Finite Group Databasebeta

← C3×#10611389 #14436337

Subgroups — C3×#10611389 #14436337

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65906C211yesmaximal, characteristic, complemented
2C3×#65895C211yesmaximal, characteristic
3C3×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C3×#65459C211yesmaximal, characteristic
5C3×#65455C211yesmaximal, characteristic, complemented
6C3×#65319C211yesmaximal, characteristic, complemented
7C3×#65307C211yesmaximal, characteristic, complemented
8C3×#65156C211yesmaximal, characteristic, complemented
9C3×#65143C211yesmaximal, characteristic, complemented
10C3×#65097C211yesmaximal, characteristic, complemented
11C3×#65083C211yesmaximal, characteristic, complemented
12C3×#65073C211yesmaximal, characteristic
13C3×#65056C211yesmaximal, characteristic, complemented
14C3×C4×Dic20C211yesmaximal, characteristic, complemented
15C3×#64979C211yesmaximal, characteristic, complemented
16#10611389C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C2×C3×#689C2211yescharacteristic
23C3×#4084C2211yescharacteristic
24C3×#4082C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×#4075—21no—
27C3×#4070—21no—
28C2×C3×Dic20C2211yescharacteristic
29C3×#4043C2211yescharacteristic
30C3×#4038—21no—
31C3×#4038C2211yescharacteristic
32C3×#4034C2211yescharacteristic
33C3×#4033—21no—
34C3×#4033C2211yescharacteristic
35C3×#4031—21no—
36C3×#4025—21no—
37C3×#4018—21no—
38C3×#4018C2211yescharacteristic
39C3×C4×Dic10—21no—
40C3×C4×Dic10C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45C3×C4×C5×C8C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3952C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3950C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×#3935C2211yescharacteristic
60C3×#3121—51nomaximal, Hall
61#65906C2×C311yescharacteristic, complemented
62#65895C2×C311yescharacteristic
63C4×C5×SD16C2×C311yescharacteristic, complemented
64#65459C2×C311yescharacteristic
65#65455C2×C311yescharacteristic, complemented
66#65319C2×C311yescharacteristic, complemented
67#65307C2×C311yescharacteristic, complemented
68#65156C2×C311yescharacteristic, complemented
69#65143C2×C311yescharacteristic, complemented
70#65097C2×C311yescharacteristic, complemented
71#65083C2×C311yescharacteristic, complemented
72#65073C2×C311yescharacteristic
73#65056C2×C311yescharacteristic, complemented
74C4×Dic20C2×C311yescharacteristic, complemented
75#64979C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×C3×C22⋊D5—21no—
80C3×Q8×D5—22no—
81C3×Q8×D5—22no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5C2311yescharacteristic
84C2×C3×Dic10—21no—
85C2×C3×Dic10—21no—
86C2×C3×Dic10C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×SD16—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95C3×C42×C5—21no—
96C3×C42×C5C2311yescharacteristic
97C3×C22⋊Dic5—21no—
98C3×C22⋊Dic5—21no—
99C3×C22⋊Dic5—21no—
100C3×#689—22no—
101C3×#687—22no—
102C3×#685—21no—
103C3×#685—21no—
104C3×#685D411yescharacteristic
105C3×#685D411yescharacteristic
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5—21no—
108C3×C4⋊Dic5C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
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×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C3×Dic20—22no—
125C3×#542—51no—
126C3×#519—51no—
127C3×#485—51no—
128C3×#482—51no—
129C3×#477—51no—
130C3×#475—51no—
131C3×#464—51no—
132C3×#464—51no—
133C3×#451—51no—
134C3×#448—51no—
135C3×#441—51no—
136C3×#440—51no—
137C3×C4×Q16—51no—
138C3×C4×SD16D511yescharacteristic, complemented
139C3×#433—51no—
140C2×Q8×D5C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C4×C5×Q8C22×C311yescharacteristic
143C4×C5×D4C22×C311yescharacteristic
144Q8×Dic5C22×C311yescharacteristic
145C2×#689C22×C311yescharacteristic
146#4084C22×C311yescharacteristic
