Finite Group Databasebeta

← C3×#10611604 #14435851

Subgroups — C3×#10611604 #14435851

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×#65896C211yesmaximal, characteristic, complemented
2C3×#65880C211yesmaximal, characteristic, complemented
3C3×C5×#442C211yesmaximal, characteristic, complemented
4C3×#65447C211yesmaximal, characteristic, complemented
5C3×#65439C211yesmaximal, characteristic, complemented
6C3×C4×#687C211yesmaximal, characteristic, complemented
7C3×C4×#686C211yesmaximal, characteristic, complemented
8C3×#65152C211yesmaximal, characteristic, complemented
9C3×#65146C211yesmaximal, characteristic, complemented
10C3×#65070C211yesmaximal, characteristic, complemented
11C3×#65063C211yesmaximal, characteristic, complemented
12C3×#65055C211yesmaximal, characteristic, complemented
13C3×#65051C211yesmaximal, characteristic, complemented
14C3×#64999C211yesmaximal, characteristic, complemented
15C3×#64998C211yesmaximal, characteristic, complemented
16#10611604C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic
18C2×C3×C5×D8C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×#4086C2211yescharacteristic
22C3×#4084C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic
24C2×C3×#687C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×#4076—21no—
27C3×#4075—21no—
28C3×C4×C22⋊D5—21no—
29C2×C3×#683—21no—
30C2×C3×#677C2211yescharacteristic
31C3×#4041C2211yescharacteristic
32C3×D5×C4⋊C4C2211yescharacteristic
33C3×#4036C2211yescharacteristic
34C3×#4033C2211yescharacteristic
35C3×#4030—21no—
36C3×#4029—21no—
37C3×#4027—21no—
38C3×#4023—21no—
39C3×C4×D20C2211yescharacteristic
40C3×#4018C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45C3×C5×#97C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3950C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×C4×#168C2211yescharacteristic
60C3×#3119—51nomaximal, Hall
61#65896C2×C311yescharacteristic, complemented
62#65880C2×C311yescharacteristic, complemented
63C5×#442C2×C311yescharacteristic, complemented
64#65447C2×C311yescharacteristic, complemented
65#65439C2×C311yescharacteristic, complemented
66C4×#687C2×C311yescharacteristic, complemented
67C4×#686C2×C311yescharacteristic, complemented
68#65152C2×C311yescharacteristic, complemented
69#65146C2×C311yescharacteristic, complemented
70#65070C2×C311yescharacteristic, complemented
71#65063C2×C311yescharacteristic, complemented
72#65055C2×C311yescharacteristic, complemented
73#65051C2×C311yescharacteristic, complemented
74#64999C2×C311yescharacteristic, complemented
75#64998C2×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—
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C22×C3×Dic5—21no—
86C3×#711—22no—
87C3×#711—22no—
88C2×C3×D20—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C3×C5×D8—22no—
95C2×C3×C5×C8C2311yescharacteristic
96C2×C3×C5×C8C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C42×C5C2311yescharacteristic
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×#687—22no—
105C3×#686—22no—
106C3×#685—21no—
107C3×#685—21no—
108C3×#685D411yescharacteristic
109C3×#685D411yescharacteristic
110C3×C4⋊Dic5—21no—
111C3×C4⋊Dic5C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×#683D411yescharacteristic
118C3×#683D411yescharacteristic
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C3×#677—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×#442D511yescharacteristic, complemented
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C2×#711C22×C311yescharacteristic
141C2×C5×D8C22×C311yescharacteristic
142C4×C5×D4C22×C311yescharacteristic
143C4×C5×D4C22×C311yescharacteristic
144#4086C22×C311yescharacteristic
145#4084C22×C311yescharacteristic
146D4×Dic5C22×C311yescharacteristic
