Finite Group Databasebeta

← C3×#10611506 #14417001

Subgroups — C3×#10611506 #14417001

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4060C211yesmaximal, characteristic
2C3×#65908C211yesmaximal, characteristic, complemented
3C3×#65879C211yesmaximal, characteristic, complemented
4C3×C5×#440C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6C3×C4×#688C211yesmaximal, characteristic, complemented
7C3×C4×#686C211yesmaximal, characteristic, complemented
8C3×#65170C211yesmaximal, characteristic, complemented
9C3×#65161C211yesmaximal, characteristic, complemented
10C3×#65106C211yesmaximal, characteristic, complemented
11C3×#65093C211yesmaximal, characteristic, complemented
12C3×#65074C211yesmaximal, characteristic, complemented
13C3×D5×#102C211yesmaximal, characteristic, complemented
14C3×#65000C211yesmaximal, characteristic, complemented
15C3×#64997C211yesmaximal, characteristic, complemented
16#10611506C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic, complemented
23C2×C3×#688C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C2×C3×#685—21no—
28C3×#4060C418yescomplemented
29C2×C3×D40C2211yescharacteristic
30C2×C3×#676C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic
32C3×#4039—21no—
33C3×#4039C2211yescharacteristic
34C3×#4039C2211yescharacteristic, complemented
35C3×#4038C2211yescharacteristic
36C3×D5×C4⋊C4—21no—
37C3×D5×C4⋊C4C2211yescharacteristic
38C3×#4027—21no—
39C3×D5×C22⋊C4—21no—
40C3×C4×D20—21no—
41C3×C4×D20C2211yescharacteristic
42C3×C4×D20C2211yescharacteristic, complemented
43C3×#4018—21no—
44C3×#4018C2211yescharacteristic
45C3×C5×#107C2211yescharacteristic, complemented
46C3×C5×#103C2211yescharacteristic, complemented
47C3×C5×#102C2211yescharacteristic
48C3×C5×#97C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3964C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic, complemented
53C3×#3949C2211yescharacteristic, complemented
54C3×#3947C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic, complemented
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×C4×#168C2211yescharacteristic, complemented
61C3×#2946—51nomaximal, Hall
62C2×#4060C2×C311yescharacteristic
63#65908C2×C311yescharacteristic, complemented
64#65879C2×C311yescharacteristic, complemented
65C5×#440C2×C311yescharacteristic, complemented
66SD16×Dic5C2×C311yescharacteristic, complemented
67C4×#688C2×C311yescharacteristic, complemented
68C4×#686C2×C311yescharacteristic, complemented
69#65170C2×C311yescharacteristic, complemented
70#65161C2×C311yescharacteristic, complemented
71#65106C2×C311yescharacteristic, complemented
72#65093C2×C311yescharacteristic, complemented
73#65074C2×C311yescharacteristic, complemented
74D5×#102C2×C311yescharacteristic, complemented
75#65000C2×C311yescharacteristic, complemented
76#64997C2×C311yescharacteristic, complemented
77C23×C3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C3×#713—22no—
84C3×#713C2×C414yescomplemented
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yescomplemented
87C2×C3×D20—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5C2311yescharacteristic
97C3×C5×SD16C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C22⋊C4—21no—
104C3×C42×C5—21no—
