Finite Group Databasebeta

← D5⋊#5132 #14412153

Subgroups — D5⋊#5132 #14412153

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C2×D5⋊#208C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
4#11752008C214yesmaximal, complemented
5D5⋊#824C212yesmaximal, complemented
6D5⋊#823C212yesmaximal, complemented
7#11751818C214yesmaximal, complemented
8D5⋊#413—31nomaximal, Hall
9C2×#6817C411yescharacteristic
10C2×C5×#235C411yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×D5×#67C412yes—
13C2×#6782C2212yes—
14D5×#235—21no—
15D5×#235—21no—
16D5×#235—21no—
17D5×#235—21no—
18D5×#235—21no—
19D5×#235—21no—
20D5×#235—21no—
21D5×#235—21no—
22C2×D5×D12C2211yescharacteristic
23C2×C4×D3×D5C412yes—
24C2×#6773C411yescharacteristic
25C2×#6772C411yescharacteristic
26C2×#6771C2212yes—
27C2×D5×Dic6C2211yescharacteristic
28C2×#6762C2212yescomplemented
29D5⋊#208—21no—
30D5⋊#208—21no—
31D5⋊#208C2212yes—
32D5⋊#208C2212yescomplemented
33C2×#6758—21no—
34C2×D5⋊(C3⋊C8)—21no—
35C2×C3×#704C2212yescomplemented
36C3×D5⋊M16—21no—
37C3×D5⋊M16—21no—
38C3×D5⋊M16C2212yes—
39C3×D5⋊M16C2212yescomplemented
40C2×C3×#700—21no—
41C2×C3×D5⋊C8—21no—
42#91175C2218yescomplemented
43#91174C2218yescomplemented
44C2×#5132—51nomaximal, Hall
45C2×D5×#41—31no—
46C2×D5⋊M16—31no—
47C2×D5⋊M16D311yescharacteristic, complemented
48D5⋊#101—32no—
49D5⋊#100—32no—
50#65777—34no—
51#65761—34no—
52C23×C3×D5C2×C411yescharacteristic
53C22×D3×D5C2×C412yes—
54C22×C3×C4×C5C2×C411yescharacteristic
55C2×#1220C2×C412yes—
56#6817—21no—
57#6817—21no—
58#6817—21no—
59#6817—21no—
60C2×D60C2×C411yescharacteristic
61C2×C4×D15C2×C412yes—
62C2×Dic30C2×C411yescharacteristic
63C2×C5×#67C2×C412yes—
64C5×#235—21no—
65C5×#235—21no—
66C5×#235—21no—
67C5×#235—21no—
68C2×C5×D12C2×C411yescharacteristic
69C2×C4×C5×D3C2×C412yes—
70C2×C5×Dic6C2×C411yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5C2×C411yescharacteristic
73C2×C3×C4×D5C2×C411yescharacteristic
74C2×C3×C4×D5D411yescharacteristic
75C2×C3×C4×D5D411yescharacteristic
76C2×C3×C4×D5D411yescharacteristic
77C2×C3×C4×D5D411yescharacteristic
78C2×C3×C4×D5D411yescharacteristic
79C2×C3×C4×D5D411yescharacteristic
80C2×C3×C4×D5D411yescharacteristic
81C2×C3×C4×D5D411yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83C2×C3×C4×D5C2311yescharacteristic
84D5×#67—22no—
85D5×#67—22no—
86D5×#67—22no—
87D5×#67—22no—
88C2×#1204C2312yes—
89C2×#1203C2312yes—
90C2×#1202C2×C412yes—
91C2×#1201C2×C412yes—
92C2×#1200C2×C412yes—
93#6782—22no—
94#6782—22no—
95#6782—22no—
96#6782—22no—
97C2×D3×Dic5C2×C412yes—
