Finite Group Databasebeta

← C3×#10614299 #14435839

Subgroups — C3×#10614299 #14435839

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#520C211yesmaximal, characteristic, complemented
2C3×#65869C211yesmaximal, characteristic, complemented
3C3×#65527C211yesmaximal, characteristic, complemented
4C3×#65527C211yesmaximal, characteristic, complemented
5C3×#65316C211yesmaximal, characteristic, complemented
6C3×#65315C211yesmaximal, characteristic, complemented
7C3×C4×#688C211yesmaximal, characteristic, complemented
8C3×#65311C211yesmaximal, characteristic, complemented
9C3×#65304C211yesmaximal, characteristic, complemented
10C3×#65303C211yesmaximal, characteristic, complemented
11C3×C4×#686C211yesmaximal, characteristic, complemented
12C3×#65298C211yesmaximal, characteristic, complemented
13C3×#65289C211yesmaximal, characteristic, complemented
14C3×#65257C211yesmaximal, characteristic, complemented
15C3×#65256C211yesmaximal, characteristic, complemented
16#10614299C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×D4—21no—
21C3×C4×C5×D4—21no—
22C3×C4×C5×D4C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24C3×C5×#117—21no—
25C3×C5×#117C2211yescharacteristic
26C2×C3×C5×C4⋊C4—21no—
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×#688C2211yescharacteristic
29C2×C3×#688C2211yescharacteristic
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076C2211yescharacteristic
33C3×#4076C2211yescharacteristic
34C3×#4040—21no—
35C3×#4040—21no—
36C3×#4030—21no—
37C3×#4030—21no—
38C3×#4020C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×C4×D20C2211yescharacteristic
41C3×#4016C2211yescharacteristic
42C3×#3967C2211yescharacteristic
43C3×#3967C2211yescharacteristic
44C3×#3964C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×#3940C2211yescharacteristic
53C3×#3940C2211yescharacteristic
54C3×#3939C2211yescharacteristic
55C3×#3939C2211yescharacteristic
56C3×C4⋊#168C2211yescharacteristic
57C3×C4⋊#168C2211yescharacteristic
58C3×#3935C2211yescharacteristic
59C3×C4×#168C2211yescharacteristic
60C3×#3119—51nomaximal, Hall
61C5×#520C2×C311yescharacteristic, complemented
62#65869C2×C311yescharacteristic, complemented
63#65527C2×C311yescharacteristic, complemented
64#65527C2×C311yescharacteristic, complemented
65#65316C2×C311yescharacteristic, complemented
66#65315C2×C311yescharacteristic, complemented
67C4×#688C2×C311yescharacteristic, complemented
68#65311C2×C311yescharacteristic, complemented
69#65304C2×C311yescharacteristic, complemented
70#65303C2×C311yescharacteristic, complemented
71C4×#686C2×C311yescharacteristic, complemented
72#65298C2×C311yescharacteristic, complemented
73#65289C2×C311yescharacteristic, complemented
74#65257C2×C311yescharacteristic, complemented
75#65256C2×C311yescharacteristic, complemented
76C3×C5×#41—22no—
77C3×C5×#41—22no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5C2311yescharacteristic
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×D20—21no—
89C2×C3×D20—21no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C4⋊C4D411yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C5×C22⋊C4D411yescharacteristic
105C3×C42×C5—21no—
106C3×C42×C5—21no—
107C3×C42×C5C2311yescharacteristic
108C3×C42×C5C2311yescharacteristic
109C3×#688—22no—
110C3×#688—22no—
111C3×#686—22no—
112C3×#686—22no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#540—51no—
126C3×#520D511yescharacteristic, complemented
127C3×#481—51no—
128C3×#480—51no—
129C3×#479—51no—
130C3×#478—51no—
131C3×#460—51no—
132C3×#459—51no—
133C3×#449—51no—
134C3×#449—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C2×C5×#41C22×C311yescharacteristic
141C4×C5×Q8C22×C311yescharacteristic
142C4×C5×Q8C22×C311yescharacteristic
143C4×C5×D4—21no—
144C4×C5×D4—21no—
145C4×C5×D4C22×C311yescharacteristic
146C4×C5×D4C22×C311yescharacteristic
147C5×#117—21no—
148C5×#117C22×C311yescharacteristic