105C3×C42×C5C2311yescharacteristic
106C3×C22⋊Dic5—21no—
107C3×#688C2×C414yescomplemented
108C3×#686C2×C414yescomplemented
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685D411yescharacteristic
115C3×#685D411yescharacteristic
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683D411yescharacteristic
121C3×#683D411yescharacteristic
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×D40C2×C414yescomplemented
128C3×#676C2×C414yescomplemented
129C3×C8×D5—22no—
130C2×C3×AGL(1,ℤ/8)—51no—
131C3×#520—51no—
132C3×#518—51no—
133C3×#442—51no—
134C3×#442—51no—
135C3×#440—51no—
136C3×#440D511yescharacteristic, complemented
137C3×C4×SD16—51no—
138C3×C4×SD16—51no—
139C3×C4×D8—51no—
140C3×C4×D8—51no—
141C3×#428—51no—
142C3×#416—51no—
143C2×C3×#102—51no—
144C3×#405—51no—
145C2×#713C22×C311yescharacteristic
146C2×D4×D5C22×C311yescharacteristic
147C2×C5×SD16C22×C311yescharacteristic
148C4×C5×Q8C22×C311yescharacteristic, complemented
149C4×C5×D4C22×C311yescharacteristic
150Q8×Dic5C22×C311yescharacteristic, complemented
151C2×#688C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154C4×C22⋊D5—21no—
155C2×#685—21no—
156#4060C3×C418yescomplemented
157C2×D40C22×C311yescharacteristic
158C2×#676C22×C311yescharacteristic
159C2×C8×D5C22×C311yescharacteristic
160#4039—21no—
161#4039C22×C311yescharacteristic
162#4039C22×C311yescharacteristic, complemented
163#4038C22×C311yescharacteristic
164D5×C4⋊C4—21no—
165D5×C4⋊C4C22×C311yescharacteristic
166#4027—21no—
167D5×C22⋊C4—21no—
168C4×D20—21no—
169C4×D20C22×C311yescharacteristic
170C4×D20C22×C311yescharacteristic, complemented
171#4018—21no—
172#4018C22×C311yescharacteristic
173C5×#107C22×C311yescharacteristic, complemented
174C5×#103C22×C311yescharacteristic, complemented
175C5×#102C22×C311yescharacteristic
176C5×#97C22×C311yescharacteristic, complemented
177#3967C22×C311yescharacteristic, complemented
178#3964C22×C311yescharacteristic
179#3953C22×C311yescharacteristic
180#3953C22×C311yescharacteristic, complemented
181#3949C22×C311yescharacteristic, complemented
182#3947C22×C311yescharacteristic, complemented
183C8×Dic5C22×C311yescharacteristic, complemented
184#3941C22×C311yescharacteristic
185#3941C22×C311yescharacteristic, complemented
186#3940C22×C311yescharacteristic, complemented
187#3939C22×C311yescharacteristic, complemented
188C4×#168C22×C311yescharacteristic, complemented
189#2946—51noSylow
190C23×C3×C5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—24no—
194C22×C3×D5—81no—
195C22×C3×D5—81no—
196C22×C3×D5C2×D411yescharacteristic
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yes—
199C3×C5×D4—21no—
200C3×C5×D4C22×C412yes—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—81no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C3×C22⋊D5—24no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5C2×D411yescharacteristic
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C3×D20—24no—
216C3×D20—21no—
217C3×D20—21no—
218C3×D20C22×C412yes—
219C3×D20C22×C412yes—
220C3×C4×D5—24no—
221C3×C4×D5—81no—
222C3×C4×D5—81no—
223C3×C4×D5—81no—
224C3×C4×D5—81no—
225C3×C4×D5—81no—
226C3×C4×D5C22×C412yes—
227C3×C4×D5#4112yes—
228C3×C5×C8—21no—
229C3×C5×C8C22×C412yes—
