Finite Group Databasebeta

← #14479252

Subgroups — #14479252

Order 1920.

3320 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92035C211yesmaximal, characteristic
2#11756333C211yesmaximal, characteristic, complemented
3C4×C5×#239C211yesmaximal, characteristic, complemented
4C3×#65908C211yesmaximal, characteristic, complemented
5#11755220C211yesmaximal, characteristic, complemented
6Dic3×#713C211yesmaximal, characteristic, complemented
7#11755200C211yesmaximal, characteristic, complemented
8#11753840C213yesmaximal, complemented
9#11753839C213yesmaximal, complemented
10D5×#893C213yesmaximal, complemented
11#11753668C213yesmaximal, complemented
12#11752729C213yesmaximal, complemented
13C4×D3×D20C213yesmaximal, complemented
14#11752725C213yesmaximal, complemented
15#11752666C213yesmaximal, complemented
16C4×#4149—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20#92035C4116yescomplemented
21C2×#6777C2213yes—
22C2×D3×D20C2213yes—
23C2×D5×D12C2213yes—
24C2×C4×D3×D5C2216yescomplemented
25C2×#6771C2213yes—
26C3×C4×C5×Q8C2211yescharacteristic, complemented
27Q8×Dic15C2211yescharacteristic, complemented
28#91782C2213yescomplemented
29C4⋊C4×D15C2213yescomplemented
30C4×D60C2213yescomplemented
31#91761C2213yescomplemented
32C5×Q8×Dic3C2211yescharacteristic, complemented
33C5×#893C2213yescomplemented
34C5×#892C2213yescomplemented
35C4×C5×D12C2213yescomplemented
36C42×C5×D3C2213yescomplemented
37C3×Q8×Dic5C2211yescharacteristic, complemented
38C3×#4039C2213yescomplemented
39C3×D5×C4⋊C4C2213yescomplemented
40C3×C4×D20C2213yescomplemented
41C3×#4018C2213yescomplemented
42#91473C2216yescomplemented
43D3×#685C2216yescomplemented
44D5×(C2×D3)⋊C4C2216yescomplemented
45#91446C2213yescomplemented
46#91446C2213yescomplemented
47C4×#1202C2216yescomplemented
48#91441C2213yescomplemented
49#91441C2213yescomplemented
50#91440C2216yescomplemented
51#91435C2213yescomplemented
52#91434C2213yescomplemented
53#91428C2213yescomplemented
54D3×C4⋊Dic5C2213yescomplemented
55Dic3×D20C2213yescomplemented
56#91418C2213yescomplemented
57Dic5×D12C2213yescomplemented
58#91406C2216yescomplemented
59C4×#1200C2213yescomplemented
60#91395C2213yescomplemented
61#91395C2213yescomplemented
62C4×D5×Dic3C2213yescomplemented
63#91371C2213yescomplemented
64#91358C2213yescomplemented
65#91347C2213yescomplemented
66#91324C2213yescomplemented
67#91324C2211yescharacteristic, complemented
68#85886—51nomaximal, Hall
69C2×#4149—31no—
