Finite Group Databasebeta

← C3×#10614283 #14436349

Subgroups — C3×#10614283 #14436349

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×C5×#519C211yesmaximal, characteristic, complemented
2C3×#65868C211yesmaximal, characteristic
3C3×#65517C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic
5C3×#65319C211yesmaximal, characteristic, complemented
6C3×C4×#689C211yesmaximal, characteristic, complemented
7C3×#65317C211yesmaximal, characteristic, complemented
8C3×#65317C211yesmaximal, characteristic, complemented
9C3×#65315C211yesmaximal, characteristic, complemented
10C3×C4×#688C211yesmaximal, characteristic, complemented
11C3×#65310C211yesmaximal, characteristic, complemented
12C3×#65309C211yesmaximal, characteristic, complemented
13C3×#65292C211yesmaximal, characteristic
14C3×#65289C211yesmaximal, characteristic, complemented
15C3×#65285C211yesmaximal, characteristic, complemented
16#10614283C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C3×C4×C5×Q8—21no—
19C3×C4×C5×Q8—21no—
20C3×C4×C5×Q8C2211yescharacteristic
21C3×C4×C5×Q8C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic
23C3×C4×C5×Q8C2211yescharacteristic
24C3×C5×#117—21no—
25C3×C5×#117—21no—
26C3×C5×#117C2211yescharacteristic
27C3×C5×#117C2211yescharacteristic
28C2×C3×#689C2211yescharacteristic
29C2×C3×#689C2211yescharacteristic
30C2×C3×#688C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C3×#4076C2211yescharacteristic
33C3×#4070C2211yescharacteristic
34C3×#4044—21no—
35C3×#4042—21no—
36C3×#4031—21no—
37C3×#4029—21no—
38C3×#4021C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×#4015C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×#3967C2211yescharacteristic
43C3×#3967C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×#3940C2211yescharacteristic
53C3×#3940C2211yescharacteristic
54C3×#3939C2211yescharacteristic
55C3×#3939C2211yescharacteristic
56C3×C4⋊#168C2211yescharacteristic
57C3×C4⋊#168C2211yescharacteristic
58C3×#3935C2211yescharacteristic
59C3×C4×#168C2211yescharacteristic
60C3×#3121—51nomaximal, Hall
61C5×#519C2×C311yescharacteristic, complemented
62#65868C2×C311yescharacteristic
63#65517C2×C311yescharacteristic, complemented
64#65516C2×C311yescharacteristic
65#65319C2×C311yescharacteristic, complemented
66C4×#689C2×C311yescharacteristic, complemented
67#65317C2×C311yescharacteristic, complemented
68#65317C2×C311yescharacteristic, complemented
69#65315C2×C311yescharacteristic, complemented
70C4×#688C2×C311yescharacteristic, complemented
71#65310C2×C311yescharacteristic, complemented
72#65309C2×C311yescharacteristic, complemented
73#65292C2×C311yescharacteristic
74#65289C2×C311yescharacteristic, complemented
75#65285C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8—22no—
77C2×C3×C5×Q8—22no—
78C2×C3×C5×Q8—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×Dic10—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C5×C22⋊C4D411yescharacteristic
98C3×C5×C22⋊C4D411yescharacteristic
99C3×C42×C5—21no—
100C3×C42×C5—21no—
101C3×C42×C5—21no—
102C3×C42×C5—21no—
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C42×C5C2311yescharacteristic
106C3×C22⋊Dic5—21no—
107C3×#689—22no—
108C3×#689—22no—
109C3×#688—22no—
110C3×#688—22no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542—51no—
126C3×#519D511yescharacteristic, complemented
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×SD16—51no—
139C3×#433—51no—
140C22×C5×Q8C22×C311yescharacteristic
141C4×C5×Q8—21no—
142C4×C5×Q8—21no—
143C4×C5×Q8C22×C311yescharacteristic
144C4×C5×Q8C22×C311yescharacteristic
145C4×C5×Q8C22×C311yescharacteristic
146C4×C5×Q8C22×C311yescharacteristic
147C5×#117—21no—
148C5×#117—21no—
149C5×#117C22×C311yescharacteristic
