Finite Group Databasebeta

← #14435675

Subgroups — #14435675

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5521C211yesmaximal, characteristic, complemented
2C3×#65868C211yesmaximal, characteristic, complemented
3#11751101C211yesmaximal, characteristic, complemented
4#11748537C211yesmaximal, characteristic, complemented
5#11748516C211yesmaximal, characteristic
6#11748402C211yesmaximal, characteristic, complemented
7#11748371C211yesmaximal, characteristic, complemented
8#11747050C211yesmaximal, characteristic, complemented
9C4×#6656C211yesmaximal, characteristic, complemented
10#11747034C211yesmaximal, characteristic, complemented
11#11747034C211yesmaximal, characteristic, complemented
12#11747021C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746900C211yesmaximal, characteristic, complemented
15#11746882C211yesmaximal, characteristic, complemented
16#10614272—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19C5×#926C2211yescharacteristic
20C5×#893—21no—
21C5×#893—21no—
22C5×D3×C22⋊C4—21no—
23C5×D3×C22⋊C4—21no—
24C4×C5×D12C2211yescharacteristic
25C4×C5×D12C2211yescharacteristic
26C4×C5×D12C2211yescharacteristic
27C4×C5×D12C2211yescharacteristic
28C3×#4076C2211yescharacteristic
29C3×#4070C2211yescharacteristic
30C3×#4044—21no—
31C3×#4042—21no—
32C3×#4031—21no—
33C3×#4029—21no—
34C3×#4021C2211yescharacteristic, complemented
35C3×C4×D20C2211yescharacteristic, complemented
36C3×#4015C2211yescharacteristic, complemented
37C3×C4×Dic10C2211yescharacteristic, complemented
38C2×#6656C2211yescharacteristic
39C2×#6656C2211yescharacteristic
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42#91114C2211yescharacteristic
43#91114C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic, complemented
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46#91087C2211yescharacteristic, complemented
47C4×C3⋊#168C2211yescharacteristic, complemented
48#90989C2211yescharacteristic, complemented
49#90989C2211yescharacteristic, complemented
50#90986C2211yescharacteristic, complemented
51#90986C2211yescharacteristic, complemented
52#90970C2211yescharacteristic, complemented
53#90970C2211yescharacteristic, complemented
54#90966C2211yescharacteristic
55#90966C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58#90964C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60#83460—51nomaximal, Hall
61C5×#518—31no—
62#65868D311yescharacteristic, complemented
63#65507—31no—
64#65506—31no—
65#65307—31no—
66C4×#687—31no—
67#65305—31no—
68#65305—31no—
69#65303—31no—
70C4×#686—31no—
71#65297—31no—
72#65296—31no—
73#65292—31no—
74#65289—31no—
75#65285—31no—
76C23×C5×D3—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×C5×D12—21no—
79C2×C5×D12—22no—
80C2×C5×D12—22no—
81C2×C5×D12C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C22⋊C4D411yescharacteristic
95C3×C5×C22⋊C4D411yescharacteristic
96C3×C42×C5C2311yescharacteristic
97C3×C42×C5C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×#217—21no—
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C5×C4⋊Dic3C2311yescharacteristic
109C4×C5×Dic3—21no—
110C3×C22⋊Dic5—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×C4×Dic5—21no—
121#6656—22no—
122#6656—22no—
123#6652—22no—
124#6652—22no—
125C3×#542—51no—
126#5521D511yescharacteristic, complemented
127#5087—51no—
128#5084—51no—
129#5057—51no—
130#5057—51no—
131#5046—51no—
132#5045—51no—
133#5036—51no—
134#5035—51no—
135#5026—51no—
136C4×#215—51no—
137#5014—51no—
138C4×#213—51no—
139#5000—51no—
140C22×C5×D4—31no—
141C4×C5×D4—31no—
142C4×C5×D4—31no—
143C4×C5×D4—31no—
144C4×C5×D4—31no—
145C4×C5×D4—61no—
146C4×C5×D4—61no—
147C5×#117—31no—
148C5×#117C2×D311yescharacteristic
149C2×C5×C22⋊C4—61no—
150C2×C5×C22⋊C4—61no—
151C2×#687—31no—
152C2×#687—31no—
153C2×#686—31no—
154C2×#686—31no—
155#4076C2×D311yescharacteristic
156#4070C2×D311yescharacteristic
