Finite Group Databasebeta

← #14412731

Subgroups — #14412731

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92030C211yesmaximal, characteristic
2C2×#91266C211yesmaximal, characteristic, complemented
3#11753667C211yesmaximal, characteristic, complemented
4#11750903C211yesmaximal, characteristic, complemented
5C5×#4803C211yesmaximal, characteristic, complemented
6C3×D5×#103C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749208C211yesmaximal, characteristic, complemented
9#11749203C211yesmaximal, characteristic, complemented
10#11748146C211yesmaximal, characteristic, complemented
11#11748135C211yesmaximal, characteristic, complemented
12#11748123C211yesmaximal, characteristic, complemented
13#11747508C211yesmaximal, characteristic, complemented
14#11747498C211yesmaximal, characteristic, complemented
15D3×#3942C211yesmaximal, characteristic, complemented
16#10610614—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20#92030—24no—
21#92030C418yescomplemented
22C2×#6772—21no—
23C2×#6772C2211yescharacteristic
24C2×#6771—21no—
25C2×#6771C2211yescharacteristic
26C2×#6768—21no—
27C2×#6768C2211yescharacteristic
28C2×D3×Dic10—21no—
29C2×D3×Dic10C2211yescharacteristic
30C2×#6705C2211yescharacteristic
31#91781C2211yescharacteristic
32C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
33C5×D3×C4⋊C4C2211yescharacteristic
34C2×C3×C8×D5C2211yescharacteristic
35C3×D5×C4⋊C4C2211yescharacteristic
36#91446—21no—
37#91444—21no—
38C4×#1201—21no—
39#91437C2211yescharacteristic
40#91358C2211yescharacteristic
41#91338C2211yescharacteristic
42#91325—21no—
43C2×#6649C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C2×D3×#168C2211yescharacteristic
46#91266—24no—
47C3×C5×#103C2211yescharacteristic
48#91119C2211yescharacteristic
49#91100C2211yescharacteristic
50#91094C2211yescharacteristic
51C5×#835C2211yescharacteristic
52C5×#821C2211yescharacteristic
53C5×#809C2211yescharacteristic
54C3×#3967C2211yescharacteristic
55C3×#3948C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57#90975C2211yescharacteristic
58#90974C2211yescharacteristic
59#90971C2211yescharacteristic
60#90970C2211yescharacteristic
61#90967C2211yescharacteristic
62#90966C2211yescharacteristic
63#78790—51nomaximal, Hall
64C2×#4150—31no—
65C2×#4053—31no—
66#65838—31no—
67C5×#417—31no—
68#65522—31no—
69#65409—31no—
70C2×#3942—31no—
71#65091—31no—
72#65091—31no—
73D5×#103—31no—
74D5×#103D311yescharacteristic, complemented
75#65061—31no—
76#65061—31no—
77#65060—31no—
78#65060—31no—
79C2×C3×C5×Q8C2311yescharacteristic
80Q8×D15—22no—
81Q8×D15C2×C414yescomplemented
82C2×C4×D15—21no—
83C2×C4×D15C2311yescharacteristic
84C2×Dic30—21no—
85C2×Dic30C2311yescharacteristic
86C5×#239—22no—
87C5×#239C2×C414yescomplemented
88C2×C5×D12—21no—
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C3×Q8×D5—22no—
94C3×Q8×D5C2×C414yescomplemented
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×Dic10—21no—
99C2×C3×Dic10C2311yescharacteristic
100C2×#1204—21no—
101C2×#1204D411yescharacteristic
102C2×#1203—21no—
103C2×#1203D411yescharacteristic
