Finite Group Databasebeta

← C3×#10610726 #14425534

Subgroups — C3×#10610726 #14425534

Order 1920.

1408 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
1C3×#66283C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3C2×C3×#4055C211yesmaximal, characteristic, complemented
4C3×#65860C211yesmaximal, characteristic, complemented
5C3×C5×#421C211yesmaximal, characteristic, complemented
6C3×#65421C211yesmaximal, characteristic, complemented
7C3×#65294C211yesmaximal, characteristic, complemented
8C3×#65115C214yesmaximal, complemented
9C3×#65114C214yesmaximal, complemented
10#10610726C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C3×#4150—21no—
13C3×#4150C2212yes—
14C3×#4149—21no—
15C3×#4149C2212yes—
16C3×D5×#41—22no—
17C3×D5×#41—22no—
18C3×#4147—21no—
19C3×#4144—21no—
20C3×#4144—22no—
21C2×C3×#709—22no—
22C2×C3×#709C2211yescharacteristic
23C2×C3×#709C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic, complemented
25C2×C3×C5×M16C2211yescharacteristic, complemented
26C3×C5×#117C2211yescharacteristic, complemented
27C3×#4097—22no—
28C3×#4097C2214yescomplemented
29C2×C3×#689—21no—
30C2×C3×#687—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32C3×#4055—22no—
33C3×#4055C2214yescomplemented
34C2×C3×Dic20—21no—
35C2×C3×#677—21no—
36C3×#4043—22no—
37C3×#4032—22no—
38C3×#4021C2212yescomplemented
39C3×#4015C2212yescomplemented
40C3×C5×#104C2214yescomplemented
41C3×#3956C2212yescomplemented
42C3×#3955C2212yescomplemented
43C3×#3937C2214yescomplemented
44C3×#3022—51nomaximal, Hall
45#66283C2×C311yescharacteristic
46C2×#4097C2×C311yescharacteristic, complemented
47C2×#4055C2×C311yescharacteristic, complemented
48#65860C2×C311yescharacteristic, complemented
49C5×#421C2×C311yescharacteristic, complemented
50#65421C2×C311yescharacteristic, complemented
51#65294C2×C311yescharacteristic, complemented
52#65115C2×C314yescomplemented
53#65114C2×C314yescomplemented
54C3×C5×#41—21no—
55C3×C5×#41—21no—
56C3×C5×#41D412yes—
57C3×C5×#41C2312yes—
58C2×C3×C5×Q8D411yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4D411yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×C3×C22⋊D5—24no—
64C2×C3×C22⋊D5—21no—
65C2×C3×C22⋊D5D412yes—
66C22×C3×Dic5—21no—
67C3×#713—22no—
68C3×#713—22no—
69C3×Q8×D5—22no—
70C3×Q8×D5—22no—
71C3×#711—24no—
72C3×#711—22no—
73C3×#711—22no—
74C3×#711—24no—
75C3×D4×D5—24no—
76C3×D4×D5—22no—
77C3×D4×D5—24no—
78C3×D4×D5—22no—
79C3×#709—24no—
80C3×#709—24no—
81C3×#709—21no—
82C3×#709—21no—
83C3×#709—21no—
84C3×#709—21no—
85C3×#709—21no—
86C3×#709—21no—
87C3×#709—22no—
88C3×#709—22no—
89C3×#709D412yes—
