Finite Group Databasebeta

← #14459166

Subgroups — #14459166

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×Q8×#67C211yesmaximal, characteristic, complemented
2#11754361C211yesmaximal, characteristic
3#11751328C211yesmaximal, characteristic, complemented
4C2×C3×#3967C211yesmaximal, characteristic, complemented
5#11749358C211yesmaximal, characteristic, complemented
6#11749280C211yesmaximal, characteristic, complemented
7#11749279C211yesmaximal, characteristic, complemented
8#11749233C211yesmaximal, characteristic, complemented
9#11749232C211yesmaximal, characteristic, complemented
10#11749200C211yesmaximal, characteristic, complemented
11D3×#3967C211yesmaximal, characteristic, complemented
12#11749187C211yesmaximal, characteristic, complemented
13#11748535C211yesmaximal, characteristic, complemented
14#67×#168C211yesmaximal, characteristic, complemented
15#11748406C211yesmaximal, characteristic, complemented
16#10615281—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×#6782—21no—
20C2×#6717C2211yescharacteristic
21C2×#6717C2211yescharacteristic
22#91819C2211yescharacteristic
23C5×#946—21no—
24C5×#946C2211yescharacteristic
25C5×Q8×Dic3C2211yescharacteristic
26C5×#944—21no—
27C5×#944C2211yescharacteristic
28C4×C5×#67—21no—
29C4×C5×#67C2211yescharacteristic
30C5×#924—21no—
31C5×#924C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C22×C3×#168C2211yescharacteristic
34#91546—21no—
35#91469C2211yescharacteristic
36#91460C2211yescharacteristic
37#91429—21no—
38#91428C2211yescharacteristic
39#91427—21no—
40D3×C4⋊Dic5C2211yescharacteristic
41C2×#6660C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43#91119C2211yescharacteristic
44#91119C2211yescharacteristic
45#91114C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3967C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50#90986C2211yescharacteristic
51#90986C2211yescharacteristic
52#90985C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90973C2211yescharacteristic
55#90972C2211yescharacteristic
56#90972C2211yescharacteristic
57#90969C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#78805—51nomaximal, Hall
61C5×D4×Q8—31no—
62#65889—31no—
63#65516—31no—
64#65516—31no—
65C2×#3967—31no—
66C2×#3967D311yescharacteristic, complemented
67#65372—31no—
68#65370—31no—
69#65337—31no—
70#65337—31no—
71#65332—31no—
72#65332—31no—
73C4×#688—31no—
74#65309—31no—
75D4×#168—31no—
76C2×C3×C5×Q8—21no—
77C2×C3×C5×Q8—22no—
78C2×C3×C5×Q8—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×D60C2311yescharacteristic
85C2×C5×#67D411yescharacteristic
86C5×D3×Q8—22no—
87C5×D3×Q8—41no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3C2311yescharacteristic
90C2×C5×Dic6—21no—
91C2×C5×Dic6C2311yescharacteristic
92C22×C3×Dic5—21no—
93C2×#1204—21no—
94C2×#1203—21no—
95C2×#1200—21no—
96#6782—44no—
97C2×D3×Dic5—21no—
98#6717—22no—
99#6717—41no—
100#6714—21no—
101C4⋊Dic15C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#217—21no—
105C5×#217D411yescharacteristic
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C3×C4⋊Dic5—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123Dic3⋊Dic5—21no—
124Dic3⋊Dic5—21no—
125#6667—21no—
126#6667—21no—
127#6660—41no—
128D3×#168—41no—
129Q8×#67D511yescharacteristic, complemented
130#5507—51no—
131C2×C3×#103—51no—
132#5227—51no—
133#5114—51no—
134C8×#67—51no—
135#4971—51no—
136#4818—51no—
137#4807—51no—
138#4806—51no—
139#4805—51no—
140D3×#103—51no—
141#4792—51no—
142#4791—51no—
143#4788—51no—
144C22×C5×Q8—31no—
145C22×C5×Q8C2×D311yescharacteristic
146C2×#711—61no—
147C5×C4⋊Q8—31no—
148C5×C4⋊Q8—61no—
149C5×C22⋊Q8—31no—
150C5×C22⋊Q8—31no—
151C5×C22⋊Q8—61no—
152C5×C22⋊Q8—61no—
153C4×C5×Q8—31no—
154C4×C5×D4—31no—
155C4×C5×D4—61no—
156C2×#688—31no—
157C2×#688—31no—
158C2×#688—31no—
159#4076—31no—
160#4076—31no—
161C2×C4⋊Dic5—31no—
