Finite Group Databasebeta

← C3×#10615165 #14435821

Subgroups — C3×#10615165 #14435821

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×#540C211yesmaximal, characteristic, complemented
2C3×#65857C211yesmaximal, characteristic, complemented
3C3×#65364C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic, complemented
5C3×#65355C211yesmaximal, characteristic, complemented
6C3×#65352C211yesmaximal, characteristic, complemented
7C3×#65326C211yesmaximal, characteristic, complemented
8C3×#65326C211yesmaximal, characteristic, complemented
9C3×#65323C211yesmaximal, characteristic, complemented
10C3×#65322C211yesmaximal, characteristic, complemented
11C3×#65307C211yesmaximal, characteristic, complemented
12C3×C4×#687C211yesmaximal, characteristic, complemented
13C3×#65303C211yesmaximal, characteristic, complemented
14C3×C4×#686C211yesmaximal, characteristic, complemented
15C3×#65289C211yesmaximal, characteristic, complemented
16#10615165C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×#127C2211yescharacteristic
19C3×C5×#125C2211yescharacteristic
20C3×C5×#123—21no—
21C3×C5×#123—21no—
22C3×C5×#121—21no—
23C3×C5×#121—21no—
24C3×C5×#121C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic
26C3×C4×C5×D4C2211yescharacteristic
27C3×C4×C5×D4C2211yescharacteristic
28C3×C5×#117C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C2×C3×#686C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C3×#4038—21no—
35C3×D5×C4⋊C4—21no—
36C3×#4027—21no—
37C3×#4027—21no—
38C3×C4×D20C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×C4×Dic10C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×#3964C2211yescharacteristic
43C3×#3964C2211yescharacteristic
44C3×#3964C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
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×#540C2×C311yescharacteristic, complemented
62#65857C2×C311yescharacteristic, complemented
63#65364C2×C311yescharacteristic, complemented
64#65361C2×C311yescharacteristic, complemented
65#65355C2×C311yescharacteristic, complemented
66#65352C2×C311yescharacteristic, complemented
67#65326C2×C311yescharacteristic, complemented
68#65326C2×C311yescharacteristic, complemented
69#65323C2×C311yescharacteristic, complemented
70#65322C2×C311yescharacteristic, complemented
71#65307C2×C311yescharacteristic, complemented
72C4×#687C2×C311yescharacteristic, complemented
73#65303C2×C311yescharacteristic, complemented
74C4×#686C2×C311yescharacteristic, complemented
75#65289C2×C311yescharacteristic, complemented
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4—21no—
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×C5C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C22×C3×Dic5—21no—
87C3×#709—22no—
88C3×#709—22no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×Dic10C2311yescharacteristic
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C5×C22⋊C4D411yescharacteristic
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C42×C5C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108C3×#687—22no—
109C3×#687—22no—
110C3×#686—22no—
111C3×#686—22no—
112C3×#685—21no—
113C3×#685—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#540D511yescharacteristic, complemented
126C3×#520—51no—
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×#709C22×C311yescharacteristic
141C5×#127C22×C311yescharacteristic
142C5×#125C22×C311yescharacteristic
143C5×#123—21no—
144C5×#123—21no—
145C5×#121—21no—
146C5×#121—21no—
147C5×#121C22×C311yescharacteristic
148C5×#121C22×C311yescharacteristic
149C4×C5×D4C22×C311yescharacteristic
150C4×C5×D4C22×C311yescharacteristic
151C5×#117C22×C311yescharacteristic
152C2×#687C22×C311yescharacteristic
153C2×#687C22×C311yescharacteristic
154C2×#686C22×C311yescharacteristic
155C2×#686C22×C311yescharacteristic
156C2×C4⋊Dic5C22×C311yescharacteristic
157#4038—21no—
158D5×C4⋊C4—21no—
159#4027—21no—
160#4027—21no—
161C4×D20C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163C4×Dic10C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165#3964C22×C311yescharacteristic
166#3964C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3942C22×C311yescharacteristic
172#3942C22×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×C5—21no—
186C23×C3×C5C2×D411yescharacteristic
187C22×C3×D5—21no—
188C3×C5×D4—21no—
189C3×C5×D4—21no—
190C3×C5×D4—21no—
191C3×C5×D4—21no—
192C3×C5×D4—81no—
193C3×C5×D4—81no—
194C3×C5×D4—81no—
195C3×C5×D4—81no—
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×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—24no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—81no—
213C3×D20—21no—
214C3×D20#4112yes—
215C3×C4×D5—24no—
216C3×C4×D5—81no—
217C3×C4×D5—81no—
218C3×Dic10—21no—
219C3×Dic10#4112yes—
220C3×#168—21no—
221C3×#168—21no—
222C3×#168—21no—
223C3×#168—21no—
224C2×C3×#41—51no—
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×#127C2×D511yescharacteristic
230C3×#125C2×D511yescharacteristic
231C3×#123—21no—
232C3×#123—21no—
233C3×#121—21no—
234C3×#121—21no—
235C3×#121C2×D511yescharacteristic
236C3×#121C2×D511yescharacteristic
237C3×C4×Q8—51no—
238C3×C4×Q8—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—101no—
242C3×C4×D4—101no—
243C3×C4×D4C2×D511yescharacteristic
244C3×C4×D4C2×D511yescharacteristic
245C3×#117—101no—
246C3×#117C2×D511yescharacteristic
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—101no—
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—
267C2×C5×D4—21no—
268C2×C5×D4—21no—
269C2×C5×D4—21no—
270C2×C5×D4—21no—
271C2×C5×D4C23×C311yescharacteristic
272C2×C5×D4C23×C311yescharacteristic
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5C23×C311yescharacteristic
276C2×C22⋊D5—21no—
277C22×Dic5—21no—
278#709—22no—
279#709—22no—
280C2×D20C23×C311yescharacteristic
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C2×C4×D5—21no—
284C2×Dic10C23×C311yescharacteristic
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4C3×D411yescharacteristic
288C5×C4⋊C4C3×D411yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C22⋊C4—21no—
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4C3×D411yescharacteristic
296C5×C22⋊C4C3×D411yescharacteristic
