Finite Group Databasebeta

← #14435585

Subgroups — #14435585

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
1C3×C5×#518C211yesmaximal, characteristic, complemented
2#11756293C211yesmaximal, characteristic, complemented
3#11751319C211yesmaximal, characteristic, complemented
4#11751318C211yesmaximal, characteristic
5#11751119C211yesmaximal, characteristic, complemented
6C4×#6716C211yesmaximal, characteristic, complemented
7#11751117C211yesmaximal, characteristic, complemented
8#11751117C211yesmaximal, characteristic, complemented
9#11751115C211yesmaximal, characteristic, complemented
10C4×#6715C211yesmaximal, characteristic, complemented
11#11751109C211yesmaximal, characteristic, complemented
12#11751108C211yesmaximal, characteristic, complemented
13#11751104C211yesmaximal, characteristic, complemented
14#11751101C211yesmaximal, characteristic, complemented
15#11751097C211yesmaximal, characteristic, complemented
16#10614272—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C3×C4×C5×D4—21no—
19C3×C4×C5×D4—21no—
20C3×C4×C5×D4C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24C3×C5×#117C2211yescharacteristic
25C3×C5×#117C2211yescharacteristic
26C2×C3×C5×C22⋊C4—21no—
27C2×C3×C5×C22⋊C4—21no—
28C2×#6716C2211yescharacteristic
29C2×#6716C2211yescharacteristic
30C2×#6715C2211yescharacteristic
31C2×#6715C2211yescharacteristic
32#91819C2211yescharacteristic
33#91813C2211yescharacteristic
34#91787—21no—
35#91785—21no—
36#91774—21no—
37#91772—21no—
38#91764C2211yescharacteristic, complemented
39C4×D60C2211yescharacteristic, complemented
40#91758C2211yescharacteristic, complemented
41C4×Dic30C2211yescharacteristic, complemented
42#91116C2211yescharacteristic
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45#91116C2211yescharacteristic
46#91114C2211yescharacteristic
47#91114C2211yescharacteristic
48#91094C2211yescharacteristic, complemented
49#91094C2211yescharacteristic, complemented
50#91093C2211yescharacteristic, complemented
51#91093C2211yescharacteristic, complemented
52#91092C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54#91091C2211yescharacteristic, complemented
55#91091C2211yescharacteristic, complemented
56C4⋊(C3⋊#168)C2211yescharacteristic, complemented
57C4⋊(C3⋊#168)C2211yescharacteristic, complemented
58#91087C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#82541—51nomaximal, Hall
61C5×#518D311yescharacteristic, complemented
62#65868—31no—
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—
76C24×C3×C5—21no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×#1220—21no—
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×Dic30—21no—
91C2×Dic30C2311yescharacteristic
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4D411yescharacteristic
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C42×C5C2311yescharacteristic
106#6719—21no—
107#6716—22no—
108#6716—22no—
109#6715—22no—
110#6715—22no—
111#6714—21no—
112#6714—21no—
113#6714—21no—
114#6714—21no—
115C4⋊Dic15—21no—
116C4⋊Dic15C2311yescharacteristic
117C4⋊Dic15C2311yescharacteristic
118#6712—21no—
119#6712—21no—
120C4×Dic15—21no—
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2311yescharacteristic
125C3×#518D511yescharacteristic, complemented
126#5534—51no—
127#5218—51no—
128#5217—51no—
129#5018—51no—
130C4×#214—51no—
131#5016—51no—
132#5016—51no—
133#5014—51no—
134C4×#213—51no—
135#5008—51no—
136#5007—51no—
137#5003—51no—
138#5000—51no—
139#4996—51no—
140C22×C5×D4C2×D311yescharacteristic
141C4×C5×D4—21no—
142C4×C5×D4—21no—
143C4×C5×D4C2×D311yescharacteristic
