Finite Group Databasebeta

← #14453963

Subgroups — #14453963

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic, complemented
2C2×#91839C211yesmaximal, characteristic, complemented
3C2×#91838C211yesmaximal, characteristic, complemented
4#11756309C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6#11751339C211yesmaximal, characteristic, complemented
7#11751187C211yesmaximal, characteristic, complemented
8#11751184C211yesmaximal, characteristic, complemented
9#11751153C211yesmaximal, characteristic, complemented
10#11751149C211yesmaximal, characteristic, complemented
11#11751148C211yesmaximal, characteristic, complemented
12#11751147C211yesmaximal, characteristic, complemented
13#11751117C211yesmaximal, characteristic, complemented
14#11751115C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615253—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic, complemented
19C2×#6817C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C3×C5×C4⋊Q8C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×#123—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×C22⋊Q8C2211yescharacteristic, complemented
26C3×C5×#121—21no—
27C3×C4×C5×D4C2211yescharacteristic
28C3×C4×C5×D4C2211yescharacteristic, complemented
29C2×C3×C5×C4⋊C4—21no—
30#91839—24no—
31#91838—24no—
32C2×#6718C2211yescharacteristic, complemented
33C2×#6718C2211yescharacteristic, complemented
34C2×#6717C2211yescharacteristic
35C2×#6717C2211yescharacteristic
36C2×#6717C2211yescharacteristic
37C2×#6717C2211yescharacteristic
38#91826—21no—
39C2×#6716C2211yescharacteristic, complemented
40C2×#6715C2211yescharacteristic
41C2×#6715C2211yescharacteristic
42#91819C2211yescharacteristic
43#91813C2211yescharacteristic
44C2×#6710C2211yescharacteristic
45C22×C3⋊#168C2211yescharacteristic, complemented
46#91783—21no—
47#91773—21no—
48C22⋊C4×D15—21no—
49#91764C2211yescharacteristic
50C4×D60C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic
55#91114C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91093C2211yescharacteristic
58#91093C2211yescharacteristic
59#91092C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83522—51nomaximal, Hall
63C5×#547D311yescharacteristic, complemented
64C2×#4096—31no—
65C2×#4095—31no—
66#65884—31no—
67#65528—31no—
68#65527—31no—
69#65375—31no—
70#65372—31no—
71#65341—31no—
72#65337—31no—
73#65336—31no—
74#65335—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C23×D15—21no—
79C3×C5×#41—22no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4D411yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—21no—
95C2×#1220—21no—
96#6817—22no—
97#6817—41no—
98C2×D60—22no—
99C2×D60—21no—
100C2×D60—41no—
101C2×D60C2311yescharacteristic
102C2×D60C2311yescharacteristic
103C2×C4×D15—21no—
104C2×C4×D15—21no—
105C2×Dic30C2311yescharacteristic
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4—21no—
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C42×C5C2311yescharacteristic
118#6719—21no—
119#6718—22no—
120#6718—41no—
121#6717—22no—
122#6717—22no—
123#6717—22no—
124#6717—41no—
125#6716—22no—
126#6715—22no—
127#6715D414yescomplemented
128#6714—21no—
129#6714—21no—
130#6714—21no—
131#6714—21no—
132C4⋊Dic15C2311yescharacteristic
133#6712—21no—
134#6710—22no—
135C2×C3⋊#168—22no—
136C2×C3⋊#168C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139C2×C3⋊#168C2311yescharacteristic
140C3×#547D511yescharacteristic, complemented
141C2×#950—51no—
