Finite Group Databasebeta

← D5×#5574 #14479110

Subgroups — D5×#5574 #14479110

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C211yesmaximal, characteristic
2#11756333C211yesmaximal, characteristic, complemented
3C5×#5574C211yesmaximal, characteristic, complemented
4C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
5#11755220C211yesmaximal, characteristic, complemented
6Q8×D5×Dic3C211yesmaximal, characteristic, complemented
7#11755149C211yesmaximal, characteristic, complemented
8D5×#893C213yesmaximal, complemented
9D3×D5×C4⋊C4C213yesmaximal, complemented
10#11753407C213yesmaximal, complemented
11#11753337C213yesmaximal, complemented
12C4×D5×D12C213yesmaximal, complemented
13D5×#872C213yesmaximal, complemented
14#11752527C213yesmaximal, complemented
15#11752525C213yesmaximal, complemented
16D5×#520—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20D5×#239C4116yescomplemented
21C2×D5×D12C2213yes—
22C2×C4×D3×D5C2216yes—
23C2×C4×D3×D5C2213yes—
24C2×#6769C2213yes—
25C2×#6768C2213yes—
26C3×C4×C5×Q8C2211yescharacteristic, complemented
27Q8×Dic15C2211yescharacteristic, complemented
28#91782C2213yescomplemented
29C4⋊C4×D15C2213yescomplemented
30C4×D60C2213yescomplemented
31#91761C2213yescomplemented
32C5×Q8×Dic3C2211yescharacteristic, complemented
33C5×#893C2213yescomplemented
34C5×D3×C4⋊C4C2213yescomplemented
35C4×C5×D12C2213yescomplemented
36C5×#872C2213yescomplemented
37C3×Q8×Dic5C2211yescharacteristic, complemented
38C3×D5×C4⋊C4C2213yes—
39C3×#4033C2213yescomplemented
40C3×C42×D5C2213yes—
41C3×C4×Dic10C2213yescomplemented
42D5×(C2×D3)⋊C4C2213yes—
43D5×(C2×D3)⋊C4C2213yes—
44#91446C2216yescomplemented
45C4×#1203C2216yescomplemented
46#91437C2213yescomplemented
47#91435C2213yescomplemented
48#91428C2213yescomplemented
49D3×C4⋊Dic5C2213yescomplemented
50#91418C2213yescomplemented
51Dic5×D12C2213yescomplemented
52D5×C4⋊Dic3C2213yes—
53#91406C2216yescomplemented
54#91405C2216yescomplemented
55#91404C2216yescomplemented
56#91402C2213yescomplemented
57#91402C2213yescomplemented
58D3×#683C2216yescomplemented
59#91398C2213yescomplemented
60#91398C2213yescomplemented
61D5×Dic3⋊C4C2211yescharacteristic
62D5×Dic3⋊C4C2213yes—
63C4×D5×Dic3C2213yes—
64#91386C2213yescomplemented
65#91371C2213yescomplemented
66#91331C2213yescomplemented
67Dic3×Dic10C2213yescomplemented
68C2×#5574—51nomaximal, Hall
69C2×D5×#41—31no—
70C5×#520—31no—
71#66161—31no—
72#65908—31no—
73#65908—31no—
74C4×Q8×D5—31no—
75C4×Q8×D5D311yescharacteristic, complemented
76#65880—33no—
77#65880—33no—
78C4×D4×D5—33no—
79C4×D4×D5—33no—
80#65857—33no—
81D5×#117—33no—
82#65838—33no—
83C2×D5×C4⋊C4—33no—
84C22×D3×D5C2313yes—
85C2×C3×C5×Q8C2311yescharacteristic
