Finite Group Databasebeta

← C3×#10613227 #14435593

Subgroups — C3×#10613227 #14435593

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×#65977C211yesmaximal, characteristic, complemented
2C3×#65855C211yesmaximal, characteristic, complemented
3C3×C5×#485C211yesmaximal, characteristic, complemented
4C3×#65335C211yesmaximal, characteristic, complemented
5C3×#65292C211yesmaximal, characteristic, complemented
6C3×#65179C211yesmaximal, characteristic, complemented
7C3×#65161C211yesmaximal, characteristic, complemented
8C3×#65159C211yesmaximal, characteristic, complemented
9C3×#65158C211yesmaximal, characteristic, complemented
10C3×#65108C211yesmaximal, characteristic, complemented
11C3×#65108C211yesmaximal, characteristic, complemented
12C3×#65106C211yesmaximal, characteristic, complemented
13C3×#65077C211yesmaximal, characteristic, complemented
14C3×#65021C211yesmaximal, characteristic
15C3×#65009C211yesmaximal, characteristic, complemented
16#10613227C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×D20C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C3×C5×#117C2211yescharacteristic
20C3×#4093C2211yescharacteristic, complemented
21C3×Q8×Dic5C2211yescharacteristic, complemented
22C2×C3×#688C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic
24C3×#4076C2211yescharacteristic
25C3×#4072C2211yescharacteristic
26C2×C3×D40C2211yescharacteristic
27C2×C3×D40C2211yescharacteristic
28C3×#4044—21no—
29C3×#4043—21no—
30C3×#4039C2211yescharacteristic
31C3×#4039C2211yescharacteristic
32C3×#4039C2211yescharacteristic
33C3×#4039C2211yescharacteristic
34C3×#4039C2211yescharacteristic, complemented
35C3×#4034C2211yescharacteristic, complemented
36C3×#4031—21no—
37C3×#4029—21no—
38C3×D5×C22⋊C4—21no—
39C3×D5×C22⋊C4—21no—
40C3×C4×D20—21no—
41C3×C4×D20—21no—
42C3×C5×#107C2211yescharacteristic, complemented
43C3×C5×#106C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#103C2211yescharacteristic, complemented
46C3×C5×C22⋊C8C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3947C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3941C2211yescharacteristic
55C3×#3941C2211yescharacteristic
56C3×#3941C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61#65977C2×C311yescharacteristic, complemented
62#65855C2×C311yescharacteristic, complemented
63C5×#485C2×C311yescharacteristic, complemented
64#65335C2×C311yescharacteristic, complemented
65#65292C2×C311yescharacteristic, complemented
66#65179C2×C311yescharacteristic, complemented
67#65161C2×C311yescharacteristic, complemented
68#65159C2×C311yescharacteristic, complemented
69#65158C2×C311yescharacteristic, complemented
70#65108C2×C311yescharacteristic, complemented
71#65108C2×C311yescharacteristic, complemented
72#65106C2×C311yescharacteristic, complemented
73#65077C2×C311yescharacteristic, complemented
74#65021C2×C311yescharacteristic
75#65009C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×C3×C22⋊D5—21no—
80C2×C3×D20—21no—
81C2×C3×D20—22no—
82C2×C3×D20—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×Dic10—21no—
92C2×C3×C5×C8C2311yescharacteristic
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C42×C5—21no—
101C3×C22⋊Dic5D411yescharacteristic
102C3×C22⋊Dic5D411yescharacteristic
103C3×#688—22no—
104C3×#688—22no—
105C3×#685—21no—
106C3×#685—21no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5D411yescharacteristic
