Finite Group Databasebeta

← #14482988

Subgroups — #14482988

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic, complemented
2C2×#92034C211yesmaximal, characteristic, complemented
3C5×#5834C211yesmaximal, characteristic, complemented
4C3×#66168C211yesmaximal, characteristic, complemented
5#11755251C211yesmaximal, characteristic, complemented
6#11755245C211yesmaximal, characteristic, complemented
7Q8×#1200C211yesmaximal, characteristic, complemented
8#11755052C213yesmaximal, complemented
9#11755026C213yesmaximal, complemented
10#11754956C213yesmaximal, complemented
11#11754819C213yesmaximal, complemented
12#11754670C213yesmaximal, complemented
13C4×#6790C213yesmaximal, complemented
14#11754557C213yesmaximal, complemented
15#11754370C213yesmaximal, complemented
16D5×#550—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18#41×D15—28no—
19C2×#6821C2211yescharacteristic, complemented
20C2×Q8×D15C2211yescharacteristic
21C2×#6819C2213yescomplemented
22C2×D4×D15C2213yes—
23C2×#6817C2213yescomplemented
24C22×C4×D15C2213yes—
25C2×C5×#239C2211yescharacteristic, complemented
26C2×C3×#713C2211yescharacteristic, complemented
27C2×#6790C2213yes—
28C2×#6790C2216yes—
29#92034—28no—
30C2×#6777C2213yes—
31C2×C4×D3×D5C2213yes—
32C2×#6772C2213yescomplemented
33C2×#6765C2213yescomplemented
34C5×Q8×Dic3C2211yescharacteristic, complemented
35C5×#940C2213yescomplemented
36C5×#938C2213yescomplemented
37C5×#930C2213yescomplemented
38C4×C5×#67C2213yescomplemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4086C2213yescomplemented
41C3×#4084C2213yescomplemented
42C3×#4076C2213yescomplemented
43C3×C4×C22⋊D5C2213yescomplemented
44#91571C2216yescomplemented
45#91567C2216yescomplemented
46#91567C2216yescomplemented
47#91561C2213yes—
48#67⋊Dic5C2213yescomplemented
49#91559C2213yescomplemented
50#91558C2216yescomplemented
51#91550C2216yescomplemented
52#91473C2213yes—
53#91466C2213yescomplemented
54#91465C2213yescomplemented
55#91461C2216yescomplemented
56#91460C2213yescomplemented
57#91458C2213yescomplemented
58#91451C2213yescomplemented
59#91450C2213yescomplemented
60C4×#1203C2213yescomplemented
61C4×#1202C2213yescomplemented
62#91437C2213yes—
63#91406C2213yescomplemented
64#91404C2211yescharacteristic
65C4×#1200C2213yes—
66#91396C2213yescomplemented
67#91340C2213yescomplemented
68#91333C2213yescomplemented
69D3×#550—51nomaximal, Hall
70C2×D5×#41—31no—
71C2×D5×#41—31no—
72C5×#550—31no—
73#66168—31no—
74#66168D311yescharacteristic, complemented
75#66052—33no—
