Finite Group Databasebeta

← #14417765

Subgroups — #14417765

Order 1920.

968 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
1C5×#5574C211yesmaximal, characteristic, complemented
2C2×#91517C211yesmaximal, characteristic
3#11752518C211yesmaximal, characteristic, complemented
4#11751131C211yesmaximal, characteristic, complemented
5C3×C4×#688C211yesmaximal, characteristic, complemented
6#11749260C211yesmaximal, characteristic, complemented
7Dic3×#688C211yesmaximal, characteristic, complemented
8#11749201C211yesmaximal, characteristic, complemented
9#11747503C211yesmaximal, characteristic, complemented
10D3×#3940C211yesmaximal, characteristic, complemented
11#11747277C211yesmaximal, characteristic, complemented
12#11747220C211yesmaximal, characteristic, complemented
13C4×#6659C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746977C211yesmaximal, characteristic, complemented
16#10614289—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×#6765C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C2×#6718C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C5×#893—21no—
24C5×#893C2211yescharacteristic
25C5×D3×C4⋊C4—21no—
26C5×D3×C4⋊C4C2211yescharacteristic
27C4×C5×D12—21no—
28C4×C5×D12C2211yescharacteristic
29C5×#872—21no—
30C5×#872C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91517C418yescomplemented
34#91442—21no—
35#91440—21no—
36D3×C4⋊Dic5C2211yescharacteristic
37Dic3×D20C2211yescharacteristic
38#91394—21no—
39D5×Dic3⋊C4—21no—
40#91340C2211yescharacteristic
41C2×#6659C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45#91119C2211yescharacteristic
46#91094C2211yescharacteristic
47#91092C2211yescharacteristic
48#91087C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52C3×C4×#168C2211yescharacteristic
53#90986C2211yescharacteristic
54#90985C2211yescharacteristic
55#90975C2211yescharacteristic
56#90967C2211yescharacteristic
57#90966C2211yescharacteristic
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic
60Dic3×#168C2211yescharacteristic
61#79650—51nomaximal, Hall
62C5×#520—31no—
63C2×#4096—31no—
64#65857—31no—
65#65521—31no—
66#65319—31no—
67#65319—31no—
68C4×#688—31no—
69C4×#688D311yescharacteristic, complemented
70C4×#687—31no—
71C4×#687—31no—
72#65303—31no—
73#65303—31no—
74#65286—31no—
75#65255—31no—
76C2×#3940—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C5×#239—22no—
80C5×#239C2×C414yescomplemented
81C2×C5×D12—21no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×#1201—21no—
91C2×D3×Dic5—21no—
92C2×D5×Dic3—21no—
93C2×D5×Dic3—21no—
94#6765—22no—
95#6765C2×C414yescomplemented
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C42×C5—21no—
99C3×C42×C5C2311yescharacteristic
100#6718C2×C414yescomplemented
101C4⋊Dic15C2311yescharacteristic
102#6712—21no—
103C4×Dic15—21no—
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×(C2×D3)⋊C4D411yescharacteristic
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4D411yescharacteristic
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C3×#688C2×C414yescomplemented
118C3×#685—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122Dic3⋊Dic5—21no—
