Finite Group Databasebeta

← #14417459

Subgroups — #14417459

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65906C211yesmaximal, characteristic, complemented
2C2×D5×#215C211yesmaximal, characteristic
3#11752725C211yesmaximal, characteristic
4C4×#6717C211yesmaximal, characteristic, complemented
5C5×#5026C211yesmaximal, characteristic, complemented
6#11749223C211yesmaximal, characteristic, complemented
7#11749221C211yesmaximal, characteristic, complemented
8#11749208C211yesmaximal, characteristic, complemented
9#11747475C211yesmaximal, characteristic
10#11747432C211yesmaximal, characteristic, complemented
11#11747224C211yesmaximal, characteristic, complemented
12#11747218C211yesmaximal, characteristic, complemented
13#11747054C211yesmaximal, characteristic, complemented
14C4×#6656C211yesmaximal, characteristic, complemented
15#11746975C211yesmaximal, characteristic, complemented
16#10611508—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic, complemented
20C2×#6717C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic, complemented
25C3×#4038—21no—
26C3×#4038C2211yescharacteristic
27C3×#4033—21no—
28C3×#4033C2211yescharacteristic, complemented
29C3×#4018—21no—
30C3×#4018C2211yescharacteristic
31C3×C4×Dic10—21no—
32C3×C4×Dic10C2211yescharacteristic, complemented
33D5×#215C418yescomplemented
34#91473—21no—
35D3×#685—21no—
36#91446—21no—
37#91418C2211yescharacteristic
38Dic5×D12C2211yescharacteristic
39#91406—21no—
40#91358C2211yescharacteristic
41C2×#6658C2211yescharacteristic
42C2×#6656C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91092C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic
51C5×#807C2211yescharacteristic, complemented
52C5×#803C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90971C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90968C2211yescharacteristic
58#90966C2211yescharacteristic
59#90952C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#82548—51nomaximal, Hall
62C2×D5×SD16—31no—
63#65906D311yescharacteristic, complemented
64#65879—31no—
65C5×#440—31no—
66#65453—31no—
67C4×#688—31no—
68C4×#687—31no—
69#65178—31no—
70#65169—31no—
71#65091—31no—
72#65077—31no—
73#65059—31no—
74#65047—31no—
75#64999—31no—
76#64997—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C3×Q8×D5—22no—
84C3×Q8×D5C2×C414yescomplemented
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×Dic10—21no—
88C2×C3×Dic10C2311yescharacteristic
89C2×#1203—21no—
90C2×#1200—21no—
91C2×D3×Dic5—21no—
92D5×D12—22no—
93D5×D12C2×C414yes—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C42×C5—21no—
97C3×C42×C5C2311yescharacteristic
98#6717C2×C414yescomplemented
99#6714—21no—
100C4⋊Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#215C2×C414yescomplemented
104C5×(C2×D3)⋊C4—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C2×C5×C3⋊C8C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C3×#685—21no—
109C3×#685D411yescharacteristic
110C3×#685D411yescharacteristic
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×#683D411yescharacteristic
116C3×#683D411yescharacteristic
117C3×C4×Dic5—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6658C2×C414yescomplemented
127#6656C2×C414yescomplemented
128#6649—22no—
129D5×C3⋊C8C2×C414yescomplemented
