Finite Group Databasebeta

← C3×#10612290 #14458888

Subgroups — C3×#10612290 #14458888

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66010C211yesmaximal, characteristic, complemented
2C3×#65892C211yesmaximal, characteristic, complemented
3C3×C5×#463C211yesmaximal, characteristic, complemented
4C3×#65461C211yesmaximal, characteristic, complemented
5C3×#65460C211yesmaximal, characteristic, complemented
6C3×#65446C211yesmaximal, characteristic, complemented
7C3×#65445C211yesmaximal, characteristic, complemented
8C3×#65345C211yesmaximal, characteristic, complemented
9C3×C4×#686C211yesmaximal, characteristic, complemented
10C3×#65136C211yesmaximal, characteristic, complemented
11C3×#65123C211yesmaximal, characteristic, complemented
12C3×#65098C211yesmaximal, characteristic, complemented
13C3×#65093C211yesmaximal, characteristic, complemented
14C3×#65068C211yesmaximal, characteristic, complemented
15C3×D5×#102C211yesmaximal, characteristic, complemented
16#10612290C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic, complemented
20C2×C3×C5×D8C2211yescharacteristic
21C3×C5×#124C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic, complemented
23C3×#4092C2211yescharacteristic
24C3×#4084C2211yescharacteristic
25C3×#4084C2211yescharacteristic
26C3×#4084C2211yescharacteristic, complemented
27C2×C3×#686C2211yescharacteristic
28C3×#4075—21no—
29C3×C4×C22⋊D5—21no—
30C2×C3×C8×D5C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic, complemented
32C3×#4038C2211yescharacteristic, complemented
33C3×D5×C4⋊C4C2211yescharacteristic
34C3×#4030—21no—
35C3×#4030—21no—
36C3×#4029—21no—
37C3×#4028—21no—
38C3×D5×C22⋊C4—21no—
39C3×#4025—21no—
40C3×C4×D20C2211yescharacteristic
41C3×C4×D20C2211yescharacteristic
42C3×#4016C2211yescharacteristic, complemented
43C3×C5×C4⋊C8C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic
46C3×#3967C2211yescharacteristic, complemented
47C3×#3967C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×#3964C2211yescharacteristic
50C3×#3964C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic
53C3×#3952C2211yescharacteristic
54C3×#3952C2211yescharacteristic, complemented
55C3×#3950C2211yescharacteristic, complemented
56C3×#3949C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3939C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3297—51nomaximal, Hall
61#66010C2×C311yescharacteristic, complemented
62#65892C2×C311yescharacteristic, complemented
63C5×#463C2×C311yescharacteristic, complemented
64#65461C2×C311yescharacteristic, complemented
65#65460C2×C311yescharacteristic, complemented
66#65446C2×C311yescharacteristic, complemented
67#65445C2×C311yescharacteristic, complemented
68#65345C2×C311yescharacteristic, complemented
69C4×#686C2×C311yescharacteristic, complemented
70#65136C2×C311yescharacteristic, complemented
71#65123C2×C311yescharacteristic, complemented
72#65098C2×C311yescharacteristic, complemented
73#65093C2×C311yescharacteristic, complemented
74#65068C2×C311yescharacteristic, complemented
75D5×#102C2×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—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C3×#713—22no—
86C3×#713—41no—
87C3×D4×D5—22no—
88C3×D4×D5—41no—
89C2×C3×D20—21no—
90C2×C3×D20D411yescharacteristic
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5C2311yescharacteristic
96C2×C3×C4×D5C2311yescharacteristic
97C3×C5×SD16—41no—
98C3×C5×D8—41no—
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C5×C22⋊C4—21no—
105C3×C42×C5C2311yescharacteristic
106C3×C22⋊Dic5—21no—
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5—21no—
109C3×#686—22no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×#685D411yescharacteristic