86#6821C2×C418yescomplemented
87C2×D60C2313yes—
88C2×C4×D15C2316yes—
89C2×C4×D15C2313yes—
90C5×#239C2×C418yescomplemented
91C2×C5×D12C2313yes—
92C2×C4×C5×D3C2316yes—
93C2×C4×C5×D3C2313yes—
94C3×Q8×D5C2×C418yescomplemented
95C2×C3×C4×D5C2311yescharacteristic
96C2×C3×C4×D5C2313yes—
97C2×C3×C4×D5C2313yes—
98C2×C3×Dic10C2313yes—
99C2×#1203C2316yes—
100C2×#1200C2316yes—
101C2×#1200C2313yes—
102C2×D3×Dic5C2316yes—
103C2×D3×Dic5C2313yes—
104C2×D5×Dic3C2313yes—
105C2×D5×Dic3C2311yescharacteristic
106C2×D5×Dic3C2311yescharacteristic
107D5×D12C2×C4124yescomplemented
108C4×D3×D5—412no—
109C4×D3×D5C2×C4124yescomplemented
110#6769C2×C4124yescomplemented
111#6768C2×C4124yescomplemented
112C3×C5×C4⋊C4C2313yes—
113C3×C42×C5C2313yes—
114#6714C2313yes—
115#6714C2313yes—
116C4⋊Dic15C2313yes—
117#6712C2311yescharacteristic
118#6712C2313yes—
119C4×Dic15C2313yes—
120C5×(C2×D3)⋊C4C2313yes—
121C5×(C2×D3)⋊C4C2313yes—
122C5×C4⋊Dic3C2313yes—
123C5×Dic3⋊C4C2311yescharacteristic
124C5×Dic3⋊C4C2313yes—
125C4×C5×Dic3C2313yes—
126C3×C4⋊Dic5C2313yes—
127C3×#683C2316yes—
128C3×C4×Dic5C2313yes—
129C3×C4×Dic5C2313yes—
130C3×C4×Dic5C2313yes—
131Dic3⋊Dic5C2311yescharacteristic
132Dic3⋊Dic5C2313yes—
133#6669C2311yescharacteristic
134#6669C2313yes—
135#6668C2316yes—
136#6667C2313yes—
137#6667C2313yes—
138(C2×D3)⋊Dic5C2313yes—
139(C2×D3)⋊Dic5C2313yes—
140Dic3×Dic5C2313yes—
141Dic3×Dic5C2313yes—
142C22×#239—51no—
143C2×C3×C4×Q8—51no—
144C2×Q8×Dic3—51no—
145#5574—51no—
146#5574—51no—
147#5574—51no—
148#5574—53no—
149#5574—53no—
150#5574—53no—
151#5574—53no—
152#5574D511yescharacteristic, direct product factor
153C2×#893—53no—
154C2×D3×C4⋊C4—53no—
155C2×C4×D12—53no—
156C2×#872—53no—
157C2×C5×#41—31no—
158D5×#41—316no—
159C2×#713—31no—
160C2×Q8×D5C2×D311yescharacteristic
161C2×#711—33no—
162C2×D4×D5—33no—
163C2×#709—33no—
164C22×C4×D5—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×C5×C4⋊C4—33no—
172Q8×Dic5—31no—
173Q8×Dic5C2×D311yescharacteristic, complemented
174D4×Dic5—33no—
175D4×Dic5—33no—
176C4×C22⋊D5—36no—
177C4×C22⋊D5—36no—
178#4072—33no—
179C2×C4⋊Dic5—33no—
180C2×#683—36no—
181#4039—33no—
182#4039—33no—
183#4038—33no—
184#4038—33no—
185D5×C4⋊C4—33no—
186D5×C4⋊C4—31no—
187D5×C4⋊C4—33no—
188D5×C4⋊C4—33no—
189D5×C4⋊C4—33no—
190D5×C4⋊C4—36no—
191D5×C4⋊C4C2×D313yes—
192#4033—33no—
193#4033C2×D313yescomplemented
194#4027—36no—
195#4027—36no—
196D5×C22⋊C4—33no—
197D5×C22⋊C4—33no—
198#4023—33no—
199#4023—33no—
200C4×D20—33no—
201C4×D20—33no—
202#4018—33no—
203#4018—33no—
204C42×D5—33no—
205C42×D5C2×D313yes—
206C4×Dic10—33no—
207C4×Dic10C2×D313yescomplemented
208C2×#520—151noSylow
209C22×D15C2413yes—
210C22×C5×D3C2413yes—
211C22×C3×D5C2411yescharacteristic
212C2×D3×D5—26no—