98C2×D5×Dic3C2×C412yes—
99D5×D12—21no—
100D5×D12—21no—
101D5×D12—21no—
102D5×D12—21no—
103C4×D3×D5—22no—
104C4×D3×D5—22no—
105C4×D3×D5—22no—
106C4×D3×D5—22no—
107#6773—21no—
108#6773—21no—
109#6773—21no—
110#6773—21no—
111#6772—21no—
112#6772—21no—
113#6772—21no—
114#6772—21no—
115#6771—22no—
116#6771—22no—
117#6771—22no—
118#6771—22no—
119D5×Dic6—21no—
120D5×Dic6—21no—
121D5×Dic6—21no—
122D5×Dic6—21no—
123#6762—22no—
124#6762C2314yes—
125C2×C3⋊#170—22no—
126#6758—22no—
127#6758—22no—
128D5⋊(C3⋊C8)—22no—
129D5⋊(C3⋊C8)—22no—
130C3×#704—22no—
131C3×#704C2314yes—
132C2×C3×#170—22no—
133C3×#700—22no—
134C3×#700—22no—
135C3×D5⋊C8—22no—
136C3×D5⋊C8—22no—
137C22×#235—51no—
138C22×C3×M16—51no—
139C22×#208—51no—
140C2×#824—52no—
141#5132—54no—
142#5132—54no—
143C2×#823—52no—
144C2×C5×#41—31no—
145D5×#41—61no—
146D5×#41—61no—
147D5×#41—61no—
148D5×#41—61no—
149D5×#41—61no—
150D5×#41—61no—
151D5×#41—61no—
152D5×#41—61no—
153C2×#713—31no—
154C2×Q8×D5—31no—
155C2×#711—32no—
156C2×#711—31no—
157C2×D4×D5—32no—
158C2×D4×D5—31no—
159C2×#709—31no—
160C2×#709—32no—
161C22×C4×D5—32no—
162C22×C4×D5C2×D311yescharacteristic
163C2×#704—32no—
164C2×#704C2×D312yescomplemented
165D5⋊M16—21no—
166D5⋊M16—21no—
167D5⋊M16—32no—
168D5⋊M16—32no—
169D5⋊M16—61no—
170D5⋊M16—61no—
171D5⋊M16C2×D312yes—
172D5⋊M16C2×D312yescomplemented
173C2×#700—21no—
174C2×#700—61no—
175C2×D5⋊C8—21no—
176C2×D5⋊C8—61no—
177#4013—38no—
178#4005—38no—
179C2×#413—151noSylow
180C23×C3×C5C22×C411yescharacteristic
181C22×D15C22×C412yes—
182C22×C5×D3C22×C412yes—
183C22×C3×D5—42no—
184C22×C3×D5C22⋊C411yescharacteristic
185C22×C3×D5C22⋊C411yescharacteristic
186C22×C3×D5C22⋊C411yescharacteristic
187C22×C3×D5C22⋊C411yescharacteristic
188C22×C3×D5C22×C411yescharacteristic
189C22×C3×D5C22×C411yescharacteristic
190C2×D3×D5—22no—
191C2×D3×D5—22no—
192C2×D3×D5—44no—
193C2×C3×C4×C5C22⋊C411yescharacteristic
194C2×C3×C4×C5C22⋊C411yescharacteristic
195C2×C3×C4×C5C22⋊C411yescharacteristic
196C2×C3×C4×C5C22⋊C411yescharacteristic
197C2×C3×C4×C5C22×C411yescharacteristic
198C2×C3×C4×C5C22×C411yescharacteristic
199#1220—22no—
200#1220—22no—
201C2×Dic15C22×C412yes—
202D60—21no—
203D60—21no—
204C4×D15—22no—
205C4×D15—22no—
206Dic30—21no—
207Dic30—21no—
208C5×#67—22no—
209C5×#67—22no—
210C2×C5×Dic3C22×C412yes—
211C5×D12—21no—
212C5×D12—21no—
213C4×C5×D3—22no—
214C4×C5×D3—22no—
215C5×Dic6—21no—
216C5×Dic6—21no—
217C2×C3×Dic5C22×C411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2411yescharacteristic
223C3×C4×D5C22⋊C411yescharacteristic