157#4044—21no—
158#4042—21no—
159#4031—21no—
160#4029—21no—
161#4021C2×D311yescharacteristic, complemented
162C4×D20C2×D311yescharacteristic, complemented
163#4015C2×D311yescharacteristic, complemented
164C4×Dic10C2×D311yescharacteristic, complemented
165#3964—31no—
166#3964—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941—31no—
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3118—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—24no—
188C22×C5×D3—81no—
189C22×C5×D3—81no—
190C22×C3×D5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2×D411yescharacteristic
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C5×D12—24no—
202C5×D12—21no—
203C5×D12—21no—
204C5×D12#4112yes—
205C5×D12#4112yes—
206C4×C5×D3—81no—
207C4×C5×D3—81no—
208C4×C5×D3—81no—
209C4×C5×D3—81no—
210C3×C22⋊D5—81no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C3×D20—21no—
215C3×D20—21no—
216C3×C4×D5—81no—
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—81no—
220C3⋊#168—21no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3⋊#168—21no—
224C22×D12C2×D511yescharacteristic
225C3×C4⋊Q8—51no—
226C3×#126—101no—
227C3×#124—51no—
228C3×#124—101no—
229C3×#123—101no—
230C3×C22⋊Q8—51no—
231C3×C22⋊Q8—101no—
232C3×#121—51no—
233C3×C4×Q8—51no—
234C3×C4×D4—51no—
235C3×#117C2×D511yescharacteristic
236C2×#215—51no—
237C2×#215—51no—
238C2×#213—51no—
239C2×#213—51no—
240#926C2×D511yescharacteristic
241#893—21no—
242#893—21no—
243D3×C22⋊C4—21no—
244D3×C22⋊C4—21no—
245C4×D12C2×D511yescharacteristic
246C4×D12C2×D511yescharacteristic
247C4×D12C2×D511yescharacteristic
248C4×D12C2×D511yescharacteristic
249#835—51no—
250#835—51no—
251#832—51no—
252#832—51no—
253#830—51no—
254#830—51no—
255#809—51no—
256#809—51no—
257#809—51no—
258#809—51no—
259#808—51no—
260#808—51no—
261#807—51no—
262#807—51no—
263C4⋊(C3⋊C8)—51no—
264C4⋊(C3⋊C8)—51no—
265#803—51no—
266C4×C3⋊C8—51no—
267C24×C5—61no—
268C2×C5×D4—31no—
269C2×C5×D4—31no—
270C2×C5×D4—62no—
271C2×C5×D4—62no—
272C2×C5×D4—61no—
273C22×C4×C5—61no—
274C22×C4×C5—61no—
275C22×C4×C5—61no—
276C22×C4×C5—61no—
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—21no—
279C2×D20C22×D311yescharacteristic
280C2×C4×D5—21no—
281C2×Dic10—21no—
282C2×Dic10C22×D311yescharacteristic
283C5×C4⋊C4—31no—
284C5×C4⋊C4—31no—
285C5×C4⋊C4#6711yescharacteristic
286C5×C4⋊C4#6711yescharacteristic
287C5×C22⋊C4—61no—
288C5×C22⋊C4—61no—
289C5×C22⋊C4—61no—
290C5×C22⋊C4—61no—
291C5×C22⋊C4—61no—
292C5×C22⋊C4#6711yescharacteristic
293C5×C22⋊C4#6711yescharacteristic
294C42×C5—61no—
295C42×C5C22×D311yescharacteristic
296C42×C5C22×D311yescharacteristic
297C22⋊Dic5—21no—
298#687—62no—
299#687—62no—
300#686—62no—
301#686—62no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5C22×D311yescharacteristic
308C4⋊Dic5C22×D311yescharacteristic
309#683—21no—
310#683—21no—
311C4×Dic5—21no—
312C2×#168—31no—
313C2×#168—31no—
314C2×#168—31no—
315C2×#168—31no—
316#542—51no—
317#518—31no—
318#485—151no—
319#482—151no—
320#476—151no—
321#474—151no—
322#463—151no—
323#463—151no—
324#450—151no—
325#447—151no—
326#442—151no—
327#440—151no—
328C4×SD16—151no—
329C4×D8—151no—
330#433—151no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5C22×D411yescharacteristic
335C2×C5×D3—22no—
336C2×C5×D3—22no—
337C2×C5×D3—41no—
338C2×C5×D3—41no—
339C2×C5×D3—41no—
340C2×C5×D3—41no—
341C2×C5×D3—84no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—41no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5C2×#4111yescharacteristic
351C3×C4×C5C2×#4111yescharacteristic
352C3×Dic5—41no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C23×D3—21no—
358C2×C3×Q8—51no—
359C2×C3×Q8—101no—
360C2×C3×D4—51no—
361C2×C3×D4—101no—
362C22×C3×C4—101no—
363C22×C3×C4C22×D511yescharacteristic
364C2×D12—21no—
365C2×D12—22no—
366C2×D12—22no—
367C2×D12C22×D511yescharacteristic