115C3×C4⋊Dic5D411yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×#683—21no—
123C3×C4×Dic5—21no—
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C3×C8×D5—41no—
127C3×C8×D5—41no—
128C3×#553—51no—
129C3×#546—51no—
130C3×#488—51no—
131C3×#484—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#466—51no—
135C3×#465—51no—
136C3×#463D511yescharacteristic, complemented
137C3×#449—51no—
138C3×#447—51no—
139C3×C4×D8—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×#713C22×C311yescharacteristic
144C2×D4×D5C22×C311yescharacteristic
145C2×C5×SD16C22×C311yescharacteristic, complemented
146C2×C5×D8C22×C311yescharacteristic
147C5×#124C22×C311yescharacteristic
148C4×C5×D4C22×C311yescharacteristic, complemented
149#4092C22×C311yescharacteristic
150#4084C22×C311yescharacteristic
151#4084C22×C311yescharacteristic
152#4084C22×C311yescharacteristic, complemented
153C2×#686C22×C311yescharacteristic
154#4075—21no—
155C4×C22⋊D5—21no—
156C2×C8×D5C22×C311yescharacteristic
157C2×C8×D5C22×C311yescharacteristic, complemented
158#4038C22×C311yescharacteristic, complemented
159D5×C4⋊C4C22×C311yescharacteristic
160#4030—21no—
161#4030—21no—
162#4029—21no—
163#4028—21no—
164D5×C22⋊C4—21no—
165#4025—21no—
166C4×D20C22×C311yescharacteristic
167C4×D20C22×C311yescharacteristic
168#4016C22×C311yescharacteristic, complemented
169C5×C4⋊C8C22×C311yescharacteristic, complemented
170C5×#103C22×C311yescharacteristic, complemented
171C5×#102C22×C311yescharacteristic
172#3967C22×C311yescharacteristic, complemented
173#3967C22×C311yescharacteristic, complemented
174#3964C22×C311yescharacteristic
175#3964C22×C311yescharacteristic
176#3964C22×C311yescharacteristic, complemented
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3952C22×C311yescharacteristic
180#3952C22×C311yescharacteristic, complemented
181#3950C22×C311yescharacteristic, complemented
182#3949C22×C311yescharacteristic, complemented
183#3941C22×C311yescharacteristic
184#3939C22×C311yescharacteristic, complemented
185C4×#168C22×C311yescharacteristic, complemented
186#3297—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—42no—
191C22×C3×D5—42no—
192C22×C3×D5—81no—
193C22×C3×D5C2×D411yescharacteristic
194C22×C3×D5C2×D411yescharacteristic
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207C3×C22⋊D5—42no—
208C3×C22⋊D5—42no—
209C3×C22⋊D5—81no—
210C3×C22⋊D5—81no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—22no—
217C3×D20—21no—
218C3×D20—42no—
219C3×D20#4112yes—
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—21no—
223C3×C4×D5—21no—
224C3×C4×D5—42no—
225C3×C4×D5—81no—
226C3×C4×D5—81no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C2×C3×SD16C2×D511yescharacteristic, complemented
234C2×C3×D8—51no—
235C2×C3×D8C2×D511yescharacteristic
236C22×C3×C8—51no—
237C22×C3×C8—51no—
238C3×#126—101no—
239C3×#125—51no—
240C3×#124C2×D511yescharacteristic
241C3×#123—101no—
242C3×#123—101no—
243C3×C22⋊Q8—51no—
244C3×#121—51no—
245C3×#121—51no—
246C3×#121—51no—
247C3×#121—101no—
248C3×#121—101no—
249C3×#120—101no—
250C3×C4×D4—51no—
251C3×C4×D4—51no—
252C3×C4×D4—101no—
253C3×C4×D4C2×D511yescharacteristic, complemented
254C3×#117—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—101no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#106—51no—
260C3×C4⋊C8C2×D511yescharacteristic, complemented
261C3×#103—51no—
262C3×#103—51no—
263C3×#103C2×D511yescharacteristic, complemented
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102C2×D511yescharacteristic
271C3×C22⋊C8—51no—
272C3×C22⋊C8—51no—
273C3×C4×C8—51no—
274C23×D5—21no—
275C2×C5×Q8C23×C311yescharacteristic
276C2×C5×D4C23×C311yescharacteristic
277C2×C5×D4C23×C311yescharacteristic