70C4×C5×#41—31no—
71#66161—31no—
72#65908—31no—
73#65908D311yescharacteristic, complemented
74C4×#713—31no—
75C4×#713—31no—
76#65879—33no—
77#65879—33no—
78C4×D4×D5—33no—
79C4×D4×D5—33no—
80#65857—33no—
81#65855—33no—
82C4×#709—33no—
83C2×C4×D20—33no—
84C22×D3×D5C2316yes—
85C2×C3×C5×Q8C2311yescharacteristic
86#6821C2×C418yescomplemented
87C2×D60C2313yes—
88C2×C4×D15C2316yes—
89C2×C4×D15C2313yes—
90C5×#239C2×C418yescomplemented
91C2×C5×D12C2313yes—
92C2×C4×C5×D3C2313yes—
93C2×C4×C5×D3C2313yes—
94C2×C4×C5×D3C2313yes—
95C3×#713C2×C418yescomplemented
96C2×C3×D20C2313yes—
97C2×C3×C4×D5C2316yes—
98C2×C3×C4×D5C2313yes—
99C2×#1204C2311yescharacteristic
100C2×#1203C2313yes—
101C2×#1202C2313yes—
102C2×#1201C2313yes—
103C2×#1200C2313yes—
104C2×#1200C2313yes—
105C2×D3×Dic5C2316yes—
106C2×D5×Dic3C2313yes—
107C2×D5×Dic3C2313yes—
108#6777C2×C4124yescomplemented
109D3×D20C2×C4124yescomplemented
110D5×D12C2×C4124yescomplemented
111C4×D3×D5—412no—
112#6771C2×C4124yescomplemented
113C3×C5×C4⋊C4C2313yes—
114C3×C42×C5C2313yes—
115#6714C2313yes—
116#6714C2313yes—
117C4⋊Dic15C2313yes—
118#6712C2313yes—
119#6712C2311yescharacteristic
120C4×Dic15C2313yes—
121C5×(C2×D3)⋊C4C2316yes—
122C5×C4⋊Dic3C2313yes—
123C4×C5×Dic3C2311yescharacteristic
124C4×C5×Dic3C2313yes—
125C4×C5×Dic3C2313yes—
126C3×#685C2313yes—
127C3×#685C2313yes—
128C3×C4⋊Dic5C2313yes—
129C3×#683C2313yes—
130C3×#683C2311yescharacteristic
131C3×C4×Dic5C2313yes—
132Dic3⋊Dic5C2311yescharacteristic
133Dic3⋊Dic5C2313yes—
134#6667C2316yes—
135(C2×D3)⋊Dic5C2313yes—
136(C2×D3)⋊Dic5C2313yes—
137#6665C2316yes—
138Dic3×Dic5C2311yescharacteristic
139Dic3×Dic5C2313yes—
140Dic3×Dic5C2313yes—
141Dic3×Dic5C2311yescharacteristic
142C2×#1009—51no—
143C3×#520—51no—
144Dic3×#41—51no—
145#5574—51no—
146#5574—51no—
147C4×#239—51no—
148C4×#239D511yescharacteristic, complemented
149#5545—53no—
150#5545—53no—
151C4×D3×D4—53no—
152C4×D3×D4—53no—
153#5522—53no—
154#5521—53no—
155#5504—53no—
156C2×#893—53no—
157C2×C5×#41—31no—
158#4149—316no—
159C2×#713—31no—
160C2×#713C2×D311yescharacteristic
161C2×D4×D5—33no—
162C2×D4×D5—33no—
163C2×#709—33no—
164C22×D20—33no—
165C22×C4×D5—36no—
166C4×C5×Q8—31no—
167C4×C5×Q8C2×D311yescharacteristic, complemented
168C4×C5×D4—33no—
169C4×C5×D4—33no—
170C5×#117—33no—
171C2×C42×C5—33no—
172Q8×Dic5—31no—
173Q8×Dic5C2×D311yescharacteristic, complemented
174D4×Dic5—33no—
175D4×Dic5—33no—
176C4×C22⋊D5—33no—
177C4×C22⋊D5—33no—
178C4×C22⋊D5—33no—