147#4082C22×C311yescharacteristic
148C2×#687C22×C311yescharacteristic
149#4075—21no—
150#4070—21no—
151C2×Dic20C22×C311yescharacteristic
152#4043C22×C311yescharacteristic
153#4038—21no—
154#4038C22×C311yescharacteristic
155#4034C22×C311yescharacteristic
156#4033—21no—
157#4033C22×C311yescharacteristic
158#4031—21no—
159#4025—21no—
160#4018—21no—
161#4018C22×C311yescharacteristic
162C4×Dic10—21no—
163C4×Dic10C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165C5×#106C22×C311yescharacteristic
166C5×#103C22×C311yescharacteristic
167C5×#102C22×C311yescharacteristic
168C4×C5×C8C22×C311yescharacteristic
169#3967C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3952C22×C311yescharacteristic
172#3952C22×C311yescharacteristic
173#3950C22×C311yescharacteristic
174#3948C22×C311yescharacteristic
175#3948C22×C311yescharacteristic
176#3946C22×C311yescharacteristic
177#3946C22×C311yescharacteristic
178#3942C22×C311yescharacteristic
179#3942C22×C311yescharacteristic
180#3940C22×C311yescharacteristic
181#3939C22×C311yescharacteristic
182#3935C22×C311yescharacteristic
183#3121—51noSylow
184C23×C3×C5—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C3×C5×D4—21no—
189C3×C5×D4—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—81no—
194C2×C3×C4×C5C2×D411yescharacteristic
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2411yescharacteristic
197C3×C22⋊D5—81no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×C4×D5—24no—
206C3×C4×D5—21no—
207C3×C4×D5—21no—
208C3×Dic10—24no—
209C3×Dic10—21no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—81no—
213C3×Dic10#4112yes—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3×#168—21no—
217C3×#168—21no—
218C22×C3×Q8—51no—
219C2×C3×Q16—51no—
220C2×C3×Q16—51no—
221C2×C3×SD16—51no—
222C2×C3×SD16C2×D511yescharacteristic
223C3×C4⋊Q8—51no—
224C3×#126—101no—
225C3×#124—51no—
226C3×#124—101no—
227C3×#123—101no—
228C3×C22⋊Q8—51no—
229C3×C22⋊Q8—101no—
230C3×#121—51no—
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×Q8—51no—
235C3×C4×Q8—101no—
236C3×C4×Q8—101no—
237C3×C4×Q8C2×D511yescharacteristic
238C3×C4×D4C2×D511yescharacteristic
239C3×#117—51no—
240C3×#117—51no—
241C3×#117—101no—
242C3×#117—101no—
243C3×#107—51no—
244C3×#107—51no—
245C3×#106—51no—
246C3×#106C2×D511yescharacteristic
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×#103—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103C2×D511yescharacteristic
255C3×#102—51no—
256C3×#102C2×D511yescharacteristic
257C3×C22⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×#97—51no—
260C3×C4×C8C2×D511yescharacteristic
261C2×C5×Q8C23×C311yescharacteristic
262C2×C5×D4C23×C311yescharacteristic
263C22×C4×C5—21no—
264C2×C22⋊D5—21no—
265Q8×D5—22no—
266Q8×D5—22no—
267C2×C4×D5—21no—
268C2×C4×D5C23×C311yescharacteristic
269C2×Dic10—21no—
270C2×Dic10—21no—
271C2×Dic10C23×C311yescharacteristic
272C2×Dic10C23×C311yescharacteristic
273C5×SD16—22no—
274C2×C5×C8C23×C311yescharacteristic
275C2×C5×C8C23×C311yescharacteristic
276C5×C4⋊C4—21no—
277C5×C4⋊C4C23×C311yescharacteristic
278C5×C4⋊C4C23×C311yescharacteristic
279C5×C22⋊C4—21no—
280C42×C5—21no—
281C42×C5C23×C311yescharacteristic
282C22⋊Dic5—21no—
283C22⋊Dic5—21no—
284C22⋊Dic5—21no—
285#689—22no—
286#687—22no—
287#685—21no—
288#685—21no—
289#685C3×D411yescharacteristic
290#685C3×D411yescharacteristic
291C4⋊Dic5—21no—
292C4⋊Dic5—21no—
293C4⋊Dic5C23×C311yescharacteristic
294C4⋊Dic5C23×C311yescharacteristic
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×Dic5—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C4×Dic5C23×C311yescharacteristic
307C2×#168C23×C311yescharacteristic
308C2×#168C23×C311yescharacteristic
309Dic20—22no—
310#542—51no—
311#519—51no—
312#485—51no—
313#482—51no—
314#477—51no—
315#475—51no—
316#464—51no—
317#464—51no—
