Finite Group Databasebeta

← #14417033

Subgroups — #14417033

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754922C211yesmaximal, characteristic, complemented
2C2×#91500C211yesmaximal, characteristic
3#11753407C211yesmaximal, characteristic, complemented
4D15×#102C211yesmaximal, characteristic, complemented
5C5×#4785C211yesmaximal, characteristic, complemented
6C3×#65046C211yesmaximal, characteristic, complemented
7Dic3×#687C211yesmaximal, characteristic, complemented
8Dic5×#213C211yesmaximal, characteristic, complemented
9#11748145C211yesmaximal, characteristic, complemented
10#11747746C211yesmaximal, characteristic, complemented
11#11747743C211yesmaximal, characteristic, complemented
12#11747668C211yesmaximal, characteristic, complemented
13#11747457C211yesmaximal, characteristic, complemented
14#11747230C211yesmaximal, characteristic, complemented
15#11747225C211yesmaximal, characteristic, complemented
16#10611597—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×#6768C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20C4⋊C4×D15C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic
22C2×C5×#213C2211yescharacteristic
23C5×#893C2211yescharacteristic, complemented
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×#4033C2211yescharacteristic, complemented
27#91561—21no—
28#91556—21no—
29#91552—21no—
30C2×#6667—21no—
31#91500C418yescomplemented
32C4×#1203—21no—
33#91428C2211yescharacteristic
34#91418C2211yescharacteristic
35Dic5×D12C2211yescharacteristic, complemented
36#91406—21no—
37D3×#683—21no—
38#91398—21no—
39#91386C2211yescharacteristic
40#91347C2211yescharacteristic
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic
46#91116C2211yescharacteristic
47#91105C2211yescharacteristic
48#91093C2211yescharacteristic
49C5×#821C2211yescharacteristic, complemented
50C5×#815C2211yescharacteristic, complemented
51C5×#808C2211yescharacteristic, complemented
52C3×#3948C2211yescharacteristic, complemented
53C3×#3947C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#79775—51nomaximal, Hall
62C2×#4057—31no—
63#65880—31no—
64#65879—31no—
65C5×#442—31no—
66D8×Dic5—31no—
67C4×#687—31no—
68C4×#686—31no—
69#65150—31no—
70#65141—31no—
71#65074—31no—
72#65061—31no—
73D5×#102—31no—
74#65046D311yescharacteristic, complemented
75#64999—31no—
76#64997—31no—
77C23×D15—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×#1220—21no—
80D4×D15—22no—
81D4×D15C2×C414yescomplemented
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C4×D15C2311yescharacteristic
85C22×C5×Dic3—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3—21no—
88C22×C3×Dic5—21no—
89C2×C3×Dic10C2311yescharacteristic
90C2×#1203—21no—
91C2×#1200—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5—21no—
95#6768—22no—
96#6768C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C4⋊Dic15C2311yescharacteristic
100#6712—21no—
101C2×C3⋊#168C2311yescharacteristic
102C8×D15—22no—
103C5×#217—21no—
104C5×#213C2×C414yescomplemented
105C5×(C2×D3)⋊C4—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C4×C5×Dic3C2311yescharacteristic
108C2×C5×C3⋊C8C2311yescharacteristic
109C3×C22⋊Dic5—21no—
110C3×#687C2×C414yescomplemented
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116#6669D411yescharacteristic
117#6669D411yescharacteristic
118#6668—21no—
119#6667—21no—
120#6667—21no—
121#6667—21no—
122#6667D411yescharacteristic
123#6667D411yescharacteristic
124(C2×D3)⋊Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6658C2×C414yescomplemented
128#6654C2×C414yescomplemented
129#6651C2×C414yescomplemented
130C2×#914—51no—
131#5574—51no—
132#5545—51no—
133C3×#440—51no—
134Dic3×SD16—51no—
135C4×#215—51no—
136C4×#213—51no—
137#4881—51no—
138#4872—51no—
139#4817—51no—
140#4804—51no—
