Finite Group Databasebeta

← C3×#10611428 #14435857

Subgroups — C3×#10611428 #14435857

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65908C211yesmaximal, characteristic, complemented
2C3×#65896C211yesmaximal, characteristic, complemented
3C3×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C3×#65461C211yesmaximal, characteristic, complemented
5C3×#65452C211yesmaximal, characteristic, complemented
6C3×#65315C211yesmaximal, characteristic, complemented
7C3×#65303C211yesmaximal, characteristic, complemented
8C3×#65160C211yesmaximal, characteristic, complemented
9C3×#65152C211yesmaximal, characteristic, complemented
10C3×#65100C211yesmaximal, characteristic, complemented
11C3×#65085C211yesmaximal, characteristic, complemented
12C3×#65075C211yesmaximal, characteristic, complemented
13C3×#65063C211yesmaximal, characteristic, complemented
14C3×C4×D40C211yesmaximal, characteristic, complemented
15C3×#64979C211yesmaximal, characteristic, complemented
16#10611428C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C2×C3×#688C2211yescharacteristic
23C3×#4086C2211yescharacteristic
24C3×#4084C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×#4076—21no—
27C3×#4075—21no—
28C2×C3×D40C2211yescharacteristic
29C3×#4041C2211yescharacteristic
30C3×#4039—21no—
31C3×#4039C2211yescharacteristic
32C3×D5×C4⋊C4—21no—
33C3×D5×C4⋊C4C2211yescharacteristic
34C3×#4036C2211yescharacteristic
35C3×#4030—21no—
36C3×#4029—21no—
37C3×C4×D20—21no—
38C3×C4×D20C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×#4018—21no—
41C3×#4018C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45C3×C4×C5×C8C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3952C2211yescharacteristic
52C3×#3950C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×#3941C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×#3935C2211yescharacteristic
60C3×#3119—51nomaximal, Hall
61#65908C2×C311yescharacteristic, complemented
62#65896C2×C311yescharacteristic, complemented
63C4×C5×SD16C2×C311yescharacteristic, complemented
64#65461C2×C311yescharacteristic, complemented
65#65452C2×C311yescharacteristic, complemented
66#65315C2×C311yescharacteristic, complemented
67#65303C2×C311yescharacteristic, complemented
68#65160C2×C311yescharacteristic, complemented
69#65152C2×C311yescharacteristic, complemented
70#65100C2×C311yescharacteristic, complemented
71#65085C2×C311yescharacteristic, complemented
72#65075C2×C311yescharacteristic, complemented
73#65063C2×C311yescharacteristic, complemented
74C4×D40C2×C311yescharacteristic, complemented
75#64979C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×C3×C22⋊D5—21no—
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C3×#713—22no—
83C3×#713—22no—
84C2×C3×D20—21no—
85C2×C3×D20—21no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5C2311yescharacteristic
94C3×C5×SD16—22no—
95C2×C3×C5×C8C2311yescharacteristic
96C2×C3×C5×C8C2311yescharacteristic
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C42×C5—21no—
102C3×C42×C5C2311yescharacteristic
103C3×C22⋊Dic5—21no—
104C3×#688—22no—
105C3×#686—22no—
106C3×#685—21no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685D411yescharacteristic
111C3×#685D411yescharacteristic
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C3×#683D411yescharacteristic
119C3×#683D411yescharacteristic
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C3×D40—22no—
125C3×#540—51no—
126C3×#520—51no—
127C3×#481—51no—
128C3×#480—51no—
129C3×#479—51no—
130C3×#478—51no—
131C3×#460—51no—
132C3×#459—51no—
133C3×#449—51no—
134C3×#449—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16D511yescharacteristic, complemented
138C3×C4×D8—51no—
139C3×#433—51no—
140C2×#713C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C4×C5×Q8C22×C311yescharacteristic
143C4×C5×D4C22×C311yescharacteristic
144Q8×Dic5C22×C311yescharacteristic
145C2×#688C22×C311yescharacteristic
146#4086C22×C311yescharacteristic
147#4084C22×C311yescharacteristic
148C2×#686C22×C311yescharacteristic
