Finite Group Databasebeta

← C3×#10615191 #14435566

Subgroups — C3×#10615191 #14435566

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×#542C211yesmaximal, characteristic, complemented
2C3×#65855C211yesmaximal, characteristic, complemented
3C3×#65376C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×#65346C211yesmaximal, characteristic, complemented
6C3×#65346C211yesmaximal, characteristic, complemented
7C3×#65335C211yesmaximal, characteristic, complemented
8C3×#65334C211yesmaximal, characteristic, complemented
9C3×#65325C211yesmaximal, characteristic
10C3×#65324C211yesmaximal, characteristic, complemented
11C3×#65315C211yesmaximal, characteristic, complemented
12C3×C4×#688C211yesmaximal, characteristic, complemented
13C3×#65303C211yesmaximal, characteristic, complemented
14C3×C4×#686C211yesmaximal, characteristic, complemented
15C3×#65289C211yesmaximal, characteristic, complemented
16#10615191C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×D20C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic, complemented
19C3×C5×#126—21no—
20C3×C5×#124—21no—
21C3×C5×#124C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic
26C3×C4×C5×Q8C2211yescharacteristic, complemented
27C3×C4×C5×D4C2211yescharacteristic, complemented
28C3×C5×#117C2211yescharacteristic
29C2×C3×#688C2211yescharacteristic
30C2×C3×#688C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C2×C3×#686C2211yescharacteristic
33C3×#4072C2211yescharacteristic
34C3×#4039—21no—
35C3×#4039—21no—
36C3×D5×C22⋊C4—21no—
37C3×D5×C22⋊C4—21no—
38C3×C4×D20C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×C4×D20C2211yescharacteristic
41C3×C4×D20C2211yescharacteristic
42C3×#3967C2211yescharacteristic, complemented
43C3×#3967C2211yescharacteristic, complemented
44C3×#3964C2211yescharacteristic, complemented
45C3×#3964C2211yescharacteristic, complemented
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×#3940C2211yescharacteristic, complemented
53C3×#3940C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55C3×#3939C2211yescharacteristic, complemented
56C3×C4⋊#168C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58C3×#3935C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61C5×#542C2×C311yescharacteristic, complemented
62#65855C2×C311yescharacteristic, complemented
63#65376C2×C311yescharacteristic, complemented
64#65373C2×C311yescharacteristic, complemented
65#65346C2×C311yescharacteristic, complemented
66#65346C2×C311yescharacteristic, complemented
67#65335C2×C311yescharacteristic, complemented
68#65334C2×C311yescharacteristic, complemented
69#65325C2×C311yescharacteristic
70#65324C2×C311yescharacteristic, complemented
71#65315C2×C311yescharacteristic, complemented
72C4×#688C2×C311yescharacteristic, complemented
73#65303C2×C311yescharacteristic, complemented
74C4×#686C2×C311yescharacteristic, complemented
75#65289C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×C3×D20—21no—
84C2×C3×D20—22no—
85C2×C3×D20—22no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4D411yescharacteristic
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
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×C5—21no—
107C3×C42×C5C2311yescharacteristic
108C3×C42×C5C2311yescharacteristic
109C3×C22⋊Dic5—21no—
110C3×#688—22no—
111C3×#688—22no—
112C3×#686—22no—
113C3×#686—22no—
114C3×#685—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×#685—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542D511yescharacteristic, complemented
126C3×#518—51no—
127C3×#485—51no—
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463—51no—
133C3×#450—51no—
134C3×#447—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C22×D20C22×C311yescharacteristic
141C5×C4⋊Q8C22×C311yescharacteristic, complemented
142C5×#126—21no—
143C5×#124—21no—
144C5×#124C22×C311yescharacteristic, complemented
145C5×#123—21no—
146C5×C22⋊Q8—21no—
147C5×C22⋊Q8C22×C311yescharacteristic
148C5×#121C22×C311yescharacteristic
149C4×C5×Q8C22×C311yescharacteristic, complemented
150C4×C5×D4C22×C311yescharacteristic, complemented
151C5×#117C22×C311yescharacteristic