142C2×#949—51no—
143#5550—51no—
144#5239—51no—
145#5238—51no—
146#5086—51no—
147#5083—51no—
148#5052—51no—
149#5048—51no—
150#5047—51no—
151#5046—51no—
152#5016—51no—
153#5014—51no—
154#5011—51no—
155C2×C5×#41C2×D311yescharacteristic
156C2×C5×#41C2×D311yescharacteristic, complemented
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8C2×D311yescharacteristic, complemented
160C5×#123—21no—
161C5×#123—21no—
162C5×C22⋊Q8C2×D311yescharacteristic
163C5×C22⋊Q8C2×D311yescharacteristic, complemented
164C5×#121—21no—
165C4×C5×D4C2×D311yescharacteristic
166C4×C5×D4C2×D311yescharacteristic, complemented
167C2×C5×C4⋊C4—21no—
168#4096—64no—
169#4095—64no—
170C2×#689—31no—
171C2×#689—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176#4083—61no—
177C2×#687—31no—
178C2×#686—31no—
179C2×#686—31no—
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3940—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3267—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—42no—
207C22×D15—42no—
208C22×D15—81no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×D4—21no—
214C3×C5×D4—41no—
215C3×C5×D4—42no—
216C3×C5×D4—42no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—42no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2×D411yescharacteristic
232C2×C3×C4×C5C2411yescharacteristic
233#1220—42no—
234#1220—81no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237D60—21no—
238D60—21no—
239D60—21no—
240D60—42no—
241D60C2×D412yes—
242C4×D15—42no—
243C4×D15—81no—
244Dic30—21no—
245Dic30—21no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3⋊#168—21no—
249C3⋊#168C2×D412yes—
250C2×C3×#41C2×D511yescharacteristic
251C2×C3×#41C2×D511yescharacteristic, complemented
252C2×#235—51no—
253C22×D12—51no—
254C3×C4⋊Q8C2×D511yescharacteristic, complemented
255C3×#123—21no—
256C3×#123—21no—
257C3×C22⋊Q8C2×D511yescharacteristic
258C3×C22⋊Q8C2×D511yescharacteristic, complemented
259C3×#121—21no—
260C3×C4×D4C2×D511yescharacteristic
261C3×C4×D4C2×D511yescharacteristic, complemented
262C2×C3×C4⋊C4—21no—
263#950—104no—
264#949—104no—
265C2×#216—51no—
266C2×#216—51no—
267C2×#215—51no—
268C2×#215—51no—
269C2×#215—51no—
270C2×#215—51no—
271#937—101no—
272C2×#214—51no—
273C2×#213—51no—
274C2×#213—51no—
275#930—51no—
276#924—51no—
277C2×#208—51no—
278C22×C3⋊C8—51no—
279#894—101no—
280#884—101no—
281D3×C22⋊C4—101no—
282#875—51no—
283C4×D12—51no—
284#835—51no—
285#835—51no—
286#832—51no—
287#830—51no—
288#830—51no—
289#810—51no—
290#809—51no—
291#809—51no—
292#808—51no—
293C4⋊(C3⋊C8)—51no—
294#803—51no—
295C23×D5—61no—
296C5×#41—22no—
297C5×#41—22no—
298C5×#41—41no—
299C5×#41—41no—
300C2×C5×Q8C22×D311yescharacteristic
301C2×C5×Q8C22×D311yescharacteristic
302C2×C5×D4—21no—
303C2×C5×D4—21no—
304C2×C5×D4#6711yescharacteristic
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5—21no—
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313#709—62no—
314#709—121no—
315C2×D20—31no—
316C2×D20—31no—
317C2×D20—62no—
318C2×D20—61no—
319C2×D20—121no—
320C2×C4×D5—61no—
321C2×C4×D5—61no—
322C2×Dic10—31no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4—21no—
327C5×C4⋊C4#6711yescharacteristic
328C5×C4⋊C4C22×D311yescharacteristic
329C5×C22⋊C4—21no—
330C5×C22⋊C4—21no—
331C5×C22⋊C4—21no—
332C5×C22⋊C4#6711yescharacteristic
333C5×C22⋊C4#6711yescharacteristic
334C42×C5C22×D311yescharacteristic
335C22⋊Dic5—61no—
336#689—62no—
337#689—121no—
338#688—62no—
339#688—62no—
