Finite Group Databasebeta

← C3×#10615329 #14458594

Subgroups — C3×#10615329 #14458594

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#552C211yesmaximal, characteristic, complemented
2C3×#65884C211yesmaximal, characteristic
3C3×#65357C211yesmaximal, characteristic, complemented
4C3×#65355C211yesmaximal, characteristic, complemented
5C3×#65340C211yesmaximal, characteristic, complemented
6C3×#65337C211yesmaximal, characteristic, complemented
7C3×#65336C211yesmaximal, characteristic, complemented
8C3×#65335C211yesmaximal, characteristic, complemented
9C3×#65317C211yesmaximal, characteristic, complemented
10C3×C4×#688C211yesmaximal, characteristic, complemented
11C3×D4×#168C211yesmaximal, characteristic, complemented
12C3×#65292C211yesmaximal, characteristic, complemented
13C3×#65291C211yesmaximal, characteristic, complemented
14C3×#65260C211yesmaximal, characteristic, complemented
15C2×C3×#3941C211yesmaximal, characteristic, complemented
16#10615329C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#125—21no—
21C3×C5×#125C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26C3×C4×C5×D4C2211yescharacteristic
27C3×C5×#117—21no—
28C3×C5×#117C2211yescharacteristic, complemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×#689C2211yescharacteristic, complemented
31C2×C3×#688C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic
33C3×#4083—21no—
34C3×#4076C2211yescharacteristic
35C3×#4070C2211yescharacteristic
36C22×C3×#168C2211yescharacteristic
37C22×C3×#168C2211yescharacteristic, complemented
38C3×#4040—21no—
39C3×#4030—21no—
40C3×D5×C22⋊C4—21no—
41C3×#4021C2211yescharacteristic
42C3×C4×D20C2211yescharacteristic
43C3×#3967C2211yescharacteristic, complemented
44C3×C22⋊#168C2211yescharacteristic
45C3×C22⋊#168C2211yescharacteristic, complemented
46C3×#3942C2211yescharacteristic, complemented
47C3×#3942C2211yescharacteristic, complemented
48C3×#3942C2211yescharacteristic, complemented
49C3×#3941C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×#3941C2211yescharacteristic
53C3×#3941C2211yescharacteristic
54C3×#3941C2211yescharacteristic
55C3×#3940C2211yescharacteristic, complemented
56C3×#3940C2211yescharacteristic, complemented
57C3×#3939C2211yescharacteristic, complemented
58C3×C4⋊#168C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3296—51nomaximal, Hall
61C5×#552C2×C311yescharacteristic, complemented
62#65884C2×C311yescharacteristic
63#65357C2×C311yescharacteristic, complemented
64#65355C2×C311yescharacteristic, complemented
65#65340C2×C311yescharacteristic, complemented
66#65337C2×C311yescharacteristic, complemented
67#65336C2×C311yescharacteristic, complemented
68#65335C2×C311yescharacteristic, complemented
69#65317C2×C311yescharacteristic, complemented
70C4×#688C2×C311yescharacteristic, complemented
71D4×#168C2×C311yescharacteristic, complemented
72#65292C2×C311yescharacteristic, complemented
73#65291C2×C311yescharacteristic, complemented
74#65260C2×C311yescharacteristic, complemented
75C2×#3941C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4D411yescharacteristic
79C22×C3×C4×C5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C3×#709—22no—
85C3×#709—41no—
86C2×C3×D20—22no—
87C2×C3×D20—21no—
88C2×C3×D20—41no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×D20C2311yescharacteristic
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⋊C4—21no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4D411yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4—21no—
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C5×C22⋊C4D411yescharacteristic
109C3×C42×C5—21no—
110C3×C42×C5—21no—
