Finite Group Databasebeta

← C3×#10612506 #14458630

Subgroups — C3×#10612506 #14458630

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×#65976C211yesmaximal, characteristic, complemented
2C3×#65964C211yesmaximal, characteristic
3C3×C5×#467C211yesmaximal, characteristic, complemented
4C3×#65476C211yesmaximal, characteristic, complemented
5C3×#65474C211yesmaximal, characteristic, complemented
6C2×C3×#3953C211yesmaximal, characteristic, complemented
7C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
8C3×#65335C211yesmaximal, characteristic, complemented
9C3×#65332C211yesmaximal, characteristic, complemented
10C3×#65180C211yesmaximal, characteristic, complemented
11C3×#65174C211yesmaximal, characteristic, complemented
12C3×#65096C211yesmaximal, characteristic, complemented
13C3×#65093C211yesmaximal, characteristic, complemented
14C3×#65089C211yesmaximal, characteristic, complemented
15C3×#65077C211yesmaximal, characteristic, complemented
16#10612506C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C2×C3×C5×Q16C2211yescharacteristic, complemented
20C22×C3×C5×C8C2211yescharacteristic
21C3×C5×C22⋊Q8C2211yescharacteristic
22C3×C5×C22⋊Q8C2211yescharacteristic
23C3×#4093C2211yescharacteristic
24C3×#4092C2211yescharacteristic, complemented
25C3×Q8×Dic5C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic
27C2×C3×#688C2211yescharacteristic
28C3×C4×C22⋊D5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic, complemented
31C3×#4044—21no—
32C3×#4041—21no—
33C3×#4041C2211yescharacteristic
34C3×#4040—21no—
35C3×#4039C2211yescharacteristic
36C3×#4038C2211yescharacteristic, complemented
37C3×#4036—21no—
38C3×#4036C2211yescharacteristic, complemented
39C3×#4032—21no—
40C3×#4028—21no—
41C3×D5×C22⋊C4—21no—
42C3×#4023—21no—
43C3×C5×#107C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#103C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×#3967C2211yescharacteristic, complemented
48C3×C22⋊#168C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic
53C3×#3952C2211yescharacteristic, complemented
54C3×#3946C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3940C2211yescharacteristic, complemented
59C3×#3940C2211yescharacteristic, complemented
60C3×#3296—51nomaximal, Hall
61#65976C2×C311yescharacteristic, complemented
62#65964C2×C311yescharacteristic
63C5×#467C2×C311yescharacteristic, complemented
64#65476C2×C311yescharacteristic, complemented
65#65474C2×C311yescharacteristic, complemented
66C2×#3953C2×C311yescharacteristic, complemented
67C8×C22⋊D5C2×C311yescharacteristic, complemented
68#65335C2×C311yescharacteristic, complemented
69#65332C2×C311yescharacteristic, complemented
70#65180C2×C311yescharacteristic, complemented
71#65174C2×C311yescharacteristic, complemented
72#65096C2×C311yescharacteristic, complemented
73#65093C2×C311yescharacteristic, complemented
74#65089C2×C311yescharacteristic, complemented
75#65077C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×Q8C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5D411yescharacteristic
81C22×C3×Dic5—21no—
82C3×#713—22no—
83C3×#713—41no—
84C2×C3×D20—22no—
85C2×C3×D20—21no—
86C2×C3×D20—21no—
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×C4×D5C2311yescharacteristic
94C3×C5×Q16—41no—
95C2×C3×C5×C8—41no—
96C2×C3×C5×C8C2311yescharacteristic
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C22⋊Dic5D411yescharacteristic
105C3×#688—22no—
106C3×#688—41no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—21no—