224C3×C4×D5C22⋊C411yescharacteristic
225C3×C4×D5C22⋊C411yescharacteristic
226C3×C4×D5C22⋊C411yescharacteristic
227C3×C4×D5C22⋊C411yescharacteristic
228C3×C4×D5C22⋊C411yescharacteristic
229C3×C4×D5C22⋊C411yescharacteristic
230C3×C4×D5C22⋊C411yescharacteristic
231C3×C4×D5C2×D411yescharacteristic
232C3×C4×D5C2×D411yescharacteristic
233C3×C4×D5C2×D411yescharacteristic
234C3×C4×D5C2×D411yescharacteristic
235C3×C4×D5C2×D411yescharacteristic
236C3×C4×D5C2×D411yescharacteristic
237C3×C4×D5C2×D411yescharacteristic
238C3×C4×D5C2×D411yescharacteristic
239#1204—22no—
240#1204—22no—
241#1203—22no—
242#1203—22no—
243#1202—22no—
244#1202—22no—
245#1201—22no—
246#1201—22no—
247#1200—22no—
248#1200—22no—
249D3×Dic5—22no—
250D3×Dic5—22no—
251D5×Dic3—22no—
252D5×Dic3—22no—
253C3⋊#170—24no—
254C3×#170—24no—
255C23×C3×C4—51no—
256C22×#67—52no—
257C2×#235—51no—
258C2×#235—52no—
259C2×#235—51no—
260C2×#235—52no—
261C2×#235—51no—
262C2×#235—101no—
263C2×#235—101no—
264C2×#235—101no—
265C2×#235—101no—
266C2×#235—101no—
267C2×#235—101no—
268C2×#235—101no—
269C2×#235—101no—
270C2×#235AGL(1,𝔽5)11yescharacteristic
271C22×D12—51no—
272C22×C4×D3—52no—
273C22×Dic6—51no—
274C2×C3×M16—52no—
275C2×C3×M16—52no—
276C2×C3×M16—52no—
277C2×C3×M16—101no—
278C2×C3×M16—101no—
279C2×C3×M16—101no—
280C22×C3×C8—101no—
281C2×#208—52no—
282C2×#208—52no—
283C2×#208—52no—
284C2×#208—101no—
285C2×#208—101no—
286C2×#208—101no—
287C22×C3⋊C8—101no—
288#824—58no—
289#823—58no—
290C23×D5—32no—
291C23×D5C4×D311yescharacteristic
292C5×#41—61no—
293C5×#41—61no—
294C5×#41—61no—
295C5×#41—61no—
296C2×C5×Q8—31no—
297C2×C5×D4—32no—
298C2×C5×D4—31no—
299C22×C4×C5—32no—
300C22×C4×C5C4×D311yescharacteristic
301C2×C22⋊D5—32no—
302C2×C22⋊D5—32no—
303C2×C22⋊D5—32no—
304C22×Dic5—32no—
305C22×Dic5C22×D311yescharacteristic
306#713—61no—
307#713—61no—
308#713—61no—
309#713—61no—
310Q8×D5—61no—
311Q8×D5—61no—
312Q8×D5—61no—
313Q8×D5—61no—
314#711—62no—
315#711—62no—
316#711—62no—
317#711—62no—
318#711—61no—
319#711—61no—
320#711—61no—
321#711—61no—
322D4×D5—62no—
323D4×D5—62no—
324D4×D5—62no—
325D4×D5—62no—
326D4×D5—61no—
327D4×D5—61no—
328D4×D5—61no—
329D4×D5—61no—
330#709—61no—
331#709—61no—
332#709—61no—
333#709—61no—
334#709—62no—
335#709—62no—
336#709—62no—
337#709—62no—
338C2×D20—32no—
339C2×D20—31no—
340C2×C4×D5—32no—
341C2×C4×D5—32no—
342C2×C4×D5—32no—
343C2×C4×D5—62no—
344C2×C4×D5—62no—
345C2×C4×D5—62no—
346C2×C4×D5—62no—
347C2×C4×D5C4×D311yescharacteristic
348C2×C4×D5C4×D311yescharacteristic
349C2×C4×D5D1211yescharacteristic
