Finite Group Databasebeta

← C3×#10611300 #14471760

Subgroups — C3×#10611300 #14471760

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65893C211yesmaximal, characteristic, complemented
2C3×#65873C211yesmaximal, characteristic, complemented
3C3×C4×C5×D8C211yesmaximal, characteristic, complemented
4C3×#65442C211yesmaximal, characteristic, complemented
5C3×#65439C211yesmaximal, characteristic
6C3×#65305C211yesmaximal, characteristic, complemented
7C3×#65298C211yesmaximal, characteristic, complemented
8C3×#65180C211yesmaximal, characteristic, complemented
9C3×#65164C211yesmaximal, characteristic, complemented
10C3×#65057C211yesmaximal, characteristic, complemented
11C3×#65049C211yesmaximal, characteristic, complemented
12C3×#65047C211yesmaximal, characteristic, complemented
13C3×#65045C211yesmaximal, characteristic, complemented
14C3×#64986C211yesmaximal, characteristic, complemented
15C3×C8×Dic10C211yesmaximal, characteristic, complemented
16#10611300C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×D8C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C3×#4086C2211yescharacteristic
21C3×#4082C2211yescharacteristic
22C3×D4×Dic5C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic
24C2×C3×#687C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×#4075—21no—
27C3×C4×C22⋊D5—21no—
28C3×#4070—21no—
29C2×C3×#683—21no—
30C3×#4039C2211yescharacteristic
31C3×#4036C2211yescharacteristic
32C3×#4034C2211yescharacteristic
33C3×#4033C2211yescharacteristic
34C3×#4031—21no—
35C3×#4029—21no—
36C3×#4024—21no—
37C3×#4024—21no—
38C3×#4021C2211yescharacteristic
39C3×#4016C2211yescharacteristic
40C3×C4×Dic10C2211yescharacteristic
41C3×C5×#107C2211yescharacteristic
42C3×C5×#102C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C4×C5×C8C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3953C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3948C2211yescharacteristic
50C3×#3948C2211yescharacteristic
51C3×#3946C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic
54C3×C8×Dic5C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×C4⋊#168C2211yescharacteristic
60C3×#3361—51nomaximal, Hall
61#65893C2×C311yescharacteristic, complemented
62#65873C2×C311yescharacteristic, complemented
63C4×C5×D8C2×C311yescharacteristic, complemented
64#65442C2×C311yescharacteristic, complemented
65#65439C2×C311yescharacteristic
66#65305C2×C311yescharacteristic, complemented
67#65298C2×C311yescharacteristic, complemented
68#65180C2×C311yescharacteristic, complemented
69#65164C2×C311yescharacteristic, complemented
70#65057C2×C311yescharacteristic, complemented
71#65049C2×C311yescharacteristic, complemented
72#65047C2×C311yescharacteristic, complemented
73#65045C2×C311yescharacteristic, complemented
74#64986C2×C311yescharacteristic, complemented
75C8×Dic10C2×C311yescharacteristic, complemented
76C2×C3×C5×D4C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5—21no—
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C22×C3×Dic5—21no—
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×Dic10—21no—
87C2×C3×Dic10D411yescharacteristic
88C2×C3×Dic10C2311yescharacteristic
89C3×C5×D8—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97C3×C22⋊Dic5—21no—
