Finite Group Databasebeta

← C3×#10610577 #14458870

Subgroups — C3×#10610577 #14458870

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×#66163C211yesmaximal, characteristic, complemented
2C3×#65864C211yesmaximal, characteristic, complemented
3C3×C5×#416C211yesmaximal, characteristic, complemented
4C3×#65527C211yesmaximal, characteristic, complemented
5C3×#65404C211yesmaximal, characteristic, complemented
6C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
7C3×#65292C211yesmaximal, characteristic, complemented
8C3×#65108C211yesmaximal, characteristic, complemented
9C3×#65098C211yesmaximal, characteristic, complemented
10C3×#65096C211yesmaximal, characteristic, complemented
11C3×#65089C211yesmaximal, characteristic, complemented
12C3×#65062C211yesmaximal, characteristic, complemented
13C3×D5×#102C211yesmaximal, characteristic, complemented
14C3×#65055C211yesmaximal, characteristic, complemented
15C3×#65045C211yesmaximal, characteristic, complemented
16#10610577C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic, complemented
20C3×C5×#117C2211yescharacteristic, complemented
21C3×#4093C2211yescharacteristic
22C3×#4092C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic, complemented
24C3×#4085—21no—
25C3×#4083—21no—
26C3×D4×Dic5C2211yescharacteristic
27C2×C3×#686C2211yescharacteristic
28C3×#4076C2211yescharacteristic
29C3×#4076C2211yescharacteristic, complemented
30C3×#4075—21no—
31C3×C4×C22⋊D5C2211yescharacteristic
32C2×C3×#685—21no—
33C2×C3×D40C2211yescharacteristic
34C2×C3×C8×D5C2211yescharacteristic
35C3×#4041C2211yescharacteristic
36C3×#4039C2211yescharacteristic, complemented
37C3×D5×C4⋊C4C2211yescharacteristic
38C3×#4036C2211yescharacteristic, complemented
39C3×#4030—21no—
40C3×#4029—21no—
41C3×#4022—21no—
42C3×C4×D20—21no—
43C3×C5×#103C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic
46C3×C5×#102C2211yescharacteristic
47C3×#3967C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×C22⋊#168C2211yescharacteristic, complemented
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic, complemented
52C3×#3952C2211yescharacteristic
53C3×#3950C2211yescharacteristic, complemented
54C3×#3946C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3297—51nomaximal, Hall
61#66163C2×C311yescharacteristic, complemented
62#65864C2×C311yescharacteristic, complemented
63C5×#416C2×C311yescharacteristic, complemented
64#65527C2×C311yescharacteristic, complemented
65#65404C2×C311yescharacteristic, complemented
66C8×C22⋊D5C2×C311yescharacteristic, complemented
67#65292C2×C311yescharacteristic, complemented
68#65108C2×C311yescharacteristic, complemented
69#65098C2×C311yescharacteristic, complemented
70#65096C2×C311yescharacteristic, complemented
71#65089C2×C311yescharacteristic, complemented
72#65062C2×C311yescharacteristic, complemented
73D5×#102C2×C311yescharacteristic, complemented
74#65055C2×C311yescharacteristic, complemented
75#65045C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C3×C5×#41—22no—
78C3×C5×#41—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5D411yescharacteristic
88C22×C3×Dic5—21no—
89C3×D4×D5—22no—
90C3×D4×D5—41no—
91C2×C3×D20—21no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5C2311yescharacteristic
97C2×C3×C5×C8—41no—
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C42×C5—21no—
104C3×C22⋊Dic5—21no—
105C3×C22⋊Dic5D411yescharacteristic
106C3×#688—41no—
107C3×#686—22no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685D411yescharacteristic
