Finite Group Databasebeta

← C3×#10612412 #14458885

Subgroups — C3×#10612412 #14458885

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×#65964C211yesmaximal, characteristic, complemented
2C3×#65952C211yesmaximal, characteristic, complemented
3C3×C5×#465C211yesmaximal, characteristic, complemented
4C3×#65461C211yesmaximal, characteristic, complemented
5C3×#65454C211yesmaximal, characteristic, complemented
6C2×C3×#3953C211yesmaximal, characteristic, complemented
7C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
8C3×#65333C211yesmaximal, characteristic, complemented
9C3×#65325C211yesmaximal, characteristic, complemented
10C3×#65160C211yesmaximal, characteristic, complemented
11C3×#65155C211yesmaximal, characteristic, complemented
12C3×#65093C211yesmaximal, characteristic, complemented
13C3×#65089C211yesmaximal, characteristic, complemented
14C3×#65064C211yesmaximal, characteristic, complemented
15C3×#65045C211yesmaximal, characteristic, complemented
16#10612412C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic, complemented
20C22×C3×C5×C8C2211yescharacteristic
21C3×C5×C22⋊Q8C2211yescharacteristic
22C3×C5×#121C2211yescharacteristic
23C3×#4093C2211yescharacteristic
24C3×#4085—21no—
25C3×#4084C2211yescharacteristic, complemented
26C3×D4×Dic5—21no—
27C3×D4×Dic5C2211yescharacteristic, complemented
28C2×C3×#686C2211yescharacteristic
29C2×C3×#686C2211yescharacteristic
30C3×C4×C22⋊D5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C8×D5C2211yescharacteristic, complemented
33C3×#4041—21no—
34C3×#4041C2211yescharacteristic
35C3×#4040—21no—
36C3×#4039C2211yescharacteristic
37C3×#4038C2211yescharacteristic, complemented
38C3×#4036C2211yescharacteristic, complemented
39C3×#4032—21no—
40C3×#4028—21no—
41C3×D5×C22⋊C4—21no—
42C3×#4025—21no—
43C3×C5×#106C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×#3967C2211yescharacteristic, complemented
48C3×C22⋊#168C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic
53C3×#3952C2211yescharacteristic, complemented
54C3×#3946C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3939C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3297—51nomaximal, Hall
61#65964C2×C311yescharacteristic, complemented
62#65952C2×C311yescharacteristic, complemented
63C5×#465C2×C311yescharacteristic, complemented
64#65461C2×C311yescharacteristic, complemented
65#65454C2×C311yescharacteristic, complemented
66C2×#3953C2×C311yescharacteristic, complemented
67C8×C22⋊D5C2×C311yescharacteristic, complemented
68#65333C2×C311yescharacteristic, complemented
69#65325C2×C311yescharacteristic, complemented
70#65160C2×C311yescharacteristic, complemented
71#65155C2×C311yescharacteristic, complemented
72#65093C2×C311yescharacteristic, complemented
73#65089C2×C311yescharacteristic, complemented
74#65064C2×C311yescharacteristic, complemented
75#65045C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5D411yescharacteristic
83C22×C3×Dic5—21no—
84C22×C3×Dic5—21no—
85C3×#713—22no—
86C3×#713—41no—
87C2×C3×D20—22no—
88C2×C3×D20—21no—
89C2×C3×D20—21no—
90C2×C3×D20—21no—
91C2×C3×D20—41no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5C2311yescharacteristic
97C3×C5×SD16—41no—
98C2×C3×C5×C8—41no—
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4—21no—
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C22⋊Dic5—21no—
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5D411yescharacteristic
109C3×#686—22no—
110C3×#686—41no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685—21no—
116C3×#685D411yescharacteristic
117C3×C4⋊Dic5—21no—
118C3×C4⋊Dic5—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4⋊Dic5C2311yescharacteristic
121C3×#683—21no—
122C3×#683D411yescharacteristic
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
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×#465D511yescharacteristic, complemented
136C3×#463—51no—
137C3×#449—51no—
138C3×#447—51no—