98C3×C22⋊Dic5—21no—
99C3×C22⋊Dic5—21no—
100C3×C22⋊Dic5—21no—
101C3×#687—22no—
102C3×#686—22no—
103C3×#685—21no—
104C3×#685—21no—
105C3×#685—21no—
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5D411yescharacteristic
108C3×C4⋊Dic5C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683—21no—
115C3×#683D411yescharacteristic
116C3×#683D411yescharacteristic
117C3×C4×Dic5—21no—
118C3×C4×Dic5C2311yescharacteristic
119C3×C4×Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C3×#559—51no—
123C3×#554—51no—
124C3×#488—51no—
125C3×#488—51no—
126C3×#486—51no—
127C3×#478—51no—
128C3×#478—51no—
129C3×#477—51no—
130C3×#463—51no—
131C3×#463—51no—
132C3×#459—51no—
133C3×C8×Q8—51no—
134C3×C4×SD16—51no—
135C3×C4×D8—51no—
136C3×C4×D8D511yescharacteristic, complemented
137C2×C5×D8C22×C311yescharacteristic
138C4×C5×D4C22×C311yescharacteristic
139C4×C5×D4C22×C311yescharacteristic
140#4086C22×C311yescharacteristic
141#4082C22×C311yescharacteristic
142D4×Dic5C22×C311yescharacteristic
143D4×Dic5C22×C311yescharacteristic
144C2×#687C22×C311yescharacteristic
145C2×#686C22×C311yescharacteristic
146#4075—21no—
147C4×C22⋊D5—21no—
148#4070—21no—
149C2×#683—21no—
150#4039C22×C311yescharacteristic
151#4036C22×C311yescharacteristic
152#4034C22×C311yescharacteristic
153#4033C22×C311yescharacteristic
154#4031—21no—
155#4029—21no—
156#4024—21no—
157#4024—21no—
158#4021C22×C311yescharacteristic
159#4016C22×C311yescharacteristic
160C4×Dic10C22×C311yescharacteristic
161C5×#107C22×C311yescharacteristic
162C5×#102C22×C311yescharacteristic
163C5×#102C22×C311yescharacteristic
164C4×C5×C8C22×C311yescharacteristic
165#3964C22×C311yescharacteristic
166#3964C22×C311yescharacteristic
167#3953C22×C311yescharacteristic
168#3953C22×C311yescharacteristic
169#3948C22×C311yescharacteristic
170#3948C22×C311yescharacteristic
171#3946C22×C311yescharacteristic
172#3946C22×C311yescharacteristic
173C8×Dic5C22×C311yescharacteristic
174C8×Dic5C22×C311yescharacteristic
175#3942C22×C311yescharacteristic
176#3941C22×C311yescharacteristic
177#3940C22×C311yescharacteristic
178#3939C22×C311yescharacteristic
179C4⋊#168C22×C311yescharacteristic
180#3361—51noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C22×C3×D5—21no—
184C3×C5×D4—21no—
185C3×C5×D4—21no—
186C3×C5×D4—21no—
187C3×C5×D4#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—81no—
191C2×C3×C4×C5—81no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195C3×C22⋊D5—42no—
196C3×C22⋊D5—81no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—42no—
201C2×C3×Dic5—81no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C3×D20—21no—
207C3×D20—21no—
208C3×C4×D5—81no—
209C3×Dic10—22no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—81no—
213C3×C5×C8—21no—
214C3×C5×C8—21no—
215C3×#168—21no—
216C3×#168—21no—
217C2×C3×SD16—51no—
218C2×C3×D8—51no—
219C2×C3×D8C2×D511yescharacteristic
220C3×C4⋊Q8—51no—
221C3×#127—51no—
222C3×#125—51no—
223C3×#125—51no—
224C3×#124—51no—
225C3×#124—51no—
226C3×#124—101no—
227C3×#123—101no—
228C3×#123—101no—
229C3×C22⋊Q8—101no—
230C3×C22⋊Q8—101no—
231C3×C22⋊Q8—101no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×D4—51no—
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237C3×C4×D4—101no—