144C4×C5×D4C2×D311yescharacteristic
145C4×C5×D4C2×D311yescharacteristic
146C4×C5×D4C2×D311yescharacteristic
147C5×#117C2×D311yescharacteristic
148C5×#117C2×D311yescharacteristic
149C2×C5×C22⋊C4—21no—
150C2×C5×C22⋊C4—21no—
151C2×#687—31no—
152C2×#687—31no—
153C2×#686—31no—
154C2×#686—31no—
155#4076—31no—
156#4070—31no—
157#4044—61no—
158#4042—61no—
159#4031—61no—
160#4029—61no—
161#4021—31no—
162C4×D20—31no—
163#4015—31no—
164C4×Dic10—31no—
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×C5—24no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—81no—
188C23×C3×C5—81no—
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C3×C5×D4—24no—
192C3×C5×D4—21no—
193C3×C5×D4—21no—
194C3×C5×D4#4112yes—
195C3×C5×D4#4112yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5—81no—
202C2×C3×C4×C5—81no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210#1220—81no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214D60—21no—
215D60—21no—
216C4×D15—81no—
217Dic30—21no—
218Dic30—21no—
219Dic30—81no—
220C3⋊#168—21no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3⋊#168—21no—
224C22×C3×D4C2×D511yescharacteristic
225C3×C4×D4—21no—
226C3×C4×D4—21no—
227C3×C4×D4C2×D511yescharacteristic
228C3×C4×D4C2×D511yescharacteristic
229C3×C4×D4C2×D511yescharacteristic
230C3×C4×D4C2×D511yescharacteristic
231C3×#117C2×D511yescharacteristic
232C3×#117C2×D511yescharacteristic
233C2×C3×C22⋊C4—21no—
234C2×C3×C22⋊C4—21no—
235C2×#214—51no—
236C2×#214—51no—
237C2×#213—51no—
238C2×#213—51no—
239#930—51no—
240#924—51no—
241#898—101no—
242#896—101no—
243#885—101no—
244#883—101no—
245#875—51no—
246C4×D12—51no—
247#869—51no—
248C4×Dic6—51no—
249#832—51no—
250#832—51no—
251#832—51no—
252#832—51no—
253#830—51no—
254#830—51no—
255#810—51no—
256#810—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—21no—
268C2×C5×D4—22no—
269C2×C5×D4—22no—
270C2×C5×D4—21no—
271C2×C5×D4C22×D311yescharacteristic
272C2×C5×D4C22×D311yescharacteristic
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—61no—
279C2×D20—31no—
280C2×C4×D5—61no—
281C2×Dic10—31no—
282C2×Dic10—61no—
283C5×C4⋊C4#6711yescharacteristic
284C5×C4⋊C4#6711yescharacteristic
285C5×C4⋊C4C22×D311yescharacteristic
286C5×C4⋊C4C22×D311yescharacteristic
287C5×C22⋊C4—21no—
288C5×C22⋊C4—21no—
289C5×C22⋊C4—21no—
290C5×C22⋊C4—21no—
291C5×C22⋊C4—21no—
292C5×C22⋊C4#6711yescharacteristic
293C5×C22⋊C4#6711yescharacteristic
294C42×C5—21no—
295C42×C5C22×D311yescharacteristic
296C42×C5C22×D311yescharacteristic
297C22⋊Dic5—61no—
298#687—62no—
299#687—62no—
300#686—62no—
301#686—62no—
302#685—61no—
303#685—61no—
304#685—61no—
305#685—61no—
306C4⋊Dic5—31no—
307C4⋊Dic5—31no—
308C4⋊Dic5—61no—
309#683—61no—
310#683—61no—
311C4×Dic5—61no—
312C2×#168—31no—
313C2×#168—31no—
314C2×#168—31no—
315C2×#168—31no—
316#542—151no—
317#518D1511yescharacteristic, complemented
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—22no—
333C22×C3×C5—22no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—84no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—41no—
343C2×D15—41no—
344C2×D15—41no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5C2×#4111yescharacteristic
353C3×C4×C5C2×#4111yescharacteristic
354Dic15—41no—
355Dic15—41no—
356Dic15—41no—
357C24×C3—21no—
358C2×C3×D4—22no—
359C2×C3×D4—22no—
360C2×C3×D4—21no—
361C2×C3×D4C22×D511yescharacteristic
362C2×C3×D4C22×D511yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4C22×D511yescharacteristic
368C2×#67—101no—
369C2×D12—51no—
370C2×C4×D3—101no—
371C2×Dic6—51no—
372C2×Dic6—101no—
373C3×C4⋊C4C22⋊D511yescharacteristic
