Finite Group Databasebeta

← #14454218

Subgroups — #14454218

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic, complemented
2C2×#91839C211yesmaximal, characteristic, complemented
3C2×#91838C211yesmaximal, characteristic, complemented
4#11756309C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6#11751339C211yesmaximal, characteristic, complemented
7#11751175C211yesmaximal, characteristic, complemented
8#11751173C211yesmaximal, characteristic, complemented
9#11751143C211yesmaximal, characteristic, complemented
10#11751139C211yesmaximal, characteristic, complemented
11#11751138C211yesmaximal, characteristic, complemented
12#11751137C211yesmaximal, characteristic, complemented
13#11751129C211yesmaximal, characteristic, complemented
14#11751127C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615308—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic, complemented
19C2×#6817C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C3×C5×#127—21no—
22C3×C5×#127C2211yescharacteristic, complemented
23C3×C5×#121—21no—
24C3×C5×#121—21no—
25C3×C5×#121C2211yescharacteristic
26C3×C5×#121C2211yescharacteristic, complemented
27C3×C4×C5×Q8C2211yescharacteristic, complemented
28C3×C4×C5×D4—21no—
29C3×C4×C5×D4C2211yescharacteristic
30#91839—24no—
31#91838—24no—
32C2×#6718C2211yescharacteristic, complemented
33C2×#6717C2211yescharacteristic
34C2×#6717C2211yescharacteristic
35#91826—21no—
36C2×#6716C2211yescharacteristic, complemented
37C2×#6716C2211yescharacteristic, complemented
38C2×#6715C2211yescharacteristic
39C2×#6715C2211yescharacteristic
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#91116C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic
55#91114C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91093C2211yescharacteristic
58#91093C2211yescharacteristic
59#91091C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83577—51nomaximal, Hall
63C5×#550D311yescharacteristic, complemented
64C2×#4096—31no—
65C2×#4095—31no—
66#65884—31no—
67#65528—31no—
68#65527—31no—
69#65363—31no—
70#65361—31no—
71#65331—31no—
72#65327—31no—
73#65326—31no—
74#65325—31no—
75#65317—31no—
76#65315—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×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—21no—
89C2×C3×C5×D4—21no—
90C2×C3×C5×D4D411yescharacteristic
91C2×C3×C5×D4C2311yescharacteristic
92C2×C3×C5×D4C2311yescharacteristic
93C22×C3×C4×C5—21no—
94C22×C3×C4×C5—21no—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—21no—
98C2×#1220—21no—
99#6817—22no—
100#6817—41no—
101C2×D60—22no—
102C2×D60—21no—
103C2×D60—41no—
104C2×D60C2311yescharacteristic
105C2×D60C2311yescharacteristic
106C2×C4×D15—21no—
107C2×C4×D15—21no—
108C2×Dic30C2311yescharacteristic
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⋊C4D411yescharacteristic
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C42×C5—21no—
117C3×C42×C5C2311yescharacteristic
118#6719—21no—
119#6718—22no—
120#6717—22no—
121#6717D414yescomplemented
122#6716—22no—
123#6716—41no—
124#6715—22no—
125#6715—22no—
126#6715—22no—
127#6715—41no—
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×#550D511yescharacteristic, complemented
141C2×#950—51no—
142C2×#949—51no—
143#5550—51no—
144#5239—51no—
145#5238—51no—
146#5074—51no—
147#5072—51no—
148#5042—51no—
149#5038—51no—
150#5037—51no—
151#5036—51no—
152#5028—51no—
153#5026—51no—
154#5011—51no—
155C2×C5×#41C2×D311yescharacteristic
156C2×C5×#41C2×D311yescharacteristic, complemented