115C3×C4⋊Dic5D411yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5C2311yescharacteristic
120C3×C4×Dic5C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C3×D40—22no—
124C3×D40—22no—
125C3×#542—51no—
126C3×#518—51no—
127C3×#485D511yescharacteristic, complemented
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463—51no—
133C3×#450—51no—
134C3×#447—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C22×D20C22×C311yescharacteristic
141C5×C22⋊Q8C22×C311yescharacteristic
142C5×#117C22×C311yescharacteristic
143#4093C22×C311yescharacteristic, complemented
144Q8×Dic5C22×C311yescharacteristic, complemented
145C2×#688C22×C311yescharacteristic
146C2×#688C22×C311yescharacteristic
147#4076C22×C311yescharacteristic
148#4072C22×C311yescharacteristic
149C2×D40C22×C311yescharacteristic
150C2×D40C22×C311yescharacteristic
151#4044—21no—
152#4043—21no—
153#4039C22×C311yescharacteristic
154#4039C22×C311yescharacteristic
155#4039C22×C311yescharacteristic
156#4039C22×C311yescharacteristic
157#4039C22×C311yescharacteristic, complemented
158#4034C22×C311yescharacteristic, complemented
159#4031—21no—
160#4029—21no—
161D5×C22⋊C4—21no—
162D5×C22⋊C4—21no—
163C4×D20—21no—
164C4×D20—21no—
165C5×#107C22×C311yescharacteristic, complemented
166C5×#106C22×C311yescharacteristic, complemented
167C5×#103C22×C311yescharacteristic, complemented
168C5×#103C22×C311yescharacteristic, complemented
169C5×C22⋊C8C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3953C22×C311yescharacteristic
172#3953C22×C311yescharacteristic
173#3947C22×C311yescharacteristic, complemented
174#3946C22×C311yescharacteristic, complemented
175#3946C22×C311yescharacteristic, complemented
176C8×Dic5C22×C311yescharacteristic, complemented
177#3941C22×C311yescharacteristic
178#3941C22×C311yescharacteristic
179#3941C22×C311yescharacteristic, complemented
180#3941C22×C311yescharacteristic, complemented
181#3940C22×C311yescharacteristic, complemented
182#3939C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—24no—
188C22×C3×D5—21no—
189C22×C3×D5—81no—
190C22×C3×D5—81no—
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C3×C22⋊D5—81no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×D20—24no—
208C3×D20—21no—
209C3×D20—21no—
210C3×D20—21no—
211C3×D20—21no—
212C3×D20#4112yes—
213C3×D20#4112yes—
214C3×C4×D5—81no—
215C3×C4×D5—81no—
216C3×C4×D5—81no—
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×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×C4⋊Q8—51no—
230C3×#126—101no—
231C3×#124—51no—
232C3×#124—101no—
233C3×#123—101no—
234C3×C22⋊Q8—101no—
235C3×C22⋊Q8C2×D511yescharacteristic
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—51no—
243C3×C4×D4—101no—
244C3×C4×D4—101no—
245C3×#117—51no—
246C3×#117C2×D511yescharacteristic
247C2×C3×C22⋊C4—101no—
248C2×C3×C22⋊C4—101no—
249C3×#107—51no—
250C3×#107C2×D511yescharacteristic, complemented
251C3×#106—51no—
252C3×#106C2×D511yescharacteristic, complemented
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103C2×D511yescharacteristic, complemented
256C3×#103C2×D511yescharacteristic, complemented
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102—51no—
263C3×C22⋊C8—51no—
264C3×C22⋊C8C2×D511yescharacteristic
265C3×#97—51no—
266C3×C4×C8—51no—
267C23×D5—21no—
268C2×C5×Q8C23×C311yescharacteristic