104C2×#1202D411yescharacteristic
105C2×#1201—21no—
106C2×#1201D411yescharacteristic
107C2×#1200—21no—
108C2×D3×Dic5—21no—
109C2×D3×Dic5—21no—
110C2×D3×Dic5—21no—
111#6772—22no—
112#6772—28no—
113#6772C2×C414yescomplemented
114#6771—28no—
115#6771C2×C414yes—
116#6771D414yes—
117#6768—22no—
118#6768—28no—
119#6768C2×C414yescomplemented
120D3×Dic10—22no—
121D3×Dic10—28no—
122D3×Dic10C2×C414yescomplemented
123C2×C3×C5×C8C2311yescharacteristic
124C3×C5×C4⋊C4C2311yescharacteristic
125#6714—21no—
126C4⋊Dic15C2311yescharacteristic
127C4×Dic15—21no—
128C2×C3⋊#168C2311yescharacteristic
129#6705—22no—
130C5×C4⋊Dic3C2311yescharacteristic
131C5×Dic3⋊C4—21no—
132C2×C5×C3⋊C8C2311yescharacteristic
133C5×ΓL(1,𝔽25)—22no—
134C3×C4⋊Dic5C2311yescharacteristic
135C3×#683—21no—
136C2×C3×#168C2311yescharacteristic
137C3×C8×D5—22no—
138#6669—21no—
139(C2×D3)⋊Dic5—21no—
140#6665—21no—
141Dic3×Dic5—21no—
142Dic3×Dic5—21no—
143#6649—22no—
144#6648—22no—
145D3×#168—22no—
146C2×#1007—51no—
147C2×#901—51no—
148#5504—51no—
149C2×C3×#103—51no—
150#5225—51no—
151#5113—51no—
152#4966—51no—
153#4804—51no—
154#4804—51no—
155#4803—51no—
156#4803D511yescharacteristic, complemented
157#4802—51no—
158#4802—51no—
159D3×#103—51no—
160D3×#103—51no—
161C2×C5×#41—31no—
162#4150—38no—
163#4150—64no—
164C2×Q8×D5—31no—
165C2×Q8×D5C2×D311yescharacteristic
166C2×#711—31no—
167C2×#711—31no—
168C2×#711—61no—
169C2×#711—61no—
170C2×#709—31no—
171C2×#709—61no—
172C22×Dic10—31no—
173C22×Dic10—61no—
174C2×C5×M16—31no—
175C2×C5×C4⋊C4—31no—
176C4×C22⋊D5—61no—
177C4×C22⋊D5—61no—
178#4072—31no—
179C22×#168—31no—
180#4053—64no—
181C2×#676—31no—
182C2×#676—31no—
183C2×C8×D5—31no—
184C2×C8×D5C2×D311yescharacteristic
185#4039—61no—
186#4038—31no—
187#4038—31no—
188D5×C4⋊C4—31no—
189D5×C4⋊C4C2×D311yescharacteristic
190#4033—61no—
191C5×#103—31no—
192C5×#103C2×D311yescharacteristic
193C5×#102—31no—
194C5×#102—31no—
195#3967—31no—
196#3967C2×D311yescharacteristic
197#3964—31no—
198#3964—31no—
199#3948—31no—
200#3948—31no—
201#3948—31no—
202#3948C2×D311yescharacteristic
203#3942—31no—
204#3942—31no—
205#3942—31no—
206#3942C2×D311yescharacteristic
207#2898—151noSylow
208C22×D15C2×D411yescharacteristic
209C22×C5×D3—21no—
210C22×C5×D3C2×D411yescharacteristic
211C22×C3×D5C2×D411yescharacteristic
212C3×C5×Q8—21no—
213C3×C5×Q8C22×C412yes—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C2411yescharacteristic
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C2×D411yescharacteristic
220C4×D15—24no—
221C4×D15C22×C412yes—
222C4×D15C2×D412yes—
223Dic30—21no—
224Dic30—24no—
225Dic30C22×C412yes—
226C2×C5×Dic3—21no—
227C2×C5×Dic3C2×D411yescharacteristic
228C5×D12—24no—
229C5×D12—21no—
230C5×D12C22×C412yes—
231C4×C5×D3—24no—
232C4×C5×D3—81no—
233C4×C5×D3C22×C412yes—
234C4×C5×D3C2×D412yes—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5C2×D411yescharacteristic
238C3×C4×D5—24no—
239C3×C4×D5—81no—
240C3×C4×D5C22×C412yes—
241C3×C4×D5C2×D412yes—
242C3×Dic10—21no—
243C3×Dic10—24no—
244C3×Dic10C22×C412yes—
245#1204—24no—
246#1204C22⋊C414yes—
247#1203—24no—
248#1203C22⋊C414yes—