111C3×C42×C5C2311yescharacteristic
112C3×C22⋊Dic5—21no—
113C3×#689—41no—
114C3×#688—22no—
115C3×#688—41no—
116C3×#685—21no—
117C3×#685—21no—
118C3×#685—21no—
119C3×#685—21no—
120C3×C4⋊Dic5C2311yescharacteristic
121C3×#683—21no—
122C2×C3×#168—41no—
123C2×C3×#168—41no—
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C3×#552D511yescharacteristic, complemented
129C3×#546—51no—
130C3×#488—51no—
131C3×#483—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#467—51no—
135C3×#465—51no—
136C3×#464—51no—
137C3×#452—51no—
138C3×#450—51no—
139C3×C4×SD16—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×#709C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C5×#126—21no—
146C5×#125—21no—
147C5×#125C22×C311yescharacteristic, complemented
148C5×#123—21no—
149C5×C22⋊Q8C22×C311yescharacteristic
150C5×C22⋊Q8C22×C311yescharacteristic, complemented
151C4×C5×Q8C22×C311yescharacteristic, complemented
152C4×C5×D4C22×C311yescharacteristic
153C5×#117—21no—
154C5×#117C22×C311yescharacteristic, complemented
155C2×C5×C4⋊C4C22×C311yescharacteristic
156C2×#689C22×C311yescharacteristic, complemented
157C2×#688C22×C311yescharacteristic
158C2×#688C22×C311yescharacteristic
159#4083—21no—
160#4076C22×C311yescharacteristic
161#4070C22×C311yescharacteristic
162C22×#168C22×C311yescharacteristic
163C22×#168C22×C311yescharacteristic, complemented
164#4040—21no—
165#4030—21no—
166D5×C22⋊C4—21no—
167#4021C22×C311yescharacteristic
168C4×D20C22×C311yescharacteristic
169#3967C22×C311yescharacteristic, complemented
170C22⋊#168C22×C311yescharacteristic
171C22⋊#168C22×C311yescharacteristic, complemented
172#3942C22×C311yescharacteristic, complemented
173#3942C22×C311yescharacteristic, complemented
174#3942C22×C311yescharacteristic, complemented
175#3941C22×C311yescharacteristic
176#3941C22×C311yescharacteristic
177#3941C22×C311yescharacteristic
178#3941C22×C311yescharacteristic
179#3941C22×C311yescharacteristic
180#3941C22×C311yescharacteristic
181#3940C22×C311yescharacteristic, complemented
182#3940C22×C311yescharacteristic, complemented
183#3939C22×C311yescharacteristic, complemented
184C4⋊#168C22×C311yescharacteristic, complemented
185C4×#168C22×C311yescharacteristic, complemented
186#3296—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5—81no—
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×D4—22no—
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—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211C3×C22⋊D5—42no—
212C3×C22⋊D5—81no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C3×D20—21no—
216C3×D20—21no—
217C3×D20—21no—
218C3×D20—42no—
219C3×D20#4112yes—
220C3×C4×D5—42no—
221C3×C4×D5—81no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224C3×#168—21no—
225C3×#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41—51no—
229C22×C3×D4—51no—
230C2×C3×Q16—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×#126—21no—
236C3×#125—21no—
237C3×#125C2×D511yescharacteristic, complemented
238C3×#124—51no—
239C3×#123—21no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8C2×D511yescharacteristic
243C3×C22⋊Q8C2×D511yescharacteristic, complemented
244C3×#121—51no—
245C3×#121—101no—
246C3×#120—101no—
247C3×C4×Q8C2×D511yescharacteristic, complemented
248C3×C4×D4—51no—
249C3×C4×D4C2×D511yescharacteristic
250C3×#117—21no—
251C3×#117C2×D511yescharacteristic, complemented
252C2×C3×C4⋊C4C2×D511yescharacteristic
253C2×C3×C22⋊C4—101no—
254C3×#107—51no—
255C3×#106—51no—
256C3×#106—51no—
257C3×C4⋊C8—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×#102—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×C22⋊C8—51no—
269C3×C22⋊C8—51no—