374C3×C4⋊C4C22⋊D511yescharacteristic
375C3×C4⋊C4C22×D511yescharacteristic
376C3×C4⋊C4C22×D511yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4C22⋊D511yescharacteristic
383C3×C22⋊C4C22⋊D511yescharacteristic
384C3×C42—21no—
385C3×C42C22×D511yescharacteristic
386C3×C42C22×D511yescharacteristic
387#217—101no—
388#214—102no—
389#214—102no—
390#213—102no—
391#213—102no—
392(C2×D3)⋊C4—101no—
393(C2×D3)⋊C4—101no—
394(C2×D3)⋊C4—101no—
395(C2×D3)⋊C4—101no—
396C4⋊Dic3—51no—
397C4⋊Dic3—51no—
398C4⋊Dic3—101no—
399Dic3⋊C4—101no—
400Dic3⋊C4—101no—
401C4×Dic3—101no—
402C2×C3⋊C8—51no—
403C2×C3⋊C8—51no—
404C2×C3⋊C8—51no—
405C2×C3⋊C8—51no—
406C23×C5—24no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—81no—
410C23×C5—81no—
411C23×C5C2×#6711yescharacteristic
412C22×D5—61no—
413C5×D4—24no—
414C5×D4—21no—
415C5×D4—21no—
416C5×D4#23512yes—
417C5×D4#23512yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—81no—
423C2×C4×C5—81no—
424C2×C4×C5—81no—
425C2×C4×C5—81no—
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—241no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436D20—61no—
437D20—61no—
438C4×D5—241no—
439Dic10—61no—
440Dic10—61no—
441Dic10—241no—
442#168—61no—
443#168—61no—
444#168—61no—
445#168—61no—
446C22×D4C2×D1511yescharacteristic
447C2×SD16—151no—
448C2×SD16—151no—
449C2×D8—151no—
450C2×D8—151no—
451C4⋊Q8—151no—
452#126—301no—
453#124—151no—
454#124—301no—
455#123—301no—
456C22⋊Q8—151no—
457C22⋊Q8—301no—
458#121—151no—
459C4×Q8—151no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—151no—
463C4×D4C2×D1511yescharacteristic
464C4×D4C2×D1511yescharacteristic
465C4×D4C2×D1511yescharacteristic
466C4×D4C2×D1511yescharacteristic
467#117C2×D1511yescharacteristic
468#117C2×D1511yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
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—42no—
491C2×C3×C5—42no—
492C2×C3×C5#52511yescharacteristic
493C2×C3×C5#57611yescharacteristic
494C2×C3×C5#57711yescharacteristic
495D15—81no—
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3C2×C22⋊D511yescharacteristic
502C22×D3—101no—
503C3×D4—24no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4#70912yes—
507C3×D4#70912yes—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—81no—
513C2×C3×C4—81no—
514C2×C3×C4—81no—
515C2×C3×C4—81no—
516C2×C3×C4C2×C22⋊D511yescharacteristic
517C2×C3×C4C2×C22⋊D511yescharacteristic
518C2×C3×C4C2×C22⋊D511yescharacteristic
519C2×C3×C4C2×C22⋊D511yescharacteristic
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C23×D511yescharacteristic
522#67—401no—
523C2×Dic3—101no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526D12—101no—
527D12—101no—
528C4×D3—401no—
529Dic6—101no—
530Dic6—101no—
531Dic6—401no—
532C3⋊C8—101no—
533C3⋊C8—101no—
534C3⋊C8—101no—
535C3⋊C8—101no—
536C22×C5—21no—
537C22×C5—22no—
538C22×C5—22no—
539C22×C5—21no—
540C22×C5—21no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—84no—
546C22×C5C22×#6711yescharacteristic
547C2×D5—121no—
548C2×D5—121no—
549C2×D5—121no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5C2×#23511yescharacteristic
558C4×C5C2×#23511yescharacteristic
559Dic5—121no—
560Dic5—121no—
561Dic5—121no—
562C24—21no—
563C2×Q8—151no—
564C2×Q8—301no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—151no—
569C2×D4—301no—
570C2×D4C22×D1511yescharacteristic
571C2×D4C22×D1511yescharacteristic
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—301no—
577C22×C4C22×D1511yescharacteristic
578SD16—302no—
579SD16—302no—
580D8—302no—
581D8—302no—
582C2×C8—151no—
583C2×C8—151no—
584C2×C8—151no—