179C4×C22⋊D5—33no—
180C2×#685—36no—
181#4072—33no—
182C2×C4⋊Dic5—33no—
183#4039—33no—
184#4039—33no—
185#4039—33no—
186#4039C2×D313yescomplemented
187#4038—33no—
188#4038—33no—
189D5×C4⋊C4—33no—
190D5×C4⋊C4C2×D313yescomplemented
191#4027—36no—
192#4027—36no—
193D5×C22⋊C4—36no—
194D5×C22⋊C4—36no—
195C4×D20—33no—
196C4×D20—36no—
197C4×D20—33no—
198C4×D20—33no—
199C4×D20—33no—
200C4×D20—33no—
201C4×D20C2×D313yescomplemented
202#4018—33no—
203#4018C2×D313yescomplemented
204C42×D5—33no—
205C42×D5—33no—
206C4×Dic10—31no—
207C4×Dic10—33no—
208C4×H(5,𝔽2)—151noSylow
209C22×D15C2413yes—
210C22×C5×D3C2413yes—
211C22×C3×D5C2413yes—
212C2×D3×D5—46no—
213C2×D3×D5—46no—
214C2×D3×D5C22×C4124yescomplemented
215C3×C5×Q8C22×C414yescomplemented
216C2×C3×C4×C5C2411yescharacteristic
217C2×C3×C4×C5C2413yes—
218C2×C3×C4×C5C2413yes—
219C2×Dic15C2413yes—
220C2×Dic15C2411yescharacteristic
221C2×Dic15C2411yescharacteristic
222D60C22×C4112yescomplemented
223C4×D15—46no—
224C4×D15C22×C4112yescomplemented
225C2×C5×Dic3C2413yes—
226C2×C5×Dic3C2411yescharacteristic
227C2×C5×Dic3C2411yescharacteristic
228C5×D12C22×C4112yescomplemented
229C4×C5×D3—26no—
230C4×C5×D3—43no—
231C4×C5×D3C22×C4112yescomplemented
232C2×C3×Dic5C2411yescharacteristic
233C2×C3×Dic5C2413yes—
234C2×C3×Dic5C2411yescharacteristic
235C3×D20C22×C4112yescomplemented
236C3×C4×D5—46no—
237C3×C4×D5C22×C4112yescomplemented
238#1204C22×C414yescomplemented
239#1203C22×C4112yescomplemented
240#1202C22×C4112yescomplemented
241#1201C22×C4112yescomplemented
242#1200—26no—
243#1200—43no—
244D3×Dic5—46no—
245D5×Dic3—26no—
246D5×Dic3—43no—
247C2×C3×#41—51no—
248#1009—516no—
249C2×#239—51no—
250C2×#239C2×D511yescharacteristic
251C2×D3×D4—53no—
252C2×D3×D4—53no—
253C2×#235—53no—
254C22×D12—53no—
255C22×C4×D3—56no—
256C3×C4×Q8—51no—
257C3×C4×Q8C2×D511yescharacteristic, complemented
258C3×C4×D4—53no—
259C3×C4×D4—53no—
260C3×#117—53no—
261C2×C3×C4⋊C4—53no—
262Q8×Dic3—51no—
263Q8×Dic3C2×D511yescharacteristic, complemented
264D4×Dic3—53no—
265D4×Dic3—53no—
266C4×#67—56no—
267C4×#67—56no—
268C2×(C2×D3)⋊C4—56no—
269#926—53no—
270C2×C4×Dic3—53no—
271#893—53no—
272#893—53no—
273#893—53no—
274#893—53no—
275#893—56no—
276#893—53no—
277#893C2×D513yescomplemented
278#892—53no—
279#892C2×D513yescomplemented
280D3×C4⋊C4—53no—
281D3×C4⋊C4—53no—
282#887—53no—
283#887—51no—
284#67⋊C4—53no—
285#67⋊C4—53no—
286#67⋊C4—53no—
287#67⋊C4—53no—
288D3×C22⋊C4—56no—
289D3×C22⋊C4—56no—
290C4×D12—53no—
