Finite Group Databasebeta

← #14411936

Subgroups — #14411936

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92016C211yesmaximal, characteristic
2D15×#117C211yesmaximal, characteristic, complemented
3#11754461C211yesmaximal, characteristic, complemented
4C5×#5006C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic, complemented
6#11748625C211yesmaximal, characteristic, complemented
7#11748624C211yesmaximal, characteristic, complemented
8#11747131C214yesmaximal, complemented
9#11747128C214yesmaximal, complemented
10D5×#410—31nomaximal, Hall
11C22×C4×D15C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C2×#6790C2212yes—
15C2×#6780C2212yes—
16#92016—21no—
17#92016—21no—
18#92016—21no—
19#92016—21no—
20#92016—21no—
21#92016—21no—
22#92016—21no—
23#92016—21no—
24C2×#6777C411yescharacteristic, complemented
25C2×C4×D3×D5C412yescomplemented
26C2×#6771C412yescomplemented
27C2×D15⋊Q8C411yescharacteristic, complemented
28C2×#6768C411yescharacteristic, complemented
29C2×#6766C411yescharacteristic, complemented
30C3×C5×#117C2211yescharacteristic, complemented
31#91815C2211yescharacteristic, complemented
32#91781—21no—
33C4⋊C4×D15—21no—
34C22⋊C4×D15C2212yes—
35#91766C2212yescomplemented
36#91761—21no—
37C42×D15—21no—
38C5×#926C2211yescharacteristic, complemented
39C3×#4072C2211yescharacteristic, complemented
40#91561C2212yes—
41#91532C2212yescomplemented
42#91437—21no—
43C4×#1200—21no—
44#91386—21no—
45#91347—21no—
46C5×#806C2214yescomplemented
47C3×#3938C2214yescomplemented
48#90996C2214yescomplemented
49#90995C2214yescomplemented
50D3×#410—51nomaximal, Hall
51C2×D5×#41—31no—
52D5×#117—31no—
53D5×#117—31no—
54C5×#410—31no—
55#65529—31no—
56#65295—31no—
57#65295D311yescharacteristic, complemented
58D5×#99—34no—
59#65029—34no—
60C23×D15C2311yescharacteristic
61C22×D3×D5C2×C412yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—22no—
65C2×C4×D15C2×C411yescharacteristic
66C2×C4×D15C2×C411yescharacteristic
67C2×C4×D15C2×C411yescharacteristic
68C2×C4×D15C2×C411yescharacteristic
69C2×C4×D15D411yescharacteristic
70C2×C4×D15D411yescharacteristic
71C2×C4×D15D411yescharacteristic
72C2×C4×D15D411yescharacteristic
73C2×C4×D15D411yescharacteristic
74C2×C4×D15D411yescharacteristic
75C2×C4×D15D411yescharacteristic
76C2×C4×D15D411yescharacteristic
77C2×C5×#67C2312yes—
78C5×#235—21no—
79C5×#235—21no—
80C5×#235—21no—
81C5×#235—21no—
82C2×C5×D12C2×C411yescharacteristic, complemented
83C2×C4×C5×D3C2×C412yescomplemented
84C2×C5×Dic6C2×C411yescharacteristic, complemented
85C2×C3×C22⋊D5C2312yes—
86C3×#709—21no—
87C3×#709—21no—
88C3×#709—21no—
89C3×#709—21no—
90C2×C3×D20C2×C411yescharacteristic, complemented
91C2×C3×C4×D5C2×C412yescomplemented
92C2×C3×Dic10C2×C411yescharacteristic, complemented
93#6790—22no—
94#6790—22no—
95#6790—22no—
96#6790—22no—
97C2×#1204C2×C412yescomplemented