149C2×C5×C4⋊C4—21no—
150C2×C5×C4⋊C4C22×C311yescharacteristic
151C2×#688C22×C311yescharacteristic
152C2×#688C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154C2×#686C22×C311yescharacteristic
155#4076C22×C311yescharacteristic
156#4076C22×C311yescharacteristic
157#4040—21no—
158#4040—21no—
159#4030—21no—
160#4030—21no—
161#4020C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163C4×D20C22×C311yescharacteristic
164#4016C22×C311yescharacteristic
165#3967C22×C311yescharacteristic
166#3967C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3941C22×C311yescharacteristic
172#3941C22×C311yescharacteristic
173#3941C22×C311yescharacteristic
174#3941C22×C311yescharacteristic
175#3940C22×C311yescharacteristic
176#3940C22×C311yescharacteristic
177#3939C22×C311yescharacteristic
178#3939C22×C311yescharacteristic
179C4⋊#168C22×C311yescharacteristic
180C4⋊#168C22×C311yescharacteristic
181#3935C22×C311yescharacteristic
182C4×#168C22×C311yescharacteristic
183#3119—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×D4—24no—
191C3×C5×D4—21no—
192C3×C5×D4#4112yes—
193C2×C3×C4×C5—24no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5—81no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C3×C22⋊D5—81no—
209C3×C22⋊D5—81no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C3×D20—21no—
213C3×D20—21no—
214C3×D20—21no—
215C3×D20—21no—
216C3×D20—81no—
217C3×D20—81no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3×#168—21no—
221C3×#168—21no—
222C3×#168—21no—
223C3×#168—21no—
224C2×C3×#41C2×D511yescharacteristic
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×#127—51no—
230C3×#125—51no—
231C3×#123—101no—
232C3×#123—101no—
233C3×#121—51no—
234C3×#121—51no—
235C3×#121—101no—
236C3×#121—101no—
237C3×C4×Q8C2×D511yescharacteristic
238C3×C4×Q8C2×D511yescharacteristic
239C3×C4×D4—21no—
240C3×C4×D4—21no—
241C3×C4×D4—51no—
242C3×C4×D4—51no—
243C3×C4×D4C2×D511yescharacteristic
244C3×C4×D4C2×D511yescharacteristic
245C3×#117—21no—
246C3×#117C2×D511yescharacteristic
247C2×C3×C4⋊C4—21no—
248C2×C3×C4⋊C4C2×D511yescharacteristic
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106—51no—
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102—51no—
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×#97—51no—
266C3×C4×C8—51no—
267C5×#41—22no—
268C5×#41—22no—
269C2×C5×Q8C23×C311yescharacteristic
270C2×C5×D4—21no—
271C2×C5×D4C23×C311yescharacteristic
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5C23×C311yescharacteristic
277C2×C22⋊D5—21no—
278C2×C22⋊D5—21no—
279C2×D20—21no—
280C2×D20—21no—
281C2×D20C23×C311yescharacteristic
282C2×D20C23×C311yescharacteristic
283C2×C4×D5—21no—
284C2×C4×D5—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4C3×D411yescharacteristic
289C5×C4⋊C4C3×D411yescharacteristic
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C4⋊C4C23×C311yescharacteristic
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4C3×D411yescharacteristic
295C5×C22⋊C4C3×D411yescharacteristic
296C42×C5—21no—
297C42×C5—21no—
298C42×C5C23×C311yescharacteristic
299C42×C5C23×C311yescharacteristic
300#688—22no—
301#688—22no—
302#686—22no—
303#686—22no—
304#685—21no—
305#685—21no—
306#685—21no—
307#685—21no—
308C4⋊Dic5C23×C311yescharacteristic
309C4⋊Dic5C23×C311yescharacteristic
310#683—21no—
311#683—21no—
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#540—51no—
317#520C3×D511yescharacteristic, complemented
318#481—51no—
319#480—51no—
320#479—51no—
321#478—51no—
322#460—51no—
323#459—51no—
324#449—51no—
325#449—51no—
326#442—51no—
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—21no—
332C22×C3×C5—22no—
333C22×C3×C5—21no—
334C22×C3×C5—21no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5C22×D411yescharacteristic
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—21no—
345C3×C4×C5—22no—
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
