Finite Group Databasebeta

← C3×#10611172 #14458873

Subgroups — C3×#10611172 #14458873

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×#65899C211yesmaximal, characteristic, complemented
2C3×#65884C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4C3×#65404C211yesmaximal, characteristic, complemented
5C3×#65403C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7C2×C3×#3953C211yesmaximal, characteristic, complemented
8C3×#65136C211yesmaximal, characteristic, complemented
9C3×#65133C211yesmaximal, characteristic, complemented
10C3×#65026C211yesmaximal, characteristic, complemented
11C3×#65023C211yesmaximal, characteristic, complemented
12C3×#65021C211yesmaximal, characteristic, complemented
13C3×#65011C211yesmaximal, characteristic, complemented
14C3×#64986C211yesmaximal, characteristic, complemented
15C3×C4×D40C211yesmaximal, characteristic, complemented
16#10611172C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C3×#4085—21no—
23C3×#4083—21no—
24C3×#4076C2211yescharacteristic
25C3×#4076C2211yescharacteristic
26C3×#4076C2211yescharacteristic, complemented
27C3×#4072C2211yescharacteristic, complemented
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C3×#4070C2211yescharacteristic
30C2×C3×D40C2211yescharacteristic
31C2×C3×D40C2211yescharacteristic
32C2×C3×#677C2211yescharacteristic, complemented
33C3×#4044—21no—
34C3×#4040—21no—
35C3×#4030—21no—
36C3×#4029—21no—
37C3×#4027—21no—
38C3×D5×C22⋊C4—21no—
39C3×#4021C2211yescharacteristic
40C3×C4×D20C2211yescharacteristic
41C3×C4×D20C2211yescharacteristic, complemented
42C3×#4016C2211yescharacteristic, complemented
43C3×C5×C4⋊C8C2211yescharacteristic, complemented
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×C5×C22⋊C8C2211yescharacteristic, complemented
46C3×C4×C5×C8C2211yescharacteristic, complemented
47C3×#3953C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic
53C3×#3953C2211yescharacteristic, complemented
54C3×#3950C2211yescharacteristic, complemented
55C3×#3950C2211yescharacteristic, complemented
56C3×#3949C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3297—51nomaximal, Hall
61#65899C2×C311yescharacteristic, complemented
62#65884C2×C311yescharacteristic, complemented
63C5×C8×D4C2×C311yescharacteristic, complemented
64#65404C2×C311yescharacteristic, complemented
65#65403C2×C311yescharacteristic, complemented
66#65402C2×C311yescharacteristic, complemented
67C2×#3953C2×C311yescharacteristic, complemented
68#65136C2×C311yescharacteristic, complemented
69#65133C2×C311yescharacteristic, complemented
70#65026C2×C311yescharacteristic, complemented
71#65023C2×C311yescharacteristic, complemented
72#65021C2×C311yescharacteristic, complemented
73#65011C2×C311yescharacteristic, complemented
74#64986C2×C311yescharacteristic, complemented
75C4×D40C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C3×#709—22no—
86C3×#709—41no—
87C2×C3×D20—22no—
88C2×C3×D20—21no—
89C2×C3×D20—41no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×D20C2311yescharacteristic
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×Dic10C2311yescharacteristic
97C2×C3×C5×C8—41no—
98C2×C3×C5×C8—41no—
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C3×C5×C4⋊C4D411yescharacteristic
104C3×C5×C22⋊C4D411yescharacteristic
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C42×C5C2311yescharacteristic
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685—21no—
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4⋊Dic5C2311yescharacteristic
121C3×#683—21no—
122C3×#683—21no—
123C3×#683—21no—
124C3×C4×Dic5—21no—
125C3×D40—22no—
126C3×D40—41no—
127C3×#677—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×D4D511yescharacteristic, complemented
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×#709C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C22×C5×C8C22×C311yescharacteristic
146C22×C5×C8C22×C311yescharacteristic, complemented
147C4×C5×D4C22×C311yescharacteristic
148#4085—21no—
149#4083—21no—
150#4076C22×C311yescharacteristic
151#4076C22×C311yescharacteristic
152#4076C22×C311yescharacteristic, complemented
