Finite Group Databasebeta

← C3×#10610553 #14430214

Subgroups — C3×#10610553 #14430214

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×Dic5C211yesmaximal, characteristic
2C3×#65851C211yesmaximal, characteristic, complemented
3C3×C5×#416C211yesmaximal, characteristic
4C3×#65522C211yesmaximal, characteristic
5C3×#65395C211yesmaximal, characteristic, complemented
6C2×C3×#3946C211yesmaximal, characteristic, complemented
7C3×#65287C211yesmaximal, characteristic, complemented
8C3×#65088C211yesmaximal, characteristic, complemented
9C3×#65085C211yesmaximal, characteristic, complemented
10C3×#65083C211yesmaximal, characteristic, complemented
11C3×#65080C211yesmaximal, characteristic, complemented
12C3×#65055C211yesmaximal, characteristic, complemented
13C3×#65052C211yesmaximal, characteristic, complemented
14C3×#65050C211yesmaximal, characteristic, complemented
15C3×#65048C211yesmaximal, characteristic, complemented
16#10610553C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×C8C2211yescharacteristic
19C3×C5×#117C2211yescharacteristic
20C3×Q8×Dic5C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×D4×Dic5—21no—
23C3×D4×Dic5—21no—
24C3×D4×Dic5C2211yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×#4072—21no—
27C3×#4072C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29C2×C3×C4×Dic5—21no—
30C2×C3×C4×Dic5C2211yescharacteristic
31C22×C3×#168C2211yescharacteristic
32C3×#4036C2211yescharacteristic
33C3×#4036C2211yescharacteristic
34C3×#4034C2211yescharacteristic
35C3×#4034C2211yescharacteristic
36C3×#4024—21no—
37C3×#4024—21no—
38C3×C4×Dic10—21no—
39C3×C4×Dic10—21no—
40C3×C5×#103C2211yescharacteristic
41C3×C5×#103C2211yescharacteristic
42C3×C5×#102C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3950C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3949C2211yescharacteristic
51C3×#3949C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×#3946C2211yescharacteristic
56C3×#3940C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×#3939C2211yescharacteristic
60C3×#3076—51nomaximal, Hall
61#41×Dic5C2×C311yescharacteristic
62#65851C2×C311yescharacteristic, complemented
63C5×#416C2×C311yescharacteristic
64#65522C2×C311yescharacteristic
65#65395C2×C311yescharacteristic, complemented
66C2×#3946C2×C311yescharacteristic, complemented
67#65287C2×C311yescharacteristic, complemented
68#65088C2×C311yescharacteristic, complemented
69#65085C2×C311yescharacteristic, complemented
70#65083C2×C311yescharacteristic, complemented
71#65080C2×C311yescharacteristic, complemented
72#65055C2×C311yescharacteristic, complemented
73#65052C2×C311yescharacteristic, complemented
74#65050C2×C311yescharacteristic, complemented
75#65048C2×C311yescharacteristic, complemented
76C3×C5×#41—22no—
77C3×C5×#41Q814yescomplemented
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×Dic5—21no—
84C22×C3×Dic5—21no—
85C22×C3×Dic5D411yescharacteristic
86C22×C3×Dic5D411yescharacteristic
87C2×C3×Dic10—21no—
88C2×C3×Dic10—21no—
89C2×C3×C5×C8—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95C3×C42×C5—21no—
96C3×C22⋊Dic5—21no—
97C3×C22⋊Dic5—21no—
98C3×C22⋊Dic5—21no—
99C3×C22⋊Dic5—21no—
100C3×C4⋊Dic5—21no—
101C3×C4⋊Dic5—21no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×C4×Dic5—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5—21no—