139C3×C4×D8—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×#713C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C2×C5×SD16C22×C311yescharacteristic, complemented
146C22×C5×C8C22×C311yescharacteristic
147C5×C22⋊Q8C22×C311yescharacteristic
148C5×#121C22×C311yescharacteristic
149#4093C22×C311yescharacteristic
150#4085—21no—
151#4084C22×C311yescharacteristic, complemented
152D4×Dic5—21no—
153D4×Dic5C22×C311yescharacteristic, complemented
154C2×#686C22×C311yescharacteristic
155C2×#686C22×C311yescharacteristic
156C4×C22⋊D5C22×C311yescharacteristic
157C2×C4⋊Dic5C22×C311yescharacteristic
158C2×C8×D5C22×C311yescharacteristic, complemented
159#4041—21no—
160#4041C22×C311yescharacteristic
161#4040—21no—
162#4039C22×C311yescharacteristic
163#4038C22×C311yescharacteristic, complemented
164#4036C22×C311yescharacteristic, complemented
165#4032—21no—
166#4028—21no—
167D5×C22⋊C4—21no—
168#4025—21no—
169C5×#106C22×C311yescharacteristic, complemented
170C5×#103C22×C311yescharacteristic, complemented
171C5×#102C22×C311yescharacteristic, complemented
172#3967C22×C311yescharacteristic, complemented
173#3967C22×C311yescharacteristic, complemented
174C22⋊#168C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3952C22×C311yescharacteristic, complemented
180#3946C22×C311yescharacteristic, complemented
181C8×Dic5C22×C311yescharacteristic, complemented
182#3941C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3939C22×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—21no—
199C3×C5×D4—42no—
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×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207C3×C22⋊D5—22no—
208C3×C22⋊D5—81no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5—81no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—21no—
217C3×D20—21no—
218C3×D20—21no—
219C3×D20—42no—
220C3×D20—42no—
221C3×D20—81no—
222C3×D20#4112yes—
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—42no—
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×D8—51no—
236C22×C3×C8—51no—
237C22×C3×C8C2×D511yescharacteristic
238C3×#126—101no—
239C3×#125—51no—
240C3×#124—51no—
241C3×#123—101no—
242C3×#123—101no—
243C3×C22⋊Q8C2×D511yescharacteristic
244C3×#121—51no—
245C3×#121—51no—
246C3×#121—101no—
247C3×#121—101no—
248C3×#121C2×D511yescharacteristic
249C3×#120—101no—
250C3×C4×D4—51no—
251C3×C4×D4—51no—
252C3×C4×D4—51no—
253C3×C4×D4—101no—
254C3×#117—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—101no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#106C2×D511yescharacteristic, complemented
260C3×C4⋊C8—51no—
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, complemented
271C3×C22⋊C8—51no—
272C3×C22⋊C8—51no—
273C3×C4×C8—51no—
274C23×D5—21no—
275C2×C5×Q8C23×C311yescharacteristic
276C2×C5×D4—21no—
277C2×C5×D4C23×C311yescharacteristic
278C22×C4×C5C23×C311yescharacteristic
279C2×C22⋊D5—21no—
280C2×C22⋊D5C3×D411yescharacteristic
281C22×Dic5—21no—
282C22×Dic5—21no—
283#713—22no—
284#713—41no—
285C2×D20—22no—
286C2×D20—21no—
287C2×D20—21no—
288C2×D20—21no—
289C2×D20—41no—
290C2×D20C23×C311yescharacteristic
291C2×D20C23×C311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5C23×C311yescharacteristic
295C5×SD16—41no—
296C2×C5×C8—41no—
297C2×C5×C8C23×C311yescharacteristic
298C2×C5×C8C23×C311yescharacteristic
299C5×C4⋊C4—21no—
300C5×C4⋊C4C23×C311yescharacteristic
301C5×C4⋊C4C23×C311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C22⋊Dic5—21no—
305C22⋊Dic5—21no—
306C22⋊Dic5C3×D411yescharacteristic
307#686—22no—
308#686—41no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685—21no—
314#685C3×D411yescharacteristic
315C4⋊Dic5—21no—
316C4⋊Dic5—21no—
317C4⋊Dic5C23×C311yescharacteristic
318C4⋊Dic5C23×C311yescharacteristic
319#683—21no—
320#683C3×D411yescharacteristic
321C4×Dic5—21no—
322C4×Dic5C23×C311yescharacteristic
323C2×#168C23×C311yescharacteristic
324C2×#168C23×C311yescharacteristic
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#465C3×D511yescharacteristic, complemented