98C2×#1203C2×C412yes—
99C2×#1202C2×C412yes—
100C2×#1201C2×C412yescomplemented
101C2×#1200—22no—
102C2×#1200C2×C412yes—
103C2×D3×Dic5C2×C412yescomplemented
104#6780—22no—
105#6780—22no—
106#6780—22no—
107#6780—22no—
108C2×D5×Dic3C2×C412yescomplemented
109#6777—21no—
110#6777—21no—
111#6777—21no—
112#6777—21no—
113C4×D3×D5—22no—
114C4×D3×D5—22no—
115C4×D3×D5—22no—
116C4×D3×D5—22no—
117#6771—22no—
118#6771—22no—
119#6771—22no—
120#6771—22no—
121D15⋊Q8—21no—
122D15⋊Q8—21no—
123D15⋊Q8—21no—
124D15⋊Q8—21no—
125#6768—21no—
126#6768—21no—
127#6768—21no—
128#6768—21no—
129#6766—21no—
130#6766—21no—
131#6766—21no—
132#6766—21no—
133C3×C5×C4⋊C4—21no—
134C3×C5×C22⋊C4C2312yes—
135C3×C42×C5—21no—
136#6719C2312yes—
137#6714—22no—
138C4⋊Dic15—21no—
139#6712—22no—
140C4×Dic15—21no—
141C4×Dic15—22no—
142C5×#217C2312yes—
143C5×C4⋊Dic3—21no—
144C4×C5×Dic3—21no—
145C3×C22⋊Dic5C2312yes—
146C3×C4⋊Dic5—21no—
147C3×C4×Dic5—21no—
148#6669—22no—
149#6667—22no—
150Dic3×Dic5—22no—
151C2×D3×#41—51no—
152D3×#117—51no—
153D3×#117—51no—
154C3×#410—51no—
155#5240—51no—
156#5006—51no—
157#5006D511yescharacteristic, complemented
158D3×#99—54no—
159#4740—54no—
160C2×C5×#41—31no—
161D5×#41—61no—
162D5×#41—61no—
163D5×#41—61no—
164D5×#41—61no—
165D5×#41—61no—
166D5×#41—61no—
167D5×#41—61no—
168D5×#41—61no—
169C2×#713—31no—
170C2×Q8×D5—31no—
171C2×#711—32no—
172C2×#711—31no—
173C2×D4×D5—32no—
174C2×D4×D5—31no—
175C2×#709—32no—
176C2×#709C2×D311yescharacteristic
177C22×C4×D5—31no—
178C22×C4×D5—32no—
179C5×#117—31no—
180C5×#117C2×D311yescharacteristic, complemented
181#4072—31no—
182#4072C2×D311yescharacteristic, complemented
183#4038—61no—
184#4038—61no—
185D5×C4⋊C4—61no—
186D5×C4⋊C4—61no—
187D5×C22⋊C4—32no—
188D5×C22⋊C4—32no—
189#4023—32no—
190#4023—32no—
191#4018—61no—
192#4018—61no—
193C42×D5—61no—
194C42×D5—61no—
195C5×#99—34no—
196#3966—34no—
197#3938—34no—
198#3938C2×D314yescomplemented
199C2×#410—151noSylow
200C23×C3×C5C2411yescharacteristic
201C22×D15—42no—
202C22×D15C22×C411yescharacteristic
203C22×D15C22×C411yescharacteristic
204C22×D15C2×D411yescharacteristic
205C22×D15C2×D411yescharacteristic
206C22×D15C2×D411yescharacteristic
207C22×D15C2×D411yescharacteristic
208C22×C5×D3C22×C412yes—
209C22×C3×D5C22×C412yes—
210C2×D3×D5—22no—
211C2×D3×D5—22no—
212C2×D3×D5—44no—
213C2×C3×C4×C5—22no—
214C2×C3×C4×C5C22×C411yescharacteristic
215C2×C3×C4×C5C22×C411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×Dic15—22no—
221C2×Dic15C22×C411yescharacteristic
222C2×Dic15C22×C411yescharacteristic
223C2×Dic15C2×D411yescharacteristic
224C2×Dic15C2×D411yescharacteristic
225C2×Dic15C2×D411yescharacteristic
226C2×Dic15C2×D411yescharacteristic
227C4×D15—44no—
228C4×D15C22⋊C411yescharacteristic
229C4×D15C22⋊C411yescharacteristic
230C4×D15C22⋊C411yescharacteristic
231C4×D15C22⋊C411yescharacteristic