368C2×D12C22×D511yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C3×C4⋊C4—51no—
374C3×C4⋊C4—51no—
375C3×C4⋊C4—101no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4—101no—
378C3×C4⋊C4C22⋊D511yescharacteristic
379C3×C4⋊C4C22⋊D511yescharacteristic
380C3×C22⋊C4—101no—
381C3×C22⋊C4—101no—
382C3×C22⋊C4—101no—
383C3×C22⋊C4—101no—
384C3×C22⋊C4—101no—
385C3×C22⋊C4C22⋊D511yescharacteristic
386C3×C22⋊C4C22⋊D511yescharacteristic
387C3×C42—101no—
388C3×C42C22×D511yescharacteristic
389C3×C42C22×D511yescharacteristic
390#217—21no—
391#215—102no—
392#215—102no—
393#213—102no—
394#213—102no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399C4⋊Dic3C22×D511yescharacteristic
400C4⋊Dic3C22×D511yescharacteristic
401C4×Dic3—21no—
402C2×C3⋊C8—51no—
403C2×C3⋊C8—51no—
404C2×C3⋊C8—51no—
405C2×C3⋊C8—51no—
406C23×C5—64no—
407C23×C5—61no—
408C23×C5—61no—
409C23×C5—241no—
410C23×C5—241no—
411C23×C5C2×#6711yescharacteristic
412C22×D5—21no—
413C5×D4—32no—
414C5×D4—32no—
415C5×D4—64no—
416C5×D4—61no—
417C5×D4—61no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—61no—
421C2×C4×C5—61no—
422C2×C4×C5—241no—
423C2×C4×C5—241no—
424C2×C4×C5—241no—
425C2×C4×C5—241no—
426C2×C4×C5C2×#6711yescharacteristic
427C2×C4×C5C2×#6711yescharacteristic
428C2×C4×C5C2×#6711yescharacteristic
429C2×C4×C5C2×#6711yescharacteristic
430C2×C4×C5C2×#6711yescharacteristic
431C2×C4×C5C23×D311yescharacteristic
432C22⋊D5—81no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436D20—21no—
437D20—21no—
438C4×D5—81no—
439Dic10—21no—
440Dic10—21no—
441Dic10—81no—
442#168—61no—
443#168—61no—
444#168—61no—
445#168—61no—
446C22×D4—31no—
447C2×SD16—151no—
448C2×SD16—151no—
449C2×D8—151no—
450C2×D8—151no—
451C4⋊Q8—51no—
452#126—101no—
453#124—51no—
454#124—101no—
455#123—101no—
456C22⋊Q8—51no—
457C22⋊Q8—101no—
458#121—51no—
459C4×Q8—51no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—51no—
465C4×D4—61no—
466C4×D4—61no—
467#117—31no—
468#117D3×D511yescharacteristic
469C2×C22⋊C4—61no—
470C2×C22⋊C4—61no—
471#107—151no—
472#107—151no—
473#106—151no—
474#106—151no—
475C4⋊C8—151no—
476C4⋊C8—151no—
477#103—151no—
478#103—151no—
479#102—151no—
480#102—151no—
481#102—151no—
482#102—151no—
483#102—151no—
484#102—151no—
485C22⋊C8—151no—
486C22⋊C8—151no—
487#97—151no—
488C4×C8—151no—
489C2×C3×C5—41no—
490C2×C3×C5#52511yescharacteristic
491C2×C3×C5#57611yescharacteristic
492C2×C3×C5#57711yescharacteristic
493C3×D5—81no—
494C5×D3—42no—
495C5×D3—42no—
496C23×C3—101no—
497C23×C3C2×C22⋊D511yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—24no—
501C22×D3—81no—
502C22×D3—81no—
503C3×Q8—101no—
504C3×Q8—101no—
505C3×Q8—401no—
506C3×D4—101no—
507C3×D4—101no—
508C3×D4—401no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—401no—
515C2×C3×C4C2×C22⋊D511yescharacteristic
516C2×C3×C4C2×C22⋊D511yescharacteristic
517C2×C3×C4C2×C22⋊D511yescharacteristic
518C2×C3×C4C2×C22⋊D511yescharacteristic
519C2×C3×C4C2×C22⋊D511yescharacteristic
520C2×C3×C4C23×D511yescharacteristic
521C2×Dic3—21no—
522C2×Dic3—21no—
523D12—24no—
524D12—21no—
525D12—21no—
526D12#70912yes—
527D12#70912yes—
528C4×D3—81no—
529C4×D3—81no—
530C4×D3—81no—
531C4×D3—81no—
532C3⋊C8—101no—
533C3⋊C8—101no—
534C3⋊C8—101no—
535C3⋊C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—62no—
540C22×C5—62no—
541C22×C5—121no—
542C22×C5—121no—
543C22×C5—121no—
544C22×C5—121no—
545C22×C5—244no—
546C22×C5C22×#6711yescharacteristic
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—41no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—121no—
556C4×C5—121no—
557C4×C5D3×#4111yescharacteristic
558C4×C5D3×#4111yescharacteristic
559Dic5—41no—
560Dic5—41no—
561Dic5—41no—
562C24—61no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×D4—31no—
566C2×D4—31no—
567C2×D4—51no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—61no—
571C2×D4—101no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—101no—