130C3×#519—51no—
131C22×#215—51no—
132#5521—51no—
133#5225—51no—
134#5026—51no—
135#5026—51no—
136#5026—51no—
137#5026D511yescharacteristic, complemented
138C4×#215—51no—
139C4×#215—51no—
140C4×#215—51no—
141C4×#215—51no—
142#5001—51no—
143#4998—51no—
144#4997—51no—
145C2×Q8×D5C2×D311yescharacteristic
146C2×D4×D5—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8C2×D311yescharacteristic, complemented
149C4×C5×D4—31no—
150Q8×Dic5C2×D311yescharacteristic, complemented
151C2×#688—31no—
152D4×Dic5—31no—
153C2×#687—31no—
154C4×C22⋊D5—61no—
155C2×#685—61no—
156D5×SD16—38no—
157C2×#677—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4039—31no—
161#4038—21no—
162#4038—31no—
163#4038C2×D311yescharacteristic
164#4033—21no—
165#4033C2×D311yescharacteristic, complemented
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—31no—
169#4018—21no—
170#4018C2×D311yescharacteristic
171C4×Dic10—21no—
172C4×Dic10C2×D311yescharacteristic, complemented
173C5×#107—31no—
174C5×#103—31no—
175C5×#102—31no—
176C5×#97—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3950—31no—
181#3948—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3941—31no—
186#3940—31no—
187#3940—31no—
188C4×#168—31no—
189#2949—151noSylow
190C22×D15—21no—
191C22×C5×D3—21no—
192C22×C3×D5C2×D411yescharacteristic
193C2×D3×D5—24no—
194C2×D3×D5—81no—
195C2×D3×D5—81no—
196C3×C5×Q8—21no—
197C3×C5×Q8C22×C412yes—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204D60—21no—
205D60C22×C412yes—
206C4×D15—81no—
207C2×C5×Dic3—21no—
208C5×D12—21no—
209C5×D12C22×C412yes—
210C4×C5×D3—81no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×C4×D5—24no—
217C3×C4×D5C22×C412yes—
218C3×C4×D5#4112yes—
219C3×Dic10—21no—
220C3×Dic10—24no—
221C3×Dic10C22×C412yes—
222#1203—24no—
223#1200—81no—
224D3×Dic5—81no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C5×C3⋊C8—21no—
228C5×C3⋊C8C22×C412yes—
229C22×C3×Q8—51no—
230C22×D12—51no—
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×Q8—101no—
235C3×C4×Q8—101no—
236C3×C4×Q8C2×D511yescharacteristic, complemented
237C3×#117—51no—
238C3×#117—51no—
239C3×#117—101no—
240C3×#117—101no—
241C2×#215—51no—
242C2×#215—51no—
243C2×#215—58no—
244C2×#215—51no—
245C2×#215C2×D511yescharacteristic
246#926—51no—
247C2×#208—51no—
248C22×C3⋊C8—51no—
249#893—101no—
250#893—101no—
251D3×C22⋊C4—101no—
252D3×C22⋊C4—101no—
253C4×D12—51no—
254C4×D12—51no—
255C4×D12—51no—
256C4×D12C2×D511yescharacteristic
257#835—51no—
258#835—51no—
259#835—51no—
260#835C2×D511yescharacteristic, complemented
261#809—51no—
262#809—51no—
263#809—51no—
264#809C2×D511yescharacteristic
265#808—51no—
266#808—51no—
267#807—51no—
268#807C2×D511yescharacteristic, complemented
269#803—51no—
270#803C2×D511yescharacteristic, complemented
271C4×C3⋊C8—51no—
272C4×C3⋊C8—51no—
273C23×D5—61no—
274C2×C5×Q8C22×D311yescharacteristic
275C2×C5×D4—31no—
276C22×C4×C5—61no—
277C2×C22⋊D5—61no—
278C22×Dic5—61no—
279Q8×D5—22no—
280Q8×D5C4×D314yescomplemented
281D4×D5—34no—
282D4×D5—62no—
283C2×D20—31no—
284C2×C4×D5—21no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—21no—
289C2×Dic10C22×D311yescharacteristic
290C5×SD16—34no—
291C2×C5×C8—31no—
292C2×C5×C8—31no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—31no—
295C5×C4⋊C4C22×D311yescharacteristic
