Finite Group Databasebeta

← #14417040

Subgroups — #14417040

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
2#11755217C211yesmaximal, characteristic, complemented
3#11754910C211yesmaximal, characteristic, complemented
4#11751265C211yesmaximal, characteristic, complemented
5C5×Dic3×SD16C211yesmaximal, characteristic, complemented
6#11749239C211yesmaximal, characteristic, complemented
7#11749234C211yesmaximal, characteristic, complemented
8#11749207C211yesmaximal, characteristic, complemented
9#11748993C211yesmaximal, characteristic, complemented
10#11748988C211yesmaximal, characteristic, complemented
11D5×#832C211yesmaximal, characteristic, complemented
12#11748050C211yesmaximal, characteristic, complemented
13#11747815C211yesmaximal, characteristic, complemented
14Dic3×D40C211yesmaximal, characteristic, complemented
15#11747618C211yesmaximal, characteristic, complemented
16#10611378—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic, complemented
21D4×Dic15C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic, complemented
23C5×D4×Dic3C2211yescharacteristic
24C2×C3×#688C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×#4060C418yescomplemented
27C2×C3×D40C2211yescharacteristic
28C2×C3×#676C2211yescharacteristic
29#91559—21no—
30Dic3×C22⋊D5—21no—
31D5×#217—21no—
32C2×#6665—21no—
33#91434—21no—
34#91434C2211yescharacteristic
35#91434C2211yescharacteristic, complemented
36Dic3×D20—21no—
37Dic3×D20C2211yescharacteristic
38Dic3×D20C2211yescharacteristic, complemented
39D5×C4⋊Dic3—21no—
40D5×C4⋊Dic3C2211yescharacteristic
41#91358C2211yescharacteristic
42#91357—21no—
43#91357C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91102C2211yescharacteristic, complemented
48#91099C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#832C2211yescharacteristic
51C5×#817C2211yescharacteristic, complemented
52C5×C8×Dic3C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55#90965C2211yescharacteristic
56#90965C2211yescharacteristic, complemented
57#90964C2211yescharacteristic
58#90964C2211yescharacteristic, complemented
59#90953C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#83930—51nomaximal, Hall
62C2×#4060D311yescharacteristic
63#65908—31no—
64#65879—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67#65315—31no—
68#65303—31no—
69#65158—31no—
70#65150—31no—
71#65093—31no—
72#65077—31no—
73D5×#102—31no—
74#65045—31no—
75C4×D40—31no—
76#64978—31no—
77C23×C3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×Dic15—21no—
81C22×C5×Dic3—21no—
82C2×C3×C22⋊D5—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×D5C2311yescharacteristic
92C2×D5×Dic3—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3—21no—
95C2×D5×Dic3—21no—
96C2×D5×Dic3—21no—
97C3×C5×SD16C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99#6719—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C4×Dic15—21no—
104C4×Dic15C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#217—21no—
107C5×C4⋊Dic3—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C3×#688C2×C414yescomplemented
114C3×#686C2×C414yescomplemented
115C2×C3×#168C2311yescharacteristic
116C3×D40C2×C414yescomplemented
117C3×#676C2×C414yescomplemented
118#6668—21no—
119#6668D411yescharacteristic
120#6668D411yescharacteristic
121#6665—21no—
122#6665—21no—
123#6665—21no—
124#6665—21no—
125#6665—21no—
126#6665D411yescharacteristic
127#6665D411yescharacteristic
128Dic3×Dic5—21no—
129D5×C3⋊C8—22no—
130C2×C3×AGL(1,ℤ/8)—51no—
131#5827—51no—
132#5798—51no—
133#5233—51no—
134C2×#832—51no—
135#5164—51no—
136#5164—51no—
137Dic3×SD16—51no—
138Dic3×SD16D511yescharacteristic, complemented