318#451—51no—
319#448—51no—
320#441—51no—
321#440—51no—
322C4×Q16—51no—
323C4×SD16C3×D511yescharacteristic, complemented
324#433—51no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—21no—
330C2×C3×D5—21no—
331C2×C3×D5—21no—
332C3×C4×C5—22no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—41no—
336C3×C4×C5—41no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339C3×Dic5—21no—
340C3×Dic5—22no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C2×C3×Q8—51no—
347C2×C3×Q8—51no—
348C2×C3×Q8—101no—
349C2×C3×Q8—101no—
350C2×C3×Q8—102no—
351C2×C3×Q8—102no—
352C2×C3×Q8C22×D511yescharacteristic
353C2×C3×D4—101no—
354C2×C3×D4C22×D511yescharacteristic
355C22×C3×C4—21no—
356C22×C3×C4—51no—
357C22×C3×C4—101no—
358C3×Q16—102no—
359C3×Q16—102no—
360C3×SD16—22no—
361C3×SD16—102no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8C22×D511yescharacteristic
365C2×C3×C8C22×D511yescharacteristic
366C3×C4⋊C4—21no—
367C3×C4⋊C4—51no—
368C3×C4⋊C4—51no—
369C3×C4⋊C4—51no—
370C3×C4⋊C4—51no—
371C3×C4⋊C4—101no—
372C3×C4⋊C4—101no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4—101no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4C22×D511yescharacteristic
378C3×C4⋊C4C22×D511yescharacteristic
379C3×C22⋊C4—21no—
380C3×C22⋊C4—51no—
381C3×C22⋊C4—51no—
382C3×C22⋊C4—101no—
383C3×C22⋊C4—101no—
384C3×C22⋊C4—101no—
385C3×C22⋊C4—101no—
386C3×C22⋊C4—101no—
387C3×C42—21no—
388C3×C42—51no—
389C3×C42—101no—
390C3×C42—101no—
391C3×C42—101no—
392C3×C42—101no—
393C3×C42—101no—
394C3×C42C22×D511yescharacteristic
395C23×C5—21no—
396C22×D5C2×C3×D411yescharacteristic
397C5×Q8—21no—
398C5×Q8C3×#4112yes—
399C5×D4—21no—
400C5×D4—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—81no—
405C2×C4×C5C2×C3×D411yescharacteristic
406C2×C4×C5C2×C3×D411yescharacteristic
407C2×C4×C5C24×C311yescharacteristic
408C22⋊D5—81no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5C2×C3×D411yescharacteristic
414C2×Dic5C2×C3×D411yescharacteristic
415C2×Dic5C2×C3×D411yescharacteristic
416C4×D5—24no—
417C4×D5—21no—
418C4×D5—21no—
419Dic10—24no—
420Dic10—21no—
421Dic10—21no—
422Dic10—21no—
423Dic10—81no—
424Dic10C3×#4112yes—
425C5×C8—21no—
426C5×C8—21no—
427#168—21no—
428#168—21no—
429C22×Q8—51no—
430C2×Q16—51no—
431C2×Q16—51no—
432C2×SD16—51no—
433C2×SD16C2×C3×D511yescharacteristic
434C4⋊Q8—51no—
435#126—101no—
436#124—51no—
437#124—101no—
438#123—101no—
439C22⋊Q8—51no—
440C22⋊Q8—101no—
441#121—51no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—51no—
445C4×Q8—51no—
446C4×Q8—101no—
447C4×Q8—101no—
448C4×Q8C2×C3×D511yescharacteristic
449C4×D4C2×C3×D511yescharacteristic
450#117—51no—
451#117—51no—
452#117—101no—
453#117—101no—
454#107—51no—
455#107—51no—
456#106—51no—
457#106C2×C3×D511yescharacteristic
458C4⋊C8—51no—
459C4⋊C8—51no—
460#103—51no—
461#103—51no—
462#103—51no—
463#103—51no—
464#103—51no—
465#103C2×C3×D511yescharacteristic
466#102—51no—
467#102C2×C3×D511yescharacteristic
468C22⋊C8—51no—
469C22⋊C8—51no—
470#97—51no—
471C4×C8C2×C3×D511yescharacteristic
472C2×C3×C5—81no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—41no—
477C23×C3—21no—
478C23×C3—51no—
479C3×Q8—21no—
480C3×Q8—52no—
481C3×Q8—104no—
482C3×Q8—101no—
483C3×Q8—101no—
484C3×Q8—101no—
485C3×Q8—401no—
486C3×Q8#70912yes—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—401no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—51no—
494C2×C3×C4—51no—
495C2×C3×C4—51no—
496C2×C3×C4—81no—
497C2×C3×C4—104no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4D4×D511yescharacteristic
505C2×C3×C4D4×D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5C22×C3×D411yescharacteristic
515C2×D5—21no—
516C2×D5—21no—
517C2×D5—21no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—22no—
521C4×C5—41no—
522C4×C5—41no—
523C4×C5C2×C3×#4111yescharacteristic