121C3×#683D411yescharacteristic
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×C8×D5—41no—
128C3×#552—51no—
129C3×#546—51no—
130C3×#488—51no—
131C3×#483—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#467D511yescharacteristic, complemented
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×#713C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C2×C5×Q16C22×C311yescharacteristic, complemented
146C22×C5×C8C22×C311yescharacteristic
147C5×C22⋊Q8C22×C311yescharacteristic
148C5×C22⋊Q8C22×C311yescharacteristic
149#4093C22×C311yescharacteristic
150#4092C22×C311yescharacteristic, complemented
151Q8×Dic5C22×C311yescharacteristic, complemented
152C2×#688C22×C311yescharacteristic
153C2×#688C22×C311yescharacteristic
154C4×C22⋊D5C22×C311yescharacteristic
155C2×C4⋊Dic5C22×C311yescharacteristic
156C2×C8×D5C22×C311yescharacteristic, complemented
157#4044—21no—
158#4041—21no—
159#4041C22×C311yescharacteristic
160#4040—21no—
161#4039C22×C311yescharacteristic
162#4038C22×C311yescharacteristic, complemented
163#4036—21no—
164#4036C22×C311yescharacteristic, complemented
165#4032—21no—
166#4028—21no—
167D5×C22⋊C4—21no—
168#4023—21no—
169C5×#107C22×C311yescharacteristic, complemented
170C5×#103C22×C311yescharacteristic, complemented
171C5×#103C22×C311yescharacteristic, complemented
172#3967C22×C311yescharacteristic, complemented
173#3967C22×C311yescharacteristic, complemented
174C22⋊#168C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3952C22×C311yescharacteristic, complemented
180#3946C22×C311yescharacteristic, complemented
181C8×Dic5C22×C311yescharacteristic, complemented
182#3941C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3940C22×C311yescharacteristic, complemented
185#3940C22×C311yescharacteristic, complemented
186#3296—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—42no—
191C22×C3×D5—42no—
192C22×C3×D5—81no—
193C22×C3×D5C2×D411yescharacteristic
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×Q8—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×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2411yescharacteristic
206C3×C22⋊D5—22no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—42no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C3×D20—21no—
214C3×D20—21no—
215C3×D20—21no—
216C3×D20—42no—
217C3×D20—42no—
218C3×D20—81no—
219C3×D20#4112yes—
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—42no—
223C3×C4×D5—81no—
224C3×C5×C8—21no—
225C3×C5×C8—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41—51no—
229C22×C3×D4—51no—
230C2×C3×Q16C2×D511yescharacteristic, complemented
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C22×C3×C8—51no—
234C22×C3×C8C2×D511yescharacteristic
235C3×#126—101no—
236C3×#125—51no—
237C3×#125—101no—
238C3×#124—51no—
239C3×#123—101no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8C2×D511yescharacteristic
243C3×C22⋊Q8C2×D511yescharacteristic
244C3×#121—51no—
245C3×#121—101no—
246C3×#120—101no—
247C3×C4×Q8—51no—
248C3×C4×D4—51no—
249C3×C4×D4—51no—
250C3×#117—51no—
251C3×#117—101no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—101no—
254C3×#107C2×D511yescharacteristic, complemented
255C3×#106—51no—
256C3×#106—51no—
257C3×C4⋊C8—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103C2×D511yescharacteristic, complemented
261C3×#103C2×D511yescharacteristic, complemented
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×Q8C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C2×C22⋊D5C3×D411yescharacteristic