147C2×#687C22×C311yescharacteristic
148C2×#686C22×C311yescharacteristic
149#4076—21no—
150#4075—21no—
151C4×C22⋊D5—21no—
152C2×#683—21no—
153C2×#677C22×C311yescharacteristic
154#4041C22×C311yescharacteristic
155D5×C4⋊C4C22×C311yescharacteristic
156#4036C22×C311yescharacteristic
157#4033C22×C311yescharacteristic
158#4030—21no—
159#4029—21no—
160#4027—21no—
161#4023—21no—
162C4×D20C22×C311yescharacteristic
163#4018C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165C5×#106C22×C311yescharacteristic
166C5×#102C22×C311yescharacteristic
167C5×#102C22×C311yescharacteristic
168C5×#97C22×C311yescharacteristic
169#3964C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3953C22×C311yescharacteristic
172#3952C22×C311yescharacteristic
173#3952C22×C311yescharacteristic
174#3950C22×C311yescharacteristic
175#3948C22×C311yescharacteristic
176#3946C22×C311yescharacteristic
177#3946C22×C311yescharacteristic
178#3942C22×C311yescharacteristic
179#3941C22×C311yescharacteristic
180#3940C22×C311yescharacteristic
181#3939C22×C311yescharacteristic
182C4×#168C22×C311yescharacteristic
183#3119—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C22×C3×D5—21no—
187C22×C3×D5C2×D411yescharacteristic
188C3×C5×D4—21no—
189C3×C5×D4—21no—
190C3×C5×D4—21no—
191C3×C5×D4#4112yes—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—81no—
195C2×C3×C4×C5—81no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C3×C22⋊D5—24no—
200C3×C22⋊D5—81no—
201C3×C22⋊D5—81no—
202C3×C22⋊D5—81no—
203C2×C3×Dic5—24no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—81no—
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C2×C3×Dic5C2×D411yescharacteristic
211C3×D20—21no—
212C3×D20—21no—
213C3×D20—81no—
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—81no—
217C3×C4×D5—81no—
218C3×Dic10—21no—
219C3×Dic10#4112yes—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C2×C3×#41—51no—
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8C2×D511yescharacteristic
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×Q8—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—101no—
242C3×C4×D4—101no—
243C3×C4×D4C2×D511yescharacteristic
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×#103—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102C2×D511yescharacteristic
262C3×#102C2×D511yescharacteristic
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×#97C2×D511yescharacteristic
266C3×C4×C8—51no—
267C2×C5×D4C23×C311yescharacteristic
268C2×C5×D4C23×C311yescharacteristic
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C2×C22⋊D5—21no—
272C2×C22⋊D5—21no—
273C2×C22⋊D5—21no—
274C2×C22⋊D5—21no—
275C22×Dic5—21no—
276C22×Dic5—21no—
277#711—22no—
278#711—22no—
279C2×D20—21no—
280C2×D20C23×C311yescharacteristic
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C2×C4×D5C23×C311yescharacteristic
284C2×Dic10C23×C311yescharacteristic
285C5×D8—22no—
286C2×C5×C8C23×C311yescharacteristic
287C2×C5×C8C23×C311yescharacteristic
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C22⋊C4—21no—
291C5×C22⋊C4—21no—
292C42×C5C23×C311yescharacteristic
293C22⋊Dic5—21no—
294C22⋊Dic5—21no—
295#687—22no—
296#686—22no—
297#685—21no—
298#685—21no—
299#685C3×D411yescharacteristic
300#685C3×D411yescharacteristic
301C4⋊Dic5—21no—
302C4⋊Dic5C23×C311yescharacteristic
303C4⋊Dic5C23×C311yescharacteristic
304#683—21no—
305#683—21no—
306#683—21no—
307#683—21no—
308#683C3×D411yescharacteristic
309#683C3×D411yescharacteristic
310C4×Dic5—21no—
311C4×Dic5—21no—
312C4×Dic5C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315#677—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#442C3×D511yescharacteristic, complemented
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5C22×D411yescharacteristic