150C5×#117C22×C311yescharacteristic
151C2×#689C22×C311yescharacteristic
152C2×#689C22×C311yescharacteristic
153C2×#688C22×C311yescharacteristic
154C2×#688C22×C311yescharacteristic
155#4076C22×C311yescharacteristic
156#4070C22×C311yescharacteristic
157#4044—21no—
158#4042—21no—
159#4031—21no—
160#4029—21no—
161#4021C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163#4015C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165#3967C22×C311yescharacteristic
166#3967C22×C311yescharacteristic
167#3967C22×C311yescharacteristic
168#3967C22×C311yescharacteristic
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3942C22×C311yescharacteristic
172#3942C22×C311yescharacteristic
173#3941C22×C311yescharacteristic
174#3941C22×C311yescharacteristic
175#3940C22×C311yescharacteristic
176#3940C22×C311yescharacteristic
177#3939C22×C311yescharacteristic
178#3939C22×C311yescharacteristic
179C4⋊#168C22×C311yescharacteristic
180C4⋊#168C22×C311yescharacteristic
181#3935C22×C311yescharacteristic
182C4×#168C22×C311yescharacteristic
183#3121—51noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C3×C5×Q8—24no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×Q8#4112yes—
191C2×C3×C4×C5—24no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C3×C22⋊D5—81no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C3×D20—21no—
209C3×D20—21no—
210C3×C4×D5—81no—
211C3×Dic10—21no—
212C3×Dic10—21no—
213C3×Dic10—81no—
214C3×#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C22×C3×Q8C2×D511yescharacteristic
219C2×C3×Q16—51no—
220C2×C3×Q16—51no—
221C2×C3×SD16—51no—
222C2×C3×SD16—51no—
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—21no—
232C3×C4×Q8—21no—
233C3×C4×Q8—51no—
234C3×C4×Q8C2×D511yescharacteristic
235C3×C4×Q8C2×D511yescharacteristic
236C3×C4×Q8C2×D511yescharacteristic
237C3×C4×Q8C2×D511yescharacteristic
238C3×C4×D4—51no—
239C3×#117—21no—
240C3×#117—21no—
241C3×#117C2×D511yescharacteristic
242C3×#117C2×D511yescharacteristic
243C3×#107—51no—
244C3×#107—51no—
245C3×#106—51no—
246C3×#106—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×#103—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103—51no—
255C3×#102—51no—
256C3×#102—51no—
257C3×C22⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×#97—51no—
260C3×C4×C8—51no—
261C2×C5×Q8—22no—
262C2×C5×Q8—22no—
263C2×C5×Q8—21no—
264C2×C5×Q8C23×C311yescharacteristic
265C2×C5×Q8C23×C311yescharacteristic
266C22×C4×C5—21no—
267C22×C4×C5C23×C311yescharacteristic
268C2×C22⋊D5—21no—
269C2×D20C23×C311yescharacteristic
270C2×C4×D5—21no—
271C2×Dic10—21no—
272C2×Dic10C23×C311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4C3×D411yescharacteristic
278C5×C4⋊C4C3×D411yescharacteristic
279C5×C4⋊C4C23×C311yescharacteristic
280C5×C4⋊C4C23×C311yescharacteristic
281C5×C22⋊C4—21no—
282C5×C22⋊C4C3×D411yescharacteristic
283C5×C22⋊C4C3×D411yescharacteristic
284C42×C5—21no—
285C42×C5—21no—
286C42×C5—21no—
287C42×C5—21no—
288C42×C5—21no—
289C42×C5C23×C311yescharacteristic
290C42×C5C23×C311yescharacteristic
291C22⋊Dic5—21no—
292#689—22no—
293#689—22no—
294#688—22no—
295#688—22no—
296#685—21no—
297#685—21no—
298#685—21no—
299#685—21no—
300C4⋊Dic5—21no—
301C4⋊Dic5C23×C311yescharacteristic
302C4⋊Dic5C23×C311yescharacteristic
303#683—21no—
304#683—21no—
305C4×Dic5—21no—
306C2×#168C23×C311yescharacteristic
307C2×#168C23×C311yescharacteristic
308C2×#168C23×C311yescharacteristic
309C2×#168C23×C311yescharacteristic
310#542—51no—
311#519C3×D511yescharacteristic, complemented
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×SD16—51no—
324#433—51no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339C3×C4×C5—41no—
340C3×C4×C5—41no—
341C3×C4×C5C2×#4111yescharacteristic