213C2×D3×D5—26no—
214C2×D3×D5C22×C4112yes—
215C3×C5×Q8C22×C414yescomplemented
216C2×C3×C4×C5C2411yescharacteristic
217C2×C3×C4×C5C2413yes—
218C2×C3×C4×C5C2413yes—
219C2×Dic15C2411yescharacteristic
220C2×Dic15C2413yes—
221C2×Dic15C2411yescharacteristic
222D60C22×C4112yescomplemented
223C4×D15—46no—
224C4×D15C22×C4112yescomplemented
225C2×C5×Dic3C2411yescharacteristic
226C2×C5×Dic3C2413yes—
227C2×C5×Dic3C2411yescharacteristic
228C5×D12C22×C4112yescomplemented
229C4×C5×D3—46no—
230C4×C5×D3C22×C4112yescomplemented
231C2×C3×Dic5C2411yescharacteristic
232C2×C3×Dic5C2413yes—
233C2×C3×Dic5C2413yes—
234C3×C4×D5—26no—
235C3×C4×D5—22no—
236C3×C4×D5C22×C4112yes—
237C3×Dic10C22×C4112yescomplemented
238#1203C22×C4124yescomplemented
239#1200—46no—
240#1200C22×C4112yescomplemented
241D3×Dic5—46no—
242D3×Dic5C22×C4112yescomplemented
243D5×Dic3—26no—
244D5×Dic3—22no—
245D5×Dic3C22×C414yes—
246C22×C3×Q8—51no—
247C2×#239—51no—
248C2×#239—516no—
249C2×#239—53no—
250C2×#239—53no—
251C2×#239C2×D511yescharacteristic
252C22×D12—53no—
253C22×C4×D3—53no—
254C22×C4×D3—56no—
255C3×C4×Q8—51no—
256C3×C4×Q8—53no—
257C3×C4×Q8—53no—
258C3×C4×Q8C2×D511yescharacteristic, complemented
259C2×C3×C4⋊C4—53no—
260C2×C3×C42—53no—
261Q8×Dic3—51no—
262Q8×Dic3—53no—
263Q8×Dic3—53no—
264Q8×Dic3C2×D511yescharacteristic, complemented
265C2×(C2×D3)⋊C4—53no—
266C2×(C2×D3)⋊C4—53no—
267C2×C4⋊Dic3—53no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—53no—
270C2×C4×Dic3—53no—
271#893—53no—
272#893—56no—
273#893—53no—
274#893—56no—
275#893—53no—
276#893C2×D513yescomplemented
277D3×C4⋊C4—56no—
278D3×C4⋊C4—53no—
279D3×C4⋊C4—53no—
280D3×C4⋊C4—53no—
281D3×C4⋊C4—56no—
282D3×C4⋊C4C2×D513yescomplemented
283C4×D12—53no—
284C4×D12—56no—
285C4×D12—53no—
286C4×D12—56no—
287C4×D12—53no—
288C4×D12C2×D513yescomplemented
289#872—53no—
290#872—53no—
291#872—53no—
292#872—53no—
293#872—53no—
294#872—53no—
295#872—53no—
296#872C2×D513yescomplemented
297C23×D5—33no—
298C5×#41—38no—
299C2×C5×Q8C22×D311yescharacteristic
300C2×C5×D4—33no—
301C22×C4×C5—33no—
302C22×C4×C5—36no—
303C2×C22⋊D5—36no—
304C22×Dic5—33no—
305C22×Dic5—36no—
306#713—38no—
307Q8×D5C4×D318yescomplemented
308#711—324no—
309D4×D5—324no—
310#709—324no—
311C2×D20—33no—
312C2×C4×D5—31no—
313C2×C4×D5—33no—
314C2×C4×D5—33no—
315C2×C4×D5—324no—
316C2×C4×D5—33no—
317C2×C4×D5—31no—
318C2×C4×D5—36no—
319C2×C4×D5—36no—
320C2×C4×D5—1212no—
321C2×C4×D5C22×D313yes—
322C2×C4×D5C22×D311yescharacteristic
323C2×C4×D5C22×D313yes—
324C2×Dic10C22×D313yes—
325C5×C4⋊C4—33no—
326C5×C4⋊C4—33no—
327C5×C4⋊C4—31no—
328C5×C4⋊C4C22×D313yes—
329C5×C22⋊C4—33no—
330C5×C22⋊C4—33no—
331C42×C5—33no—
332C42×C5C22×D313yes—
333C22⋊Dic5—33no—
334C22⋊Dic5—33no—