115C3×C4×Dic5—21no—
116C3×C4×Dic5D411yescharacteristic
117C3×C4×Dic5D411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119C3×C4×Dic5C2311yescharacteristic
120C2×C3×#168—22no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C3×#533—51no—
124C3×C4×#41—51no—
125C3×#479—51no—
126C3×#479—51no—
127C3×#478—51no—
128C3×#478—51no—
129C3×#477—51no—
130C3×#476—51no—
131C3×#475—51no—
132C3×#474—51no—
133C3×#427—51no—
134C3×#427—51no—
135C2×C3×C4⋊C8—51no—
136C3×#416—51no—
137C3×#416D511yescharacteristic
138C2×C5×#41C22×C311yescharacteristic
139C22×C5×C8C22×C311yescharacteristic
140C5×#117C22×C311yescharacteristic
141Q8×Dic5C22×C311yescharacteristic
142Q8×Dic5C22×C311yescharacteristic
143D4×Dic5—21no—
144D4×Dic5—21no—
145D4×Dic5C22×C311yescharacteristic
146D4×Dic5C22×C311yescharacteristic
147#4072—21no—
148#4072C22×C311yescharacteristic
149#4072C22×C311yescharacteristic
150C2×C4×Dic5—21no—
151C2×C4×Dic5C22×C311yescharacteristic
152C22×#168C22×C311yescharacteristic
153#4036C22×C311yescharacteristic
154#4036C22×C311yescharacteristic
155#4034C22×C311yescharacteristic
156#4034C22×C311yescharacteristic
157#4024—21no—
158#4024—21no—
159C4×Dic10—21no—
160C4×Dic10—21no—
161C5×#103C22×C311yescharacteristic
162C5×#103C22×C311yescharacteristic
163C5×#102C22×C311yescharacteristic
164C5×#102C22×C311yescharacteristic
165#3967C22×C311yescharacteristic
166#3967C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169#3950C22×C311yescharacteristic
170#3950C22×C311yescharacteristic
171#3949C22×C311yescharacteristic
172#3949C22×C311yescharacteristic
173#3946C22×C311yescharacteristic
174#3946C22×C311yescharacteristic
175#3946C22×C311yescharacteristic
176#3946C22×C311yescharacteristic
177#3940C22×C311yescharacteristic
178#3940C22×C311yescharacteristic
179#3939C22×C311yescharacteristic
180#3939C22×C311yescharacteristic
181#3076—51noSylow
182C23×C3×C5—21no—
183C23×C3×C5C2×D411yescharacteristic
184C3×C5×Q8—21no—
185C3×C5×Q8C2×Q812yes—
186C3×C5×D4—24no—
187C3×C5×D4—21no—
188C3×C5×D4C2×Q812yes—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—24no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2×Q812yes—
195C2×C3×C4×C5#4112yes—
196C2×C3×C4×C5C2411yescharacteristic
197C2×C3×Dic5—22no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—41no—
203C2×C3×Dic5—42no—
204C2×C3×Dic5—42no—
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C3×Dic10—42no—
210C3×Dic10—42no—
211C3×C5×C8—21no—
212C3×C5×C8—21no—
213C3×#168—21no—
214C3×#168—21no—
215C2×C3×#41C2×D511yescharacteristic
216C22×C3×C8—51no—
217C22×C3×C8C2×D511yescharacteristic
218C3×C4⋊Q8—51no—
219C3×C4⋊Q8—51no—
220C3×#125—51no—
221C3×#125—51no—
222C3×C22⋊Q8—101no—
223C3×C22⋊Q8—101no—
224C3×C4×Q8—51no—
225C3×C4×Q8—51no—
226C3×C4×Q8—101no—
227C3×C4×Q8—101no—
228C3×C4×D4—51no—
229C3×C4×D4—51no—
230C3×C4×D4—101no—
231C3×C4×D4—101no—
232C3×#117—51no—
233C3×#117—51no—
234C3×#117—101no—
235C3×#117C2×D511yescharacteristic
236C2×C3×C42—51no—
237C2×C3×C42—101no—
238C3×#107—51no—
239C3×#107—51no—
240C3×#107—51no—
241C3×#107—51no—
242C3×#106—51no—
243C3×#106—51no—
244C3×#106—51no—
245C3×#106—51no—
246C3×C4⋊C8—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×C4⋊C8—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103C2×D511yescharacteristic