139#5152—51no—
140#5152—51no—
141Dic3×D8—51no—
142Dic3×D8—51no—
143#5122—51no—
144#5121—51no—
145C2×#713C2×D311yescharacteristic
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×SD16C2×D311yescharacteristic
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#688C2×D311yescharacteristic
152D4×Dic5—31no—
153C2×#686C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C2×#685—61no—
156#4060Dic318yescomplemented
157C2×D40C2×D311yescharacteristic
158C2×#676C2×D311yescharacteristic
159C2×C8×D5—31no—
160#4039—31no—
161#4039—31no—
162#4039—61no—
163#4038—31no—
164D5×C4⋊C4—31no—
165D5×C4⋊C4—61no—
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—31no—
169C4×D20—31no—
170C4×D20—61no—
171#4018—31no—
172#4018—61no—
173C5×#106—31no—
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3950—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3939—31no—
188#3935—31no—
189#2946—151noSylow
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×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—81no—
206C2×Dic15C2×D411yescharacteristic
207C2×Dic15C2×D411yescharacteristic
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—81no—
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C3×C22⋊D5—24no—
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×D5C22×C412yes—
222C3×C4×D5#4112yes—
223D5×Dic3—81no—
224D5×Dic3—81no—
225D5×Dic3—81no—
226D5×Dic3—81no—
227D5×Dic3—81no—
228C3×C5×C8C22×C412yes—
229C3⋊#168—21no—
230C3×#168C22×C412yes—
231C5×C3⋊C8—21no—
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—
240C2×#217—101no—
241C2×#217—101no—
242Q8×Dic3—51no—
243Q8×Dic3C2×D511yescharacteristic, complemented
244D4×Dic3—51no—
245D4×Dic3—51no—
246D4×Dic3—51no—
247D4×Dic3—51no—
248D4×Dic3—51no—
249D4×Dic3—101no—
250D4×Dic3—101no—
251D4×Dic3—101no—
252D4×Dic3—101no—
253D4×Dic3C2×D511yescharacteristic
254#926—51no—
255#926—51no—
256#926—101no—
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3—101no—
259C22×C3⋊C8—51no—
260#835—51no—
261#835C2×D511yescharacteristic, complemented
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#832—51no—
267#832C2×D511yescharacteristic
268#818—51no—
269#818—51no—
270#817—51no—
271#817C2×D511yescharacteristic, complemented
272#815—51no—
273#815—51no—
274C8×Dic3—51no—
275C8×Dic3C2×D511yescharacteristic, complemented
276C23×D5—21no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—61no—
280C2×C22⋊D5—21no—
281C22×Dic5—61no—
282#713—22no—
283#713C2×Dic314yescomplemented
284D4×D5—22no—
285D4×D5C2×Dic314yescomplemented
286C2×D20—21no—
287C2×D20C22×D311yescharacteristic
288C2×D20C22×D311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—61no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5C22×D311yescharacteristic
296C5×SD16C2×Dic314yescomplemented
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C42×C5—61no—
305C22⋊Dic5—61no—
306#688C2×Dic314yescomplemented
307#686C2×Dic314yescomplemented
308#685—31no—
309#685—31no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318#683—31no—
319#683—31no—
320#683—61no—
321C4×Dic5—31no—
322C4×Dic5—61no—
323C4×Dic5—61no—
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326D40C2×Dic314yescomplemented
327#676C2×Dic314yescomplemented
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—51no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—31no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
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×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—21no—
363Dic15—41no—
364Dic15—41no—
365C3×Dic5C4×D412yes—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C5×Dic3—41no—
