Finite Group Databasebeta

← D3×#65174 #14431595

Subgroups — D3×#65174 #14431595

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4041C211yesmaximal, characteristic
2D3×#4038C211yesmaximal, characteristic, complemented
3#11750986C211yesmaximal, characteristic, complemented
4C5×D3×#107C211yesmaximal, characteristic, complemented
5C3×#65174C211yesmaximal, characteristic, complemented
6D3×#3953C211yesmaximal, characteristic, complemented
7D3×#3952C211yesmaximal, characteristic, complemented
8#11747670C211yesmaximal, characteristic, complemented
9#11747572C211yesmaximal, characteristic, complemented
10D3×#3941C211yesmaximal, characteristic, complemented
11D3×#3940C211yesmaximal, characteristic, complemented
12#11747334C211yesmaximal, characteristic, complemented
13#11747213C211yesmaximal, characteristic, complemented
14#11747206C211yesmaximal, characteristic, complemented
15#11747166C211yesmaximal, characteristic, complemented
16C2×#65174—31nomaximal, Hall
17C2×D3×D20—21no—
18C2×D3×D20C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20#91784C2211yescharacteristic
21#91781C2211yescharacteristic, complemented
22C2×C5×D3×C8C2211yescharacteristic
23C5×D3×C4⋊C4C2211yescharacteristic
24C5×D3×C4⋊C4C2211yescharacteristic
25C3×#4041C2211yescharacteristic
26C3×#4038C2211yescharacteristic, complemented
27D3×#685—21no—
28D3×#685—21no—
29#91465C2211yescharacteristic
30#91459—21no—
31#91450C2211yescharacteristic
32D3×C4⋊Dic5C2211yescharacteristic
33#91409—21no—
34#91402—21no—
35C4×D3×Dic5—21no—
36#91394—21no—
37#91358C2211yescharacteristic, complemented
38#91347C2211yescharacteristic, complemented
39C2×D3×#168C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic, complemented
41#91105C2211yescharacteristic, complemented
42#91104C2211yescharacteristic, complemented
43#91093C2211yescharacteristic, complemented
44#91092C2211yescharacteristic, complemented
45C5×#818C2211yescharacteristic, complemented
46C5×#807C2211yescharacteristic, complemented
47C5×#807C2211yescharacteristic, complemented
48C3×#3953C2211yescharacteristic, complemented
49C3×#3952C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic, complemented
51C3×#3940C2211yescharacteristic, complemented
52#90986C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90969C2211yescharacteristic, complemented
55#90968C2211yescharacteristic, complemented
56#90965C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58#90957C2211yescharacteristic, complemented
59#90955C2211yescharacteristic, complemented
60D3×#482—51nomaximal, Hall
61C2×#4041—31no—
62C2×#4038—31no—
63C2×C5×#107—31no—
64C2×#3953—31no—
65C2×#3952—31no—
66C2×#3941—31no—
67C2×#3940—31no—
68#65174—31no—
69#65174—31no—
70#65174—31no—
71#65174—31no—
72#65174—31no—
73#65174—31no—
74#65174—31no—
75#65174D311yescharacteristic, direct product factor
76C22×D3×D5—21no—
77C22×D3×D5D411yescharacteristic
78C2×D60—21no—
79C2×D60C2311yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3—21no—
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×D20—21no—
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1202—21no—
88C2×#1202—21no—
89C2×#1202—21no—
90C2×#1200D411yescharacteristic
91C2×D3×Dic5—21no—
92C2×D3×Dic5D411yescharacteristic
93C2×D5×Dic3D411yescharacteristic
94D3×D20—22no—
95D3×D20—22no—
96D3×D20—44no—
97C4×D3×D5—22no—
98C4×D3×D5—22no—
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6714—21no—
103#6714—21no—
104C4⋊Dic15C2311yescharacteristic
105C4×Dic15—21no—
106C2×C3⋊#168C2311yescharacteristic