141#4785D511yescharacteristic, complemented
142D3×#102—51no—
143#4711—51no—
144#4708—51no—
145C2×#711—31no—
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5C2×D311yescharacteristic
152C2×#687C2×D311yescharacteristic
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#683—61no—
158#4057—38no—
159C2×#677—31no—
160C2×#676—31no—
161C2×C8×D5—31no—
162#4039—31no—
163#4038—31no—
164D5×C4⋊C4—31no—
165#4033C2×D311yescharacteristic, complemented
166#4027—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169#4023—61no—
170C4×D20—31no—
171#4018—31no—
172C4×Dic10—31no—
173C5×#106—31no—
174C5×#102—31no—
175C5×#102C2×D311yescharacteristic
176C5×#97—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3950—31no—
181#3948C2×D311yescharacteristic, complemented
182#3947C2×D311yescharacteristic, complemented
183C8×Dic5—31no—
184#3942—31no—
185#3941—31no—
186#3940—31no—
187#3939C2×D311yescharacteristic, complemented
188C4×#168—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×D15—24no—
193C22×D15—81no—
194C22×D15—81no—
195C22×D15C2×D411yescharacteristic
196C22×C5×D3—21no—
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201#1220—24no—
202C2×Dic15—21no—
203C2×Dic15C2×D411yescharacteristic
204D60—21no—
205D60C22×C412yes—
206C4×D15—81no—
207C4×D15C22×C412yes—
208C4×D15#4112yes—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—81no—
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—81no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—81no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×Dic10—21no—
222C3×Dic10C22×C412yes—
223#1203—24no—
224#1200—81no—
225#1200—81no—
226D3×Dic5—24no—
227D3×Dic5—81no—
228C3×C5×C8—21no—
229C3⋊#168—21no—
230C3×#168C22×C412yes—
231C5×C3⋊C8C22×C412yes—
232C2×#239—51no—
233C2×D3×D4—51no—
234C2×C3×SD16—51no—
235C3×C4×Q8—51no—
236C3×C4×D4—51no—
237Q8×Dic3—51no—
238C2×#215—51no—
239D4×Dic3C2×D511yescharacteristic
240C2×#213C2×D511yescharacteristic
241C4×#67—101no—
242C2×(C2×D3)⋊C4—101no—
243#914—58no—
244C2×D24—51no—
245C2×ΓL(1,𝔽25)—51no—
246C2×D3×C8—51no—
247#893—51no—
248#893—101no—
249#893C2×D511yescharacteristic, complemented
250#892—51no—
251D3×C4⋊C4—51no—
252D3×C4⋊C4—101no—
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—51no—
256C4×D12—51no—
257C4×D12—101no—
258#872—51no—
259#872—101no—
260C3×#107—51no—
261C3×#103—51no—
262C3×#102C2×D511yescharacteristic
263C3×#97—51no—
264#835—51no—
265#832—51no—
266#821—51no—
267#821C2×D511yescharacteristic, complemented
268#817—51no—
269#815C2×D511yescharacteristic, complemented
270C8×Dic3—51no—
271#809—51no—
272#809—51no—
273#808C2×D511yescharacteristic, complemented
274#807—51no—
275C4×C3⋊C8—51no—
276C23×D5—61no—
277C2×C5×D4—31no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C2×C22⋊D5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—21no—
284C22×Dic5—61no—
285C22×Dic5—61no—
286#711—34no—
287#711—62no—
288D4×D5—34no—
289D4×D5—62no—
290C2×D20—31no—
291C2×C4×D5—31no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×Dic10C22×D311yescharacteristic
296C5×D8—34no—
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C22⋊Dic5—21no—
305C22⋊Dic5—61no—
306#687C4×D314yescomplemented
307#686—34no—
308#685—31no—
309#685—31no—
310#685—61no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5C22×D311yescharacteristic
315#683—21no—
316#683—31no—
317#683—31no—
318#683—61no—
319#683—61no—
320C4×Dic5—21no—
321C4×Dic5—61no—
322C4×Dic5—61no—
323C4×Dic5C22×D311yescharacteristic
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326#677—34no—
327#676—34no—
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—31no—
333#442—151no—
334#440—51no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—21no—
349C2×D15—21no—
350C2×D15—22no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—84no—