276C22×Dic5—21no—
277#713—22no—
278#713—41no—
279C2×D20—22no—
280C2×D20—21no—
281C2×D20—21no—
282C2×D20—21no—
283C2×D20—41no—
284C2×D20C23×C311yescharacteristic
285C2×D20C23×C311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—21no—
288C2×C4×D5C23×C311yescharacteristic
289C5×Q16—41no—
290C2×C5×C8—41no—
291C2×C5×C8C23×C311yescharacteristic
292C2×C5×C8C23×C311yescharacteristic
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4C23×C311yescharacteristic
296C5×C4⋊C4C23×C311yescharacteristic
297C5×C22⋊C4—21no—
298C5×C22⋊C4—21no—
299C22⋊Dic5C3×D411yescharacteristic
300#688—22no—
301#688—41no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306#685—21no—
307#685—21no—
308#685C3×D411yescharacteristic
309C4⋊Dic5—21no—
310C4⋊Dic5—21no—
311C4⋊Dic5—21no—
312C4⋊Dic5C23×C311yescharacteristic
313C4⋊Dic5C23×C311yescharacteristic
314#683—21no—
315#683—21no—
316#683C3×D411yescharacteristic
317C4×Dic5—21no—
318C4×Dic5—21no—
319C4×Dic5C23×C311yescharacteristic
320C2×#168C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322C8×D5—41no—
323#552—51no—
324#546—51no—
325#488—51no—
326#483—51no—
327#482—51no—
328#478—51no—
329#467C3×D511yescharacteristic, complemented
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#13512yes—
341C22×C3×C5C22×D411yescharacteristic
342C2×C3×D5—21no—
343C2×C3×D5—22no—
344C2×C3×D5—21no—
345C2×C3×D5—21no—
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—41no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5—41no—
357C3×C4×C5C2×#4111yescharacteristic
358C3×C4×C5H(5,𝔽2)11yescharacteristic
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—21no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C24×C3—101no—
365C3×#41—102no—
366C3×#41—201no—
367C2×C3×Q8C22×D511yescharacteristic
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—51no—
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—102no—
373C2×C3×D4—101no—
374C2×C3×D4—101no—
375C2×C3×D4—101no—
376C2×C3×D4—201no—
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C22×C3×C4C22×D511yescharacteristic
382C3×Q16—41no—
383C3×SD16—102no—
384C3×SD16—201no—
385C2×C3×C8—41no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—201no—
389C2×C3×C8C22×D511yescharacteristic
390C2×C3×C8C22×D511yescharacteristic
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—51no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4—101no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—51no—
406C3×C22⋊C4—51no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4—101no—
412C3×C22⋊C4—101no—
413C3×C42—51no—
414C3×C42—101no—
415C3×C42—101no—
416C23×C5C2×C3×D411yescharacteristic
417C22×D5—21no—
418C22×D5—21no—
419C22×D5—42no—
420C22×D5—42no—
421C22×D5—81no—
422C22×D5C2×C3×D411yescharacteristic
423C5×Q8—21no—
424C5×Q8—21no—
425C5×Q8—21no—
426C5×Q8—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×C5C2×C3×D411yescharacteristic
434C2×C4×C5C24×C311yescharacteristic
435C22⋊D5—22no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—42no—
439C2×Dic5C2×C3×D411yescharacteristic
440C2×Dic5C2×C3×D411yescharacteristic
441C2×Dic5C2×C3×D411yescharacteristic
442D20—21no—
443D20—21no—
444D20—21no—
445D20—42no—
446D20—42no—
447D20—81no—
448D20C3×#4112yes—
449C4×D5—21no—
450C4×D5—21no—
451C4×D5—42no—
452C4×D5—81no—
453C5×C8—21no—
454C5×C8—21no—
455#168—21no—
456#168—21no—
457C2×#41—51no—
458C22×D4—51no—
459C2×Q16C2×C3×D511yescharacteristic, complemented
460C2×SD16—51no—
461C2×SD16—51no—
462C22×C8—51no—
