Finite Group Databasebeta

← C3×#10612698 #14430760

Subgroups — C3×#10612698 #14430760

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66063C211yesmaximal, characteristic, complemented
2C3×#65879C211yesmaximal, characteristic
3C3×C5×#474C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×#65298C211yesmaximal, characteristic, complemented
6C3×#65180C211yesmaximal, characteristic, complemented
7C3×#65179C211yesmaximal, characteristic, complemented
8C3×#65170C211yesmaximal, characteristic, complemented
9C3×#65169C211yesmaximal, characteristic, complemented
10C3×#65136C211yesmaximal, characteristic, complemented
11C3×#65128C211yesmaximal, characteristic, complemented
12C3×#65059C211yesmaximal, characteristic
13C3×D5×#102C211yesmaximal, characteristic
14C3×#65055C211yesmaximal, characteristic, complemented
15C3×#65050C211yesmaximal, characteristic, complemented
16#10612698C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic, complemented
19C3×C4×C5×D4C2211yescharacteristic
20C3×#4092—21no—
21C3×#4090—21no—
22C3×D4×Dic5C2211yescharacteristic
23C3×C4×C22⋊D5—21no—
24C2×C3×#685—21no—
25C2×C3×#676C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic
27C3×#4042—21no—
28C3×#4039C2211yescharacteristic
29C3×#4038C2211yescharacteristic
30C3×#4038C2211yescharacteristic
31C3×D5×C4⋊C4C2211yescharacteristic
32C3×#4036C2211yescharacteristic, complemented
33C3×#4035—21no—
34C3×#4034C2211yescharacteristic, complemented
35C3×#4027—21no—
36C3×D5×C22⋊C4—21no—
37C3×C4×D20C2211yescharacteristic
38C3×#4018C2211yescharacteristic
39C3×#4016C2211yescharacteristic, complemented
40C3×C5×#107C2211yescharacteristic, complemented
41C3×C5×#107C2211yescharacteristic, complemented
42C3×C5×C4⋊C8C2211yescharacteristic, complemented
43C3×C5×#102C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3953C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3950C2211yescharacteristic, complemented
50C3×#3949C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×#3941C2211yescharacteristic
54C3×#3941C2211yescharacteristic
55C3×#3940C2211yescharacteristic, complemented
56C3×#3940C2211yescharacteristic, complemented
57C3×#3940C2211yescharacteristic, complemented
58C3×#3939C2211yescharacteristic, complemented
59C3×C4⋊#168C2211yescharacteristic, complemented
60C3×#3081—51nomaximal, Hall
61#66063C2×C311yescharacteristic, complemented
62#65879C2×C311yescharacteristic
63C5×#474C2×C311yescharacteristic, complemented
64#65373C2×C311yescharacteristic, complemented
65#65298C2×C311yescharacteristic, complemented
66#65180C2×C311yescharacteristic, complemented
67#65179C2×C311yescharacteristic, complemented
68#65170C2×C311yescharacteristic, complemented
69#65169C2×C311yescharacteristic, complemented
70#65136C2×C311yescharacteristic, complemented
71#65128C2×C311yescharacteristic, complemented
72#65059C2×C311yescharacteristic
73D5×#102C2×C311yescharacteristic
74#65055C2×C311yescharacteristic, complemented
75#65050C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×C3×C22⋊D5—21no—
81C22×C3×Dic5—21no—