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×#41—22no—
357C3×#41—22no—
358C2×C3×Q8C22×D511yescharacteristic
359C2×C3×D4—21no—
360C2×C3×D4—51no—
361C2×C3×D4—51no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4—101no—
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4C22×D511yescharacteristic
374C3×SD16—102no—
375C3×SD16—102no—
376C3×D8—102no—
377C3×D8—102no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8—51no—
381C2×C3×C8—51no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22⋊D511yescharacteristic
390C3×C4⋊C4C22⋊D511yescharacteristic
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4C22⋊D511yescharacteristic
400C3×C22⋊C4C22⋊D511yescharacteristic
401C3×C42—21no—
402C3×C42—21no—
403C3×C42C22×D511yescharacteristic
404C3×C42C22×D511yescharacteristic
405C23×C5—21no—
406C23×C5C2×C3×D411yescharacteristic
407C22×D5—21no—
408C22×D5—21no—
409C5×Q8—21no—
410C5×Q8C3×#4112yes—
411C5×D4—24no—
412C5×D4—21no—
413C5×D4C3×#4112yes—
414C2×C4×C5—24no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—81no—
421C2×C4×C5—81no—
422C2×C4×C5—81no—
423C2×C4×C5C2×C3×D411yescharacteristic
424C2×C4×C5C2×C3×D411yescharacteristic
425C2×C4×C5C2×C3×D411yescharacteristic
426C2×C4×C5C2×C3×D411yescharacteristic
427C2×C4×C5C2×C3×D411yescharacteristic
428C2×C4×C5C24×C311yescharacteristic
429C22⋊D5—81no—
430C22⋊D5—81no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433D20—21no—
434D20—21no—
435D20—21no—
436D20—21no—
437D20—81no—
438D20—81no—
439C4×D5—81no—
440C4×D5—81no—
441#168—21no—
442#168—21no—
443#168—21no—
444#168—21no—
445C2×#41C2×C3×D511yescharacteristic
446C2×SD16—51no—
447C2×SD16—51no—
448C2×D8—51no—
449C2×D8—51no—
450#127—51no—
451#125—51no—
452#123—101no—
453#123—101no—
454#121—51no—
455#121—51no—
456#121—101no—
457#121—101no—
458C4×Q8C2×C3×D511yescharacteristic
459C4×Q8C2×C3×D511yescharacteristic
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4C2×C3×D511yescharacteristic
465C4×D4C2×C3×D511yescharacteristic
466#117—21no—
467#117C2×C3×D511yescharacteristic
468C2×C4⋊C4—21no—
469C2×C4⋊C4C2×C3×D511yescharacteristic
470#107—51no—
471#107—51no—
472#106—51no—
473#106—51no—
474C4⋊C8—51no—
475C4⋊C8—51no—
476#103—51no—
477#103—51no—
478#102—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102—51no—
484C22⋊C8—51no—
485C22⋊C8—51no—
486#97—51no—
487C4×C8—51no—
488C2×C3×C5—41no—
489C2×C3×C5—42no—
490C2×C3×C5#52511yescharacteristic
491C2×C3×C5#57611yescharacteristic
492C2×C3×C5#57711yescharacteristic
493C3×D5—81no—
494C3×D5—81no—
495C23×C3—21no—
496C23×C3—101no—
497C23×C3—101no—
498C23×C3C2×C22⋊D511yescharacteristic
499C3×Q8—21no—
500C3×Q8#70912yes—
501C3×D4—24no—
502C3×D4—21no—
503C3×D4—101no—
504C3×D4—101no—
505C3×D4—101no—
506C3×D4—101no—
507C3×D4—401no—
508C3×D4—401no—
509C3×D4—401no—
510C3×D4—401no—
511C3×D4#70912yes—
512C2×C3×C4—24no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—81no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—401no—
524C2×C3×C4—401no—
525C2×C3×C4C2×C22⋊D511yescharacteristic
526C2×C3×C4C2×C22⋊D511yescharacteristic
527C2×C3×C4C2×C22⋊D511yescharacteristic
528C2×C3×C4C2×C22⋊D511yescharacteristic
529C2×C3×C4C2×C22⋊D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531C3×C8—101no—
532C3×C8—101no—
533C3×C8—101no—
534C3×C8—101no—
535C22×C5—21no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—22no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5C22×C3×D411yescharacteristic
542C2×D5—41no—
543C2×D5—41no—
544C2×D5—41no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C4×C5—21no—
549C4×C5—21no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—22no—
554C4×C5—41no—
555C4×C5—41no—
556C4×C5C2×C3×#4111yescharacteristic
557C4×C5C2×C3×#4111yescharacteristic
558Dic5—41no—
559Dic5—41no—
560#41—22no—
561#41—22no—
562C2×Q8C22×C3×D511yescharacteristic
563C2×D4—21no—
564C2×D4—51no—
565C2×D4—51no—
566C2×D4—101no—
567C2×D4—101no—
568C2×D4—101no—