577C22×C4C2×D3×D511yescharacteristic
578SD16—302no—
579SD16—302no—
580D8—302no—
581D8—302no—
582C2×C8—151no—
583C2×C8—151no—
584C2×C8—151no—
585C2×C8—151no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—101no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4#120111yescharacteristic
594C4⋊C4#120111yescharacteristic
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4#120111yescharacteristic
606C22⋊C4#120111yescharacteristic
607C42—61no—
608C42—101no—
609C42C2×D3×D511yescharacteristic
610C42C2×D3×D511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—201no—
616C22×C3—201no—
617C22×C3—201no—
618C22×C3C22×C22⋊D511yescharacteristic
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—84no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4—201no—
634C3×C4C2×#70911yescharacteristic
635C3×C4C2×#70911yescharacteristic
636Dic3—41no—
637Dic3—41no—
638C2×C5—41no—
639C2×C5—122no—
640C2×C5—122no—
641C2×C5#582811yescharacteristic
642C2×C5#583511yescharacteristic
643C2×C5#583711yescharacteristic
644D5—81no—
645C23—64no—
646C23—61no—
647C23—61no—
648C23—101no—
649C23—241no—
650C23—241no—
651C23C2×#120111yescharacteristic
652Q8—101no—
653Q8—101no—
654Q8—401no—
655D4—32no—
656D4—32no—
657D4—64no—
658D4—61no—
659D4—61no—
660D4—101no—
661D4—101no—
662D4—401no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—241no—
671C2×C4—241no—
672C2×C4—241no—
673C2×C4—241no—
674C2×C4—401no—
675C2×C4C2×#120111yescharacteristic
676C2×C4C2×#120111yescharacteristic
677C2×C4C2×#120111yescharacteristic
678C2×C4C2×#120111yescharacteristic
679C2×C4C2×#120111yescharacteristic
680C2×C4C22×D3×D511yescharacteristic
681C8—301no—
682C8—301no—
683C8—301no—
684C8—301no—
685C2×C3—41no—
686C2×C3—401no—
687C2×C3#6612511yescharacteristic
688C2×C3#6616911yescharacteristic
689C2×C3#6617011yescharacteristic
690D3—42no—
691D3—42no—
692C5#8346011yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—62no—
697C22—62no—
698C22—121no—
699C22—121no—
700C22—121no—
701C22—121no—
702C22—201no—
703C22—201no—
704C22—201no—
705C22—244no—
706C22C22×#120111yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—121no—
713C4—121no—
714C4—201no—
715C4—201no—
716C4—201no—
717C4D3×#70911yescharacteristic
718C4D3×#70911yescharacteristic
719C3#1061427211yescharacteristic, complemented, Sylow
720C2—41no—
721C2—122no—
722C2—122no—
723C2—401no—
724C2#1175457711yescharacteristic
725C2#1175530111yescharacteristic
726C2#1175530411yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11748516C2
hypercenter#117D3×D5
hypocenterC3×C5#3118
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5521C2semidirect
2. C3×#65868C2semidirect
3. #11751101C2semidirect
4. #11748537C2semidirect
6. #11748402C2semidirect
7. #11748371C2semidirect
8. #11747050C2semidirect
9. C4×#6656C2semidirect
10. #11747034C2semidirect
11. #11747034C2semidirect
12. #11747021C2semidirect
13. C4×#6652C2semidirect
14. #11746900C2semidirect
15. #11746882C2semidirect
34. C3×#4021C22semidirect
35. C3×C4×D20C22semidirect
36. C3×#4015C22semidirect
37. C3×C4×Dic10C22semidirect
44. C4⋊(C3⋊#168)C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. #91087C22semidirect
47. C4×C3⋊#168C22semidirect
48. #90989C22semidirect
49. #90989C22semidirect
50. #90986C22semidirect
51. #90986C22semidirect
52. #90970C22semidirect
53. #90970C22semidirect
58. #90964C22semidirect
59. #90964C22semidirect
62. #65868D3semidirect
126. #5521D5semidirect
161. #4021C2×D3semidirect
162. C4×D20C2×D3semidirect
163. #4015C2×D3semidirect
164. C4×Dic10C2×D3semidirect
611. C3×C5#3118semidirect
692. C5#83460semidirect
719. C3#10614272semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C3×#658682
#117511012
#117485372
#117485162
#117484022
#117483712
#117470502
C4×#66562
#117470342
#117470212
C4×#66522
#117469002
#117468822
#106142723
#834605