82C3×D4×D5—22no—
83C3×D4×D5Q814yescomplemented
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5C2311yescharacteristic
89C2×C3×Dic10—21no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C42×C5C2311yescharacteristic
98C3×C22⋊Dic5—21no—
99C3×#685—21no—
100C3×#685—21no—
101C3×#685—21no—
102C3×#685—21no—
103C3×#685D411yescharacteristic
104C3×#685D411yescharacteristic
105C3×C4⋊Dic5—21no—
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×C4⋊Dic5C2311yescharacteristic
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683D411yescharacteristic
115C3×#683D411yescharacteristic
116C3×C4×Dic5—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C3×#676—22no—
122C3×C8×D5—22no—
123C3×#544—51no—
124C3×#518—51no—
125C3×#478—51no—
126C3×#478—51no—
127C3×#478—51no—
128C3×#478—51no—
129C3×#476—51no—
130C3×#476—51no—
131C3×#474—51no—
132C3×#474D511yescharacteristic, complemented
133C3×#428—51no—
134C3×#427—51no—
135C3×#424—51no—
136C3×#418—51no—
137C2×C3×#102—51no—
138C2×D4×D5C22×C311yescharacteristic
139C5×C4⋊Q8C22×C311yescharacteristic, complemented
140C4×C5×D4C22×C311yescharacteristic
141#4092—21no—
142#4090—21no—
143D4×Dic5C22×C311yescharacteristic
144C4×C22⋊D5—21no—
145C2×#685—21no—
146C2×#676C22×C311yescharacteristic
147C2×C8×D5C22×C311yescharacteristic
148#4042—21no—
149#4039C22×C311yescharacteristic
150#4038C22×C311yescharacteristic
151#4038C22×C311yescharacteristic
152D5×C4⋊C4C22×C311yescharacteristic
153#4036C22×C311yescharacteristic, complemented
154#4035—21no—
155#4034C22×C311yescharacteristic, complemented
156#4027—21no—
157D5×C22⋊C4—21no—
158C4×D20C22×C311yescharacteristic
159#4018C22×C311yescharacteristic
160#4016C22×C311yescharacteristic, complemented
161C5×#107C22×C311yescharacteristic, complemented
162C5×#107C22×C311yescharacteristic, complemented
163C5×C4⋊C8C22×C311yescharacteristic, complemented
164C5×#102C22×C311yescharacteristic
165C5×#102C22×C311yescharacteristic
166#3964C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3953C22×C311yescharacteristic
169#3953C22×C311yescharacteristic
170#3950C22×C311yescharacteristic, complemented
171#3949C22×C311yescharacteristic, complemented
172#3946C22×C311yescharacteristic, complemented
173#3946C22×C311yescharacteristic, complemented
174#3941C22×C311yescharacteristic
175#3941C22×C311yescharacteristic
176#3940C22×C311yescharacteristic, complemented
177#3940C22×C311yescharacteristic, complemented
178#3940C22×C311yescharacteristic, complemented
179#3939C22×C311yescharacteristic, complemented
180C4⋊#168C22×C311yescharacteristic, complemented
181#3081—51noSylow
182C23×C3×C5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—24no—
185C22×C3×D5—81no—
186C22×C3×D5—81no—
187C22×C3×D5C2×D411yescharacteristic
188C3×C5×Q8—81no—
189C3×C5×D4—21no—
190C3×C5×D4C2×Q812yes—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—81no—
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2411yescharacteristic
198C3×C22⋊D5—24no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—81no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C3×D20—21no—