230C3×#168—21no—
231C3×#168C22×C412yes—
232C2×C3×#41—51no—
233C22×C3×D4—51no—
234C3×AGL(1,ℤ/8)—58no—
235C2×C3×SD16—51no—
236C2×C3×SD16C2×D511yescharacteristic
237C2×C3×D8—51no—
238C2×C3×D8—51no—
239C2×C3×M16—51no—
240C22×C3×C8—51no—
241C3×C4×Q8—51no—
242C3×C4×Q8C2×D511yescharacteristic, complemented
243C3×C4×D4—51no—
244C3×C4×D4—51no—
245C3×C4×D4—51no—
246C3×C4×D4—51no—
247C3×C4×D4—51no—
248C3×C4×D4—101no—
249C3×C4×D4—101no—
250C3×C4×D4—101no—
251C3×C4×D4—101no—
252C3×C4×D4C2×D511yescharacteristic
253C3×#117—51no—
254C3×#117—51no—
255C3×#117—101no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—101no—
258C2×C3×C22⋊C4—101no—
259C2×C3×C22⋊C4—101no—
260C3×#107—51no—
261C3×#107C2×D511yescharacteristic, complemented
262C3×#106—51no—
263C3×#106—51no—
264C3×#103—51no—
265C3×#103C2×D511yescharacteristic, complemented
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102—51no—
271C3×#102C2×D511yescharacteristic
272C3×#97—51no—
273C3×#97C2×D511yescharacteristic, complemented
274C3×C4×C8—51no—
275C3×C4×C8—51no—
276C23×D5—21no—
277C2×C5×Q8C23×C311yescharacteristic
278C2×C5×D4C23×C311yescharacteristic
279C22×C4×C5—21no—
280C2×C22⋊D5—21no—
281C22×Dic5—21no—
282#713—22no—
283#713C2×C3×C414yescomplemented
284D4×D5—22no—
285D4×D5C2×C3×C414yescomplemented
286C2×D20—21no—
287C2×D20C23×C311yescharacteristic
288C2×D20C23×C311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—21no—
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5—21no—
295C2×C4×D5C23×C311yescharacteristic
296C5×SD16C2×C3×C414yescomplemented
297C2×C5×C8C23×C311yescharacteristic
298C2×C5×C8C23×C311yescharacteristic
299C5×C4⋊C4—21no—
300C5×C4⋊C4C23×C311yescharacteristic
301C5×C4⋊C4C23×C311yescharacteristic
302C5×C22⋊C4—21no—
303C42×C5—21no—
304C42×C5C23×C311yescharacteristic
305C22⋊Dic5—21no—
306#688C2×C3×C414yescomplemented
307#686C2×C3×C414yescomplemented
308#685—21no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685C3×D411yescharacteristic
314#685C3×D411yescharacteristic
315C4⋊Dic5—21no—
316C4⋊Dic5C23×C311yescharacteristic
317C4⋊Dic5C23×C311yescharacteristic
318#683—21no—
319#683C3×D411yescharacteristic
320#683C3×D411yescharacteristic
321C4×Dic5—21no—
322C4×Dic5—21no—
323C4×Dic5C23×C311yescharacteristic
324C2×#168C23×C311yescharacteristic
325C2×#168C23×C311yescharacteristic
326D40C2×C3×C414yescomplemented
327#676C2×C3×C414yescomplemented
328C8×D5—22no—
329C2×AGL(1,ℤ/8)—51no—
330#520—51no—
331#518—51no—
332#442—51no—
333#442—51no—
334#440—51no—
335#440C3×D511yescharacteristic, complemented
336C4×SD16—51no—
337C4×SD16—51no—
338C4×D8—51no—
339C4×D8—51no—
340#428—51no—
341#416—51no—
342C2×#102—51no—
343#405—51no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5C4×D412yes—
358C3×C4×C5—22no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×C4×C5C23×C411yescharacteristic
364C3×C4×C5C2×#4111yescharacteristic
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5C4×D412yes—
370C24×C3—101no—
371C3×#41—54no—
372C3×#41—102no—
373C2×C3×Q8C22×D511yescharacteristic
374C2×C3×D4—54no—
375C2×C3×D4—51no—
376C2×C3×D4—51no—
377C2×C3×D4—101no—
378C2×C3×D4—102no—
379C2×C3×D4—101no—
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4—21no—
382C22×C3×C4—51no—