291C4×D12—53no—
292C4×D12—53no—
293C4×D12C2×D513yescomplemented
294#872—53no—
295#872—53no—
296C42×D3—53no—
297C42×D3C2×D513yescomplemented
298C23×D5—36no—
299C5×#41—38no—
300C2×C5×Q8C22×D311yescharacteristic
301C2×C5×D4—33no—
302C22×C4×C5—33no—
303C22×C4×C5—33no—
304C22×C4×C5—33no—
305C2×C22⋊D5—33no—
306C2×C22⋊D5—33no—
307C22×Dic5—36no—
308#713—38no—
309#713C4×D318yescomplemented
310D4×D5—324no—
311D4×D5—324no—
312#709—324no—
313C2×D20—33no—
314C2×D20—33no—
315C2×D20—324no—
316C2×D20C22×D313yes—
317C2×C4×D5—33no—
318C2×C4×D5—33no—
319C2×C4×D5—33no—
320C2×C4×D5—33no—
321C2×C4×D5—36no—
322C2×C4×D5—33no—
323C2×C4×D5—1212no—
324C2×C4×D5C22×D316yes—
325C2×C4×D5C22×D313yes—
326C2×Dic10—31no—
327C5×C4⋊C4—33no—
328C5×C4⋊C4C22×D313yes—
329C5×C22⋊C4—36no—
330C42×C5—31no—
331C42×C5—33no—
332C42×C5—33no—
333C42×C5C22×D313yes—
334C22⋊Dic5—33no—
335C22⋊Dic5—33no—
336#685—36no—
337#685—33no—
338#685—33no—
339#685—36no—
340#685C22×D313yes—
341#685C22×D313yes—
342C4⋊Dic5—33no—
343C4⋊Dic5—33no—
344C4⋊Dic5—31no—
345C4⋊Dic5C22×D313yes—
346#683—31no—
347#683—33no—
348#683C22×D311yescharacteristic
349#683C22×D313yes—
350C4×Dic5—33no—
351C4×Dic5—31no—
352C4×Dic5—31no—
353C4×Dic5—33no—
354C4×Dic5—33no—
355C4×Dic5C22×D313yes—
356C2×H(5,𝔽2)—151no—
357#520—51no—
358#520—153no—
359#520—151no—
360#520—151no—
361#518—153no—
362#518—153no—
363#518—153no—
364C4×#41—31no—
365C4×#41—153no—
366C4×#41—151no—
367C4×#41—151no—
368C2×C4×D4—153no—
369C2×C4×D4—153no—
370C2×C4×D4—153no—
371C22×C3×C5C2511yescharacteristic
372C2×D15—23no—
373C2×D15—23no—
374C2×D15C23×C416yes—
375C2×C5×D3—23no—
376C2×C5×D3—23no—
377C2×C5×D3C23×C416yes—
378C2×C3×D5—23no—
379C2×C3×D5—23no—
380C2×C3×D5C23×C416yes—
381D3×D5—424no—
382C3×C4×C5—23no—
383C3×C4×C5—21no—
384C3×C4×C5C23×C416yes—
385Dic15—23no—
386Dic15—21no—
387Dic15C23×C412yes—
388C3×Dic5—23no—
389C3×Dic5—21no—
390C3×Dic5C23×C412yes—
391C5×Dic3—23no—
392C5×Dic3C23×C412yes—
393C5×Dic3H(5,𝔽2)12yescomplemented
394C23×D3—56no—
395C3×#41—58no—
396C2×C3×Q8C22×D511yescharacteristic
397C2×C3×D4—53no—
398C22×C3×C4—53no—
399C22×C3×C4—56no—
400C2×#67—53no—
401C2×#67—53no—
402C22×Dic3—53no—
403C22×Dic3—53no—
404#239—58no—
405#239C4×D518yescomplemented
406D3×D4—524no—
407D3×D4—524no—
408#235—524no—
409C2×D12—53no—
410C2×D12—53no—
411C2×D12—524no—
412C2×D12C22×D513yes—
413C2×C4×D3—53no—
414C2×C4×D3—53no—
415C2×C4×D3—56no—
416C2×C4×D3—56no—
417C2×C4×D3—53no—
418C2×C4×D3—2012no—
419C2×C4×D3C22×D513yes—
