Finite Group Databasebeta

← #14458811

Subgroups — #14458811

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
1C5×#5676C211yesmaximal, characteristic
2#11752613C211yesmaximal, characteristic, complemented
3#11751155C211yesmaximal, characteristic, complemented
4C3×#65345C211yesmaximal, characteristic, complemented
5#11749301C211yesmaximal, characteristic, complemented
6#11749300C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749200C211yesmaximal, characteristic, complemented
9#11749056C211yesmaximal, characteristic, complemented
10#11749055C211yesmaximal, characteristic, complemented
11#11748968C211yesmaximal, characteristic, complemented
12D3×#3964C211yesmaximal, characteristic, complemented
13C4×#6659C211yesmaximal, characteristic, complemented
14D12×#168C211yesmaximal, characteristic, complemented
15#11746902C211yesmaximal, characteristic, complemented
16#10615225—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C2×#6718C2211yescharacteristic, complemented
21C2×#6716C2211yescharacteristic
22C4×Dic30C2211yescharacteristic, complemented
23C5×#946C2211yescharacteristic
24C5×#938C2211yescharacteristic
25C5×#884—21no—
26C5×#883—21no—
27C5×#882—21no—
28C5×D3×C22⋊C4—21no—
29C4×C5×D12C2211yescharacteristic
30C4×C5×D12C2211yescharacteristic
31C3×#4016C2211yescharacteristic, complemented
32D3×C4⋊Dic5C2211yescharacteristic
33#91423—21no—
34#91400—21no—
35#91367—21no—
36#91365C2211yescharacteristic
37#91365C2211yescharacteristic, complemented
38#91338C2211yescharacteristic, complemented
39#91335—21no—
40C2×#6659C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91116C2211yescharacteristic
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×#3967C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×#3964C2211yescharacteristic
50C3×C4×#168C2211yescharacteristic, complemented
51#90989C2211yescharacteristic, complemented
52#90986C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#81652—51nomaximal, Hall
61C5×#546—31no—
62#65875—31no—
63#65528—31no—
64#65522—31no—
65#65507—31no—
66C2×#3964—31no—
67#65345D311yescharacteristic, complemented
68#65343—31no—
69#65340—31no—
70#65332—31no—
71#65330—31no—
72#65324—31no—
73C4×#687—31no—
74D4×#168—31no—
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67—21no—
82C5×#239—22no—
83C5×#239—41no—
84C5×D3×D4—22no—
85C5×D3×D4—41no—
86C2×C5×D12—21no—
87C2×C5×D12D411yescharacteristic
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3C2311yescharacteristic
92C2×C4×C5×D3C2311yescharacteristic
93C2×D3×Dic5—21no—
94C3×C5×C22⋊C4—21no—
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97#6718—41no—
98#6716—41no—
99C4⋊Dic15C2311yescharacteristic
100#6712—21no—
101C4×Dic15—21no—
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#217—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×C4⋊Dic3D411yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C3×#683—21no—
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118Dic3⋊Dic5—21no—
119#6668—21no—
120#6668—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124Dic3×Dic5—21no—
125#6659—22no—
126D3×#168—41no—
127D3×#168—41no—
128#5694—51no—
129#5676D511yescharacteristic
130C3×#488—51no—
131#5066—51no—
132#5054—51no—
133#4813—51no—
134#4808—51no—
135#4805—51no—
136#4804—51no—
137#4779—51no—
138#4778—51no—
139#4776—51no—
140D3×#102—51no—
141C4×#204—51no—
142C8×D12—51no—
143C2×C5×#41—31no—
144C22×C5×D4—31no—
145C5×#124C2×D311yescharacteristic
146C5×#123—61no—
147C5×C22⋊Q8—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C2×C5×C22⋊C4—61no—
154C2×#689—31no—
155#4081—61no—
156C2×#687—31no—