342C3×C4×C5C2×#4111yescharacteristic
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C2×C3×Q8—22no—
347C2×C3×Q8—22no—
348C2×C3×Q8—21no—
349C2×C3×Q8—51no—
350C2×C3×Q8—101no—
351C2×C3×Q8C22×D511yescharacteristic
352C2×C3×Q8C22×D511yescharacteristic
353C2×C3×D4—51no—
354C2×C3×D4—101no—
355C22×C3×C4—21no—
356C22×C3×C4—101no—
357C22×C3×C4C22×D511yescharacteristic
358C3×Q16—102no—
359C3×Q16—102no—
360C3×SD16—102no—
361C3×SD16—102no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8—51no—
365C2×C3×C8—51no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—51no—
371C3×C4⋊C4—51no—
372C3×C4⋊C4—101no—
373C3×C4⋊C4—101no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4C22⋊D511yescharacteristic
376C3×C4⋊C4C22⋊D511yescharacteristic
377C3×C4⋊C4C22×D511yescharacteristic
378C3×C4⋊C4C22×D511yescharacteristic
379C3×C22⋊C4—21no—
380C3×C22⋊C4—101no—
381C3×C22⋊C4—101no—
382C3×C22⋊C4—101no—
383C3×C22⋊C4—101no—
384C3×C22⋊C4—101no—
385C3×C22⋊C4C22⋊D511yescharacteristic
386C3×C22⋊C4C22⋊D511yescharacteristic
387C3×C42—21no—
388C3×C42—21no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—21no—
392C3×C42—101no—
393C3×C42C22×D511yescharacteristic
394C3×C42C22×D511yescharacteristic
395C23×C5C2×C3×D411yescharacteristic
396C22×D5—21no—
397C5×Q8—24no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8C3×#4112yes—
401C5×Q8C3×#4112yes—
402C2×C4×C5—24no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5C2×C3×D411yescharacteristic
410C2×C4×C5C2×C3×D411yescharacteristic
411C2×C4×C5C2×C3×D411yescharacteristic
412C2×C4×C5C2×C3×D411yescharacteristic
413C2×C4×C5C2×C3×D411yescharacteristic
414C2×C4×C5C24×C311yescharacteristic
415C22⋊D5—81no—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419D20—21no—
420D20—21no—
421C4×D5—81no—
422Dic10—21no—
423Dic10—21no—
424Dic10—81no—
425#168—21no—
426#168—21no—
427#168—21no—
428#168—21no—
429C22×Q8C2×C3×D511yescharacteristic
430C2×Q16—51no—
431C2×Q16—51no—
432C2×SD16—51no—
433C2×SD16—51no—
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—21no—
443C4×Q8—21no—
444C4×Q8—51no—
445C4×Q8C2×C3×D511yescharacteristic
446C4×Q8C2×C3×D511yescharacteristic
447C4×Q8C2×C3×D511yescharacteristic
448C4×Q8C2×C3×D511yescharacteristic
449C4×D4—51no—
450#117—21no—
451#117—21no—
452#117C2×C3×D511yescharacteristic
453#117C2×C3×D511yescharacteristic
454#107—51no—
455#107—51no—
456#106—51no—
457#106—51no—
458C4⋊C8—51no—
459C4⋊C8—51no—
460#103—51no—
461#103—51no—
462#103—51no—
463#103—51no—
464#103—51no—
465#103—51no—
466#102—51no—
467#102—51no—
468C22⋊C8—51no—
469C22⋊C8—51no—
470#97—51no—
471C4×C8—51no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—81no—
477C23×C3—101no—
478C23×C3C2×C22⋊D511yescharacteristic
479C3×Q8—24no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—101no—
483C3×Q8—101no—
484C3×Q8—401no—
485C3×Q8#70912yes—
486C3×Q8#70912yes—
487C3×D4—101no—
488C3×D4—101no—
489C3×D4—401no—
490C2×C3×C4—24no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—101no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—401no—
501C2×C3×C4C2×C22⋊D511yescharacteristic
502C2×C3×C4C2×C22⋊D511yescharacteristic
503C2×C3×C4C2×C22⋊D511yescharacteristic
504C2×C3×C4C2×C22⋊D511yescharacteristic
505C2×C3×C4C2×C22⋊D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C3×C8—101no—
508C3×C8—101no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×C3×D411yescharacteristic
515C2×D5—41no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—22no—
523C4×C5—22no—
524C4×C5—21no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5C2×C3×#4111yescharacteristic
528C4×C5C2×C3×#4111yescharacteristic
529Dic5—41no—
530Dic5—41no—
531Dic5—41no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—51no—
536C2×Q8—101no—