90C3×#709C2312yes—
91C2×C3×D20—22no—
92C2×C3×D20D411yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×C4×D5—24no—
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5D412yes—
97C2×C3×Dic10—22no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—21no—
100C2×C3×Dic10—21no—
101C2×C3×Dic10—21no—
102C2×C3×Dic10—21no—
103C2×C3×Dic10D411yescharacteristic
104C2×C3×Dic10C2312yes—
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×M16—21no—
107C3×C5×M16C2312yes—
108C2×C3×C5×C8—21no—
109C3×C5×C4⋊C4—21no—
110C3×C5×C22⋊C4—21no—
111C3×C42×C5C2312yes—
112C3×#689—24no—
113C3×#687—24no—
114C3×#685—24no—
115C3×C4⋊Dic5—24no—
116C3×#681—21no—
117C3×#681C2312yes—
118C2×C3×#168—21no—
119C3×Dic20—24no—
120C3×#677—24no—
121C3×#585—51no—
122C2×C3×#137—51no—
123C2×C3×#137—51no—
124C3×#536—51no—
125C3×#456—54no—
126C3×#455—54no—
127C3×#421—51no—
128C3×#421D511yescharacteristic, complemented
129C3×#413—51no—
130C2×C5×#41C22×C311yescharacteristic
131#4150—21no—
132#4150C22×C312yes—
133#4149—21no—
134#4149C22×C312yes—
135D5×#41—22no—
136D5×#41—22no—
137#4147—21no—
138#4144—21no—
139#4144—22no—
140C2×#709—22no—
141C2×#709C22×C311yescharacteristic
142C2×#709C22×C311yescharacteristic
143C22×Dic10C22×C311yescharacteristic, complemented
144C2×C5×M16C22×C311yescharacteristic, complemented
145C5×#117C22×C311yescharacteristic, complemented
146#4097—22no—
147#4097C22×C314yescomplemented
148C2×#689—21no—
149C2×#687—21no—
150C2×#681C22×C311yescharacteristic, complemented
151#4055—22no—
152#4055C22×C314yescomplemented
153C2×Dic20—21no—
154C2×#677—21no—
155#4043—22no—
156#4032—22no—
157#4021C22×C312yescomplemented
158#4015C22×C312yescomplemented
159C5×#104C22×C314yescomplemented
160#3956C22×C312yescomplemented
161#3955C22×C312yescomplemented
162#3937C22×C314yescomplemented
163#3022—51noSylow
164C23×C3×C5—21no—
165C23×C3×C5C2×D411yescharacteristic
166C22×C3×D5—24no—
167C22×C3×D5—21no—
168C22×C3×D5C2×D412yes—
169C3×C5×Q8—21no—
170C3×C5×Q8C2×D412yes—
171C3×C5×D4—22no—
172C3×C5×D4—22no—
173C3×C5×D4—21no—
174C3×C5×D4C2×D412yes—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5—22no—
178C2×C3×C4×C5—22no—
179C2×C3×C4×C5C2×D411yescharacteristic
180C2×C3×C4×C5C2×D411yescharacteristic
181C2×C3×C4×C5C2×D411yescharacteristic
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2411yescharacteristic
185C3×C22⋊D5—24no—
186C3×C22⋊D5—24no—
187C3×C22⋊D5—22no—
188C3×C22⋊D5—22no—
189C3×C22⋊D5—22no—
190C3×C22⋊D5—22no—
191C2×C3×Dic5—24no—
192C2×C3×Dic5—21no—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—41no—
195C2×C3×Dic5—41no—