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×#683D411yescharacteristic
123C3×C4×Dic5C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C3×D40—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×#463—51no—
137C3×#449—51no—
138C3×#447—51no—
139C3×C4×D8—51no—
140C3×C8×D4—51no—
141C3×#416D511yescharacteristic, complemented
142C2×C3×#102—51no—
143C2×C5×#41C22×C311yescharacteristic
144C2×D4×D5C22×C311yescharacteristic
145C22×C5×C8C22×C311yescharacteristic, complemented
146C5×#117C22×C311yescharacteristic, complemented
147#4093C22×C311yescharacteristic
148#4092C22×C311yescharacteristic
149C2×#688C22×C311yescharacteristic, complemented
150#4085—21no—
151#4083—21no—
152D4×Dic5C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154#4076C22×C311yescharacteristic
155#4076C22×C311yescharacteristic, complemented
156#4075—21no—
157C4×C22⋊D5C22×C311yescharacteristic
158C2×#685—21no—
159C2×D40C22×C311yescharacteristic
160C2×C8×D5C22×C311yescharacteristic
161#4041C22×C311yescharacteristic
162#4039C22×C311yescharacteristic, complemented
163D5×C4⋊C4C22×C311yescharacteristic
164#4036C22×C311yescharacteristic, complemented
165#4030—21no—
166#4029—21no—
167#4022—21no—
168C4×D20—21no—
169C5×#103C22×C311yescharacteristic, complemented
170C5×#103C22×C311yescharacteristic, complemented
171C5×#102C22×C311yescharacteristic
172C5×#102C22×C311yescharacteristic
173#3967C22×C311yescharacteristic, complemented
174#3964C22×C311yescharacteristic
175C22⋊#168C22×C311yescharacteristic, complemented
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic, complemented
178#3952C22×C311yescharacteristic
179#3950C22×C311yescharacteristic, complemented
180#3946C22×C311yescharacteristic, complemented
181C8×Dic5C22×C311yescharacteristic, complemented
182#3941C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3940C22×C311yescharacteristic, complemented
185#3939C22×C311yescharacteristic, complemented
186#3297—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5—81no—
194C22×C3×D5C2×D411yescharacteristic
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—21no—
198C3×C5×D4—42no—
199C3×C5×D4#4112yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C3×C22⋊D5—22no—
209C3×C22⋊D5—42no—
210C3×C22⋊D5—81no—
211C3×C22⋊D5—81no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—81no—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—21no—
222C3×D20—42no—
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—81no—
226C3×C4×D5—81no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×C3×#41C2×D511yescharacteristic
232C22×C3×D4—51no—
233C2×C3×SD16—51no—
234C2×C3×D8—51no—
235C2×C3×D8—51no—
236C22×C3×C8—51no—
237C22×C3×C8C2×D511yescharacteristic, complemented
238C3×#126—101no—
239C3×#125—51no—
240C3×#124—51no—
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—51no—
253C3×C4×D4—101no—
254C3×#117C2×D511yescharacteristic, complemented
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—101no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#106—51no—
260C3×C4⋊C8—51no—
261C3×#103—51no—
262C3×#103C2×D511yescharacteristic, complemented
263C3×#103C2×D511yescharacteristic, complemented
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102C2×D511yescharacteristic
270C3×#102C2×D511yescharacteristic
271C3×C22⋊C8—51no—
272C3×C22⋊C8—51no—
273C3×C4×C8—51no—
274C23×D5—21no—
275C5×#41—22no—
276C5×#41—41no—
277C2×C5×Q8C23×C311yescharacteristic
278C2×C5×D4—21no—
279C2×C5×D4C23×C311yescharacteristic
280C22×C4×C5—21no—
281C22×C4×C5C23×C311yescharacteristic
282C2×C22⋊D5—21no—