238C3×C4×D4C2×D511yescharacteristic
239C3×C4×D4C2×D511yescharacteristic
240C2×C3×C4⋊C4—101no—
241C3×#107—51no—
242C3×#107C2×D511yescharacteristic
243C3×#106—51no—
244C3×C4⋊C8—51no—
245C3×C4⋊C8—51no—
246C3×C4⋊C8—51no—
247C3×#103—51no—
248C3×#103—51no—
249C3×#103—51no—
250C3×#102—51no—
251C3×#102—51no—
252C3×#102—51no—
253C3×#102—51no—
254C3×#102—51no—
255C3×#102C2×D511yescharacteristic
256C3×#102C2×D511yescharacteristic
257C3×C4×C8—51no—
258C3×C4×C8—51no—
259C3×C4×C8C2×D511yescharacteristic
260C2×C5×D4C23×C311yescharacteristic
261C2×C5×D4C23×C311yescharacteristic
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C2×C22⋊D5—21no—
265C2×C22⋊D5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268C2×D20C23×C311yescharacteristic
269C2×C4×D5—21no—
270C2×Dic10—21no—
271C2×Dic10C3×D411yescharacteristic
272C2×Dic10C23×C311yescharacteristic
273C5×D8—22no—
274C2×C5×C8C23×C311yescharacteristic
275C2×C5×C8C23×C311yescharacteristic
276C5×C4⋊C4C23×C311yescharacteristic
277C5×C4⋊C4C23×C311yescharacteristic
278C5×C22⋊C4—21no—
279C5×C22⋊C4—21no—
280C42×C5C23×C311yescharacteristic
281C22⋊Dic5—21no—
282C22⋊Dic5—21no—
283C22⋊Dic5—21no—
284C22⋊Dic5—21no—
285#687—22no—
286#686—22no—
287#685—21no—
288#685—21no—
289#685—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5C3×D411yescharacteristic
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×Dic5C23×C311yescharacteristic
303C4×Dic5C23×C311yescharacteristic
304C2×#168C23×C311yescharacteristic
305C2×#168C23×C311yescharacteristic
306#559—51no—
307#554—51no—
308#488—51no—
309#488—51no—
310#486—51no—
311#478—51no—
312#478—51no—
313#477—51no—
314#463—51no—
315#463—51no—
316#459—51no—
317C8×Q8—51no—
318C4×SD16—51no—
319C4×D8—51no—
320C4×D8C3×D511yescharacteristic, complemented
321C22×C3×C5—22no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5C22×D411yescharacteristic
328C2×C3×D5—41no—
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C3×C4×C5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C52−1+411yescharacteristic
337C3×Dic5—21no—
338C3×Dic5—21no—
339C3×Dic5—21no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C3×Dic5—41no—
343C3×Dic5#13512yes—
344C2×C3×Q8—51no—
345C2×C3×Q8—51no—
346C2×C3×Q8—101no—
347C2×C3×D4—51no—
348C2×C3×D4—101no—
349C2×C3×D4—101no—
350C2×C3×D4C22×D511yescharacteristic
351C2×C3×D4C22×D511yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C22×C3×C4—101no—
357C3×SD16—102no—
358C3×D8—22no—
359C3×D8—102no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C2×C3×C8C22×D511yescharacteristic
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—51no—
367C3×C4⋊C4—51no—
368C3×C4⋊C4—51no—
369C3×C4⋊C4—101no—
370C3×C4⋊C4—101no—
371C3×C4⋊C4—101no—
372C3×C4⋊C4—101no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4C22×D511yescharacteristic
376C3×C4⋊C4C22×D511yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—101no—
380C3×C22⋊C4—101no—
381C3×C22⋊C4—101no—
382C3×C22⋊C4—101no—
383C3×C22⋊C4—101no—
384C3×C22⋊C4—101no—
385C3×C22⋊C4—101no—
386C3×C42—51no—
387C3×C42—51no—
388C3×C42—101no—
389C3×C42C22×D511yescharacteristic
390C23×C5—21no—
391C23×C5—21no—
392C22×D5—21no—
393C5×D4—21no—
394C5×D4—21no—
395C5×D4—21no—