76D5×#127—33no—
77D5×#121—33no—
78D5×#121—33no—
79#65933—33no—
80#65933—33no—
81#65911—31no—
82C4×Q8×D5—31no—
83#65887—33no—
84C4×D4×D5—33no—
85C23×D15C2313yes—
86C22×D3×D5C2313yes—
87C3×C5×#41—24no—
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2316yes—
92C22×Dic15C2313yes—
93#6821—24no—
94Q8×D15D418yescomplemented
95#6819—212no—
96D4×D15—212no—
97#6817—212no—
98C2×D60C2313yes—
99C2×C4×D15—212no—
100C2×C4×D15C2313yes—
101C2×C4×D15C2311yescharacteristic
102C2×C4×D15C2313yes—
103C2×C4×D15C2313yes—
104C2×Dic30C2313yes—
105C2×C5×#67C2313yes—
106C2×C5×#67C2316yes—
107C5×#239—24no—
108C2×C5×D12C2313yes—
109C2×C4×C5×D3C2313yes—
110C2×C3×C22⋊D5C2313yes—
111C2×C3×C22⋊D5C2316yes—
112C3×#713—24no—
113C2×C3×D20C2313yes—
114C2×C3×C4×D5C2313yes—
115#6790—212no—
116#6790—412no—
117C2×#1203C2313yes—
118C2×#1203C2316yes—
119C2×#1202C2313yes—
120C2×#1202C2316yes—
121C2×#1201C2316yes—
122C2×#1200C2313yes—
123C2×#1200C2311yescharacteristic
124C2×#1200C2311yescharacteristic
125C2×D3×Dic5C2313yes—
126C2×D5×Dic3C2313yes—
127#6777—212no—
128C4×D3×D5—212no—
129#6772—212no—
130#6765—212no—
131C5×#217C2313yes—
132C5×(C2×D3)⋊C4C2313yes—
133C5×C4⋊Dic3C2313yes—
134C5×Dic3⋊C4C2311yescharacteristic
135C4×C5×Dic3C2313yes—
136C3×C22⋊Dic5C2313yes—
137C3×#685C2313yes—
138C3×C4⋊Dic5C2313yes—
139C3×#683C2311yescharacteristic
140C3×C4×Dic5C2313yes—
141Dic3⋊Dic5C2311yescharacteristic
142#6669C2316yes—
143#6668C2311yescharacteristic
144#6667C2313yes—
145#6667C2313yes—
146(C2×D3)⋊Dic5C2313yes—
147#6665C2313yes—
148Dic3×Dic5C2313yes—
149Dic3×Dic5C2313yes—
150C2×D3×#41—51no—
151C2×D3×#41—51no—
152C3×#550—51no—
153#5834—51no—
154#5834D511yescharacteristic, complemented
155#5718—53no—
156D3×#127—53no—
157D3×#121—53no—
158D3×#121—53no—
159#5599—53no—
160#5599—53no—
161#5577—51no—
162C4×D3×Q8—51no—
163#5553—53no—
164C4×D3×D4—53no—
165C2×C5×#41—31no—
166C2×C5×#41C2×D311yescharacteristic, complemented
167D5×#41—68no—
168D5×#41—68no—
169C2×#713—31no—
170C2×#713C2×D311yescharacteristic, complemented
171C2×Q8×D5—31no—
172C2×#711—33no—
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×D4×D5—36no—
177C2×D4×D5—33no—
178C2×#709—33no—
179C2×#709—33no—
180C22×C4×D5—33no—
181C22×C4×D5—33no—
182C5×#127—33no—
183C5×#121—33no—
184C5×#121—33no—
185C4×C5×Q8—31no—
186C4×C5×D4—33no—
187Q8×Dic5C2×D311yescharacteristic, complemented
188#4086—36no—
189#4086—36no—
190#4086—33no—
191#4086C2×D313yescomplemented
192#4085—36no—
193#4085—36no—
194#4084—33no—
195#4084C2×D313yescomplemented
196D4×Dic5—33no—