335#685—33no—
336#685—33no—
337#685—33no—
338#685—33no—
339C4⋊Dic5—33no—
340C4⋊Dic5—33no—
341C4⋊Dic5—31no—
342C4⋊Dic5C22×D313yes—
343#683—31no—
344#683—33no—
345#683—36no—
346#683—31no—
347#683—33no—
348#683C22×D316yes—
349C4×Dic5—33no—
350C4×Dic5—33no—
351C4×Dic5—33no—
352C4×Dic5C22×D313yes—
353C4×Dic5C22×D313yes—
354C4×Dic5C22×D313yes—
355C22×#41—151no—
356#520—31no—
357#520—153no—
358#520—153no—
359#520—153no—
360#520—153no—
361#520—151no—
362#520—151no—
363#520—151no—
364C2×C4×Q8—51no—
365C2×C4×Q8—151no—
366C2×C4×D4—153no—
367C2×C4×D4—153no—
368C2×#117—153no—
369C22×C4⋊C4—153no—
370C22×C3×C5C2511yescharacteristic
371C2×D15—23no—
372C2×D15—23no—
373C2×D15C23×C416yes—
374C2×C5×D3—23no—
375C2×C5×D3—23no—
376C2×C5×D3C23×C416yes—
377C2×C3×D5C23×C412yes—
378C2×C3×D5H(5,𝔽2)12yes—
379C2×C3×D52−1+412yes—
380D3×D5—224no—
381C3×C4×C5—23no—
382C3×C4×C5—21no—
383C3×C4×C5C23×C416yes—
384Dic15—23no—
385Dic15—21no—
386Dic15C23×C412yes—
387C3×Dic5—23no—
388C3×Dic5—21no—
389C3×Dic5C23×C416yes—
390C5×Dic3—23no—
391C5×Dic3—21no—
392C5×Dic3C23×C412yes—
393C23×D3—53no—
394C2×C3×Q8—58no—
395C2×C3×Q8—53no—
396C2×C3×Q8C22×D511yescharacteristic
397C22×C3×C4—53no—
398C22×C3×C4—51no—
399C22×C3×C4—53no—
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—53no—
403#239—58no—
404#239—524no—
405#239—524no—
406#239C4×D518yescomplemented
407C2×D12—56no—
408C2×D12—53no—
409C2×D12—524no—
410C2×D12C22×D513yes—
411C2×C4×D3—53no—
412C2×C4×D3—53no—
413C2×C4×D3—53no—
414C2×C4×D3—524no—
415C2×C4×D3—56no—
416C2×C4×D3—56no—
417C2×C4×D3—56no—
418C2×C4×D3—2012no—
419C2×C4×D3C22×D516yes—
420C2×C4×D3C22×D513yes—
421C3×C4⋊C4—56no—
422C3×C4⋊C4—53no—
423C3×C4⋊C4C22×D513yes—
424C3×C42—53no—
425C3×C42—53no—
426C3×C42—53no—
427C3×C42C22×D513yes—
428(C2×D3)⋊C4—53no—
429(C2×D3)⋊C4—53no—
430(C2×D3)⋊C4—53no—
431(C2×D3)⋊C4—53no—
432(C2×D3)⋊C4—53no—
433(C2×D3)⋊C4—53no—
434(C2×D3)⋊C4C22×D513yes—
435(C2×D3)⋊C4C22×D513yes—
436C4⋊Dic3—53no—
437C4⋊Dic3—56no—
438C4⋊Dic3C22×D513yes—
439Dic3⋊C4—51no—
440Dic3⋊C4—53no—
441Dic3⋊C4—51no—
442Dic3⋊C4—53no—
443Dic3⋊C4—51no—
444Dic3⋊C4—53no—
445Dic3⋊C4C22×D511yescharacteristic
446Dic3⋊C4C22×D513yes—
447C4×Dic3—53no—
448C4×Dic3—53no—
449C4×Dic3—53no—
450C4×Dic3C22×D513yes—
451C23×C5—33no—
452C22×D5—33no—
453C22×D5—312no—
454C22×D5—66no—
455C22×D5—66no—
456C22×D5C23×D311yescharacteristic
457C5×Q8C2×C4×D314yescomplemented
458C5×D4—312no—
459C2×C4×C5—31no—
460C2×C4×C5—312no—
461C2×C4×C5—31no—
462C2×C4×C5—33no—
463C2×C4×C5—126no—
464C2×C4×C5C23×D311yescharacteristic
465C2×C4×C5C23×D313yes—
466C2×C4×C5C23×D313yes—
467C22⋊D5—324no—
468C2×Dic5—31no—
469C2×Dic5—312no—
470C2×Dic5—31no—
471C2×Dic5—33no—
472C2×Dic5—126no—
473C2×Dic5C23×D311yescharacteristic