296C5×C22⋊C4—61no—
297C42×C5—21no—
298C42×C5C22×D311yescharacteristic
299C22⋊Dic5—61no—
300#688—34no—
301#687—34no—
302#685—21no—
303#685—61no—
304#685—61no—
305#685—61no—
306#685#6711yescharacteristic
307#685#6711yescharacteristic
308C4⋊Dic5—21no—
309C4⋊Dic5—31no—
310C4⋊Dic5C22×D311yescharacteristic
311#683—21no—
312#683—21no—
313#683#6711yescharacteristic
314#683#6711yescharacteristic
315C4×Dic5—21no—
316C4×Dic5—21no—
317C4×Dic5—21no—
318C4×Dic5—21no—
319C4×Dic5—61no—
320C4×Dic5C22×D311yescharacteristic
321C2×#168—31no—
322C2×#168—31no—
323#677—34no—
324#676—62no—
325C8×D5—34no—
326C22×SD16—151no—
327#519—51no—
328#518—151no—
329#440—31no—
330#440—151no—
331#440—151no—
332#440—151no—
333C4×SD16—151no—
334C4×SD16—151no—
335C4×SD16—151no—
336C4×SD16—151no—
337#427—151no—
338#419—151no—
339#418—151no—
340#405—151no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—22no—
343C2×D15—41no—
344C2×D15—41no—
345C2×C5×D3—22no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5C4×D412yes—
351D3×D5—84no—
352C3×C4×C5—22no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—41no—
356C3×C4×C5C23×C411yescharacteristic
357C3×C4×C5C2×#4111yescharacteristic
358Dic15—41no—
359C3×Dic5—22no—
360C3×Dic5—21no—
361C3×Dic5—21no—
362C3×Dic5—41no—
363C3×Dic5C4×D412yes—
364C5×Dic3—41no—
365C23×D3—101no—
366C2×C3×Q8—54no—
367C2×C3×Q8—51no—
368C2×C3×Q8—101no—
369C2×C3×Q8—102no—
370C2×C3×Q8C22×D511yescharacteristic
371C22×C3×C4—51no—
372C22×C3×C4—101no—
373C2×D12—51no—
374C2×D12—54no—
375C2×D12—102no—
376C2×D12—101no—
377C2×D12C22×D511yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×C4×D3—101no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—51no—
391C3×C22⋊C4—51no—
392C3×C22⋊C4—101no—
393C3×C42—21no—
394C3×C42—51no—
395C3×C42—101no—
396C3×C42—101no—
397C3×C42—101no—
398C3×C42—101no—
399C3×C42C22×D511yescharacteristic
400#217—101no—
401#215—54no—
402#215—54no—
403#215—54no—
404#215C4×D514yescomplemented
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3C22×D511yescharacteristic
411C4×Dic3—101no—
412#208—102no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—54no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8C22×D511yescharacteristic
417C2×C3⋊C8C22×D511yescharacteristic
418C23×C5—61no—
419C22×D5—61no—
420C22×D5—64no—
421C22×D5—241no—
422C22×D5—241no—
423C22×D5C2×#6711yescharacteristic
424C5×Q8—21no—
425C5×Q8C2×C4×D312yes—
426C5×D4—32no—
427C5×D4—61no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—61no—
431C2×C4×C5—241no—
432C2×C4×C5C2×#6711yescharacteristic
433C2×C4×C5C2×#6711yescharacteristic
434C2×C4×C5C23×D311yescharacteristic
435C22⋊D5—64no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—61no—
439C2×Dic5—241no—
440C2×Dic5C2×#6711yescharacteristic
441C2×Dic5C2×#6711yescharacteristic
442C2×Dic5C2×#6711yescharacteristic
443D20—32no—
444D20—61no—
445C4×D5—24no—
446C4×D5—241no—
447C4×D5—241no—
448C4×D5C2×C4×D312yes—
449C4×D5#23512yes—
450Dic10—21no—
451Dic10—24no—
452Dic10C2×C4×D312yes—
453C5×C8—32no—
454C5×C8—61no—
455#168—32no—
456#168—61no—
457C22×Q8—51no—
458C22×D4—151no—
459C2×SD16—31no—
460C2×SD16—151no—
461C2×SD16—158no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×M16—151no—
465C22×C8—151no—
466C4×Q8—51no—
467C4×Q8—51no—
468C4×Q8—51no—
469C4×Q8—101no—