149#4076—21no—
150#4075—21no—
151C2×D40C22×C311yescharacteristic
152#4041C22×C311yescharacteristic
153#4039—21no—
154#4039C22×C311yescharacteristic
155D5×C4⋊C4—21no—
156D5×C4⋊C4C22×C311yescharacteristic
157#4036C22×C311yescharacteristic
158#4030—21no—
159#4029—21no—
160C4×D20—21no—
161C4×D20C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163#4018—21no—
164#4018C22×C311yescharacteristic
165C5×#106C22×C311yescharacteristic
166C5×#103C22×C311yescharacteristic
167C5×#102C22×C311yescharacteristic
168C4×C5×C8C22×C311yescharacteristic
169#3967C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3953C22×C311yescharacteristic
172#3953C22×C311yescharacteristic
173#3952C22×C311yescharacteristic
174#3952C22×C311yescharacteristic
175#3950C22×C311yescharacteristic
176#3946C22×C311yescharacteristic
177#3946C22×C311yescharacteristic
178#3941C22×C311yescharacteristic
179#3941C22×C311yescharacteristic
180#3940C22×C311yescharacteristic
181#3939C22×C311yescharacteristic
182#3935C22×C311yescharacteristic
183#3119—51noSylow
184C23×C3×C5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5C2×D411yescharacteristic
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×D4—21no—
191C3×C5×D4—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—81no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C3×C22⋊D5—81no—
200C3×C22⋊D5—81no—
201C3×C22⋊D5—81no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×D20—24no—
208C3×D20—21no—
209C3×D20—21no—
210C3×D20—21no—
211C3×D20—81no—
212C3×D20#4112yes—
213C3×C4×D5—24no—
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—81no—
217C3×C4×D5—81no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C2×C3×#41—51no—
225C2×C3×SD16—51no—
226C2×C3×SD16C2×D511yescharacteristic
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×#127—51no—
230C3×#125—51no—
231C3×#123—101no—
232C3×#123—101no—
233C3×#121—51no—
234C3×#121—51no—
235C3×#121—101no—
236C3×#121—101no—
237C3×C4×Q8—51no—
238C3×C4×Q8C2×D511yescharacteristic
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—51no—
242C3×C4×D4—101no—
243C3×C4×D4—101no—
244C3×C4×D4C2×D511yescharacteristic
245C3×#117—51no—
246C3×#117—101no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—101no—
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106C2×D511yescharacteristic
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103C2×D511yescharacteristic
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×#97—51no—
266C3×C4×C8C2×D511yescharacteristic
267C2×C5×Q8C23×C311yescharacteristic
268C2×C5×D4C23×C311yescharacteristic
269C22×C4×C5—21no—
270C2×C22⋊D5—21no—
271C2×C22⋊D5—21no—
272C2×C22⋊D5—21no—
273#713—22no—
274#713—22no—
275C2×D20—21no—
276C2×D20—21no—
277C2×D20C23×C311yescharacteristic
278C2×D20C23×C311yescharacteristic
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C2×C4×D5—21no—
284C2×C4×D5C23×C311yescharacteristic
285C5×SD16—22no—
286C2×C5×C8C23×C311yescharacteristic
287C2×C5×C8C23×C311yescharacteristic
288C5×C4⋊C4—21no—
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C22⋊C4—21no—
292C42×C5—21no—
293C42×C5C23×C311yescharacteristic
294C22⋊Dic5—21no—
295#688—22no—
296#686—22no—
297#685—21no—
298#685—21no—
299#685—21no—
300#685—21no—
301#685C3×D411yescharacteristic
302#685C3×D411yescharacteristic
303C4⋊Dic5—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5C23×C311yescharacteristic
306C4⋊Dic5C23×C311yescharacteristic
307#683—21no—
308#683—21no—
309#683C3×D411yescharacteristic
310#683C3×D411yescharacteristic
311C4×Dic5—21no—
312C4×Dic5C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315D40—22no—
316#540—51no—
317#520—51no—
318#481—51no—
319#480—51no—
320#479—51no—
321#478—51no—
322#460—51no—
323#459—51no—
324#449—51no—
325#449—51no—
326#442—51no—
327#440—51no—
328C4×SD16C3×D511yescharacteristic, complemented
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—41no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5C22×D411yescharacteristic
335C2×C3×D5—21no—
336C2×C3×D5—22no—