249#1202C22⋊C414yes—
250#1201—24no—
251#1201C22⋊C414yes—
252#1200—81no—
253D3×Dic5—24no—
254D3×Dic5—24no—
255D3×Dic5—24no—
256C3×C5×C8—21no—
257C3⋊#168—21no—
258C3×#168—21no—
259C5×C3⋊C8—21no—
260C22×C3×Q8—51no—
261#1007—58no—
262#1007—104no—
263C2×#239—51no—
264C2×#239—101no—
265C2×#239C2×D511yescharacteristic
266C2×D3×Q8—51no—
267C2×D3×Q8—51no—
268C2×D3×Q8—101no—
269C2×#235—51no—
270C2×#235—51no—
271C2×#235—101no—
272C2×#235—101no—
273C22×C3×C8—51no—
274C2×C3×C4⋊C4—51no—
275C4×#67—101no—
276C4×#67—101no—
277#926—51no—
278C2×#208—51no—
279#901—104no—
280C2×ΓL(1,𝔽25)—51no—
281C2×ΓL(1,𝔽25)C2×D511yescharacteristic
282C2×D3×C8—51no—
283C2×D3×C8—51no—
284#893—101no—
285#892—51no—
286#892—51no—
287D3×C4⋊C4—51no—
288D3×C4⋊C4C2×D511yescharacteristic
289#887—101no—
290C3×#103—51no—
291C3×#103—51no—
292C3×#103—51no—
293C3×#103C2×D511yescharacteristic
294#835—51no—
295#835—51no—
296#835—51no—
297#835C2×D511yescharacteristic
298#821—51no—
299#821C2×D511yescharacteristic
300#816—51no—
301#816—51no—
302#810—51no—
303#810—51no—
304#809—51no—
305#809C2×D511yescharacteristic
306C5×#41—34no—
307C5×#41—62no—
308C2×C5×Q8C22×D311yescharacteristic
309C2×C5×D4—31no—
310C2×C5×D4—61no—
311C22×C4×C5—31no—
312C22×C4×C5—61no—
313C22×C4×C5—61no—
314C2×C22⋊D5—31no—
315C2×C22⋊D5—31no—
316C2×C22⋊D5—61no—
317C2×C22⋊D5—61no—
318C22×Dic5—61no—
319C22×Dic5—61no—
320C22×Dic5—61no—
321Q8×D5—22no—
322Q8×D5—34no—
323Q8×D5—62no—
324Q8×D5C4×D314yescomplemented
325#711—34no—
326#711—34no—
327#711—62no—
328#711—68no—
329#711—68no—
330#711—62no—
331#709—34no—
332#709—34no—
333#709—68no—
334C2×D20—31no—
335C2×C4×D5—21no—
336C2×C4×D5—21no—
337C2×C4×D5—31no—
338C2×C4×D5—61no—
339C2×C4×D5—61no—
340C2×C4×D5C22×D311yescharacteristic
341C2×Dic10—21no—
342C2×Dic10—31no—
343C2×Dic10—31no—
344C2×Dic10—34no—
345C2×Dic10—68no—
346C2×Dic10—62no—
347C2×Dic10—61no—
348C2×Dic10—61no—
349C2×Dic10C22×D311yescharacteristic
350C5×M16—62no—
351C2×C5×C8—31no—
352C2×C5×C8C22×D311yescharacteristic
353C5×C4⋊C4—31no—
354C5×C4⋊C4—61no—
355C5×C4⋊C4C22×D311yescharacteristic
356C22⋊Dic5—61no—
357#685—61no—
358#685—61no—
359C4⋊Dic5—31no—
360C4⋊Dic5C22×D311yescharacteristic
361#683—21no—
362#683—61no—
363C4×Dic5—61no—
364C4×Dic5—61no—
365C4×Dic5—61no—
366C2×#168—31no—
367C2×#168—62no—
368C2×#168C22×D311yescharacteristic
369#676—62no—
370#676—62no—
371C8×D5—22no—
372C8×D5—62no—
373C2×2−1+4—151no—
374C2×#131—151no—
375#520—151no—
376#419—151no—
377#419—151no—
378#419—151no—
379#417—31no—
380#417—151no—
381#417—151no—
382#416—151no—
383#416—151no—
384#416—151no—
385C2×#103—51no—
386C2×#103—151no—
387C2×#103—151no—
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—21no—
390C2×D15—21no—
391C2×D15C2×C22⋊C412yes—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—22no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3C2×C22⋊C412yes—
398C2×C3×D5—21no—
399C2×C3×D5—21no—
400C2×C3×D5C2×C22⋊C412yes—
401C3×C4×C5—22no—
402C3×C4×C5—41no—
403C3×C4×C5C23×C411yescharacteristic
404C3×C4×C5C22×D411yescharacteristic
405Dic15—22no—
406Dic15—41no—
407Dic15C2×C22⋊C412yes—
408C3×Dic5—22no—