354C2×D15C4×D412yes—
355C2×C5×D3—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C3×C4×C5—41no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—41no—
362Dic15C4×D412yes—
363C3×Dic5—22no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C5×Dic3—21no—
368C5×Dic3—21no—
369C5×Dic3—41no—
370C23×D3—101no—
371C2×C3×Q8—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C2×#67—101no—
375C22×Dic3—21no—
376#239—54no—
377#239—102no—
378D3×D4—54no—
379D3×D4—102no—
380C2×D12—51no—
381C2×D12—101no—
382C2×D12C22×D511yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—51no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C3×SD16—54no—
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C42—51no—
398C3×C42—101no—
399#217—21no—
400#215—54no—
401#213C4×D514yescomplemented
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—51no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—51no—
413Dic3⋊C4—51no—
414Dic3⋊C4—101no—
415C4×Dic3—101no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8C22×D511yescharacteristic
420D24—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—21no—
424C23×C5—61no—
425C22×D5—31no—
426C22×D5—64no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×D4—21no—
431C5×D4—32no—
432C5×D4—61no—
433C5×D4C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—31no—
436C2×C4×C5—31no—
437C2×C4×C5—61no—
438C2×C4×C5—241no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—31no—
446C2×Dic5—64no—
447C2×Dic5—61no—
448C2×Dic5—81no—
449C2×Dic5—241no—
450C2×Dic5D3×D411yescharacteristic
451C2×Dic5D3×D411yescharacteristic
452D20—32no—
453D20—61no—
454C4×D5—32no—
455C4×D5—32no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—21no—
460Dic10C2×C4×D312yes—
461C5×C8—21no—
462C5×C8—32no—
463#168—61no—
464#168C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—51no—
469C2×SD16—151no—
470C2×D8—31no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—51no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—31no—
478C4×D4—51no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—51no—
494#107—151no—
495#106—31no—
496#106—151no—
497#103—51no—
498#103—151no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102D3×D511yescharacteristic
505#97—31no—
506#97—51no—
507C4×C8—151no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—22no—
514D15—42no—
515C5×D3—42no—
516C23×C3—21no—
517C22×D3—21no—
518C22×D3—51no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C3×Q8—52no—
524C3×Q8—101no—
525C3×D4—21no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—401no—
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535C2×Dic3—21no—
536C2×Dic3—51no—
537C2×Dic3—81no—
538C2×Dic3—101no—
539C2×Dic3D4×D511yescharacteristic
540C2×Dic3D4×D511yescharacteristic
541D12—21no—
542D12—52no—
543D12—104no—
544D12—101no—
545D12C2×C4×D512yes—
546C4×D3—52no—
547C4×D3—52no—
548C4×D3—81no—
549C4×D3—104no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3—401no—
553C4×D3—401no—
554C3×C8—21no—
555C3×C8—52no—
556C3⋊C8—101no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5—62no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—32no—
566C2×D5—61no—
567C2×D5—61no—
568C2×D5—62no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—41no—
573C4×C5—61no—
574C4×C5—61no—
575C4×C5—121no—
576C4×C5C22×C4×D311yescharacteristic
577C4×C5D3×#4111yescharacteristic
578Dic5—21no—
579Dic5—21no—
580Dic5—22no—
581Dic5—32no—
582Dic5—41no—
583Dic5—121no—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8—51no—
588C2×D4—31no—
589C2×D4—154no—
590C2×D4—151no—
591C2×D4—301no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—101no—
598C22×C4—151no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—54no—
605SD16—154no—