524C4×C5C2×C3×#4111yescharacteristic
525Dic5—21no—
526Dic5—21no—
527Dic5—21no—
528Dic5—22no—
529Dic5—41no—
530Dic5—41no—
531Dic5—41no—
532C2×Q8—51no—
533C2×Q8—51no—
534C2×Q8—101no—
535C2×Q8—101no—
536C2×Q8—102no—
537C2×Q8—102no—
538C2×Q8C22×C3×D511yescharacteristic
539C2×D4—101no—
540C2×D4C22×C3×D511yescharacteristic
541C22×C4—21no—
542C22×C4—51no—
543C22×C4—101no—
544Q16—102no—
545Q16—102no—
546SD16—22no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8C22×C3×D511yescharacteristic
551C2×C8C22×C3×D511yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4C22×C3×D511yescharacteristic
564C4⋊C4C22×C3×D511yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—51no—
567C22⋊C4—51no—
568C22⋊C4—101no—
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C42—21no—
574C42—51no—
575C42—101no—
576C42—101no—
577C42—101no—
578C42—101no—
579C42—101no—
580C42C22×C3×D511yescharacteristic
581C3×C5#312111yescharacteristic, complemented, Hall
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—101no—
586C22×C3—101no—
587C22×C3—101no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—101no—
597C3×C4—102no—
598C3×C4—201no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4C2×#70911yescharacteristic
602C3×C4D5×#4111yescharacteristic
603C2×C5—81no—
604C2×C5C3×#52511yescharacteristic
605C2×C5C3×#57711yescharacteristic
606C2×C5C3×#57811yescharacteristic
607D5—41no—
608C23—21no—
609C23—51no—
610Q8—21no—
611Q8—52no—
612Q8—104no—
613Q8—101no—
614Q8—101no—
615Q8—101no—
616Q8—401no—
617Q8C3×#70912yes—
618D4—21no—
619D4—21no—
620D4—401no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—51no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—81no—
628C2×C4—104no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—101no—
635C2×C4C3×D4×D511yescharacteristic
636C2×C4C3×D4×D511yescharacteristic
637C2×C4C23×C3×D511yescharacteristic
638C8—21no—
639C8—21no—
640C8—101no—
641C8—101no—
642C2×C3—81no—
643C2×C3—201no—
644C2×C3#6588111yescharacteristic
645C2×C3#6609611yescharacteristic
646C2×C3#6610511yescharacteristic
647C5C3×#312111yescharacteristic, complemented, Sylow
648C22—41no—
649C22—41no—
650C22—41no—
651C22—101no—
652C22—101no—
653C22—101no—
654C22C2×C3×D4×D511yescharacteristic
655C4—21no—
656C4—22no—
657C4—21no—
658C4—41no—
659C4—41no—
660C4—101no—
661C4—101no—
662C4—102no—
663C4—101no—
664C4—201no—
665C4—201no—
666C4—201no—
667C4C2×C3×#70911yescharacteristic
668C4C3×D5×#4111yescharacteristic
669C3#1061138911yescharacteristic, direct product factor, Sylow
670C2—81no—
671C2—201no—
672C2C3×#6588111yescharacteristic
673C2C3×#6609611yescharacteristic
674C2C3×#6610511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC3×#4084C22
hypercenterC3×C4×SD16D5
hypocenterC5C3×#3121
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#65906C2semidirect
3. C3×C4×C5×SD16C2semidirect
5. C3×#65455C2semidirect
6. C3×#65319C2semidirect
7. C3×#65307C2semidirect
8. C3×#65156C2semidirect
9. C3×#65143C2semidirect
10. C3×#65097C2semidirect
11. C3×#65083C2semidirect
13. C3×#65056C2semidirect
14. C3×C4×Dic20C2semidirect
15. C3×#64979C2semidirect
16. #10611389C3direct (N × H)
61. #65906C2×C3semidirect
63. C4×C5×SD16C2×C3semidirect
65. #65455C2×C3semidirect
66. #65319C2×C3semidirect
67. #65307C2×C3semidirect
68. #65156C2×C3semidirect
69. #65143C2×C3semidirect
70. #65097C2×C3semidirect
71. #65083C2×C3semidirect
73. #65056C2×C3semidirect
74. C4×Dic20C2×C3semidirect
75. #64979C2×C3semidirect
138. C3×C4×SD16D5semidirect
323. C4×SD16C3×D5semidirect
581. C3×C5#3121semidirect
647. C5C3×#3121semidirect
669. C3#10611389direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659062
C3×#658952
C3×C4×C5×SD162
C3×#654592
C3×#654552
C3×#653192
C3×#653072
C3×#651562
C3×#651432
C3×#650972
C3×#650832
C3×#650732
C3×#650562
C3×C4×Dic202
C3×#649792
#106113893
C3×#31215