409C3×Dic5—41no—
410C3×Dic5C2×C22⋊C412yes—
411C5×Dic3—41no—
412C5×Dic3C2×C22⋊C412yes—
413C2×C3×Q8—54no—
414C2×C3×Q8—51no—
415C2×C3×Q8—101no—
416C2×C3×Q8—102no—
417C2×C3×Q8C22×D511yescharacteristic
418C22×C3×C4—51no—
419C22×C3×C4—101no—
420C22×C3×C4—101no—
421C2×#67—51no—
422C2×#67—51no—
423C2×#67—101no—
424#239—22no—
425#239—54no—
426#239—102no—
427#239—108no—
428#239C4×D514yescomplemented
429D3×Q8—54no—
430D3×Q8—54no—
431D3×Q8—108no—
432D3×Q8—102no—
433D3×Q8—102no—
434#235—54no—
435#235—54no—
436#235—54no—
437#235—108no—
438#235—108no—
439#235—102no—
440C2×D12—21no—
441C2×D12—51no—
442C2×D12—101no—
443C2×D12C22×D511yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—21no—
446C2×C4×D3—51no—
447C2×C4×D3—101no—
448C2×C4×D3—101no—
449C2×C4×D3—101no—
450C2×C4×D3—101no—
451C2×C4×D3—101no—
452C2×C4×D3C22×D511yescharacteristic
453C2×Dic6—51no—
454C2×Dic6—51no—
455C2×Dic6—101no—
456C2×Dic6—101no—
457C2×C3×C8—51no—
458C2×C3×C8—102no—
459C2×C3×C8C22×D511yescharacteristic
460C3×C4⋊C4—51no—
461C3×C4⋊C4—101no—
462C3×C4⋊C4C22×D511yescharacteristic
463#217—101no—
464(C2×D3)⋊C4—101no—
465(C2×D3)⋊C4—101no—
466C4⋊Dic3—51no—
467C4⋊Dic3C22×D511yescharacteristic
468Dic3⋊C4—21no—
469Dic3⋊C4—101no—
470C4×Dic3—101no—
471C4×Dic3—101no—
472C4×Dic3—101no—
473#208—102no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8C22×D511yescharacteristic
476ΓL(1,𝔽25)—22no—
477ΓL(1,𝔽25)—102no—
478D3×C8—102no—
479D3×C8—102no—
480C23×C5—31no—
481C23×C5—61no—
482C22×D5—31no—
483C22×D5D3×D411yescharacteristic
484C5×Q8—21no—
485C5×Q8C2×C4×D312yes—
486C5×D4—32no—
487C5×D4—64no—
488C5×D4—61no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—31no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
494C2×C4×C5—64no—
495C2×C4×C5—61no—
496C2×C4×C5—241no—
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—34no—
499C22⋊D5—34no—
500C22⋊D5—64no—
501C22⋊D5—64no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—31no—
505C2×Dic5—64no—
506C2×Dic5—64no—
507C2×Dic5—61no—
508C2×Dic5—64no—
509C2×Dic5—61no—
510C2×Dic5D3×D411yescharacteristic
511D20—34no—
512C4×D5—24no—
513C4×D5—32no—
514C4×D5—32no—
515C4×D5—64no—
516C4×D5—81no—
517C4×D5—241no—
518C4×D5C2×C4×D312yes—
519C4×D5D3×D412yes—
520Dic10—21no—
521Dic10—24no—
522Dic10—34no—
523Dic10—32no—
524Dic10—64no—
525Dic10—64no—
526Dic10—61no—
527Dic10C2×C4×D312yes—
528C5×C8—21no—
529C5×C8—61no—
530#168—21no—
531#168—61no—
5322−1+4—158no—
5332−1+4—304no—
534C2×#41—31no—
535C2×#41—151no—
536C2×#41—151no—
537C2×#41—151no—
538C2×#41—301no—
539C2×#41—301no—
540C2×#41—301no—
541C22×Q8—51no—
542C22×Q8—151no—
543C22×Q8—151no—
544C22×Q8—301no—
545#131—304no—
546C2×M16—31no—
547C2×M16—151no—
548C2×M16—151no—
549C22×C8—51no—
550C22×C8—151no—
551C22×C8—151no—
552C4×Q8—301no—
553C4×D4—301no—
554C4×D4—301no—
555C4×D4—301no—
556#117—151no—
557#117—151no—
558#117—151no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—51no—
561C2×C4⋊C4—151no—
562#103—31no—
563#103—51no—
564#103—51no—
565#103—51no—
566#103—151no—
567#103—151no—
568#103—151no—
569#103—151no—
570#103—151no—
571#103—151no—
572#103—151no—
