Finite Group Databasebeta

← D5×#5828 #14479560

Subgroups — D5×#5828 #14479560

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic, complemented
2C22×C4×D3×D5C211yesmaximal, characteristic, complemented
3#11756587C211yesmaximal, characteristic, complemented
4C5×#5828C211yesmaximal, characteristic, complemented
5#11755270C212yesmaximal, complemented
6D5×#946C212yesmaximal, complemented
7#11755060C212yesmaximal, complemented
8D5×#938C212yesmaximal, complemented
9D5×#937C212yesmaximal, complemented
10#11754800C212yesmaximal, complemented
11#11754795C212yesmaximal, complemented
12D5×#935C212yesmaximal, complemented
13#11754631C214yesmaximal, complemented
14C4×D5×#67C214yesmaximal, complemented
15#11754590C211yesmaximal, characteristic, complemented
16#11754577C211yesmaximal, characteristic, complemented
17D5×#926C211yesmaximal, characteristic, complemented
18D5×#525—31nomaximal, Hall
19C23×D3×D5C2211yescharacteristic
20C2×C3×C5×#41C2211yescharacteristic, complemented
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C3×D5×#41—28no—
24C2×C3×#713C2211yescharacteristic, complemented
25C2×C3×Q8×D5C2211yescharacteristic, complemented
26C2×C3×#711C2211yescharacteristic, complemented
27C2×C3×#711C2212yescomplemented
28C2×C3×D4×D5C2212yes—
29C2×C3×D4×D5C2211yescharacteristic, complemented
30C2×C3×#709C2212yescomplemented
31C2×C3×#709C2211yescharacteristic, complemented
32C22×C3×C4×D5C2211yescharacteristic
33C22×C3×C4×D5C2212yescomplemented
34C2×D5×#67C2214yes—
35C22×#1200C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic
38C2×C4×D3×D5—28no—
39C2×C4×D3×D5C2212yes—
40C2×C4×D3×D5C2212yes—
41C2×C4×D3×D5C2212yescomplemented
42C2×C4×D3×D5C2212yescomplemented
43#91835C2212yescomplemented
44#91827C2212yescomplemented
45#91826C2212yescomplemented
46#91824C2212yescomplemented
47C4×#1220C2214yescomplemented
48#91815C2211yescharacteristic, complemented
49C5×#946C2212yescomplemented
50C5×#938C2212yescomplemented
51C5×#937C2212yescomplemented
52C5×#935C2212yescomplemented
53C4×C5×#67C2214yescomplemented
54C5×#926C2211yescharacteristic, complemented
55#91577C2214yescomplemented
56#91572C2212yescomplemented
57#91568C2212yescomplemented
58#91565C2214yescomplemented
59#91552C2214yescomplemented
60Dic5×#67C2214yescomplemented
61#91548C2214yescomplemented
62D5×#217C2212yes—
63D5×#217C2214yescomplemented
64#91537C2212yescomplemented
65#91536C2212yescomplemented
66#91533C2214yescomplemented
67#91528C2212yescomplemented
68#91474C2214yescomplemented
69D5×(C2×D3)⋊C4C2214yes—
70#91465C2212yescomplemented
71#91456C2212yescomplemented
72#91444C2214yescomplemented
73C4×#1202C2214yescomplemented
74#91440C2214yescomplemented
75C4×#1201C2214yescomplemented
76D5×C4⋊Dic3C2212yescomplemented
77#91411C2214yescomplemented
78#91410C2214yescomplemented
79#91407C2214yescomplemented
80D5×Dic3⋊C4C2214yescomplemented
81C4×D5×Dic3C2212yescomplemented
82#91390C2212yescomplemented
83#91369C2212yescomplemented
84#91358C2212yescomplemented
85#91357C2212yescomplemented
86C2×#5828—51nomaximal, Hall
87C2×D5×#41D311yescharacteristic, complemented
88C23×C4×D5—31no—
89C5×#525—31no—
90#66162—31no—
91#66125—31no—
92#65990—32no—
93D5×#123—32no—
94#65961—32no—
95D5×C22⋊Q8—32no—
96#65940—32no—
97D5×#121—32no—
98D5×#120—32no—
99#65920—32no—
100#65881—34no—
101C4×D4×D5—34no—
102#65858—31no—
103D5×#117—31no—
104C23×D15C2311yescharacteristic
105C23×C5×D3C2311yescharacteristic
106C23×C3×D5C2312yes—
107C23×C3×D5C2311yescharacteristic
108C22×D3×D5—24no—
109C22×D3×D5—28no—
110C22×D3×D5C2312yes—
111C22×D3×D5C2312yes—
112C3×C5×#41—24no—
