Finite Group Databasebeta

← C3×#10612240 #14435581

Subgroups — C3×#10612240 #14435581

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66016C211yesmaximal, characteristic, complemented
2C3×#65879C211yesmaximal, characteristic, complemented
3C3×C5×#463C211yesmaximal, characteristic, complemented
4C3×#65458C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6C3×#65445C211yesmaximal, characteristic
7C3×#65441C211yesmaximal, characteristic, complemented
8C3×#65346C211yesmaximal, characteristic, complemented
9C3×#65296C211yesmaximal, characteristic, complemented
10C3×#65131C211yesmaximal, characteristic, complemented
11C3×#65129C211yesmaximal, characteristic, complemented
12C3×#65106C211yesmaximal, characteristic, complemented
13C3×#65104C211yesmaximal, characteristic, complemented
14C3×#65068C211yesmaximal, characteristic, complemented
15C3×#65045C211yesmaximal, characteristic, complemented
16#10612240C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C2×C3×C5×D8C2211yescharacteristic
20C3×C5×#124C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C3×#4092C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic, complemented
24C2×C3×#688C2211yescharacteristic
25C3×#4084C2211yescharacteristic
26C3×D4×Dic5C2211yescharacteristic
27C3×D4×Dic5C2211yescharacteristic, complemented
28C2×C3×#686C2211yescharacteristic
29C3×C4×C22⋊D5—21no—
30C2×C3×#685—21no—
31C3×#4039C2211yescharacteristic
32C3×#4038C2211yescharacteristic
33C3×#4032—21no—
34C3×#4031—21no—
35C3×#4027—21no—
36C3×D5×C22⋊C4—21no—
37C3×#4025—21no—
38C3×#4024—21no—
39C3×C4×D20C2211yescharacteristic
40C3×#4018C2211yescharacteristic
41C3×#4015C2211yescharacteristic, complemented
42C3×C5×C4⋊C8C2211yescharacteristic, complemented
43C3×C5×#103C2211yescharacteristic, complemented
44C3×C5×#102C2211yescharacteristic, complemented
45C3×#3967C2211yescharacteristic, complemented
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic, complemented
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3952C2211yescharacteristic
52C3×#3952C2211yescharacteristic
53C3×#3949C2211yescharacteristic, complemented
54C3×#3949C2211yescharacteristic, complemented
55C3×#3947C2211yescharacteristic, complemented
56C3×C8×Dic5C2211yescharacteristic, complemented
57C3×#3939C2211yescharacteristic, complemented
58C3×#3939C2211yescharacteristic, complemented
59C3×C4⋊#168C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61#66016C2×C311yescharacteristic, complemented
62#65879C2×C311yescharacteristic, complemented
63C5×#463C2×C311yescharacteristic, complemented
64#65458C2×C311yescharacteristic, complemented
65SD16×Dic5C2×C311yescharacteristic, complemented
66#65445C2×C311yescharacteristic
67#65441C2×C311yescharacteristic, complemented
68#65346C2×C311yescharacteristic, complemented
69#65296C2×C311yescharacteristic, complemented
70#65131C2×C311yescharacteristic, complemented
71#65129C2×C311yescharacteristic, complemented
72#65106C2×C311yescharacteristic, complemented
73#65104C2×C311yescharacteristic, complemented
74#65068C2×C311yescharacteristic, complemented
75#65045C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5—21no—
83C22×C3×Dic5—21no—
84C22×C3×Dic5—21no—
85C3×D4×D5—22no—
86C3×D4×D5—22no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10—21no—
92C3×C5×SD16—22no—
93C3×C5×D8—22no—
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C42×C5C2311yescharacteristic
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
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×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683D411yescharacteristic
119C3×#683D411yescharacteristic
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542—51no—
126C3×#518—51no—
127C3×#485—51no—
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463D511yescharacteristic, complemented
133C3×#450—51no—
134C3×#447—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C2×D4×D5C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C2×C5×D8C22×C311yescharacteristic
143C5×#124C22×C311yescharacteristic, complemented
144C4×C5×D4C22×C311yescharacteristic
145#4092C22×C311yescharacteristic
146Q8×Dic5C22×C311yescharacteristic, complemented