474C2×Dic5C23×D313yes—
475C2×Dic5C23×D313yes—
476D20—312no—
477C4×D5—22no—
478C4×D5—26no—
479C4×D5—34no—
480C4×D5—312no—
481C4×D5—312no—
482C4×D5—62no—
483C4×D5—66no—
484C4×D5—126no—
485C4×D5—126no—
486C4×D5C2×C4×D3112yes—
487Dic10C2×C4×D3112yescomplemented
488C2×#41—31no—
489C2×#41—153no—
490C2×#41—153no—
491C2×#41—1516no—
492C2×#41—151no—
493C22×Q8—51no—
494C22×D4—153no—
495C23×C4—153no—
496C23×C4—156no—
497C4×Q8—31no—
498C4×Q8—51no—
499C4×Q8—53no—
500C4×Q8—53no—
501C4×Q8—153no—
502C4×Q8—153no—
503C4×Q8—151no—
504C4×Q8D3×D511yescharacteristic, complemented
505C4×D4—33no—
506C4×D4—33no—
507C4×D4—153no—
508C4×D4—156no—
509C4×D4—153no—
510C4×D4—156no—
511C4×D4—153no—
512C4×D4—156no—
513C4×D4—156no—
514C4×D4—153no—
515C4×D4—153no—
516C4×D4—153no—
517#117—33no—
518#117—153no—
519#117—153no—
520#117—153no—
521#117—153no—
522#117—153no—
523#117—153no—
524#117—153no—
525C2×C4⋊C4—33no—
526C2×C4⋊C4—53no—
527C2×C4⋊C4—156no—
528C2×C4⋊C4—153no—
529C2×C4⋊C4—153no—
530C2×C4⋊C4—153no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—156no—
533C2×C4⋊C4—153no—
534C2×C4⋊C4—153no—
535C2×C22⋊C4—153no—
536C2×C22⋊C4—153no—
537C2×C42—53no—
538C2×C42—153no—
539C2×C3×C5C24×C411yescharacteristic
540C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
541C2×C3×C5C2×2−1+411yescharacteristic
542D15—26no—
543C3×D5#52014yescomplemented
544C5×D3—26no—
545C23×C3—51no—
546C22×D3—53no—
547C22×D3—512no—
548C22×D3—106no—
549C22×D3—106no—
550C22×D3C23×D513yes—
551C3×Q8—512no—
552C3×Q8C2×C4×D514yescomplemented
553C2×C3×C4—53no—
554C2×C3×C4—512no—
555C2×C3×C4—51no—
556C2×C3×C4—53no—
557C2×C3×C4—106no—
558C2×C3×C4—102no—
559C2×C3×C4C23×D511yescharacteristic
560C2×C3×C4C23×D513yes—
561C2×C3×C4C23×D513yes—
562C2×Dic3—51no—
563C2×Dic3—54no—
564C2×Dic3—51no—
565C2×Dic3—53no—
566C2×Dic3—106no—
567C2×Dic3—102no—
568C2×Dic3C23×D511yescharacteristic
569C2×Dic3C23×D513yes—
570C2×Dic3C23×D511yescharacteristic
571D12—524no—
572D12—512no—
573D12C2×C4×D5112yescomplemented
574C4×D3—46no—
575C4×D3—512no—
576C4×D3—512no—
577C4×D3—512no—
578C4×D3—206no—
579C4×D3—206no—
580C4×D3—206no—
581C4×D3C2×C4×D5112yescomplemented
582C22×C5—36no—
583C22×C5—63no—
584C22×C5—63no—
585C22×C5C24×D311yescharacteristic
586C2×D5—36no—
587C2×D5—63no—
588C2×D5—63no—
589C2×D5—624no—
590C2×D5C22×C4×D312yes—
591C2×D5#100712yes—
592C2×D5#100912yes—
593C4×C5—21no—
594C4×C5—23no—
595C4×C5—32no—
596C4×C5—61no—
597C4×C5—63no—
598C4×C5C22×C4×D316yes—
599Dic5—21no—
600Dic5—23no—
601Dic5—32no—
602Dic5—61no—
603Dic5—63no—
604Dic5C22×C4×D316yes—
605C24—153no—
606#41—38no—
607#41—1524no—
608#41—1524no—
609#41—158no—
610C2×Q8—58no—
611C2×Q8—53no—
612C2×Q8C2×D3×D511yescharacteristic
613C2×D4—33no—