196C2×C3×Dic5C2×D412yes—
197C3×D20—24no—
198C3×D20—21no—
199C3×D20—21no—
200C3×D20—21no—
201C3×D20C2×D412yes—
202C3×C4×D5—24no—
203C3×C4×D5—24no—
204C3×C4×D5—22no—
205C3×C4×D5—22no—
206C3×C4×D5—22no—
207C3×C4×D5—22no—
208C3×Dic10—24no—
209C3×Dic10—21no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—22no—
213C3×Dic10—22no—
214C3×Dic10—41no—
215C3×Dic10—41no—
216C3×Dic10C2×D412yes—
217C3×C5×C8—22no—
218C3×#168—22no—
219C3×2−1+4—52no—
220C3×2−1+4—101no—
221C3×2−1+4—101no—
222C3×H(5,𝔽2)—52no—
223C3×H(5,𝔽2)—102no—
224C3×H(5,𝔽2)—101no—
225C3×H(5,𝔽2)—101no—
226C2×C3×#41—51no—
227C2×C3×#41—51no—
228C2×C3×#41—102no—
229C2×C3×#41—102no—
230C2×C3×#41—102no—
231C2×C3×#41C2×D511yescharacteristic
232C22×C3×Q8—51no—
233C3×#137—54no—
234C3×#137—54no—
235C3×#137—102no—
236C3×#137—102no—
237C2×C3×Q16—101no—
238C2×C3×Q16—101no—
239C2×C3×SD16—101no—
240C2×C3×SD16—101no—
241C2×C3×M16—51no—
242C2×C3×M16C2×D511yescharacteristic, complemented
243C3×C4⋊Q8—52no—
244C3×#124—52no—
245C3×#123—102no—
246C3×C22⋊Q8—102no—
247C3×#117C2×D511yescharacteristic, complemented
248C3×#104—54no—
249C3×#104C2×D514yescomplemented
250C3×#101—52no—
251C3×#100—52no—
252C5×#41—21no—
253C5×#41—21no—
254C5×#41C3×D412yes—
255C5×#41C23×C312yes—
256C2×C5×Q8C3×D411yescharacteristic
257C2×C5×D4—21no—
258C2×C5×D4C3×D411yescharacteristic
259C22×C4×C5—21no—
260C22×C4×C5C23×C311yescharacteristic
261C2×C22⋊D5—24no—
262C2×C22⋊D5—21no—
263C2×C22⋊D5C3×D412yes—
264C22×Dic5—21no—
265#713—22no—
266#713—22no—
267Q8×D5—22no—
268Q8×D5—22no—
269#711—24no—
270#711—22no—
271#711—22no—
272#711—24no—
273D4×D5—24no—
274D4×D5—22no—
275D4×D5—24no—
276D4×D5—22no—
277#709—24no—
278#709—24no—
279#709—21no—
280#709—21no—
281#709—21no—
282#709—21no—
283#709—21no—
284#709—21no—
285#709—22no—
286#709—22no—
287#709C3×D412yes—
288#709C23×C312yes—
289C2×D20—22no—
290C2×D20C3×D411yescharacteristic
291C2×D20C23×C311yescharacteristic
292C2×C4×D5—24no—
293C2×C4×D5—21no—
294C2×C4×D5C3×D412yes—
295C2×Dic10—22no—
296C2×Dic10—21no—
297C2×Dic10—21no—
298C2×Dic10—21no—
299C2×Dic10—21no—
300C2×Dic10—21no—
301C2×Dic10C3×D411yescharacteristic
302C2×Dic10C23×C312yes—
303C2×Dic10C23×C311yescharacteristic
304C5×M16—21no—
305C5×M16C23×C312yes—
306C2×C5×C8—21no—
307C5×C4⋊C4—21no—
308C5×C22⋊C4—21no—
309C42×C5C23×C312yes—
310#689—24no—
311#687—24no—
312#685—24no—
313C4⋊Dic5—24no—
314#681—21no—
315#681C23×C312yes—
316C2×#168—21no—
317Dic20—24no—
318#677—24no—
319#585—51no—
320C2×#137—51no—
321C2×#137—51no—
322#536—51no—
323#456—54no—
324#455—54no—
325#421—51no—
326#421C3×D511yescharacteristic, complemented
327#413—51no—