232C4×D15C22⋊C411yescharacteristic
233C4×D15C22⋊C411yescharacteristic
234C4×D15C22⋊C411yescharacteristic
235C4×D15C22⋊C411yescharacteristic
236C4×D15C22⋊C411yescharacteristic
237C4×D15C22⋊C411yescharacteristic
238C4×D15C22⋊C411yescharacteristic
239C4×D15C22⋊C411yescharacteristic
240C4×D15C22⋊C411yescharacteristic
241C4×D15C22⋊C411yescharacteristic
242C4×D15C22⋊C411yescharacteristic
243C4×D15C22⋊C411yescharacteristic
244C5×#67—22no—
245C5×#67—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3C22×C412yes—
248C5×D12—21no—
249C5×D12—21no—
250C4×C5×D3—22no—
251C4×C5×D3—22no—
252C5×Dic6—21no—
253C5×Dic6—21no—
254C3×C22⋊D5—22no—
255C3×C22⋊D5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5C22×C412yes—
258C3×D20—21no—
259C3×D20—21no—
260C3×C4×D5—22no—
261C3×C4×D5—22no—
262C3×Dic10—21no—
263C3×Dic10—21no—
264#1204—22no—
265#1204—22no—
266#1203—22no—
267#1203—22no—
268#1202—22no—
269#1202—22no—
270#1201—22no—
271#1201—22no—
272#1200—22no—
273#1200—22no—
274#1200—44no—
275D3×Dic5—22no—
276D3×Dic5—22no—
277D5×Dic3—22no—
278D5×Dic3—22no—
279C2×C3×#41—51no—
280D3×#41—101no—
281D3×#41—101no—
282D3×#41—101no—
283D3×#41—101no—
284D3×#41—101no—
285D3×#41—101no—
286D3×#41—101no—
287D3×#41—101no—
288C2×#239—51no—
289C2×D3×Q8—51no—
290C2×#237—52no—
291C2×#237—51no—
292C2×D3×D4—52no—
293C2×D3×D4—51no—
294C2×#235—52no—
295C2×#235C2×D511yescharacteristic
296C22×C4×D3—51no—
297C22×C4×D3—52no—
298C3×#117—51no—
299C3×#117C2×D511yescharacteristic, complemented
300#926—51no—
301#926C2×D511yescharacteristic, complemented
302#892—101no—
303#892—101no—
304D3×C4⋊C4—101no—
305D3×C4⋊C4—101no—
306D3×C22⋊C4—52no—
307D3×C22⋊C4—52no—
308#877—52no—
309#877—52no—
310#872—101no—
311#872—101no—
312C42×D3—101no—
313C42×D3—101no—
314C3×#99—54no—
315#834—54no—
316#806—54no—
317#806C2×D514yescomplemented
318C23×D5—31no—
319C23×D5—32no—
320C5×#41—61no—
321C5×#41—61no—
322C5×#41—61no—
323C5×#41—61no—
324C2×C5×Q8—31no—
325C2×C5×D4—32no—
326C2×C5×D4—31no—
327C22×C4×C5—32no—
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—32no—
330C2×C22⋊D5—32no—
331C2×C22⋊D5C22×D312yes—
332C22×Dic5—31no—
333C22×Dic5—32no—
334#713—61no—
335#713—61no—
336#713—61no—
337#713—61no—
338Q8×D5—61no—
339Q8×D5—61no—
340Q8×D5—61no—
341Q8×D5—61no—
342#711—61no—
343#711—61no—
344#711—61no—
345#711—61no—
346#711—62no—
347#711—62no—
348#711—62no—
349#711—62no—
350D4×D5—61no—
351D4×D5—61no—
352D4×D5—61no—
353D4×D5—61no—
354D4×D5—62no—
355D4×D5—62no—
356D4×D5—62no—
357D4×D5—62no—
358#709—21no—
359#709—21no—
360#709—21no—
361#709—21no—
362#709—62no—
363#709—62no—
364#709—62no—
365#709—62no—
366C2×D20—32no—
367C2×D20C4×D311yescharacteristic, complemented
368C2×C4×D5—31no—
369C2×C4×D5—31no—
370C2×C4×D5—31no—
371C2×C4×D5—31no—
372C2×C4×D5—31no—
373C2×C4×D5—31no—
374C2×C4×D5—31no—
375C2×C4×D5—31no—
376C2×C4×D5—31no—
377C2×C4×D5—31no—