278C22×C4×C5—21no—
279C2×C22⋊D5—21no—
280C2×C22⋊D5—21no—
281C2×C22⋊D5—21no—
282C2×C22⋊D5—21no—
283#713—22no—
284#713—41no—
285D4×D5—22no—
286D4×D5—41no—
287C2×D20—21no—
288C2×D20C3×D411yescharacteristic
289C2×D20C23×C311yescharacteristic
290C2×C4×D5—21no—
291C2×C4×D5—21no—
292C2×C4×D5—21no—
293C2×C4×D5C23×C311yescharacteristic
294C2×C4×D5C23×C311yescharacteristic
295C5×SD16—41no—
296C5×D8—41no—
297C2×C5×C8C23×C311yescharacteristic
298C2×C5×C8C23×C311yescharacteristic
299C5×C4⋊C4C23×C311yescharacteristic
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C42×C5C23×C311yescharacteristic
304C22⋊Dic5—21no—
305C22⋊Dic5—21no—
306C22⋊Dic5—21no—
307#686—22no—
308#685—21no—
309#685—21no—
310#685—21no—
311#685C3×D411yescharacteristic
312#685C3×D411yescharacteristic
313C4⋊Dic5C3×D411yescharacteristic
314C4⋊Dic5C23×C311yescharacteristic
315C4⋊Dic5C23×C311yescharacteristic
316C4⋊Dic5C23×C311yescharacteristic
317#683—21no—
318#683—21no—
319#683—21no—
320#683—21no—
321C4×Dic5—21no—
322C2×#168C23×C311yescharacteristic
323C2×#168C23×C311yescharacteristic
324C8×D5—41no—
325C8×D5—41no—
326#553—51no—
327#546—51no—
328#488—51no—
329#484—51no—
330#482—51no—
331#478—51no—
332#466—51no—
333#465—51no—
334#463C3×D511yescharacteristic, complemented
335#449—51no—
336#447—51no—
337C4×D8—51no—
338C8×D4—51no—
339#416—51no—
340C2×#102—51no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5—21no—
351C2×C3×D5—22no—
352C2×C3×D5—21no—
353C2×C3×D5—21no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5#13512yes—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5—41no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—51no—
374C2×C3×D4—51no—
375C2×C3×D4—101no—
376C2×C3×D4—101no—
377C2×C3×D4—102no—
378C2×C3×D4—101no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4—201no—
382C2×C3×D4C22×D511yescharacteristic
383C2×C3×D4C22×D511yescharacteristic
384C22×C3×C4—21no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—101no—
388C22×C3×C4—101no—
389C22×C3×C4—101no—
390C3×SD16—41no—
391C3×D8—41no—
392C3×D8—102no—
393C2×C3×C8—51no—
394C2×C3×C8—51no—
395C2×C3×C8—201no—
396C2×C3×C8—201no—
397C2×C3×C8C22×D511yescharacteristic
398C2×C3×C8C22×D511yescharacteristic
399C3×C4⋊C4—51no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—51no—
403C3×C4⋊C4—101no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4—101no—
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—51no—
412C3×C22⋊C4—51no—
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C22⋊C4—101no—
416C3×C22⋊C4—101no—
417C3×C22⋊C4—101no—
418C3×C22⋊C4—101no—
419C3×C42—101no—
420C3×C42C22×D511yescharacteristic
421C23×C5—21no—
422C23×C5—21no—
423C22×D5—21no—
424C22×D5—42no—
425C22×D5—42no—
426C22×D5—81no—
427C22×D5C2×C3×D411yescharacteristic
428C22×D5C2×C3×D411yescharacteristic
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—21no—
432C5×D4—21no—
433C5×D4—21no—
434C5×D4—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—81no—
438C2×C4×C5C2×C3×D411yescharacteristic
439C2×C4×C5C2×C3×D411yescharacteristic
440C2×C4×C5C24×C311yescharacteristic
441C22⋊D5—42no—
442C22⋊D5—42no—
443C22⋊D5—81no—
444C22⋊D5—81no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5C2×C3×D411yescharacteristic
449C2×Dic5C2×C3×D411yescharacteristic
450D20—22no—
451D20—21no—
452D20—42no—
453D20C3×#4112yes—
454C4×D5—21no—
455C4×D5—21no—
456C4×D5—21no—
457C4×D5—21no—
458C4×D5—42no—
459C4×D5—81no—
460C4×D5—81no—
461C5×C8—21no—
462C5×C8—21no—
463#168—21no—
464#168—21no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16C2×C3×D511yescharacteristic, complemented
468C2×D8—51no—
469C2×D8C2×C3×D511yescharacteristic
470C22×C8—51no—
471C22×C8—51no—
472#126—101no—
473#125—51no—
474#124C2×C3×D511yescharacteristic