197#4076—33no—
198#4076C2×D313yescomplemented
199C4×C22⋊D5—33no—
200C4×C22⋊D5C2×D313yescomplemented
201#4041—33no—
202#4041—33no—
203#4039—33no—
204D5×C4⋊C4—33no—
205D5×C4⋊C4—31no—
206#4033—33no—
207#4030—36no—
208#4030—36no—
209#4027—33no—
210#4027—33no—
211D5×C22⋊C4—33no—
212D5×C22⋊C4—33no—
213#4020—33no—
214C4×D20—33no—
215C42×D5—33no—
216C4×Dic10—33no—
217C2×#550—151noSylow
218C23×C3×C5C2413yes—
219C22×D15—26no—
220C22×D15—26no—
221C22×D15—26no—
222C22×D15C2413yes—
223C22×D15C2411yescharacteristic
224C22×C5×D3C2413yes—
225C22×C3×D5C2413yes—
226C2×D3×D5—26no—
227C2×D3×D5—26no—
228C2×D3×D5—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C2×C3×C4×C5—26no—
232C2×C3×C4×C5C2411yescharacteristic
233C2×C3×C4×C5C2413yes—
234#1220—212no—
235C2×Dic15—26no—
236C2×Dic15C2411yescharacteristic
237C2×Dic15C2413yes—
238D60—26no—
239C4×D15—22no—
240C4×D15—26no—
241C4×D15—26no—
242C4×D15C2×D4112yes—
243Dic30C2×D4112yescomplemented
244C5×#67—26no—
245C5×#67—46no—
246C2×C5×Dic3C2413yes—
247C2×C5×Dic3C2411yescharacteristic
248C2×C5×Dic3C2411yescharacteristic
249C5×D12—26no—
250C4×C5×D3—26no—
251C3×C22⋊D5—26no—
252C3×C22⋊D5—46no—
253C2×C3×Dic5C2413yes—
254C2×C3×Dic5C2411yescharacteristic
255C2×C3×Dic5C2411yescharacteristic
256C3×D20—26no—
257C3×C4×D5—26no—
258#1203—26no—
259#1203—46no—
260#1202—26no—
261#1202—46no—
262#1201—212no—
263#1200—22no—
264#1200—26no—
265#1200#4114yescomplemented
266D3×Dic5—26no—
267D5×Dic3—26no—
268C2×C3×#41—51no—
269C2×C3×#41C2×D511yescharacteristic, complemented
270D3×#41—108no—
271D3×#41—108no—
272C2×#239—51no—
273C2×#239C2×D511yescharacteristic, complemented
274C2×D3×Q8—51no—
275C2×#237—53no—
276C2×#237—53no—
277C2×D3×D4—53no—
278C2×D3×D4—53no—
279C2×D3×D4—56no—
280C2×D3×D4—53no—
281C2×#235—53no—
282C2×#235—53no—
283C22×C4×D3—53no—
284C22×C4×D3—53no—
285C3×#127—53no—
286C3×#121—53no—
287C3×#121—53no—
288C3×C4×Q8—51no—
289C3×C4×D4—53no—
290Q8×Dic3C2×D511yescharacteristic, complemented
291#940—56no—
292#940—56no—
293#940—53no—
294#940C2×D513yescomplemented
295#939—56no—
296#939—56no—
297#938—53no—
298#938C2×D513yescomplemented
299D4×Dic3—53no—
300#930—53no—
301#930C2×D513yescomplemented
302C4×#67—53no—
303C4×#67C2×D513yescomplemented
304#895—53no—
305#895—53no—
306#893—53no—
307D3×C4⋊C4—53no—
308D3×C4⋊C4—51no—
309#887—53no—
310#884—56no—
311#884—56no—
312#67⋊C4—53no—
313#67⋊C4—53no—
314D3×C22⋊C4—53no—
315D3×C22⋊C4—53no—
316#874—53no—
317C4×D12—53no—
318C42×D3—53no—
319C4×Dic6—53no—
320C23×D5—33no—
321C23×D5—33no—
322C5×#41—24no—