153#4072C22×C311yescharacteristic, complemented
154C2×C4⋊Dic5C22×C311yescharacteristic
155#4070C22×C311yescharacteristic
156C2×D40C22×C311yescharacteristic
157C2×D40C22×C311yescharacteristic
158C2×#677C22×C311yescharacteristic, complemented
159#4044—21no—
160#4040—21no—
161#4030—21no—
162#4029—21no—
163#4027—21no—
164D5×C22⋊C4—21no—
165#4021C22×C311yescharacteristic
166C4×D20C22×C311yescharacteristic
167C4×D20C22×C311yescharacteristic, complemented
168#4016C22×C311yescharacteristic, complemented
169C5×C4⋊C8C22×C311yescharacteristic, complemented
170C5×C22⋊C8C22×C311yescharacteristic
171C5×C22⋊C8C22×C311yescharacteristic, complemented
172C4×C5×C8C22×C311yescharacteristic, complemented
173#3953C22×C311yescharacteristic
174#3953C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3953C22×C311yescharacteristic, complemented
180#3950C22×C311yescharacteristic, complemented
181#3950C22×C311yescharacteristic, complemented
182#3949C22×C311yescharacteristic, complemented
183#3948C22×C311yescharacteristic, complemented
184#3948C22×C311yescharacteristic, complemented
185#3948C22×C311yescharacteristic, complemented
186#3297—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—81no—
195C3×C5×D4—22no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C3×C22⋊D5—42no—
206C3×C22⋊D5—42no—
207C3×C22⋊D5—81no—
208C3×C22⋊D5—81no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—81no—
215C3×D20—21no—
216C3×D20—21no—
217C3×D20—21no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—42no—
221C3×D20#4112yes—
222C3×C4×D5—42no—
223C3×C4×D5—81no—
224C3×C4×D5—81no—
225C3×Dic10—21no—
226C3×Dic10—21no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×C5×C8—21no—
230C3×C5×C8—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C2×C3×SD16—51no—
234C2×C3×D8—51no—
235C2×C3×D8—51no—
236C22×C3×C8C2×D511yescharacteristic
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—101no—
253C3×C4×D4C2×D511yescharacteristic
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×#103—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102—51no—
271C3×C22⋊C8C2×D511yescharacteristic
272C3×C22⋊C8C2×D511yescharacteristic, complemented
273C3×C4×C8C2×D511yescharacteristic, complemented
274C23×D5—21no—
275C2×C5×D4C3×D411yescharacteristic
276C22×C4×C5C23×C311yescharacteristic
277C22×C4×C5C23×C311yescharacteristic
278C2×C22⋊D5—21no—
279C2×C22⋊D5—21no—
280C2×C22⋊D5—21no—
281C2×C22⋊D5—21no—
282C22×Dic5—21no—
283#709—22no—
284#709—41no—
285C2×D20—22no—
286C2×D20—21no—
287C2×D20—41no—
288C2×D20C23×C311yescharacteristic
289C2×D20C23×C311yescharacteristic
290C2×D20C23×C311yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×Dic10C23×C311yescharacteristic
295C2×C5×C8—41no—
296C2×C5×C8—41no—
297C2×C5×C8C23×C311yescharacteristic
298C2×C5×C8C23×C311yescharacteristic
299C2×C5×C8C23×C311yescharacteristic
300C2×C5×C8C23×C311yescharacteristic
301C5×C4⋊C4C3×D411yescharacteristic
302C5×C22⋊C4C3×D411yescharacteristic
303C5×C22⋊C4C3×D411yescharacteristic
304C42×C5C23×C311yescharacteristic
305C22⋊Dic5—21no—
306C22⋊Dic5—21no—
307#685—21no—
308#685—21no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685—21no—
314C4⋊Dic5—21no—
315C4⋊Dic5C23×C311yescharacteristic
316C4⋊Dic5C23×C311yescharacteristic
317C4⋊Dic5C23×C311yescharacteristic
318C4⋊Dic5C23×C311yescharacteristic
319#683—21no—
320#683—21no—
321#683—21no—
322C4×Dic5—21no—
323D40—22no—
324D40—41no—
325#677—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×D4C3×D511yescharacteristic, complemented
339#416—51no—
340C2×#102—51no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—22no—
349C2×C3×D5—41no—
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—41no—
357C2×C3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364C3×Dic5—41no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8—51no—
373C2×C3×D4—51no—
374C2×C3×D4—51no—
375C2×C3×D4—51no—
376C2×C3×D4—102no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4—101no—
382C2×C3×D4—201no—
383C2×C3×D4D2011yescharacteristic
384C22×C3×C4—101no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4C22×D511yescharacteristic
389C22×C3×C4C22×D511yescharacteristic