350C2×C4×D5D1211yescharacteristic
351C2×C4×D5D1211yescharacteristic
352C2×C4×D5D1211yescharacteristic
353C2×C4×D5#6711yescharacteristic
354C2×C4×D5#6711yescharacteristic
355C2×C4×D5#6711yescharacteristic
356C2×C4×D5#6711yescharacteristic
357C2×C4×D5C22×D311yescharacteristic
358C2×C4×D5C22×D311yescharacteristic
359C2×Dic10—31no—
360C2×Dic10—32no—
361#704—22no—
362#704—34no—
363#704—62no—
364#704C22×D314yes—
365C2×#170—22no—
366C2×#170—62no—
367#700—22no—
368#700—22no—
369#700—62no—
370#700—62no—
371D5⋊C8—22no—
372D5⋊C8—22no—
373D5⋊C8—62no—
374D5⋊C8—62no—
375C22×#41—151no—
376C22×M16—51no—
377C22×M16—151no—
378#413—154no—
379#413—154no—
380C2×#101—152no—
381C2×#100—152no—
382C22×C3×C5—41no—
383C22×C3×C5C2×C22⋊C411yescharacteristic
384C22×C3×C5C2×C22⋊C411yescharacteristic
385C22×C3×C5C23×C411yescharacteristic
386C2×D15—22no—
387C2×D15—42no—
388C2×C5×D3—22no—
389C2×C5×D3—42no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5C2×C22⋊C411yescharacteristic
397C2×C3×D5C2×C22⋊C411yescharacteristic
398C2×C3×D5C2×C22⋊C411yescharacteristic
399C2×C3×D5C2×C22⋊C411yescharacteristic
400D3×D5—44no—
401D3×D5—44no—
402C3×C4×C5C2×C22⋊C411yescharacteristic
403C3×C4×C5C2×C22⋊C411yescharacteristic
404C3×C4×C5C2×C22⋊C411yescharacteristic
405C3×C4×C5C2×C22⋊C411yescharacteristic
406Dic15—22no—
407C3×Dic5C2×C22⋊C411yescharacteristic
408C3×Dic5C2×C22⋊C411yescharacteristic
409C3×Dic5C22×D411yescharacteristic
410C3×Dic5C22×D411yescharacteristic
411C5×Dic3—22no—
412C24×C3—51no—
413C23×D3—52no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
428C2×#67—52no—
429C2×#67—52no—
430C2×#67—52no—
431C2×#67—102no—
432C2×#67—102no—
433C2×#67—102no—
434C2×#67—102no—
435C2×#67C2×AGL(1,𝔽5)12yes—
436C22×Dic3—52no—
437#235—21no—
438#235—21no—
439#235—21no—
440#235—21no—
441#235—101no—
442#235—101no—
443#235—101no—
444#235—101no—
445#235—102no—
446#235—102no—
447#235—102no—
448#235—102no—
449#235—101no—
450#235—101no—
451#235—101no—
452#235—101no—
453#235—102no—
454#235—102no—
455#235—102no—
456#235—102no—
457#235—101no—
458#235—101no—
459#235—101no—
460#235—101no—
461C2×D12—52no—
462C2×D12—51no—
463C2×D12—101no—
464C2×D12—101no—
465C2×D12—101no—
466C2×D12—101no—
467C2×D12C2×AGL(1,𝔽5)11yescharacteristic
468C2×C4×D3—52no—
469C2×C4×D3—52no—
470C2×C4×D3—52no—
471C2×C4×D3—102no—
472C2×C4×D3—102no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3C2×AGL(1,𝔽5)12yes—
476C2×Dic6—51no—
477C2×Dic6—52no—
478C2×Dic6—101no—
479C2×Dic6—101no—
480C2×Dic6—101no—
481C2×Dic6—101no—