323C5×#41—64no—
324C2×C5×Q8C22×D311yescharacteristic
325C2×C5×D4—33no—
326C2×C5×D4—36no—
327C2×C5×D4—33no—
328C2×C5×D4C22×D313yes—
329C22×C4×C5—33no—
330C22×C4×C5C22×D313yes—
331C2×C22⋊D5—36no—
332C2×C22⋊D5—36no—
333C2×C22⋊D5—33no—
334C2×C22⋊D5—36no—
335C2×C22⋊D5C22×D313yes—
336C2×C22⋊D5C22×D316yes—
337C22×Dic5—33no—
338C22×Dic5—33no—
339#713—24no—
340#713—64no—
341Q8×D5—38no—
342#711—612no—
343#711—612no—
344D4×D5—612no—
345D4×D5—612no—
346D4×D5—612no—
347D4×D5—1212no—
348#709—612no—
349#709—612no—
350C2×D20—33no—
351C2×D20—33no—
352C2×D20—36no—
353C2×D20C22×D313yes—
354C2×C4×D5—33no—
355C2×C4×D5—31no—
356C2×C4×D5—33no—
357C2×C4×D5—31no—
358C2×C4×D5—33no—
359C2×C4×D5—33no—
360C2×C4×D5—31no—
361C2×C4×D5—33no—
362C2×C4×D5—612no—
363C2×C4×D5—612no—
364C2×C4×D5C22×D313yes—
365C2×Dic10—33no—
366C5×C4⋊C4—31no—
367C5×C4⋊C4—33no—
368C5×C22⋊C4—33no—
369C5×C22⋊C4—33no—
370C42×C5—33no—
371C22⋊Dic5—33no—
372C22⋊Dic5C22×D313yes—
373#685—33no—
374#685—33no—
375#685—33no—
376#685C22×D313yes—
377C4⋊Dic5—31no—
378C4⋊Dic5C22×D313yes—
379#683—31no—
380#683—36no—
381#683C22×D311yescharacteristic
382C4×Dic5—33no—
383C4×Dic5—33no—
384C4×Dic5C22×D313yes—
385C22×#41—151no—
386C22×#41—151no—
387#550—31no—
388#550—51no—
389#550—153no—
390#550—153no—
391#550—151no—
392#550—151no—
393#550—153no—
394#550—153no—
395C2×#127—153no—
396C2×#121—153no—
397C2×#121—153no—
398C2×C4×Q8—151no—
399C2×C4×D4—153no—
400C22×C3×C5—23no—
401C22×C3×C5—23no—
402C22×C3×C5—23no—
403C22×C3×C5C2511yescharacteristic
404C2×D15—23no—
405C2×D15—23no—
406C2×D15—23no—
407C2×D15—412no—
408C2×D15C22×D412yes—
409C2×D15C2×#4112yes—
410C2×D15H(5,𝔽2)12yes—
411C2×C5×D3—23no—
412C2×C5×D3—23no—
413C2×C5×D3—23no—
414C2×C3×D5—23no—
415C2×C3×D5—23no—
416C2×C3×D5—23no—
417D3×D5—412no—
418C3×C4×C5—21no—
419C3×C4×C5C22×D416yes—
420Dic15—21no—
421Dic15C22×D416yes—
422C3×Dic5—21no—
423C3×Dic5—23no—
424C3×Dic5C2×#4112yescomplemented
425C5×Dic3—21no—
426C5×Dic3—23no—
427C5×Dic3C2×#4112yescomplemented
428C23×D3—53no—
429C23×D3—53no—
430C3×#41—24no—
431C3×#41—104no—
432C2×C3×Q8C22×D511yescharacteristic
433C2×C3×D4—53no—
434C2×C3×D4—56no—
435C2×C3×D4—53no—
436C2×C3×D4C22×D513yes—
437C22×C3×C4—53no—
438C22×C3×C4C22×D513yes—
439C2×#67—56no—
440C2×#67—56no—
441C2×#67—53no—
442C2×#67—56no—
443C2×#67C22×D513yes—
444C2×#67C22×D516yes—
445C22×Dic3—53no—
446C22×Dic3—53no—
447#239—24no—
448#239—104no—
449D3×Q8—58no—
450#237—1012no—
451#237—1012no—
452D3×D4—1012no—
453D3×D4—1012no—
454D3×D4—1012no—
455D3×D4—2012no—
456#235—1012no—