283C2×C22⋊D5—21no—
284C2×C22⋊D5—21no—
285C2×C22⋊D5C3×D411yescharacteristic
286C22×Dic5—21no—
287D4×D5—22no—
288D4×D5—41no—
289C2×D20—21no—
290C2×D20C23×C311yescharacteristic
291C2×D20C23×C311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5C23×C311yescharacteristic
295C2×C5×C8—41no—
296C2×C5×C8C23×C311yescharacteristic
297C2×C5×C8C23×C311yescharacteristic
298C5×C4⋊C4C23×C311yescharacteristic
299C5×C4⋊C4C23×C311yescharacteristic
300C5×C22⋊C4—21no—
301C42×C5—21no—
302C22⋊Dic5—21no—
303C22⋊Dic5C3×D411yescharacteristic
304#688—41no—
305#686—22no—
306#685—21no—
307#685—21no—
308#685—21no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685C3×D411yescharacteristic
314C4⋊Dic5—21no—
315C4⋊Dic5C23×C311yescharacteristic
316C4⋊Dic5C23×C311yescharacteristic
317#683—21no—
318#683—21no—
319#683—21no—
320#683C3×D411yescharacteristic
321C4×Dic5C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323C2×#168C23×C311yescharacteristic
324D40—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#463—51no—
335#449—51no—
336#447—51no—
337C4×D8—51no—
338C8×D4—51no—
339#416C3×D511yescharacteristic, complemented
340C2×#102—51no—
341C22×C3×C5—22no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5—41no—
351C2×C3×D5—41no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5#13512yes—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
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—21no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C24×C3—101no—
370C3×#41—22no—
371C3×#41—41no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—51no—
375C2×C3×D4—51no—
376C2×C3×D4—51no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4—102no—
380C2×C3×D4—101no—
381C2×C3×D4—101no—
382C2×C3×D4—201no—
383C2×C3×D4C22×D511yescharacteristic
384C22×C3×C4—21no—
385C22×C3×C4—51no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4—101no—
389C22×C3×C4C22×D511yescharacteristic
390C3×SD16—201no—
391C3×D8—102no—
392C3×D8—201no—
393C2×C3×C8—41no—
394C2×C3×C8—51no—
395C2×C3×C8—51no—
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—101no—
403C3×C4⋊C4—101no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4C22×D511yescharacteristic
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—51no—
410C3×C22⋊C4—51no—
411C3×C22⋊C4—101no—
412C3×C22⋊C4—101no—
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—21no—
420C3×C42—51no—
421C23×C5—21no—
422C23×C5C2×C3×D411yescharacteristic
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—42no—
426C22×D5—42no—
427C22×D5—81no—
428C22×D5C2×C3×D411yescharacteristic
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—21no—
432C5×D4—42no—
433C5×D4C3×#4112yes—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—42no—
440C2×C4×C5C2×C3×D411yescharacteristic
441C2×C4×C5C24×C311yescharacteristic
442C22⋊D5—22no—
443C22⋊D5—42no—
444C22⋊D5—81no—
445C22⋊D5—81no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—81no—
449C2×Dic5C2×C3×D411yescharacteristic
450C2×Dic5C2×C3×D411yescharacteristic
451C2×Dic5C2×C3×D411yescharacteristic
452D20—21no—
453D20—21no—
454D20—21no—
455D20—21no—
456D20—42no—
457C4×D5—21no—
458C4×D5—21no—
459C4×D5—81no—
460C4×D5—81no—
461C5×C8—21no—
462C5×C8—21no—
463#168—21no—
464#168—21no—
465C2×#41C2×C3×D511yescharacteristic
466C22×D4—51no—
467C2×SD16—51no—
468C2×D8—51no—
469C2×D8—51no—
470C22×C8—51no—
471C22×C8C2×C3×D511yescharacteristic, complemented
472#126—101no—
473#125—51no—
474#124—51no—
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—51no—
487C4×D4—101no—