378C2×C4×D5—31no—
379C2×C4×D5—31no—
380C2×C4×D5—32no—
381C2×C4×D5—32no—
382C2×C4×D5—62no—
383C2×C4×D5—62no—
384C2×C4×D5—62no—
385C2×C4×D5—62no—
386C2×C4×D5—62no—
387C2×C4×D5—62no—
388C2×C4×D5C4×D312yescomplemented
389C2×Dic10—32no—
390C2×Dic10C4×D311yescharacteristic, complemented
391C5×C4⋊C4—21no—
392C5×C4⋊C4—61no—
393C5×C22⋊C4—32no—
394C5×C22⋊C4C22×D312yes—
395C42×C5—21no—
396C42×C5—61no—
397C22⋊Dic5—32no—
398C22⋊Dic5C22×D312yes—
399#685—62no—
400#685—62no—
401C4⋊Dic5—21no—
402C4⋊Dic5—61no—
403#683—62no—
404#683—62no—
405C4×Dic5—21no—
406C4×Dic5—62no—
407C4×Dic5—62no—
408C4×Dic5—61no—
409C22×#41—151no—
410C2×#117—151no—
411C2×#117—151no—
412#410—31no—
413#410—51no—
414#410—154no—
415#410—151no—
416#410—151no—
417C2×#99—154no—
418C22×C3×C5—41no—
419C22×C3×C5C23×C411yescharacteristic
420C22×C3×C5C22×D411yescharacteristic
421C22×C3×C5C22×D411yescharacteristic
422C2×D15—22no—
423C2×D15—22no—
424C2×D15—22no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15C2×C22⋊C411yescharacteristic
429C2×D15C2×C22⋊C411yescharacteristic
430C2×D15C2×C22⋊C411yescharacteristic
431C2×D15C2×C22⋊C411yescharacteristic
432C2×C5×D3—22no—
433C2×C5×D3—42no—
434C2×C3×D5—22no—
435C2×C3×D5—42no—
436D3×D5—44no—
437D3×D5—44no—
438C3×C4×C5—42no—
439C3×C4×C5C2×C22⋊C411yescharacteristic
440C3×C4×C5C2×C22⋊C411yescharacteristic
441C3×C4×C5C2×C22⋊C411yescharacteristic
442C3×C4×C5C2×C22⋊C411yescharacteristic
443Dic15—42no—
444Dic15C2×C22⋊C411yescharacteristic
445Dic15C2×C22⋊C411yescharacteristic
446Dic15C2×C22⋊C411yescharacteristic
447Dic15C2×C22⋊C411yescharacteristic
448C3×Dic5—22no—
449C3×Dic5—42no—
450C5×Dic3—22no—
451C5×Dic3—42no—
452C23×D3—51no—
453C23×D3—52no—
454C3×#41—101no—
455C3×#41—101no—
456C3×#41—101no—
457C3×#41—101no—
458C2×C3×Q8—51no—
459C2×C3×D4—52no—
460C2×C3×D4—51no—
461C22×C3×C4—52no—
462C22×C3×C4C22×D511yescharacteristic
463C2×#67—52no—
464C2×#67—52no—
465C2×#67C22×D512yes—
466C22×Dic3—51no—
467C22×Dic3—52no—
468#239—101no—
469#239—101no—
470#239—101no—
471#239—101no—
472D3×Q8—101no—
473D3×Q8—101no—
474D3×Q8—101no—
475D3×Q8—101no—
476#237—101no—
477#237—101no—
478#237—101no—
479#237—101no—
480#237—102no—
481#237—102no—
482#237—102no—
483#237—102no—
484D3×D4—101no—
485D3×D4—101no—
486D3×D4—101no—
487D3×D4—101no—
488D3×D4—102no—
489D3×D4—102no—
490D3×D4—102no—
491D3×D4—102no—
492#235—21no—
493#235—21no—
494#235—21no—
495#235—21no—
496#235—102no—
497#235—102no—
498#235—102no—
499#235—102no—
500C2×D12—52no—
501C2×D12C4×D511yescharacteristic, complemented
502C2×C4×D3—51no—
503C2×C4×D3—51no—
504C2×C4×D3—51no—
505C2×C4×D3—51no—
506C2×C4×D3—51no—
507C2×C4×D3—51no—
508C2×C4×D3—51no—
509C2×C4×D3—51no—
510C2×C4×D3—51no—
511C2×C4×D3—51no—
512C2×C4×D3—51no—
513C2×C4×D3—51no—
514C2×C4×D3—52no—
515C2×C4×D3—52no—
516C2×C4×D3—102no—
517C2×C4×D3—102no—
518C2×C4×D3—102no—
519C2×C4×D3—102no—