107C5×C4⋊Dic3C2311yescharacteristic
108C5×C4⋊Dic3C2311yescharacteristic
109C5×Dic3⋊C4—21no—
110C5×Dic3⋊C4—21no—
111C2×C5×C3⋊C8C2311yescharacteristic
112C5×D3×C8—22no—
113C3×#685—21no—
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4×Dic5—21no—
117C2×C3×#168C2311yescharacteristic
118Dic3⋊Dic5—21no—
119#6667—21no—
120#6667—21no—
121#6665—21no—
122#6665—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125D3×#168—22no—
126D3×#121—51no—
127D3×#117—51no—
128C3×#482—51no—
129#5035—51no—
130#5003—51no—
131#4885—51no—
132D3×#107D511yescharacteristic, complemented
133#4866—51no—
134D3×#106—51no—
135#4784—51no—
136#4779—51no—
137D3×#102—51no—
138D3×#102—51no—
139#4737—51no—
140D3×C22⋊C8—51no—
141C22×D20—31no—
142C22×D20—61no—
143C22×C4×D5—31no—
144C22×C5×C8—31no—
145C2×C5×C4⋊C4—31no—
146C2×C5×C4⋊C4—31no—
147C2×#685—61no—
148C2×#685—61no—
149C2×C4⋊Dic5—31no—
150C2×C4×Dic5—61no—
151C22×#168—31no—
152#4041—31no—
153#4041—31no—
154#4041—31no—
155#4041—61no—
156#4041—61no—
157#4041C2×D311yescharacteristic
158#4038—31no—
159#4038—31no—
160#4038—31no—
161#4038—61no—
162#4038—61no—
163#4038C2×D311yescharacteristic, complemented
164C5×#107—31no—
165C5×#107—31no—
166C5×#107—31no—
167C5×#107C2×D311yescharacteristic, complemented
168#3953—31no—
169#3953—31no—
170#3953—31no—
171#3953C2×D311yescharacteristic, complemented
172#3952—31no—
173#3952—31no—
174#3952—31no—
175#3952C2×D311yescharacteristic, complemented
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941C2×D311yescharacteristic, complemented
180#3940—31no—
181#3940—31no—
182#3940—31no—
183#3940C2×D311yescharacteristic, complemented
184C2×#482—151noSylow
185C22×D15—21no—
186C22×D15C2×D411yescharacteristic
187C22×C5×D3C2×D411yescharacteristic
188C22×C3×D5—21no—
189C22×C3×D5C2×D411yescharacteristic
190C2×D3×D5—22no—
191C2×D3×D5—22no—
192C2×D3×D5—22no—
193C2×D3×D5—42no—
194C2×D3×D5—42no—
195C2×D3×D5—42no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15C2×D411yescharacteristic
201D60—21no—
202D60—21no—
203D60—42no—
204C4×D15—21no—
205C4×D15—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3C2×D411yescharacteristic
209C4×C5×D3—42no—
210C4×C5×D3—42no—
211C4×C5×D3#4112yes—
212C4×C5×D3#4112yes—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C3×D20—21no—
216C3×D20—21no—
217C3×D20—42no—
218C3×C4×D5—21no—
219C3×C4×D5—21no—
220#1202—42no—
221#1202—42no—
222#1202—42no—
223#1200—22no—
224D3×Dic5—22no—
225D3×Dic5—42no—
226D5×Dic3—22no—
227C3×C5×C8—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C5×C3⋊C8—21no—
231C2×D3×D4—51no—
232C2×D3×D4—101no—
233C22×C4×D3—51no—
234C3×#121—51no—
235C3×#117—51no—
236#939—101no—
237#938—51no—
238#930—51no—
239#926—51no—
240C2×D3×C8—51no—
241C2×D3×C8C2×D511yescharacteristic
242#895—51no—
243#892—51no—
244#892—51no—
245D3×C4⋊C4—51no—
246D3×C4⋊C4C2×D511yescharacteristic
247D3×C4⋊C4C2×D511yescharacteristic
248#884—101no—
249D3×C22⋊C4—101no—
250D3×C22⋊C4—101no—
251#877—101no—
252#872—101no—
253C42×D3—101no—
254C3×#107C2×D511yescharacteristic, complemented
255C3×#106—51no—
256C3×#102—51no—
257C3×#102—51no—
258C3×C22⋊C8—51no—
259#832—51no—
260#832—51no—
261#830—51no—
262#821—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265(C2×D3)⋊C8—51no—
266#818C2×D511yescharacteristic, complemented
267#817—51no—
268#809—51no—
269#809—51no—
270#808—51no—
271#808—51no—
272#807C2×D511yescharacteristic, complemented
273#807C2×D511yescharacteristic, complemented
274C23×D5—31no—
275C23×D5—61no—
276C22×C4×C5—31no—
277C22×C4×C5—61no—
278C22×C4×C5—61no—
279C22×Dic5—31no—