463C22×C8C2×C3×D511yescharacteristic
464#126—101no—
465#125—51no—
466#125—101no—
467#124—51no—
468#123—101no—
469#123—101no—
470C22⋊Q8—51no—
471C22⋊Q8C2×C3×D511yescharacteristic
472C22⋊Q8C2×C3×D511yescharacteristic
473#121—51no—
474#121—101no—
475#120—101no—
476C4×Q8—51no—
477C4×D4—51no—
478C4×D4—51no—
479#117—51no—
480#117—101no—
481C2×C4⋊C4—51no—
482C2×C22⋊C4—101no—
483#107C2×C3×D511yescharacteristic, complemented
484#106—51no—
485#106—51no—
486C4⋊C8—51no—
487#103—51no—
488#103—51no—
489#103C2×C3×D511yescharacteristic, complemented
490#103C2×C3×D511yescharacteristic, complemented
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#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C3×D5—41no—
505C3×D5—42no—
506C3×D5—81no—
507C23×C3—51no—
508C23×C3—101no—
509C23×C3—101no—
510C23×C3—202no—
511C23×C3—202no—
512C23×C3—401no—
513C23×C3D4×D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×D4—52no—
519C3×D4—102no—
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—51no—
533C2×C3×C4—51no—
534C2×C3×C4—51no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—202no—
540C2×C3×C4—202no—
541C2×C3×C4—401no—
542C2×C3×C4D4×D511yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—101no—
547C3×C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5C3×#13512yes—
551C22×C5C22×C3×D411yescharacteristic
552C2×D5—21no—
553C2×D5—21no—
554C2×D5—21no—
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—41no—
564C4×C5—41no—
565C4×C5—41no—
566C4×C5—41no—
567C4×C5C2×C3×#4111yescharacteristic
568C4×C5C3×H(5,𝔽2)11yescharacteristic
569Dic5—21no—
570Dic5—21no—
571Dic5—21no—
572Dic5—41no—
573Dic5—41no—
574C24—101no—
575#41—102no—
576#41—201no—
577C2×Q8C22×C3×D511yescharacteristic
578C2×Q8C22×C3×D511yescharacteristic
579C2×D4—51no—
580C2×D4—51no—
581C2×D4—51no—
582C2×D4—102no—
583C2×D4—101no—
584C2×D4—101no—
585C2×D4—101no—
586C2×D4—201no—
587C22×C4—51no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4C22×C3×D511yescharacteristic
592Q16—41no—
593SD16—102no—
594SD16—201no—
595C2×C8—41no—
596C2×C8—51no—
597C2×C8—51no—
598C2×C8—201no—
599C2×C8C22×C3×D511yescharacteristic
600C2×C8C22×C3×D511yescharacteristic
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—51no—
604C4⋊C4—51no—
605C4⋊C4—51no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4C22×C3×D511yescharacteristic
612C4⋊C4C22×C3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—51no—
616C22⋊C4—51no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C22⋊C4—101no—
622C22⋊C4—101no—
623C42—51no—
624C42—101no—
625C42—101no—
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—101no—
630C22×C3—101no—
631C22×C3—101no—
632C22×C3—102no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3—201no—
636C22×C3—201no—
637C22×C3—201no—
638C22×C3—404no—
639C22×C3#406512yes—
640C22×C3C2×D4×D511yescharacteristic
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—101no—
647C3×C4—101no—
648C3×C4—101no—
649C3×C4—201no—
650C3×C4—201no—
651C3×C4#414411yescharacteristic
652C3×C4D5×#4111yescharacteristic
653C2×C5—22no—
654C2×C5C3×#54611yescharacteristic
655C2×C5C2×C3×#13511yescharacteristic
656C2×C5C3×#57711yescharacteristic
657D5—41no—
658D5—42no—
659D5—81no—
660C23—51no—
661C23—101no—
662C23—101no—
663C23—202no—
664C23—202no—
665C23—401no—
666C23C3×D4×D511yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671D4—52no—
672D4—102no—
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—51no—
686C2×C4—51no—
687C2×C4—51no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—202no—