162C2×C4⋊Dic5C2×D311yescharacteristic
163C22×#168—31no—
164C22×#168C2×D311yescharacteristic
165#4043—61no—
166#4032—61no—
167#4032—61no—
168C4×D20—31no—
169#4015—31no—
170#3967—31no—
171#3967—31no—
172#3967—31no—
173#3967—31no—
174#3967—31no—
175#3967C2×D311yescharacteristic
176#3967C2×D311yescharacteristic
177#3967C2×D311yescharacteristic
178#3967C2×D311yescharacteristic
179C22⋊#168—31no—
180C22⋊#168—31no—
181#3941—31no—
182#3940—31no—
183#3940—31no—
184#3940—31no—
185C4⋊#168—31no—
186C4×#168—31no—
187#3298—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3C2×D411yescharacteristic
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C3×C5×Q8—21no—
194C3×C5×Q8—42no—
195C3×C5×Q8#4112yescomplemented
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—42no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203#1220—42no—
204C2×Dic15—21no—
205D60—21no—
206D60—21no—
207C5×#67SD1614yescomplemented
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C4×C5×D3—21no—
214C4×C5×D3—21no—
215C4×C5×D3—42no—
216C5×Dic6—21no—
217C5×Dic6—21no—
218C5×Dic6—42no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—42no—
222#1204—42no—
223#1203—42no—
224#1200—42no—
225D3×Dic5—42no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C22×C3×Q8C2×D511yescharacteristic
231C2×D3×Q8C2×D511yescharacteristic
232C2×#235—101no—
233C22×C3×C8—51no—
234C2×C3×C4⋊C4—51no—
235#946—21no—
236#946C2×D511yescharacteristic
237Q8×Dic3C2×D511yescharacteristic
238#944—21no—
239#944C2×D511yescharacteristic
240C2×#215—51no—
241C2×#215—51no—
242#930—51no—
243#929—101no—
244C4×#67—21no—
245C4×#67C2×D511yescharacteristic
246#924—21no—
247#924C2×D511yescharacteristic
248C2×#204—51no—
249C2×D3×C8—51no—
250#896—101no—
251#895—51no—
252#894—101no—
253#893—51no—
254D3×C4⋊C4—51no—
255#888—51no—
256C3×#103—51no—
257C3×#103—51no—
258C3×#103—51no—
259C3×#103—51no—
260#835—51no—
261#835—51no—
262#830—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265#817—51no—
266#816—51no—
267Dic3⋊C8—51no—
268C8×Dic3—51no—
269#810—51no—
270#810—51no—
271#808—51no—
272#808—51no—
273C2×C5×Q8—21no—
274C2×C5×Q8—22no—
275C2×C5×Q8—31no—
276C2×C5×Q8—41no—
277C2×C5×Q8—61no—
278C2×C5×Q8—62no—
279C2×C5×Q8—121no—
280C2×C5×Q8C22×D311yescharacteristic
281C2×C5×Q8C22×D311yescharacteristic
282C2×C5×D4—31no—
283C22×C4×C5—21no—
284C22×C4×C5—31no—
285C22×C4×C5—61no—
286C22×C4×C5C22×D311yescharacteristic
287C2×C22⋊D5—61no—
288C2×C22⋊D5—61no—
289C22×Dic5—21no—
290C22×Dic5—61no—
291#711—124no—
292C2×D20—31no—
293C2×C4×D5—61no—
294C2×Dic10—61no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—61no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4—61no—
302C5×C22⋊C4—31no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C42×C5—31no—
307C42×C5—61no—
308#688—62no—
309#688—121no—
310#688—121no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—21no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317C4⋊Dic5—61no—
318C4⋊Dic5C22×D311yescharacteristic
319C4⋊Dic5C22×D311yescharacteristic
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—41no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D4×Q8—31no—
327#547—151no—
328#487—151no—
329#483—151no—
330#483—151no—
331#475—151no—
332#465—151no—
333#465—151no—
334#461—151no—
335#448—151no—
336#448—151no—
337C4×SD16—151no—
338C8×D4—151no—
339C2×#103—51no—
340C2×#103—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5C2×SD1612yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—41no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3C2×SD1612yes—
351C3×C4×C5—22no—
352C3×C4×C5—21no—
353C3×C4×C5—41no—
354C3×C4×C5C2×#4111yescharacteristic
355C3×C4×C5H(5,𝔽2)11yescharacteristic
356Dic15—41no—
357C3×Dic5—41no—
358C3×Dic5—41no—
359C5×Dic3—21no—
360C5×Dic3—21no—
361C5×Dic3—41no—
362C5×Dic3—41no—
363C5×Dic3C2×SD1612yes—
364C2×C3×Q8—21no—