488#117C2×C3×D511yescharacteristic, complemented
489C2×C4⋊C4—51no—
490C2×C22⋊C4—101no—
491#107—51no—
492#107—51no—
493#106—51no—
494C4⋊C8—51no—
495#103—51no—
496#103C2×C3×D511yescharacteristic, complemented
497#103C2×C3×D511yescharacteristic, complemented
498#102—51no—
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102C2×C3×D511yescharacteristic
504#102C2×C3×D511yescharacteristic
505C22⋊C8—51no—
506C22⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—42no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—22no—
514C3×D5—81no—
515C3×D5—81no—
516C23×C3—21no—
517C23×C3—51no—
518C23×C3—101no—
519C23×C3—101no—
520C23×C3—202no—
521C23×C3—202no—
522C23×C3—401no—
523C23×C3D4×D511yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—21no—
527C3×D4—42no—
528C3×D4—102no—
529C3×D4—101no—
530C3×D4—101no—
531C3×D4—101no—
532C3×D4—101no—
533C3×D4—202no—
534C3×D4—202no—
535C3×D4—401no—
536C3×D4—401no—
537C3×D4#70912yes—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—42no—
544C2×C3×C4—51no—
545C2×C3×C4—51no—
546C2×C3×C4—51no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—401no—
552C2×C3×C4—401no—
553C2×C3×C4—401no—
554C2×C3×C4D4×D511yescharacteristic
555C2×C3×C4C23×D511yescharacteristic
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—101no—
559C3×C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—22no—
563C22×C5—21no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5C22×C3×D411yescharacteristic
567C2×D5—21no—
568C2×D5—21no—
569C2×D5—41no—
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—84no—
576C2×D5C3×#13512yes—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5—41no—
581C4×C5C2×C3×#4111yescharacteristic
582C4×C5C3×H(5,𝔽2)11yescharacteristic
583Dic5—21no—
584Dic5—21no—
585Dic5—21no—
586Dic5—41no—
587Dic5—41no—
588C24—101no—
589#41—22no—
590#41—41no—
591C2×Q8C22×C3×D511yescharacteristic
592C2×D4—21no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—101no—
597C2×D4—101no—
598C2×D4—102no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—201no—
602C2×D4C22×C3×D511yescharacteristic
603C22×C4—21no—
604C22×C4—51no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4C22×C3×D511yescharacteristic
609SD16—201no—
610D8—102no—
611D8—201no—
612C2×C8—41no—
613C2×C8—51no—
614C2×C8—51no—
615C2×C8—201no—
616C2×C8C22×C3×D511yescharacteristic
617C2×C8C22×C3×D511yescharacteristic
618C4⋊C4—51no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4C22×C3×D511yescharacteristic
626C4⋊C4C22×C3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—51no—
629C22⋊C4—51no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—101no—
638C42—21no—
639C42—51no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—52no—
648C22×C3—101no—
649C22×C3—101no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3—404no—
657C22×C3C2×D4×D511yescharacteristic
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4—101no—
665C3×C4—201no—
666C3×C4—201no—
667C3×C4C2×#70911yescharacteristic
668C3×C4#414411yescharacteristic
669C2×C5—42no—
670C2×C5—41no—
671C2×C5C3×#54611yescharacteristic
672C2×C5C2×C3×#13511yescharacteristic
673C2×C5C3×#57611yescharacteristic
674D5—22no—
675D5—81no—
676D5—81no—
677C23—21no—
678C23—51no—
679C23—101no—
680C23—101no—
681C23—202no—
682C23—202no—
683C23—401no—
684C23C3×D4×D511yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—21no—
688D4—42no—
689D4—102no—
690D4—101no—
691D4—101no—
692D4—101no—
693D4—101no—
694D4—202no—
695D4—202no—
696D4—401no—
697D4—401no—
698D4C3×#70912yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—42no—