152C2×#688C22×C311yescharacteristic
153C2×#688C22×C311yescharacteristic
154C2×#686C22×C311yescharacteristic
155C2×#686C22×C311yescharacteristic
156#4072C22×C311yescharacteristic
157#4039—21no—
158#4039—21no—
159D5×C22⋊C4—21no—
160D5×C22⋊C4—21no—
161C4×D20C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163C4×D20C22×C311yescharacteristic
164C4×D20C22×C311yescharacteristic
165#3967C22×C311yescharacteristic, complemented
166#3967C22×C311yescharacteristic, complemented
167#3964C22×C311yescharacteristic, complemented
168#3964C22×C311yescharacteristic, complemented
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3941C22×C311yescharacteristic
172#3941C22×C311yescharacteristic
173#3941C22×C311yescharacteristic
174#3941C22×C311yescharacteristic
175#3940C22×C311yescharacteristic, complemented
176#3940C22×C311yescharacteristic, complemented
177#3939C22×C311yescharacteristic, complemented
178#3939C22×C311yescharacteristic, complemented
179C4⋊#168C22×C311yescharacteristic, complemented
180C4⋊#168C22×C311yescharacteristic, complemented
181#3935C22×C311yescharacteristic, complemented
182C4×#168C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—24no—
189C22×C3×D5—81no—
190C22×C3×D5—81no—
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C3×C5×Q8—81no—
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4—81no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—81no—
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C3×D20—24no—
212C3×D20—21no—
213C3×D20—21no—
214C3×D20#4112yes—
215C3×D20#4112yes—
216C3×C4×D5—81no—
217C3×C4×D5—81no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3×#168—21no—
221C3×#168—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×D4—51no—
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×C4⋊Q8C2×D511yescharacteristic, complemented
230C3×#126—21no—
231C3×#124—21no—
232C3×#124C2×D511yescharacteristic, complemented
233C3×#123—21no—
234C3×C22⋊Q8—21no—
235C3×C22⋊Q8C2×D511yescharacteristic
236C3×#121C2×D511yescharacteristic
237C3×C4×Q8C2×D511yescharacteristic, complemented
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—51no—
242C3×C4×D4—101no—
243C3×C4×D4—101no—
244C3×C4×D4C2×D511yescharacteristic, complemented
245C3×#117—51no—
246C3×#117C2×D511yescharacteristic
247C2×C3×C22⋊C4—101no—
248C2×C3×C22⋊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—
267C23×D5—21no—
268C2×C5×Q8—21no—
269C2×C5×Q8C23×C311yescharacteristic
270C2×C5×D4—21no—
271C2×C5×D4C23×C311yescharacteristic
272C22×C4×C5—21no—
273C22×C4×C5C23×C311yescharacteristic
274C2×D20—21no—
275C2×D20—22no—
276C2×D20—22no—
277C2×D20C23×C311yescharacteristic
278C2×D20C23×C311yescharacteristic
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4C3×D411yescharacteristic
287C5×C4⋊C4C3×D411yescharacteristic
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C22⋊C4—21no—
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×C5—21no—
298C42×C5C23×C311yescharacteristic
299C42×C5C23×C311yescharacteristic
300C22⋊Dic5—21no—
301#688—22no—
302#688—22no—
303#686—22no—
304#686—22no—
305#685—21no—
306#685—21no—
307#685—21no—
308#685—21no—
309C4⋊Dic5C23×C311yescharacteristic
310C4⋊Dic5C23×C311yescharacteristic
311C4×Dic5—21no—
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#542C3×D511yescharacteristic, complemented
317#518—51no—
318#485—51no—
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463—51no—
324#450—51no—
325#447—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×C5C22×D411yescharacteristic
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—84no—
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×C5—41no—
353C3×C4×C5C2×#4111yescharacteristic
354C3×C4×C5C2×#4111yescharacteristic
355C3×Dic5—41no—
356C3×Dic5—41no—
357C24×C3—101no—
358C2×C3×Q8—21no—
359C2×C3×Q8C22×D511yescharacteristic
360C2×C3×D4—21no—
361C2×C3×D4—51no—
362C2×C3×D4—51no—
363C2×C3×D4—102no—
364C2×C3×D4—102no—
365C2×C3×D4—101no—
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C3×SD16—102no—
374C3×SD16—102no—
375C3×D8—102no—
376C3×D8—102no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8—51no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4C22⋊D511yescharacteristic