614C2×D4—1524no—
615C2×D4—156no—
616C2×D4—153no—
617C22×C4—33no—
618C22×C4—36no—
619C22×C4—53no—
620C22×C4—51no—
621C22×C4—53no—
622C22×C4—153no—
623C22×C4—1524no—
624C22×C4—156no—
625C22×C4—151no—
626C22×C4—151no—
627C22×C4—153no—
628C22×C4—153no—
629C22×C4—156no—
630C22×C4—153no—
631C22×C4—156no—
632C22×C4—6012no—
633C4⋊C4—33no—
634C4⋊C4—33no—
635C4⋊C4—31no—
636C4⋊C4—56no—
637C4⋊C4—53no—
638C4⋊C4—153no—
639C4⋊C4—153no—
640C4⋊C4—156no—
641C4⋊C4—151no—
642C4⋊C4—151no—
643C4⋊C4—153no—
644C4⋊C4—153no—
645C4⋊C4—151no—
646C4⋊C4C2×D3×D513yes—
647C22⋊C4—33no—
648C22⋊C4—33no—
649C22⋊C4—153no—
650C22⋊C4—153no—
651C22⋊C4—153no—
652C22⋊C4—153no—
653C22⋊C4—153no—
654C22⋊C4—153no—
655C42—33no—
656C42—53no—
657C42—53no—
658C42—53no—
659C42—153no—
660C42—153no—
661C42—153no—
662C42C2×D3×D513yes—
663C3×C5C2×#52011yescharacteristic, complemented, Hall
664C22×C3—52no—
665C22×C3—52no—
666C22×C3—52no—
667C22×C3C24×D511yescharacteristic
668C2×D3—23no—
669C2×D3—23no—
670C2×D3—56no—
671C2×D3—1024no—
672C2×D3—103no—
673C2×D3—103no—
674C2×D3C22×C4×D516yes—
675C3×C4—23no—
676C3×C4—21no—
677C3×C4—56no—
678C3×C4—103no—
679C3×C4—101no—
680C3×C4C22×C4×D516yes—
681Dic3—23no—
682Dic3—21no—
683Dic3—52no—
684Dic3—103no—
685Dic3—101no—
686Dic3C22×C4×D512yes—
687C2×C5—66no—
688C2×C5C23×C4×D311yescharacteristic
689C2×C5C2×#100711yescharacteristic
690C2×C5C2×#100911yescharacteristic
691D5—66no—
692D5#557414yesdirect product factor
693C23—33no—
694C23—51no—
695C23—1512no—
696C23—153no—
697C23—306no—
698C23—306no—
699Q8—512no—
700Q8C4×D3×D514yescomplemented
701D4—312no—
702D4—1524no—
703D4—1512no—
704C2×C4—31no—
705C2×C4—312no—
706C2×C4—31no—
707C2×C4—33no—
708C2×C4—53no—
709C2×C4—512no—
710C2×C4—51no—
711C2×C4—53no—
712C2×C4—106no—
713C2×C4—102no—
714C2×C4—126no—
715C2×C4—1512no—
716C2×C4—154no—
717C2×C4—1512no—
718C2×C4—151no—
719C2×C4—1512no—
720C2×C4—151no—
721C2×C4—153no—
722C2×C4—306no—
723C2×C4—302no—
724C2×C4—606no—
725C2×C4—606no—
726C2×C4—606no—
727C2×C4C22×D3×D511yescharacteristic
728C2×C4C22×D3×D513yes—
729C2×C4C22×D3×D513yes—
730C2×C3—54no—
731C2×C3C23×C4×D511yescharacteristic
732C2×C3D5×H(5,𝔽2)11yescharacteristic
733C2×C3D5×2−1+411yescharacteristic
734D3—26no—
735D3—106no—
736C5C2×#557411yescharacteristic, complemented, Sylow
737C22—36no—
738C22—52no—
739C22—52no—
740C22—52no—
741C22—63no—
742C22—63no—
743C22—156no—
744C22—3024no—
745C22—303no—
746C22—303no—
747C22C23×D3×D511yescharacteristic
748C4—21no—
749C4—23no—
750C4—32no—
751C4—56no—
752C4—61no—
753C4—63no—
754C4—101no—
755C4—103no—
756C4—152no—
757C4—301no—
758C4—303no—
759C4C2×C4×D3×D516yes—
760C3D5×#52011yescharacteristic, complemented, Sylow
761C2—54no—
762C2—66no—
763C2—306no—