297C42×C5C23×C311yescharacteristic
298C42×C5C23×C311yescharacteristic
299#687—22no—
300#687—22no—
301#686—22no—
302#686—22no—
303#685—21no—
304#685—21no—
305C4⋊Dic5—21no—
306C4⋊Dic5C23×C311yescharacteristic
307C4⋊Dic5C23×C311yescharacteristic
308#683—21no—
309#683—21no—
310C4×Dic5—21no—
311C4×Dic5—21no—
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#540C3×D511yescharacteristic, complemented
317#520—51no—
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—21no—
333C22×C3×C5—21no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5C22×D411yescharacteristic
341C2×C3×D5—22no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—21no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—41no—
350C3×C4×C5—41no—
351C3×C4×C5C2×#4111yescharacteristic
352C3×C4×C5C2×#4111yescharacteristic
353C3×Dic5—22no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×#41—102no—
357C3×#41—102no—
358C2×C3×Q8—51no—
359C2×C3×D4—21no—
360C2×C3×D4—21no—
361C2×C3×D4—21no—
362C2×C3×D4—21no—
363C2×C3×D4—51no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
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—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
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—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4C22⋊D511yescharacteristic
400C3×C22⋊C4C22⋊D511yescharacteristic
401C3×C42—101no—
402C3×C42—101no—
403C3×C42C22×D511yescharacteristic
404C3×C42C22×D511yescharacteristic
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C2×C3×D411yescharacteristic
408C22×D5—21no—
409C5×D4—21no—
410C5×D4—21no—
411C5×D4—21no—
412C5×D4—21no—
413C5×D4—81no—
414C5×D4—81no—
415C5×D4—81no—
416C5×D4—81no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
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—24no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—81no—
434D20—21no—
435D20C3×#4112yes—
436C4×D5—24no—
437C4×D5—81no—
438C4×D5—81no—
439Dic10—21no—
440Dic10C3×#4112yes—
441#168—21no—
442#168—21no—
443#168—21no—
444#168—21no—
445C2×#41—51no—
446C2×SD16—51no—
447C2×SD16—51no—
448C2×D8—51no—
449C2×D8—51no—
450#127C2×C3×D511yescharacteristic
451#125C2×C3×D511yescharacteristic
452#123—21no—
453#123—21no—
454#121—21no—
455#121—21no—
456#121C2×C3×D511yescharacteristic
457#121C2×C3×D511yescharacteristic
458C4×Q8—51no—
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—101no—
463C4×D4—101no—
464C4×D4C2×C3×D511yescharacteristic
465C4×D4C2×C3×D511yescharacteristic
466#117—101no—
467#117C2×C3×D511yescharacteristic
468C2×C4⋊C4—51no—
469C2×C4⋊C4—101no—
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—81no—
490C2×C3×C5—81no—
491C2×C3×C5#52511yescharacteristic
492C2×C3×C5#57611yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C3×D5—42no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—101no—
498C23×C3C2×C22⋊D511yescharacteristic
499C3×Q8—52no—
500C3×Q8—101no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—52no—
506C3×D4—81no—
507C3×D4—81no—
508C3×D4—81no—
509C3×D4—81no—
510C3×D4—104no—
511C3×D4—101no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—81no—
517C2×C3×C4—81no—
518C2×C3×C4—104no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—401no—
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—41no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5C22×C3×D411yescharacteristic
545C2×D5—22no—
546C2×D5—41no—
547C2×D5—41no—
548C4×C5—21no—
549C4×C5—21no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—41no—
554C4×C5—41no—
555C4×C5C2×C3×#4111yescharacteristic
556C4×C5C2×C3×#4111yescharacteristic
557Dic5—22no—
558Dic5—41no—
559Dic5—41no—
560#41—102no—
561#41—102no—
562C2×Q8—51no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—51no—
568C2×D4—101no—
569C2×D4C22×C3×D511yescharacteristic
570C2×D4C22×C3×D511yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—101no—
574C22×C4—101no—
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—51no—
589C4⋊C4—51no—
590C4⋊C4—101no—
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—21no—
600C22⋊C4—21no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4C3×C22⋊D511yescharacteristic
604C22⋊C4C3×C22⋊D511yescharacteristic
605C42—101no—
606C42—101no—
607C42C22×C3×D511yescharacteristic
608C42C22×C3×D511yescharacteristic
609C3×C5#311911yescharacteristic, complemented, Hall
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—102no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3C22×C22⋊D511yescharacteristic
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—102no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4D5×#4111yescharacteristic
634C3×C4D5×#4111yescharacteristic
635C2×C5—41no—
636C2×C5—81no—
637C2×C5—81no—
638C2×C5C3×#52511yescharacteristic
639C2×C5C3×#57611yescharacteristic
640C2×C5C3×#57711yescharacteristic
641D5—42no—
642C23—21no—
643C23—21no—
644C23—101no—
645C23C2×C3×C22⋊D511yescharacteristic
646Q8—52no—
647Q8—101no—
648D4—21no—
649D4—21no—
650D4—21no—
651D4—21no—
652D4—52no—
653D4—81no—
654D4—81no—
655D4—81no—
656D4—81no—
657D4—104no—
658D4—101no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—104no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—401no—
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—81no—
684C2×C3—81no—
685C2×C3—202no—
686C2×C3#6616211yescharacteristic
687C2×C3#6616911yescharacteristic
688C2×C3#6617011yescharacteristic
689C5C3×#311911yescharacteristic, complemented, Sylow
690C22—21no—
691C22—21no—
692C22—21no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—102no—
700C22—201no—
701C22—201no—
702C22C22×C3×C22⋊D511yescharacteristic
703C4—21no—
704C4—21no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—41no—
709C4—41no—
710C4—102no—
711C4—201no—
712C4—201no—
713C4C3×D5×#4111yescharacteristic
714C4C3×D5×#4111yescharacteristic
715C3#1061516511yescharacteristic, direct product factor, Sylow
716C2—41no—
717C2—81no—
718C2—81no—
719C2—202no—
720C2C3×#6616211yescharacteristic
721C2C3×#6616911yescharacteristic
722C2C3×#6617011yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#540C2
socleC22×C3×C5C22×D4
hypercenterC3×#540D5
hypocenterC5C3×#3119
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#540