387C3×C4⋊C4C22⋊D511yescharacteristic
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
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⋊C4—101no—
400C3×C22⋊C4C22⋊D511yescharacteristic
401C3×C22⋊C4C22⋊D511yescharacteristic
402C3×C42—21no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405C3×C42C22×D511yescharacteristic
406C23×C5—21no—
407C23×C5C2×C3×D411yescharacteristic
408C22×D5—21no—
409C22×D5—21no—
410C22×D5—24no—
411C22×D5—81no—
412C22×D5—81no—
413C5×Q8—21no—
414C5×Q8—21no—
415C5×Q8—81no—
416C5×D4—21no—
417C5×D4—21no—
418C5×D4—81no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—81no—
425C2×C4×C5C2×C3×D411yescharacteristic
426C2×C4×C5C2×C3×D411yescharacteristic
427C2×C4×C5C2×C3×D411yescharacteristic
428C2×C4×C5C2×C3×D411yescharacteristic
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C24×C311yescharacteristic
431C2×Dic5—21no—
432C2×Dic5—21no—
433D20—24no—
434D20—21no—
435D20—21no—
436D20C3×#4112yes—
437D20C3×#4112yes—
438C4×D5—81no—
439C4×D5—81no—
440C4×D5—81no—
441C4×D5—81no—
442#168—21no—
443#168—21no—
444#168—21no—
445#168—21no—
446C22×D4—51no—
447C2×SD16—51no—
448C2×SD16—51no—
449C2×D8—51no—
450C2×D8—51no—
451C4⋊Q8C2×C3×D511yescharacteristic, complemented
452#126—21no—
453#124—21no—
454#124C2×C3×D511yescharacteristic, complemented
455#123—21no—
456C22⋊Q8—21no—
457C22⋊Q8C2×C3×D511yescharacteristic
458#121C2×C3×D511yescharacteristic
459C4×Q8C2×C3×D511yescharacteristic, complemented
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—101no—
465C4×D4—101no—
466C4×D4C2×C3×D511yescharacteristic, complemented
467#117—51no—
468#117C2×C3×D511yescharacteristic
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—51no—
472#107—51no—
473#106—51no—
474#106—51no—
475C4⋊C8—51no—
476C4⋊C8—51no—
477#103—51no—
478#103—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102—51no—
484#102—51no—
485C22⋊C8—51no—
486C22⋊C8—51no—
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—41no—
490C2×C3×C5—81no—
491C2×C3×C5#52511yescharacteristic
492C2×C3×C5#57611yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C3×D5—42no—
495C3×D5—42no—
496C23×C3—21no—
497C23×C3—104no—
498C23×C3—101no—
499C23×C3—101no—
500C23×C3—401no—
501C23×C3—401no—
502C23×C3C2×C22⋊D511yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—81no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—52no—
509C3×D4—52no—
510C3×D4—81no—
511C3×D4—104no—
512C3×D4—101no—
513C3×D4—101no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—81no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—401no—
523C2×C3×C4—401no—
524C2×C3×C4—401no—
525C2×C3×C4—401no—
526C2×C3×C4C2×C22⋊D511yescharacteristic
527C2×C3×C4C2×C22⋊D511yescharacteristic
528C2×C3×C4C2×C22⋊D511yescharacteristic
529C2×C3×C4C2×C22⋊D511yescharacteristic
530C2×C3×C4C2×C22⋊D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—101no—
533C3×C8—101no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5C22×C3×D411yescharacteristic
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—84no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5—41no—
558C4×C5C2×C3×#4111yescharacteristic
559C4×C5C2×C3×#4111yescharacteristic
560Dic5—41no—
561Dic5—41no—
562C24—101no—
563C2×Q8—21no—
564C2×Q8C22×C3×D511yescharacteristic
565C2×D4—21no—
566C2×D4—51no—
567C2×D4—51no—
568C2×D4—102no—
569C2×D4—102no—
570C2×D4—101no—
571C2×D4C22×C3×D511yescharacteristic
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—21no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4C3×C22⋊D511yescharacteristic
592C4⋊C4C3×C22⋊D511yescharacteristic
593C4⋊C4C22×C3×D511yescharacteristic
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4C3×C22⋊D511yescharacteristic
606C22⋊C4C3×C22⋊D511yescharacteristic
607C42—21no—
608C42—101no—
609C42C22×C3×D511yescharacteristic
610C42C22×C3×D511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—102no—
619C22×C3—102no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3—201no—
623C22×C3—201no—
624C22×C3—404no—
625C22×C3C22×C22⋊D511yescharacteristic