157C2×#687—31no—
158#4072—31no—
159C2×C4⋊Dic5—31no—
160#4070—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4035—61no—
165#4025—61no—
166#4023—61no—
167#4016C2×D311yescharacteristic, complemented
168C4×Dic10—31no—
169#3967—31no—
170#3967C2×D311yescharacteristic, complemented
171#3967C2×D311yescharacteristic, complemented
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964C2×D311yescharacteristic
177#3964C2×D311yescharacteristic
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3942—31no—
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168C2×D311yescharacteristic, complemented
186#3296—151noSylow
187C23×C3×C5—21no—
188C22×C5×D3—21no—
189C22×C5×D3—42no—
190C22×C5×D3—42no—
191C22×C5×D3—81no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C5×D3C2×D411yescharacteristic
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×D4—21no—
197C3×C5×D4—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—21no—
204Dic30—21no—
205Dic30—21no—
206C5×#67—42no—
207C5×#67—81no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—22no—
212C5×D12—21no—
213C5×D12—42no—
214C5×D12#4112yes—
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C4×C5×D3—42no—
220C4×C5×D3—81no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223D3×Dic5—42no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×#239C2×D511yescharacteristic
229C2×D3×D4C2×D511yescharacteristic
230C3×#125—51no—
231C3×#124C2×D511yescharacteristic
232#946C2×D511yescharacteristic
233C2×#216—51no—
234#938C2×D511yescharacteristic
235C2×#214—51no—
236C2×#204—51no—
237C2×D3×C8—51no—
238C2×D3×C8—51no—
239#898—101no—
240#897—51no—
241#897—51no—
242#894—101no—
243#892—51no—
244#892—101no—
245D3×C4⋊C4—51no—
246#890—101no—
247#884—21no—
248#883—21no—
249#882—21no—
250D3×C22⋊C4—21no—
251C4×D12C2×D511yescharacteristic
252C4×D12C2×D511yescharacteristic
253C4×Dic6—51no—
254C3×#103—51no—
255C3×#103—51no—
256C3×#102—51no—
257C3×#102—51no—
258C3×C4×C8—51no—
259#835—51no—
260#832—51no—
261#821—51no—
262(C2×D3)⋊C8—51no—
263(C2×D3)⋊C8—51no—
264#817—51no—
265#816—51no—
266#809—51no—
267#809—51no—
268#808—51no—
269#807—51no—
270C4⋊(C3⋊C8)—51no—
271C24×C5—61no—
272C5×#41—62no—
273C5×#41—121no—
274C2×C5×Q8C22×D311yescharacteristic
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C2×C5×D4—62no—
280C2×C5×D4—61no—
281C2×C5×D4—121no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—31no—
284C22×C4×C5—31no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C22×Dic5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—31no—
290C5×C4⋊C4—31no—
291C5×C4⋊C4—61no—
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—31no—
295C5×C22⋊C4—31no—
296C5×C22⋊C4—61no—
297C5×C22⋊C4—61no—
298C5×C22⋊C4—61no—
299C42×C5C22×D311yescharacteristic
300C22⋊Dic5—61no—
301C22⋊Dic5—61no—
302C22⋊Dic5—61no—
303#689—121no—
304#687—62no—
305#687—121no—
306C4⋊Dic5—31no—
307C4⋊Dic5—61no—
308C4⋊Dic5C22×D311yescharacteristic
309C4⋊Dic5C22×D311yescharacteristic
310#683—21no—
311#683—21no—
312#683—61no—
313#683—61no—
314#683—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—121no—
320C2×#168—121no—
321C2×#168C22×D311yescharacteristic
322C2×#168C22×D311yescharacteristic
323#552—151no—
324#546—31no—
325#488—51no—
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—41no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C5×D3—21no—
343C2×C5×D3—21no—
344C2×C5×D3—21no—
345C2×C5×D3—22no—
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—84no—
351C2×C5×D3#13512yes—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5C2×#4111yescharacteristic
356C3×C4×C5H(5,𝔽2)11yescharacteristic