269C22×C4×C5C23×C311yescharacteristic
270C2×C22⋊D5—21no—
271C2×D20—21no—
272C2×D20—22no—
273C2×D20—22no—
274C2×D20C23×C311yescharacteristic
275C2×D20C23×C311yescharacteristic
276C2×D20C23×C311yescharacteristic
277C2×C4×D5—21no—
278C2×C4×D5—21no—
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×Dic10—21no—
283C2×C5×C8C23×C311yescharacteristic
284C2×C5×C8C23×C311yescharacteristic
285C5×C4⋊C4—21no—
286C5×C4⋊C4C23×C311yescharacteristic
287C5×C4⋊C4C23×C311yescharacteristic
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C22⋊C4—21no—
290C5×C22⋊C4—21no—
291C42×C5—21no—
292C22⋊Dic5C3×D411yescharacteristic
293C22⋊Dic5C3×D411yescharacteristic
294#688—22no—
295#688—22no—
296#685—21no—
297#685—21no—
298#685—21no—
299#685—21no—
300#685—21no—
301#685—21no—
302#685—21no—
303#685—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5C3×D411yescharacteristic
306C4⋊Dic5C3×D411yescharacteristic
307C4⋊Dic5C23×C311yescharacteristic
308#683—21no—
309C4×Dic5—21no—
310C4×Dic5C23×C311yescharacteristic
311C4×Dic5C23×C311yescharacteristic
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314D40—22no—
315D40—22no—
316#542—51no—
317#518—51no—
318#485C3×D511yescharacteristic, complemented
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463—51no—
324#450—51no—
325#447—51no—
326#442—51no—
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5C22×D411yescharacteristic
335C2×C3×D5—22no—
336C2×C3×D5—22no—
337C2×C3×D5—41no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—84no—
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349C3×C4×C5—41no—
350C3×C4×C5C2×#4111yescharacteristic
351C3×C4×C5C2×#4111yescharacteristic
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—21no—
355C3×Dic5—21no—
356C3×Dic5—41no—
357C24×C3—101no—
358C2×C3×Q8—101no—
359C2×C3×Q8C22×D511yescharacteristic
360C2×C3×D4—51no—
361C2×C3×D4—51no—
362C2×C3×D4—51no—
363C2×C3×D4—102no—
364C2×C3×D4—102no—
365C2×C3×D4—101no—
366C2×C3×D4—101no—
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C3×SD16—102no—
374C3×SD16—102no—
375C3×D8—102no—
376C3×D8—102no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8C22×D511yescharacteristic
380C2×C3×C8C22×D511yescharacteristic
381C3×C4⋊C4—21no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—101no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—51no—
393C3×C22⋊C4—51no—
394C3×C22⋊C4—101no—
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—21no—
403C3×C42—51no—
404C3×C42—51no—
405C3×C42—101no—
406C23×C5C2×C3×D411yescharacteristic
407C22×D5—21no—
408C22×D5—21no—
409C22×D5—24no—
410C22×D5—21no—
411C22×D5—81no—
412C22×D5—81no—
413C5×Q8—21no—
414C5×Q8—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5C2×C3×D411yescharacteristic
422C2×C4×C5C24×C311yescharacteristic
423C22⋊D5—81no—
424C2×Dic5—21no—
425C2×Dic5C2×C3×D411yescharacteristic
426C2×Dic5C2×C3×D411yescharacteristic
427C2×Dic5C2×C3×D411yescharacteristic
428C2×Dic5C2×C3×D411yescharacteristic
429D20—24no—
430D20—21no—
431D20—21no—
432D20—21no—
433D20—21no—
434D20C3×#4112yes—
435D20C3×#4112yes—
436C4×D5—81no—
437C4×D5—81no—
438C4×D5—81no—
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×SD16—51no—
449C2×D8—51no—
450C2×D8—51no—
451C4⋊Q8—51no—
452#126—101no—
453#124—51no—
454#124—101no—
455#123—101no—
456C22⋊Q8—101no—
457C22⋊Q8C2×C3×D511yescharacteristic
458#121—51no—