123#6669—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6659C2×C414yescomplemented
127#6652C2×C414yescomplemented
128#6650—22no—
129D3×#168C2×C414yescomplemented
130C2×#916—51no—
131#5574D511yescharacteristic, complemented
132#5546—51no—
133C3×C4×SD16—51no—
134Dic3×SD16—51no—
135#5030—51no—
136#5014—51no—
137D3×#106—51no—
138#4852—51no—
139#4803—51no—
140#4789—51no—
141#4785—51no—
142#4771—51no—
143C4×#204—51no—
144#4689—51no—
145C2×C5×#41—31no—
146C2×#709—31no—
147C4×C5×Q8—31no—
148C4×C5×Q8C2×D311yescharacteristic
149C4×C5×D4—31no—
150C4×C5×D4—31no—
151C4×C5×D4—61no—
152C4×C5×D4—61no—
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4—61no—
157#4096—38no—
158C2×#689—31no—
159C2×#688C2×D311yescharacteristic
160C2×#687—31no—
161C2×#686—31no—
162C2×C4⋊Dic5—31no—
163C2×#681—31no—
164C22×#168—31no—
165#4038—61no—
166D5×C4⋊C4—61no—
167#4027—61no—
168#4027—61no—
169C4×D20—31no—
170C4×D20C2×D311yescharacteristic
171C4×Dic10—31no—
172C4×Dic10—31no—
173#3967—31no—
174#3967C2×D311yescharacteristic
175#3964—31no—
176#3964—31no—
177#3942—31no—
178#3942—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940—31no—
183#3940—31no—
184#3940C2×D311yescharacteristic
185#3935—31no—
186#3935—31no—
187C4×#168—31no—
188C4×#168C2×D311yescharacteristic
189#2952—151noSylow
190C22×C5×D3—21no—
191C22×C5×D3C2×D411yescharacteristic
192C22×C3×D5—21no—
193C3×C5×Q8—21no—
194C3×C5×Q8C22×C412yes—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201C2×Dic15—21no—
202Dic30—21no—
203Dic30C22×C412yes—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C5×Dic3C2×D411yescharacteristic
208C5×D12—24no—
209C5×D12—21no—
210C5×D12C22×C412yes—
211C4×C5×D3—24no—
212C4×C5×D3—81no—
213C4×C5×D3—81no—
214C4×C5×D3—81no—
215C4×C5×D3C22×C412yes—
216C4×C5×D3#4112yes—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20C22×C412yes—
220C3×C4×D5—81no—
221#1201—24no—
222D3×Dic5—81no—
223D5×Dic3—24no—
224D5×Dic3—81no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C3×#168—21no—
228C3×#168C22×C412yes—
229C2×#239C2×D511yescharacteristic
230C2×#237—51no—
231C2×C3×SD16—51no—
232C3×C4×Q8C2×D511yescharacteristic
233C3×C4×D4—51no—
234Q8×Dic3C2×D511yescharacteristic
235C2×#216—51no—
236D4×Dic3—51no—
237C2×#213—51no—
238C4×#67—101no—
239C2×Dic3⋊C4—101no—
240#916—58no—
241C2×#204—51no—
242C2×ΓL(1,𝔽25)—51no—
243C2×D3×C8—51no—
244#893—21no—
245#893C2×D511yescharacteristic
246D3×C4⋊C4—21no—
247D3×C4⋊C4—51no—
248D3×C4⋊C4C2×D511yescharacteristic
249#887—51no—
250#67⋊C4—101no—
251#877—101no—
252C4×D12—21no—
253C4×D12C2×D511yescharacteristic
254#872—21no—
255#872C2×D511yescharacteristic
256C4×Dic6—51no—
257C3×#106—51no—
258C3×#103—51no—
259C3×#102—51no—
260C3×C4×C8—51no—
261#835—51no—
262#832—51no—
263#821—51no—
264#817—51no—
265#816—51no—
266#815—51no—
267C8×Dic3—51no—
268#810—51no—
269#809—51no—
270#808—51no—
271#808—51no—
272#803—51no—
273C5×#41—34no—
274C5×#41—62no—
275C2×C5×Q8C22×D311yescharacteristic
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C22×C4×C5—31no—
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C22×Dic5—61no—
285#709—34no—
286#709—62no—
287C2×D20C22×D311yescharacteristic
288C2×C4×D5—21no—
289C2×C4×D5—61no—