334#463—51no—
335#449—51no—
336#447—51no—
337C4×D8—51no—
338C8×D4—51no—
339#416—51no—
340C2×#102—51no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—21no—
349C2×C3×D5—22no—
350C2×C3×D5—21no—
351C2×C3×D5—21no—
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—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—102no—
371C3×#41—201no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—51no—
375C2×C3×D4—51no—
376C2×C3×D4—51no—
377C2×C3×D4—102no—
378C2×C3×D4—101no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4—101no—
382C2×C3×D4—201no—
383C2×C3×D4C22×D511yescharacteristic
384C22×C3×C4—51no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4—101no—
389C22×C3×C4C22×D511yescharacteristic
390C3×SD16—41no—
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—21no—
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⋊C4C22×D511yescharacteristic
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—51no—
411C3×C22⋊C4—51no—
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—51no—
420C3×C42—101no—
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—21no—
433C5×D4—42no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5C2×C3×D411yescharacteristic
440C2×C4×C5C24×C311yescharacteristic
441C22⋊D5—22no—
442C22⋊D5—81no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—81no—
446C2×Dic5—81no—
447C2×Dic5C2×C3×D411yescharacteristic
448C2×Dic5C2×C3×D411yescharacteristic
449C2×Dic5C2×C3×D411yescharacteristic
450D20—21no—
451D20—21no—
452D20—21no—
453D20—42no—
454D20—42no—
455D20—81no—
456D20C3×#4112yes—
457C4×D5—21no—
458C4×D5—21no—
459C4×D5—42no—
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×D8—51no—
470C22×C8—51no—
471C22×C8C2×C3×D511yescharacteristic
472#126—101no—
473#125—51no—
474#124—51no—
475#123—101no—
476#123—101no—
477C22⋊Q8C2×C3×D511yescharacteristic
478#121—51no—
479#121—51no—
480#121—101no—
481#121—101no—
482#121C2×C3×D511yescharacteristic
483#120—101no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—51no—
487C4×D4—101no—
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—101no—
491#107—51no—
492#107—51no—
493#106C2×C3×D511yescharacteristic, complemented
494C4⋊C8—51no—
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, complemented
505C22⋊C8—51no—
506C22⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—22no—
509C2×C3×C5—81no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—41no—
514C3×D5—42no—
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—21no—
528C3×D4—42no—
529C3×D4—52no—
530C3×D4—102no—
531C3×D4—101no—
532C3×D4—101no—
533C3×D4—101no—
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—21no—
543C2×C3×C4—51no—
544C2×C3×C4—51no—
545C2×C3×C4—51no—
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×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—41no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5C3×#13512yes—
566C22×C5C22×C3×D411yescharacteristic
567C2×D5—21no—
568C2×D5—21no—
569C2×D5—21no—
570C2×D5—22no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—84no—
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—102no—
590#41—201no—
591C2×Q8C22×C3×D511yescharacteristic
592C2×D4—21no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—102no—
597C2×D4—101no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—201no—
602C2×D4C22×C3×D511yescharacteristic
603C22×C4—51no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4C22×C3×D511yescharacteristic
609SD16—41no—
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—21no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4C22×C3×D511yescharacteristic
626C4⋊C4C22×C3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—51no—
630C22⋊C4—51no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—101no—
638C42—51no—
639C42—101no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—101no—
647C22×C3—101no—
648C22×C3—101no—
649C22×C3—102no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—404no—
656C22×C3#406212yes—