365C2×C3×Q8—22no—
366C2×C3×Q8—41no—
367C2×C3×Q8C22×D511yescharacteristic
368C2×C3×Q8C22×D511yescharacteristic
369C22×C3×C4—21no—
370C22×C3×C4—101no—
371C22×C3×C4C22×D511yescharacteristic
372C2×#67—101no—
373C2×#67C22⋊D511yescharacteristic
374D3×Q8—22no—
375D3×Q8—41no—
376#235—204no—
377C2×D12—51no—
378C2×D12—101no—
379C2×C4×D3—21no—
380C2×C4×D3—101no—
381C2×C4×D3—101no—
382C2×C4×D3C22×D511yescharacteristic
383C2×Dic6—21no—
384C2×Dic6—101no—
385C2×Dic6C22×D511yescharacteristic
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—201no—
389C3×C4⋊C4—51no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—101no—
392#217—21no—
393#217C22⋊D511yescharacteristic
394#215—102no—
395#215—201no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399(C2×D3)⋊C4—101no—
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—21no—
402C4⋊Dic3—51no—
403C4⋊Dic3C22×D511yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410Dic3⋊C4C22⋊D511yescharacteristic
411C4×Dic3—21no—
412C4×Dic3C22×D511yescharacteristic
413C2×C3⋊C8—51no—
414C2×C3⋊C8—51no—
415#204—201no—
416D3×C8—201no—
417C23×C5—31no—
418C23×C5D3×D411yescharacteristic
419C22×D5—61no—
420C5×Q8—21no—
421C5×Q8—21no—
422C5×Q8—21no—
423C5×Q8—42no—
424C5×Q8—61no—
425C5×Q8—61no—
426C5×Q8—122no—
427C5×Q8#23512yescomplemented
428C5×D4—34no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—31no—
434C2×C4×C5—31no—
435C2×C4×C5—31no—
436C2×C4×C5—42no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—122no—
442C2×C4×C5D3×D411yescharacteristic
443C2×C4×C5C23×D311yescharacteristic
444C22⋊D5—122no—
445C22⋊D5—122no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—42no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451D20—61no—
452D20—61no—
453C4×D5—122no—
454Dic10—122no—
455#168—21no—
456#168—21no—
457#168—61no—
458#168—61no—
459C2×#41—301no—
460C22×Q8—31no—
461C22×Q8D3×D511yescharacteristic
462C2×SD16—151no—
463C2×SD16—151no—
464C2×SD16—151no—
465C22×C8—51no—
466C22×C8—151no—
467C4⋊Q8—31no—
468C4⋊Q8—61no—
469C4⋊Q8—151no—
470#123—301no—
471#123—301no—
472C22⋊Q8—31no—
473C22⋊Q8—31no—
474C22⋊Q8—61no—
475C22⋊Q8—61no—
476C22⋊Q8—301no—
477#121—151no—
478#121—151no—
479C4×Q8—31no—
480C4×D4—31no—
481C4×D4—61no—
482C4×D4—151no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—151no—
485#106—151no—
486#106—151no—
487#106—151no—
488C4⋊C8—151no—
489#103—51no—
490#103—51no—
491#103—51no—
492#103—51no—
493#103—151no—
494#103—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499C22⋊C8—151no—
500C22⋊C8—151no—
501C4×C8—151no—
502C2×C3×C5—22no—
503C2×C3×C5#54611yescharacteristic
504C2×C3×C5C22×SD1611yescharacteristic
505C2×C3×C5#57811yescharacteristic
506D15—81no—
507C5×D3—22no—
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—101no—
510C22×D3C2×C22⋊D511yescharacteristic
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—42no—
515C3×Q8#71112yescomplemented
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—42no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—202no—
524C2×C3×C4C2×C22⋊D511yescharacteristic
525C2×C3×C4C23×D511yescharacteristic
526#67—202no—
527#67#68814yescomplemented
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—101no—
531C2×Dic3C2×C22⋊D511yescharacteristic
532C2×Dic3C2×C22⋊D511yescharacteristic
533C2×Dic3C2×C22⋊D511yescharacteristic
534D12—101no—
535D12—101no—
536D12—202no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—202no—
541C4×D3—202no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6—202no—
546C3×C8—101no—
547C3×C8—101no—
548C3⋊C8—101no—
549C3⋊C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—32no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5D3×SD1612yes—
556C22×C5C2×D3×D411yescharacteristic
557C2×D5—121no—
558C2×D5—121no—
559C2×D5—121no—
560C4×C5—21no—
561C4×C5—22no—
562C4×C5—32no—
563C4×C5—41no—
564C4×C5—61no—
565C4×C5—61no—