290C2×C4×D5—61no—
291C2×Dic10—31no—
292C5×C4⋊C4—21no—
293C5×C4⋊C4—31no—
294C5×C4⋊C4—31no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4—61no—
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C22⋊C4—31no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—21no—
304C42×C5—31no—
305C42×C5—61no—
306C42×C5C22×D311yescharacteristic
307#689—34no—
308#688C4×D314yescomplemented
309#687—34no—
310#686—34no—
311#685—21no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—61no—
315C4⋊Dic5C22×D311yescharacteristic
316#683—61no—
317#683—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320#681—62no—
321C2×#168—31no—
322C2×#168—34no—
323C2×#168—31no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326C2×#135—151no—
327#520—31no—
328#520—151no—
329#442—151no—
330#442—151no—
331#441—151no—
332#441—151no—
333C4×SD16—51no—
334C4×SD16—151no—
335C4×SD16—151no—
336C4×SD16—151no—
337C2×#106—151no—
338#417—151no—
339#417—151no—
340#405—151no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C5×D3—21no—
343C2×C5×D3—21no—
344C2×C5×D3—22no—
345C2×C5×D3—41no—
346C2×C5×D3—41no—
347C2×C5×D3C4×D412yes—
348C2×C3×D5—22no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351C3×C4×C5—22no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5C23×C411yescharacteristic
356C3×C4×C5C2×#4111yescharacteristic
357Dic15—22no—
358Dic15—41no—
359C3×Dic5—41no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3C4×D412yes—
364C2×C3×Q8C22×D511yescharacteristic
365C2×C3×D4—51no—
366C22×C3×C4—101no—
367C2×#67—101no—
368C22×Dic3—101no—
369C22×Dic3—101no—
370#239—22no—
371#239C4×D514yescomplemented
372#237—54no—
373#237—102no—
374C2×D12—21no—
375C2×D12C22×D511yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3—101no—
381C2×C4×D3C22×D511yescharacteristic
382C2×Dic6—51no—
383C3×SD16—54no—
384C2×C3×C8—51no—
385C2×C3×C8—51no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—51no—
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C22⋊C4—101no—
390C3×C42—21no—
391C3×C42C22×D511yescharacteristic
392#217—101no—
393#216—54no—
394#213—54no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4C22⋊D511yescharacteristic
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399C4⋊Dic3—21no—
400C4⋊Dic3—51no—
401C4⋊Dic3C22×D511yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—101no—
404Dic3⋊C4—101no—
405Dic3⋊C4—101no—
406Dic3⋊C4C22⋊D511yescharacteristic
407Dic3⋊C4C22⋊D511yescharacteristic
408C4×Dic3—21no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C4×Dic3C22×D511yescharacteristic
412C2×C3⋊C8—51no—
413C2×C3⋊C8—51no—
414#204—54no—
415ΓL(1,𝔽25)—102no—
416D3×C8—54no—
417C23×C5—31no—
418C23×C5—61no—
419C22×D5—21no—
420C5×Q8—21no—
421C5×Q8C2×C4×D312yes—
422C5×D4—32no—
423C5×D4—64no—
424C5×D4—61no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—31no—
428C2×C4×C5—32no—
429C2×C4×C5—32no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—64no—
433C2×C4×C5—61no—
434C2×C4×C5—241no—
435C2×C4×C5—241no—
436C2×C4×C5—241no—
437C2×C4×C5D3×D411yescharacteristic
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—64no—
441C2×Dic5—21no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—241no—