585C2×C8—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4—301no—
589C4⋊C4—301no—
590C4⋊C4—301no—
591C4⋊C4#122011yescharacteristic
592C4⋊C4#122011yescharacteristic
593C4⋊C4C22×D1511yescharacteristic
594C4⋊C4C22×D1511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—301no—
601C22⋊C4—301no—
602C22⋊C4—301no—
603C22⋊C4—301no—
604C22⋊C4—301no—
605C22⋊C4#122011yescharacteristic
606C22⋊C4#122011yescharacteristic
607C42—21no—
608C42—301no—
609C42C22×D1511yescharacteristic
610C42C22×D1511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—84no—
622C22×C3C22×C22⋊D511yescharacteristic
623C2×D3—201no—
624C2×D3—201no—
625C2×D3—201no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4C2×#70911yescharacteristic
634C3×C4C2×#70911yescharacteristic
635Dic3—201no—
636Dic3—201no—
637Dic3—201no—
638C2×C5—41no—
639C2×C5—42no—
640C2×C5—42no—
641C2×C5#579111yescharacteristic
642C2×C5#583511yescharacteristic
643C2×C5#583611yescharacteristic
644D5—241no—
645C23—24no—
646C23—21no—
647C23—21no—
648C23—81no—
649C23—81no—
650C23—301no—
651C23C2×#122011yescharacteristic
652Q8—301no—
653Q8—301no—
654Q8—1201no—
655D4—24no—
656D4—21no—
657D4—21no—
658D4—301no—
659D4—301no—
660D4—1201no—
661D4#681712yes—
662D4#681712yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—1201no—
675C2×C4C2×#122011yescharacteristic
676C2×C4C2×#122011yescharacteristic
677C2×C4C2×#122011yescharacteristic
678C2×C4C2×#122011yescharacteristic
679C2×C4C2×#122011yescharacteristic
680C2×C4C23×D1511yescharacteristic
681C8—301no—
682C8—301no—
683C8—301no—
684C8—301no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3#6612511yescharacteristic
689C2×C3#6616911yescharacteristic
690C2×C3#6617011yescharacteristic
691D3—401no—
692C5#8254111yescharacteristic, complemented, Sylow
693C22—21no—
694C22—22no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—84no—
703C22—601no—
704C22—601no—
705C22—601no—
706C22C22×#122011yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—601no—
715C4—601no—
716C4—601no—
717C4C2×#681711yescharacteristic
718C4C2×#681711yescharacteristic
719C3#1061427211yescharacteristic, complemented, Sylow
720C2—41no—
721C2—42no—
722C2—42no—
723C2—1201no—
724C2#1175655011yescharacteristic
725C2#1175659411yescharacteristic
726C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#518C2
socleC22×C3×C5C22×D4
prime radical#11751318C2
hypercenter#518D15
hypocenterC3×C5#3118
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
2. #11756293C2semidirect
3. #11751319C2semidirect
5. #11751119C2semidirect
6. C4×#6716C2semidirect
7. #11751117C2semidirect
8. #11751117C2semidirect
9. #11751115C2semidirect
10. C4×#6715C2semidirect
11. #11751109C2semidirect
12. #11751108C2semidirect
13. #11751104C2semidirect
14. #11751101C2semidirect
15. #11751097C2semidirect
38. #91764C22semidirect
39. C4×D60C22semidirect
40. #91758C22semidirect
41. C4×Dic30C22semidirect
48. #91094C22semidirect
49. #91094C22semidirect
50. #91093C22semidirect
51. #91093C22semidirect
52. #91092C22semidirect
53. #91092C22semidirect
54. #91091C22semidirect
55. #91091C22semidirect
56. C4⋊(C3⋊#168)C22semidirect
57. C4⋊(C3⋊#168)C22semidirect
58. #91087C22semidirect
59. C4×C3⋊#168C22semidirect
61. C5×#518D3semidirect
125. C3×#518D5semidirect
317. #518D15semidirect
611. C3×C5#3118semidirect
692. C5#82541semidirect
719. C3#10614272semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
#117562932
#117513192
#117513182
#117511192
C4×#67162
#117511172
#117511152
C4×#67152
#117511092
#117511082
#117511042
#117511012
#117510972
#106142723
#825415