338C2×C3×D5—21no—
339C2×C3×D5—21no—
340C2×C3×D5—21no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—21no—
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5C2×#4111yescharacteristic
349C3×C4×C5C2×#4111yescharacteristic
350C3×Dic5—22no—
351C3×Dic5—21no—
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×#41—102no—
357C3×#41—102no—
358C2×C3×Q8—51no—
359C2×C3×D4—51no—
360C2×C3×D4—101no—
361C2×C3×D4—101no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—51no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C3×SD16—102no—
375C3×SD16—102no—
376C3×D8—22no—
377C3×D8—102no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8C22×D511yescharacteristic
381C2×C3×C8C22×D511yescharacteristic
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
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—21no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—51no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C42—51no—
402C3×C42—101no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405C23×C5—21no—
406C23×C5—21no—
407C22×D5—21no—
408C22×D5C2×C3×D411yescharacteristic
409C5×D4—21no—
410C5×D4—21no—
411C5×D4—21no—
412C5×D4C3×#4112yes—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—81no—
416C2×C4×C5—81no—
417C2×C4×C5C2×C3×D411yescharacteristic
418C2×C4×C5C2×C3×D411yescharacteristic
419C2×C4×C5C24×C311yescharacteristic
420C22⋊D5—24no—
421C22⋊D5—81no—
422C22⋊D5—81no—
423C22⋊D5—81no—
424C2×Dic5—24no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—81no—
429C2×Dic5C2×C3×D411yescharacteristic
430C2×Dic5C2×C3×D411yescharacteristic
431C2×Dic5C2×C3×D411yescharacteristic
432D20—21no—
433D20—21no—
434D20—81no—
435C4×D5—21no—
436C4×D5—21no—
437C4×D5—81no—
438C4×D5—81no—
439Dic10—21no—
440Dic10C3×#4112yes—
441C5×C8—21no—
442C5×C8—21no—
443#168—21no—
444#168—21no—
445C2×#41—51no—
446C2×SD16—51no—
447C2×SD16—51no—
448C2×D8—51no—
449C2×D8C2×C3×D511yescharacteristic
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×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—101no—
463C4×D4—101no—
464C4×D4C2×C3×D511yescharacteristic
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#103—51no—
478#102—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102C2×C3×D511yescharacteristic
483#102C2×C3×D511yescharacteristic
484C22⋊C8—51no—
485C22⋊C8—51no—
486#97C2×C3×D511yescharacteristic
487C4×C8—51no—
488C2×C3×C5—42no—
489C2×C3×C5—81no—
490C2×C3×C5#52511yescharacteristic
491C2×C3×C5#57611yescharacteristic
492C2×C3×C5#57711yescharacteristic
493C3×D5—41no—
494C3×D5—81no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—51no—
498C23×C3—101no—
499C3×Q8—52no—
500C3×Q8—101no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—104no—
505C3×D4—101no—
506C3×D4—101no—
507C3×D4—401no—
508C3×D4—401no—
509C3×D4—401no—
510C3×D4—401no—
511C3×D4#70912yes—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—51no—
515C2×C3×C4—51no—
516C2×C3×C4—51no—
517C2×C3×C4—81no—
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—101no—
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—22no—
536C22×C5—41no—
537C22×C5—41no—
538C22×C5—41no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5C22×C3×D411yescharacteristic
542C2×D5—21no—
543C2×D5—21no—
544C2×D5—21no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C4×C5—21no—
549C4×C5—21no—
550C4×C5—41no—
551C4×C5—41no—
552C4×C5C2×C3×#4111yescharacteristic
553C4×C5C2×C3×#4111yescharacteristic
554Dic5—21no—
555Dic5—21no—
556Dic5—22no—
557Dic5—21no—
558Dic5—41no—
559Dic5—41no—
560#41—102no—
561#41—102no—
562C2×Q8—51no—
563C2×D4—51no—
564C2×D4—101no—
565C2×D4—101no—
566C2×D4—101no—
567C2×D4—101no—
568C2×D4—101no—
569C2×D4C22×C3×D511yescharacteristic