569C2×D4—101no—
570C2×D4C22×C3×D511yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—102no—
579SD16—102no—
580D8—102no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8—51no—
585C2×C8—51no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4C3×C22⋊D511yescharacteristic
594C4⋊C4C3×C22⋊D511yescharacteristic
595C4⋊C4C22×C3×D511yescharacteristic
596C4⋊C4C22×C3×D511yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4C3×C22⋊D511yescharacteristic
604C22⋊C4C3×C22⋊D511yescharacteristic
605C42—21no—
606C42—21no—
607C42C22×C3×D511yescharacteristic
608C42C22×C3×D511yescharacteristic
609C3×C5#311911yescharacteristic, complemented, Hall
610C22×C3—21no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—201no—
617C22×C3—201no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3C22×C22⋊D511yescharacteristic
623C3×C4—21no—
624C3×C4—22no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4C2×#70911yescharacteristic
634C3×C4C2×#70911yescharacteristic
635C2×C5—41no—
636C2×C5—42no—
637C2×C5C3×#52511yescharacteristic
638C2×C5C3×#57611yescharacteristic
639C2×C5C3×#57711yescharacteristic
640D5—81no—
641D5—81no—
642C23—21no—
643C23—101no—
644C23—101no—
645C23C2×C3×C22⋊D511yescharacteristic
646Q8—21no—
647Q8C3×#70912yes—
648D4—24no—
649D4—21no—
650D4—101no—
651D4—101no—
652D4—101no—
653D4—101no—
654D4—401no—
655D4—401no—
656D4—401no—
657D4—401no—
658D4C3×#70912yes—
659C2×C4—24no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—401no—
671C2×C4—401no—
672C2×C4C2×C3×C22⋊D511yescharacteristic
673C2×C4C2×C3×C22⋊D511yescharacteristic
674C2×C4C2×C3×C22⋊D511yescharacteristic
675C2×C4C2×C3×C22⋊D511yescharacteristic
676C2×C4C2×C3×C22⋊D511yescharacteristic
677C2×C4C23×C3×D511yescharacteristic
678C8—101no—
679C8—101no—
680C8—101no—
681C8—101no—
682C2×C3—41no—
683C2×C3—42no—
684C2×C3—401no—
685C2×C3—401no—
686C2×C3#6612511yescharacteristic
687C2×C3#6616911yescharacteristic
688C2×C3#6617111yescharacteristic
689C5C3×#311911yescharacteristic, complemented, Sylow
690C22—21no—
691C22—22no—
692C22—21no—
693C22—21no—
694C22—41no—
695C22—41no—
696C22—201no—
697C22—201no—
698C22—201no—
699C22—201no—
700C22—201no—
701C22—201no—
702C22C22×C3×C22⋊D511yescharacteristic
703C4—21no—
704C4—22no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—41no—
710C4—41no—
711C4—201no—
712C4—201no—
713C4C2×C3×#70911yescharacteristic
714C4C2×C3×#70911yescharacteristic
715C3#1061429911yescharacteristic, direct product factor, Sylow
716C2—41no—
717C2—42no—
718C2—401no—
719C2—401no—
720C2C3×#6612511yescharacteristic
721C2C3×#6616911yescharacteristic
722C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
hypercenterC3×#520D5
hypocenterC5C3×#3119
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
1. C3×C5×#520C2semidirect
2. C3×#65869C2semidirect
3. C3×#65527C2semidirect
4. C3×#65527C2semidirect
5. C3×#65316C2semidirect
6. C3×#65315C2semidirect
7. C3×C4×#688C2semidirect
8. C3×#65311C2semidirect
9. C3×#65304C2semidirect
10. C3×#65303C2semidirect
11. C3×C4×#686C2semidirect
12. C3×#65298C2semidirect
13. C3×#65289C2semidirect
14. C3×#65257C2semidirect
15. C3×#65256C2semidirect
16. #10614299C3direct (N × H)
61. C5×#520C2×C3semidirect
62. #65869C2×C3semidirect
63. #65527C2×C3semidirect
64. #65527C2×C3semidirect
65. #65316C2×C3semidirect
66. #65315C2×C3semidirect
67. C4×#688C2×C3semidirect
68. #65311C2×C3semidirect
69. #65304C2×C3semidirect
70. #65303C2×C3semidirect
71. C4×#686C2×C3semidirect
72. #65298C2×C3semidirect
73. #65289C2×C3semidirect
74. #65257C2×C3semidirect
75. #65256C2×C3semidirect
126. C3×#520D5semidirect
317. #520C3×D5semidirect
609. C3×C5#3119semidirect
689. C5C3×#3119semidirect
715. C3#10614299direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C3×#658692
C3×#655272
C3×#653162
C3×#653152
C3×C4×#6882
C3×#653112
C3×#653042
C3×#653032
C3×C4×#6862
C3×#652982
C3×#652892
C3×#652572
C3×#652562
#106142993
C3×#31195