113C2×C3×C5×Q8C2311yescharacteristic, complemented
114C2×C3×C5×D4C2312yes—
115C2×C3×C5×D4C2311yescharacteristic, complemented
116C22×C3×C4×C5C2311yescharacteristic
117C22×C3×C4×C5C2312yescomplemented
118C2×#1220C2314yes—
119C22×Dic15C2311yescharacteristic
120C2×C4×D15—24no—
121C2×C4×D15C2312yes—
122C2×C4×D15C2312yes—
123C2×C5×#67C2314yes—
124C22×C5×Dic3C2311yescharacteristic
125C2×C4×C5×D3—24no—
126C2×C4×C5×D3C2312yes—
127C2×C4×C5×D3C2312yes—
128C2×C3×C22⋊D5C2312yes—
129C2×C3×C22⋊D5C2312yes—
130C2×C3×C22⋊D5C2312yescomplemented
131C22×C3×Dic5C2311yescharacteristic
132C22×C3×Dic5C2312yescomplemented
133C3×#713—24no—
134C3×Q8×D5—24no—
135C3×#711—28no—
136C3×#711—24no—
137C3×D4×D5—28no—
138C3×D4×D5—24no—
139C3×#709—24no—
140C3×#709—28no—
141C2×C3×D20C2312yes—
142C2×C3×D20C2311yescharacteristic, complemented
143C2×C3×C4×D5—28no—
144C2×C3×C4×D5D418yescomplemented
145C2×C3×C4×D5C2312yes—
146C2×C3×C4×D5C2311yescharacteristic
147C2×C3×C4×D5C2311yescharacteristic
148C2×C3×C4×D5C2311yescharacteristic
149C2×C3×C4×D5C2311yescharacteristic
150C2×C3×C4×D5C2312yescomplemented
151C2×C3×C4×D5C2312yescomplemented
152C2×C3×Dic10C2312yescomplemented
153C2×C3×Dic10C2311yescharacteristic, complemented
154D5×#67—216no—
155C2×#1202C2314yes—
156C2×#1201C2314yes—
157C2×#1200—24no—
158C2×#1200C2312yes—
159C2×#1200C2312yes—
160C2×D3×Dic5—24no—
161C2×D3×Dic5C2312yes—
162C2×D3×Dic5C2312yes—
163C2×D5×Dic3—24no—
164C2×D5×Dic3C2312yes—
165C2×D5×Dic3C2314yes—
166C2×D5×Dic3C2312yes—
167C4×D3×D5—28no—
168C4×D3×D5—28no—
169C4×D3×D5—28no—
170C4×D3×D5—28no—
171#6719C2312yes—
172#6719C2314yescomplemented
173#6714C2314yes—
174C4⋊Dic15C2312yescomplemented
175#6712C2314yescomplemented
176C4×Dic15C2312yescomplemented
177C5×#217C2312yes—
178C5×#217C2314yescomplemented
179C5×(C2×D3)⋊C4C2314yes—
180C5×C4⋊Dic3C2312yescomplemented
181C5×Dic3⋊C4C2314yescomplemented
182C4×C5×Dic3C2312yescomplemented
183Dic3⋊Dic5C2314yescomplemented
184#6669C2314yescomplemented
185#6668C2314yescomplemented
186#6667C2314yes—
187(C2×D3)⋊Dic5C2314yes—
188#6665C2314yes—
189#6665C2314yescomplemented
190#6665C2314yescomplemented
191Dic3×Dic5C2314yescomplemented
192C22×C3×#41—51no—
193C23×C4×D3—51no—
194#5828—51no—
195#5828—51no—
196#5828—52no—
197#5828—52no—
198#5828—52no—
199#5828—52no—
200#5828—54no—
201#5828—51no—
202#5828D511yescharacteristic, direct product factor
203C2×#946—52no—
204C2×#938—52no—
205C2×#937—52no—
206C2×#935—52no—
207C2×C4×#67—54no—
208C2×#926—51no—
209C24×D5—31no—
210C2×C5×#41C2×D311yescharacteristic, complemented
211C23×C4×C5—31no—
212C23×Dic5—31no—
213D5×#41—28no—
214C2×#713C2×D311yescharacteristic, complemented
215C2×Q8×D5C2×D311yescharacteristic, complemented
216C2×#711C2×D311yescharacteristic, complemented
217C2×#711C2×D312yescomplemented
218C2×D4×D5—34no—
219C2×D4×D5C2×D312yes—
220C2×D4×D5C2×D311yescharacteristic, complemented
221C2×#709C2×D312yescomplemented
222C2×#709C2×D311yescharacteristic, complemented
223C22×C4×D5—31no—
224C22×C4×D5—31no—
225C22×C4×D5—31no—
226C22×C4×D5—32no—
227C22×C4×D5—32no—
228C22×C4×D5—32no—
229C22×C4×D5—32no—
230C22×C4×D5—68no—
231C22×C4×D5C2×D311yescharacteristic
232C22×C4×D5C2×D312yescomplemented
233C5×#123—32no—
234C5×C22⋊Q8—32no—
235C5×#121—32no—
236C5×#120—32no—
237C4×C5×D4—34no—
238C5×#117—31no—
239#4099—32no—
240#4092—32no—
241#4085—34no—
242#4084—32no—
243#4083—32no—
244#4083—34no—
245#4081—32no—
246D4×Dic5—34no—
247#4076—32no—
248#4075—32no—
249C4×C22⋊D5—34no—
250C4×C22⋊D5—34no—
251#4072—31no—
252#4070—32no—
253#4043—32no—
254#4042—34no—
255#4041—32no—
256#4040—34no—
257#4039—34no—