157C2×#709—31no—
158C22×D20—31no—
159C5×#127—21no—
160C5×#127C2×D311yescharacteristic, complemented
161C5×#121—21no—
162C5×#121—21no—
163C5×#121C2×D311yescharacteristic
164C5×#121C2×D311yescharacteristic, complemented
165C4×C5×Q8C2×D311yescharacteristic, complemented
166C4×C5×D4—21no—
167C4×C5×D4C2×D311yescharacteristic
168#4096—64no—
169#4095—64no—
170C2×#689—31no—
171C2×#688—31no—
172C2×#688—31no—
173#4083—61no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#686—31no—
177C2×#686—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#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3268—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C23×C3×C5C2×D411yescharacteristic
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—42no—
208C22×D15—42no—
209C22×D15—81no—
210C3×C5×Q8—21no—
211C3×C5×Q8C2×D412yes—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—41no—
217C3×C5×D4—42no—
218C3×C5×D4—42no—
219C3×C5×D4—42no—
220C3×C5×D4—81no—
221C3×C5×D4—81no—
222C3×C5×D4—81no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—42no—
230C2×C3×C4×C5—42no—
231C2×C3×C4×C5C2×D411yescharacteristic
232C2×C3×C4×C5C2×D411yescharacteristic
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2411yescharacteristic
236#1220—42no—
237#1220—81no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240D60—21no—
241D60—21no—
242D60—21no—
243D60—42no—
244D60C2×D412yes—
245C4×D15—42no—
246C4×D15—81no—
247Dic30—21no—
248Dic30—21no—
249C3⋊#168—21no—
250C3⋊#168—21no—
251C3⋊#168—21no—
252C3⋊#168C2×D412yes—
253C2×C3×#41C2×D511yescharacteristic
254C2×C3×#41C2×D511yescharacteristic, complemented
255C2×#235—51no—
256C22×D12—51no—
257C3×#127—21no—
258C3×#127C2×D511yescharacteristic, complemented
259C3×#121—21no—
260C3×#121—21no—
261C3×#121C2×D511yescharacteristic
262C3×#121C2×D511yescharacteristic, complemented
263C3×C4×Q8C2×D511yescharacteristic, complemented
264C3×C4×D4—21no—
265C3×C4×D4C2×D511yescharacteristic
266#950—104no—
267#949—104no—
268C2×#216—51no—
269C2×#215—51no—
270C2×#215—51no—
271#937—101no—
272C2×#214—51no—
273C2×#214—51no—
274C2×#213—51no—
275C2×#213—51no—
276C2×#213—51no—
277C2×#213—51no—
278#930—51no—
279#924—51no—
280C2×#208—51no—
281C22×C3⋊C8—51no—
282#894—101no—
283#884—101no—
284D3×C22⋊C4—101no—
285#875—51no—
286C4×D12—51no—
287#835—51no—
288#832—51no—
289#832—51no—
290#830—51no—
291#830—51no—
292#810—51no—
293#809—51no—
294#809—51no—
295#807—51no—
296C4⋊(C3⋊C8)—51no—
297#803—51no—
298C23×D5—61no—
299C5×#41—22no—
300C5×#41—22no—
301C5×#41—41no—
302C5×#41—41no—
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4—21no—
305C2×C5×D4—21no—
306C2×C5×D4—21no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4#6711yescharacteristic
311C2×C5×D4C22×D311yescharacteristic
312C2×C5×D4C22×D311yescharacteristic
313C22×C4×C5—21no—
314C22×C4×C5—21no—
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C2×C22⋊D5—61no—
318C2×C22⋊D5—61no—
319#709—62no—
320#709—121no—
321C2×D20—31no—
322C2×D20—31no—
323C2×D20—62no—
324C2×D20—61no—
325C2×D20—121no—
326C2×C4×D5—61no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C5×C4⋊C4—21no—
330C5×C4⋊C4#6711yescharacteristic
331C5×C4⋊C4C22×D311yescharacteristic
332C5×C22⋊C4—21no—
333C5×C22⋊C4—21no—
334C5×C22⋊C4#6711yescharacteristic
335C5×C22⋊C4#6711yescharacteristic
336C42×C5—21no—
337C42×C5C22×D311yescharacteristic
338C22⋊Dic5—61no—
339#689—62no—
340#688—34no—
341#688—62no—
342#687—62no—
343#687—121no—
344#686—62no—
345#686—62no—
346#686—62no—
347#686—121no—