337C2×C3×D5—21no—
338C2×C3×D5—21no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—22no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349C3×C4×C5C2×#4111yescharacteristic
350C3×C4×C5C2×#4111yescharacteristic
351C3×Dic5—21no—
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×#41—102no—
357C3×#41—102no—
358C2×C3×Q8C22×D511yescharacteristic
359C2×C3×D4—51no—
360C2×C3×D4—51no—
361C2×C3×D4—101no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4—101no—
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—51no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C3×SD16—22no—
375C3×SD16—102no—
376C3×D8—102no—
377C3×D8—102no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8C22×D511yescharacteristic
381C2×C3×C8C22×D511yescharacteristic
382C3×C4⋊C4—21no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4—101no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C42—21no—
402C3×C42—51no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405C23×C5—21no—
406C22×D5—21no—
407C22×D5—21no—
408C22×D5C2×C3×D411yescharacteristic
409C5×Q8—21no—
410C5×Q8C3×#4112yes—
411C5×D4—21no—
412C5×D4—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—81no—
417C2×C4×C5C2×C3×D411yescharacteristic
418C2×C4×C5C2×C3×D411yescharacteristic
419C2×C4×C5C24×C311yescharacteristic
420C22⋊D5—81no—
421C22⋊D5—81no—
422C22⋊D5—81no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5C2×C3×D411yescharacteristic
426C2×Dic5C2×C3×D411yescharacteristic
427C2×Dic5C2×C3×D411yescharacteristic
428D20—24no—
429D20—21no—
430D20—21no—
431D20—21no—
432D20—81no—
433D20C3×#4112yes—
434C4×D5—24no—
435C4×D5—21no—
436C4×D5—21no—
437C4×D5—81no—
438C4×D5—81no—
439C4×D5—81no—
440C4×D5—81no—
441C5×C8—21no—
442C5×C8—21no—
443#168—21no—
444#168—21no—
445C2×#41—51no—
446C2×SD16—51no—
447C2×SD16C2×C3×D511yescharacteristic
448C2×D8—51no—
449C2×D8—51no—
450#127—51no—
451#125—51no—
452#123—101no—
453#123—101no—
454#121—51no—
455#121—51no—
456#121—101no—
457#121—101no—
458C4×Q8—51no—
459C4×Q8C2×C3×D511yescharacteristic
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—101no—
464C4×D4—101no—
465C4×D4C2×C3×D511yescharacteristic
466#117—51no—
467#117—101no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—101no—
470#107—51no—
471#107—51no—
472#106—51no—
473#106C2×C3×D511yescharacteristic
474C4⋊C8—51no—
475C4⋊C8—51no—
476#103—51no—
477#103C2×C3×D511yescharacteristic
478#102—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102C2×C3×D511yescharacteristic
484C22⋊C8—51no—
485C22⋊C8—51no—
486#97—51no—
487C4×C8C2×C3×D511yescharacteristic
488C2×C3×C5—81no—
489C2×C3×C5#52511yescharacteristic
490C2×C3×C5#57611yescharacteristic
491C2×C3×C5#57711yescharacteristic
492C3×D5—41no—
493C3×D5—42no—
494C3×D5—81no—
495C23×C3—21no—
496C23×C3—51no—
497C23×C3—101no—
498C23×C3—101no—
499C3×Q8—21no—
500C3×Q8#70912yes—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—52no—
504C3×D4—104no—
505C3×D4—101no—
506C3×D4—101no—
507C3×D4—101no—
508C3×D4—401no—
509C3×D4—401no—
510C3×D4—401no—
511C3×D4—401no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—51no—
516C2×C3×C4—51no—
517C2×C3×C4—51no—
518C2×C3×C4—81no—
519C2×C3×C4—104no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—401no—
525C2×C3×C4—401no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4D4×D511yescharacteristic
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—101no—
534C3×C8—101no—
535C22×C5—41no—
536C22×C5—41no—
537C22×C5—41no—
538C22×C5C22×C3×D411yescharacteristic
539C2×D5—21no—
540C2×D5—21no—
541C2×D5—21no—
542C2×D5—22no—
543C2×D5—41no—
544C2×D5—41no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C4×C5—21no—
549C4×C5—21no—
550C4×C5—22no—
551C4×C5—41no—
552C4×C5—41no—
553C4×C5C2×C3×#4111yescharacteristic
554C4×C5C2×C3×#4111yescharacteristic
555Dic5—21no—
556Dic5—21no—
557Dic5—21no—
558Dic5—41no—
559Dic5—41no—
560#41—102no—
561#41—102no—
562C2×Q8C22×C3×D511yescharacteristic
563C2×D4—51no—
564C2×D4—51no—
565C2×D4—101no—
566C2×D4—101no—
567C2×D4—101no—