258#4038—32no—
259D5×C4⋊C4—34no—
260D5×C4⋊C4—32no—
261#4032—32no—
262#4030—34no—
263#4029—34no—
264#4028—32no—
265#4028—34no—
266#4027—34no—
267#4027—34no—
268D5×C22⋊C4—32no—
269D5×C22⋊C4—34no—
270D5×C22⋊C4—34no—
271#4024—34no—
272#4023—32no—
273C4×D20—34no—
274#4018—32no—
275C42×D5—32no—
276C2×#525—151noSylow
277C23×C3×C5C2412yes—
278C23×C3×C5C2411yescharacteristic
279C22×D15—22no—
280C22×D15—24no—
281C22×D15C2412yes—
282C22×C5×D3—22no—
283C22×C5×D3—24no—
284C22×C5×D3C2412yes—
285C22×C3×D5—24no—
286C22×C3×D5—24no—
287C22×C3×D5—28no—
288C22×C3×D5C2×D414yes—
289C22×C3×D5C2412yes—
290C22×C3×D5C2411yescharacteristic
291C22×C3×D5C2411yescharacteristic
292C2×D3×D5—232no—
293C2×D3×D5—24no—
294C2×D3×D5—24no—
295C2×D3×D5—24no—
296C2×D3×D5—24no—
297C2×D3×D5—24no—
298C2×D3×D5#4118yescomplemented
299C3×C5×Q8—22no—
300C3×C5×D4—24no—
301C3×C5×D4—22no—
302C2×C3×C4×C5—24no—
303C2×C3×C4×C5C2×D414yescomplemented
304C2×C3×C4×C5C2412yes—
305C2×C3×C4×C5C2411yescharacteristic
306C2×C3×C4×C5C2411yescharacteristic
307#1220—28no—
308C2×Dic15—22no—
309C2×Dic15C2414yes—
310C2×Dic15C2412yes—
311C4×D15—24no—
312C4×D15—24no—
313C5×#67—28no—
314C2×C5×Dic3—22no—
315C2×C5×Dic3C2414yes—
316C2×C5×Dic3C2412yes—
317C4×C5×D3—24no—
318C4×C5×D3—24no—
319C3×C22⋊D5—24no—
320C3×C22⋊D5—24no—
321C3×C22⋊D5—24no—
322C2×C3×Dic5—24no—
323C2×C3×Dic5C2×D414yescomplemented
324C2×C3×Dic5C2412yes—
325C2×C3×Dic5C2411yescharacteristic
326C2×C3×Dic5C2411yescharacteristic
327C3×D20—24no—
328C3×D20—22no—
329C3×C4×D5—24no—
330C3×C4×D5—24no—
331C3×C4×D5—24no—
332C3×C4×D5C2×D414yes—
333C3×C4×D5C2×D414yes—
334C3×C4×D5C2×D414yescomplemented
335C3×C4×D5C2×D414yescomplemented
336C3×Dic10—22no—
337C3×Dic10—24no—
338#1202—28no—
339#1201—28no—
340#1200—24no—
341#1200—24no—
342D3×Dic5—24no—
343D3×Dic5—24no—
344D5×Dic3—24no—
345D5×Dic3—24no—
346D5×Dic3—28no—
347C24×D3—51no—
348C2×C3×#41—51no—
349C2×C3×#41—52no—
350C2×C3×#41—51no—
351C2×C3×#41—51no—
352C2×C3×#41—52no—
353C2×C3×#41—108no—
354C2×C3×#41C2×D511yescharacteristic, complemented
355C22×C3×Q8—51no—
356C22×C3×D4—52no—
357C22×C3×D4—51no—
358C23×C3×C4—51no—
359C23×C3×C4—52no—
360C22×#67—54no—
361C23×Dic3—51no—
362C22×C4×D3—51no—
363C22×C4×D3—51no—
364C22×C4×D3—51no—
365C22×C4×D3—52no—
366C22×C4×D3—52no—
367C22×C4×D3—52no—
368C22×C4×D3—52no—
369C22×C4×D3—108no—
370C22×C4×D3C2×D511yescharacteristic, complemented
371C2×#217—52no—
372C2×#217—54no—
373#946—52no—
374#946—52no—
375#946—54no—
376#946—52no—
377#946—54no—
378#946C2×D512yescomplemented
379#938—52no—
380#938—54no—
381#938—52no—
382#938—54no—
383#938—52no—
384#938C2×D512yescomplemented
385#937—52no—
386#937—52no—
387#937—54no—
388#937—52no—
389#937—54no—
390#937C2×D512yescomplemented
391#935—52no—
392#935—52no—
393#935—52no—
394#935—54no—
395#935—54no—
396#935C2×D512yescomplemented
397C4×#67—54no—
398C4×#67—54no—
399C4×#67—54no—
400C4×#67—54no—
401C4×#67—54no—
402C4×#67—54no—
403C4×#67—54no—
404C4×#67C2×D514yescomplemented
405C2×(C2×D3)⋊C4—54no—
406#926—51no—
407#926—52no—
408#926—52no—
409#926—52no—
410#926C2×D511yescharacteristic, complemented
411C2×C4⋊Dic3—52no—
412C2×Dic3⋊C4—54no—
413C2×C4×Dic3—52no—
414C24×C5—31no—
415C23×D5—32no—
416C23×D5—31no—
417C23×D5—32no—
418C23×D5—68no—
419C23×D5—64no—
420C23×D5C22×D312yes—
421C23×D5C22×D311yescharacteristic
422C5×#41—24no—
423C2×C5×Q8C22×D311yescharacteristic, complemented
424C2×C5×D4—34no—
425C2×C5×D4C22×D312yes—
426C2×C5×D4C22×D311yescharacteristic, complemented
427C22×C4×C5—31no—
428C22×C4×C5—32no—
429C22×C4×C5—32no—
430C22×C4×C5—64no—
431C22×C4×C5C22×D311yescharacteristic