357Dic15—41no—
358Dic15—41no—
359C3×Dic5—41no—
360C3×Dic5—41no—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C23×D3—21no—
365C2×C3×Q8C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C2×#67—21no—
368C2×#67—21no—
369#239—22no—
370#239—41no—
371D3×D4—22no—
372D3×D4—41no—
373C2×D12—21no—
374C2×D12C22⋊D511yescharacteristic
375C2×D12C22×D511yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—101no—
379C2×C4×D3C22×D511yescharacteristic
380C2×C4×D3C22×D511yescharacteristic
381C2×Dic6—51no—
382C2×C3×C8—51no—
383C2×C3×C8—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C42C22×D511yescharacteristic
391#217—21no—
392#216—201no—
393#214—201no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399(C2×D3)⋊C4C22⋊D511yescharacteristic
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—51no—
402C4⋊Dic3—101no—
403C4⋊Dic3—101no—
404C4⋊Dic3C22⋊D511yescharacteristic
405C4⋊Dic3C22×D511yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—101no—
408Dic3⋊C4—101no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413#204—102no—
414D3×C8—201no—
415D3×C8—201no—
416C23×C5—21no—
417C23×C5—31no—
418C23×C5—31no—
419C23×C5—61no—
420C23×C5—122no—
421C23×C5—122no—
422C23×C5—241no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—21no—
426C5×D4—21no—
427C5×D4—32no—
428C5×D4—62no—
429C5×D4—61no—
430C5×D4—122no—
431C5×D4—122no—
432C5×D4—241no—
433C2×C4×C5—21no—
434C2×C4×C5—31no—
435C2×C4×C5—31no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—122no—
442C2×C4×C5—241no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451Dic10—61no—
452Dic10—61no—
453#168—21no—
454#168—21no—
455#168—61no—
456#168—61no—
457C2×#41—31no—
458C22×D4—31no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—301no—
465#125—51no—
466#125—301no—
467#124D3×D511yescharacteristic
468#123—61no—
469#123—301no—
470C22⋊Q8—31no—
471C22⋊Q8—151no—
472C22⋊Q8—151no—
473#121—31no—
474#121—61no—
475#120—61no—
476C4×Q8—151no—
477C4×D4—31no—
478C4×D4—31no—
479#117—151no—
480#117—301no—
481C2×C4⋊C4—151no—
482C2×C22⋊C4—61no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—151no—
487#103—51no—
488#103—51no—
489#103—151no—
490#103—151no—
491#102—51no—
492#102—51no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—51no—
500C2×C3×C5—81no—
501C2×C3×C5#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C5×D3—22no—
505C5×D3—41no—
506C5×D3—42no—
507C23×C3—21no—
508C22×D3—21no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—81no—
512C22×D3C2×C22⋊D511yescharacteristic
513C22×D3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×D4—21no—
517C3×D4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C2×C22⋊D511yescharacteristic
523C2×C3×C4C23×D511yescharacteristic
524#67—42no—
525#67—81no—
526C2×Dic3—21no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531D12—22no—
532D12—21no—
533D12—42no—
534D12#71112yes—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—81no—
541C4×D3—202no—
542Dic6—101no—
543Dic6—101no—
544C3×C8—101no—
545C3×C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—32no—
549C22×C5—41no—
550C22×C5—41no—
551C22×C5—41no—
552C22×C5—61no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5—62no—
556C22×C5—61no—
557C22×C5—61no—
558C22×C5—121no—
559C22×C5—121no—
560C22×C5—244no—
561C22×C5C2×D3×D411yescharacteristic
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—41no—
565C4×C5—61no—
566C4×C5—61no—
567C4×C5—121no—
568C4×C5D3×#4111yescharacteristic
569C4×C5#100911yescharacteristic
570Dic5—41no—
571Dic5—41no—
572Dic5—121no—
573Dic5—121no—
574C24—61no—
575#41—62no—
576#41—121no—
577C2×Q8—151no—