207C3×D20C2×Q812yes—
208C3×C4×D5—81no—
209C3×C4×D5—81no—
210C3×C4×D5—81no—
211C3×C4×D5C2×Q812yes—
212C3×C4×D5#4112yes—
213C3×Dic10—81no—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3×#168—21no—
217C3×#168—21no—
218C22×C3×D4—51no—
219C2×C3×M16—51no—
220C22×C3×C8—51no—
221C3×C4⋊Q8—51no—
222C3×C4⋊Q8—101no—
223C3×C4⋊Q8C2×D511yescharacteristic, complemented
224C3×#125—51no—
225C3×#125—51no—
226C3×#125—101no—
227C3×C22⋊Q8—101no—
228C3×C22⋊Q8—101no—
229C3×C4×D4—51no—
230C3×C4×D4—51no—
231C3×C4×D4—51no—
232C3×C4×D4—101no—
233C3×C4×D4—101no—
234C3×C4×D4C2×D511yescharacteristic
235C3×#117—51no—
236C3×#117—51no—
237C3×#117—51no—
238C2×C3×C4⋊C4—51no—
239C2×C3×C22⋊C4—101no—
240C2×C3×C22⋊C4—101no—
241C3×#107—51no—
242C3×#107—51no—
243C3×#107C2×D511yescharacteristic, complemented
244C3×#107C2×D511yescharacteristic, complemented
245C3×#106—51no—
246C3×#106—51no—
247C3×#106—51no—
248C3×#106—51no—
249C3×C4⋊C8—51no—
250C3×C4⋊C8—51no—
251C3×C4⋊C8—51no—
252C3×C4⋊C8C2×D511yescharacteristic, complemented
253C3×#102—51no—
254C3×#102—51no—
255C3×#102—51no—
256C3×#102—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102C2×D511yescharacteristic
260C3×#102C2×D511yescharacteristic
261C23×D5—21no—
262C2×C5×Q8—21no—
263C2×C5×D4C23×C311yescharacteristic
264C22×C4×C5—21no—
265C2×C22⋊D5—21no—
266C22×Dic5—21no—
267D4×D5—22no—
268D4×D5C3×Q814yescomplemented
269C2×D20C23×C311yescharacteristic
270C2×C4×D5—21no—
271C2×C4×D5—21no—
272C2×C4×D5—21no—
273C2×C4×D5C23×C311yescharacteristic
274C2×Dic10—21no—
275C2×C5×C8C23×C311yescharacteristic
276C2×C5×C8C23×C311yescharacteristic
277C5×C4⋊C4—21no—
278C5×C4⋊C4C23×C311yescharacteristic
279C5×C4⋊C4C23×C311yescharacteristic
280C5×C4⋊C4C23×C311yescharacteristic
281C5×C22⋊C4—21no—
282C42×C5C23×C311yescharacteristic
283C22⋊Dic5—21no—
284#685—21no—
285#685—21no—
286#685—21no—
287#685—21no—
288#685C3×D411yescharacteristic
289#685C3×D411yescharacteristic
290C4⋊Dic5—21no—
291C4⋊Dic5C23×C311yescharacteristic
292C4⋊Dic5C23×C311yescharacteristic
293C4⋊Dic5C23×C311yescharacteristic
294#683—21no—
295#683—21no—
296#683—21no—
297#683—21no—
298#683—21no—
299#683C3×D411yescharacteristic
300#683C3×D411yescharacteristic
301C4×Dic5—21no—
302C4×Dic5—21no—
303C4×Dic5C23×C311yescharacteristic
304C2×#168C23×C311yescharacteristic
305C2×#168C23×C311yescharacteristic
306#676—22no—
307C8×D5—22no—
308#544—51no—
309#518—51no—
310#478—51no—
311#478—51no—
312#478—51no—
313#478—51no—
314#476—51no—
315#476—51no—
316#474—51no—
317#474C3×D511yescharacteristic, complemented
318#428—51no—
319#427—51no—
320#424—51no—
321#418—51no—
322C2×#102—51no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5C22×D411yescharacteristic
327C2×C3×D5—21no—
328C2×C3×D5—21no—
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C2×C3×D5—84no—
333C2×C3×D5C22⋊Q812yes—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—41no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5C22×Q811yescharacteristic
340C3×C4×C5C2×#4111yescharacteristic
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C3×Dic5C22⋊Q812yes—