482C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
483C3×M16—54no—
484C3×M16—102no—
485C3×M16—102no—
486C3×M16—102no—
487C2×C3×C8—102no—
488C2×C3×C8—102no—
489C2×C3×C8—102no—
490#208—54no—
491#208—102no—
492#208—102no—
493#208—102no—
494C2×C3⋊C8—102no—
495C2×C3⋊C8—102no—
496C2×C3⋊C8—102no—
497C23×C5—32no—
498C23×C5C2×C4×D311yescharacteristic
499C22×D5—32no—
500C22×D5—42no—
501C22×D5—62no—
502C22×D5—62no—
503C22×D5—124no—
504C22×D5(C2×D3)⋊C411yescharacteristic
505C22×D5(C2×D3)⋊C411yescharacteristic
506C22×D5(C2×D3)⋊C411yescharacteristic
507C22×D5(C2×D3)⋊C411yescharacteristic
508C22×D5C2×C4×D311yescharacteristic
509C22×D5C2×C4×D311yescharacteristic
510C5×Q8—61no—
511C5×Q8—61no—
512C5×D4—62no—
513C5×D4—62no—
514C5×D4—61no—
515C5×D4—61no—
516C2×C4×C5—32no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5(C2×D3)⋊C411yescharacteristic
520C2×C4×C5(C2×D3)⋊C411yescharacteristic
521C2×C4×C5(C2×D3)⋊C411yescharacteristic
522C2×C4×C5(C2×D3)⋊C411yescharacteristic
523C2×C4×C5C2×C4×D311yescharacteristic
524C2×C4×C5C2×C4×D311yescharacteristic
525C22⋊D5—62no—
526C22⋊D5—62no—
527C22⋊D5—62no—
528C22⋊D5—62no—
529C22⋊D5—62no—
530C22⋊D5—62no—
531C2×Dic5—32no—
532C2×Dic5—62no—
533C2×Dic5—62no—
534C2×Dic5C2×C4×D311yescharacteristic
535C2×Dic5C2×D1211yescharacteristic
536C2×Dic5C2×D1211yescharacteristic
537C2×Dic5C2×#6711yescharacteristic
538C2×Dic5C2×#6711yescharacteristic
539C2×Dic5C23×D311yescharacteristic
540D20—62no—
541D20—62no—
542D20—61no—
543D20—61no—
544C4×D5—62no—
545C4×D5—62no—
546C4×D5—62no—
547C4×D5—62no—
548C4×D5—62no—
549C4×D5—62no—
550C4×D5(C2×D3)⋊C411yescharacteristic
551C4×D5(C2×D3)⋊C411yescharacteristic
552C4×D5(C2×D3)⋊C411yescharacteristic
553C4×D5(C2×D3)⋊C411yescharacteristic
554C4×D5(C2×D3)⋊C411yescharacteristic
555C4×D5(C2×D3)⋊C411yescharacteristic
556C4×D5(C2×D3)⋊C411yescharacteristic
557C4×D5(C2×D3)⋊C411yescharacteristic
558C4×D5C2×D1211yescharacteristic
559C4×D5C2×D1211yescharacteristic
560C4×D5C2×D1211yescharacteristic
561C4×D5C2×D1211yescharacteristic
562C4×D5C2×#6711yescharacteristic
563C4×D5C2×#6711yescharacteristic
564C4×D5C2×#6711yescharacteristic
565C4×D5C2×#6711yescharacteristic
566Dic10—61no—
567Dic10—61no—
568Dic10—62no—
569Dic10—62no—
570#170—24no—
571#170—64no—
572C2×#41—31no—
573C2×#41—152no—
574C2×#41—152no—
575C2×#41—151no—
576C2×#41—151no—
577C2×#41—151no—
578C2×#41—301no—
579C2×#41—301no—
580C2×#41—301no—
581C2×#41—301no—
582C2×#41—301no—
583C2×#41—301no—
584C2×#41—301no—
585C2×#41—301no—
586C22×Q8—151no—
587C22×D4—151no—
588C22×D4—152no—
589C23×C4—51no—