253C3×#103C2×D511yescharacteristic
254C3×#102—51no—
255C3×#102—51no—
256C3×#102C2×D511yescharacteristic
257C3×#102C2×D511yescharacteristic
258C5×#41—22no—
259C5×#41C3×Q814yescomplemented
260C2×C5×Q8C23×C311yescharacteristic
261C2×C5×D4—21no—
262C2×C5×D4C23×C311yescharacteristic
263C22×C4×C5—21no—
264C22×C4×C5C23×C311yescharacteristic
265C22×Dic5—21no—
266C22×Dic5—21no—
267C22×Dic5C3×D411yescharacteristic
268C22×Dic5C3×D411yescharacteristic
269C2×Dic10—21no—
270C2×Dic10—21no—
271C2×C5×C8—22no—
272C2×C5×C8C23×C311yescharacteristic
273C2×C5×C8C23×C311yescharacteristic
274C5×C4⋊C4C23×C311yescharacteristic
275C5×C4⋊C4C23×C311yescharacteristic
276C5×C22⋊C4—21no—
277C42×C5—21no—
278C22⋊Dic5—21no—
279C22⋊Dic5—21no—
280C22⋊Dic5—21no—
281C22⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—21no—
286C4⋊Dic5C23×C311yescharacteristic
287C4⋊Dic5C23×C311yescharacteristic
288C4⋊Dic5C23×C311yescharacteristic
289C4⋊Dic5C23×C311yescharacteristic
290#683—21no—
291#683—21no—
292#683—21no—
293#683—21no—
294C4×Dic5—21no—
295C4×Dic5—21no—
296C4×Dic5—21no—
297C4×Dic5—21no—
298C4×Dic5C3×D411yescharacteristic
299C4×Dic5C3×D411yescharacteristic
300C4×Dic5C23×C311yescharacteristic
301C4×Dic5C23×C311yescharacteristic
302C2×#168—22no—
303C2×#168C23×C311yescharacteristic
304C2×#168C23×C311yescharacteristic
305#533—51no—
306C4×#41—51no—
307#479—51no—
308#479—51no—
309#478—51no—
310#478—51no—
311#477—51no—
312#476—51no—
313#475—51no—
314#474—51no—
315#427—51no—
316#427—51no—
317C2×C4⋊C8—51no—
318#416—51no—
319#416C3×D511yescharacteristic
320C22×C3×C5—21no—
321C22×C3×C5—21no—
322C22×C3×C5—22no—
323C22×C3×C5—41no—
324C22×C3×C5—41no—
325C22×C3×C5C22⋊Q812yes—
326C22×C3×C5C22×D411yescharacteristic
327C3×C4×C5—22no—
328C3×C4×C5—41no—
329C3×C4×C5—41no—
330C3×C4×C5C22⋊Q812yes—
331C3×C4×C5C22×Q811yescharacteristic
332C3×C4×C5C2×#4111yescharacteristic
333C3×Dic5—21no—
334C3×Dic5—21no—
335C3×Dic5—21no—
336C3×Dic5—41no—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C3×Dic5—41no—
340C3×Dic5#13512yes—
341C3×#41—22no—
342C3×#41Dic1014yescomplemented
343C2×C3×Q8—101no—
344C2×C3×Q8—101no—
345C2×C3×Q8C22×D511yescharacteristic
346C2×C3×D4—21no—
347C2×C3×D4C22×D511yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—101no—
352C22×C3×C4—101no—
353C22×C3×C4C22×D511yescharacteristic
354C2×C3×C8—22no—
355C2×C3×C8—51no—
356C2×C3×C8—51no—
357C2×C3×C8—102no—
358C2×C3×C8C22×D511yescharacteristic
359C2×C3×C8C22×D511yescharacteristic
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4—101no—
370C3×C4⋊C4—101no—
371C3×C4⋊C4—101no—
372C3×C4⋊C4C22×D511yescharacteristic
373C3×C4⋊C4C22×D511yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—101no—
376C3×C22⋊C4—101no—
377C3×C22⋊C4—101no—
378C3×C22⋊C4—101no—
379C3×C42—21no—
380C3×C42—51no—
381C3×C42—51no—
382C3×C42—51no—
383C3×C42—51no—
384C3×C42—101no—
385C3×C42—101no—
386C3×C42—101no—
387C3×C42—101no—
388C23×C5—21no—
389C23×C5C2×C3×D411yescharacteristic
390C5×Q8—21no—
391C5×Q8C2×C3×Q812yes—
392C5×D4—24no—
393C5×D4—21no—
394C5×D4C2×C3×Q812yes—
395C2×C4×C5—21no—
396C2×C4×C5—24no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5C2×C3×D411yescharacteristic
400C2×C4×C5C2×C3×Q812yes—
401C2×C4×C5C3×#4112yes—
402C2×C4×C5C24×C311yescharacteristic