537C2×Q8C22×C3×D511yescharacteristic
538C2×Q8C22×C3×D511yescharacteristic
539C2×D4—51no—
540C2×D4—101no—
541C22×C4—21no—
542C22×C4—101no—
543C22×C4C22×C3×D511yescharacteristic
544Q16—102no—
545Q16—102no—
546SD16—102no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—51no—
551C2×C8—51no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4C3×C22⋊D511yescharacteristic
562C4⋊C4C3×C22⋊D511yescharacteristic
563C4⋊C4C22×C3×D511yescharacteristic
564C4⋊C4C22×C3×D511yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—101no—
567C22⋊C4—101no—
568C22⋊C4—101no—
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4C3×C22⋊D511yescharacteristic
572C22⋊C4C3×C22⋊D511yescharacteristic
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—101no—
579C42C22×C3×D511yescharacteristic
580C42C22×C3×D511yescharacteristic
581C3×C5#312111yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—201no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C22×C22⋊D511yescharacteristic
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—201no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4C2×#70911yescharacteristic
602C3×C4C2×#70911yescharacteristic
603C2×C5—41no—
604C2×C5C3×#52511yescharacteristic
605C2×C5C3×#57711yescharacteristic
606C2×C5C3×#57811yescharacteristic
607D5—81no—
608C23—101no—
609C23C2×C3×C22⋊D511yescharacteristic
610Q8—24no—
611Q8—21no—
612Q8—21no—
613Q8—101no—
614Q8—101no—
615Q8—401no—
616Q8C3×#70912yes—
617Q8C3×#70912yes—
618D4—101no—
619D4—101no—
620D4—401no—
621C2×C4—24no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—401no—
632C2×C4C2×C3×C22⋊D511yescharacteristic
633C2×C4C2×C3×C22⋊D511yescharacteristic
634C2×C4C2×C3×C22⋊D511yescharacteristic
635C2×C4C2×C3×C22⋊D511yescharacteristic
636C2×C4C2×C3×C22⋊D511yescharacteristic
637C2×C4C23×C3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—101no—
641C8—101no—
642C2×C3—41no—
643C2×C3—401no—
644C2×C3#6612511yescharacteristic
645C2×C3#6617111yescharacteristic
646C2×C3#6617211yescharacteristic
647C5C3×#312111yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—201no—
652C22—201no—
653C22—201no—
654C22C22×C3×C22⋊D511yescharacteristic
655C4—22no—
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—41no—
663C4—41no—
664C4—201no—
665C4—201no—
666C4—201no—
667C4C2×C3×#70911yescharacteristic
668C4C2×C3×#70911yescharacteristic
669C3#1061428311yescharacteristic, direct product factor, Sylow
670C2—41no—
671C2—401no—
672C2C3×#6612511yescharacteristic
673C2C3×#6617111yescharacteristic
674C2C3×#6617211yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#519C2
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC3×#519D5
hypocenterC5C3×#3121
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C3×C5×#519C2semidirect
3. C3×#65517C2semidirect
5. C3×#65319C2semidirect
6. C3×C4×#689C2semidirect
7. C3×#65317C2semidirect
8. C3×#65317C2semidirect
9. C3×#65315C2semidirect
10. C3×C4×#688C2semidirect
11. C3×#65310C2semidirect
12. C3×#65309C2semidirect
14. C3×#65289C2semidirect
15. C3×#65285C2semidirect
16. #10614283C3direct (N × H)
61. C5×#519C2×C3semidirect
63. #65517C2×C3semidirect
65. #65319C2×C3semidirect
66. C4×#689C2×C3semidirect
67. #65317C2×C3semidirect
68. #65317C2×C3semidirect
69. #65315C2×C3semidirect
70. C4×#688C2×C3semidirect
71. #65310C2×C3semidirect
72. #65309C2×C3semidirect
74. #65289C2×C3semidirect
75. #65285C2×C3semidirect
126. C3×#519D5semidirect
311. #519C3×D5semidirect
581. C3×C5#3121semidirect
647. C5C3×#3121semidirect
669. C3#10614283direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5192
C3×#658682
C3×#655172
C3×#655162
C3×#653192
C3×C4×#6892
C3×#653172
C3×#653152
C3×C4×#6882
C3×#653102
C3×#653092
C3×#652922
C3×#652892
C3×#652852
#106142833
C3×#31215