520C2×C4×D3—102no—
521C2×C4×D3—102no—
522C2×C4×D3C4×D512yescomplemented
523C2×Dic6—52no—
524C2×Dic6C4×D511yescharacteristic, complemented
525C3×C4⋊C4—21no—
526C3×C4⋊C4—101no—
527C3×C22⋊C4—52no—
528C3×C22⋊C4C22×D512yes—
529C3×C42—21no—
530C3×C42—101no—
531#217—52no—
532#217C22×D512yes—
533(C2×D3)⋊C4—102no—
534(C2×D3)⋊C4—102no—
535C4⋊Dic3—21no—
536C4⋊Dic3—101no—
537Dic3⋊C4—102no—
538Dic3⋊C4—102no—
539C4×Dic3—21no—
540C4×Dic3—102no—
541C4×Dic3—102no—
542C4×Dic3—101no—
543C23×C5—32no—
544C23×C5C23×D311yescharacteristic
545C22×D5—31no—
546C22×D5—31no—
547C22×D5—31no—
548C22×D5—31no—
549C22×D5—31no—
550C22×D5—31no—
551C22×D5—62no—
552C22×D5—62no—
553C22×D5—124no—
554C22×D5—122no—
555C22×D5C2×C4×D312yes—
556C5×Q8—61no—
557C5×Q8—61no—
558C5×D4—62no—
559C5×D4—62no—
560C5×D4—61no—
561C5×D4—61no—
562C2×C4×C5—22no—
563C2×C4×C5—32no—
564C2×C4×C5—62no—
565C2×C4×C5—62no—
566C2×C4×C5—62no—
567C2×C4×C5C2×C4×D311yescharacteristic
568C2×C4×C5C2×C4×D311yescharacteristic
569C2×C4×C5D3×D411yescharacteristic
570C2×C4×C5D3×D411yescharacteristic
571C2×C4×C5D3×D411yescharacteristic
572C2×C4×C5D3×D411yescharacteristic
573C22⋊D5—22no—
574C22⋊D5—22no—
575C22⋊D5—62no—
576C22⋊D5—62no—
577C22⋊D5—62no—
578C22⋊D5—62no—
579C2×Dic5—22no—
580C2×Dic5—31no—
581C2×Dic5—31no—
582C2×Dic5—31no—
583C2×Dic5—31no—
584C2×Dic5—31no—
585C2×Dic5—31no—
586C2×Dic5—62no—
587C2×Dic5—62no—
588C2×Dic5—62no—
589C2×Dic5C2×C4×D312yes—
590D20—21no—
591D20—21no—
592D20—62no—
593D20—62no—
594C4×D5—22no—
595C4×D5—22no—
596C4×D5—31no—
597C4×D5—31no—
598C4×D5—31no—
599C4×D5—31no—
600C4×D5—31no—
601C4×D5—31no—
602C4×D5—31no—
603C4×D5—31no—
604C4×D5—31no—
605C4×D5—31no—
606C4×D5—31no—
607C4×D5—31no—
608C4×D5—31no—
609C4×D5—31no—
610C4×D5—31no—
611C4×D5—31no—
612C4×D5—62no—
613C4×D5—62no—
614C4×D5—62no—
615C4×D5—62no—
616C4×D5—124no—
617C4×D5—124no—
618Dic10—21no—
619Dic10—21no—
620Dic10—62no—
621Dic10—62no—
622C2×#41—31no—
623C2×#41—51no—
624C2×#41—152no—
625C2×#41—152no—
626C2×#41—151no—
627C2×#41—151no—
628C2×#41—301no—
629C2×#41—301no—
630C2×#41—301no—
631C2×#41—301no—
632C2×#41—301no—
633C2×#41—301no—
634C2×#41—301no—
635C2×#41—301no—
636C22×Q8—151no—
637C22×D4—152no—
638C22×D4—151no—
639C23×C4—152no—
640C23×C4—151no—
641#117—31no—
642#117—51no—
643#117—152no—
644#117—151no—
645#117—152no—
646#117—301no—
647#117—301no—
648#117—301no—
649#117—301no—
650#117D3×D511yescharacteristic, complemented
651C2×C4⋊C4—301no—
652C2×C4⋊C4—301no—
653C2×C22⋊C4—152no—
654C2×C22⋊C4—152no—
655C2×C42—301no—
656C2×C42—301no—
657#99—34no—
658#99—54no—
659#99—154no—
660#99—154no—
661C2×C3×C5—21no—
662C2×C3×C5—21no—
663C2×C3×C5—21no—
664C2×C3×C5C22×C22⋊C411yescharacteristic
665D15—21no—
666D15—21no—
667D15—21no—
668D15#41012yescomplemented
669C3×D5—42no—
670C5×D3—42no—
671C23×C3—52no—
672C23×C3C23×D511yescharacteristic
673C22×D3—51no—
674C22×D3—51no—