764C2C22×C4×D3×D511yescharacteristic
765C2D5×#100711yescharacteristic
766C2D5×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC2×D5×#239C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#520
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. C5×#5574C2semidirect
4. C3×C4×Q8×D5C2semidirect
5. #11755220C2semidirect
6. Q8×D5×Dic3C2semidirect
7. #11755149C2semidirect
8. D5×#893C2semidirect
9. D3×D5×C4⋊C4C2semidirect
10. #11753407C2semidirect
11. #11753337C2semidirect
12. C4×D5×D12C2semidirect
13. D5×#872C2semidirect
14. #11752527C2semidirect
15. #11752525C2semidirect
20. D5×#239C4semidirect
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×D3×C4⋊C4C22semidirect
35. C4×C5×D12C22semidirect
36. C5×#872C22semidirect
37. C3×Q8×Dic5C22semidirect
39. C3×#4033C22semidirect
41. C3×C4×Dic10C22semidirect
44. #91446C22semidirect
45. C4×#1203C22semidirect
46. #91437C22semidirect
47. #91435C22semidirect
48. #91428C22semidirect
49. D3×C4⋊Dic5C22semidirect
50. #91418C22semidirect
51. Dic5×D12C22semidirect
53. #91406C22semidirect
54. #91405C22semidirect
55. #91404C22semidirect
56. #91402C22semidirect
57. #91402C22semidirect
58. D3×#683C22semidirect
59. #91398C22semidirect
60. #91398C22semidirect
64. #91386C22semidirect
65. #91371C22semidirect
66. #91331C22semidirect
67. Dic3×Dic10C22semidirect
75. C4×Q8×D5D3semidirect
86. #6821C2×C4semidirect
90. C5×#239C2×C4semidirect
94. C3×Q8×D5C2×C4semidirect
107. D5×D12C2×C4semidirect
109. C4×D3×D5C2×C4semidirect
110. #6769C2×C4semidirect
111. #6768C2×C4semidirect
152. #5574D5direct (N × H)
167. C4×C5×Q8C2×D3semidirect
173. Q8×Dic5C2×D3semidirect
193. #4033C2×D3semidirect
207. C4×Dic10C2×D3semidirect
215. C3×C5×Q8C22×C4semidirect
222. D60C22×C4semidirect
224. C4×D15C22×C4semidirect
228. C5×D12C22×C4semidirect
230. C4×C5×D3C22×C4semidirect
237. C3×Dic10C22×C4semidirect
238. #1203C22×C4semidirect
240. #1200C22×C4semidirect
242. D3×Dic5C22×C4semidirect
258. C3×C4×Q8C2×D5semidirect
264. Q8×Dic3C2×D5semidirect
276. #893C2×D5semidirect
282. D3×C4⋊C4C2×D5semidirect
288. C4×D12C2×D5semidirect
296. #872C2×D5semidirect
307. Q8×D5C4×D3semidirect
406. #239C4×D5semidirect
457. C5×Q8C2×C4×D3semidirect
487. Dic10C2×C4×D3semidirect
504. C4×Q8D3×D5semidirect
543. C3×D5#520semidirect
552. C3×Q8C2×C4×D5semidirect
573. D12C2×C4×D5semidirect
581. C4×D3C2×C4×D5semidirect
663. C3×C5C2×#520semidirect
692. D5#5574direct (N × H)
700. Q8C4×D3×D5semidirect
736. C5C2×#5574semidirect
760. C3D5×#520semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2392
#117563332
C5×#55742
C3×C4×Q8×D52
#117552202
Q8×D5×Dic32
#117551492
D5×#8932
D3×D5×C4⋊C42
#117534072
#117533372
C4×D5×D122
D5×#8722
#117525272
#117525252
D5×#5203
C2×#55745