445D20—21no—
446D20C2×C4×D312yes—
447C4×D5—64no—
448C4×D5—81no—
449C4×D5—241no—
450Dic10—32no—
451Dic10—61no—
452#168—21no—
453#168—32no—
454#168—61no—
455#168C2×C4×D312yes—
456C2×#41—31no—
457C2×#41—151no—
458#135—158no—
459C2×Q16—151no—
460C2×SD16—51no—
461C2×SD16—151no—
462C2×D8—151no—
463C2×M16—151no—
464C22×C8—151no—
465C4×Q8—31no—
466C4×Q8—151no—
467C4×Q8—151no—
468C4×Q8D3×D511yescharacteristic
469C4×D4—31no—
470C4×D4—31no—
471C4×D4—51no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4—151no—
475C4×D4—301no—
476C4×D4—301no—
477#117—31no—
478#117—61no—
479#117—301no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—61no—
482C2×C4⋊C4—151no—
483C2×C4⋊C4—301no—
484#106—51no—
485#106—151no—
486#106—151no—
487#106—151no—
488#103—51no—
489#103—151no—
490#103—151no—
491#103—151no—
492#102—51no—
493#102—151no—
494#102—151no—
495#102—151no—
496#97—151no—
497#97—151no—
498C4×C8—51no—
499C4×C8—151no—
500C2×C3×C5C2×C4×D411yescharacteristic
501C2×C3×C5#57711yescharacteristic
502C2×C3×C5#57711yescharacteristic
503C3×D5—42no—
504C5×D3—22no—
505C5×D3—42no—
506C23×C3—101no—
507C22×D3—21no—
508C22×D3C2×C22⋊D511yescharacteristic
509C3×Q8—21no—
510C3×Q8C2×C4×D512yes—
511C3×D4—52no—
512C3×D4—101no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—101no—
516C2×C3×C4—401no—
517C2×C3×C4C2×C22⋊D511yescharacteristic
518C2×C3×C4C2×C22⋊D511yescharacteristic
519C2×C3×C4C23×D511yescharacteristic
520#67—104no—
521C2×Dic3—21no—
522C2×Dic3—101no—
523C2×Dic3—104no—
524C2×Dic3—101no—
525C2×Dic3—401no—
526C2×Dic3C2×C22⋊D511yescharacteristic
527C2×Dic3C2×C22⋊D511yescharacteristic
528C2×Dic3C2×C22⋊D511yescharacteristic
529D12—24no—
530D12—21no—
531D12C2×C4×D512yes—
532C4×D3—24no—
533C4×D3—81no—
534C4×D3—81no—
535C4×D3—81no—
536C4×D3—401no—
537C4×D3C2×C4×D512yes—
538C4×D3#70912yes—
539Dic6—52no—
540Dic6—101no—
541C3×C8—52no—
542C3×C8—101no—
543C3⋊C8—52no—
544C3⋊C8—101no—
545C22×C5—32no—
546C22×C5—61no—
547C22×C5—61no—
548C22×C5—62no—
549C22×C5—121no—
550C22×C5—121no—
551C22×C5C2×D3×D411yescharacteristic
552C2×D5—22no—
553C2×D5—41no—
554C2×D5—41no—
555C4×C5—21no—
556C4×C5—21no—
557C4×C5—22no—
558C4×C5—32no—
559C4×C5—41no—
560C4×C5—61no—
561C4×C5—61no—
562C4×C5—121no—
563C4×C5C22×C4×D311yescharacteristic
564C4×C5D3×#4111yescharacteristic
565Dic5—41no—
566Dic5—62no—
567Dic5—121no—
568#41—34no—
569#41—62no—
570#41—154no—
571#41—302no—
572C2×Q8—151no—
573C2×Q8C2×D3×D511yescharacteristic
574C2×D4—31no—
575C2×D4—51no—
576C2×D4—61no—
577C2×D4—301no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—101no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587Q16—154no—
588SD16—54no—
589SD16—154no—
590D8—154no—
591M16—302no—
592C2×C8—51no—
593C2×C8—51no—
594C2×C8—154no—
595C2×C8—151no—
596C2×C8—151no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—51no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—151no—
605C4⋊C4—301no—
606C4⋊C4—301no—
607C4⋊C4—301no—
608C4⋊C4C2×D3×D511yescharacteristic
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—101no—
614C22⋊C4—301no—
615C42—21no—
616C42—31no—
617C42—61no—
618C42—301no—
619C42—301no—
620C42C2×D3×D511yescharacteristic