675C22×D3—51no—
676C22×D3—51no—
677C22×D3—51no—
678C22×D3—51no—
679C22×D3—102no—
680C22×D3—102no—
681C22×D3—204no—
682C22×D3—202no—
683C22×D3C2×C4×D512yes—
684C3×Q8—101no—
685C3×Q8—101no—
686C3×D4—102no—
687C3×D4—102no—
688C3×D4—101no—
689C3×D4—101no—
690C2×C3×C4—22no—
691C2×C3×C4—52no—
692C2×C3×C4—102no—
693C2×C3×C4—102no—
694C2×C3×C4—102no—
695C2×C3×C4C2×C4×D511yescharacteristic
696C2×C3×C4C2×C4×D511yescharacteristic
697C2×C3×C4D4×D511yescharacteristic
698C2×C3×C4D4×D511yescharacteristic
699C2×C3×C4D4×D511yescharacteristic
700C2×C3×C4D4×D511yescharacteristic
701#67—22no—
702#67—22no—
703#67—102no—
704#67—102no—
705#67—102no—
706#67—102no—
707C2×Dic3—22no—
708C2×Dic3—51no—
709C2×Dic3—51no—
710C2×Dic3—51no—
711C2×Dic3—51no—
712C2×Dic3—51no—
713C2×Dic3—51no—
714C2×Dic3—102no—
715C2×Dic3—102no—
716C2×Dic3—102no—
717C2×Dic3C2×C4×D512yes—
718D12—21no—
719D12—21no—
720D12—102no—
721D12—102no—
722C4×D3—22no—
723C4×D3—22no—
724C4×D3—51no—
725C4×D3—51no—
726C4×D3—51no—
727C4×D3—51no—
728C4×D3—51no—
729C4×D3—51no—
730C4×D3—51no—
731C4×D3—51no—
732C4×D3—51no—
733C4×D3—51no—
734C4×D3—51no—
735C4×D3—51no—
736C4×D3—51no—
737C4×D3—51no—
738C4×D3—51no—
739C4×D3—51no—
740C4×D3—102no—
741C4×D3—102no—
742C4×D3—102no—
743C4×D3—102no—
744C4×D3—204no—
745C4×D3—204no—
746Dic6—21no—
747Dic6—21no—
748Dic6—102no—
749Dic6—102no—
750C22×C5—41no—
751C22×C5—62no—
752C22×C5—122no—
753C22×C5C22×C4×D311yescharacteristic
754C22×C5C2×D3×D411yescharacteristic
755C22×C5C2×D3×D411yescharacteristic
756C2×D5—22no—
757C2×D5—31no—
758C2×D5—31no—
759C2×D5—31no—
760C2×D5—31no—
761C2×D5—42no—
762C2×D5—62no—
763C2×D5—62no—
764C2×D5—62no—
765C2×D5—124no—
766C2×D5—124no—
767C2×D5—121no—
768C2×D5—121no—
769C2×D5—121no—
770C4×C5—42no—
771C4×C5—62no—
772C4×C5—122no—
773C4×C5D3×C22⋊C411yescharacteristic
774C4×C5D3×C22⋊C411yescharacteristic
775C4×C5D3×C22⋊C411yescharacteristic
776C4×C5D3×C22⋊C411yescharacteristic
777Dic5—22no—
778Dic5—31no—
779Dic5—31no—
780Dic5—31no—
781Dic5—31no—
782Dic5—42no—
783Dic5—122no—
784C24—152no—
785C24—151no—
786#41—61no—
787#41—61no—
788#41—61no—
789#41—61no—
790#41—101no—
791#41—101no—
792#41—101no—
793#41—101no—
794#41—302no—
795#41—302no—
796#41—302no—
797#41—302no—
798#41—302no—
799#41—302no—
800#41—302no—
801#41—302no—
802#41—301no—
803#41—301no—
804#41—301no—
805#41—301no—
806#41—301no—
807#41—301no—
808#41—301no—
809#41—301no—
810C2×Q8—31no—
811C2×Q8—51no—
812C2×Q8—152no—
813C2×Q8—301no—
814C2×Q8—301no—
815C2×Q8—301no—
816C2×Q8—301no—
817C2×D4—32no—
818C2×D4—31no—
819C2×D4—52no—
820C2×D4—51no—
821C2×D4—152no—
822C2×D4—152no—
823C2×D4—152no—
824C2×D4—301no—
825C2×D4—301no—
826C2×D4—301no—
827C2×D4—301no—
828C2×D4—302no—
829C2×D4—302no—
830C2×D4—302no—
831C2×D4—302no—
832C22×C4—32no—
833C22×C4—52no—
834C22×C4—152no—
835C22×C4—152no—
836C22×C4—152no—
837C22×C4—151no—