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×C4#414411yescharacteristic
668C3×C4D5×#4111yescharacteristic
669C2×C5—22no—
670C2×C5—81no—
671C2×C5C3×#54611yescharacteristic
672C2×C5C2×C3×#13511yescharacteristic
673C2×C5C3×#57611yescharacteristic
674D5—41no—
675D5—42no—
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—21no—
689D4—42no—
690D4—52no—
691D4—102no—
692D4—101no—
693D4—101no—
694D4—101no—
695D4—202no—
696D4—202no—
697D4—401no—
698D4—401no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—51no—
705C2×C4—51no—
706C2×C4—51no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—202no—
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—22no—
722C2×C3—81no—
723C2×C3—201no—
724C2×C3—202no—
725C2×C3—401no—
726C2×C3#6594411yescharacteristic
727C2×C3C2×#406211yescharacteristic
728C2×C3#6610311yescharacteristic
729C5C3×#329711yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—101no—
736C22—101no—
737C22—102no—
738C22—101no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—404no—
745C22C3×#406212yes—
746C22C2×C3×D4×D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—101no—
752C4—101no—
753C4—101no—
754C4—201no—
755C4—201no—
756C4C3×#414411yescharacteristic
757C4C3×D5×#4111yescharacteristic
758C3#1061241211yescharacteristic, direct product factor, Sylow
759C2—22no—
760C2—81no—
761C2—201no—
762C2—202no—
763C2—401no—
764C2C3×#6594411yescharacteristic
765C2C2×C3×#406211yescharacteristic
766C2C3×#6610311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#465C2
socleC22×C3×C5C22×D4
hypercenterC3×#465D5
hypocenterC5C3×#3297
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C3×#65964C2semidirect
2. C3×#65952C2semidirect
3. C3×C5×#465C2semidirect
4. C3×#65461C2semidirect
5. C3×#65454C2semidirect
6. C2×C3×#3953C2semidirect
7. C3×C8×C22⋊D5C2semidirect
8. C3×#65333C2semidirect
9. C3×#65325C2semidirect
10. C3×#65160C2semidirect
11. C3×#65155C2semidirect
12. C3×#65093C2semidirect
13. C3×#65089C2semidirect
14. C3×#65064C2semidirect
15. C3×#65045C2semidirect
16. #10612412C3direct (N × H)
19. C2×C3×C5×SD16C22semidirect
25. C3×#4084C22semidirect
27. C3×D4×Dic5C22semidirect
32. C2×C3×C8×D5C22semidirect
37. C3×#4038C22semidirect
38. C3×#4036C22semidirect
43. C3×C5×#106C22semidirect
44. C3×C5×#103C22semidirect
45. C3×C5×#102C22semidirect
46. C3×#3967C22semidirect
47. C3×#3967C22semidirect
53. C3×#3952C22semidirect
54. C3×#3946C22semidirect
55. C3×C8×Dic5C22semidirect
58. C3×#3939C22semidirect
59. C3×#3939C22semidirect
61. #65964C2×C3semidirect
62. #65952C2×C3semidirect
63. C5×#465C2×C3semidirect
64. #65461C2×C3semidirect
65. #65454C2×C3semidirect
66. C2×#3953C2×C3semidirect
67. C8×C22⋊D5C2×C3semidirect
68. #65333C2×C3semidirect
69. #65325C2×C3semidirect
70. #65160C2×C3semidirect
71. #65155C2×C3semidirect
72. #65093C2×C3semidirect
73. #65089C2×C3semidirect
74. #65064C2×C3semidirect
75. #65045C2×C3semidirect
135. C3×#465D5semidirect
145. C2×C5×SD16C22×C3semidirect
151. #4084C22×C3semidirect
153. D4×Dic5C22×C3semidirect
158. C2×C8×D5C22×C3semidirect
163. #4038C22×C3semidirect
164. #4036C22×C3semidirect
169. C5×#106C22×C3semidirect
170. C5×#103C22×C3semidirect
171. C5×#102C22×C3semidirect
172. #3967C22×C3semidirect
173. #3967C22×C3semidirect
179. #3952C22×C3semidirect
180. #3946C22×C3semidirect
181. C8×Dic5C22×C3semidirect
184. #3939C22×C3semidirect
185. #3939C22×C3semidirect
233. C2×C3×SD16C2×D5semidirect
259. C3×#106C2×D5semidirect
263. C3×#103C2×D5semidirect
270. C3×#102C2×D5semidirect
333. #465C3×D5semidirect
467. C2×SD16C2×C3×D5semidirect
493. #106C2×C3×D5semidirect
497. #103C2×C3×D5semidirect
504. #102C2×C3×D5semidirect
640. C3×C5#3297semidirect
729. C5C3×#3297semidirect
758. C3#10612412direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659642
C3×#659522
C3×C5×#4652
C3×#654612
C3×#654542
C2×C3×#39532
C3×C8×C22⋊D52
C3×#653332
C3×#653252
C3×#651602
C3×#651552
C3×#650932
C3×#650892
C3×#650642
C3×#650452
#106124123
C3×#32975