705C2×C4—51no—
706C2×C4—51no—
707C2×C4—51no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—401no—
713C2×C4—401no—
714C2×C4—401no—
715C2×C4C3×D4×D511yescharacteristic
716C2×C4C23×C3×D511yescharacteristic
717C8—21no—
718C8—21no—
719C8—101no—
720C8—101no—
721C2×C3—41no—
722C2×C3—42no—
723C2×C3—102no—
724C2×C3—401no—
725C2×C3—401no—
726C2×C3#6582411yescharacteristic
727C2×C3D5×#13511yescharacteristic
728C2×C3#6610311yescharacteristic
729C5C3×#329711yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—101no—
738C22—101no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—201no—
745C22—404no—
746C22C2×C3×D4×D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—101no—
752C4—101no—
753C4—101no—
754C4—201no—
755C4—201no—
756C4C2×C3×#70911yescharacteristic
757C4C3×#414411yescharacteristic
758C3#1061057711yescharacteristic, direct product factor, Sylow
759C2—41no—
760C2—42no—
761C2—102no—
762C2—401no—
763C2—401no—
764C2C3×#6582411yescharacteristic
765C2C3×D5×#13511yescharacteristic
766C2C3×#6610311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#416C2
socleC22×C3×C5C22×D4
hypercenterC3×#416D5
hypocenterC5C3×#3297
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
1. C3×#66163C2semidirect
2. C3×#65864C2semidirect
3. C3×C5×#416C2semidirect
4. C3×#65527C2semidirect
5. C3×#65404C2semidirect
6. C3×C8×C22⋊D5C2semidirect
7. C3×#65292C2semidirect
8. C3×#65108C2semidirect
9. C3×#65098C2semidirect
10. C3×#65096C2semidirect
11. C3×#65089C2semidirect
12. C3×#65062C2semidirect
13. C3×D5×#102C2semidirect
14. C3×#65055C2semidirect
15. C3×#65045C2semidirect
16. #10610577C3direct (N × H)
19. C22×C3×C5×C8C22semidirect
20. C3×C5×#117C22semidirect
23. C2×C3×#688C22semidirect
29. C3×#4076C22semidirect
36. C3×#4039C22semidirect
38. C3×#4036C22semidirect
43. C3×C5×#103C22semidirect
44. C3×C5×#103C22semidirect
47. C3×#3967C22semidirect
49. C3×C22⋊#168C22semidirect
51. C3×#3953C22semidirect
53. C3×#3950C22semidirect
54. C3×#3946C22semidirect
55. C3×C8×Dic5C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
61. #66163C2×C3semidirect
62. #65864C2×C3semidirect
63. C5×#416C2×C3semidirect
64. #65527C2×C3semidirect
65. #65404C2×C3semidirect
66. C8×C22⋊D5C2×C3semidirect
67. #65292C2×C3semidirect
68. #65108C2×C3semidirect
69. #65098C2×C3semidirect
70. #65096C2×C3semidirect
71. #65089C2×C3semidirect
72. #65062C2×C3semidirect
73. D5×#102C2×C3semidirect
74. #65055C2×C3semidirect
75. #65045C2×C3semidirect
141. C3×#416D5semidirect
145. C22×C5×C8C22×C3semidirect
146. C5×#117C22×C3semidirect
149. C2×#688C22×C3semidirect
155. #4076C22×C3semidirect
162. #4039C22×C3semidirect
164. #4036C22×C3semidirect
169. C5×#103C22×C3semidirect
170. C5×#103C22×C3semidirect
173. #3967C22×C3semidirect
175. C22⋊#168C22×C3semidirect
177. #3953C22×C3semidirect
179. #3950C22×C3semidirect
180. #3946C22×C3semidirect
181. C8×Dic5C22×C3semidirect
184. #3940C22×C3semidirect
185. #3939C22×C3semidirect
237. C22×C3×C8C2×D5semidirect
254. C3×#117C2×D5semidirect
262. C3×#103C2×D5semidirect
263. C3×#103C2×D5semidirect
339. #416C3×D5semidirect
471. C22×C8C2×C3×D5semidirect
488. #117C2×C3×D5semidirect
496. #103C2×C3×D5semidirect
497. #103C2×C3×D5semidirect
640. C3×C5#3297semidirect
729. C5C3×#3297semidirect
758. C3#10610577direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661632
C3×#658642
C3×C5×#4162
C3×#655272
C3×#654042
C3×C8×C22⋊D52
C3×#652922
C3×#651082
C3×#650982
C3×#650962
C3×#650892
C3×#650622
C3×D5×#1022
C3×#650552
C3×#650452
#106105773
C3×#32975