420C2×C4×D3C22×D513yes—
421C2×C4×D3C22×D513yes—
422C2×Dic6—51no—
423C3×C4⋊C4—53no—
424C3×C4⋊C4—51no—
425C3×C4⋊C4—53no—
426C3×C4⋊C4C22×D513yes—
427C3×C22⋊C4—53no—
428C3×C22⋊C4—53no—
429C3×C42—53no—
430C3×C42C22×D513yes—
431#217—56no—
432(C2×D3)⋊C4—53no—
433(C2×D3)⋊C4—53no—
434(C2×D3)⋊C4—53no—
435(C2×D3)⋊C4—53no—
436(C2×D3)⋊C4—56no—
437(C2×D3)⋊C4C22×D516yes—
438C4⋊Dic3—53no—
439C4⋊Dic3C22×D513yes—
440Dic3⋊C4—51no—
441Dic3⋊C4—53no—
442Dic3⋊C4—51no—
443Dic3⋊C4—53no—
444C4×Dic3—53no—
445C4×Dic3—51no—
446C4×Dic3—53no—
447C4×Dic3—51no—
448C4×Dic3—53no—
449C4×Dic3C22×D513yes—
450C4×Dic3C22×D511yescharacteristic
451C4×Dic3C22×D513yes—
452C23×C5—33no—
453C22×D5—33no—
454C22×D5—324no—
455C22×D5—126no—
456C22×D5—126no—
457C22×D5C23×D313yes—
458C5×Q8C2×C4×D314yescomplemented
459C5×D4—312no—
460C2×C4×C5—31no—
461C2×C4×C5—31no—
462C2×C4×C5—312no—
463C2×C4×C5—33no—
464C2×C4×C5—66no—
465C2×C4×C5—123no—
466C2×C4×C5C23×D311yescharacteristic
467C2×C4×C5C23×D313yes—
468C2×C4×C5C23×D313yes—
469C22⋊D5—312no—
470C22⋊D5—312no—
471C2×Dic5—31no—
472C2×Dic5—31no—
473C2×Dic5—33no—
474C2×Dic5—126no—
475C2×Dic5C23×D311yescharacteristic
476C2×Dic5C23×D313yes—
477C2×Dic5C23×D311yescharacteristic
478D20—312no—
479D20—312no—
480D20C2×C4×D3112yescomplemented
481C4×D5—312no—
482C4×D5—46no—
483C4×D5—66no—
484C4×D5—66no—
485C4×D5—123no—
486C4×D5—126no—
487C4×D5—123no—
488C4×D5C2×C4×D3112yescomplemented
489Dic10—34no—
490H(5,𝔽2)—1516no—
491C2×#41—31no—
492C2×#41—51no—
493C2×#41—153no—
494C2×#41—151no—
495C22×D4—153no—
496C22×D4—153no—
497C22×D4—153no—
498C23×C4—156no—
499C4×Q8—31no—
500C4×Q8—51no—
501C4×Q8—151no—
502C4×Q8—153no—
503C4×Q8—151no—
504C4×Q8D3×D511yescharacteristic, complemented
505C4×D4—33no—
506C4×D4—33no—
507C4×D4—53no—
508C4×D4—53no—
509C4×D4—153no—
510C4×D4—153no—
511C4×D4—153no—
512C4×D4—156no—
513C4×D4—153no—
514C4×D4—153no—
515C4×D4—153no—
516C4×D4—156no—
517C4×D4—156no—
518C4×D4—153no—
519C4×D4—153no—
520C4×D4—153no—
521C4×D4—153no—
522C4×D4—153no—
523C4×D4—153no—
524C4×D4—153no—
525C4×D4—153no—
526#117—33no—
527#117—53no—
528#117—153no—
529#117—153no—
530#117—153no—
531#117—153no—
532C2×C4⋊C4—53no—
533C2×C4⋊C4—153no—
534C2×C4⋊C4—153no—
535C2×C22⋊C4—156no—
536C2×C22⋊C4—156no—
537C2×C22⋊C4—156no—
538C2×C42—33no—
539C2×C42—153no—
540C2×C42—153no—
541C2×C3×C5C24×C411yescharacteristic
542C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
543C2×C3×C5#58511yescharacteristic
544D15—26no—
545C3×D5—26no—