457#235—1012no—
458C2×D12—53no—
459C2×D12—53no—
460C2×D12—56no—
461C2×D12C22×D513yes—
462C2×C4×D3—53no—
463C2×C4×D3—51no—
464C2×C4×D3—53no—
465C2×C4×D3—53no—
466C2×C4×D3—51no—
467C2×C4×D3—53no—
468C2×C4×D3—53no—
469C2×C4×D3—51no—
470C2×C4×D3—1012no—
471C2×C4×D3—1012no—
472C2×C4×D3C22×D513yes—
473C2×Dic6—53no—
474C3×C4⋊C4—51no—
475C3×C4⋊C4—53no—
476C3×C22⋊C4—53no—
477C3×C22⋊C4—53no—
478C3×C42—53no—
479#217—53no—
480#217C22×D513yes—
481(C2×D3)⋊C4—53no—
482(C2×D3)⋊C4—53no—
483(C2×D3)⋊C4—53no—
484(C2×D3)⋊C4C22×D513yes—
485C4⋊Dic3—51no—
486C4⋊Dic3C22×D513yes—
487Dic3⋊C4—56no—
488Dic3⋊C4—51no—
489Dic3⋊C4C22×D511yescharacteristic
490C4×Dic3—53no—
491C4×Dic3—53no—
492C4×Dic3C22×D513yes—
493C23×C5—33no—
494C23×C5C23×D313yes—
495C22×D5—31no—
496C22×D5—33no—
497C22×D5—66no—
498C22×D5—66no—
499C22×D5—66no—
500C22×D5—66no—
501C22×D5—66no—
502C22×D5—66no—
503C22×D5C23×D313yes—
504C5×Q8D3×D414yescomplemented
505C5×D4—26no—
506C5×D4—66no—
507C5×D4—66no—
508C5×D4—126no—
509C2×C4×C5—26no—
510C2×C4×C5—31no—
511C2×C4×C5—33no—
512C2×C4×C5—31no—
513C2×C4×C5—66no—
514C2×C4×C5C23×D311yescharacteristic
515C2×C4×C5C23×D313yes—
516C22⋊D5—26no—
517C22⋊D5—46no—
518C22⋊D5—612no—
519C22⋊D5—612no—
520C22⋊D5—66no—
521C22⋊D5—126no—
522C2×Dic5—33no—
523C2×Dic5—31no—
524C2×Dic5—66no—
525C2×Dic5—66no—
526C2×Dic5C23×D313yes—
527C2×Dic5C23×D311yescharacteristic
528C2×Dic5C23×D311yescharacteristic
529D20—26no—
530D20—66no—
531D20—66no—
532D20—126no—
533C4×D5—26no—
534C4×D5—312no—
535C4×D5—34no—
536C4×D5—62no—
537C4×D5—66no—
538C4×D5—66no—
539C4×D5—66no—
540C4×D5—62no—
541C4×D5—66no—
542Dic10—312no—
543C2×#41—31no—
544C2×#41—51no—
545C2×#41—153no—
546C2×#41—153no—
547C2×#41—151no—
548C2×#41—153no—
549C2×#41—153no—
550C2×#41—308no—
551C2×#41—308no—
552C2×#41D3×D511yescharacteristic, complemented
553C22×Q8—151no—
554C22×D4—153no—
555C22×D4—153no—
556C22×D4—156no—
557C22×D4—153no—
558C23×C4—153no—
559C23×C4—153no—
560#127—33no—
561#127—53no—
562#127—153no—
563#127—153no—
564#127—156no—
565#127—156no—
566#121—33no—
567#121—33no—
568#121—53no—
569#121—53no—
570#121—156no—
571#121—156no—
572#121—156no—
573#121—153no—
574#121—153no—
575#121—153no—
576#121—153no—
577#121—156no—
578C4×Q8—31no—
579C4×Q8—51no—
580C4×Q8—153no—
581C4×Q8—153no—
582C4×D4—33no—
583C4×D4—53no—
584C4×D4—153no—
585C4×D4—153no—
586C4×D4—153no—
587C4×D4—153no—
588C4×D4—153no—
589C4×D4—153no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—153no—
592C2×C22⋊C4—153no—
593C2×C22⋊C4—153no—
594C2×C42—153no—
595C2×C3×C5—43no—