340#688—62no—
341#688—121no—
342#687—62no—
343#686—34no—
344#686—62no—
345#685—61no—
346#685—61no—
347#685—61no—
348#685—61no—
349C4⋊Dic5—31no—
350#683—61no—
351#681—62no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—31no—
355C2×#168—31no—
356C2×#168—62no—
357C2×AGL(1,ℤ/8)—151no—
358C2×#135—151no—
359#547D1511yescharacteristic, complemented
360#546—151no—
361#497—151no—
362#470—151no—
363#465—151no—
364#463—151no—
365#461—151no—
366#452—151no—
367#452—151no—
368#450—151no—
369#449—151no—
370#442—151no—
371#435—151no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—22no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C22×D411yescharacteristic
382C2×D15—22no—
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—21no—
392C3×C4×C5—21no—
393C3×C4×C5—41no—
394C3×C4×C5—41no—
395C3×C4×C5—41no—
396C3×C4×C5C22×D411yescharacteristic
397C3×C4×C5H(5,𝔽2)11yescharacteristic
398Dic15—41no—
399Dic15—41no—
400C23×D3—101no—
401C3×#41—22no—
402C3×#41—22no—
403C3×#41—41no—
404C3×#41—41no—
405C2×C3×Q8C22×D511yescharacteristic
406C2×C3×Q8C22×D511yescharacteristic
407C2×C3×D4—21no—
408C2×C3×D4—21no—
409C2×C3×D4C22⋊D511yescharacteristic
410C2×C3×D4C22×D511yescharacteristic
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C2×#67—101no—
417C2×#67—101no—
418#235—102no—
419#235—201no—
420C2×D12—51no—
421C2×D12—51no—
422C2×D12—102no—
423C2×D12—101no—
424C2×D12—201no—
425C2×C4×D3—101no—
426C2×C4×D3—101no—
427C2×Dic6—51no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4—21no—
430C3×C4⋊C4—21no—
431C3×C4⋊C4—21no—
432C3×C4⋊C4C22⋊D511yescharacteristic
433C3×C4⋊C4C22×D511yescharacteristic
434C3×C22⋊C4—21no—
435C3×C22⋊C4—21no—
436C3×C22⋊C4—21no—
437C3×C22⋊C4C22⋊D511yescharacteristic
438C3×C22⋊C4C22⋊D511yescharacteristic
439C3×C42C22×D511yescharacteristic
440#217—101no—
441#216—102no—
442#216—201no—
443#215—102no—
444#215—102no—
445#215—102no—
446#215—201no—
447#214—102no—
448#213—54no—
449#213—102no—
450(C2×D3)⋊C4—101no—
451(C2×D3)⋊C4—101no—
452(C2×D3)⋊C4—101no—
453(C2×D3)⋊C4—101no—
454C4⋊Dic3—51no—
455Dic3⋊C4—101no—
456#208—102no—
457C2×C3⋊C8—51no—
458C2×C3⋊C8—51no—
459C2×C3⋊C8—51no—
460C2×C3⋊C8—51no—
461C2×C3⋊C8—102no—
462C23×C5—21no—
463C23×C5C2×#6711yescharacteristic
464C23×C5C2×#6711yescharacteristic
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—241no—
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—21no—
473C5×Q8—21no—
474C5×D4—21no—
475C5×D4—41no—
476C5×D4—42no—
477C5×D4—42no—
478C5×D4D3×D412yes—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—42no—
487C2×C4×C5—42no—
488C2×C4×C5—42no—
489C2×C4×C5C2×#6711yescharacteristic
490C2×C4×C5C2×#6711yescharacteristic
491C2×C4×C5C2×#6711yescharacteristic
492C2×C4×C5C2×#6711yescharacteristic
493C2×C4×C5C23×D311yescharacteristic
494C22⋊D5—122no—
495C22⋊D5—241no—
496C2×Dic5—61no—
497C2×Dic5—61no—
498D20—32no—
499D20—61no—
500D20—61no—
501D20—61no—
502D20—122no—
503C4×D5—122no—
504C4×D5—241no—
505Dic10—61no—
506Dic10—61no—
507#168—32no—
508#168—61no—
509#168—61no—
510#168—61no—
511C2×#41—151no—
512C2×#41C2×D1511yescharacteristic
513C2×#41C2×D1511yescharacteristic, complemented
514C22×D4—151no—
515AGL(1,ℤ/8)—304no—
516#135—304no—
517C2×Q16—151no—
518C2×Q16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—151no—
522C2×SD16—151no—
523C2×SD16—151no—
524C2×D8—151no—
525C2×D8—151no—
526C2×M16—151no—
527C22×C8—151no—
528C4⋊Q8C2×D1511yescharacteristic, complemented
529#124—151no—