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4D5×#4111yescharacteristic
637C3×C4D5×#4111yescharacteristic
638C2×C5—41no—
639C2×C5—81no—
640C2×C5C3×#52511yescharacteristic
641C2×C5C3×#57611yescharacteristic
642C2×C5C3×#57711yescharacteristic
643D5—42no—
644D5—42no—
645C23—21no—
646C23—104no—
647C23—101no—
648C23—101no—
649C23—401no—
650C23—401no—
651C23C2×C3×C22⋊D511yescharacteristic
652Q8—21no—
653Q8—21no—
654Q8—81no—
655D4—21no—
656D4—21no—
657D4—52no—
658D4—52no—
659D4—81no—
660D4—104no—
661D4—101no—
662D4—101no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—81no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—401no—
672C2×C4—401no—
673C2×C4—401no—
674C2×C4—401no—
675C2×C4C2×C3×C22⋊D511yescharacteristic
676C2×C4C2×C3×C22⋊D511yescharacteristic
677C2×C4C2×C3×C22⋊D511yescharacteristic
678C2×C4C2×C3×C22⋊D511yescharacteristic
679C2×C4C2×C3×C22⋊D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—101no—
682C8—101no—
683C8—101no—
684C8—101no—
685C2×C3—41no—
686C2×C3—81no—
687C2×C3—202no—
688C2×C3—202no—
689C2×C3#6616211yescharacteristic
690C2×C3#6616911yescharacteristic
691C2×C3#6617111yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—102no—
700C22—102no—
701C22—201no—
702C22—201no—
703C22—201no—
704C22—201no—
705C22—404no—
706C22C22×C3×C22⋊D511yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—201no—
716C4—201no—
717C4C3×D5×#4111yescharacteristic
718C4C3×D5×#4111yescharacteristic
719C3#1061519111yescharacteristic, direct product factor, Sylow
720C2—41no—
721C2—81no—
722C2—202no—
723C2—202no—
724C2C3×#6616211yescharacteristic
725C2C3×#6616911yescharacteristic
726C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#542C2
socleC22×C3×C5C22×D4
prime radicalC3×#65325C2
hypercenterC3×#542D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#542

Complements

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

NH ≅ G/Ntype
1. C3×C5×#542C2semidirect
2. C3×#65855C2semidirect
3. C3×#65376C2semidirect
4. C3×#65373C2semidirect
5. C3×#65346C2semidirect
6. C3×#65346C2semidirect
7. C3×#65335C2semidirect
8. C3×#65334C2semidirect
10. C3×#65324C2semidirect
11. C3×#65315C2semidirect
12. C3×C4×#688C2semidirect
13. C3×#65303C2semidirect
14. C3×C4×#686C2semidirect
15. C3×#65289C2semidirect
16. #10615191C3direct (N × H)
18. C3×C5×C4⋊Q8C22semidirect
21. C3×C5×#124C22semidirect
26. C3×C4×C5×Q8C22semidirect
27. C3×C4×C5×D4C22semidirect
42. C3×#3967C22semidirect
43. C3×#3967C22semidirect
44. C3×#3964C22semidirect
45. C3×#3964C22semidirect
52. C3×#3940C22semidirect
53. C3×#3940C22semidirect
54. C3×#3939C22semidirect
55. C3×#3939C22semidirect
56. C3×C4⋊#168C22semidirect
57. C3×C4⋊#168C22semidirect
58. C3×#3935C22semidirect
59. C3×C4×#168C22semidirect
61. C5×#542C2×C3semidirect
62. #65855C2×C3semidirect
63. #65376C2×C3semidirect
64. #65373C2×C3semidirect
65. #65346C2×C3semidirect
66. #65346C2×C3semidirect
67. #65335C2×C3semidirect
68. #65334C2×C3semidirect
70. #65324C2×C3semidirect
71. #65315C2×C3semidirect
72. C4×#688C2×C3semidirect
73. #65303C2×C3semidirect
74. C4×#686C2×C3semidirect
75. #65289C2×C3semidirect
125. C3×#542D5semidirect
141. C5×C4⋊Q8C22×C3semidirect
144. C5×#124C22×C3semidirect
149. C4×C5×Q8C22×C3semidirect
150. C4×C5×D4C22×C3semidirect
165. #3967C22×C3semidirect
166. #3967C22×C3semidirect
167. #3964C22×C3semidirect
168. #3964C22×C3semidirect
175. #3940C22×C3semidirect
176. #3940C22×C3semidirect
177. #3939C22×C3semidirect
178. #3939C22×C3semidirect
179. C4⋊#168C22×C3semidirect
180. C4⋊#168C22×C3semidirect
181. #3935C22×C3semidirect
182. C4×#168C22×C3semidirect
229. C3×C4⋊Q8C2×D5semidirect
232. C3×#124C2×D5semidirect
237. C3×C4×Q8C2×D5semidirect
244. C3×C4×D4C2×D5semidirect
316. #542C3×D5semidirect
451. C4⋊Q8C2×C3×D5semidirect
454. #124C2×C3×D5semidirect
459. C4×Q8C2×C3×D5semidirect
466. C4×D4C2×C3×D5semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10615191direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5422
C3×#658552
C3×#653762
C3×#653732
C3×#653462
C3×#653352
C3×#653342
C3×#653252
C3×#653242
C3×#653152
C3×C4×#6882
C3×#653032
C3×C4×#6862
C3×#652892
#106151913
C3×#31185