383C22×C3×C4—101no—
384C22×C3×C4—101no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4—101no—
389C22×C3×C4—101no—
390C3×SD16—54no—
391C3×SD16C4×D514yescomplemented
392C3×D8—54no—
393C3×D8—54no—
394C3×M16—54no—
395C2×C3×C8—51no—
396C2×C3×C8—51no—
397C2×C3×C8—102no—
398C2×C3×C8C22×D511yescharacteristic
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—51no—
403C3×C4⋊C4—51no—
404C3×C4⋊C4—51no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4—101no—
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C4⋊C4C22×D511yescharacteristic
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×C42—21no—
419C3×C42—51no—
420C3×C42—101no—
421C3×C42—101no—
422C3×C42C22×D511yescharacteristic
423C23×C5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—24no—
427C22×D5—81no—
428C22×D5—81no—
429C22×D5C2×C3×D411yescharacteristic
430C5×Q8—21no—
431C5×Q8C22×C3×C412yes—
432C5×D4—21no—
433C5×D4C22×C3×C412yes—
434C2×C4×C5—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—24no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—81no—
445C2×Dic5C2×C3×D411yescharacteristic
446C2×Dic5C2×C3×D411yescharacteristic
447C2×Dic5C2×C3×D411yescharacteristic
448D20—24no—
449D20—21no—
450D20—21no—
451D20C22×C3×C412yes—
452D20C22×C3×C412yes—
453C4×D5—24no—
454C4×D5—81no—
455C4×D5—81no—
456C4×D5—81no—
457C4×D5—81no—
458C4×D5—81no—
459C4×D5C22×C3×C412yes—
460C4×D5C3×#4112yes—
461C5×C8—21no—
462C5×C8C22×C3×C412yes—
463#168—21no—
464#168C22×C3×C412yes—
465C2×#41—51no—
466C22×D4—51no—
467AGL(1,ℤ/8)—58no—
468C2×SD16—51no—
469C2×SD16C2×C3×D511yescharacteristic
470C2×D8—51no—
471C2×D8—51no—
472C2×M16—51no—
473C22×C8—51no—
474C4×Q8—51no—
475C4×Q8C2×C3×D511yescharacteristic, complemented
476C4×D4—51no—
477C4×D4—51no—
478C4×D4—51no—
479C4×D4—51no—
480C4×D4—51no—
481C4×D4—101no—
482C4×D4—101no—
483C4×D4—101no—
484C4×D4—101no—
485C4×D4C2×C3×D511yescharacteristic
486#117—51no—
487#117—51no—
488#117—101no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493#107—51no—
494#107C2×C3×D511yescharacteristic, complemented
495#106—51no—
496#106—51no—
497#103—51no—
498#103C2×C3×D511yescharacteristic, complemented
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102—51no—
504#102C2×C3×D511yescharacteristic
505#97—51no—
506#97C2×C3×D511yescharacteristic, complemented
507C4×C8—51no—
508C4×C8—51no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513C3×D5—22no—
514C3×D5—42no—
515C3×D5—42no—
516C23×C3—21no—
517C23×C3—51no—
518C23×C3—104no—
519C23×C3—101no—
520C23×C3—101no—
521C23×C3—401no—
522C23×C3—401no—
523C3×Q8—21no—
524C3×Q8C2×C4×D512yes—
525C3×D4—21no—
526C3×D4—52no—
527C3×D4—52no—
528C3×D4—104no—
529C3×D4—104no—
530C3×D4—101no—
531C3×D4—101no—
532C3×D4C2×C4×D512yes—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—51no—
537C2×C3×C4—52no—
538C2×C3×C4—52no—
539C2×C3×C4—51no—
540C2×C3×C4—51no—
541C2×C3×C4—81no—
542C2×C3×C4—104no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—401no—
546C2×C3×C4—401no—
547C2×C3×C4—401no—
548C2×C3×C4—401no—
549C2×C3×C4—401no—
550C2×C3×C4—401no—
551C2×C3×C4D4×D511yescharacteristic
552C2×C3×C4D4×D511yescharacteristic
553C2×C3×C4C23×D511yescharacteristic
554C3×C8—21no—
555C3×C8—52no—
556C3×C8—101no—