432C22×C4×C5C22×D312yescomplemented
433C2×C22⋊D5—34no—
434C2×C22⋊D5—34no—
435C2×C22⋊D5C22×D312yes—
436C2×C22⋊D5C22×D312yes—
437C2×C22⋊D5C22×D312yescomplemented
438C22×Dic5—31no—
439C22×Dic5—32no—
440C22×Dic5—32no—
441C22×Dic5—64no—
442C22×Dic5C22×D311yescharacteristic
443C22×Dic5C22×D312yescomplemented
444#713—24no—
445Q8×D5—24no—
446#711—28no—
447#711—24no—
448D4×D5—28no—
449D4×D5—24no—
450D4×D5—616no—
451#709—24no—
452#709—28no—
453C2×D20—34no—
454C2×D20C22×D312yes—
455C2×D20C22×D311yescharacteristic, complemented
456C2×C4×D5—28no—
457C2×C4×D5—32no—
458C2×C4×D5—32no—
459C2×C4×D5—34no—
460C2×C4×D5—32no—
461C2×C4×D5—32no—
462C2×C4×D5—32no—
463C2×C4×D5—32no—
464C2×C4×D5—64no—
465C2×C4×D5—64no—
466C2×C4×D5—64no—
467C2×C4×D5—68no—
468C2×C4×D5—68no—
469C2×C4×D5—68no—
470C2×C4×D5—68no—
471C2×C4×D5#6718yescomplemented
472C2×C4×D5C22×D312yes—
473C2×C4×D5C22×D311yescharacteristic
474C2×C4×D5C22×D311yescharacteristic
475C2×C4×D5C22×D311yescharacteristic
476C2×C4×D5C22×D311yescharacteristic
477C2×C4×D5C22×D312yescomplemented
478C2×C4×D5C22×D312yescomplemented
479C2×Dic10C22×D312yescomplemented
480C2×Dic10C22×D311yescharacteristic, complemented
481C5×C4⋊C4—32no—
482C5×C4⋊C4—34no—
483C5×C22⋊C4—32no—
484C5×C22⋊C4—34no—
485C5×C22⋊C4—34no—
486C42×C5—32no—
487C22⋊Dic5—32no—
488C22⋊Dic5—34no—
489C22⋊Dic5—34no—
490#685—34no—
491#685—34no—
492#685—34no—
493#685—34no—
494#685—34no—
495C4⋊Dic5—32no—
496C4⋊Dic5—34no—
497#683—34no—
498#683—34no—
499#683—34no—
500C4×Dic5—32no—
501C4×Dic5—34no—
502C22×#41—51no—
503C24×C4—151no—
504#525—31no—
505#525—151no—
506#525—154no—
507#525—152no—
508#525—152no—
509#525—152no—
510#525—152no—
511#525—151no—
512#525—151no—
513C2×#123—152no—
514C2×C22⋊Q8—152no—
515C2×#121—152no—
516C2×#120—152no—
517C2×C4×D4—154no—
518C2×#117—151no—
519C22×C3×C5—22no—
520C22×C3×C5—22no—
521C22×C3×C5—24no—
522C22×C3×C5C22×D412yes—
523C22×C3×C5C2511yescharacteristic
524C2×D15—28no—
525C2×D15—22no—
526C2×D15—22no—
527C2×D15C2×#4114yescomplemented
528C2×C5×D3—28no—
529C2×C5×D3—22no—
530C2×C5×D3—22no—
531C2×C5×D3C2×#4114yescomplemented
532C2×C3×D5—22no—
533C2×C3×D5—28no—
534C2×C3×D5—22no—
535C2×C3×D5—24no—
536C2×C3×D5—48no—
537C2×C3×D5C22×D412yes—
538C2×C3×D5C22×D412yes—
539C2×C3×D5C2×#4114yes—
540D3×D5—216no—
541D3×D5—216no—
542C3×C4×C5—22no—
543C3×C4×C5C22×D412yes—
544C3×C4×C5C22×D412yes—
545Dic15—22no—
546Dic15—24no—
547C3×Dic5—22no—
548C3×Dic5C22×D412yes—
549C3×Dic5C22×D412yes—
550C5×Dic3—22no—
551C5×Dic3—24no—
552C24×C3—51no—
553C24×C3—52no—
554C23×D3—52no—
555C23×D3—51no—
556C23×D3—52no—
557C23×D3—108no—
558C23×D3—104no—
559C23×D3C22×D511yescharacteristic
560C3×#41—24no—
561C3×#41—108no—
562C3×#41—108no—
563C3×#41—104no—
564C3×#41—104no—
565C3×#41—104no—
566C2×C3×Q8—52no—
567C2×C3×Q8—51no—
568C2×C3×Q8—104no—
569C2×C3×Q8C22×D511yescharacteristic, complemented
570C2×C3×D4—52no—
571C2×C3×D4—52no—
572C2×C3×D4—52no—
573C2×C3×D4—52no—
574C2×C3×D4—51no—
575C2×C3×D4—104no—
576C2×C3×D4—108no—
577C2×C3×D4C22×D512yes—
578C2×C3×D4C22×D511yescharacteristic, complemented
579C22×C3×C4—51no—
580C22×C3×C4—58no—
581C22×C3×C4—51no—
582C22×C3×C4—51no—
583C22×C3×C4—51no—
584C22×C3×C4—51no—
585C22×C3×C4—52no—
586C22×C3×C4—52no—
587C22×C3×C4—52no—
588C22×C3×C4—52no—
589C22×C3×C4—108no—
590C22×C3×C4C22×D511yescharacteristic
591C22×C3×C4C22×D512yescomplemented
592C2×#67—54no—
593C2×#67—54no—
594C2×#67—54no—
595C2×#67—1016no—
596C2×#67C22×D514yes—
597C22×Dic3—51no—
598C22×Dic3—54no—
599C22×Dic3—52no—
600C22×Dic3—52no—
601C22×Dic3—104no—
602C22×Dic3C22×D511yescharacteristic
603C2×C4×D3—24no—
604C2×C4×D3—52no—
605C2×C4×D3—52no—