328C22×C3×C5—22no—
329C22×C3×C5—41no—
330C22×C3×C5—81no—
331C22×C3×C5#12011yescharacteristic
332C22×C3×C5#12011yescharacteristic
333C22×C3×C5C22×D411yescharacteristic
334C2×C3×D5—22no—
335C2×C3×D5—22no—
336C2×C3×D5—42no—
337C2×C3×D5—81no—
338C2×C3×D5—84no—
339C3×C4×C5—22no—
340C3×C4×C5—42no—
341C3×C4×C5#12011yescharacteristic
342C3×C4×C5#12011yescharacteristic
343C3×C4×C5C22×D411yescharacteristic
344C3×C4×C5C22×D411yescharacteristic
345C3×Dic5—22no—
346C3×Dic5—22no—
347C3×Dic5—42no—
348C3×#41—21no—
349C3×#41—21no—
350C3×#41—52no—
351C3×#41—52no—
352C3×#41—102no—
353C3×#41—102no—
354C3×#41—104no—
355C3×#41—104no—
356C3×#41—104no—
357C3×#41—104no—
358C3×#41—102no—
359C3×#41—102no—
360C3×#41—102no—
361C3×#41—102no—
362C3×#41—101no—
363C3×#41—101no—
364C3×#41—101no—
365C3×#41—101no—
366C3×#41—101no—
367C3×#41—101no—
368C3×#41D2012yes—
369C3×#41C22×D512yes—
370C2×C3×Q8—51no—
371C2×C3×Q8—51no—
372C2×C3×Q8—52no—
373C2×C3×Q8—102no—
374C2×C3×Q8—102no—
375C2×C3×Q8—102no—
376C2×C3×Q8—101no—
377C2×C3×Q8—101no—
378C2×C3×Q8—101no—
379C2×C3×Q8—101no—
380C2×C3×Q8—101no—
381C2×C3×Q8D2011yescharacteristic
382C2×C3×D4—21no—
383C2×C3×D4—52no—
384C2×C3×D4—51no—
385C2×C3×D4—51no—
386C2×C3×D4—102no—
387C2×C3×D4—104no—
388C2×C3×D4—104no—
389C2×C3×D4—102no—
390C2×C3×D4—104no—
391C2×C3×D4—101no—
392C2×C3×D4—102no—
393C2×C3×D4D2011yescharacteristic
394C22×C3×C4—21no—
395C22×C3×C4—52no—
396C22×C3×C4—104no—
397C22×C3×C4—101no—
398C22×C3×C4—101no—
399C22×C3×C4C22×D511yescharacteristic
400C3×Q16—104no—
401C3×Q16—104no—
402C3×SD16—104no—
403C3×SD16—104no—
404C3×M16—21no—
405C3×M16—52no—
406C3×M16—101no—
407C3×M16C22×D512yes—
408C2×C3×C8—21no—
409C2×C3×C8—101no—
410C3×C4⋊C4—21no—
411C3×C4⋊C4—104no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—104no—
414C3×C42C22×D512yes—
415C23×C5—21no—
416C23×C5C2×C3×D411yescharacteristic
417C22×D5—24no—
418C22×D5—21no—
419C22×D5C2×C3×D412yes—
420C5×Q8—21no—
421C5×Q8C2×C3×D412yes—
422C5×D4—22no—
423C5×D4—22no—
424C5×D4—21no—
425C5×D4C2×C3×D412yes—
426C2×C4×C5—21no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5C2×C3×D411yescharacteristic
431C2×C4×C5C2×C3×D411yescharacteristic
432C2×C4×C5C2×C3×D411yescharacteristic
433C2×C4×C5C2×C3×D411yescharacteristic
434C2×C4×C5C2×C3×D411yescharacteristic
435C2×C4×C5C24×C311yescharacteristic
436C22⋊D5—24no—
437C22⋊D5—24no—
438C22⋊D5—22no—
439C22⋊D5—22no—
440C22⋊D5—22no—
441C22⋊D5—22no—
442C2×Dic5—24no—
443C2×Dic5—21no—
444C2×Dic5—22no—
445C2×Dic5—41no—
446C2×Dic5—41no—
447C2×Dic5C2×C3×D412yes—
448D20—24no—
449D20—21no—
450D20—21no—
451D20—21no—