606D8—34no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—302no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—51no—
616C4⋊C4—101no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—101no—
626C22⋊C4—151no—
627C22⋊C4—151no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—51no—
634C42—101no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—52no—
646C2×D3—101no—
647C2×D3—101no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—41no—
653C3×C4—101no—
654C3×C4—101no—
655C3×C4—102no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4D5×#4111yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—52no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5—122no—
666C2×C5C4×D3×D411yescharacteristic
667C2×C5#577411yescharacteristic
668C2×C5#577811yescharacteristic
669D5—62no—
670D5—122no—
671C23—21no—
672C23—61no—
673C23—151no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—52no—
679Q8—101no—
680D4—21no—
681D4—32no—
682D4—61no—
683D4—152no—
684D4—304no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—51no—
692C2×C4—51no—
693C2×C4—61no—
694C2×C4—101no—
695C2×C4—101no—
696C2×C4—151no—
697C2×C4—152no—
698C2×C4—152no—
699C2×C4—241no—
700C2×C4—241no—
701C2×C4—304no—
702C2×C4—301no—
703C2×C4—401no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—32no—
711C8—52no—
712C8—301no—
713C2×C3—42no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3#6610811yescharacteristic
716C2×C3#6610911yescharacteristic
717D3—42no—
718D3—102no—
719D3—202no—
720C5#7977511yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—62no—
725C22—121no—
726C22—121no—
727C22—152no—
728C22—301no—
729C22—301no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—41no—
736C4—61no—
737C4—61no—
738C4—101no—
739C4—101no—
740C4—102no—
741C4—121no—
742C4—152no—
743C4—201no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4#9202411yescharacteristic
747C3#1061159711yescharacteristic, complemented, Sylow
748C2—42no—
749C2—122no—
750C2—302no—
751C2—602no—
752C2#1175320311yescharacteristic
753C2#1175405911yescharacteristic
754C2#1175409011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91500C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #11754922C2semidirect
3. #11753407C2semidirect
4. D15×#102C2semidirect
5. C5×#4785C2semidirect
6. C3×#65046C2semidirect
7. Dic3×#687C2semidirect
8. Dic5×#213C2semidirect
9. #11748145C2semidirect
10. #11747746C2semidirect
11. #11747743C2semidirect
12. #11747668C2semidirect
13. #11747457C2semidirect
14. #11747230C2semidirect
15. #11747225C2semidirect
23. C5×#893C22semidirect
26. C3×#4033C22semidirect
31. #91500C4semidirect
35. Dic5×D12C22semidirect
41. Dic3×Dic10C22semidirect
49. C5×#821C22semidirect
50. C5×#815C22semidirect
51. C5×#808C22semidirect
52. C3×#3948C22semidirect
53. C3×#3947C22semidirect
54. C3×#3939C22semidirect
55. #90990C22semidirect
56. #90985C22semidirect
57. #90970C22semidirect
58. #90966C22semidirect
59. Dic3×#168C22semidirect
60. Dic5×C3⋊C8C22semidirect
74. #65046D3semidirect
81. D4×D15C2×C4semidirect
96. #6768C2×C4semidirect
104. C5×#213C2×C4semidirect
110. C3×#687C2×C4semidirect
127. #6658C2×C4semidirect
128. #6654C2×C4semidirect
129. #6651C2×C4semidirect
141. #4785D5semidirect
165. #4033C2×D3semidirect
181. #3948C2×D3semidirect
182. #3947C2×D3semidirect
187. #3939C2×D3semidirect
249. #893C2×D5semidirect
267. #821C2×D5semidirect
269. #815C2×D5semidirect
273. #808C2×D5semidirect
306. #687C4×D3semidirect
401. #213C4×D5semidirect
637. C3×C5#2946semidirect
720. C5#79775semidirect
747. C3#10611597semidirect

Maximal subgroups

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

subgroupindex
#117549222
C2×#915002
#117534072
D15×#1022
C5×#47852
C3×#650462
Dic3×#6872
Dic5×#2132
#117481452
#117477462
#117477432
#117476682
#117474572
#117472302
#117472252
#106115973
#797755