546C5×D3—26no—
547C23×C3—53no—
548C22×D3—53no—
549C22×D3—524no—
550C22×D3—206no—
551C22×D3—206no—
552C22×D3C23×D513yes—
553C3×Q8C2×C4×D514yescomplemented
554C3×D4—512no—
555C2×C3×C4—51no—
556C2×C3×C4—512no—
557C2×C3×C4—51no—
558C2×C3×C4—53no—
559C2×C3×C4—206no—
560C2×C3×C4C23×D511yescharacteristic
561C2×C3×C4C23×D513yes—
562C2×C3×C4C23×D513yes—
563#67—512no—
564#67—512no—
565C2×Dic3—51no—
566C2×Dic3—51no—
567C2×Dic3—53no—
568C2×Dic3—106no—
569C2×Dic3—203no—
570C2×Dic3C23×D513yes—
571C2×Dic3C23×D511yescharacteristic
572C2×Dic3C23×D511yescharacteristic
573D12—512no—
574D12—512no—
575D12C2×C4×D5112yescomplemented
576C4×D3—26no—
577C4×D3—43no—
578C4×D3—512no—
579C4×D3—106no—
580C4×D3—203no—
581C4×D3—206no—
582C4×D3—206no—
583C4×D3C2×C4×D5112yescomplemented
584Dic6—54no—
585C22×C5—36no—
586C22×C5—63no—
587C22×C5—63no—
588C22×C5C24×D311yescharacteristic
589C2×D5—23no—
590C2×D5—23no—
591C2×D5—36no—
592C2×D5—63no—
593C2×D5—63no—
594C2×D5—1224no—
595C2×D5C22×C4×D316yes—
596C4×C5—23no—
597C4×C5—21no—
598C4×C5—32no—
599C4×C5—32no—
600C4×C5—63no—
601C4×C5C22×C4×D316yes—
602Dic5—23no—
603Dic5—21no—
604Dic5—32no—
605Dic5—63no—
606Dic5—61no—
607Dic5C22×C4×D312yes—
608C24—156no—
609#41—38no—
610#41—58no—
611#41—1524no—
612#41—158no—
613C2×Q8—151no—
614C2×Q8C2×D3×D511yescharacteristic
615C2×D4—33no—
616C2×D4—53no—
617C2×D4—1524no—
618C2×D4—153no—
619C2×D4—1524no—
620C2×D4—153no—
621C2×D4—1524no—
622C2×D4—153no—
623C2×D4—153no—
624C22×C4—33no—
625C22×C4—33no—
626C22×C4—33no—
627C22×C4—53no—
628C22×C4—56no—
629C22×C4—153no—
630C22×C4—153no—
631C22×C4—153no—
632C22×C4—153no—
633C22×C4—156no—
634C22×C4—153no—
635C22×C4—156no—
636C22×C4—6012no—
637C4⋊C4—33no—
638C4⋊C4—53no—
639C4⋊C4—53no—
640C4⋊C4—51no—
641C4⋊C4—153no—
642C4⋊C4—151no—
643C4⋊C4—153no—
644C4⋊C4—153no—
645C4⋊C4—151no—
646C4⋊C4C2×D3×D513yes—
647C22⋊C4—36no—
648C22⋊C4—53no—
649C22⋊C4—53no—
650C22⋊C4—156no—
651C22⋊C4—156no—
652C22⋊C4—153no—
653C22⋊C4—153no—
654C22⋊C4—153no—
655C22⋊C4—153no—
656C42—31no—
657C42—33no—
658C42—33no—
659C42—53no—
660C42—151no—
661C42—151no—
662C42—153no—
663C42—153no—
664C42—153no—
665C42C2×D3×D513yes—
666C3×C5C4×H(5,𝔽2)11yescharacteristic, complemented, Hall
667C22×C3—56no—
668C22×C3—103no—
669C22×C3—103no—
670C22×C3C24×D511yescharacteristic
671C2×D3—23no—
672C2×D3—23no—
673C2×D3—56no—
674C2×D3—103no—
675C2×D3—103no—
676C2×D3—2024no—
677C2×D3C22×C4×D516yes—
678C3×C4—23no—
679C3×C4—21no—
680C3×C4—52no—
681C3×C4—103no—