590C23×C4—152no—
591C2×M16—52no—
592C2×M16—52no—
593C2×M16—52no—
594C2×M16—101no—
595C2×M16—101no—
596C2×M16—101no—
597C2×M16—152no—
598C2×M16—152no—
599C2×M16—152no—
600C2×M16—301no—
601C2×M16—301no—
602C2×M16—301no—
603C22×C8—101no—
604C22×C8—301no—
605#101—158no—
606#100—158no—
607C2×C3×C5—21no—
608C2×C3×C5—21no—
609C2×C3×C5—21no—
610C2×C3×C5C22×C22⋊C411yescharacteristic
611D15—42no—
612C3×D5—21no—
613C3×D5—21no—
614C3×D5—21no—
615C3×D5#41312yescomplemented
616C5×D3—42no—
617C23×C3—51no—
618C23×C3—51no—
619C23×C3—51no—
620C23×C3—51no—
621C23×C3—51no—
622C23×C3—51no—
623C23×C3—202no—
624C23×C3C22×AGL(1,𝔽5)11yescharacteristic
625C22×D3—52no—
626C22×D3—102no—
627C22×D3—102no—
628C22×D3—204no—
629C22×D3C22×AGL(1,𝔽5)12yes—
630C2×C3×C4—51no—
631C2×C3×C4—51no—
632C2×C3×C4—51no—
633C2×C3×C4—51no—
634C2×C3×C4—51no—
635C2×C3×C4—51no—
636C2×C3×C4—51no—
637C2×C3×C4—51no—
638C2×C3×C4—51no—
639C2×C3×C4—51no—
640C2×C3×C4—51no—
641C2×C3×C4—51no—
642C2×C3×C4—51no—
643C2×C3×C4—51no—
644C2×C3×C4—51no—
645C2×C3×C4—51no—
646C2×C3×C4—51no—
647C2×C3×C4—51no—
648C2×C3×C4—51no—
649C2×C3×C4—51no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
653C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
654C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
655C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
656C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
657C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
658#67—22no—
659#67—22no—
660#67—102no—
661#67—102no—
662#67—102no—
663#67—102no—
664#67—102no—
665#67—102no—
666C2×Dic3—52no—
667C2×Dic3—102no—
668C2×Dic3—102no—
669C2×Dic3C22×AGL(1,𝔽5)12yes—
670D12—21no—
671D12—21no—
672D12—102no—
673D12—102no—
674D12—101no—
675D12—101no—
676C4×D3—22no—
677C4×D3—22no—
678C4×D3—102no—
679C4×D3—102no—
680C4×D3—102no—
681C4×D3—102no—
682C4×D3—102no—
683C4×D3—102no—
684Dic6—21no—
685Dic6—21no—
686Dic6—102no—
687Dic6—102no—
688Dic6—101no—
689Dic6—101no—
690C3×C8—104no—
691C3⋊C8—104no—
692C22×C5—41no—
693C22×C5—62no—
694C22×C5—122no—
695C22×C5C2×(C2×D3)⋊C411yescharacteristic
696C22×C5C2×(C2×D3)⋊C411yescharacteristic
697C22×C5C22×C4×D311yescharacteristic
698C2×D5—22no—
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—41no—
702C2×D5—41no—
703C2×D5—41no—
704C2×D5—62no—
705C2×D5—124no—
706C2×D5—124no—
707C2×D5—122no—
708C2×D5C2×(C2×D3)⋊C411yescharacteristic
709C2×D5C2×(C2×D3)⋊C411yescharacteristic
710C2×D5C2×(C2×D3)⋊C411yescharacteristic
711C2×D5C2×(C2×D3)⋊C411yescharacteristic
712C4×C5—62no—
713C4×C5C2×(C2×D3)⋊C411yescharacteristic