270C3×C4×C8—51no—
271C23×D5—21no—
272C2×C5×Q8C23×C311yescharacteristic
273C2×C5×D4C3×D411yescharacteristic
274C22×C4×C5—21no—
275C22×C4×C5C23×C311yescharacteristic
276C22×C4×C5C23×C311yescharacteristic
277C2×C22⋊D5—21no—
278C2×C22⋊D5—21no—
279#709—22no—
280#709—41no—
281C2×D20—22no—
282C2×D20—21no—
283C2×D20—41no—
284C2×D20C23×C311yescharacteristic
285C2×D20C23×C311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—21no—
288C2×Dic10C23×C311yescharacteristic
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—21no—
292C5×C4⋊C4—21no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4C3×D411yescharacteristic
296C5×C4⋊C4C23×C311yescharacteristic
297C5×C4⋊C4C23×C311yescharacteristic
298C5×C4⋊C4C23×C311yescharacteristic
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4C3×D411yescharacteristic
303C5×C22⋊C4C3×D411yescharacteristic
304C42×C5—21no—
305C42×C5—21no—
306C42×C5C23×C311yescharacteristic
307C22⋊Dic5—21no—
308#689—41no—
309#688—22no—
310#688—41no—
311#685—21no—
312#685—21no—
313#685—21no—
314#685—21no—
315C4⋊Dic5C23×C311yescharacteristic
316#683—21no—
317C2×#168—41no—
318C2×#168—41no—
319C2×#168C23×C311yescharacteristic
320C2×#168C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323#552C3×D511yescharacteristic, complemented
324#546—51no—
325#488—51no—
326#483—51no—
327#482—51no—
328#478—51no—
329#467—51no—
330#465—51no—
331#464—51no—
332#452—51no—
333#450—51no—
334C4×SD16—51no—
335C8×D4—51no—
336#416—51no—
337C2×#102—51no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—22no—
346C2×C3×D5—41no—
347C2×C3×D5—41no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351C2×C3×D5—84no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5—41no—
357C3×C4×C5—41no—
358C3×C4×C5—41no—
359C3×C4×C5—41no—
360C3×C4×C5C2×#4111yescharacteristic
361C3×C4×C5H(5,𝔽2)11yescharacteristic
362C3×Dic5—41no—
363C3×Dic5—41no—
364C24×C3—101no—
365C3×#41—102no—
366C3×#41—201no—
367C2×C3×Q8—51no—
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—51no—
370C2×C3×D4—51no—
371C2×C3×D4—102no—
372C2×C3×D4—101no—
373C2×C3×D4—101no—
374C2×C3×D4—101no—
375C2×C3×D4—201no—
376C2×C3×D4C22⋊D511yescharacteristic
377C22×C3×C4—21no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C3×Q16—201no—
383C3×SD16—102no—
384C3×SD16—201no—
385C2×C3×C8—51no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—51no—
389C2×C3×C8—201no—
390C2×C3×C8—201no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—51no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4C22⋊D511yescharacteristic
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4C22⋊D511yescharacteristic
412C3×C22⋊C4C22⋊D511yescharacteristic
413C3×C42—21no—
414C3×C42—21no—
415C3×C42C22×D511yescharacteristic
416C23×C5C2×C3×D411yescharacteristic
417C23×C5C2×C3×D411yescharacteristic
418C22×D5—21no—
419C22×D5—21no—
420C22×D5—42no—
421C22×D5—42no—
422C22×D5—81no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—22no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—42no—
435C2×C4×C5C2×C3×D411yescharacteristic
436C2×C4×C5C2×C3×D411yescharacteristic
437C2×C4×C5C2×C3×D411yescharacteristic
438C2×C4×C5C2×C3×D411yescharacteristic
439C2×C4×C5C24×C311yescharacteristic
440C22⋊D5—42no—
441C22⋊D5—81no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444D20—21no—
445D20—21no—
446D20—21no—
447D20—42no—
448D20C3×#4112yes—
449C4×D5—42no—
450C4×D5—81no—
451Dic10—21no—
452Dic10—21no—
453#168—21no—
454#168—21no—
455#168—21no—
456#168—21no—
457C2×#41—51no—
458C22×D4—51no—
459C2×Q16—51no—
460C2×SD16—51no—
461C2×SD16—51no—
462C22×C8—51no—
463C22×C8—51no—
464#126—21no—
465#125—21no—
466#125C2×C3×D511yescharacteristic, complemented