682C3×C4—101no—
683C3×C4C22×C4×D516yes—
684Dic3—23no—
685Dic3—52no—
686Dic3—103no—
687Dic3—101no—
688Dic3C22×C4×D512yes—
689Dic3#414912yescomplemented
690C2×C5—66no—
691C2×C5C23×C4×D311yescharacteristic
692C2×C5D3×H(5,𝔽2)11yescharacteristic
693C2×C5#596811yescharacteristic
694D5—26no—
695D5—66no—
696C23—33no—
697C23—53no—
698C23—1524no—
699C23—153no—
700C23—606no—
701C23—606no—
702Q8—154no—
703Q8C4×D3×D514yescomplemented
704D4—312no—
705D4—512no—
706D4—1512no—
707D4—1512no—
708D4—1512no—
709D4—1512no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—312no—
713C2×C4—33no—
714C2×C4—51no—
715C2×C4—512no—
716C2×C4—51no—
717C2×C4—53no—
718C2×C4—66no—
719C2×C4—123no—
720C2×C4—151no—
721C2×C4—1512no—
722C2×C4—151no—
723C2×C4—153no—
724C2×C4—206no—
725C2×C4—306no—
726C2×C4—306no—
727C2×C4—606no—
728C2×C4—603no—
729C2×C4—603no—
730C2×C4—606no—
731C2×C4C22×D3×D511yescharacteristic
732C2×C4C22×D3×D513yes—
733C2×C4C22×D3×D513yes—
734C2×C3—106no—
735C2×C3C23×C4×D511yescharacteristic
736C2×C3C2×#414911yescharacteristic
737C2×C3#6628311yescharacteristic
738D3—26no—
739D3—106no—
740C5#8588611yescharacteristic, complemented, Sylow
741C22—36no—
742C22—56no—
743C22—63no—
744C22—63no—
745C22—103no—
746C22—103no—
747C22—156no—
748C22—303no—
749C22—303no—
750C22—6024no—
751C22C23×D3×D511yescharacteristic
752C4—21no—
753C4—23no—
754C4—32no—
755C4—32no—
756C4—52no—
757C4—63no—
758C4—101no—
759C4—103no—
760C4—152no—
761C4—301no—
762C4—303no—
763C4C2×C4×D3×D516yes—
764C3C4×#414911yescharacteristic, complemented, Sylow
765C2—66no—
766C2—106no—
767C2—306no—
768C2C22×C4×D3×D511yescharacteristic
769C2#1175704911yescharacteristic
770C2D3×#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC2×#92035C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5C4×H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11756333C2semidirect
3. C4×C5×#239C2semidirect
4. C3×#65908C2semidirect
5. #11755220C2semidirect
6. Dic3×#713C2semidirect
7. #11755200C2semidirect
8. #11753840C2semidirect
9. #11753839C2semidirect
10. D5×#893C2semidirect
11. #11753668C2semidirect
12. #11752729C2semidirect
13. C4×D3×D20C2semidirect
14. #11752725C2semidirect
15. #11752666C2semidirect
20. #92035C4semidirect
24. C2×C4×D3×D5C22semidirect
26. C3×C4×C5×Q8C22semidirect
27. Q8×Dic15C22semidirect
28. #91782C22semidirect
29. C4⋊C4×D15C22semidirect
30. C4×D60C22semidirect
31. #91761C22semidirect
32. C5×Q8×Dic3C22semidirect
33. C5×#893C22semidirect