573#103D3×D511yescharacteristic
574#102—31no—
575#102—31no—
576#102—151no—
577#102—151no—
578C2×C3×C5C22×C22⋊C411yescharacteristic
579C2×C3×C5#57711yescharacteristic
580C2×C3×C5#57811yescharacteristic
581D15—22no—
582C3×D5—22no—
583C5×D3—22no—
584C5×D3—42no—
585C23×C3—51no—
586C22×D3—21no—
587C22×D3—51no—
588C22×D3D4×D511yescharacteristic
589C3×Q8—21no—
590C3×Q8—52no—
591C3×Q8—104no—
592C3×Q8—101no—
593C3×Q8C2×C4×D512yes—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—51no—
597C2×C3×C4—52no—
598C2×C3×C4—52no—
599C2×C3×C4—104no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—401no—
603C2×C3×C4C23×D511yescharacteristic
604#67—54no—
605#67—54no—
606#67—104no—
607C2×Dic3—21no—
608C2×Dic3—51no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3D4×D511yescharacteristic
612D12—24no—
613D12—21no—
614D12—54no—
615D12—104no—
616D12C2×C4×D512yes—
617C4×D3—24no—
618C4×D3—52no—
619C4×D3—52no—
620C4×D3—81no—
621C4×D3—104no—
622C4×D3—104no—
623C4×D3—104no—
624C4×D3—104no—
625C4×D3—401no—
626C4×D3C2×C4×D512yes—
627C4×D3D4×D512yes—
628Dic6—54no—
629Dic6—52no—
630Dic6—104no—
631Dic6—101no—
632Dic6—104no—
633C3×C8—21no—
634C3×C8—101no—
635C3⋊C8—21no—
636C3⋊C8—101no—
637C22×C5—32no—
638C22×C5—61no—
639C22×C5—61no—
640C22×C5—62no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5C2×D3×D411yescharacteristic
644C2×D5—21no—
645C2×D5—21no—
646C2×D5—32no—
647C2×D5—61no—
648C2×D5—61no—
649C2×D5D3×C22⋊C412yes—
650C4×C5—22no—
651C4×C5—32no—
652C4×C5—41no—
653C4×C5—121no—
654C4×C5C22×C4×D311yescharacteristic
655C4×C5C2×D3×D411yescharacteristic
656Dic5—22no—
657Dic5—32no—
658Dic5—41no—
659Dic5—62no—
660Dic5—121no—
661Dic5D3×C22⋊C412yes—
662#41—34no—
663#41—62no—
664#41—154no—
665#41—154no—
666#41—154no—
667#41—154no—
668#41—302no—
669#41—308no—
670#41—308no—
671#41—302no—
672#41—308no—
673C2×Q8—54no—
674C2×Q8—51no—
675C2×Q8—101no—
676C2×Q8—102no—
677C2×Q8—151no—
678C2×Q8—154no—
679C2×Q8—154no—
680C2×Q8—151no—
681C2×Q8—301no—
682C2×Q8—301no—
683C2×Q8—302no—
684C2×Q8—308no—
685C2×Q8—302no—
686C2×Q8C2×D3×D511yescharacteristic
687C2×D4—31no—
688C2×D4—61no—
689C2×D4—151no—
690C2×D4—151no—
691C2×D4—151no—
692C2×D4—301no—
693C2×D4—301no—
694C22×C4—31no—
695C22×C4—51no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—101no—
699C22×C4—101no—
700C22×C4—151no—
701C22×C4—301no—
702C22×C4—301no—
703C22×C4—301no—
704C22×C4—301no—
705C22×C4—301no—
706M16—62no—
707M16—302no—
708M16—302no—
709C2×C8—31no—
710C2×C8—51no—
711C2×C8—102no—
712C2×C8—151no—
713C2×C8—302no—
714C2×C8—302no—
715C2×C8C2×D3×D511yescharacteristic
716C4⋊C4—31no—
717C4⋊C4—51no—
718C4⋊C4—61no—
719C4⋊C4—101no—
720C4⋊C4—151no—
721C4⋊C4—301no—
722C4⋊C4C2×D3×D511yescharacteristic
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C42—301no—
727C42—301no—
728C42—301no—
729C3×C5#289811yescharacteristic, complemented, Hall
730C22×C3—52no—
731C22×C3—101no—
732C22×C3—101no—
733C22×C3C2×D4×D511yescharacteristic
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—52no—
740C2×D3—101no—
741C2×D3—101no—
742C2×D3D5×C22⋊C412yes—
743C3×C4—22no—
744C3×C4—41no—
745C3×C4—52no—