348#685—61no—
349#685—61no—
350#685—61no—
351#685—61no—
352C4⋊Dic5—31no—
353#683—61no—
354#681—62no—
355C2×#168—31no—
356C2×#168—31no—
357C2×#168—31no—
358C2×#168—31no—
359C2×#168—62no—
360C2×AGL(1,ℤ/8)—151no—
361C2×#135—151no—
362#550D1511yescharacteristic, complemented
363#546—151no—
364#496—151no—
365#468—151no—
366#466—151no—
367#464—151no—
368#459—151no—
369#452—151no—
370#449—151no—
371#449—151no—
372#447—151no—
373#440—151no—
374#435—151no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5C22×D411yescharacteristic
388C2×D15—22no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—84no—
395C3×C4×C5—21no—
396C3×C4×C5—21no—
397C3×C4×C5—22no—
398C3×C4×C5—21no—
399C3×C4×C5—21no—
400C3×C4×C5—41no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403Dic15—41no—
404Dic15—41no—
405C23×D3—101no—
406C3×#41—22no—
407C3×#41—22no—
408C3×#41—41no—
409C3×#41—41no—
410C2×C3×Q8C22×D511yescharacteristic
411C2×C3×D4—21no—
412C2×C3×D4—21no—
413C2×C3×D4—21no—
414C2×C3×D4—21no—
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4C22⋊D511yescharacteristic
418C2×C3×D4C22×D511yescharacteristic
419C2×C3×D4C22×D511yescharacteristic
420C22×C3×C4—21no—
421C22×C3×C4—21no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—101no—
425C2×#67—101no—
426#235—102no—
427#235—201no—
428C2×D12—51no—
429C2×D12—51no—
430C2×D12—102no—
431C2×D12—101no—
432C2×D12—201no—
433C2×C4×D3—101no—
434C2×C4×D3—101no—
435C2×Dic6—51no—
436C3×C4⋊C4—21no—
437C3×C4⋊C4C22⋊D511yescharacteristic
438C3×C4⋊C4C22×D511yescharacteristic
439C3×C22⋊C4—21no—
440C3×C22⋊C4—21no—
441C3×C22⋊C4C22⋊D511yescharacteristic
442C3×C22⋊C4C22⋊D511yescharacteristic
443C3×C42—21no—
444C3×C42C22×D511yescharacteristic
445#217—101no—
446#216—102no—
447#215—54no—
448#215—102no—
449#214—102no—
450#214—201no—
451#213—102no—
452#213—102no—
453#213—102no—
454#213—201no—
455(C2×D3)⋊C4—101no—
456(C2×D3)⋊C4—101no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459C4⋊Dic3—51no—
460Dic3⋊C4—101no—
461#208—102no—
462C2×C3⋊C8—51no—
463C2×C3⋊C8—51no—
464C2×C3⋊C8—51no—
465C2×C3⋊C8—51no—
466C2×C3⋊C8—102no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5C2×#6711yescharacteristic
470C23×C5C2×#6711yescharacteristic
471C22×D5—61no—
472C22×D5—61no—
473C22×D5—122no—
474C22×D5—122no—
475C22×D5—241no—
476C5×Q8—21no—
477C5×Q8D3×D412yes—
478C5×D4—21no—
479C5×D4—21no—
480C5×D4—21no—
481C5×D4—21no—
482C5×D4—41no—
483C5×D4—42no—
484C5×D4—42no—
485C5×D4—42no—
486C5×D4—81no—
487C5×D4—81no—
488C5×D4—81no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—42no—
496C2×C4×C5—42no—
497C2×C4×C5C2×#6711yescharacteristic
498C2×C4×C5C2×#6711yescharacteristic
499C2×C4×C5C2×#6711yescharacteristic
500C2×C4×C5C2×#6711yescharacteristic
501C2×C4×C5C23×D311yescharacteristic
502C22⋊D5—122no—
503C22⋊D5—241no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506D20—32no—
507D20—61no—
508D20—61no—
509D20—61no—
510D20—122no—
511C4×D5—122no—
512C4×D5—241no—
513Dic10—61no—
514Dic10—61no—
515#168—32no—
516#168—61no—
517#168—61no—
518#168—61no—
519C2×#41—151no—
520C2×#41C2×D1511yescharacteristic
521C2×#41C2×D1511yescharacteristic, complemented
522C22×D4—151no—
523AGL(1,ℤ/8)—304no—
524#135—304no—
525C2×Q16—151no—
526C2×SD16—151no—
527C2×SD16—151no—
528C2×SD16—151no—
529C2×SD16—151no—
530C2×D8—151no—
531C2×D8—151no—
532C2×D8—151no—
533C2×D8—151no—
534C2×M16—151no—
535C22×C8—151no—
536#127—21no—
537#127C2×D1511yescharacteristic, complemented
538#124—151no—
539#123—301no—
540C22⋊Q8—151no—