596C2×C3×C5C23×D411yescharacteristic
597C2×C3×C5C22×#4111yescharacteristic
598C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
599D15—43no—
600D15#55014yescomplemented
601C3×D5—43no—
602C5×D3—43no—
603C23×C3—53no—
604C23×C3C23×D513yes—
605C22×D3—51no—
606C22×D3—53no—
607C22×D3—106no—
608C22×D3—106no—
609C22×D3—106no—
610C22×D3—106no—
611C22×D3—106no—
612C22×D3—106no—
613C22×D3C23×D513yes—
614C3×Q8D4×D514yescomplemented
615C3×D4—26no—
616C3×D4—106no—
617C3×D4—106no—
618C3×D4—206no—
619C2×C3×C4—26no—
620C2×C3×C4—51no—
621C2×C3×C4—53no—
622C2×C3×C4—51no—
623C2×C3×C4—106no—
624C2×C3×C4C23×D511yescharacteristic
625C2×C3×C4C23×D513yes—
626#67—26no—
627#67—46no—
628#67—1012no—
629#67—1012no—
630#67—106no—
631#67—206no—
632C2×Dic3—53no—
633C2×Dic3—51no—
634C2×Dic3—106no—
635C2×Dic3—106no—
636C2×Dic3C23×D513yes—
637C2×Dic3C23×D511yescharacteristic
638C2×Dic3C23×D511yescharacteristic
639D12—26no—
640D12—106no—
641D12—106no—
642D12—206no—
643C4×D3—26no—
644C4×D3—512no—
645C4×D3—54no—
646C4×D3—102no—
647C4×D3—106no—
648C4×D3—106no—
649C4×D3—106no—
650C4×D3—102no—
651C4×D3—106no—
652Dic6—512no—
653C22×C5—23no—
654C22×C5—23no—
655C22×C5—23no—
656C22×C5—63no—
657C22×C5—63no—
658C22×C5—63no—
659C22×C5C24×D311yescharacteristic
660C2×D5—23no—
661C2×D5—23no—
662C2×D5—23no—
663C2×D5—32no—
664C2×D5—32no—
665C2×D5—32no—
666C2×D5—63no—
667C2×D5—63no—
668C2×D5—63no—
669C2×D5—1212no—
670C2×D5—1212no—
671C4×C5—21no—
672C4×C5—32no—
673C4×C5—61no—
674C4×C5—63no—
675C4×C5C2×D3×D416yes—
676Dic5—21no—
677Dic5—23no—
678Dic5—36no—
679Dic5—61no—
680Dic5D3×#4112yescomplemented
681C24—153no—
682C24—153no—
683#41—24no—
684#41—64no—
685#41—104no—
686#41—3012no—
687#41—3012no—
688#41—3012no—
689#41—3012no—
690#41—304no—
691C2×Q8—158no—
692C2×Q8—153no—
693C2×Q8C2×D3×D511yescharacteristic
694C2×D4—33no—
695C2×D4—36no—
696C2×D4—33no—
697C2×D4—53no—
698C2×D4—56no—
699C2×D4—53no—
700C2×D4—153no—
701C2×D4—156no—
702C2×D4—153no—
703C2×D4—156no—
704C2×D4—156no—
705C2×D4—156no—
706C2×D4—153no—
707C2×D4—3012no—
708C2×D4—3012no—
709C2×D4—3012no—
710C2×D4—6012no—
711C2×D4C2×D3×D513yes—
712C22×C4—33no—
713C22×C4—53no—
714C22×C4—151no—
715C22×C4—153no—
716C22×C4—151no—
717C22×C4—153no—
718C22×C4—153no—
719C22×C4—153no—
720C22×C4—153no—
721C22×C4—151no—
722C22×C4—153no—
723C22×C4—153no—
724C22×C4—3012no—
725C22×C4—3012no—
726C22×C4C2×D3×D513yes—
727C4⋊C4—31no—
728C4⋊C4—33no—
729C4⋊C4—51no—
730C4⋊C4—53no—
731C4⋊C4—151no—
732C4⋊C4—151no—
733C4⋊C4—156no—
734C22⋊C4—33no—
735C22⋊C4—33no—