467#124—51no—
468#123—21no—
469#123—101no—
470C22⋊Q8—51no—
471C22⋊Q8C2×C3×D511yescharacteristic
472C22⋊Q8C2×C3×D511yescharacteristic, complemented
473#121—51no—
474#121—101no—
475#120—101no—
476C4×Q8C2×C3×D511yescharacteristic, complemented
477C4×D4—51no—
478C4×D4C2×C3×D511yescharacteristic
479#117—21no—
480#117C2×C3×D511yescharacteristic, complemented
481C2×C4⋊C4C2×C3×D511yescharacteristic
482C2×C22⋊C4—101no—
483#107—51no—
484#106—51no—
485#106—51no—
486C4⋊C8—51no—
487#103—51no—
488#103—51no—
489#103—51no—
490#103—51no—
491#102—51no—
492#102—51no—
493#102—51no—
494#102—51no—
495#102—51no—
496#102—51no—
497C22⋊C8—51no—
498C22⋊C8—51no—
499C4×C8—51no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C3×D5—42no—
506C3×D5—81no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—202no—
510C23×C3—202no—
511C23×C3—401no—
512C23×C3C2×C22⋊D511yescharacteristic
513C23×C3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—101no—
517C3×Q8—101no—
518C3×D4—22no—
519C3×D4—52no—
520C3×D4—101no—
521C3×D4—101no—
522C3×D4—101no—
523C3×D4—202no—
524C3×D4—202no—
525C3×D4—401no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—42no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4—401no—
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—101no—
545C3×C8—101no—
546C3×C8—101no—
547C3×C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5C3×#13512yes—
554C22×C5C22×C3×D411yescharacteristic
555C2×D5—22no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—41no—
559C2×D5—41no—
560C2×D5—41no—
561C2×D5—84no—
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—41no—
567C4×C5—41no—
568C4×C5—41no—
569C4×C5—41no—
570C4×C5C2×C3×#4111yescharacteristic
571C4×C5C3×H(5,𝔽2)11yescharacteristic
572Dic5—41no—
573Dic5—41no—
574C24—101no—
575#41—102no—
576#41—201no—
577C2×Q8—51no—
578C2×Q8C22×C3×D511yescharacteristic
579C2×D4—51no—
580C2×D4—51no—
581C2×D4—102no—
582C2×D4—101no—
583C2×D4—101no—
584C2×D4—101no—
585C2×D4—201no—
586C2×D4C3×C22⋊D511yescharacteristic
587C22×C4—21no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4C22×C3×D511yescharacteristic
591C22×C4C22×C3×D511yescharacteristic
592Q16—201no—
593SD16—102no—
594SD16—201no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—51no—
598C2×C8—51no—
599C2×C8—201no—
600C2×C8—201no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—51no—
608C4⋊C4—101no—
609C4⋊C4C3×C22⋊D511yescharacteristic
610C4⋊C4C22×C3×D511yescharacteristic
611C4⋊C4C22×C3×D511yescharacteristic
612C4⋊C4C22×C3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—101no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C22⋊C4C3×C22⋊D511yescharacteristic
622C22⋊C4C3×C22⋊D511yescharacteristic
623C42—21no—
624C42—21no—
625C42C22×C3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—102no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3—201no—
636C22×C3—201no—
637C22×C3—201no—
638C22×C3—404no—
639C22×C3#409612yes—
640C22×C3C22×C22⋊D511yescharacteristic
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—201no—
650C3×C4—201no—
651C3×C4D5×#4111yescharacteristic
652C3×C4#414911yescharacteristic
653C2×C5—22no—
654C2×C5—41no—
655C2×C5C3×#54611yescharacteristic
656C2×C5C2×C3×#13511yescharacteristic
657C2×C5C3×#57711yescharacteristic
658D5—42no—
659D5—81no—
660C23—101no—
661C23—101no—
662C23—202no—
663C23—202no—
664C23—401no—
665C23C2×C3×C22⋊D511yescharacteristic
666C23C2×C3×C22⋊D511yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—101no—
670Q8—101no—
671D4—22no—
672D4—52no—
673D4—101no—
674D4—101no—
675D4—101no—
676D4—202no—
677D4—202no—