147C2×#688C22×C311yescharacteristic
148#4084C22×C311yescharacteristic
149D4×Dic5C22×C311yescharacteristic
150D4×Dic5C22×C311yescharacteristic, complemented
151C2×#686C22×C311yescharacteristic
152C4×C22⋊D5—21no—
153C2×#685—21no—
154#4039C22×C311yescharacteristic
155#4038C22×C311yescharacteristic
156#4032—21no—
157#4031—21no—
158#4027—21no—
159D5×C22⋊C4—21no—
160#4025—21no—
161#4024—21no—
162C4×D20C22×C311yescharacteristic
163#4018C22×C311yescharacteristic
164#4015C22×C311yescharacteristic, complemented
165C5×C4⋊C8C22×C311yescharacteristic, complemented
166C5×#103C22×C311yescharacteristic, complemented
167C5×#102C22×C311yescharacteristic, complemented
168#3967C22×C311yescharacteristic, complemented
169#3964C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3964C22×C311yescharacteristic, complemented
172#3953C22×C311yescharacteristic
173#3953C22×C311yescharacteristic
174#3952C22×C311yescharacteristic
175#3952C22×C311yescharacteristic
176#3949C22×C311yescharacteristic, complemented
177#3949C22×C311yescharacteristic, complemented
178#3947C22×C311yescharacteristic, complemented
179C8×Dic5C22×C311yescharacteristic, complemented
180#3939C22×C311yescharacteristic, complemented
181#3939C22×C311yescharacteristic, complemented
182C4⋊#168C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—24no—
188C22×C3×D5—81no—
189C22×C3×D5—81no—
190C22×C3×D5C2×D411yescharacteristic
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C3×C5×D4—21no—
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4#4112yes—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C3×C22⋊D5—24no—
204C3×C22⋊D5—81no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—81no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C3×D20—21no—
214C3×D20#4112yes—
215C3×C4×D5—21no—
216C3×C4×D5—21no—
217C3×C4×D5—81no—
218C3×C4×D5—81no—
219C3×Dic10—81no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×D4—51no—
225C2×C3×SD16—51no—
226C2×C3×SD16C2×D511yescharacteristic
227C2×C3×D8—51no—
228C2×C3×D8C2×D511yescharacteristic
229C3×C4⋊Q8—51no—
230C3×#126—101no—
231C3×#124—101no—
232C3×#124C2×D511yescharacteristic, complemented
233C3×#123—101no—
234C3×C22⋊Q8—51no—
235C3×C22⋊Q8—101no—
236C3×#121—51no—
237C3×C4×Q8—51no—
238C3×C4×D4—51no—
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—51no—
247C2×C3×C22⋊C4—101no—
248C2×C3×C22⋊C4—101no—
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106—51no—
253C3×C4⋊C8—51no—
254C3×C4⋊C8C2×D511yescharacteristic, complemented
255C3×#103—51no—
256C3×#103C2×D511yescharacteristic, complemented
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic, complemented
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×#97—51no—
266C3×C4×C8—51no—
267C23×D5—21no—
268C2×C5×Q8C23×C311yescharacteristic
269C2×C5×D4C23×C311yescharacteristic
270C2×C5×D4C23×C311yescharacteristic
271C22×C4×C5—21no—
272C2×C22⋊D5—21no—
273C2×C22⋊D5—21no—
274C22×Dic5—21no—
275C22×Dic5—21no—
276D4×D5—22no—
277D4×D5—22no—
278C2×D20C23×C311yescharacteristic
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5C23×C311yescharacteristic
282C2×Dic10—21no—
283C5×SD16—22no—
284C5×D8—22no—
285C2×C5×C8C23×C311yescharacteristic
286C2×C5×C8C23×C311yescharacteristic
287C5×C4⋊C4C23×C311yescharacteristic
288C5×C22⋊C4—21no—
289C5×C22⋊C4—21no—
290C5×C22⋊C4—21no—
291C42×C5C23×C311yescharacteristic
292C22⋊Dic5—21no—
293C22⋊Dic5—21no—
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
307C4⋊Dic5C23×C311yescharacteristic
308#683—21no—
309#683C3×D411yescharacteristic
310#683C3×D411yescharacteristic
311C4×Dic5—21no—
312C4×Dic5—21no—
313C4×Dic5C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#542—51no—
317#518—51no—
318#485—51no—
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463C3×D511yescharacteristic, complemented
324#450—51no—
325#447—51no—
326#442—51no—
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—22no—
340C2×C3×D5—21no—
341C2×C3×D5—21no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—84no—
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×Dic5—41no—
357C24×C3—101no—
358C2×C3×Q8—101no—
359C2×C3×Q8C22×D511yescharacteristic
360C2×C3×D4—51no—
361C2×C3×D4—101no—
362C2×C3×D4—102no—