838C22×C4—151no—
839C22×C4—151no—
840C22×C4—151no—
841C22×C4—151no—
842C22×C4—151no—
843C22×C4—151no—
844C22×C4—151no—
845C22×C4—151no—
846C22×C4—151no—
847C22×C4—151no—
848C22×C4—151no—
849C22×C4—151no—
850C22×C4—302no—
851C22×C4—302no—
852C22×C4—302no—
853C22×C4—302no—
854C22×C4—302no—
855C22×C4—302no—
856C22×C4C2×D3×D511yescharacteristic
857C4⋊C4—21no—
858C4⋊C4—61no—
859C4⋊C4—101no—
860C4⋊C4—302no—
861C4⋊C4—302no—
862C4⋊C4—301no—
863C22⋊C4—32no—
864C22⋊C4—52no—
865C22⋊C4—152no—
866C22⋊C4—302no—
867C22⋊C4—302no—
868C22⋊C4C2×D3×D512yes—
869C42—21no—
870C42—61no—
871C42—101no—
872C42—302no—
873C42—302no—
874C42—301no—
875C3×C5C2×#41011yescharacteristic, complemented, Hall
876C22×C3—41no—
877C22×C3—102no—
878C22×C3—202no—
879C22×C3C22×C4×D511yescharacteristic
880C22×C3C2×D4×D511yescharacteristic
881C22×C3C2×D4×D511yescharacteristic
882C2×D3—22no—
883C2×D3—42no—
884C2×D3—51no—
885C2×D3—51no—
886C2×D3—51no—
887C2×D3—51no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—102no—
891C2×D3—204no—
892C2×D3—204no—
893C2×D3—201no—
894C2×D3—201no—
895C2×D3—201no—
896C3×C4—42no—
897C3×C4—102no—
898C3×C4—202no—
899C3×C4D5×C22⋊C411yescharacteristic
900C3×C4D5×C22⋊C411yescharacteristic
901C3×C4D5×C22⋊C411yescharacteristic
902C3×C4D5×C22⋊C411yescharacteristic
903Dic3—22no—
904Dic3—42no—
905Dic3—51no—
906Dic3—51no—
907Dic3—51no—
908Dic3—51no—
909Dic3—202no—
910C2×C5—21no—
911C2×C5—21no—
912C2×C5—21no—
913C2×C5—122no—
914C2×C5C2×D3×C22⋊C411yescharacteristic
915D5—32no—
916D5—42no—
917D5—61no—
918D5—61no—
919D5—61no—
920C23—32no—
921C23—52no—
922C23—151no—
923C23—151no—
924C23—151no—
925C23—151no—
926C23—151no—
927C23—151no—
928C23—302no—
929C23—302no—
930C23—602no—
931C23—604no—
932C23C22×D3×D511yescharacteristic
933Q8—61no—
934Q8—61no—
935Q8—101no—
936Q8—101no—
937Q8—302no—
938Q8—302no—
939D4—62no—
940D4—62no—
941D4—61no—
942D4—61no—
943D4—102no—
944D4—102no—
945D4—101no—
946D4—101no—
947D4—302no—
948D4—302no—
949D4—302no—
950D4—302no—
951D4—302no—
952D4—302no—
953C2×C4—22no—
954C2×C4—32no—
955C2×C4—52no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—102no—
960C2×C4—102no—
961C2×C4—102no—
962C2×C4—151no—
963C2×C4—151no—
964C2×C4—151no—
965C2×C4—151no—
966C2×C4—151no—
967C2×C4—151no—
968C2×C4—151no—
969C2×C4—151no—
970C2×C4—151no—
971C2×C4—151no—
972C2×C4—151no—
973C2×C4—151no—
974C2×C4—151no—
975C2×C4—151no—
976C2×C4—151no—
977C2×C4—151no—
978C2×C4—151no—
979C2×C4—151no—
980C2×C4—151no—
981C2×C4—151no—
982C2×C4—151no—
983C2×C4—151no—
984C2×C4—302no—
985C2×C4—302no—
986C2×C4—302no—
987C2×C4—302no—
988C2×C4—302no—
989C2×C4—302no—
990C2×C4—302no—
991C2×C4—604no—
992C2×C4—604no—
993C2×C4C4×D3×D511yescharacteristic
994C2×C4C4×D3×D511yescharacteristic
995C2×C4#677711yescharacteristic
996C2×C4#677711yescharacteristic
997C2×C4#679011yescharacteristic
998C2×C4#679011yescharacteristic