736C22⋊C4—53no—
737C22⋊C4—53no—
738C22⋊C4—153no—
739C22⋊C4—153no—
740C22⋊C4—153no—
741C22⋊C4—153no—
742C42—33no—
743C42—53no—
744C42—153no—
745C42—153no—
746C3×C5C2×#55011yescharacteristic, complemented, Hall
747C22×C3—23no—
748C22×C3—23no—
749C22×C3—23no—
750C22×C3—103no—
751C22×C3—103no—
752C22×C3—103no—
753C22×C3C24×D511yescharacteristic
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—52no—
758C2×D3—52no—
759C2×D3—52no—
760C2×D3—103no—
761C2×D3—103no—
762C2×D3—103no—
763C2×D3—2012no—
764C2×D3—2012no—
765C3×C4—21no—
766C3×C4—52no—
767C3×C4—101no—
768C3×C4—103no—
769C3×C4C2×D4×D516yes—
770Dic3—21no—
771Dic3—23no—
772Dic3—56no—
773Dic3—101no—
774Dic3D5×#4112yescomplemented
775C2×C5—43no—
776C2×C5—123no—
777C2×C5C22×D3×D411yescharacteristic
778C2×C5C2×D3×#4111yescharacteristic
779C2×C5D3×H(5,𝔽2)11yescharacteristic
780D5—34no—
781D5—43no—
782D5—123no—
783C23—33no—
784C23—53no—
785C23—151no—
786C23—153no—
787C23—306no—
788C23—306no—
789C23—306no—
790C23—306no—
791C23—306no—
792C23—306no—
793C23C22×D3×D513yes—
794Q8—1512no—
795Q8#679014yescomplemented
796D4—26no—
797D4—66no—
798D4—66no—
799D4—106no—
800D4—106no—
801D4—126no—
802D4—206no—
803D4—306no—
804D4—306no—
805D4—3012no—
806D4—3012no—
807D4—306no—
808D4—606no—
809D4—606no—
810C2×C4—26no—
811C2×C4—31no—
812C2×C4—33no—
813C2×C4—31no—
814C2×C4—51no—
815C2×C4—53no—
816C2×C4—51no—
817C2×C4—66no—
818C2×C4—106no—
819C2×C4—154no—
820C2×C4—153no—
821C2×C4—1512no—
822C2×C4—151no—
823C2×C4—306no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—306no—
827C2×C4—306no—
828C2×C4—306no—
829C2×C4—306no—
830C2×C4—306no—
831C2×C4C22×D3×D511yescharacteristic
832C2×C4C22×D3×D513yes—
833C2×C3—43no—
834C2×C3—203no—
835C2×C3C22×D4×D511yescharacteristic
836C2×C3C2×D5×#4111yescharacteristic
837C2×C3D5×H(5,𝔽2)11yescharacteristic
838D3—43no—
839D3—54no—
840D3—203no—
841C5D3×#55011yescharacteristic, complemented, Sylow
842C22—23no—
843C22—23no—
844C22—23no—
845C22—63no—
846C22—63no—
847C22—63no—
848C22—103no—
849C22—103no—
850C22—103no—
851C22—152no—
852C22—152no—
853C22—152no—
854C22—303no—
855C22—303no—
856C22—303no—
857C22—6012no—
858C22—6012no—
859C22C23×D3×D511yescharacteristic
860C4—21no—
861C4—32no—
862C4—52no—
863C4—61no—
864C4—63no—
865C4—101no—
866C4—103no—
867C4—156no—
868C4—301no—
869C4C2×#679016yes—
870C3D5×#55011yescharacteristic, complemented, Sylow
871C2—43no—
872C2—123no—
873C2—154no—
874C2—203no—
875C2—603no—
876C2D3×D5×#4111yescharacteristic
877C2#1175705411yescharacteristic