557C3×C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5C22×C3×D411yescharacteristic
562C2×D5—21no—
563C2×D5—21no—
564C2×D5—22no—
565C2×D5—22no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—84no—
571C2×D5C3×C4×D412yes—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—22no—
575C4×C5—41no—
576C4×C5—41no—
577C4×C5C23×C3×C411yescharacteristic
578C4×C5C2×C3×#4111yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—41no—
582Dic5—41no—
583Dic5C3×C4×D412yes—
584C24—101no—
585#41—54no—
586#41—102no—
587C2×Q8C22×C3×D511yescharacteristic
588C2×D4—54no—
589C2×D4—51no—
590C2×D4—51no—
591C2×D4—101no—
592C2×D4—102no—
593C2×D4—101no—
594C2×D4C22×C3×D511yescharacteristic
595C22×C4—21no—
596C22×C4—51no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604SD16—54no—
605SD16C3×C4×D514yescomplemented
606D8—54no—
607D8—54no—
608M16—54no—
609C2×C8—51no—
610C2×C8—51no—
611C2×C8—102no—
612C2×C8C22×C3×D511yescharacteristic
613C2×C8C22×C3×D511yescharacteristic
614C4⋊C4—21no—
615C4⋊C4—51no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—51no—
619C4⋊C4—101no—
620C4⋊C4—101no—
621C4⋊C4C22×C3×D511yescharacteristic
622C4⋊C4C22×C3×D511yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—51no—
625C22⋊C4—51no—
626C22⋊C4—101no—
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C42—21no—
633C42—51no—
634C42—101no—
635C42—101no—
636C42C22×C3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—52no—
642C22×C3—101no—
643C22×C3—101no—
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—201no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—404no—
651C22×C3C2×D4×D511yescharacteristic
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—52no—
658C3×C4—101no—
659C3×C4—101no—
660C3×C4—201no—
661C3×C4—201no—
662C3×C4C22×C4×D511yescharacteristic
663C3×C4D5×#4111yescharacteristic
664C2×C5—42no—
665C2×C5C2×C3×C4×D411yescharacteristic
666C2×C5C3×#57611yescharacteristic
667C2×C5C3×#57711yescharacteristic
668D5—22no—
669D5—42no—
670D5—42no—
671C23—21no—
672C23—51no—
673C23—104no—
674C23—101no—
675C23—101no—
676C23—401no—
677C23—401no—
678Q8—21no—
679Q8C2×C3×C4×D512yes—
680D4—21no—
681D4—52no—
682D4—52no—
683D4—104no—
684D4—104no—
685D4—101no—
686D4—101no—
687D4C2×C3×C4×D512yes—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—51no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—51no—
695C2×C4—51no—
696C2×C4—81no—
697C2×C4—104no—
698C2×C4—101no—
699C2×C4—101no—
700C2×C4—401no—
701C2×C4—401no—
702C2×C4—401no—
703C2×C4—401no—
704C2×C4—401no—
705C2×C4—401no—
706C2×C4C3×D4×D511yescharacteristic
707C2×C4C3×D4×D511yescharacteristic
708C2×C4C23×C3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—101no—
712C8C2×C3×C4×D512yes—
713C2×C3—42no—
714C2×C3—102no—
715C2×C3—202no—
716C2×C3—202no—
717C2×C3C4×D4×D511yescharacteristic
718C2×C3#6610811yescharacteristic
719C2×C3#6611211yescharacteristic
720C5C3×#294611yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—52no—
725C22—101no—
726C22—101no—
727C22—102no—
728C22—102no—
729C22—201no—
730C22—201no—
731C22—201no—
732C22—201no—
733C22—404no—
734C22C2×C3×D4×D511yescharacteristic
735C4—21no—
736C4—21no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—52no—
741C4—101no—
742C4—101no—
743C4—201no—