280C22×Dic5—61no—
281C2×D20—21no—
282C2×D20—31no—
283C2×D20—62no—
284C2×D20—62no—
285C2×D20—61no—
286C2×D20—61no—
287C2×D20—61no—
288C2×D20—61no—
289C2×D20—124no—
290C2×D20C22×D311yescharacteristic
291C2×C4×D5—31no—
292C2×C4×D5—31no—
293C2×C4×D5—31no—
294C2×C4×D5—62no—
295C2×C4×D5—62no—
296C2×C4×D5C22×D311yescharacteristic
297C2×C5×C8—31no—
298C2×C5×C8—62no—
299C2×C5×C8C22×D311yescharacteristic
300C5×C4⋊C4—31no—
301C5×C4⋊C4—31no—
302C5×C4⋊C4—61no—
303C5×C4⋊C4—61no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C4⋊C4C22×D311yescharacteristic
306#685—21no—
307#685—21no—
308#685—61no—
309#685—61no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5C22×D311yescharacteristic
317C4×Dic5—21no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C4×Dic5—61no—
321C2×#168—31no—
322C2×#168—62no—
323C2×#168C22×D311yescharacteristic
324C2×#121—151no—
325C2×#117—151no—
326#482—51no—
327#482—151no—
328#482—151no—
329#482—151no—
330#482—151no—
331#482—151no—
332#482—151no—
333#482—151no—
334C2×#107—31no—
335C2×#106—151no—
336C2×#102—151no—
337C2×#102—151no—
338C2×C22⋊C8—151no—
339C22×C3×C5C22×D411yescharacteristic
340C2×D15—21no—
341C2×D15—21no—
342C2×D15—21no—
343C2×D15—41no—
344C2×D15—41no—
345C2×D15—41no—
346C2×C5×D3#12312yes—
347C2×C5×D3#13512yes—
348C2×C5×D3AGL(1,ℤ/8)12yes—
349C2×C3×D5—21no—
350C2×C3×D5—21no—
351C2×C3×D5—21no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355D3×D5—44no—
356D3×D5—84no—
357C3×C4×C5—41no—
358C3×C4×C5—41no—
359C3×C4×C5C2×#4111yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—41no—
363C3×Dic5—21no—
364C3×Dic5—41no—
365C5×Dic3—41no—
366C5×Dic3—41no—
367C5×Dic3#12312yes—
368C23×D3—51no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C22×C3×C4—51no—
373C2×#67—101no—
374C2×#67—101no—
375C2×#67—101no—
376C22×Dic3—51no—
377D3×D4—102no—
378D3×D4—102no—
379D3×D4—204no—
380C2×D12—51no—
381C2×D12—101no—
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—51no—
385C2×C4×D3—51no—
386C2×C4×D3—51no—
387C2×C4×D3—102no—
388C2×C4×D3—102no—
389C2×C4×D3—101no—
390C2×C4×D3C22×D511yescharacteristic
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C42—101no—
399#217—101no—
400#217—101no—
401(C2×D3)⋊C4—101no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405C4⋊Dic3—51no—
406C4⋊Dic3C22×D511yescharacteristic
407C4⋊Dic3C22×D511yescharacteristic
408Dic3⋊C4—21no—
409Dic3⋊C4—21no—
410Dic3⋊C4—101no—
411C4×Dic3—101no—
412C4×Dic3—101no—
413C4×Dic3—101no—
414C2×C3⋊C8—51no—
415C2×C3⋊C8C22×D511yescharacteristic
416D3×C8—22no—
417D3×C8—102no—
418C23×C5—31no—
419C22×D5—21no—
420C22×D5—31no—
421C22×D5—62no—
422C22×D5—62no—
423C22×D5—62no—
424C22×D5—61no—
425C22×D5—122no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5D3×D411yescharacteristic
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—31no—
432C2×C4×C5—32no—
433C2×C4×C5—32no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—122no—
437C2×C4×C5—122no—
438C2×C4×C5C23×D311yescharacteristic
439C2×Dic5—21no—
440C2×Dic5—31no—
441C2×Dic5—62no—
442C2×Dic5—61no—
443C2×Dic5—122no—
444C2×Dic5D3×D411yescharacteristic
445D20—21no—
446D20—21no—
447D20—42no—
448D20—61no—
449D20—61no—
450D20—122no—
451D20—122no—
452D20—122no—
453D20—122no—
454C4×D5—21no—
455C4×D5—21no—
456C4×D5—62no—
457C4×D5—62no—
458C4×D5—61no—
459C4×D5—61no—
460C5×C8—21no—
461C5×C8—61no—
462#168—21no—
463#168—61no—
464C22×D4—151no—
465C22×D4—301no—
466C23×C4—151no—
467C22×C8—31no—
468C22×C8—151no—
469#121—51no—
470#121—151no—
471#121—151no—
472#121—151no—
473#121—301no—
474#121—301no—