452D20C2×C3×D412yes—
453C4×D5—24no—
454C4×D5—24no—
455C4×D5—22no—
456C4×D5—22no—
457C4×D5—22no—
458C4×D5—22no—
459Dic10—24no—
460Dic10—21no—
461Dic10—21no—
462Dic10—21no—
463Dic10—22no—
464Dic10—22no—
465Dic10—41no—
466Dic10—41no—
467Dic10C2×C3×D412yes—
468C5×C8—22no—
469#168—22no—
4702−1+4—52no—
4712−1+4—101no—
4722−1+4—101no—
473H(5,𝔽2)—52no—
474H(5,𝔽2)—102no—
475H(5,𝔽2)—101no—
476H(5,𝔽2)—101no—
477C2×#41—51no—
478C2×#41—51no—
479C2×#41—102no—
480C2×#41—102no—
481C2×#41—102no—
482C2×#41C2×C3×D511yescharacteristic
483C22×Q8—51no—
484#137—54no—
485#137—54no—
486#137—102no—
487#137—102no—
488C2×Q16—101no—
489C2×Q16—101no—
490C2×SD16—101no—
491C2×SD16—101no—
492C2×M16—51no—
493C2×M16C2×C3×D511yescharacteristic, complemented
494C4⋊Q8—52no—
495#124—52no—
496#123—102no—
497C22⋊Q8—102no—
498#117C2×C3×D511yescharacteristic, complemented
499#104—54no—
500#104C2×C3×D514yescomplemented
501#101—52no—
502#100—52no—
503C2×C3×C5—21no—
504C2×C3×C5—21no—
505C2×C3×C5—21no—
506C2×C3×C5—42no—
507C2×C3×C5C2×#12011yescharacteristic
508C3×D5—42no—
509C3×D5—42no—
510C23×C3—21no—
511C23×C3—52no—
512C23×C3—104no—
513C23×C3—101no—
514C23×C3D4×D511yescharacteristic
515C3×Q8—21no—
516C3×Q8—52no—
517C3×Q8—104no—
518C3×Q8—101no—
519C3×Q8—101no—
520C3×Q8—101no—
521C3×Q8—102no—
522C3×Q8—102no—
523C3×Q8—201no—
524C3×Q8—201no—
525C3×Q8C2×D2012yes—
526C3×D4—22no—
527C3×D4—22no—
528C3×D4—21no—
529C3×D4—52no—
530C3×D4—104no—
531C3×D4—104no—
532C3×D4—104no—
533C3×D4—102no—
534C3×D4—102no—
535C3×D4—102no—
536C3×D4—102no—
537C3×D4—101no—
538C3×D4—101no—
539C3×D4—101no—
540C3×D4C2×D2012yes—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—52no—
546C2×C3×C4—104no—
547C2×C3×C4—104no—
548C2×C3×C4—104no—
549C2×C3×C4—101no—
550C2×C3×C4—102no—
551C2×C3×C4—102no—
552C2×C3×C4—102no—
553C2×C3×C4—102no—
554C2×C3×C4—102no—
555C2×C3×C4—201no—
556C2×C3×C4—201no—
557C2×C3×C4C2×D2011yescharacteristic
558C2×C3×C4C2×D2011yescharacteristic
559C2×C3×C4D4×D511yescharacteristic
560C2×C3×C4D4×D511yescharacteristic
561C2×C3×C4D4×D511yescharacteristic
562C2×C3×C4C23×D511yescharacteristic
563C3×C8—22no—
564C3×C8—102no—
565C22×C5—22no—
566C22×C5—41no—
567C22×C5—81no—
568C22×C5C3×#12011yescharacteristic
569C22×C5C3×#12011yescharacteristic
570C22×C5C22×C3×D411yescharacteristic
571C2×D5—22no—
572C2×D5—22no—
573C2×D5—42no—
574C2×D5—81no—
575C2×D5—84no—
576C4×C5—22no—
577C4×C5—42no—
578C4×C5C3×#12011yescharacteristic
579C4×C5C3×#12011yescharacteristic
580C4×C5C22×C3×D411yescharacteristic
581C4×C5C22×C3×D411yescharacteristic
582Dic5—22no—
583Dic5—22no—
584Dic5—42no—
585#41—21no—