403C2×Dic5—22no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—41no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411C2×Dic5C2×C3×D411yescharacteristic
412C2×Dic5C2×C3×D411yescharacteristic
413C2×Dic5C2×C3×D411yescharacteristic
414C2×Dic5C2×C3×D411yescharacteristic
415Dic10—42no—
416Dic10—42no—
417C5×C8—21no—
418C5×C8—21no—
419#168—21no—
420#168—21no—
421C2×#41C2×C3×D511yescharacteristic
422C22×C8—51no—
423C22×C8C2×C3×D511yescharacteristic
424C4⋊Q8—51no—
425C4⋊Q8—51no—
426#125—51no—
427#125—51no—
428C22⋊Q8—101no—
429C22⋊Q8—101no—
430C4×Q8—51no—
431C4×Q8—51no—
432C4×Q8—101no—
433C4×Q8—101no—
434C4×D4—51no—
435C4×D4—51no—
436C4×D4—101no—
437C4×D4—101no—
438#117—51no—
439#117—51no—
440#117—101no—
441#117C2×C3×D511yescharacteristic
442C2×C42—51no—
443C2×C42—101no—
444#107—51no—
445#107—51no—
446#107—51no—
447#107—51no—
448#106—51no—
449#106—51no—
450#106—51no—
451#106—51no—
452C4⋊C8—51no—
453C4⋊C8—51no—
454C4⋊C8—51no—
455C4⋊C8—51no—
456#103—51no—
457#103—51no—
458#103C2×C3×D511yescharacteristic
459#103C2×C3×D511yescharacteristic
460#102—51no—
461#102—51no—
462#102C2×C3×D511yescharacteristic
463#102C2×C3×D511yescharacteristic
464C2×C3×C5—22no—
465C2×C3×C5—42no—
466C2×C3×C5C2×C22⋊Q811yescharacteristic
467C2×C3×C5C2×#13511yescharacteristic
468C2×C3×C5#57511yescharacteristic
469C23×C3—21no—
470C23×C3D4×D511yescharacteristic
471C3×Q8—21no—
472C3×Q8—202no—
473C3×Q8—202no—
474C3×Q8C2×Dic1012yes—
475C3×D4—24no—
476C3×D4—21no—
477C3×D4C2×Dic1012yes—
478C2×C3×C4—21no—
479C2×C3×C4—24no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—51no—
483C2×C3×C4—51no—
484C2×C3×C4—51no—
485C2×C3×C4—51no—
486C2×C3×C4—102no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—202no—
492C2×C3×C4—201no—
493C2×C3×C4—202no—
494C2×C3×C4C2×Dic1012yes—
495C2×C3×C4D4×D511yescharacteristic
496C2×C3×C4#71112yes—
497C2×C3×C4C23×D511yescharacteristic
498C3×C8—21no—
499C3×C8—21no—
500C3×C8—101no—
501C3×C8—101no—
502C22×C5—21no—
503C22×C5—21no—
504C22×C5—22no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5C3×C22⋊Q812yes—
508C22×C5C22×C3×D411yescharacteristic
509C4×C5—22no—
510C4×C5—41no—
511C4×C5—41no—
512C4×C5C3×C22⋊Q812yes—
513C4×C5C22×C3×Q811yescharacteristic
514C4×C5C2×C3×#4111yescharacteristic
515Dic5—21no—
516Dic5—21no—
517Dic5—21no—
518Dic5—41no—
519Dic5—41no—
520Dic5—41no—
521Dic5—41no—
522Dic5C3×#13512yes—
523#41—22no—
524#41C3×Dic1014yescomplemented
525C2×Q8—101no—
526C2×Q8—101no—
527C2×Q8C22×C3×D511yescharacteristic
528C2×D4—21no—
529C2×D4C22×C3×D511yescharacteristic
530C22×C4—21no—
531C22×C4—51no—
532C22×C4—51no—
533C22×C4—101no—
534C22×C4—101no—
535C22×C4C22×C3×D511yescharacteristic
536C2×C8—22no—
537C2×C8—51no—
538C2×C8—51no—
539C2×C8—102no—
540C2×C8C22×C3×D511yescharacteristic
541C2×C8C22×C3×D511yescharacteristic
542C4⋊C4—51no—
543C4⋊C4—51no—
544C4⋊C4—51no—
545C4⋊C4—51no—
546C4⋊C4—101no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—101no—
550C4⋊C4—101no—
551C4⋊C4—101no—
552C4⋊C4—101no—
553C4⋊C4—101no—
554C4⋊C4C22×C3×D511yescharacteristic
555C4⋊C4C22×C3×D511yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—101no—
558C22⋊C4—101no—
559C22⋊C4—101no—
560C22⋊C4—101no—
561C42—21no—
562C42—51no—
563C42—51no—
564C42—51no—
565C42—51no—
566C42—101no—
567C42—101no—
568C42—101no—