475#117—51no—
476#117—151no—
477#117—151no—
478#117—151no—
479#117—301no—
480#117—301no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—151no—
484C2×C22⋊C4—301no—
485C2×C22⋊C4—301no—
486C2×C42—301no—
487#107—31no—
488#107—31no—
489#107—31no—
490#107D3×D511yescharacteristic, complemented
491#106—51no—
492#106—151no—
493#106—151no—
494#106—151no—
495#102—51no—
496#102—51no—
497#102—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503C22⋊C8—51no—
504C22⋊C8—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C2×C3×C5C2×#12311yescharacteristic
508C2×C3×C5C2×#13511yescharacteristic
509C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
510D15—41no—
511D15—81no—
512C3×D5—41no—
513C3×D5—81no—
514C5×D3#48214yescomplemented
515C23×C3—51no—
516C23×C3—101no—
517C22×D3—51no—
518C22×D3—102no—
519C22×D3—102no—
520C22×D3—102no—
521C22×D3—101no—
522C22×D3—202no—
523C22×D3—202no—
524C22×D3—202no—
525C22×D3D4×D511yescharacteristic
526C3×D4—101no—
527C3×D4—101no—
528C3×D4—202no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—51no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4C23×D511yescharacteristic
536#67—202no—
537#67—202no—
538#67—202no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—51no—
542C2×Dic3—102no—
543C2×Dic3—101no—
544C2×Dic3D4×D511yescharacteristic
545D12—101no—
546D12—101no—
547D12—202no—
548C4×D3—42no—
549C4×D3—42no—
550C4×D3—102no—
551C4×D3—101no—
552C4×D3—101no—
553C4×D3—102no—
554C4×D3—202no—
555C4×D3#70912yes—
556C4×D3#71312yes—
557C3×C8—21no—
558C3×C8—101no—
559C3⋊C8—21no—
560C3⋊C8—101no—
561C22×C5—32no—
562C22×C5—32no—
563C22×C5—32no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—21no—
566C2×D5—21no—
567C2×D5—21no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—41no—
571C2×D5—61no—
572C2×D5—61no—
573C2×D5—61no—
574C2×D5—124no—
575C2×D5—121no—
576C2×D5—121no—
577C2×D5—121no—
578C2×D5—244no—
579C4×C5—32no—
580C4×C5—41no—
581C4×C5—41no—
582C4×C5—121no—
583C4×C5—121no—
584C4×C5D3×#4111yescharacteristic
585C4×C5D3×#4111yescharacteristic
586Dic5—21no—
587Dic5—41no—
588Dic5—61no—
589Dic5—121no—
590C24—151no—
591C24—301no—
592C2×D4—51no—
593C2×D4—101no—
594C2×D4—151no—
595C2×D4—301no—
596C2×D4—302no—
597C2×D4—302no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—301no—
601C2×D4—604no—
602C22×C4—31no—
603C22×C4—51no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—302no—
611C22×C4—302no—
612C22×C4—301no—
613C2×C8—31no—
614C2×C8—51no—
615C2×C8—62no—
616C2×C8—151no—
617C2×C8—302no—
618C2×C8C2×D3×D511yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—51no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—151no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C4⋊C4C2×D3×D511yescharacteristic
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C42—101no—
637C42—301no—
638C42—301no—
639C42—301no—
640C3×C5C2×#48211yescharacteristic, complemented, Hall
641C22×C3—101no—
642C22×C3—101no—
643C22×C3—101no—
644C22×C3—201no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3C2×D4×D511yescharacteristic
648C2×D3—101no—
649C2×D3—101no—
650C2×D3—101no—
651C2×D3—204no—
652C2×D3—201no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—404no—
656C2×D3#404012yes—
657C2×D3#405712yes—
658C2×D3#406512yes—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—101no—
662C3×C4—201no—
663C3×C4C2×#70911yescharacteristic
664C3×C4C2×#71311yescharacteristic
665Dic3—41no—
666Dic3—41no—
667Dic3—101no—
668Dic3—201no—
669Dic3#404012yes—
670C2×C5—34no—
671C2×C5D3×#12311yescharacteristic