578C2×Q8C2×D3×D511yescharacteristic
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—62no—
584C2×D4—61no—
585C2×D4—121no—
586C2×D4C2×D3×D511yescharacteristic
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—301no—
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—51no—
604C4⋊C4—51no—
605C4⋊C4—61no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—151no—
609C4⋊C4—301no—
610C4⋊C4—301no—
611C4⋊C4—301no—
612C4⋊C4—301no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—301no—
624C42—301no—
625C42C2×D3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—84no—
640C2×D3#409612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—201no—
645C3×C4—201no—
646C3×C4C2×#71111yescharacteristic
647C3×C4#414411yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—201no—
652Dic3—201no—
653C2×C5—62no—
654C2×C5—81no—
655C2×C5—121no—
656C2×C5—122no—
657C2×C5#567611yescharacteristic
658C2×C5D3×#13511yescharacteristic
659C2×C5#577011yescharacteristic
660C23—21no—
661C23—31no—
662C23—31no—
663C23—61no—
664C23—122no—
665C23—122no—
666C23—241no—
667Q8—21no—
668Q8—21no—
669Q8—301no—
670Q8—301no—
671D4—21no—
672D4—21no—
673D4—32no—
674D4—62no—
675D4—61no—
676D4—122no—
677D4—122no—
678D4—241no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—122no—
690C2×C4—241no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—602no—
694C2×C4D3×C22⋊D511yescharacteristic
695C2×C4D3×C22⋊D511yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—301no—
700C8—301no—
701C2×C3—81no—
702C2×C3#6614011yescharacteristic
703C2×C3C2×#409611yescharacteristic
704C2×C3#6617011yescharacteristic
705D3—22no—
706D3—41no—
707D3—42no—
708C5#8165211yescharacteristic, complemented, Sylow
709C22—32no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—244no—
722C22C2×D3×C22⋊D511yescharacteristic
723C4—21no—
724C4—21no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—121no—
729C4—201no—
730C4—201no—
731C4—601no—
732C4—601no—
733C4D3×#71111yescharacteristic
734C4#9202711yescharacteristic
735C3#1061522511yescharacteristic, complemented, Sylow
736C2—62no—
737C2—81no—
738C2—121no—
739C2—122no—
740C2#1175494911yescharacteristic
741C2D3×#409611yescharacteristic
742C2#1175534711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#5676C2
hypercenter#124D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752613C2semidirect
3. #11751155C2semidirect
4. C3×#65345C2semidirect
5. #11749301C2semidirect
6. #11749300C2semidirect
7. #11749211C2semidirect
8. #11749200C2semidirect
9. #11749056C2semidirect
10. #11749055C2semidirect
11. #11748968C2semidirect
12. D3×#3964C2semidirect
13. C4×#6659C2semidirect
14. D12×#168C2semidirect
15. #11746902C2semidirect
20. C2×#6718C22semidirect
22. C4×Dic30C22semidirect
31. C3×#4016C22semidirect
37. #91365C22semidirect
38. #91338C22semidirect
42. C2×D3×#168C22semidirect
43. #91119C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. C3×#3967C22semidirect
47. C3×#3967C22semidirect
50. C3×C4×#168C22semidirect
51. #90989C22semidirect
52. #90986C22semidirect
53. #90985C22semidirect
54. #90975C22semidirect
59. (C2×D3)⋊#168C22semidirect
67. #65345D3semidirect
167. #4016C2×D3semidirect
170. #3967C2×D3semidirect
171. #3967C2×D3semidirect
185. C4×#168C2×D3semidirect
626. C3×C5#3296semidirect
708. C5#81652semidirect
735. C3#10615225semidirect

Maximal subgroups

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

subgroupindex
C5×#56762
#117526132
#117511552
C3×#653452
#117493012
#117493002
#117492112
#117492002
#117490562
#117490552
#117489682
D3×#39642
C4×#66592
D12×#1682
#117469022
#106152253
#816525