878C2C22×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#550
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C2×#92034C2semidirect
3. C5×#5834C2semidirect
4. C3×#66168C2semidirect
5. #11755251C2semidirect
6. #11755245C2semidirect
7. Q8×#1200C2semidirect
8. #11755052C2semidirect
9. #11755026C2semidirect
10. #11754956C2semidirect
11. #11754819C2semidirect
12. #11754670C2semidirect
13. C4×#6790C2semidirect
14. #11754557C2semidirect
15. #11754370C2semidirect
17. C2×C3×C5×#41C22semidirect
19. C2×#6821C22semidirect
21. C2×#6819C22semidirect
23. C2×#6817C22semidirect
25. C2×C5×#239C22semidirect
26. C2×C3×#713C22semidirect
32. C2×#6772C22semidirect
33. C2×#6765C22semidirect
34. C5×Q8×Dic3C22semidirect
35. C5×#940C22semidirect
36. C5×#938C22semidirect
37. C5×#930C22semidirect
38. C4×C5×#67C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4086C22semidirect
41. C3×#4084C22semidirect
42. C3×#4076C22semidirect
43. C3×C4×C22⋊D5C22semidirect
44. #91571C22semidirect
45. #91567C22semidirect
46. #91567C22semidirect
48. #67⋊Dic5C22semidirect
49. #91559C22semidirect
50. #91558C22semidirect
51. #91550C22semidirect
53. #91466C22semidirect
54. #91465C22semidirect
55. #91461C22semidirect
56. #91460C22semidirect
57. #91458C22semidirect
58. #91451C22semidirect
59. #91450C22semidirect
60. C4×#1203C22semidirect
61. C4×#1202C22semidirect
63. #91406C22semidirect
66. #91396C22semidirect
67. #91340C22semidirect
68. #91333C22semidirect
74. #66168D3semidirect
94. Q8×D15D4semidirect
154. #5834D5semidirect
166. C2×C5×#41C2×D3semidirect
170. C2×#713C2×D3semidirect
187. Q8×Dic5C2×D3semidirect
191. #4086C2×D3semidirect
195. #4084C2×D3semidirect
198. #4076C2×D3semidirect
200. C4×C22⋊D5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
243. Dic30C2×D4semidirect
265. #1200#41semidirect
269. C2×C3×#41C2×D5semidirect
273. C2×#239C2×D5semidirect
290. Q8×Dic3C2×D5semidirect
294. #940C2×D5semidirect
298. #938C2×D5semidirect
301. #930C2×D5semidirect
303. C4×#67C2×D5semidirect
424. C3×Dic5C2×#41semidirect
427. C5×Dic3C2×#41semidirect
504. C5×Q8D3×D4semidirect
552. C2×#41D3×D5semidirect
600. D15#550semidirect
614. C3×Q8D4×D5semidirect
680. Dic5D3×#41semidirect
746. C3×C5C2×#550semidirect
774. Dic3D5×#41semidirect
795. Q8#6790semidirect
841. C5D3×#550semidirect
870. C3D5×#550semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C2×#920342
C5×#58342
C3×#661682
#117552512
#117552452
Q8×#12002
#117550522
#117550262
#117549562
#117548192
#117546702
C4×#67902
#117545572
#117543702
D5×#5503
D3×#5505