530#123—21no—
531#123—21no—
532#123—301no—
533C22⋊Q8—151no—
534C22⋊Q8C2×D1511yescharacteristic
535C22⋊Q8C2×D1511yescharacteristic, complemented
536#121—21no—
537#121—151no—
538#121—301no—
539#120—301no—
540C4×D4—151no—
541C4×D4C2×D1511yescharacteristic
542C4×D4C2×D1511yescharacteristic, complemented
543C2×C4⋊C4—21no—
544C2×C22⋊C4—301no—
545#106—151no—
546C4⋊C8—151no—
547#103—151no—
548#103—151no—
549#103—151no—
550#102—151no—
551#102—151no—
552#102—151no—
553C22⋊C8—151no—
554C22⋊C8—151no—
555#97—151no—
556C2×C3×C5—41no—
557C2×C3×C5—41no—
558C2×C3×C5—42no—
559C2×C3×C5D4211yescharacteristic
560C2×C3×C5#57511yescharacteristic
561C2×C3×C5#57711yescharacteristic
562D15—42no—
563D15—81no—
564C23×C3—21no—
565C23×C3C2×C22⋊D511yescharacteristic
566C23×C3C2×C22⋊D511yescharacteristic
567C22×D3—101no—
568C22×D3—101no—
569C22×D3—202no—
570C22×D3—202no—
571C22×D3—401no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×D4—21no—
577C3×D4—41no—
578C3×D4—42no—
579C3×D4—42no—
580C3×D4D4×D512yes—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4C2×C22⋊D511yescharacteristic
592C2×C3×C4C2×C22⋊D511yescharacteristic
593C2×C3×C4C2×C22⋊D511yescharacteristic
594C2×C3×C4C2×C22⋊D511yescharacteristic
595C2×C3×C4C23×D511yescharacteristic
596#67—202no—
597#67—401no—
598C2×Dic3—101no—
599C2×Dic3—101no—
600D12—52no—
601D12—101no—
602D12—101no—
603D12—101no—
604D12—202no—
605C4×D3—202no—
606C4×D3—401no—
607Dic6—101no—
608Dic6—101no—
609C3⋊C8—52no—
610C3⋊C8—101no—
611C3⋊C8—101no—
612C3⋊C8—101no—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—22no—
616C22×C5—21no—
617C22×C5—21no—
618C22×C5—21no—
619C22×C5—21no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5C22×#6711yescharacteristic
623C2×D5—62no—
624C2×D5—121no—
625C2×D5—121no—
626C2×D5—121no—
627C2×D5—121no—
628C2×D5—121no—
629C2×D5—244no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—21no—
633C4×C5—21no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5C2×D3×D411yescharacteristic
638C4×C5#100411yescharacteristic
639Dic5—121no—
640Dic5—121no—
641C24—301no—
642#41—22no—
643#41—22no—
644#41—41no—
645#41—41no—
646#41—302no—
647#41—601no—
648C2×Q8—151no—
649C2×Q8C22×D1511yescharacteristic
650C2×Q8C22×D1511yescharacteristic
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—151no—
654C2×D4—151no—
655C2×D4—302no—
656C2×D4—301no—
657C2×D4—301no—
658C2×D4—301no—
659C2×D4—601no—
660C2×D4#122011yescharacteristic
661C2×D4C22×D1511yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—301no—
666C22×C4—301no—
667C22×C4C22×D1511yescharacteristic
668C22×C4C22×D1511yescharacteristic
669Q16—302no—
670Q16—601no—
671SD16—302no—
672SD16—302no—
673SD16—302no—
674SD16—302no—
675SD16—601no—
676D8—154no—
677D8—302no—
678M16—302no—
679C2×C8—151no—
680C2×C8—151no—
681C2×C8—151no—
682C2×C8—151no—
683C2×C8—302no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—151no—
689C4⋊C4—301no—
690C4⋊C4#122011yescharacteristic
691C4⋊C4C22×D1511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—301no—
696C22⋊C4—301no—
697C22⋊C4—301no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4#122011yescharacteristic
701C22⋊C4#122011yescharacteristic
702C42C22×D1511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3C22×C22⋊D511yescharacteristic
714C2×D3—102no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—201no—
719C2×D3—201no—
720C2×D3—404no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4C2×D4×D511yescharacteristic