396C5×D4C3×#4112yes—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—81no—
400C2×C4×C5—81no—
401C2×C4×C5C2×C3×D411yescharacteristic
402C2×C4×C5C2×C3×D411yescharacteristic
403C2×C4×C5C24×C311yescharacteristic
404C22⋊D5—42no—
405C22⋊D5—81no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—42no—
410C2×Dic5—81no—
411C2×Dic5C2×C3×D411yescharacteristic
412C2×Dic5C2×C3×D411yescharacteristic
413C2×Dic5C2×C3×D411yescharacteristic
414C2×Dic5C2×C3×D411yescharacteristic
415D20—21no—
416D20—21no—
417C4×D5—81no—
418Dic10—22no—
419Dic10—21no—
420Dic10—21no—
421Dic10—81no—
422C5×C8—21no—
423C5×C8—21no—
424#168—21no—
425#168—21no—
426C2×SD16—51no—
427C2×D8—51no—
428C2×D8C2×C3×D511yescharacteristic
429C4⋊Q8—51no—
430#127—51no—
431#125—51no—
432#125—51no—
433#124—51no—
434#124—51no—
435#124—101no—
436#123—101no—
437#123—101no—
438C22⋊Q8—101no—
439C22⋊Q8—101no—
440C22⋊Q8—101no—
441C4×Q8—51no—
442C4×Q8—51no—
443C4×D4—51no—
444C4×D4—51no—
445C4×D4—51no—
446C4×D4—101no—
447C4×D4C2×C3×D511yescharacteristic
448C4×D4C2×C3×D511yescharacteristic
449C2×C4⋊C4—101no—
450#107—51no—
451#107C2×C3×D511yescharacteristic
452#106—51no—
453C4⋊C8—51no—
454C4⋊C8—51no—
455C4⋊C8—51no—
456#103—51no—
457#103—51no—
458#103—51no—
459#102—51no—
460#102—51no—
461#102—51no—
462#102—51no—
463#102—51no—
464#102C2×C3×D511yescharacteristic
465#102C2×C3×D511yescharacteristic
466C4×C8—51no—
467C4×C8—51no—
468C4×C8C2×C3×D511yescharacteristic
469C2×C3×C5—42no—
470C2×C3×C5—81no—
471C2×C3×C5#54811yescharacteristic
472C2×C3×C5C2×#13511yescharacteristic
473C2×C3×C5#57611yescharacteristic
474C3×D5—81no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—101no—
478C3×Q8—102no—
479C3×Q8—101no—
480C3×Q8—101no—
481C3×Q8—401no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—101no—
486C3×D4—101no—
487C3×D4—202no—
488C3×D4—401no—
489C3×D4#70912yes—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—51no—
493C2×C3×C4—51no—
494C2×C3×C4—51no—
495C2×C3×C4—51no—
496C2×C3×C4—81no—
497C2×C3×C4—81no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—202no—
502C2×C3×C4—401no—
503C2×C3×C4—401no—
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—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5C22×C3×D411yescharacteristic
518C2×D5—41no—
519C2×D5—41no—
520C2×D5—41no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—41no—
524C4×C5—41no—
525C4×C5C2×C3×#4111yescharacteristic
526C4×C5C3×2−1+411yescharacteristic
527Dic5—21no—
528Dic5—21no—
529Dic5—21no—
530Dic5—41no—
531Dic5—41no—
532Dic5—41no—
533Dic5C3×#13512yes—
534C2×Q8—51no—
535C2×Q8—51no—
536C2×Q8—101no—
537C2×D4—51no—
538C2×D4—101no—
539C2×D4—101no—
540C2×D4C22×C3×D511yescharacteristic
541C2×D4C22×C3×D511yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—101no—
547SD16—102no—
548D8—22no—
549D8—102no—
550C2×C8—51no—
551C2×C8—51no—
552C2×C8C22×C3×D511yescharacteristic
553C2×C8C22×C3×D511yescharacteristic
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—51no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4C22×C3×D511yescharacteristic
566C4⋊C4C22×C3×D511yescharacteristic
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C22⋊C4—101no—
574C22⋊C4—101no—
575C22⋊C4—101no—
576C42—51no—
577C42—51no—
578C42—101no—
579C42C22×C3×D511yescharacteristic