744C4—201no—
745C4C22×C3×C4×D511yescharacteristic
746C4C3×D5×#4111yescharacteristic
747C3#1061150611yescharacteristic, direct product factor, Sylow
748C2—42no—
749C2—102no—
750C2—202no—
751C2—202no—
752C2C3×C4×D4×D511yescharacteristic
753C2C3×#6610811yescharacteristic
754C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4060C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#440D5
hypocenterC5C3×#2946
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×#65908C2semidirect
3. C3×#65879C2semidirect
4. C3×C5×#440C2semidirect
5. C3×SD16×Dic5C2semidirect
6. C3×C4×#688C2semidirect
7. C3×C4×#686C2semidirect
8. C3×#65170C2semidirect
9. C3×#65161C2semidirect
10. C3×#65106C2semidirect
11. C3×#65093C2semidirect
12. C3×#65074C2semidirect
13. C3×D5×#102C2semidirect
14. C3×#65000C2semidirect
15. C3×#64997C2semidirect
16. #10611506C3direct (N × H)
20. C3×C4×C5×Q8C22semidirect
22. C3×Q8×Dic5C22semidirect
28. C3×#4060C4semidirect
34. C3×#4039C22semidirect
42. C3×C4×D20C22semidirect
45. C3×C5×#107C22semidirect
46. C3×C5×#103C22semidirect
48. C3×C5×#97C22semidirect
49. C3×#3967C22semidirect
52. C3×#3953C22semidirect
53. C3×#3949C22semidirect
54. C3×#3947C22semidirect
55. C3×C8×Dic5C22semidirect
57. C3×#3941C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
60. C3×C4×#168C22semidirect
63. #65908C2×C3semidirect
64. #65879C2×C3semidirect
65. C5×#440C2×C3semidirect
66. SD16×Dic5C2×C3semidirect
67. C4×#688C2×C3semidirect
68. C4×#686C2×C3semidirect
69. #65170C2×C3semidirect
70. #65161C2×C3semidirect
71. #65106C2×C3semidirect
72. #65093C2×C3semidirect
73. #65074C2×C3semidirect
74. D5×#102C2×C3semidirect
75. #65000C2×C3semidirect
76. #64997C2×C3semidirect
84. C3×#713C2×C4semidirect
86. C3×D4×D5C2×C4semidirect
97. C3×C5×SD16C2×C4semidirect
107. C3×#688C2×C4semidirect
108. C3×#686C2×C4semidirect
127. C3×D40C2×C4semidirect
128. C3×#676C2×C4semidirect
136. C3×#440D5semidirect
148. C4×C5×Q8C22×C3semidirect
150. Q8×Dic5C22×C3semidirect
156. #4060C3×C4semidirect
162. #4039C22×C3semidirect
170. C4×D20C22×C3semidirect
173. C5×#107C22×C3semidirect
174. C5×#103C22×C3semidirect
176. C5×#97C22×C3semidirect
177. #3967C22×C3semidirect
180. #3953C22×C3semidirect
181. #3949C22×C3semidirect
182. #3947C22×C3semidirect
183. C8×Dic5C22×C3semidirect
185. #3941C22×C3semidirect
186. #3940C22×C3semidirect
187. #3939C22×C3semidirect
188. C4×#168C22×C3semidirect
242. C3×C4×Q8C2×D5semidirect
261. C3×#107C2×D5semidirect
265. C3×#103C2×D5semidirect
273. C3×#97C2×D5semidirect
283. #713C2×C3×C4semidirect
285. D4×D5C2×C3×C4semidirect
296. C5×SD16C2×C3×C4semidirect
306. #688C2×C3×C4semidirect
307. #686C2×C3×C4semidirect
326. D40C2×C3×C4semidirect
327. #676C2×C3×C4semidirect
335. #440C3×D5semidirect
391. C3×SD16C4×D5semidirect
475. C4×Q8C2×C3×D5semidirect
494. #107C2×C3×D5semidirect
498. #103C2×C3×D5semidirect
506. #97C2×C3×D5semidirect
605. SD16C3×C4×D5semidirect
637. C3×C5#2946semidirect
720. C5C3×#2946semidirect
747. C3#10611506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40602
C3×#659082
C3×#658792
C3×C5×#4402
C3×SD16×Dic52
C3×C4×#6882
C3×C4×#6862
C3×#651702
C3×#651612
C3×#651062
C3×#650932
C3×#650742
C3×D5×#1022
C3×#650002
C3×#649972
#106115063
C3×#29465