678D4—401no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—42no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—202no—
691C2×C4—401no—
692C2×C4C2×C3×C22⋊D511yescharacteristic
693C2×C4C2×C3×C22⋊D511yescharacteristic
694C2×C4C2×C3×C22⋊D511yescharacteristic
695C2×C4C2×C3×C22⋊D511yescharacteristic
696C2×C4C23×C3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—101no—
700C8—101no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3—202no—
704C2×C3—401no—
705C2×C3C2×#409611yescharacteristic
706C2×C3#6616311yescharacteristic
707C2×C3#6617111yescharacteristic
708C5C3×#329611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—102no—
715C22—201no—
716C22—201no—
717C22—201no—
718C22—201no—
719C22—201no—
720C22—404no—
721C22C3×#409612yes—
722C22C22×C3×C22⋊D511yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—201no—
732C4—201no—
733C4C3×D5×#4111yescharacteristic
734C4C3×#414911yescharacteristic
735C3#1061532911yescharacteristic, direct product factor, Sylow
736C2—22no—
737C2—41no—
738C2—202no—
739C2—401no—
740C2C2×C3×#409611yescharacteristic
741C2C3×#6616311yescharacteristic
742C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#552C2
socleC22×C3×C5C22×D4
prime radicalC3×#65884C2
hypercenterC3×#552D5
hypocenterC5C3×#3296
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#552

Complements

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

NH ≅ G/Ntype
1. C3×C5×#552C2semidirect
3. C3×#65357C2semidirect
4. C3×#65355C2semidirect
5. C3×#65340C2semidirect
6. C3×#65337C2semidirect
7. C3×#65336C2semidirect
8. C3×#65335C2semidirect
9. C3×#65317C2semidirect
10. C3×C4×#688C2semidirect
11. C3×D4×#168C2semidirect
12. C3×#65292C2semidirect
13. C3×#65291C2semidirect
14. C3×#65260C2semidirect
15. C2×C3×#3941C2semidirect
16. #10615329C3direct (N × H)
21. C3×C5×#125C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
25. C3×C4×C5×Q8C22semidirect
28. C3×C5×#117C22semidirect
30. C2×C3×#689C22semidirect
37. C22×C3×#168C22semidirect
43. C3×#3967C22semidirect
45. C3×C22⋊#168C22semidirect
46. C3×#3942C22semidirect
47. C3×#3942C22semidirect
48. C3×#3942C22semidirect
55. C3×#3940C22semidirect
56. C3×#3940C22semidirect
57. C3×#3939C22semidirect
58. C3×C4⋊#168C22semidirect
59. C3×C4×#168C22semidirect
61. C5×#552C2×C3semidirect
63. #65357C2×C3semidirect
64. #65355C2×C3semidirect
65. #65340C2×C3semidirect
66. #65337C2×C3semidirect
67. #65336C2×C3semidirect
68. #65335C2×C3semidirect
69. #65317C2×C3semidirect
70. C4×#688C2×C3semidirect
71. D4×#168C2×C3semidirect
72. #65292C2×C3semidirect
73. #65291C2×C3semidirect
74. #65260C2×C3semidirect
75. C2×#3941C2×C3semidirect
128. C3×#552D5semidirect
147. C5×#125C22×C3semidirect
150. C5×C22⋊Q8C22×C3semidirect
151. C4×C5×Q8C22×C3semidirect
154. C5×#117C22×C3semidirect
156. C2×#689C22×C3semidirect
163. C22×#168C22×C3semidirect
169. #3967C22×C3semidirect
171. C22⋊#168C22×C3semidirect
172. #3942C22×C3semidirect
173. #3942C22×C3semidirect
174. #3942C22×C3semidirect
181. #3940C22×C3semidirect
182. #3940C22×C3semidirect
183. #3939C22×C3semidirect
184. C4⋊#168C22×C3semidirect
185. C4×#168C22×C3semidirect
237. C3×#125C2×D5semidirect
243. C3×C22⋊Q8C2×D5semidirect
247. C3×C4×Q8C2×D5semidirect
251. C3×#117C2×D5semidirect
323. #552C3×D5semidirect
466. #125C2×C3×D5semidirect
472. C22⋊Q8C2×C3×D5semidirect
476. C4×Q8C2×C3×D5semidirect
480. #117C2×C3×D5semidirect
626. C3×C5#3296semidirect
708. C5C3×#3296semidirect
735. C3#10615329direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5522
C3×#658842
C3×#653572
C3×#653552
C3×#653402
C3×#653372
C3×#653362
C3×#653352
C3×#653172
C3×C4×#6882
C3×D4×#1682
C3×#652922
C3×#652912
C3×#652602
C2×C3×#39412
#106153293
C3×#32965