672C2×C5D3×#13511yescharacteristic
673C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
674D5—41no—
675D5—81no—
676D5—121no—
677D5—241no—
678C23—31no—
679C23—51no—
680C23—101no—
681C23—151no—
682C23—302no—
683C23—302no—
684C23—302no—
685C23—301no—
686C23—602no—
687C23—602no—
688C23—602no—
689D4—101no—
690D4—101no—
691D4—202no—
692D4—301no—
693D4—301no—
694D4—602no—
695D4—602no—
696D4—602no—
697D4—602no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—51no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—151no—
712C2×C4—302no—
713C2×C4—302no—
714C2×C4—302no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—301no—
718C2×C4—602no—
719C2×C4C22×D3×D511yescharacteristic
720C8—21no—
721C8—61no—
722C8—101no—
723C8—301no—
724C2×C3—201no—
725C2×C3—401no—
726C2×C3C2×#404011yescharacteristic
727C2×C3C2×#405711yescharacteristic
728C2×C3C2×#406511yescharacteristic
729D3—201no—
730D3—401no—
731D3#6517414yesdirect product factor
732C5D3×#48211yescharacteristic, complemented, Sylow
733C22—32no—
734C22—32no—
735C22—32no—
736C22—101no—
737C22—101no—
738C22—101no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—301no—
743C22—301no—
744C22—301no—
745C22—604no—
746C22—601no—
747C22—601no—
748C22—601no—
749C22—1204no—
750C22D3×D4×D511yescharacteristic
751C4—32no—
752C4—41no—
753C4—41no—
754C4—101no—
755C4—121no—
756C4—121no—
757C4—201no—
758C4—301no—
759C4—601no—
760C4D3×#70911yescharacteristic
761C4D3×#71311yescharacteristic
762C3C2×#6517411yescharacteristic, complemented, Sylow
763C2—34no—
764C2—201no—
765C2—401no—
766C2—601no—
767C2—1201no—
768C2D3×#404011yescharacteristic
769C2D3×#405711yescharacteristic
770C2D3×#406511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalD3×#4041C2
hypercenter#107D3×D5
hypocenterC3×C5C2×#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D3×#4038C2semidirect
3. #11750986C2semidirect
4. C5×D3×#107C2semidirect
5. C3×#65174C2semidirect
6. D3×#3953C2semidirect
7. D3×#3952C2semidirect
8. #11747670C2semidirect
9. #11747572C2semidirect
10. D3×#3941C2semidirect
11. D3×#3940C2semidirect
12. #11747334C2semidirect
13. #11747213C2semidirect
14. #11747206C2semidirect
15. #11747166C2semidirect
21. #91781C22semidirect
26. C3×#4038C22semidirect
37. #91358C22semidirect
38. #91347C22semidirect
40. C3×C5×#107C22semidirect
41. #91105C22semidirect
42. #91104C22semidirect
43. #91093C22semidirect
44. #91092C22semidirect
45. C5×#818C22semidirect
46. C5×#807C22semidirect
47. C5×#807C22semidirect
48. C3×#3953C22semidirect
49. C3×#3952C22semidirect
50. C3×#3941C22semidirect
51. C3×#3940C22semidirect
52. #90986C22semidirect
53. #90985C22semidirect
54. #90969C22semidirect
55. #90968C22semidirect
56. #90965C22semidirect
57. #90964C22semidirect
58. #90957C22semidirect
59. #90955C22semidirect
75. #65174D3direct (N × H)
132. D3×#107D5semidirect
163. #4038C2×D3semidirect
167. C5×#107C2×D3semidirect
171. #3953C2×D3semidirect
175. #3952C2×D3semidirect
179. #3941C2×D3semidirect
183. #3940C2×D3semidirect
254. C3×#107C2×D5semidirect
266. #818C2×D5semidirect
272. #807C2×D5semidirect
273. #807C2×D5semidirect
490. #107D3×D5semidirect
514. C5×D3#482semidirect
640. C3×C5C2×#482semidirect
731. D3#65174direct (N × H)
732. C5D3×#482semidirect
762. C3C2×#65174semidirect

Maximal subgroups

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

subgroupindex
D3×#40412
D3×#40382
#117509862
C5×D3×#1072
C3×#651742
D3×#39532
D3×#39522
#117476702
#117475722
D3×#39412
D3×#39402
#117473342
#117472132
#117472062
#117471662
C2×#651743
D3×#4825