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—51no—
382C22×C3×C4—101no—
383C22×Dic3—21no—
384C22×Dic3—101no—
385C22×Dic3—101no—
386C22×Dic3—101no—
387C22×Dic3—101no—
388C22×Dic3—101no—
389C22×Dic3—101no—
390C3×SD16—54no—
391C3×SD16C4×D514yescomplemented
392C3×D8—54no—
393C3×D8—54no—
394C3×M16—54no—
395C2×C3×C8—51no—
396C2×C3×C8C22×D511yescharacteristic
397#217—21no—
398#217—51no—
399#217—51no—
400#217—101no—
401#217—101no—
402#217—101no—
403#217—101no—
404#217—101no—
405#217—101no—
406C4⋊Dic3—21no—
407C4⋊Dic3—51no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412C4⋊Dic3—101no—
413C4⋊Dic3C22×D511yescharacteristic
414C4⋊Dic3C22×D511yescharacteristic
415C4×Dic3—21no—
416C4×Dic3—51no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419C4×Dic3C22×D511yescharacteristic
420C2×C3⋊C8—51no—
421C2×C3⋊C8—102no—
422C2×C3⋊C8C22×D511yescharacteristic
423C23×C5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—24no—
427C22×D5—81no—
428C22×D5—81no—
429C22×D5D3×D411yescharacteristic
430C5×Q8—21no—
431C5×Q8C22×Dic312yes—
432C5×D4—21no—
433C5×D4C22×Dic312yes—
434C2×C4×C5—21no—
435C2×C4×C5—31no—
436C2×C4×C5—31no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—24no—
442C2×Dic5—31no—
443C2×Dic5—31no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—241no—
447C2×Dic5D3×D411yescharacteristic
448D20—24no—
449D20—21no—
450D20—21no—
451D20C22×Dic312yes—
452D20C22×Dic312yes—
453C4×D5—24no—
454C4×D5—241no—
455C4×D5—241no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459C4×D5#23712yes—
460C4×D5C22×Dic312yes—
461C5×C8—61no—
462C5×C8C22×Dic312yes—
463#168—61no—
464#168C22×Dic312yes—
465C2×#41—51no—
466C22×D4—51no—
467AGL(1,ℤ/8)—58no—
468C2×SD16—51no—
469C2×SD16D3×D511yescharacteristic
470C2×D8—51no—
471C2×D8—51no—
472C2×M16—51no—
473C22×C8—151no—
474C4×Q8—31no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—151no—
478C4×D4—151no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—31no—
496#106—151no—
497#103—31no—
498#103—151no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—151no—
506#97—151no—
507C4×C8—31no—
508C4×C8—151no—
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—51no—
535C2×C3×C4—52no—
536C2×C3×C4—52no—
537C2×C3×C4—104no—
538C2×C3×C4C23×D511yescharacteristic
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—51no—
542C2×Dic3—51no—
543C2×Dic3—81no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—401no—
547C2×Dic3—401no—
548C2×Dic3—401no—
549C2×Dic3—401no—
550C2×Dic3—401no—
551C2×Dic3—401no—
552C2×Dic3D4×D511yescharacteristic
553C2×Dic3D4×D511yescharacteristic
554C3×C8—52no—
555C3×C8C2×C4×D512yes—
556C3⋊C8—21no—
557C3⋊C8—101no—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5C2×D3×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×D5D4×Dic312yes—
572C4×C5—22no—
573C4×C5—61no—
574C4×C5—61no—
575C4×C5—121no—
576C4×C5—121no—
577C4×C5C2×#23711yescharacteristic
578C4×C5C23×Dic311yescharacteristic
579Dic5—61no—
580Dic5—61no—
581Dic5—121no—
582Dic5—121no—
583Dic5D4×Dic312yes—
584C24—101no—
585#41—54no—
586#41—102no—
587C2×Q8C2×D3×D511yescharacteristic
588C2×D4—54no—
589C2×D4—51no—
590C2×D4—51no—
591C2×D4—101no—
592C2×D4—102no—
593C2×D4—101no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—51no—
596C22×C4—61no—
597C22×C4—101no—
598C22×C4—301no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—54no—
605SD16D5×Dic314yescomplemented
606D8—54no—
607D8—54no—
608M16—54no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—302no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—301no—
622C4⋊C4—301no—
623C22⋊C4—61no—
624C22⋊C4—151no—
625C22⋊C4—151no—