606C2×C4×D3—52no—
607C2×C4×D3—52no—
608C2×C4×D3—52no—
609C2×C4×D3—52no—
610C2×C4×D3—108no—
611C2×C4×D3—108no—
612C2×C4×D3—108no—
613C2×C4×D3—108no—
614C2×C4×D3—104no—
615C2×C4×D3—104no—
616C2×C4×D3—104no—
617C2×C4×D3C22×D512yes—
618C2×C4×D3C22×D512yes—
619#217—52no—
620#217—54no—
621#217—54no—
622#217—54no—
623#217—54no—
624#217C22×D512yes—
625#217C22×D514yescomplemented
626(C2×D3)⋊C4—54no—
627(C2×D3)⋊C4—54no—
628(C2×D3)⋊C4—54no—
629(C2×D3)⋊C4C22×D514yes—
630C4⋊Dic3—52no—
631C4⋊Dic3—54no—
632C4⋊Dic3C22×D512yescomplemented
633Dic3⋊C4—54no—
634Dic3⋊C4—54no—
635Dic3⋊C4—54no—
636Dic3⋊C4C22×D514yescomplemented
637C4×Dic3—52no—
638C4×Dic3—54no—
639C4×Dic3C22×D512yescomplemented
640C23×C5—32no—
641C23×C5—64no—
642C23×C5—62no—
643C23×C5C23×D312yes—
644C23×C5C23×D311yescharacteristic
645C22×D5—24no—
646C22×D5—28no—
647C22×D5—24no—
648C22×D5—32no—
649C22×D5—38no—
650C22×D5—64no—
651C22×D5—64no—
652C22×D5—632no—
653C22×D5—64no—
654C22×D5—62no—
655C22×D5—64no—
656C22×D5—64no—
657C22×D5—64no—
658C22×D5C2×#6714yes—
659C22×D5C23×D312yes—
660C22×D5C23×D311yescharacteristic
661C22×D5C23×D311yescharacteristic
662C5×Q8—22no—
663C5×D4—24no—
664C5×D4—22no—
665C5×D4—68no—
666C2×C4×C5—24no—
667C2×C4×C5—34no—
668C2×C4×C5—32no—
669C2×C4×C5—62no—
670C2×C4×C5—64no—
671C2×C4×C5—64no—
672C2×C4×C5C2×#6714yescomplemented
673C2×C4×C5C23×D312yes—
674C2×C4×C5C23×D311yescharacteristic
675C2×C4×C5C23×D311yescharacteristic
676C22⋊D5—24no—
677C22⋊D5—24no—
678C22⋊D5—24no—
679C22⋊D5—68no—
680C22⋊D5—68no—
681C2×Dic5—24no—
682C2×Dic5—34no—
683C2×Dic5—32no—
684C2×Dic5—62no—
685C2×Dic5—64no—
686C2×Dic5—64no—
687C2×Dic5C2×#6714yescomplemented
688C2×Dic5C23×D312yes—
689C2×Dic5C23×D311yescharacteristic
690C2×Dic5C23×D311yescharacteristic
691D20—24no—
692D20—22no—
693D20—68no—
694C4×D5—24no—
695C4×D5—24no—
696C4×D5—24no—
697C4×D5—68no—
698C4×D5—64no—
699C4×D5—64no—
700C4×D5—64no—
701C4×D5—64no—
702C4×D5—64no—
703C4×D5—64no—
704C4×D5C2×#6714yes—
705C4×D5C2×#6714yes—
706C4×D5C2×#6714yescomplemented
707C4×D5C2×#6714yescomplemented
708Dic10—22no—
709Dic10—24no—
710C25—151no—
711C2×#41—51no—
712C2×#41—52no—
713C2×#41—51no—
714C2×#41—51no—
715C2×#41—52no—
716C2×#41—108no—
717C2×#41D3×D511yescharacteristic, complemented
718C22×Q8—51no—
719C22×D4—52no—
720C22×D4—51no—
721C22×D4—154no—
722C23×C4—31no—
723C23×C4—51no—
724C23×C4—52no—
725C23×C4—152no—
726C23×C4—152no—
727C23×C4—151no—
728C23×C4—152no—
729C23×C4—152no—
730C23×C4—151no—
731C23×C4—151no—
732C23×C4—151no—
733C23×C4—308no—
734#123—32no—
735#123—154no—
736#123—152no—
737#123—154no—
738#123—152no—
739#123—152no—
740C22⋊Q8—32no—
741C22⋊Q8—154no—
742C22⋊Q8—154no—
743C22⋊Q8—152no—
744C22⋊Q8—152no—
745C22⋊Q8—152no—
746#121—32no—
747#121—154no—
748#121—152no—
749#121—152no—
750#121—154no—
751#121—152no—
752#120—32no—
753#120—152no—
754#120—154no—
755#120—154no—
756#120—152no—
757#120—152no—
758C4×D4—34no—
759C4×D4—154no—
760C4×D4—154no—
761C4×D4—154no—
762C4×D4—154no—
763C4×D4—154no—
764C4×D4—154no—
765C4×D4—154no—
766#117—31no—
767#117—152no—
768#117—152no—
769#117—152no—
770#117—151no—
771C2×C4⋊C4—152no—
772C2×C4⋊C4—154no—
773C2×C22⋊C4—154no—
774C2×C22⋊C4—152no—
775C2×C22⋊C4—154no—
776C2×C42—152no—
777C2×C3×C5—22no—
778C2×C3×C5—42no—
779C2×C3×C5C23×D411yescharacteristic
780C2×C3×C5C22×#4112yes—
781D15—24no—
782C3×D5—22no—
783C3×D5—42no—
784C3×D5#52514yescomplemented
785C5×D3—24no—
786C23×C3—51no—
787C23×C3—54no—
788C23×C3—51no—
789C23×C3—52no—
790C23×C3—104no—
791C23×C3—108no—
792C23×C3—104no—
793C23×C3C23×D512yes—
794C23×C3C23×D511yescharacteristic
795C22×D3—22no—