586#41—21no—
587#41—52no—
588#41—52no—
589#41—102no—
590#41—102no—
591#41—104no—
592#41—104no—
593#41—104no—
594#41—104no—
595#41—102no—
596#41—102no—
597#41—102no—
598#41—102no—
599#41—101no—
600#41—101no—
601#41—101no—
602#41—101no—
603#41—101no—
604#41—101no—
605#41C3×D2012yes—
606#41C22×C3×D512yes—
607C2×Q8—51no—
608C2×Q8—51no—
609C2×Q8—52no—
610C2×Q8—102no—
611C2×Q8—102no—
612C2×Q8—102no—
613C2×Q8—101no—
614C2×Q8—101no—
615C2×Q8—101no—
616C2×Q8—101no—
617C2×Q8—101no—
618C2×Q8C3×D2011yescharacteristic
619C2×D4—21no—
620C2×D4—52no—
621C2×D4—51no—
622C2×D4—51no—
623C2×D4—102no—
624C2×D4—104no—
625C2×D4—104no—
626C2×D4—102no—
627C2×D4—104no—
628C2×D4—101no—
629C2×D4—102no—
630C2×D4C3×D2011yescharacteristic
631C22×C4—21no—
632C22×C4—52no—
633C22×C4—104no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4C22×C3×D511yescharacteristic
637Q16—104no—
638Q16—104no—
639SD16—104no—
640SD16—104no—
641M16—21no—
642M16—52no—
643M16—101no—
644M16C22×C3×D512yes—
645C2×C8—21no—
646C2×C8—101no—
647C4⋊C4—21no—
648C4⋊C4—104no—
649C22⋊C4—21no—
650C22⋊C4—104no—
651C42C22×C3×D512yes—
652C3×C5#302211yescharacteristic, complemented, Hall
653C22×C3—22no—
654C22×C3—41no—
655C22×C3—81no—
656C22×C3—102no—
657C22×C3—102no—
658C22×C3—202no—
659C22×C3—401no—
660C22×C3—404no—
661C22×C3#402811yescharacteristic
662C22×C3#402811yescharacteristic
663C22×C3C2×D4×D511yescharacteristic
664C3×C4—22no—
665C3×C4—42no—
666C3×C4—102no—
667C3×C4—102no—
668C3×C4—202no—
669C3×C4#402811yescharacteristic
670C3×C4#402811yescharacteristic
671C3×C4C22×D2011yescharacteristic
672C3×C4C2×D4×D511yescharacteristic
673C2×C5—21no—
674C2×C5—21no—
675C2×C5—21no—
676C2×C5—42no—
677C2×C5C2×C3×#12011yescharacteristic
678D5—42no—
679D5—42no—
680C23—21no—
681C23—52no—
682C23—104no—
683C23—101no—
684C23C3×D4×D511yescharacteristic
685Q8—21no—
686Q8—52no—
687Q8—104no—
688Q8—101no—
689Q8—101no—
690Q8—101no—
691Q8—102no—
692Q8—102no—
693Q8—201no—
694Q8—201no—
695Q8C2×C3×D2012yes—
696D4—22no—
697D4—22no—
698D4—21no—
699D4—52no—
700D4—104no—
701D4—104no—
702D4—104no—
703D4—102no—
704D4—102no—
705D4—102no—
706D4—102no—
707D4—101no—
708D4—101no—
709D4—101no—
710D4C2×C3×D2012yes—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—52no—
716C2×C4—104no—
717C2×C4—104no—
718C2×C4—104no—
719C2×C4—101no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—201no—
726C2×C4—201no—
727C2×C4C2×C3×D2011yescharacteristic
728C2×C4C2×C3×D2011yescharacteristic
729C2×C4C3×D4×D511yescharacteristic
730C2×C4C3×D4×D511yescharacteristic
731C2×C4C3×D4×D511yescharacteristic
732C2×C4C23×C3×D511yescharacteristic
