—
475C4⋊C8—151no—
476C4⋊C8—151no—
477#103—151no—
478#103—151no—
479#102—151no—
480#102—151no—
481#102—151no—
482#102—151no—
483#102—151no—
484#102—151no—
485C22⋊C8—151no—
486C22⋊C8—151no—
487#97—151no—
488C4×C8—151no—
489C2×C3×C5—41no—
490C2×C3×C5—81no—
491C2×C3×C5#52511yescharacteristic
492C2×C3×C5#57611yescharacteristic
493C2×C3×C5#57711yescharacteristic
494D15—42no—
495D15—42no—
496C23×C3—21no—
497C23×C3C2×C22⋊D511yescharacteristic
498C22×D3—101no—
499C22×D3—101no—
500C22×D3—104no—
501C22×D3—401no—
502C22×D3—401no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—81no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—81no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—81no—
515C2×C3×C4C2×C22⋊D511yescharacteristic
516C2×C3×C4C2×C22⋊D511yescharacteristic
517C2×C3×C4C2×C22⋊D511yescharacteristic
518C2×C3×C4C2×C22⋊D511yescharacteristic
519C2×C3×C4C2×C22⋊D511yescharacteristic
520C2×C3×C4C23×D511yescharacteristic
521C2×Dic3—101no—
522C2×Dic3—101no—
523D12—52no—
524D12—52no—
525D12—104no—
526D12—101no—
527D12—101no—
528C4×D3—401no—
529C4×D3—401no—
530C4×D3—401no—
531C4×D3—401no—
532C3⋊C8—101no—
533C3⋊C8—101no—
534C3⋊C8—101no—
535C3⋊C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5C22×#6711yescharacteristic
543C2×D5—62no—
544C2×D5—62no—
545C2×D5—121no—
546C2×D5—121no—
547C2×D5—121no—
548C2×D5—121no—
549C2×D5—244no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5—41no—
558C4×C5D3×#4111yescharacteristic
559C4×C5D3×#4111yescharacteristic
560Dic5—121no—
561Dic5—121no—
562C24—301no—
563C2×Q8—21no—
564C2×Q8C22×D1511yescharacteristic
565C2×D4—21no—
566C2×D4—151no—
567C2×D4—151no—
568C2×D4—302no—
569C2×D4—302no—
570C2×D4—301no—
571C2×D4C22×D1511yescharacteristic
572C22×C4—21no—
573C22×C4—301no—
574C22×C4—301no—
575C22×C4—301no—
576C22×C4—301no—
577C22×C4C22×D1511yescharacteristic
578SD16—302no—
579SD16—302no—
580D8—302no—
581D8—302no—
582C2×C8—151no—
583C2×C8—151no—
584C2×C8—151no—
585C2×C8—151no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—151no—
590C4⋊C4—151no—
591C4⋊C4#122011yescharacteristic
592C4⋊C4#122011yescharacteristic
593C4⋊C4C22×D1511yescharacteristic
594C4⋊C4C22×D1511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—301no—
601C22⋊C4—301no—
602C22⋊C4—301no—
603C22⋊C4—301no—
604C22⋊C4—301no—
605C22⋊C4#122011yescharacteristic
606C22⋊C4#122011yescharacteristic
607C42—21no—
608C42—301no—
609C42C22×D1511yescharacteristic
610C42C22×D1511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3C22×C22⋊D511yescharacteristic
619C2×D3—102no—
620C2×D3—102no—
621C2×D3—201no—
622C2×D3—201no—
623C2×D3—201no—
624C2×D3—201no—
625C2×D3—404no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4D5×#4111yescharacteristic
635C3×C4D5×#4111yescharacteristic
636Dic3—201no—
637Dic3—201no—
638C2×C5—41no—
639C2×C5—81no—
640C2×C5#582811yescharacteristic
641C2×C5#583511yescharacteristic
642C2×C5#583711yescharacteristic
643D5—122no—
644D5—122no—
645C23—21no—
646C23—304no—
647C23—301no—
648C23—301no—