796C22×D3—24no—
797C22×D3—52no—
798C22×D3—58no—
799C22×D3—104no—
800C22×D3—104no—
801C22×D3—104no—
802C22×D3—104no—
803C22×D3—1032no—
804C22×D3—104no—
805C22×D3—102no—
806C22×D3—104no—
807C22×D3C23×D512yes—
808C3×Q8—22no—
809C3×Q8—104no—
810C3×Q8—102no—
811C3×D4—24no—
812C3×D4—22no—
813C3×D4—104no—
814C3×D4—104no—
815C3×D4—104no—
816C3×D4—104no—
817C3×D4—102no—
818C2×C3×C4—24no—
819C2×C3×C4—54no—
820C2×C3×C4—51no—
821C2×C3×C4—51no—
822C2×C3×C4—54no—
823C2×C3×C4—54no—
824C2×C3×C4—54no—
825C2×C3×C4—54no—
826C2×C3×C4—52no—
827C2×C3×C4—104no—
828C2×C3×C4—104no—
829C2×C3×C4—104no—
830C2×C3×C4—104no—
831C2×C3×C4D4×D514yescomplemented
832C2×C3×C4C23×D512yes—
833C2×C3×C4C23×D511yescharacteristic
834C2×C3×C4C23×D511yescharacteristic
835#67—28no—
836#67—108no—
837#67—108no—
838#67—108no—
839C2×Dic3—22no—
840C2×Dic3—54no—
841C2×Dic3—52no—
842C2×Dic3—104no—
843C2×Dic3—104no—
844C2×Dic3—108no—
845C2×Dic3—102no—
846C2×Dic3C23×D514yes—
847C2×Dic3C23×D512yes—
848C4×D3—24no—
849C4×D3—24no—
850C4×D3—104no—
851C4×D3—104no—
852C4×D3—104no—
853C4×D3—104no—
854C4×D3—104no—
855C4×D3—104no—
856C22×C5—22no—
857C22×C5—24no—
858C22×C5—22no—
859C22×C5—34no—
860C22×C5—68no—
861C22×C5—62no—
862C22×C5—62no—
863C22×C5C22×#6712yes—
864C22×C5C24×D311yescharacteristic
865C2×D5—22no—
866C2×D5—28no—
867C2×D5—24no—
868C2×D5—22no—
869C2×D5—34no—
870C2×D5—48no—
871C2×D5—616no—
872C2×D5—68no—
873C2×D5—62no—
874C2×D5—62no—
875C2×D5—616no—
876C2×D5D3×#4114yes—
877C2×D5C22×#6712yes—
878C2×D5C22×#6712yes—
879C4×C5—22no—
880C4×C5—64no—
881C4×C5—62no—
882C4×C5C22×#6712yes—
883C4×C5C22×#6712yes—
884Dic5—22no—
885Dic5—64no—
886Dic5—62no—
887Dic5C22×#6712yes—
888Dic5C22×#6712yes—
889C24—31no—
890C24—51no—
891C24—52no—
892C24—152no—
893C24—152no—
894C24—151no—
895C24—304no—
896C24—308no—
897#41—24no—
898#41—108no—
899#41—108no—
900#41—104no—
901#41—104no—
902#41—104no—
903C2×Q8—52no—
904C2×Q8—51no—
905C2×Q8—104no—
906C2×Q8C2×D3×D511yescharacteristic, complemented
907C2×D4—34no—
908C2×D4—52no—
909C2×D4—52no—
910C2×D4—52no—
911C2×D4—52no—
912C2×D4—51no—
913C2×D4—104no—
914C2×D4—108no—
915C2×D4—154no—
916C2×D4—154no—
917C2×D4—154no—
918C2×D4—3016no—
919C2×D4C2×D3×D512yes—
920C2×D4C2×D3×D511yescharacteristic, complemented
921C22×C4—31no—
922C22×C4—32no—
923C22×C4—32no—
924C22×C4—51no—
925C22×C4—58no—
926C22×C4—51no—
927C22×C4—51no—
928C22×C4—51no—
929C22×C4—51no—
930C22×C4—52no—
931C22×C4—52no—
932C22×C4—52no—
933C22×C4—52no—
934C22×C4—64no—
935C22×C4—108no—
936C22×C4—152no—
937C22×C4—152no—
938C22×C4—154no—
939C22×C4—152no—
940C22×C4—152no—
941C22×C4—152no—
942C22×C4—152no—
943C22×C4—151no—
944C22×C4—152no—
945C22×C4—152no—
946C22×C4—304no—
947C22×C4—308no—
948C22×C4—308no—
949C22×C4—308no—
950C22×C4—308no—
951C22×C4—304no—
952C22×C4—304no—
953C22×C4—304no—
954C22×C4C2×D3×D511yescharacteristic
955C22×C4C2×D3×D512yescomplemented
956C4⋊C4—32no—
957C4⋊C4—34no—
958C4⋊C4—154no—
959C4⋊C4—154no—
960C4⋊C4—154no—
961C4⋊C4—152no—
962C4⋊C4—154no—
963C22⋊C4—32no—
964C22⋊C4—34no—
965C22⋊C4—34no—
966C22⋊C4—154no—
967C22⋊C4—154no—
968C22⋊C4—154no—
969C22⋊C4—154no—
970C22⋊C4—154no—
971C22⋊C4—152no—
972C22⋊C4—154no—
973C22⋊C4—154no—
974C42—32no—
975C42—154no—
976C42—152no—
977C3×C5C2×#52511yescharacteristic, complemented, Hall
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—24no—
981C22×C3—52no—
982C22×C3—54no—
983C22×C3—52no—
984C22×C3—108no—
985C22×C3—102no—
986C22×C3—102no—
987C22×C3—104no—
988C22×C3—208no—
989C22×C3C2×D4×D512yes—
990C22×C3C24×D511yescharacteristic
991C2×D3—28no—
992C2×D3—22no—
993C2×D3—22no—
994C2×D3—54no—
995C2×D3—1016no—