568C2×D4—101no—
569C2×D4—101no—
570C2×D4C22×C3×D511yescharacteristic
571C22×C4—21no—
572C22×C4—51no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578SD16—22no—
579SD16—102no—
580D8—102no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4—101no—
595C4⋊C4C22×C3×D511yescharacteristic
596C4⋊C4C22×C3×D511yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—51no—
599C22⋊C4—51no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C42—21no—
606C42—51no—
607C42—101no—
608C42C22×C3×D511yescharacteristic
609C3×C5#311911yescharacteristic, complemented, Hall
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—101no—
614C22×C3—101no—
615C22×C3—102no—
616C22×C3—101no—
617C22×C3—201no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3C2×D4×D511yescharacteristic
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—22no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—101no—
629C3×C4—101no—
630C3×C4—101no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4C2×#70911yescharacteristic
634C3×C4D5×#4111yescharacteristic
635C2×C5—81no—
636C2×C5C3×#52511yescharacteristic
637C2×C5C3×#57611yescharacteristic
638C2×C5C3×#57711yescharacteristic
639D5—41no—
640D5—42no—
641D5—81no—
642C23—21no—
643C23—51no—
644C23—101no—
645C23—101no—
646Q8—21no—
647Q8C3×#70912yes—
648D4—21no—
649D4—21no—
650D4—52no—
651D4—104no—
652D4—101no—
653D4—101no—
654D4—101no—
655D4—401no—
656D4—401no—
657D4—401no—
658D4—401no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—51no—
663C2×C4—51no—
664C2×C4—51no—
665C2×C4—81no—
666C2×C4—104no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—401no—
672C2×C4—401no—
673C2×C4—401no—
674C2×C4—401no—
675C2×C4C3×D4×D511yescharacteristic
676C2×C4C3×D4×D511yescharacteristic
677C2×C4C23×C3×D511yescharacteristic
678C8—21no—
679C8—21no—
680C8—101no—
681C8—101no—
682C2×C3—81no—
683C2×C3—201no—
684C2×C3—202no—
685C2×C3—401no—
686C2×C3#6588111yescharacteristic
687C2×C3#6609611yescharacteristic
688C2×C3#6610311yescharacteristic
689C5C3×#311911yescharacteristic, complemented, Sylow
690C22—41no—
691C22—41no—
692C22—41no—
693C22—101no—
694C22—102no—
695C22—101no—
696C22—101no—
697C22—201no—
698C22—201no—
699C22—201no—
700C22—201no—
701C22—201no—
702C22C2×C3×D4×D511yescharacteristic
703C4—21no—
704C4—22no—
705C4—21no—
706C4—41no—
707C4—41no—
708C4—101no—
709C4—101no—
710C4—101no—
711C4—201no—
712C4—201no—
713C4C2×C3×#70911yescharacteristic
714C4C3×D5×#4111yescharacteristic
715C3#1061142811yescharacteristic, direct product factor, Sylow
716C2—81no—
717C2—201no—
718C2—202no—
719C2—401no—
720C2C3×#6588111yescharacteristic
721C2C3×#6609611yescharacteristic
722C2C3×#6610311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
hypercenterC3×C4×SD16D5
hypocenterC5C3×#3119
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×#65908C2semidirect
2. C3×#65896C2semidirect
3. C3×C4×C5×SD16C2semidirect
4. C3×#65461C2semidirect
5. C3×#65452C2semidirect
6. C3×#65315C2semidirect
7. C3×#65303C2semidirect
8. C3×#65160C2semidirect
9. C3×#65152C2semidirect
10. C3×#65100C2semidirect
11. C3×#65085C2semidirect
12. C3×#65075C2semidirect
13. C3×#65063C2semidirect
14. C3×C4×D40C2semidirect
15. C3×#64979C2semidirect
16. #10611428C3direct (N × H)
61. #65908C2×C3semidirect
62. #65896C2×C3semidirect
63. C4×C5×SD16C2×C3semidirect
64. #65461C2×C3semidirect
65. #65452C2×C3semidirect
66. #65315C2×C3semidirect
67. #65303C2×C3semidirect
68. #65160C2×C3semidirect
69. #65152C2×C3semidirect
70. #65100C2×C3semidirect
71. #65085C2×C3semidirect
72. #65075C2×C3semidirect
73. #65063C2×C3semidirect
74. C4×D40C2×C3semidirect
75. #64979C2×C3semidirect
137. C3×C4×SD16D5semidirect
328. C4×SD16C3×D5semidirect
609. C3×C5#3119semidirect
689. C5C3×#3119semidirect
715. C3#10611428direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659082
C3×#658962
C3×C4×C5×SD162
C3×#654612
C3×#654522
C3×#653152
C3×#653032
C3×#651602
C3×#651522
C3×#651002
C3×#650852
C3×#650752
C3×#650632
C3×C4×D402
C3×#649792
#106114283
C3×#31195