746C3×C4—102no—
747C3×C4—201no—
748C3×C4C22×C4×D511yescharacteristic
749C3×C4C2×D4×D511yescharacteristic
750Dic3—41no—
751Dic3—52no—
752Dic3—102no—
753Dic3—201no—
754Dic3D5×C22⋊C412yes—
755C2×C5—62no—
756C2×C5—122no—
757C2×C5C2×D3×C22⋊C411yescharacteristic
758C2×C5#576211yescharacteristic
759C2×C5#576611yescharacteristic
760D5—22no—
761D5—62no—
762C23—31no—
763C23—51no—
764C23—61no—
765C23—151no—
766Q8—21no—
767Q8—52no—
768Q8—104no—
769Q8—101no—
770Q8—154no—
771Q8—152no—
772Q8—304no—
773Q8—304no—
774Q8—301no—
775Q8C4×D3×D512yes—
776D4—32no—
777D4—64no—
778D4—61no—
779D4—154no—
780D4—154no—
781D4—154no—
782D4—304no—
783D4—304no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—31no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—51no—
790C2×C4—52no—
791C2×C4—52no—
792C2×C4—64no—
793C2×C4—61no—
794C2×C4—104no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—151no—
798C2×C4—152no—
799C2×C4—152no—
800C2×C4—241no—
801C2×C4—304no—
802C2×C4—304no—
803C2×C4—304no—
804C2×C4—304no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—401no—
808C2×C4—1201no—
809C2×C4C22×D3×D511yescharacteristic
810C8—21no—
811C8—61no—
812C8—101no—
813C8—301no—
814C2×C3—102no—
815C2×C3C2×D5×C22⋊C411yescharacteristic
816C2×C3#6610911yescharacteristic
817C2×C3#6611311yescharacteristic
818D3—22no—
819D3—42no—
820D3—102no—
821C5#7879011yescharacteristic, complemented, Sylow
822C22—32no—
823C22—52no—
824C22—61no—
825C22—61no—
826C22—62no—
827C22—101no—
828C22—101no—
829C22—121no—
830C22—121no—
831C22—152no—
832C22—301no—
833C22—301no—
834C22D3×D4×D511yescharacteristic
835C4—22no—
836C4—32no—
837C4—41no—
838C4—52no—
839C4—102no—
840C4—121no—
841C4—152no—
842C4—201no—
843C4—302no—
844C4—601no—
845C4C2×C4×D3×D511yescharacteristic
846C4D3×D4×D511yescharacteristic
847C3#1061061411yescharacteristic, complemented, Sylow
848C2—62no—
849C2—102no—
850C2—122no—
851C2—302no—
852C2D3×D5×C22⋊C411yescharacteristic
853C2#1175408111yescharacteristic
854C2#1175410711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#92030C2
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#91266C2semidirect
3. #11753667C2semidirect
4. #11750903C2semidirect
5. C5×#4803C2semidirect
6. C3×D5×#103C2semidirect
7. #11749211C2semidirect
8. #11749208C2semidirect
9. #11749203C2semidirect
10. #11748146C2semidirect
11. #11748135C2semidirect
12. #11748123C2semidirect
13. #11747508C2semidirect
14. #11747498C2semidirect
15. D3×#3942C2semidirect
21. #92030C4semidirect
74. D5×#103D3semidirect
81. Q8×D15C2×C4semidirect
87. C5×#239C2×C4semidirect
94. C3×Q8×D5C2×C4semidirect
113. #6772C2×C4semidirect
119. #6768C2×C4semidirect
122. D3×Dic10C2×C4semidirect
156. #4803D5semidirect
324. Q8×D5C4×D3semidirect
428. #239C4×D5semidirect
729. C3×C5#2898semidirect
821. C5#78790semidirect
847. C3#10610614semidirect

Maximal subgroups

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

subgroupindex
C2×#920302
C2×#912662
#117536672
#117509032
C5×#48032
C3×D5×#1032
#117492112
#117492082
#117492032
#117481462
#117481352
#117481232
#117475082
#117474982
D3×#39422
#106106143
#787905