570C2×D4C22×C3×D511yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—51no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578SD16—102no—
579SD16—102no—
580D8—22no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—51no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—101no—
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—21no—
599C22⋊C4—51no—
600C22⋊C4—51no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C42—51no—
606C42—101no—
607C42—101no—
608C42C22×C3×D511yescharacteristic
609C3×C5#311911yescharacteristic, complemented, Hall
610C22×C3—22no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—101no—
617C22×C3—101no—
618C22×C3—101no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3C2×D4×D511yescharacteristic
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—101no—
628C3×C4—101no—
629C3×C4—101no—
630C3×C4—102no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4C2×#70911yescharacteristic
634C3×C4D5×#4111yescharacteristic
635C2×C5—42no—
636C2×C5—81no—
637C2×C5C3×#52511yescharacteristic
638C2×C5C3×#57611yescharacteristic
639C2×C5C3×#57711yescharacteristic
640D5—41no—
641D5—81no—
642C23—21no—
643C23—21no—
644C23—51no—
645C23—101no—
646Q8—52no—
647Q8—101no—
648D4—21no—
649D4—21no—
650D4—21no—
651D4—104no—
652D4—101no—
653D4—101no—
654D4—401no—
655D4—401no—
656D4—401no—
657D4—401no—
658D4C3×#70912yes—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—51no—
662C2×C4—51no—
663C2×C4—51no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—104no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—101no—
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—42no—
683C2×C3—81no—
684C2×C3—201no—
685C2×C3—401no—
686C2×C3#6588111yescharacteristic
687C2×C3#6610811yescharacteristic
688C2×C3#6610911yescharacteristic
689C5C3×#311911yescharacteristic, complemented, Sylow
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—101no—
697C22—101no—
698C22—101no—
699C22—201no—
700C22—201no—
701C22—201no—
702C22C2×C3×D4×D511yescharacteristic
703C4—21no—
704C4—21no—
705C4—41no—
706C4—41no—
707C4—101no—
708C4—101no—
709C4—101no—
710C4—102no—
711C4—201no—
712C4—201no—
713C4C2×C3×#70911yescharacteristic
714C4C3×D5×#4111yescharacteristic
715C3#1061160411yescharacteristic, direct product factor, Sylow
716C2—42no—
717C2—81no—
718C2—201no—
719C2—401no—
720C2C3×#6588111yescharacteristic
721C2C3×#6610811yescharacteristic
722C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#442C2
socleC22×C3×C5C22×D4
hypercenterC3×#442D5
hypocenterC5C3×#3119
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#65896C2semidirect
2. C3×#65880C2semidirect
3. C3×C5×#442C2semidirect
4. C3×#65447C2semidirect
5. C3×#65439C2semidirect
6. C3×C4×#687C2semidirect
7. C3×C4×#686C2semidirect
8. C3×#65152C2semidirect
9. C3×#65146C2semidirect
10. C3×#65070C2semidirect
11. C3×#65063C2semidirect
12. C3×#65055C2semidirect
13. C3×#65051C2semidirect
14. C3×#64999C2semidirect
15. C3×#64998C2semidirect
16. #10611604C3direct (N × H)
61. #65896C2×C3semidirect
62. #65880C2×C3semidirect
63. C5×#442C2×C3semidirect
64. #65447C2×C3semidirect
65. #65439C2×C3semidirect
66. C4×#687C2×C3semidirect
67. C4×#686C2×C3semidirect
68. #65152C2×C3semidirect
69. #65146C2×C3semidirect
70. #65070C2×C3semidirect
71. #65063C2×C3semidirect
72. #65055C2×C3semidirect
73. #65051C2×C3semidirect
74. #64999C2×C3semidirect
75. #64998C2×C3semidirect
135. C3×#442D5semidirect
326. #442C3×D5semidirect
609. C3×C5#3119semidirect
689. C5C3×#3119semidirect
715. C3#10611604direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658962
C3×#658802
C3×C5×#4422
C3×#654472
C3×#654392
C3×C4×#6872
C3×C4×#6862
C3×#651522
C3×#651462
C3×#650702
C3×#650632
C3×#650552
C3×#650512
C3×#649992
C3×#649982
#106116043
C3×#31195