347C24×C3—101no—
348C2×C3×Q8—21no—
349C2×C3×Q8—101no—
350C2×C3×D4—54no—
351C2×C3×D4—51no—
352C2×C3×D4—102no—
353C2×C3×D4—101no—
354C2×C3×D4C22×D511yescharacteristic
355C22×C3×C4—21no—
356C22×C3×C4—51no—
357C22×C3×C4—101no—
358C22×C3×C4—101no—
359C22×C3×C4—101no—
360C22×C3×C4—101no—
361C3×M16—102no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8—102no—
365C2×C3×C8C22×D511yescharacteristic
366C2×C3×C8C22×D511yescharacteristic
367C3×C4⋊C4—21no—
368C3×C4⋊C4—51no—
369C3×C4⋊C4—51no—
370C3×C4⋊C4—51no—
371C3×C4⋊C4—51no—
372C3×C4⋊C4—51no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4—101no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4—101no—
378C3×C4⋊C4—101no—
379C3×C4⋊C4C22×D511yescharacteristic
380C3×C4⋊C4C22×D511yescharacteristic
381C3×C4⋊C4C22×D511yescharacteristic
382C3×C22⋊C4—21no—
383C3×C22⋊C4—51no—
384C3×C22⋊C4—51no—
385C3×C22⋊C4—101no—
386C3×C22⋊C4—101no—
387C3×C22⋊C4—101no—
388C3×C22⋊C4—101no—
389C3×C22⋊C4—101no—
390C3×C42—51no—
391C3×C42—101no—
392C3×C42—101no—
393C3×C42C22×D511yescharacteristic
394C23×C5—21no—
395C22×D5—21no—
396C22×D5—24no—
397C22×D5—81no—
398C22×D5—81no—
399C22×D5C2×C3×D411yescharacteristic
400C5×Q8—81no—
401C5×D4—21no—
402C5×D4C2×C3×Q812yes—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—81no—
407C2×C4×C5C2×C3×D411yescharacteristic
408C2×C4×C5C2×C3×D411yescharacteristic
409C2×C4×C5C24×C311yescharacteristic
410C22⋊D5—24no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—81no—
415C2×Dic5C2×C3×D411yescharacteristic
416C2×Dic5C2×C3×D411yescharacteristic
417C2×Dic5C2×C3×D411yescharacteristic
418D20—21no—
419D20C2×C3×Q812yes—
420C4×D5—81no—
421C4×D5—81no—
422C4×D5—81no—
423C4×D5C2×C3×Q812yes—
424C4×D5C3×#4112yes—
425Dic10—81no—
426C5×C8—21no—
427C5×C8—21no—
428#168—21no—
429#168—21no—
430C22×D4—51no—
431C2×M16—51no—
432C22×C8—51no—
433C4⋊Q8—51no—
434C4⋊Q8—101no—
435C4⋊Q8C2×C3×D511yescharacteristic, complemented
436#125—51no—
437#125—51no—
438#125—101no—
439C22⋊Q8—101no—
440C22⋊Q8—101no—
441C4×D4—51no—
442C4×D4—51no—
443C4×D4—51no—
444C4×D4—101no—
445C4×D4—101no—
446C4×D4C2×C3×D511yescharacteristic
447#117—51no—
448#117—51no—
449#117—51no—
450C2×C4⋊C4—51no—
451C2×C22⋊C4—101no—
452C2×C22⋊C4—101no—
453#107—51no—
454#107—51no—
455#107C2×C3×D511yescharacteristic, complemented
456#107C2×C3×D511yescharacteristic, complemented
457#106—51no—
458#106—51no—
459#106—51no—
460#106—51no—
461C4⋊C8—51no—
462C4⋊C8—51no—
463C4⋊C8—51no—
464C4⋊C8C2×C3×D511yescharacteristic, complemented
465#102—51no—
466#102—51no—
467#102—51no—
468#102—51no—
469#102—51no—
470#102—51no—
471#102C2×C3×D511yescharacteristic
472#102C2×C3×D511yescharacteristic
473C2×C3×C5—42no—
474C2×C3×C5C2×C22⋊Q811yescharacteristic
475C2×C3×C5#57611yescharacteristic
476C2×C3×C5#57711yescharacteristic
477C3×D5—22no—
478C3×D5—42no—
479C23×C3—21no—
480C23×C3—51no—
481C23×C3—104no—
482C23×C3—101no—
483C23×C3—401no—
484C23×C3—401no—
485C3×Q8—81no—
486C3×Q8—401no—
487C3×D4—21no—
488C3×D4—52no—
489C3×D4—104no—
490C3×D4—101no—