475#123—101no—
476#123—101no—
477C22⋊Q8—51no—
478#121—51no—
479#121—51no—
480#121—51no—
481#121—101no—
482#121—101no—
483#120—101no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—101no—
487C4×D4C2×C3×D511yescharacteristic, complemented
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—101no—
491#107—51no—
492#107—51no—
493#106—51no—
494C4⋊C8C2×C3×D511yescharacteristic, complemented
495#103—51no—
496#103—51no—
497#103C2×C3×D511yescharacteristic, complemented
498#102—51no—
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102—51no—
504#102C2×C3×D511yescharacteristic
505C22⋊C8—51no—
506C22⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—81no—
509C2×C3×C5—81no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—22no—
514C3×D5—41no—
515C3×D5—42no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—51no—
519C23×C3—51no—
520C23×C3—101no—
521C23×C3—202no—
522C23×C3—202no—
523C23×C3—401no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—52no—
531C3×D4—102no—
532C3×D4—101no—
533C3×D4—202no—
534C3×D4—202no—
535C3×D4—202no—
536C3×D4—401no—
537C3×D4—401no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—51no—
541C2×C3×C4—51no—
542C2×C3×C4—81no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—202no—
551C2×C3×C4—401no—
552C2×C3×C4—401no—
553C2×C3×C4D4×D511yescharacteristic
554C2×C3×C4D4×D511yescharacteristic
555C2×C3×C4C23×D511yescharacteristic
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—101no—
559C3×C8—101no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—41no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5C22×C3×D411yescharacteristic
567C2×D5—21no—
568C2×D5—21no—
569C2×D5—21no—
570C2×D5—21no—
571C2×D5—21no—
572C2×D5—22no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—84no—
576C2×D5C3×#13512yes—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—41no—
580C4×C5—41no—
581C4×C5C2×C3×#4111yescharacteristic
582C4×C5C3×H(5,𝔽2)11yescharacteristic
583Dic5—21no—
584Dic5—21no—
585Dic5—41no—
586Dic5—41no—
587Dic5—41no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8C22×C3×D511yescharacteristic
592C2×D4—51no—
593C2×D4—51no—
594C2×D4—101no—
595C2×D4—101no—
596C2×D4—102no—
597C2×D4—101no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—201no—
601C2×D4C22×C3×D511yescharacteristic
602C2×D4C22×C3×D511yescharacteristic
603C22×C4—21no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609SD16—41no—
610D8—41no—
611D8—102no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—201no—
615C2×C8—201no—
616C2×C8C22×C3×D511yescharacteristic
617C2×C8C22×C3×D511yescharacteristic
618C4⋊C4—51no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—101no—
626C4⋊C4C22×C3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—51no—
631C22⋊C4—51no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—101no—
638C42—101no—
639C42C22×C3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—52no—
648C22×C3—101no—
649C22×C3—101no—
650C22×C3—101no—
651C22×C3—101no—
652C22×C3—101no—
653C22×C3—102no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3—404no—
657C22×C3C2×D4×D511yescharacteristic
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4—201no—
665C3×C4—201no—
666C3×C4—201no—
667C3×C4#414411yescharacteristic
668C3×C4D5×#4111yescharacteristic
669C2×C5—81no—
670C2×C5—81no—
671C2×C5C3×#54611yescharacteristic
672C2×C5C2×C3×#13511yescharacteristic
673C2×C5C3×#57611yescharacteristic
674D5—22no—
675D5—41no—
676D5—42no—
677C23—21no—
678C23—21no—
679C23—51no—
680C23—51no—
681C23—101no—
682C23—202no—
683C23—202no—
684C23—401no—
685Q8—21no—
686Q8—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—52no—
692D4—102no—
693D4—101no—
694D4—202no—
695D4—202no—