470C4×Q8—101no—
471C4×Q8D3×D511yescharacteristic, complemented
472C4×D4—31no—
473C4×D4—151no—
474C4×D4—151no—
475C4×D4—151no—
476C4×D4—301no—
477C4×D4—301no—
478#117—51no—
479#117—51no—
480#117—101no—
481#117—101no—
482#117—151no—
483C2×C22⋊C4—301no—
484C2×C22⋊C4—301no—
485#107—31no—
486#107—151no—
487#106—151no—
488#106—151no—
489#103—31no—
490#103—151no—
491#103—151no—
492#103—151no—
493#102—31no—
494#102—151no—
495#102—151no—
496#102—151no—
497#97—31no—
498#97—151no—
499C4×C8—151no—
500C4×C8—151no—
501C2×C3×C5C2×C4×D411yescharacteristic
502C2×C3×C5#57711yescharacteristic
503C2×C3×C5#57711yescharacteristic
504D15—42no—
505C3×D5—22no—
506C5×D3—42no—
507C23×C3—51no—
508C22×D3—21no—
509C22×D3—104no—
510C22×D3—101no—
511C22×D3—401no—
512C22×D3—401no—
513C3×Q8—21no—
514C3×Q8—52no—
515C3×Q8—104no—
516C3×Q8—101no—
517C3×Q8C2×C4×D512yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—51no—
521C2×C3×C4—52no—
522C2×C3×C4—52no—
523C2×C3×C4—51no—
524C2×C3×C4—51no—
525C2×C3×C4—104no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4D4×D511yescharacteristic
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531C2×Dic3—21no—
532C2×Dic3—101no—
533D12—21no—
534D12—52no—
535D12—104no—
536D12—101no—
537D12C2×C4×D512yes—
538C4×D3—81no—
539C4×D3—401no—
540C4×D3—401no—
541C4×D3—401no—
542C3⋊C8—21no—
543C3⋊C8—52no—
544C3⋊C8—101no—
545C3⋊C8C2×C4×D512yes—
546C22×C5—62no—
547C22×C5—121no—
548C22×C5—121no—
549C22×C5C22×#6711yescharacteristic
550C2×D5—21no—
551C2×D5—21no—
552C2×D5—62no—
553C2×D5—121no—
554C2×D5—121no—
555C2×D5—244no—
556C2×D5C4×#6712yes—
557C4×C5—22no—
558C4×C5—21no—
559C4×C5—21no—
560C4×C5—41no—
561C4×C5—121no—
562C4×C5C22×C4×D311yescharacteristic
563C4×C5C2×#23511yescharacteristic
564Dic5—22no—
565Dic5—21no—
566Dic5—21no—
567Dic5—41no—
568Dic5—121no—
569Dic5C4×#6712yes—
570C24—301no—
571C2×Q8—54no—
572C2×Q8—51no—
573C2×Q8—101no—
574C2×Q8—102no—
575C2×Q8C2×D3×D511yescharacteristic
576C2×D4—31no—
577C2×D4—154no—
578C2×D4—151no—
579C2×D4—302no—
580C2×D4—301no—
581C22×C4—51no—
582C22×C4—61no—
583C22×C4—101no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587SD16—34no—
588SD16—154no—
589SD16—154no—
590SD16—154no—
591M16—302no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—154no—
595C2×C8—151no—
596C2×C8—151no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—51no—
600C4⋊C4—51no—
601C4⋊C4—51no—
602C4⋊C4—101no—
603C4⋊C4—101no—
604C4⋊C4—101no—
605C4⋊C4—151no—
606C4⋊C4C2×D3×D511yescharacteristic
607C22⋊C4—51no—
608C22⋊C4—51no—
609C22⋊C4—61no—
610C22⋊C4—101no—
611C22⋊C4—301no—
612C22⋊C4—301no—
613C22⋊C4—301no—
614C22⋊C4—301no—
615C42—21no—
616C42—51no—
617C42—101no—
618C42—101no—
619C42—101no—
620C42—101no—
621C42—301no—
622C42C2×D3×D511yescharacteristic
623C3×C5#294911yescharacteristic, complemented, Hall
624C22×C3—52no—
625C22×C3—101no—
626C22×C3—101no—
627C22×C3C2×D4×D511yescharacteristic
628C2×D3—22no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—102no—
632C2×D3—201no—
633C2×D3—201no—
634C2×D3—404no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—22no—
638C3×C4—41no—
639C3×C4—52no—
640C3×C4—101no—
641C3×C4—101no—
642C3×C4—102no—
643C3×C4—201no—
644C3×C4C22×C4×D511yescharacteristic
645C3×C4D5×#4111yescharacteristic
646Dic3—41no—
647Dic3—201no—
648C2×C5—122no—