491C3×D4Q8×D512yes—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—51no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—81no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—401no—
505C2×C3×C4—401no—
506C2×C3×C4—401no—
507C2×C3×C4—401no—
508C2×C3×C4D4×D511yescharacteristic
509C2×C3×C4D4×D511yescharacteristic
510C2×C3×C4C23×D511yescharacteristic
511C3×C8—21no—
512C3×C8—21no—
513C3×C8—101no—
514C3×C8—101no—
515C22×C5—22no—
516C22×C5—41no—
517C22×C5—41no—
518C22×C5C22×C3×D411yescharacteristic
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—22no—
522C2×D5—41no—
523C2×D5—41no—
524C2×D5—84no—
525C2×D5C3×C22⋊Q812yes—
526C4×C5—21no—
527C4×C5—21no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5—41no—
531C4×C5C22×C3×Q811yescharacteristic
532C4×C5C2×C3×#4111yescharacteristic
533Dic5—21no—
534Dic5—21no—
535Dic5—41no—
536Dic5—41no—
537Dic5—41no—
538Dic5C3×C22⋊Q812yes—
539C24—101no—
540C2×Q8—21no—
541C2×Q8—101no—
542C2×D4—54no—
543C2×D4—51no—
544C2×D4—102no—
545C2×D4—101no—
546C2×D4C22×C3×D511yescharacteristic
547C22×C4—21no—
548C22×C4—51no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—101no—
553M16—102no—
554C2×C8—51no—
555C2×C8—51no—
556C2×C8—102no—
557C2×C8C22×C3×D511yescharacteristic
558C2×C8C22×C3×D511yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—51no—
561C4⋊C4—51no—
562C4⋊C4—51no—
563C4⋊C4—51no—
564C4⋊C4—51no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4—101no—
569C4⋊C4—101no—
570C4⋊C4—101no—
571C4⋊C4C22×C3×D511yescharacteristic
572C4⋊C4C22×C3×D511yescharacteristic
573C4⋊C4C22×C3×D511yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—51no—
576C22⋊C4—51no—
577C22⋊C4—101no—
578C22⋊C4—101no—
579C22⋊C4—101no—
580C22⋊C4—101no—
581C22⋊C4—101no—
582C42—51no—
583C42—101no—
584C42—101no—
585C42C22×C3×D511yescharacteristic
586C3×C5#308111yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—52no—
591C22×C3—101no—
592C22×C3—101no—
593C22×C3—102no—
594C22×C3—201no—
595C22×C3—201no—
596C22×C3—404no—
597C22×C3C2×D4×D511yescharacteristic
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—52no—
604C3×C4—101no—
605C3×C4—101no—
606C3×C4—201no—
607C3×C4—201no—
608C3×C4—201no—
609C3×C4C2×Q8×D511yescharacteristic
610C3×C4D5×#4111yescharacteristic
611C2×C5—42no—
612C2×C5C2×C3×C22⋊Q811yescharacteristic
613C2×C5C3×#57611yescharacteristic
614C2×C5C3×#57711yescharacteristic
615D5—22no—
616D5—42no—
617C23—21no—
618C23—51no—
619C23—104no—
620C23—101no—
621C23—401no—
622C23—401no—
623Q8—81no—
624Q8—401no—
625D4—21no—
626D4—52no—
627D4—104no—
628D4—101no—
629D4C3×Q8×D512yes—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—51no—
634C2×C4—52no—
635C2×C4—52no—
636C2×C4—51no—
637C2×C4—51no—
638C2×C4—81no—
639C2×C4—101no—
640C2×C4—101no—
641C2×C4—101no—
642C2×C4—401no—
643C2×C4—401no—
644C2×C4—401no—
645C2×C4—401no—
646C2×C4C3×D4×D511yescharacteristic
647C2×C4C3×D4×D511yescharacteristic
648C2×C4C23×C3×D511yescharacteristic
649C8—21no—
650C8—21no—
651C8—101no—
652C8—101no—
653C2×C3—42no—
654C2×C3—102no—
655C2×C3—202no—
656C2×C3D5×C22⋊Q811yescharacteristic
657C2×C3#6609111yescharacteristic