363C2×C3×D4—102no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
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—
373C3×SD16—22no—
374C3×SD16—102no—
375C3×D8—22no—
376C3×D8—102no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8C22×D511yescharacteristic
380C2×C3×C8C22×D511yescharacteristic
381C3×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—51no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C42—51no—
403C3×C42—101no—
404C3×C42—101no—
405C3×C42C22×D511yescharacteristic
406C23×C5—21no—
407C23×C5—21no—
408C22×D5—21no—
409C22×D5—24no—
410C22×D5—81no—
411C22×D5—81no—
412C22×D5C2×C3×D411yescharacteristic
413C5×Q8—21no—
414C5×Q8—21no—
415C5×D4—21no—
416C5×D4—21no—
417C5×D4—21no—
418C5×D4C3×#4112yes—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—81no—
422C2×C4×C5C2×C3×D411yescharacteristic
423C2×C4×C5C2×C3×D411yescharacteristic
424C2×C4×C5C24×C311yescharacteristic
425C22⋊D5—24no—
426C22⋊D5—81no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—81no—
431C2×Dic5—81no—
432C2×Dic5C2×C3×D411yescharacteristic
433C2×Dic5C2×C3×D411yescharacteristic
434C2×Dic5C2×C3×D411yescharacteristic
435D20—21no—
436D20C3×#4112yes—
437C4×D5—21no—
438C4×D5—21no—
439C4×D5—81no—
440C4×D5—81no—
441Dic10—81no—
442C5×C8—21no—
443C5×C8—21no—
444#168—21no—
445#168—21no—
446C22×D4—51no—
447C2×SD16—51no—
448C2×SD16C2×C3×D511yescharacteristic
449C2×D8—51no—
450C2×D8C2×C3×D511yescharacteristic
451C4⋊Q8—51no—
452#126—101no—
453#124—101no—
454#124C2×C3×D511yescharacteristic, complemented
455#123—101no—
456C22⋊Q8—51no—
457C22⋊Q8—101no—
458#121—51no—
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—101no—
465C4×D4—101no—
466C4×D4C2×C3×D511yescharacteristic
467#117—51no—
468#117—51no—
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—51no—
472#107—51no—
473#106—51no—
474#106—51no—
475C4⋊C8—51no—
476C4⋊C8C2×C3×D511yescharacteristic, complemented
477#103—51no—
478#103C2×C3×D511yescharacteristic, complemented
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102—51no—
484#102C2×C3×D511yescharacteristic, complemented
485C22⋊C8—51no—
486C22⋊C8—51no—
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—42no—
490C2×C3×C5—81no—
491C2×C3×C5#52511yescharacteristic
492C2×C3×C5#57611yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C3×D5—41no—
495C3×D5—42no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—51no—
499C23×C3—104no—
500C23×C3—101no—
501C23×C3—401no—
502C23×C3—401no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—401no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—52no—
510C3×D4—104no—
511C3×D4—101no—
512C3×D4—401no—
513C3×D4#71112yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—51no—
517C2×C3×C4—51no—
518C2×C3×C4—51no—
519C2×C3×C4—81no—
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×C4—401no—
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—22no—
537C22×C5—41no—
538C22×C5—41no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5C22×C3×D411yescharacteristic
543C2×D5—21no—
544C2×D5—21no—
545C2×D5—21no—
546C2×D5—22no—
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—84no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—41no—
553C4×C5—41no—
554C4×C5C2×C3×#4111yescharacteristic
555C4×C5C2×C3×#4111yescharacteristic
556Dic5—21no—
557Dic5—21no—
558Dic5—21no—
559Dic5—41no—
560Dic5—41no—
561Dic5—41no—
562C24—101no—
563C2×Q8—101no—
564C2×Q8C22×C3×D511yescharacteristic
565C2×D4—51no—
566C2×D4—101no—
567C2×D4—102no—
568C2×D4—102no—
569C2×D4—101no—
570C2×D4C22×C3×D511yescharacteristic
571C2×D4C22×C3×D511yescharacteristic
572C22×C4—21no—
573C22×C4—51no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578SD16—22no—
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—51no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—51no—
599C22⋊C4—51no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4—101no—
606C22⋊C4—101no—
607C42—51no—
608C42—101no—
609C42—101no—
610C42C22×C3×D511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—22no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—101no—
619C22×C3—101no—
620C22×C3—101no—
621C22×C3—102no—
622C22×C3—201no—
623C22×C3—201no—
624C22×C3—404no—