Complements

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

NH ≅ G/Ntype
1. C3×C5×#540C2semidirect
2. C3×#65857C2semidirect
3. C3×#65364C2semidirect
4. C3×#65361C2semidirect
5. C3×#65355C2semidirect
6. C3×#65352C2semidirect
7. C3×#65326C2semidirect
8. C3×#65326C2semidirect
9. C3×#65323C2semidirect
10. C3×#65322C2semidirect
11. C3×#65307C2semidirect
12. C3×C4×#687C2semidirect
13. C3×#65303C2semidirect
14. C3×C4×#686C2semidirect
15. C3×#65289C2semidirect
16. #10615165C3direct (N × H)
61. C5×#540C2×C3semidirect
62. #65857C2×C3semidirect
63. #65364C2×C3semidirect
64. #65361C2×C3semidirect
65. #65355C2×C3semidirect
66. #65352C2×C3semidirect
67. #65326C2×C3semidirect
68. #65326C2×C3semidirect
69. #65323C2×C3semidirect
70. #65322C2×C3semidirect
71. #65307C2×C3semidirect
72. C4×#687C2×C3semidirect
73. #65303C2×C3semidirect
74. C4×#686C2×C3semidirect
75. #65289C2×C3semidirect
125. C3×#540D5semidirect
316. #540C3×D5semidirect
609. C3×C5#3119semidirect
689. C5C3×#3119semidirect
715. C3#10615165direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5402
C3×#658572
C3×#653642
C3×#653612
C3×#653552
C3×#653522
C3×#653262
C3×#653232
C3×#653222
C3×#653072
C3×C4×#6872
C3×#653032
C3×C4×#6862
C3×#652892
#106151653
C3×#31195