696D4—202no—
697D4—401no—
698D4—401no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—51no—
702C2×C4—51no—
703C2×C4—81no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—202no—
712C2×C4—401no—
713C2×C4—401no—
714C2×C4C3×D4×D511yescharacteristic
715C2×C4C3×D4×D511yescharacteristic
716C2×C4C23×C3×D511yescharacteristic
717C8—21no—
718C8—21no—
719C8—101no—
720C8—101no—
721C2×C3—81no—
722C2×C3—81no—
723C2×C3—102no—
724C2×C3—201no—
725C2×C3—202no—
726C2×C3#6594611yescharacteristic
727C2×C3D5×#13511yescharacteristic
728C2×C3#6610811yescharacteristic
729C5C3×#329711yescharacteristic, complemented, Sylow
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—101no—
738C22—101no—
739C22—101no—
740C22—101no—
741C22—101no—
742C22—102no—
743C22—201no—
744C22—201no—
745C22—404no—
746C22C2×C3×D4×D511yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—41no—
751C4—101no—
752C4—101no—
753C4—201no—
754C4—201no—
755C4—201no—
756C4C3×#414411yescharacteristic
757C4C3×D5×#4111yescharacteristic
758C3#1061229011yescharacteristic, direct product factor, Sylow
759C2—81no—
760C2—81no—
761C2—102no—
762C2—201no—
763C2—202no—
764C2C3×#6594611yescharacteristic
765C2C3×D5×#13511yescharacteristic
766C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#463C2
socleC22×C3×C5C22×D4
hypercenterC3×#463D5
hypocenterC5C3×#3297
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×#66010C2semidirect
2. C3×#65892C2semidirect
3. C3×C5×#463C2semidirect
4. C3×#65461C2semidirect
5. C3×#65460C2semidirect
6. C3×#65446C2semidirect
7. C3×#65445C2semidirect
8. C3×#65345C2semidirect
9. C3×C4×#686C2semidirect
10. C3×#65136C2semidirect
11. C3×#65123C2semidirect
12. C3×#65098C2semidirect
13. C3×#65093C2semidirect
14. C3×#65068C2semidirect
15. C3×D5×#102C2semidirect
16. #10612290C3direct (N × H)
19. C2×C3×C5×SD16C22semidirect
22. C3×C4×C5×D4C22semidirect
26. C3×#4084C22semidirect
31. C2×C3×C8×D5C22semidirect
32. C3×#4038C22semidirect
42. C3×#4016C22semidirect
43. C3×C5×C4⋊C8C22semidirect
44. C3×C5×#103C22semidirect
46. C3×#3967C22semidirect
47. C3×#3967C22semidirect
50. C3×#3964C22semidirect
54. C3×#3952C22semidirect
55. C3×#3950C22semidirect
56. C3×#3949C22semidirect
58. C3×#3939C22semidirect
59. C3×C4×#168C22semidirect
61. #66010C2×C3semidirect
62. #65892C2×C3semidirect
63. C5×#463C2×C3semidirect
64. #65461C2×C3semidirect
65. #65460C2×C3semidirect
66. #65446C2×C3semidirect
67. #65445C2×C3semidirect
68. #65345C2×C3semidirect
69. C4×#686C2×C3semidirect
70. #65136C2×C3semidirect
71. #65123C2×C3semidirect
72. #65098C2×C3semidirect
73. #65093C2×C3semidirect
74. #65068C2×C3semidirect
75. D5×#102C2×C3semidirect
136. C3×#463D5semidirect
145. C2×C5×SD16C22×C3semidirect
148. C4×C5×D4C22×C3semidirect
152. #4084C22×C3semidirect
157. C2×C8×D5C22×C3semidirect
158. #4038C22×C3semidirect
168. #4016C22×C3semidirect
169. C5×C4⋊C8C22×C3semidirect
170. C5×#103C22×C3semidirect
172. #3967C22×C3semidirect
173. #3967C22×C3semidirect
176. #3964C22×C3semidirect
180. #3952C22×C3semidirect
181. #3950C22×C3semidirect
182. #3949C22×C3semidirect
184. #3939C22×C3semidirect
185. C4×#168C22×C3semidirect
233. C2×C3×SD16C2×D5semidirect
253. C3×C4×D4C2×D5semidirect
260. C3×C4⋊C8C2×D5semidirect
263. C3×#103C2×D5semidirect
334. #463C3×D5semidirect
467. C2×SD16C2×C3×D5semidirect
487. C4×D4C2×C3×D5semidirect
494. C4⋊C8C2×C3×D5semidirect
497. #103C2×C3×D5semidirect
640. C3×C5#3297semidirect
729. C5C3×#3297semidirect
758. C3#10612290direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660102
C3×#658922
C3×C5×#4632
C3×#654612
C3×#654602
C3×#654462
C3×#654452
C3×#653452
C3×C4×#6862
C3×#651362
C3×#651232
C3×#650982
C3×#650932
C3×#650682
C3×D5×#1022
#106122903
C3×#32975