621C3×C5#295211yescharacteristic, complemented, Hall
622C22×C3—102no—
623C22×C3—201no—
624C22×C3—201no—
625C22×C3C22×C22⋊D511yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—22no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3C4×C22⋊D512yes—
632C3×C4—22no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—201no—
637C3×C4C22×C4×D511yescharacteristic
638C3×C4C2×#70911yescharacteristic
639Dic3—21no—
640Dic3—21no—
641Dic3—41no—
642Dic3—102no—
643Dic3—201no—
644Dic3C4×C22⋊D512yes—
645C2×C5—62no—
646C2×C5—122no—
647C2×C5C4×D3×D411yescharacteristic
648C2×C5#576211yescharacteristic
649C2×C5#577011yescharacteristic
650D5—42no—
651C23—31no—
652C23—61no—
653C23—101no—
654Q8—21no—
655Q8—152no—
656Q8—301no—
657Q8C4×D3×D512yes—
658D4—32no—
659D4—52no—
660D4—64no—
661D4—61no—
662D4—101no—
663D4—304no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—31no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—64no—
672C2×C4—61no—
673C2×C4—101no—
674C2×C4—241no—
675C2×C4—241no—
676C2×C4—241no—
677C2×C4—304no—
678C2×C4—301no—
679C2×C4—301no—
680C2×C4—401no—
681C2×C4—1201no—
682C2×C4—1201no—
683C2×C4D3×C22⋊D511yescharacteristic
684C2×C4D3×C22⋊D511yescharacteristic
685C2×C4C22×D3×D511yescharacteristic
686C8—52no—
687C8—101no—
688C8—152no—
689C8—301no—
690C2×C3—202no—
691C2×C3C2×C4×C22⋊D511yescharacteristic
692C2×C3#6617011yescharacteristic
693C2×C3#6617111yescharacteristic
694D3—22no—
695D3—42no—
696C5#7965011yescharacteristic, complemented, Sylow
697C22—32no—
698C22—61no—
699C22—61no—
700C22—62no—
701C22—102no—
702C22—121no—
703C22—121no—
704C22—201no—
705C22—201no—
706C22C2×D3×C22⋊D511yescharacteristic
707C4—21no—
708C4—21no—
709C4—22no—
710C4—32no—
711C4—41no—
712C4—61no—
713C4—61no—
714C4—121no—
715C4—201no—
716C4—302no—
717C4—601no—
718C4C2×C4×D3×D511yescharacteristic
719C4D3×#70911yescharacteristic
720C3#1061428911yescharacteristic, complemented, Sylow
721C2—62no—
722C2—122no—
723C2—202no—
724C2C4×D3×C22⋊D511yescharacteristic
725C2#1175509111yescharacteristic
726C2#1175534711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91517C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5574C2semidirect
3. #11752518C2semidirect
4. #11751131C2semidirect
5. C3×C4×#688C2semidirect
6. #11749260C2semidirect
7. Dic3×#688C2semidirect
8. #11749201C2semidirect
9. #11747503C2semidirect
10. D3×#3940C2semidirect
11. #11747277C2semidirect
12. #11747220C2semidirect
13. C4×#6659C2semidirect
14. #11747021C2semidirect
15. #11746977C2semidirect
33. #91517C4semidirect
69. C4×#688D3semidirect
80. C5×#239C2×C4semidirect
95. #6765C2×C4semidirect
100. #6718C2×C4semidirect
117. C3×#688C2×C4semidirect
126. #6659C2×C4semidirect
127. #6652C2×C4semidirect
129. D3×#168C2×C4semidirect
131. #5574D5semidirect
308. #688C4×D3semidirect
371. #239C4×D5semidirect
621. C3×C5#2952semidirect
696. C5#79650semidirect
720. C3#10614289semidirect

Maximal subgroups

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

subgroupindex
C5×#55742
C2×#915172
#117525182
#117511312
C3×C4×#6882
#117492602
Dic3×#6882
#117492012
#117475032
D3×#39402
#117472772
#117472202
C4×#66592
#117470212
#117469772
#106142893
#796505