626C22⋊C4—301no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—61no—
634C42—151no—
635C42—301no—
636C42—301no—
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—22no—
653C3×C4—52no—
654C3×C4C22×C4×D511yescharacteristic
655C3×C4D5×#4111yescharacteristic
656Dic3—21no—
657Dic3—21no—
658Dic3—41no—
659Dic3—41no—
660Dic3—101no—
661Dic3—101no—
662Dic3—201no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5#577411yescharacteristic
666C2×C5#577511yescharacteristic
667C2×C5C2×D4×Dic311yescharacteristic
668D5—22no—
669D5—42no—
670D5—42no—
671C23—21no—
672C23—51no—
673C23—104no—
674C23—101no—
675C23—101no—
676C23—401no—
677C23—401no—
678Q8—21no—
679Q8C2×D5×Dic312yes—
680D4—21no—
681D4—52no—
682D4—52no—
683D4—104no—
684D4—104no—
685D4—101no—
686D4—101no—
687D4C2×D5×Dic312yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—51no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—104no—
697C2×C4—151no—
698C2×C4—151no—
699C2×C4—241no—
700C2×C4—301no—
701C2×C4—301no—
702C2×C4—1201no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—52no—
710C8—61no—
711C8—301no—
712C8C2×D5×Dic312yes—
713C2×C3—42no—
714C2×C3—102no—
715C2×C3—202no—
716C2×C3—202no—
717C2×C3C4×D4×D511yescharacteristic
718C2×C3#6609611yescharacteristic
719C2×C3#6610311yescharacteristic
720C5#8393011yescharacteristic, 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—
734C22D3×D4×D511yescharacteristic
735C4—22no—
736C4—52no—
737C4—61no—
738C4—61no—
739C4—121no—
740C4—121no—
741C4—301no—
742C4—301no—
743C4—601no—
744C4—601no—
745C4D5×#23711yescharacteristic
746C4C22×D5×Dic311yescharacteristic
747C3#1061137811yescharacteristic, complemented, Sylow
748C2—42no—
749C2—102no—
750C2—202no—
751C2—202no—
752C2#1175408211yescharacteristic
753C2#1175408911yescharacteristic
754C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4060C2
cosocleC2×C3×C4×C5C24
hypercenterC2×SD16D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #11755217C2semidirect
3. #11754910C2semidirect
4. #11751265C2semidirect
5. C5×Dic3×SD16C2semidirect
6. #11749239C2semidirect
7. #11749234C2semidirect
8. #11749207C2semidirect
9. #11748993C2semidirect
10. #11748988C2semidirect
11. D5×#832C2semidirect
12. #11748050C2semidirect
13. #11747815C2semidirect
14. Dic3×D40C2semidirect
15. #11747618C2semidirect
20. Q8×Dic15C22semidirect
22. C5×Q8×Dic3C22semidirect
26. C3×#4060C4semidirect
35. #91434C22semidirect
38. Dic3×D20C22semidirect
45. #91119C22semidirect
47. #91102C22semidirect
48. #91099C22semidirect
49. C5×#835C22semidirect
51. C5×#817C22semidirect
52. C5×C8×Dic3C22semidirect
53. #90988C22semidirect
54. #90985C22semidirect
56. #90965C22semidirect
58. #90964C22semidirect
59. #90953C22semidirect
60. #90951C22semidirect
84. C3×#713C2×C4semidirect
86. C3×D4×D5C2×C4semidirect
97. C3×C5×SD16C2×C4semidirect
113. C3×#688C2×C4semidirect
114. C3×#686C2×C4semidirect
116. C3×D40C2×C4semidirect
117. C3×#676C2×C4semidirect
138. Dic3×SD16D5semidirect
156. #4060Dic3semidirect
243. Q8×Dic3C2×D5semidirect
261. #835C2×D5semidirect
271. #817C2×D5semidirect
275. C8×Dic3C2×D5semidirect
283. #713C2×Dic3semidirect
285. D4×D5C2×Dic3semidirect
296. C5×SD16C2×Dic3semidirect
306. #688C2×Dic3semidirect
307. #686C2×Dic3semidirect
326. D40C2×Dic3semidirect
327. #676C2×Dic3semidirect
391. C3×SD16C4×D5semidirect
605. SD16D5×Dic3semidirect
637. C3×C5#2946semidirect
720. C5#83930semidirect
747. C3#10611378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40602
#117552172
#117549102
#117512652
C5×Dic3×SD162
#117492392
#117492342
#117492072
#117489932
#117489882
D5×#8322
#117480502
#117478152
Dic3×D402
#117476182
#106113783
#839305