658C2×C3#6611211yescharacteristic
659C5C3×#308111yescharacteristic, complemented, Sylow
660C22—22no—
661C22—41no—
662C22—41no—
663C22—52no—
664C22—101no—
665C22—101no—
666C22—102no—
667C22—201no—
668C22—201no—
669C22—404no—
670C22C2×C3×D4×D511yescharacteristic
671C4—21no—
672C4—21no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—52no—
677C4—101no—
678C4—101no—
679C4—201no—
680C4—201no—
681C4—201no—
682C4C2×C3×Q8×D511yescharacteristic
683C4C3×D5×#4111yescharacteristic
684C3#1061269811yescharacteristic, direct product factor, Sylow
685C2—42no—
686C2—102no—
687C2—202no—
688C2C3×D5×C22⋊Q811yescharacteristic
689C2C3×#6609111yescharacteristic
690C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#474C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
hypercenterC3×#474D5
hypocenterC5C3×#3081
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#66063C2semidirect
3. C3×C5×#474C2semidirect
4. C3×#65373C2semidirect
5. C3×#65298C2semidirect
6. C3×#65180C2semidirect
7. C3×#65179C2semidirect
8. C3×#65170C2semidirect
9. C3×#65169C2semidirect
10. C3×#65136C2semidirect
11. C3×#65128C2semidirect
14. C3×#65055C2semidirect
15. C3×#65050C2semidirect
16. #10612698C3direct (N × H)
18. C3×C5×C4⋊Q8C22semidirect
32. C3×#4036C22semidirect
34. C3×#4034C22semidirect
39. C3×#4016C22semidirect
40. C3×C5×#107C22semidirect
41. C3×C5×#107C22semidirect
42. C3×C5×C4⋊C8C22semidirect
49. C3×#3950C22semidirect
50. C3×#3949C22semidirect
51. C3×#3946C22semidirect
52. C3×#3946C22semidirect
55. C3×#3940C22semidirect
56. C3×#3940C22semidirect
57. C3×#3940C22semidirect
58. C3×#3939C22semidirect
59. C3×C4⋊#168C22semidirect
61. #66063C2×C3semidirect
63. C5×#474C2×C3semidirect
64. #65373C2×C3semidirect
65. #65298C2×C3semidirect
66. #65180C2×C3semidirect
67. #65179C2×C3semidirect
68. #65170C2×C3semidirect
69. #65169C2×C3semidirect
70. #65136C2×C3semidirect
71. #65128C2×C3semidirect
74. #65055C2×C3semidirect
75. #65050C2×C3semidirect
83. C3×D4×D5Q8semidirect
132. C3×#474D5semidirect
139. C5×C4⋊Q8C22×C3semidirect
153. #4036C22×C3semidirect
155. #4034C22×C3semidirect
160. #4016C22×C3semidirect
161. C5×#107C22×C3semidirect
162. C5×#107C22×C3semidirect
163. C5×C4⋊C8C22×C3semidirect
170. #3950C22×C3semidirect
171. #3949C22×C3semidirect
172. #3946C22×C3semidirect
173. #3946C22×C3semidirect
176. #3940C22×C3semidirect
177. #3940C22×C3semidirect
178. #3940C22×C3semidirect
179. #3939C22×C3semidirect
180. C4⋊#168C22×C3semidirect
223. C3×C4⋊Q8C2×D5semidirect
243. C3×#107C2×D5semidirect
244. C3×#107C2×D5semidirect
252. C3×C4⋊C8C2×D5semidirect
268. D4×D5C3×Q8semidirect
317. #474C3×D5semidirect
435. C4⋊Q8C2×C3×D5semidirect
455. #107C2×C3×D5semidirect
456. #107C2×C3×D5semidirect
464. C4⋊C8C2×C3×D5semidirect
586. C3×C5#3081semidirect
659. C5C3×#3081semidirect
684. C3#10612698direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660632
C3×#658792
C3×C5×#4742
C3×#653732
C3×#652982
C3×#651802
C3×#651792
C3×#651702
C3×#651692
C3×#651362
C3×#651282
C3×#650592
C3×D5×#1022
C3×#650552
C3×#650502
#106126983
C3×#30815