996C2×D3—1016no—
997C2×D3—108no—
998C2×D3—102no—
999C2×D3—102no—
1000C2×D3D5×#4114yescomplemented
1001C3×C4—22no—
1002C3×C4—52no—
1003C3×C4—52no—
1004C3×C4—102no—
1005C3×C4C2×D4×D512yes—
1006C3×C4C2×D4×D512yes—
1007Dic3—22no—
1008Dic3—24no—
1009Dic3—102no—
1010Dic3—104no—
1011C2×C5—22no—
1012C2×C5—42no—
1013C2×C5—64no—
1014C2×C5C2×D3×#4112yes—
1015C2×C5C23×#6711yescharacteristic
1016D5—22no—
1017D5—42no—
1018D5—64no—
1019D5#582814yesdirect product factor
1020C23—32no—
1021C23—51no—
1022C23—54no—
1023C23—51no—
1024C23—52no—
1025C23—64no—
1026C23—62no—
1027C23—104no—
1028C23—104no—
1029C23—108no—
1030C23—158no—
1031C23—152no—
1032C23—304no—
1033C23—304no—
1034C23—304no—
1035C23—304no—
1036C23—304no—
1037C23—304no—
1038C23—3032no—
1039C23—302no—
1040C23C22×D3×D512yes—
1041C23C22×D3×D511yescharacteristic
1042Q8—22no—
1043Q8—104no—
1044Q8—102no—
1045D4—24no—
1046D4—22no—
1047D4—68no—
1048D4—104no—
1049D4—104no—
1050D4—104no—
1051D4—104no—
1052D4—102no—
1053D4—308no—
1054D4—308no—
1055D4—308no—
1056C2×C4—24no—
1057C2×C4—34no—
1058C2×C4—32no—
1059C2×C4—54no—
1060C2×C4—51no—
1061C2×C4—51no—
1062C2×C4—54no—
1063C2×C4—54no—
1064C2×C4—54no—
1065C2×C4—54no—
1066C2×C4—52no—
1067C2×C4—62no—
1068C2×C4—64no—
1069C2×C4—64no—
1070C2×C4—104no—
1071C2×C4—104no—
1072C2×C4—104no—
1073C2×C4—104no—
1074C2×C4—154no—
1075C2×C4—152no—
1076C2×C4—304no—
1077C2×C4—304no—
1078C2×C4—304no—
1079C2×C4—304no—
1080C2×C4—304no—
1081C2×C4—304no—
1082C2×C4—308no—
1083C2×C4—302no—
1084C2×C4—304no—
1085C2×C4—304no—
1086C2×C4D5×#6714yescomplemented
1087C2×C4C22×D3×D512yes—
1088C2×C4C22×D3×D511yescharacteristic
1089C2×C4C22×D3×D511yescharacteristic
1090C2×C3—22no—
1091C2×C3—42no—
1092C2×C3—54no—
1093C2×C3—102no—
1094C2×C3—202no—
1095C2×C3C22×D4×D511yescharacteristic
1096C2×C3C2×D5×#4112yes—
1097D3—24no—
1098D3—104no—
1099C5C2×#582811yescharacteristic, complemented, Sylow
1100C22—22no—
1101C22—22no—
1102C22—24no—
1103C22—34no—
1104C22—52no—
1105C22—54no—
1106C22—52no—
1107C22—68no—
1108C22—62no—
1109C22—62no—
1110C22—108no—
1111C22—102no—
1112C22—102no—
1113C22—104no—
1114C22—154no—
1115C22—208no—
1116C22—308no—
1117C22—3016no—
1118C22—3016no—
1119C22—302no—
1120C22—302no—
1121C22C2×D5×#6712yes—
1122C22C23×D3×D511yescharacteristic
1123C4—22no—
1124C4—52no—
1125C4—52no—
1126C4—62no—
1127C4—64no—
1128C4—102no—
1129C4—302no—
1130C4—304no—
1131C4C2×D5×#6712yes—
1132C4C2×D5×#6712yes—
1133C3D5×#52511yescharacteristic, complemented, Sylow
1134C2—22no—
1135C2—42no—
1136C2—54no—
1137C2—64no—
1138C2—102no—
1139C2—202no—
1140C2—304no—
1141C2D3×D5×#4112yes—
1142C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C22×C4×D3×D5C2semidirect
3. #11756587C2semidirect
4. C5×#5828C2semidirect
5. #11755270C2semidirect
6. D5×#946C2semidirect
7. #11755060C2semidirect
8. D5×#938C2semidirect
9. D5×#937C2semidirect
10. #11754800C2semidirect
11. #11754795C2semidirect
12. D5×#935C2semidirect
13. #11754631C2semidirect
14. C4×D5×#67C2semidirect
15. #11754590C2semidirect
16. #11754577C2semidirect
17. D5×#926C2semidirect
20. C2×C3×C5×#41C22semidirect
21. C22×C4×D15C22semidirect
22. C22×C4×C5×D3C22semidirect
24. C2×C3×#713C22semidirect
25. C2×C3×Q8×D5C22semidirect
26. C2×C3×#711C22semidirect
27. C2×C3×#711C22semidirect
29. C2×C3×D4×D5C22semidirect
30. C2×C3×#709C22semidirect
31. C2×C3×#709C22semidirect
33. C22×C3×C4×D5C22semidirect
35. C22×#1200C22semidirect
36. C22×D3×Dic5C22semidirect
41. C2×C4×D3×D5C22semidirect
42. C2×C4×D3×D5C22semidirect
43. #91835C22semidirect
44. #91827C22semidirect
45. #91826C22semidirect
46. #91824C22semidirect