569C42—101no—
570C3×C5#307611yescharacteristic, complemented, Hall
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—22no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3#402412yes—
577C22×C3C2×D4×D511yescharacteristic
578C3×C4—22no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—52no—
582C3×C4—101no—
583C3×C4—101no—
584C3×C4—101no—
585C3×C4—201no—
586C3×C4—201no—
587C3×C4—201no—
588C3×C4—201no—
589C3×C4#402412yes—
590C3×C4C22×Dic1011yescharacteristic
591C3×C4C2×#71111yescharacteristic
592C2×C5—22no—
593C2×C5—42no—
594C2×C5C2×C3×C22⋊Q811yescharacteristic
595C2×C5C2×C3×#13511yescharacteristic
596C2×C5C3×#57511yescharacteristic
597C23—21no—
598C23C3×D4×D511yescharacteristic
599Q8—21no—
600Q8—202no—
601Q8—202no—
602Q8C2×C3×Dic1012yes—
603D4—24no—
604D4—21no—
605D4C2×C3×Dic1012yes—
606C2×C4—21no—
607C2×C4—24no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—51no—
611C2×C4—51no—
612C2×C4—51no—
613C2×C4—51no—
614C2×C4—102no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—101no—
619C2×C4—202no—
620C2×C4—201no—
621C2×C4—202no—
622C2×C4C2×C3×Dic1012yes—
623C2×C4C3×D4×D511yescharacteristic
624C2×C4C3×#71112yes—
625C2×C4C23×C3×D511yescharacteristic
626C8—21no—
627C8—21no—
628C8—101no—
629C8—101no—
630C2×C3—22no—
631C2×C3—42no—
632C2×C3C2×#402411yescharacteristic
633C2×C3D5×#13511yescharacteristic
634C2×C3#6610211yescharacteristic
635C5C3×#307611yescharacteristic, complemented, Sylow
636C22—21no—
637C22—21no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22C3×#402412yes—
642C22C2×C3×D4×D511yescharacteristic
643C4—22no—
644C4—41no—
645C4—41no—
646C4—52no—
647C4—101no—
648C4—101no—
649C4—101no—
650C4—201no—
651C4—201no—
652C4—201no—
653C4—201no—
654C4C3×#402412yes—
655C4C22×C3×Dic1011yescharacteristic
656C4C2×C3×#71111yescharacteristic
657C3#1061055311yescharacteristic, direct product factor, Sylow
658C2—22no—
659C2—42no—
660C2C2×C3×#402411yescharacteristic
661C2C3×D5×#13511yescharacteristic
662C2C3×#6610211yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#416C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
hypercenterC3×#416D5
hypocenterC5C3×#3076
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
2. C3×#65851C2semidirect
5. C3×#65395C2semidirect
6. C2×C3×#3946C2semidirect
7. C3×#65287C2semidirect
8. C3×#65088C2semidirect
9. C3×#65085C2semidirect
10. C3×#65083C2semidirect
11. C3×#65080C2semidirect
12. C3×#65055C2semidirect
13. C3×#65052C2semidirect
14. C3×#65050C2semidirect
15. C3×#65048C2semidirect
16. #10610553C3direct (N × H)
62. #65851C2×C3semidirect
65. #65395C2×C3semidirect
66. C2×#3946C2×C3semidirect
67. #65287C2×C3semidirect
68. #65088C2×C3semidirect
69. #65085C2×C3semidirect
70. #65083C2×C3semidirect
71. #65080C2×C3semidirect
72. #65055C2×C3semidirect
73. #65052C2×C3semidirect
74. #65050C2×C3semidirect
75. #65048C2×C3semidirect
77. C3×C5×#41Q8semidirect
259. C5×#41C3×Q8semidirect
342. C3×#41Dic10semidirect
524. #41C3×Dic10semidirect
570. C3×C5#3076semidirect
635. C5C3×#3076semidirect
657. C3#10610553direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41×Dic52
C3×#658512
C3×C5×#4162
C3×#655222
C3×#653952
C2×C3×#39462
C3×#652872
C3×#650882
C3×#650852
C3×#650832
C3×#650802
C3×#650552
C3×#650522
C3×#650502
C3×#650482
#106105533
C3×#30765