625C22×C3C2×D4×D511yescharacteristic
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—101no—
631C3×C4—101no—
632C3×C4—101no—
633C3×C4—201no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4C2×#71111yescharacteristic
637C3×C4D5×#4111yescharacteristic
638C2×C5—42no—
639C2×C5—81no—
640C2×C5C3×#52511yescharacteristic
641C2×C5C3×#57611yescharacteristic
642C2×C5C3×#57711yescharacteristic
643D5—41no—
644D5—42no—
645C23—21no—
646C23—21no—
647C23—51no—
648C23—104no—
649C23—101no—
650C23—401no—
651C23—401no—
652Q8—21no—
653Q8—21no—
654Q8—401no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—52no—
659D4—104no—
660D4—101no—
661D4—401no—
662D4C3×#71112yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—51no—
666C2×C4—51no—
667C2×C4—51no—
668C2×C4—81no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—401no—
675C2×C4—401no—
676C2×C4—401no—
677C2×C4—401no—
678C2×C4C3×D4×D511yescharacteristic
679C2×C4C3×D4×D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—21no—
682C8—21no—
683C8—101no—
684C8—101no—
685C2×C3—42no—
686C2×C3—81no—
687C2×C3—201no—
688C2×C3—202no—
689C2×C3#6594011yescharacteristic
690C2×C3#6610411yescharacteristic
691C2×C3#6610811yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—101no—
700C22—101no—
701C22—101no—
702C22—102no—
703C22—201no—
704C22—201no—
705C22—404no—
706C22C2×C3×D4×D511yescharacteristic
707C4—21no—
708C4—21no—
709C4—41no—
710C4—41no—
711C4—101no—
712C4—101no—
713C4—101no—
714C4—201no—
715C4—201no—
716C4—201no—
717C4C2×C3×#71111yescharacteristic
718C4C3×D5×#4111yescharacteristic
719C3#1061224011yescharacteristic, direct product factor, Sylow
720C2—42no—
721C2—81no—
722C2—201no—
723C2—202no—
724C2C3×#6594011yescharacteristic
725C2C3×#6610411yescharacteristic
726C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#463C2
socleC22×C3×C5C22×D4
prime radicalC3×#65445C2
hypercenterC3×#463D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#66016C2semidirect
2. C3×#65879C2semidirect
3. C3×C5×#463C2semidirect
4. C3×#65458C2semidirect
5. C3×SD16×Dic5C2semidirect
7. C3×#65441C2semidirect
8. C3×#65346C2semidirect
9. C3×#65296C2semidirect
10. C3×#65131C2semidirect
11. C3×#65129C2semidirect
12. C3×#65106C2semidirect
13. C3×#65104C2semidirect
14. C3×#65068C2semidirect
15. C3×#65045C2semidirect
16. #10612240C3direct (N × H)
20. C3×C5×#124C22semidirect
23. C3×Q8×Dic5C22semidirect
27. C3×D4×Dic5C22semidirect
41. C3×#4015C22semidirect
42. C3×C5×C4⋊C8C22semidirect
43. C3×C5×#103C22semidirect
44. C3×C5×#102C22semidirect
45. C3×#3967C22semidirect
48. C3×#3964C22semidirect
53. C3×#3949C22semidirect
54. C3×#3949C22semidirect
55. C3×#3947C22semidirect
56. C3×C8×Dic5C22semidirect
57. C3×#3939C22semidirect
58. C3×#3939C22semidirect
59. C3×C4⋊#168C22semidirect
61. #66016C2×C3semidirect
62. #65879C2×C3semidirect
63. C5×#463C2×C3semidirect
64. #65458C2×C3semidirect
65. SD16×Dic5C2×C3semidirect
67. #65441C2×C3semidirect
68. #65346C2×C3semidirect
69. #65296C2×C3semidirect
70. #65131C2×C3semidirect
71. #65129C2×C3semidirect
72. #65106C2×C3semidirect
73. #65104C2×C3semidirect
74. #65068C2×C3semidirect
75. #65045C2×C3semidirect
132. C3×#463D5semidirect
143. C5×#124C22×C3semidirect
146. Q8×Dic5C22×C3semidirect
150. D4×Dic5C22×C3semidirect
164. #4015C22×C3semidirect
165. C5×C4⋊C8C22×C3semidirect
166. C5×#103C22×C3semidirect
167. C5×#102C22×C3semidirect
168. #3967C22×C3semidirect
171. #3964C22×C3semidirect
176. #3949C22×C3semidirect
177. #3949C22×C3semidirect
178. #3947C22×C3semidirect
179. C8×Dic5C22×C3semidirect
180. #3939C22×C3semidirect
181. #3939C22×C3semidirect
182. C4⋊#168C22×C3semidirect
232. C3×#124C2×D5semidirect
254. C3×C4⋊C8C2×D5semidirect
256. C3×#103C2×D5semidirect
262. C3×#102C2×D5semidirect
323. #463C3×D5semidirect
454. #124C2×C3×D5semidirect
476. C4⋊C8C2×C3×D5semidirect
478. #103C2×C3×D5semidirect
484. #102C2×C3×D5semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10612240direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660162
C3×#658792
C3×C5×#4632
C3×#654582
C3×SD16×Dic52
C3×#654452
C3×#654412
C3×#653462
C3×#652962
C3×#651312
C3×#651292
C3×#651062
C3×#651042
C3×#650682
C3×#650452
#106122403
C3×#31185