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—51no—
465C4×D4—101no—
466C4×D4—101no—
467#117—51no—
468#117C2×C3×D511yescharacteristic
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—51no—
472#107C2×C3×D511yescharacteristic, complemented
473#106—51no—
474#106C2×C3×D511yescharacteristic, complemented
475C4⋊C8—51no—
476C4⋊C8—51no—
477#103C2×C3×D511yescharacteristic, complemented
478#103C2×C3×D511yescharacteristic, complemented
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102—51no—
484#102—51no—
485C22⋊C8—51no—
486C22⋊C8C2×C3×D511yescharacteristic
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—41no—
490C2×C3×C5#52511yescharacteristic
491C2×C3×C5#57611yescharacteristic
492C2×C3×C5#57711yescharacteristic
493C3×D5—42no—
494C3×D5—42no—
495C3×D5—81no—
496C23×C3—104no—
497C23×C3—101no—
498C23×C3—101no—
499C23×C3—101no—
500C23×C3—401no—
501C23×C3—401no—
502C23×C3D4×D511yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—401no—
506C3×D4—52no—
507C3×D4—52no—
508C3×D4—104no—
509C3×D4—101no—
510C3×D4—101no—
511C3×D4—101no—
512C3×D4—101no—
513C3×D4—401no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—51no—
521C2×C3×C4—51no—
522C2×C3×C4—51no—
523C2×C3×C4—51no—
524C2×C3×C4—101no—
525C2×C3×C4—401no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4—401no—
529C2×C3×C4—401no—
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5C22×C3×D411yescharacteristic
540C2×D5—22no—
541C2×D5—22no—
542C2×D5—41no—
543C2×D5—41no—
544C2×D5—41no—
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—84no—
550C4×C5—21no—
551C4×C5—41no—
552C4×C5—41no—
553C4×C5—41no—
554C4×C5—41no—
555C4×C5C2×C3×#4111yescharacteristic
556C4×C5C2×C3×#4111yescharacteristic
557Dic5—21no—
558Dic5—21no—
559Dic5—21no—
560Dic5—21no—
561Dic5—41no—
562C24—101no—
563C2×Q8—101no—
564C2×Q8C22×C3×D511yescharacteristic
565C2×D4—51no—
566C2×D4—51no—
567C2×D4—51no—
568C2×D4—102no—
569C2×D4—102no—
570C2×D4—101no—
571C2×D4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—102no—
579SD16—102no—
580D8—102no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—101no—
591C4⋊C4—101no—
592C4⋊C4C22×C3×D511yescharacteristic
593C4⋊C4C22×C3×D511yescharacteristic
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—51no—
598C22⋊C4—51no—
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4—101no—
606C22⋊C4—101no—
607C42—21no—
608C42—51no—
609C42—51no—
610C42—101no—
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—102no—
616C22×C3—102no—
617C22×C3—201no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3—201no—
623C22×C3—201no—
624C22×C3—404no—
625C22×C3C2×D4×D511yescharacteristic
626C3×C4—21no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—101no—
632C3×C4—101no—
633C3×C4—101no—
634C3×C4—101no—
635C3×C4—201no—
636C3×C4D5×#4111yescharacteristic
637C3×C4D5×#4111yescharacteristic
638C2×C5—41no—
639C2×C5C3×#52511yescharacteristic
640C2×C5C3×#57611yescharacteristic
641C2×C5C3×#57711yescharacteristic
642D5—42no—
643D5—42no—
644D5—81no—
645C23—104no—
646C23—101no—
647C23—101no—
648C23—101no—
649C23—401no—
650C23—401no—
651C23C3×D4×D511yescharacteristic
652Q8—21no—
653Q8—21no—
654Q8—401no—
655D4—52no—
656D4—52no—
657D4—104no—
658D4—101no—
659D4—101no—
660D4—101no—
661D4—101no—
662D4—401no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—51no—
670C2×C4—51no—
671C2×C4—51no—