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—202no—
1003C2×C3C2×D5×C22⋊C411yescharacteristic
1004D3—42no—
1005D3—52no—
1006D3—101no—
1007D3—101no—
1008D3—101no—
1009C5D3×#41011yescharacteristic, complemented, Sylow
1010C22—41no—
1011C22—62no—
1012C22—102no—
1013C22—122no—
1014C22—151no—
1015C22—151no—
1016C22—151no—
1017C22—151no—
1018C22—202no—
1019C22—302no—
1020C22—302no—
1021C22—302no—
1022C22—601no—
1023C22—601no—
1024C22—601no—
1025C22—604no—
1026C22—604no—
1027C22C2×C4×D3×D511yescharacteristic
1028C22C2×#677711yescharacteristic
1029C22C2×#679011yescharacteristic
1030C4—42no—
1031C4—62no—
1032C4—102no—
1033C4—122no—
1034C4—151no—
1035C4—151no—
1036C4—151no—
1037C4—151no—
1038C4—202no—
1039C4—602no—
1040C4#9147311yescharacteristic
1041C4#9147311yescharacteristic
1042C4#9147311yescharacteristic
1043C4#9147311yescharacteristic
1044C3D5×#41011yescharacteristic, complemented, Sylow
1045C2—21no—
1046C2—21no—
1047C2—21no—
1048C2—122no—
1049C2—152no—
1050C2—202no—
1051C2—301no—
1052C2—301no—
1053C2—301no—
1054C2C2×#9147311yescharacteristic
subgroupG/H
centerC4#91473
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92016C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. D15×#117C2semidirect
3. #11754461C2semidirect
4. C5×#5006C2semidirect
5. C3×#65295C2semidirect
6. #11748625C2semidirect
7. #11748624C2semidirect
8. #11747131C2semidirect
9. #11747128C2semidirect
24. C2×#6777C4semidirect
25. C2×C4×D3×D5C4semidirect
26. C2×#6771C4semidirect
27. C2×D15⋊Q8C4semidirect
28. C2×#6768C4semidirect
29. C2×#6766C4semidirect
30. C3×C5×#117C22semidirect
31. #91815C22semidirect
35. #91766C22semidirect
38. C5×#926C22semidirect
39. C3×#4072C22semidirect
41. #91532C22semidirect
46. C5×#806C22semidirect
47. C3×#3938C22semidirect
48. #90996C22semidirect
49. #90995C22semidirect
57. #65295D3semidirect
82. C2×C5×D12C2×C4semidirect
83. C2×C4×C5×D3C2×C4semidirect
84. C2×C5×Dic6C2×C4semidirect
90. C2×C3×D20C2×C4semidirect
91. C2×C3×C4×D5C2×C4semidirect
92. C2×C3×Dic10C2×C4semidirect
97. C2×#1204C2×C4semidirect
100. C2×#1201C2×C4semidirect
103. C2×D3×Dic5C2×C4semidirect
108. C2×D5×Dic3C2×C4semidirect
157. #5006D5semidirect
180. C5×#117C2×D3semidirect
182. #4072C2×D3semidirect
198. #3938C2×D3semidirect
299. C3×#117C2×D5semidirect
301. #926C2×D5semidirect
317. #806C2×D5semidirect
367. C2×D20C4×D3semidirect
388. C2×C4×D5C4×D3semidirect
390. C2×Dic10C4×D3semidirect
501. C2×D12C4×D5semidirect
522. C2×C4×D3C4×D5semidirect
524. C2×Dic6C4×D5semidirect
650. #117D3×D5semidirect
668. D15#410semidirect
875. C3×C5C2×#410semidirect
1009. C5D3×#410semidirect
1044. C3D5×#410semidirect

Maximal subgroups

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

subgroupindex
C2×#920162
D15×#1172
#117544612
C5×#50062
C3×#652952
#117486252
#117486242
#117471312
#117471282
D5×#4103
D3×#4105