34. C5×#892C22semidirect
35. C4×C5×D12C22semidirect
36. C42×C5×D3C22semidirect
37. C3×Q8×Dic5C22semidirect
38. C3×#4039C22semidirect
39. C3×D5×C4⋊C4C22semidirect
40. C3×C4×D20C22semidirect
41. C3×#4018C22semidirect
42. #91473C22semidirect
43. D3×#685C22semidirect
44. D5×(C2×D3)⋊C4C22semidirect
45. #91446C22semidirect
46. #91446C22semidirect
47. C4×#1202C22semidirect
48. #91441C22semidirect
49. #91441C22semidirect
50. #91440C22semidirect
51. #91435C22semidirect
52. #91434C22semidirect
53. #91428C22semidirect
54. D3×C4⋊Dic5C22semidirect
55. Dic3×D20C22semidirect
56. #91418C22semidirect
57. Dic5×D12C22semidirect
58. #91406C22semidirect
59. C4×#1200C22semidirect
60. #91395C22semidirect
61. #91395C22semidirect
62. C4×D5×Dic3C22semidirect
63. #91371C22semidirect
64. #91358C22semidirect
65. #91347C22semidirect
66. #91324C22semidirect
67. #91324C22semidirect
73. #65908D3semidirect
86. #6821C2×C4semidirect
90. C5×#239C2×C4semidirect
95. C3×#713C2×C4semidirect
108. #6777C2×C4semidirect
109. D3×D20C2×C4semidirect
110. D5×D12C2×C4semidirect
112. #6771C2×C4semidirect
148. C4×#239D5semidirect
167. C4×C5×Q8C2×D3semidirect
173. Q8×Dic5C2×D3semidirect
186. #4039C2×D3semidirect
190. D5×C4⋊C4C2×D3semidirect
201. C4×D20C2×D3semidirect
203. #4018C2×D3semidirect
214. C2×D3×D5C22×C4semidirect
215. C3×C5×Q8C22×C4semidirect
222. D60C22×C4semidirect
224. C4×D15C22×C4semidirect
228. C5×D12C22×C4semidirect
231. C4×C5×D3C22×C4semidirect
235. C3×D20C22×C4semidirect
237. C3×C4×D5C22×C4semidirect
238. #1204C22×C4semidirect
239. #1203C22×C4semidirect
240. #1202C22×C4semidirect
241. #1201C22×C4semidirect
257. C3×C4×Q8C2×D5semidirect
263. Q8×Dic3C2×D5semidirect
277. #893C2×D5semidirect
279. #892C2×D5semidirect
293. C4×D12C2×D5semidirect
297. C42×D3C2×D5semidirect
309. #713C4×D3semidirect
393. C5×Dic3H(5,𝔽2)semidirect
405. #239C4×D5semidirect
458. C5×Q8C2×C4×D3semidirect
480. D20C2×C4×D3semidirect
488. C4×D5C2×C4×D3semidirect
504. C4×Q8D3×D5semidirect
553. C3×Q8C2×C4×D5semidirect
575. D12C2×C4×D5semidirect
583. C4×D3C2×C4×D5semidirect
666. C3×C5C4×H(5,𝔽2)semidirect
689. Dic3#4149semidirect
703. Q8C4×D3×D5semidirect
740. C5#85886semidirect
764. C3C4×#4149semidirect

Maximal subgroups

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

subgroupindex
C2×#920352
#117563332
C4×C5×#2392
C3×#659082
#117552202
Dic3×#7132
#117552002
#117538402
#117538392
D5×#8932
#117536682
#117527292
C4×D3×D202
#117527252
#117526662
C4×#41493
#858865