390C3×SD16—201no—
391C3×D8—102no—
392C3×D8—201no—
393C2×C3×C8—41no—
394C2×C3×C8—41no—
395C2×C3×C8C22×D511yescharacteristic
396C2×C3×C8C22×D511yescharacteristic
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⋊C4D2011yescharacteristic
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
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⋊C4D2011yescharacteristic
418C3×C22⋊C4D2011yescharacteristic
419C3×C42—101no—
420C3×C42C22×D511yescharacteristic
421C23×C5C2×C3×D411yescharacteristic
422C23×C5C2×C3×D411yescharacteristic
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—42no—
427C22×D5—42no—
428C22×D5—81no—
429C5×D4—22no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5C2×C3×D411yescharacteristic
435C2×C4×C5C2×C3×D411yescharacteristic
436C2×C4×C5C2×C3×D411yescharacteristic
437C2×C4×C5C2×C3×D411yescharacteristic
438C2×C4×C5C24×C311yescharacteristic
439C22⋊D5—42no—
440C22⋊D5—42no—
441C22⋊D5—81no—
442C22⋊D5—81no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—81no—
449D20—21no—
450D20—21no—
451D20—21no—
452D20—21no—
453D20—21no—
454D20—42no—
455D20C3×#4112yes—
456C4×D5—42no—
457C4×D5—81no—
458C4×D5—81no—
459Dic10—21no—
460Dic10—21no—
461C5×C8—21no—
462C5×C8—21no—
463C5×C8—21no—
464C5×C8—21no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16—51no—
468C2×D8—51no—
469C2×D8—51no—
470C22×C8C2×C3×D511yescharacteristic
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—101no—
487C4×D4C2×C3×D511yescharacteristic
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#103—51no—
498#102—51no—
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102—51no—
504#102—51no—
505C22⋊C8C2×C3×D511yescharacteristic
506C22⋊C8C2×C3×D511yescharacteristic, complemented
507C4×C8C2×C3×D511yescharacteristic, complemented
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—42no—
514C3×D5—81no—
515C3×D5—81no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—101no—
519C23×C3—202no—
520C23×C3—202no—
521C23×C3—401no—
522C23×C3C2×D2011yescharacteristic
523C23×C3C2×D2011yescharacteristic
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—22no—
527C3×D4—52no—
528C3×D4—101no—
529C3×D4—101no—
530C3×D4—101no—
531C3×D4—101no—
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—21no—
541C2×C3×C4—21no—
542C2×C3×C4—101no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—202no—
548C2×C3×C4—401no—
549C2×C3×C4—401no—
550C2×C3×C4—401no—
551C2×C3×C4C2×D2011yescharacteristic
552C2×C3×C4C2×D2011yescharacteristic
553C2×C3×C4C2×D2011yescharacteristic
554C2×C3×C4C2×D2011yescharacteristic
555C2×C3×C4C23×D511yescharacteristic
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5C3×#13512yes—
566C22×C5C22×C3×D411yescharacteristic
567C2×D5—22no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—84no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5C2×C3×#4111yescharacteristic
582C4×C5C3×H(5,𝔽2)11yescharacteristic
583Dic5—41no—
584Dic5—41no—
585Dic5—41no—
586Dic5—41no—
587Dic5—41no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8—51no—
592C2×D4—51no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—102no—
596C2×D4—101no—
597C2×D4—101no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—201no—
602C2×D4C3×D2011yescharacteristic
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4C22×C3×D511yescharacteristic
608C22×C4C22×C3×D511yescharacteristic
609SD16—201no—
610D8—102no—
611D8—201no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8C22×C3×D511yescharacteristic
615C2×C8C22×C3×D511yescharacteristic
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⋊C4C3×D2011yescharacteristic
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4C3×D2011yescharacteristic
637C22⋊C4C3×D2011yescharacteristic
638C42—101no—
639C42C22×C3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—102no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—404no—
656C22×C3#405012yes—
657C22×C3C22×D2011yescharacteristic
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4—201no—
665C3×C4—201no—
666C3×C4—201no—
667C3×C4#414411yescharacteristic
668C3×C4D5×#4111yescharacteristic
669C2×C5—22no—
670C2×C5—41no—