541#121—21no—
542#121—21no—
543#121—151no—
544#121—301no—
545#121C2×D1511yescharacteristic
546#121C2×D1511yescharacteristic, complemented
547#120—301no—
548C4×Q8C2×D1511yescharacteristic, complemented
549C4×D4—21no—
550C4×D4—151no—
551C4×D4C2×D1511yescharacteristic
552C2×C22⋊C4—301no—
553#107—151no—
554C4⋊C8—151no—
555#103—151no—
556#103—151no—
557#102—151no—
558#102—151no—
559#102—151no—
560#102—151no—
561C22⋊C8—151no—
562C22⋊C8—151no—
563#97—151no—
564C2×C3×C5—41no—
565C2×C3×C5—41no—
566C2×C3×C5—81no—
567C2×C3×C5—81no—
568C2×C3×C5D4211yescharacteristic
569C2×C3×C5#57511yescharacteristic
570C2×C3×C5#57611yescharacteristic
571D15—42no—
572D15—81no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3C2×C22⋊D511yescharacteristic
576C23×C3C2×C22⋊D511yescharacteristic
577C22×D3—101no—
578C22×D3—101no—
579C22×D3—202no—
580C22×D3—202no—
581C22×D3—401no—
582C3×Q8—21no—
583C3×Q8D4×D512yes—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—41no—
589C3×D4—42no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—81no—
593C3×D4—81no—
594C3×D4—81no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—42no—
602C2×C3×C4—42no—
603C2×C3×C4C2×C22⋊D511yescharacteristic
604C2×C3×C4C2×C22⋊D511yescharacteristic
605C2×C3×C4C2×C22⋊D511yescharacteristic
606C2×C3×C4C2×C22⋊D511yescharacteristic
607C2×C3×C4C23×D511yescharacteristic
608#67—202no—
609#67—401no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612D12—52no—
613D12—101no—
614D12—101no—
615D12—101no—
616D12—202no—
617C4×D3—202no—
618C4×D3—401no—
619Dic6—101no—
620Dic6—101no—
621C3⋊C8—52no—
622C3⋊C8—101no—
623C3⋊C8—101no—
624C3⋊C8—101no—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—21no—
628C22×C5—21no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5C22×#6711yescharacteristic
638C2×D5—62no—
639C2×D5—121no—
640C2×D5—121no—
641C2×D5—121no—
642C2×D5—121no—
643C2×D5—121no—
644C2×D5—244no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—22no—
648C4×C5—21no—
649C4×C5—21no—
650C4×C5—41no—
651C4×C5C2×D3×D411yescharacteristic
652C4×C5#100411yescharacteristic
653Dic5—121no—
654Dic5—121no—
655C24—301no—
656#41—22no—
657#41—22no—
658#41—41no—
659#41—41no—
660#41—302no—
661#41—601no—
662C2×Q8—151no—
663C2×Q8C22×D1511yescharacteristic
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—151no—
671C2×D4—151no—
672C2×D4—302no—
673C2×D4—301no—
674C2×D4—301no—
675C2×D4—301no—
676C2×D4—601no—
677C2×D4#122011yescharacteristic
678C2×D4C22×D1511yescharacteristic
679C2×D4C22×D1511yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—301no—
683C22×C4—301no—
684C22×C4C22×D1511yescharacteristic
685C22×C4C22×D1511yescharacteristic
686Q16—302no—
687SD16—154no—
688SD16—302no—
689SD16—302no—
690SD16—601no—
691D8—302no—
692D8—302no—
693D8—302no—
694D8—601no—
695M16—302no—
696C2×C8—151no—
697C2×C8—151no—
698C2×C8—151no—
699C2×C8—151no—
700C2×C8—302no—
701C4⋊C4—21no—
702C4⋊C4—151no—
703C4⋊C4—301no—
704C4⋊C4#122011yescharacteristic
705C4⋊C4C22×D1511yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—301no—
709C22⋊C4—301no—
710C22⋊C4—301no—
711C22⋊C4—301no—
712C22⋊C4—301no—
713C22⋊C4#122011yescharacteristic
714C22⋊C4#122011yescharacteristic
715C42—21no—
716C42C22×D1511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3C22×C22⋊D511yescharacteristic
731C2×D3—102no—
732C2×D3—201no—
733C2×D3—201no—
734C2×D3—201no—
735C2×D3—201no—
736C2×D3—201no—
737C2×D3—404no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4C2×D4×D511yescharacteristic