729C3×C4#414411yescharacteristic
730Dic3—201no—
731Dic3—201no—
732C2×C5—41no—
733C2×C5—41no—
734C2×C5—42no—
735C2×C5D4×#6711yescharacteristic
736C2×C5#582211yescharacteristic
737C2×C5#583711yescharacteristic
738D5—122no—
739D5—241no—
740C23—21no—
741C23—301no—
742C23—301no—
743C23—602no—
744C23—602no—
745C23—1201no—
746C23C2×#122011yescharacteristic
747C23C2×#122011yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—301no—
753Q8—301no—
754D4—21no—
755D4—41no—
756D4—42no—
757D4—42no—
758D4—152no—
759D4—301no—
760D4—301no—
761D4—301no—
762D4—602no—
763D4—602no—
764D4—1201no—
765D4D4×D1512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—301no—
777C2×C4—301no—
778C2×C4—602no—
779C2×C4—1201no—
780C2×C4C2×#122011yescharacteristic
781C2×C4C2×#122011yescharacteristic
782C2×C4C2×#122011yescharacteristic
783C2×C4C2×#122011yescharacteristic
784C2×C4C23×D1511yescharacteristic
785C8—152no—
786C8—301no—
787C8—301no—
788C8—301no—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—42no—
792C2×C3D4×C22⋊D511yescharacteristic
793C2×C3#6615611yescharacteristic
794C2×C3#6617111yescharacteristic
795D3—202no—
796D3—401no—
797C5#8352211yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—22no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—302no—
808C22—601no—
809C22—601no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22C22×#122011yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—601no—
823C4—601no—
824C4C2×D4×D1511yescharacteristic
825C4#9209511yescharacteristic
826C3#1061525311yescharacteristic, complemented, Sylow
827C2—41no—
828C2—41no—
829C2—42no—
830C2—602no—
831C2—1201no—
832C2D4×#122011yescharacteristic
833C2#1175658111yescharacteristic
834C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#547C2
socleC22×C3×C5C22×D4
hypercenter#547D15
hypocenterC3×C5#3267
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C3×C5×#547C2semidirect
2. C2×#91839C2semidirect
3. C2×#91838C2semidirect
4. #11756309C2semidirect
5. #11751340C2semidirect
6. #11751339C2semidirect
7. #11751187C2semidirect
8. #11751184C2semidirect
9. #11751153C2semidirect
10. #11751149C2semidirect
11. #11751148C2semidirect
12. #11751147C2semidirect
13. #11751117C2semidirect
14. #11751115C2semidirect
15. #11751112C2semidirect
18. C2×C3×C5×#41C22semidirect
21. C3×C5×C4⋊Q8C22semidirect
25. C3×C5×C22⋊Q8C22semidirect
28. C3×C4×C5×D4C22semidirect
32. C2×#6718C22semidirect
33. C2×#6718C22semidirect
39. C2×#6716C22semidirect
45. C22×C3⋊#168C22semidirect
51. #91119C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
55. #91114C22semidirect
56. #91094C22semidirect
59. #91092C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×#547D3semidirect
127. #6715D4semidirect
140. C3×#547D5semidirect
156. C2×C5×#41C2×D3semidirect
159. C5×C4⋊Q8C2×D3semidirect
163. C5×C22⋊Q8C2×D3semidirect
166. C4×C5×D4C2×D3semidirect
251. C2×C3×#41C2×D5semidirect
254. C3×C4⋊Q8C2×D5semidirect
258. C3×C22⋊Q8C2×D5semidirect
261. C3×C4×D4C2×D5semidirect
359. #547D15semidirect
513. C2×#41C2×D15semidirect
528. C4⋊Q8C2×D15semidirect
535. C22⋊Q8C2×D15semidirect
542. C4×D4C2×D15semidirect
703. C3×C5#3267semidirect
797. C5#83522semidirect
826. C3#10615253semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5472
C2×#918392
C2×#918382
#117563092
#117513402
#117513392
#117511872
#117511842
#117511532
#117511492
#117511482
#117511472
#117511172
#117511152
#117511122
#106152533
#835225