672C2×C4—51no—
673C2×C4—101no—
674C2×C4—401no—
675C2×C4—401no—
676C2×C4—401no—
677C2×C4—401no—
678C2×C4—401no—
679C2×C4C3×D4×D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—21no—
682C8—21no—
683C8—101no—
684C8—101no—
685C2×C3—41no—
686C2×C3—202no—
687C2×C3—202no—
688C2×C3—401no—
689C2×C3#6599011yescharacteristic
690C2×C3#6610311yescharacteristic
691C2×C3#6611211yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—102no—
697C22—102no—
698C22—201no—
699C22—201no—
700C22—201no—
701C22—201no—
702C22—201no—
703C22—201no—
704C22—201no—
705C22—404no—
706C22C2×C3×D4×D511yescharacteristic
707C4—21no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—101no—
713C4—101no—
714C4—101no—
715C4—101no—
716C4—201no—
717C4C3×D5×#4111yescharacteristic
718C4C3×D5×#4111yescharacteristic
719C3#1061322711yescharacteristic, direct product factor, Sylow
720C2—41no—
721C2—202no—
722C2—202no—
723C2—401no—
724C2C3×#6599011yescharacteristic
725C2C3×#6610311yescharacteristic
726C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#485C2
socleC22×C3×C5C22×D4
prime radicalC3×#65021C2
hypercenterC3×#485D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
1. C3×#65977C2semidirect
2. C3×#65855C2semidirect
3. C3×C5×#485C2semidirect
4. C3×#65335C2semidirect
5. C3×#65292C2semidirect
6. C3×#65179C2semidirect
7. C3×#65161C2semidirect
8. C3×#65159C2semidirect
9. C3×#65158C2semidirect
10. C3×#65108C2semidirect
11. C3×#65108C2semidirect
12. C3×#65106C2semidirect
13. C3×#65077C2semidirect
15. C3×#65009C2semidirect
16. #10613227C3direct (N × H)
20. C3×#4093C22semidirect
21. C3×Q8×Dic5C22semidirect
34. C3×#4039C22semidirect
35. C3×#4034C22semidirect
42. C3×C5×#107C22semidirect
43. C3×C5×#106C22semidirect
44. C3×C5×#103C22semidirect
45. C3×C5×#103C22semidirect
50. C3×#3947C22semidirect
51. C3×#3946C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
56. C3×#3941C22semidirect
57. C3×#3941C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
61. #65977C2×C3semidirect
62. #65855C2×C3semidirect
63. C5×#485C2×C3semidirect
64. #65335C2×C3semidirect
65. #65292C2×C3semidirect
66. #65179C2×C3semidirect
67. #65161C2×C3semidirect
68. #65159C2×C3semidirect
69. #65158C2×C3semidirect
70. #65108C2×C3semidirect
71. #65108C2×C3semidirect
72. #65106C2×C3semidirect
73. #65077C2×C3semidirect
75. #65009C2×C3semidirect
127. C3×#485D5semidirect
143. #4093C22×C3semidirect
144. Q8×Dic5C22×C3semidirect
157. #4039C22×C3semidirect
158. #4034C22×C3semidirect
165. C5×#107C22×C3semidirect
166. C5×#106C22×C3semidirect
167. C5×#103C22×C3semidirect
168. C5×#103C22×C3semidirect
173. #3947C22×C3semidirect
174. #3946C22×C3semidirect
175. #3946C22×C3semidirect
176. C8×Dic5C22×C3semidirect
179. #3941C22×C3semidirect
180. #3941C22×C3semidirect
181. #3940C22×C3semidirect
182. #3939C22×C3semidirect
250. C3×#107C2×D5semidirect
252. C3×#106C2×D5semidirect
255. C3×#103C2×D5semidirect
256. C3×#103C2×D5semidirect
318. #485C3×D5semidirect
472. #107C2×C3×D5semidirect
474. #106C2×C3×D5semidirect
477. #103C2×C3×D5semidirect
478. #103C2×C3×D5semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10613227direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659772
C3×#658552
C3×C5×#4852
C3×#653352
C3×#652922
C3×#651792
C3×#651612
C3×#651592
C3×#651582
C3×#651082
C3×#651062
C3×#650772
C3×#650212
C3×#650092
#106132273
C3×#31185