745C3×C4#414411yescharacteristic
746Dic3—201no—
747Dic3—201no—
748C2×C5—41no—
749C2×C5—41no—
750C2×C5—81no—
751C2×C5—81no—
752C2×C5D4×#6711yescharacteristic
753C2×C5#582211yescharacteristic
754C2×C5#583511yescharacteristic
755D5—122no—
756D5—241no—
757C23—21no—
758C23—21no—
759C23—301no—
760C23—301no—
761C23—602no—
762C23—602no—
763C23—1201no—
764C23C2×#122011yescharacteristic
765C23C2×#122011yescharacteristic
766Q8—21no—
767Q8—301no—
768Q8—301no—
769Q8D4×D1512yes—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—41no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—152no—
782D4—301no—
783D4—301no—
784D4—301no—
785D4—602no—
786D4—602no—
787D4—1201no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—301no—
797C2×C4—301no—
798C2×C4—602no—
799C2×C4—1201no—
800C2×C4C2×#122011yescharacteristic
801C2×C4C2×#122011yescharacteristic
802C2×C4C2×#122011yescharacteristic
803C2×C4C2×#122011yescharacteristic
804C2×C4C23×D1511yescharacteristic
805C8—152no—
806C8—301no—
807C8—301no—
808C8—301no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—81no—
812C2×C3—81no—
813C2×C3D4×C22⋊D511yescharacteristic
814C2×C3#6615611yescharacteristic
815C2×C3#6616911yescharacteristic
816D3—202no—
817D3—401no—
818C5#8357711yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—302no—
832C22—601no—
833C22—601no—
834C22—601no—
835C22—601no—
836C22—601no—
837C22—1204no—
838C22C22×#122011yescharacteristic
839C4—21no—
840C4—21no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—41no—
845C4—601no—
846C4—601no—
847C4C2×D4×D1511yescharacteristic
848C4#9209511yescharacteristic
849C3#1061530811yescharacteristic, complemented, Sylow
850C2—41no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—602no—
855C2—1201no—
856C2D4×#122011yescharacteristic
857C2#1175658111yescharacteristic
858C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#550C2
socleC22×C3×C5C22×D4
hypercenter#550D15
hypocenterC3×C5#3268
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C3×C5×#550C2semidirect
2. C2×#91839C2semidirect
3. C2×#91838C2semidirect
4. #11756309C2semidirect
5. #11751340C2semidirect
6. #11751339C2semidirect
7. #11751175C2semidirect
8. #11751173C2semidirect
9. #11751143C2semidirect
10. #11751139C2semidirect
11. #11751138C2semidirect
12. #11751137C2semidirect
13. #11751129C2semidirect
14. #11751127C2semidirect
15. #11751112C2semidirect
18. C2×C3×C5×#41C22semidirect
22. C3×C5×#127C22semidirect
26. C3×C5×#121C22semidirect
27. C3×C4×C5×Q8C22semidirect
32. C2×#6718C22semidirect
36. C2×#6716C22semidirect
37. C2×#6716C22semidirect
45. C22×C3⋊#168C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91116C22semidirect
55. #91114C22semidirect
56. #91094C22semidirect
59. #91091C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×#550D3semidirect
121. #6717D4semidirect
140. C3×#550D5semidirect
156. C2×C5×#41C2×D3semidirect
160. C5×#127C2×D3semidirect
164. C5×#121C2×D3semidirect
165. C4×C5×Q8C2×D3semidirect
254. C2×C3×#41C2×D5semidirect
258. C3×#127C2×D5semidirect
262. C3×#121C2×D5semidirect
263. C3×C4×Q8C2×D5semidirect
362. #550D15semidirect
521. C2×#41C2×D15semidirect
537. #127C2×D15semidirect
546. #121C2×D15semidirect
548. C4×Q8C2×D15semidirect
717. C3×C5#3268semidirect
818. C5#83577semidirect
849. C3#10615308semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
C2×#918392
C2×#918382
#117563092
#117513402
#117513392
#117511752
#117511732
#117511432
#117511392
#117511382
#117511372
#117511292
#117511272
#117511122
#106153083
#835775