566C4×C5—121no—
567C4×C5—121no—
568C4×C5C2×#23511yescharacteristic
569C4×C5#100411yescharacteristic
570Dic5—41no—
571Dic5—41no—
572Dic5—121no—
573#41—604no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—31no—
577C2×Q8—41no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8—121no—
581C2×Q8—301no—
582C2×Q8C2×D3×D511yescharacteristic
583C2×Q8C2×D3×D511yescharacteristic
584C2×D4—31no—
585C2×D4—151no—
586C2×D4—301no—
587C2×D4—301no—
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—101no—
592C22×C4—301no—
593C22×C4—301no—
594C22×C4C2×D3×D511yescharacteristic
595SD16—302no—
596SD16—601no—
597SD16—601no—
598C2×C8—51no—
599C2×C8—51no—
600C2×C8—151no—
601C2×C8—151no—
602C2×C8—201no—
603C2×C8—601no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—51no—
607C4⋊C4—51no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—101no—
614C4⋊C4—151no—
615C4⋊C4—301no—
616C4⋊C4—301no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C22⋊C4—301no—
624C42—31no—
625C42—61no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3C2×#68812yes—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—201no—
634C2×D3—201no—
635C2×D3—201no—
636C2×D3C2×#68812yes—
637C3×C4—22no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—201no—
641C3×C4—201no—
642C3×C4C2×#71111yescharacteristic
643C3×C4#414411yescharacteristic
644Dic3—21no—
645Dic3—21no—
646Dic3—41no—
647Dic3—41no—
648Dic3—201no—
649Dic3C2×#68812yes—
650C2×C5—22no—
651C2×C5—62no—
652C2×C5#549011yescharacteristic
653C2×C5C2×D3×SD1611yescharacteristic
654C2×C5#576611yescharacteristic
655D5—241no—
656C23—31no—
657C23—301no—
658C23D3×C22⋊D511yescharacteristic
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—42no—
663Q8—61no—
664Q8—61no—
665Q8—122no—
666Q8—602no—
667Q8#678212yescomplemented
668D4—34no—
669D4—301no—
670D4—301no—
671D4—602no—
672D4—602no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—42no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—122no—
688C2×C4—202no—
689C2×C4—301no—
690C2×C4—602no—
691C2×C4—602no—
692C2×C4D3×C22⋊D511yescharacteristic
693C2×C4C22×D3×D511yescharacteristic
694C8—101no—
695C8—101no—
696C8—301no—
697C8—301no—
698C2×C3—22no—
699C2×C3#6614011yescharacteristic
700C2×C3C22×#68811yescharacteristic
701C2×C3#6617211yescharacteristic
702D3—22no—
703D3—401no—
704C5#7880511yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—601no—
711C22—601no—
712C22—601no—
713C22D3×#68812yes—
714C22C2×D3×C22⋊D511yescharacteristic
715C4—21no—
716C4—22no—
717C4—32no—
718C4—41no—
719C4—61no—
720C4—61no—
721C4—121no—
722C4—121no—
723C4—201no—
724C4—201no—
725C4—601no—
726C4C2×#678211yescharacteristic
727C4#9204911yescharacteristic
728C3#1061528111yescharacteristic, complemented, Sylow
729C2—22no—
730C2—62no—
731C2—1201no—
732C2C2×D3×#68811yescharacteristic
733C2#1175510511yescharacteristic
734C2#1175539311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11754361C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C5×Q8×#67C2semidirect
3. #11751328C2semidirect
4. C2×C3×#3967C2semidirect
5. #11749358C2semidirect
6. #11749280C2semidirect
7. #11749279C2semidirect
8. #11749233C2semidirect
9. #11749232C2semidirect
10. #11749200C2semidirect
11. D3×#3967C2semidirect
12. #11749187C2semidirect
13. #11748535C2semidirect
14. #67×#168C2semidirect
15. #11748406C2semidirect
66. C2×#3967D3semidirect
129. Q8×#67D5semidirect
195. C3×C5×Q8#41semidirect
207. C5×#67SD16semidirect
427. C5×Q8#235semidirect
515. C3×Q8#711semidirect
527. #67#688semidirect
626. C3×C5#3298semidirect
667. Q8#6782semidirect
704. C5#78805semidirect
728. C3#10615281semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×#672
#117543612
#117513282
C2×C3×#39672
#117493582
#117492802
#117492792
#117492332
#117492322
#117492002
D3×#39672
#117491872
#117485352
#67×#1682
#117484062
#106152813
#788055