693C2×C4—202no—
694C2×C4—401no—
695C2×C4C3×D4×D511yescharacteristic
696C2×C4C23×C3×D511yescharacteristic
697C8—21no—
698C8—21no—
699C8—101no—
700C8—101no—
701C2×C3—22no—
702C2×C3—201no—
703C2×C3—202no—
704C2×C3—401no—
705C2×C3#6594411yescharacteristic
706C2×C3C2×#406511yescharacteristic
707C2×C3#6610411yescharacteristic
708C5C3×#329611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—101no—
712C22—101no—
713C22—101no—
714C22—102no—
715C22—201no—
716C22—201no—
717C22—201no—
718C22—201no—
719C22—201no—
720C22—404no—
721C22C3×#406512yes—
722C22C2×C3×D4×D511yescharacteristic
723C4—21no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—101no—
729C4—101no—
730C4—101no—
731C4—201no—
732C4—201no—
733C4C3×#414411yescharacteristic
734C4C3×D5×#4111yescharacteristic
735C3#1061250611yescharacteristic, direct product factor, Sylow
736C2—22no—
737C2—201no—
738C2—202no—
739C2—401no—
740C2C3×#6594411yescharacteristic
741C2C2×C3×#406511yescharacteristic
742C2C3×#6610411yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#467C2
socleC22×C3×C5C22×D4
prime radicalC3×#65964C2
hypercenterC3×#467D5
hypocenterC5C3×#3296
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
1. C3×#65976C2semidirect
3. C3×C5×#467C2semidirect
4. C3×#65476C2semidirect
5. C3×#65474C2semidirect
6. C2×C3×#3953C2semidirect
7. C3×C8×C22⋊D5C2semidirect
8. C3×#65335C2semidirect
9. C3×#65332C2semidirect
10. C3×#65180C2semidirect
11. C3×#65174C2semidirect
12. C3×#65096C2semidirect
13. C3×#65093C2semidirect
14. C3×#65089C2semidirect
15. C3×#65077C2semidirect
16. #10612506C3direct (N × H)
19. C2×C3×C5×Q16C22semidirect
24. C3×#4092C22semidirect
25. C3×Q8×Dic5C22semidirect
30. C2×C3×C8×D5C22semidirect
36. C3×#4038C22semidirect
38. C3×#4036C22semidirect
43. C3×C5×#107C22semidirect
44. C3×C5×#103C22semidirect
45. C3×C5×#103C22semidirect
46. C3×#3967C22semidirect
47. C3×#3967C22semidirect
53. C3×#3952C22semidirect
54. C3×#3946C22semidirect
55. C3×C8×Dic5C22semidirect
58. C3×#3940C22semidirect
59. C3×#3940C22semidirect
61. #65976C2×C3semidirect
63. C5×#467C2×C3semidirect
64. #65476C2×C3semidirect
65. #65474C2×C3semidirect
66. C2×#3953C2×C3semidirect
67. C8×C22⋊D5C2×C3semidirect
68. #65335C2×C3semidirect
69. #65332C2×C3semidirect
70. #65180C2×C3semidirect
71. #65174C2×C3semidirect
72. #65096C2×C3semidirect
73. #65093C2×C3semidirect
74. #65089C2×C3semidirect
75. #65077C2×C3semidirect
134. C3×#467D5semidirect
145. C2×C5×Q16C22×C3semidirect
150. #4092C22×C3semidirect
151. Q8×Dic5C22×C3semidirect
156. C2×C8×D5C22×C3semidirect
162. #4038C22×C3semidirect
164. #4036C22×C3semidirect
169. C5×#107C22×C3semidirect
170. C5×#103C22×C3semidirect
171. C5×#103C22×C3semidirect
172. #3967C22×C3semidirect
173. #3967C22×C3semidirect
179. #3952C22×C3semidirect
180. #3946C22×C3semidirect
181. C8×Dic5C22×C3semidirect
184. #3940C22×C3semidirect
185. #3940C22×C3semidirect
230. C2×C3×Q16C2×D5semidirect
254. C3×#107C2×D5semidirect
260. C3×#103C2×D5semidirect
261. C3×#103C2×D5semidirect
329. #467C3×D5semidirect
459. C2×Q16C2×C3×D5semidirect
483. #107C2×C3×D5semidirect
489. #103C2×C3×D5semidirect
490. #103C2×C3×D5semidirect
626. C3×C5#3296semidirect
708. C5C3×#3296semidirect
735. C3#10612506direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659762
C3×#659642
C3×C5×#4672
C3×#654762
C3×#654742
C2×C3×#39532
C3×C8×C22⋊D52
C3×#653352
C3×#653322
C3×#651802
C3×#651742
C3×#650962
C3×#650932
C3×#650892
C3×#650772
#106125063
C3×#32965