47. C4×#1220C22semidirect
48. #91815C22semidirect
49. C5×#946C22semidirect
50. C5×#938C22semidirect
51. C5×#937C22semidirect
52. C5×#935C22semidirect
53. C4×C5×#67C22semidirect
54. C5×#926C22semidirect
55. #91577C22semidirect
56. #91572C22semidirect
57. #91568C22semidirect
58. #91565C22semidirect
59. #91552C22semidirect
60. Dic5×#67C22semidirect
61. #91548C22semidirect
63. D5×#217C22semidirect
64. #91537C22semidirect
65. #91536C22semidirect
66. #91533C22semidirect
67. #91528C22semidirect
68. #91474C22semidirect
70. #91465C22semidirect
71. #91456C22semidirect
72. #91444C22semidirect
73. C4×#1202C22semidirect
74. #91440C22semidirect
75. C4×#1201C22semidirect
76. D5×C4⋊Dic3C22semidirect
77. #91411C22semidirect
78. #91410C22semidirect
79. #91407C22semidirect
80. D5×Dic3⋊C4C22semidirect
81. C4×D5×Dic3C22semidirect
82. #91390C22semidirect
83. #91369C22semidirect
84. #91358C22semidirect
85. #91357C22semidirect
87. C2×D5×#41D3semidirect
113. C2×C3×C5×Q8C23semidirect
115. C2×C3×C5×D4C23semidirect
117. C22×C3×C4×C5C23semidirect
130. C2×C3×C22⋊D5C23semidirect
132. C22×C3×Dic5C23semidirect
142. C2×C3×D20C23semidirect
144. C2×C3×C4×D5D4semidirect
150. C2×C3×C4×D5C23semidirect
151. C2×C3×C4×D5C23semidirect
152. C2×C3×Dic10C23semidirect
153. C2×C3×Dic10C23semidirect
172. #6719C23semidirect
174. C4⋊Dic15C23semidirect
175. #6712C23semidirect
176. C4×Dic15C23semidirect
178. C5×#217C23semidirect
180. C5×C4⋊Dic3C23semidirect
181. C5×Dic3⋊C4C23semidirect
182. C4×C5×Dic3C23semidirect
183. Dic3⋊Dic5C23semidirect
184. #6669C23semidirect
185. #6668C23semidirect
189. #6665C23semidirect
190. #6665C23semidirect
191. Dic3×Dic5C23semidirect
202. #5828D5direct (N × H)
210. C2×C5×#41C2×D3semidirect
214. C2×#713C2×D3semidirect
215. C2×Q8×D5C2×D3semidirect
216. C2×#711C2×D3semidirect
217. C2×#711C2×D3semidirect
220. C2×D4×D5C2×D3semidirect
221. C2×#709C2×D3semidirect
222. C2×#709C2×D3semidirect
232. C22×C4×D5C2×D3semidirect
298. C2×D3×D5#41semidirect
303. C2×C3×C4×C5C2×D4semidirect
323. C2×C3×Dic5C2×D4semidirect
334. C3×C4×D5C2×D4semidirect
335. C3×C4×D5C2×D4semidirect
354. C2×C3×#41C2×D5semidirect
370. C22×C4×D3C2×D5semidirect
378. #946C2×D5semidirect
384. #938C2×D5semidirect
390. #937C2×D5semidirect
396. #935C2×D5semidirect
404. C4×#67C2×D5semidirect
410. #926C2×D5semidirect
423. C2×C5×Q8C22×D3semidirect
426. C2×C5×D4C22×D3semidirect
432. C22×C4×C5C22×D3semidirect
437. C2×C22⋊D5C22×D3semidirect
443. C22×Dic5C22×D3semidirect
455. C2×D20C22×D3semidirect
471. C2×C4×D5#67semidirect
477. C2×C4×D5C22×D3semidirect
478. C2×C4×D5C22×D3semidirect
479. C2×Dic10C22×D3semidirect
480. C2×Dic10C22×D3semidirect
527. C2×D15C2×#41semidirect
531. C2×C5×D3C2×#41semidirect
569. C2×C3×Q8C22×D5semidirect
578. C2×C3×D4C22×D5semidirect
591. C22×C3×C4C22×D5semidirect
625. #217C22×D5semidirect
632. C4⋊Dic3C22×D5semidirect
636. Dic3⋊C4C22×D5semidirect
639. C4×Dic3C22×D5semidirect
672. C2×C4×C5C2×#67semidirect
687. C2×Dic5C2×#67semidirect
706. C4×D5C2×#67semidirect
707. C4×D5C2×#67semidirect
717. C2×#41D3×D5semidirect
784. C3×D5#525semidirect
831. C2×C3×C4D4×D5semidirect
906. C2×Q8C2×D3×D5semidirect
920. C2×D4C2×D3×D5semidirect
955. C22×C4C2×D3×D5semidirect
977. C3×C5C2×#525semidirect
1000. C2×D3D5×#41semidirect
1019. D5#5828direct (N × H)
1086. C2×C4D5×#67semidirect
1099. C5C2×#5828semidirect
1133. C3D5×#525semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C22×C4×D3×D52
#117565872
C5×#58282
#117552702
D5×#9462
#117550602
D5×#9382
D5×#9372
#117548002
#117547952
D5×#9352
#117546312
C4×D5×#672
#117545902
#117545772
D5×#9262
D5×#5253
C2×#58285