671C2×C5C3×#54611yescharacteristic
672C2×C5C2×C3×#13511yescharacteristic
673C2×C5C3×#57611yescharacteristic
674D5—42no—
675D5—81no—
676D5—81no—
677C23—101no—
678C23—101no—
679C23—101no—
680C23—202no—
681C23—202no—
682C23—401no—
683C23C2×C3×D2011yescharacteristic
684C23C2×C3×D2011yescharacteristic
685Q8—101no—
686Q8—101no—
687D4—22no—
688D4—52no—
689D4—101no—
690D4—101no—
691D4—101no—
692D4—101no—
693D4—101no—
694D4—202no—
695D4—202no—
696D4—202no—
697D4—401no—
698D4—401no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—202no—
709C2×C4—401no—
710C2×C4—401no—
711C2×C4—401no—
712C2×C4C2×C3×D2011yescharacteristic
713C2×C4C2×C3×D2011yescharacteristic
714C2×C4C2×C3×D2011yescharacteristic
715C2×C4C2×C3×D2011yescharacteristic
716C2×C4C23×C3×D511yescharacteristic
717C8—21no—
718C8—21no—
719C8—21no—
720C8—21no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—202no—
724C2×C3—401no—
725C2×C3—401no—
726C2×C3#6588811yescharacteristic
727C2×C3C2×#405011yescharacteristic
728C2×C3#6608611yescharacteristic
729C5C3×#329711yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—102no—
736C22—201no—
737C22—201no—
738C22—201no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—404no—
745C22C3×#405012yes—
746C22C22×C3×D2011yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—201no—
752C4—201no—
753C4—201no—
754C4—201no—
755C4—201no—
756C4C3×#414411yescharacteristic
757C4C3×D5×#4111yescharacteristic
758C3#1061117211yescharacteristic, direct product factor, Sylow
759C2—22no—
760C2—41no—
761C2—202no—
762C2—401no—
763C2—401no—
764C2C3×#6588811yescharacteristic
765C2C2×C3×#405011yescharacteristic
766C2C3×#6608611yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
hypercenterC3×C8×D4D5
hypocenterC5C3×#3297
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65899C2semidirect
2. C3×#65884C2semidirect
3. C3×C5×C8×D4C2semidirect
4. C3×#65404C2semidirect
5. C3×#65403C2semidirect
6. C3×#65402C2semidirect
7. C2×C3×#3953C2semidirect
8. C3×#65136C2semidirect
9. C3×#65133C2semidirect
10. C3×#65026C2semidirect
11. C3×#65023C2semidirect
12. C3×#65021C2semidirect
13. C3×#65011C2semidirect
14. C3×#64986C2semidirect
15. C3×C4×D40C2semidirect
16. #10611172C3direct (N × H)
20. C22×C3×C5×C8C22semidirect
26. C3×#4076C22semidirect
27. C3×#4072C22semidirect
32. C2×C3×#677C22semidirect
41. C3×C4×D20C22semidirect
42. C3×#4016C22semidirect
43. C3×C5×C4⋊C8C22semidirect
45. C3×C5×C22⋊C8C22semidirect
46. C3×C4×C5×C8C22semidirect
53. C3×#3953C22semidirect
54. C3×#3950C22semidirect
55. C3×#3950C22semidirect
56. C3×#3949C22semidirect
57. C3×#3948C22semidirect
58. C3×#3948C22semidirect
59. C3×#3948C22semidirect
61. #65899C2×C3semidirect
62. #65884C2×C3semidirect
63. C5×C8×D4C2×C3semidirect
64. #65404C2×C3semidirect
65. #65403C2×C3semidirect
66. #65402C2×C3semidirect
67. C2×#3953C2×C3semidirect
68. #65136C2×C3semidirect
69. #65133C2×C3semidirect
70. #65026C2×C3semidirect
71. #65023C2×C3semidirect
72. #65021C2×C3semidirect
73. #65011C2×C3semidirect
74. #64986C2×C3semidirect
75. C4×D40C2×C3semidirect
140. C3×C8×D4D5semidirect
146. C22×C5×C8C22×C3semidirect
152. #4076C22×C3semidirect
153. #4072C22×C3semidirect
158. C2×#677C22×C3semidirect
167. C4×D20C22×C3semidirect
168. #4016C22×C3semidirect
169. C5×C4⋊C8C22×C3semidirect
171. C5×C22⋊C8C22×C3semidirect
172. C4×C5×C8C22×C3semidirect
179. #3953C22×C3semidirect
180. #3950C22×C3semidirect
181. #3950C22×C3semidirect
182. #3949C22×C3semidirect
183. #3948C22×C3semidirect
184. #3948C22×C3semidirect
185. #3948C22×C3semidirect
237. C22×C3×C8C2×D5semidirect
260. C3×C4⋊C8C2×D5semidirect
272. C3×C22⋊C8C2×D5semidirect
273. C3×C4×C8C2×D5semidirect
338. C8×D4C3×D5semidirect
471. C22×C8C2×C3×D5semidirect
494. C4⋊C8C2×C3×D5semidirect
506. C22⋊C8C2×C3×D5semidirect
507. C4×C8C2×C3×D5semidirect
640. C3×C5#3297semidirect
729. C5C3×#3297semidirect
758. C3#10611172direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658992
C3×#658842
C3×C5×C8×D42
C3×#654042
C3×#654032
C3×#654022
C2×C3×#39532
C3×#651362
C3×#651332
C3×#650262
C3×#650232
C3×#650212
C3×#650112
C3×#649862
C3×C4×D402
#106111723
C3×#32975