580C3×C5#336111yescharacteristic, complemented, Hall
581C22×C3—22no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—201no—
588C22×C3—201no—
589C22×C3—201no—
590C22×C3C2×D4×D511yescharacteristic
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—52no—
596C3×C4—101no—
597C3×C4—101no—
598C3×C4—101no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4—201no—
602C3×C4C2×#70911yescharacteristic
603C3×C4#415011yescharacteristic
604C2×C5—42no—
605C2×C5—81no—
606C2×C5C3×#54811yescharacteristic
607C2×C5C2×C3×#13511yescharacteristic
608C2×C5C3×#57611yescharacteristic
609D5—81no—
610C23—21no—
611C23—21no—
612C23—101no—
613Q8—102no—
614Q8—101no—
615Q8—101no—
616Q8—401no—
617D4—21no—
618D4—21no—
619D4—21no—
620D4—101no—
621D4—101no—
622D4—202no—
623D4—401no—
624D4C3×#70912yes—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—51no—
628C2×C4—51no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—101no—
634C2×C4—101no—
635C2×C4—101no—
636C2×C4—202no—
637C2×C4—401no—
638C2×C4—401no—
639C2×C4C3×D4×D511yescharacteristic
640C2×C4C3×D4×D511yescharacteristic
641C2×C4C23×C3×D511yescharacteristic
642C8—21no—
643C8—21no—
644C8—101no—
645C8—101no—
646C2×C3—42no—
647C2×C3—81no—
648C2×C3—401no—
649C2×C3#6588611yescharacteristic
650C2×C3#6609111yescharacteristic
651C2×C3D5×#13511yescharacteristic
652C5C3×#336111yescharacteristic, complemented, Sylow
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—201no—
660C22—201no—
661C22—201no—
662C22C2×C3×D4×D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—41no—
666C4—41no—
667C4—52no—
668C4—101no—
669C4—101no—
670C4—101no—
671C4—201no—
672C4—201no—
673C4—201no—
674C4C2×C3×#70911yescharacteristic
675C4C3×#415011yescharacteristic
676C3#1061130011yescharacteristic, direct product factor, Sylow
677C2—42no—
678C2—81no—
679C2—401no—
680C2C3×#6588611yescharacteristic
681C2C3×#6609111yescharacteristic
682C2C3×D5×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
prime radicalC3×#65439C2
hypercenterC3×C4×D8D5
hypocenterC5C3×#3361
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#65893C2semidirect
2. C3×#65873C2semidirect
3. C3×C4×C5×D8C2semidirect
4. C3×#65442C2semidirect
6. C3×#65305C2semidirect
7. C3×#65298C2semidirect
8. C3×#65180C2semidirect
9. C3×#65164C2semidirect
10. C3×#65057C2semidirect
11. C3×#65049C2semidirect
12. C3×#65047C2semidirect
13. C3×#65045C2semidirect
14. C3×#64986C2semidirect
15. C3×C8×Dic10C2semidirect
16. #10611300C3direct (N × H)
61. #65893C2×C3semidirect
62. #65873C2×C3semidirect
63. C4×C5×D8C2×C3semidirect
64. #65442C2×C3semidirect
66. #65305C2×C3semidirect
67. #65298C2×C3semidirect
68. #65180C2×C3semidirect
69. #65164C2×C3semidirect
70. #65057C2×C3semidirect
71. #65049C2×C3semidirect
72. #65047C2×C3semidirect
73. #65045C2×C3semidirect
74. #64986C2×C3semidirect
75. C8×Dic10C2×C3semidirect
136. C3×C4×D8D5semidirect
320. C4×D8C3×D5semidirect
580. C3×C5#3361semidirect
652. C5C3×#3361semidirect
676. C3#10611300direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658932
C3×#658732
C3×C4×C5×D82
C3×#654422
C3×#654392
C3×#653052
C3×#652982
C3×#651802
C3×#651642
C3×#650572
C3×#650492
C3×#650472
C3×#650452
C3×#649862
C3×C8×Dic102
#106113003
C3×#33615