649C2×C5C2×C4×#6711yescharacteristic
650C2×C5#583711yescharacteristic
651C2×C5#583711yescharacteristic
652D5—22no—
653D5—122no—
654C23—51no—
655C23—61no—
656C23—304no—
657C23—301no—
658C23—1201no—
659C23—1201no—
660Q8—21no—
661Q8—52no—
662Q8—104no—
663Q8—101no—
664Q8C4×D3×D512yes—
665D4—32no—
666D4—61no—
667D4—152no—
668D4—304no—
669D4—301no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—51no—
673C2×C4—52no—
674C2×C4—52no—
675C2×C4—51no—
676C2×C4—51no—
677C2×C4—61no—
678C2×C4—104no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—241no—
682C2×C4—301no—
683C2×C4—1201no—
684C2×C4—1201no—
685C2×C4—1201no—
686C2×C4D5×#6711yescharacteristic
687C2×C4D5×#6711yescharacteristic
688C2×C4C22×D3×D511yescharacteristic
689C8—32no—
690C8—61no—
691C8—152no—
692C8—301no—
693C2×C3—102no—
694C2×C3C4×D4×D511yescharacteristic
695C2×C3#6610911yescharacteristic
696C2×C3#6611211yescharacteristic
697D3—42no—
698D3—202no—
699C5#8254811yescharacteristic, complemented, Sylow
700C22—52no—
701C22—62no—
702C22—101no—
703C22—101no—
704C22—121no—
705C22—121no—
706C22—302no—
707C22—601no—
708C22—601no—
709C22—1204no—
710C22C2×D5×#6711yescharacteristic
711C4—21no—
712C4—21no—
713C4—22no—
714C4—41no—
715C4—52no—
716C4—101no—
717C4—101no—
718C4—102no—
719C4—121no—
720C4—201no—
721C4—601no—
722C4C2×C4×D3×D511yescharacteristic
723C4D5×#23511yescharacteristic
724C3#1061150811yescharacteristic, complemented, Sylow
725C2—102no—
726C2—122no—
727C2—602no—
728C2C4×D5×#6711yescharacteristic
729C2#1175508611yescharacteristic
730C2#1175531711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2949
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. C3×#65906C2semidirect
4. C4×#6717C2semidirect
5. C5×#5026C2semidirect
6. #11749223C2semidirect
7. #11749221C2semidirect
8. #11749208C2semidirect
10. #11747432C2semidirect
11. #11747224C2semidirect
12. #11747218C2semidirect
13. #11747054C2semidirect
14. C4×#6656C2semidirect
15. #11746975C2semidirect
19. C3×C4×C5×Q8C22semidirect
24. C3×Q8×Dic5C22semidirect
28. C3×#4033C22semidirect
32. C3×C4×Dic10C22semidirect
33. D5×#215C4semidirect
45. #91119C22semidirect
47. #91092C22semidirect
48. C4×C3⋊#168C22semidirect
49. C5×#835C22semidirect
51. C5×#807C22semidirect
52. C5×#803C22semidirect
53. #90990C22semidirect
54. #90986C22semidirect
55. #90971C22semidirect
56. #90970C22semidirect
59. #90952C22semidirect
60. Dic5×C3⋊C8C22semidirect
63. #65906D3semidirect
84. C3×Q8×D5C2×C4semidirect
98. #6717C2×C4semidirect
103. C5×#215C2×C4semidirect
126. #6658C2×C4semidirect
127. #6656C2×C4semidirect
129. D5×C3⋊C8C2×C4semidirect
137. #5026D5semidirect
148. C4×C5×Q8C2×D3semidirect
150. Q8×Dic5C2×D3semidirect
165. #4033C2×D3semidirect
172. C4×Dic10C2×D3semidirect
236. C3×C4×Q8C2×D5semidirect
260. #835C2×D5semidirect
268. #807C2×D5semidirect
270. #803C2×D5semidirect
280. Q8×D5C4×D3semidirect
404. #215C4×D5semidirect
471. C4×Q8D3×D5semidirect
623. C3×C5#2949semidirect
699. C5#82548semidirect
724. C3#10611508semidirect

Maximal subgroups

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

subgroupindex
C3×#659062
C2×D5×#2152
#117527252
C4×#67172
C5×#50262
#117492232
#117492212
#117492082
#117474752
#117474322
#117472242
#117472182
#117470542
C4×#66562
#117469752
#106115083
#825485