649C23—1201no—
650C23—1201no—
651C23C2×#122011yescharacteristic
652Q8—21no—
653Q8—21no—
654Q8—81no—
655D4—21no—
656D4—21no—
657D4—81no—
658D4—152no—
659D4—152no—
660D4—304no—
661D4—301no—
662D4—301no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—81no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—1201no—
672C2×C4—1201no—
673C2×C4—1201no—
674C2×C4—1201no—
675C2×C4C2×#122011yescharacteristic
676C2×C4C2×#122011yescharacteristic
677C2×C4C2×#122011yescharacteristic
678C2×C4C2×#122011yescharacteristic
679C2×C4C2×#122011yescharacteristic
680C2×C4C23×D1511yescharacteristic
681C8—301no—
682C8—301no—
683C8—301no—
684C8—301no—
685C2×C3—41no—
686C2×C3—81no—
687C2×C3#6616211yescharacteristic
688C2×C3#6616911yescharacteristic
689C2×C3#6617111yescharacteristic
690D3—202no—
691D3—202no—
692C5#8346011yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—302no—
700C22—302no—
701C22—601no—
702C22—601no—
703C22—601no—
704C22—601no—
705C22—1204no—
706C22C22×#122011yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—601no—
716C4—601no—
717C4#41×D1511yescharacteristic
718C4#41×D1511yescharacteristic
719C3#1061519111yescharacteristic, complemented, Sylow
720C2—41no—
721C2—81no—
722C2—602no—
723C2—602no—
724C2#1175658711yescharacteristic
725C2#1175659411yescharacteristic
726C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#542C2
socleC22×C3×C5C22×D4
prime radical#11751137C2
hypercenter#542D15
hypocenterC3×C5#3118
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C3×C5×#542C2semidirect
2. #11756280C2semidirect
3. #11751188C2semidirect
4. #11751185C2semidirect
5. #11751158C2semidirect
6. #11751158C2semidirect
7. #11751147C2semidirect
8. #11751146C2semidirect
10. #11751136C2semidirect
11. #11751127C2semidirect
12. C4×#6717C2semidirect
13. #11751115C2semidirect
14. C4×#6715C2semidirect
15. #11751101C2semidirect
18. C3×C5×C4⋊Q8C22semidirect
21. C3×C5×#124C22semidirect
26. C3×C4×C5×Q8C22semidirect
27. C3×C4×C5×D4C22semidirect
42. #91119C22semidirect
43. #91119C22semidirect
44. #91116C22semidirect
45. #91116C22semidirect
52. #91092C22semidirect
53. #91092C22semidirect
54. #91091C22semidirect
55. #91091C22semidirect
56. C4⋊(C3⋊#168)C22semidirect
57. C4⋊(C3⋊#168)C22semidirect
58. #91087C22semidirect
59. C4×C3⋊#168C22semidirect
61. C5×#542D3semidirect
125. C3×#542D5semidirect
141. C5×C4⋊Q8C2×D3semidirect
144. C5×#124C2×D3semidirect
149. C4×C5×Q8C2×D3semidirect
150. C4×C5×D4C2×D3semidirect
225. C3×C4⋊Q8C2×D5semidirect
228. C3×#124C2×D5semidirect
233. C3×C4×Q8C2×D5semidirect
234. C3×C4×D4C2×D5semidirect
316. #542D15semidirect
451. C4⋊Q8C2×D15semidirect
454. #124C2×D15semidirect
459. C4×Q8C2×D15semidirect
466. C4×D4C2×D15semidirect
611. C3×C5#3118semidirect
692. C5#83460semidirect
719. C3#10615191semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5422
#117562802
#117511882
#117511852
#117511582
#117511472
#117511462
#117511372
#117511362
#117511272
C4×#67172
#117511152
C4×#67152
#117511012
#106151913
#834605