733C8—22no—
734C8—102no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—202no—
740C2×C3—202no—
741C2×C3C2×#402811yescharacteristic
742C5C3×#302211yescharacteristic, complemented, Sylow
743C22—22no—
744C22—41no—
745C22—81no—
746C22—102no—
747C22—102no—
748C22—202no—
749C22—401no—
750C22—404no—
751C22C3×#402811yescharacteristic
752C22C3×#402811yescharacteristic
753C22C2×C3×D4×D511yescharacteristic
754C4—22no—
755C4—42no—
756C4—102no—
757C4—102no—
758C4—202no—
759C4C3×#402811yescharacteristic
760C4C3×#402811yescharacteristic
761C4C22×C3×D2011yescharacteristic
762C4C2×C3×D4×D511yescharacteristic
763C3#1061072611yescharacteristic, direct product factor, Sylow
764C2—21no—
765C2—21no—
766C2—21no—
767C2—42no—
768C2—202no—
769C2—202no—
770C2C2×C3×#402811yescharacteristic
subgroupG/H
centerC2×C3C2×#4028
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5C2×#120
prime radicalC3×#66283C2
hypercenterC3×#421D5
hypocenterC5C3×#3022
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C2×C3×#4055C2semidirect
4. C3×#65860C2semidirect
5. C3×C5×#421C2semidirect
6. C3×#65421C2semidirect
7. C3×#65294C2semidirect
8. C3×#65115C2semidirect
9. C3×#65114C2semidirect
10. #10610726C3direct (N × H)
24. C22×C3×Dic10C22semidirect
25. C2×C3×C5×M16C22semidirect
26. C3×C5×#117C22semidirect
28. C3×#4097C22semidirect
31. C2×C3×#681C22semidirect
33. C3×#4055C22semidirect
38. C3×#4021C22semidirect
39. C3×#4015C22semidirect
40. C3×C5×#104C22semidirect
41. C3×#3956C22semidirect
42. C3×#3955C22semidirect
43. C3×#3937C22semidirect
46. C2×#4097C2×C3semidirect
47. C2×#4055C2×C3semidirect
48. #65860C2×C3semidirect
49. C5×#421C2×C3semidirect
50. #65421C2×C3semidirect
51. #65294C2×C3semidirect
52. #65115C2×C3semidirect
53. #65114C2×C3semidirect
128. C3×#421D5semidirect
143. C22×Dic10C22×C3semidirect
144. C2×C5×M16C22×C3semidirect
145. C5×#117C22×C3semidirect
147. #4097C22×C3semidirect
150. C2×#681C22×C3semidirect
152. #4055C22×C3semidirect
157. #4021C22×C3semidirect
158. #4015C22×C3semidirect
159. C5×#104C22×C3semidirect
160. #3956C22×C3semidirect
161. #3955C22×C3semidirect
162. #3937C22×C3semidirect
242. C2×C3×M16C2×D5semidirect
247. C3×#117C2×D5semidirect
249. C3×#104C2×D5semidirect
326. #421C3×D5semidirect
493. C2×M16C2×C3×D5semidirect
498. #117C2×C3×D5semidirect
500. #104C2×C3×D5semidirect
652. C3×C5#3022semidirect
742. C5C3×#3022semidirect
763. C3#10610726direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662832
C2×C3×#40972
C2×C3×#40552
C3×#658602
C3×C5×#4212
C3×#654212
C3×#652942
C3×#651152
C3×#651142
#106107263
C3×#30225