714C4×C5C2×(C2×D3)⋊C411yescharacteristic
715C4×C5C2×(C2×D3)⋊C411yescharacteristic
716C4×C5C2×(C2×D3)⋊C411yescharacteristic
717Dic5—62no—
718Dic5C2×(C2×D3)⋊C411yescharacteristic
719Dic5C2×(C2×D3)⋊C411yescharacteristic
720Dic5C22×D1211yescharacteristic
721Dic5C22×#6711yescharacteristic
722C24—51no—
723C24—152no—
724#41—61no—
725#41—61no—
726#41—61no—
727#41—61no—
728#41—302no—
729#41—302no—
730#41—302no—
731#41—302no—
732#41—302no—
733#41—302no—
734#41—302no—
735#41—302no—
736#41—301no—
737#41—301no—
738#41—301no—
739#41—301no—
740#41—301no—
741#41—301no—
742#41—301no—
743#41—301no—
744#41—301no—
745#41—301no—
746#41—301no—
747#41—301no—
748C2×Q8—31no—
749C2×Q8—152no—
750C2×Q8—151no—
751C2×Q8—301no—
752C2×Q8—301no—
753C2×Q8—301no—
754C2×Q8—301no—
755C2×D4—32no—
756C2×D4—31no—
757C2×D4—152no—
758C2×D4—152no—
759C2×D4—152no—
760C2×D4—152no—
761C2×D4—151no—
762C2×D4—301no—
763C2×D4—301no—
764C2×D4—301no—
765C2×D4—301no—
766C2×D4—302no—
767C2×D4—302no—
768C2×D4—302no—
769C2×D4—302no—
770C22×C4—32no—
771C22×C4—51no—
772C22×C4—51no—
773C22×C4—51no—
774C22×C4—51no—
775C22×C4—51no—
776C22×C4—51no—
777C22×C4—51no—
778C22×C4—51no—
779C22×C4—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—152no—
785C22×C4—152no—
786C22×C4—152no—
787C22×C4—152no—
788C22×C4—302no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4D3×AGL(1,𝔽5)11yescharacteristic
793M16—54no—
794M16—102no—
795M16—102no—
796M16—102no—
797M16—154no—
798M16—302no—
799M16—302no—
800M16—302no—
801C2×C8—102no—
802C2×C8—102no—
803C2×C8—102no—
804C2×C8—302no—
805C2×C8—302no—
806C2×C8—302no—
807C3×C5C2×#41311yescharacteristic, complemented, Hall
808C22×C3—41no—
809C22×C3—51no—
810C22×C3—51no—
811C22×C3—51no—
812C22×C3—51no—
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—201no—
817C22×C3—201no—
818C22×C3—201no—
819C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
820C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
821C22×C3C23×AGL(1,𝔽5)11yescharacteristic
822C2×D3—22no—
823C2×D3—42no—
824C2×D3—102no—
825C2×D3—204no—
826C2×D3—204no—
827C2×D3—202no—
828C3×C4—51no—
829C3×C4—51no—
830C3×C4—51no—
831C3×C4—51no—
832C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
833C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
834C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
835C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
836Dic3—22no—
837Dic3—102no—
838C2×C5—21no—
839C2×C5—21no—
840C2×C5—21no—
841C2×C5—122no—
842C2×C5C22×(C2×D3)⋊C411yescharacteristic
843D5—21no—
844D5—21no—
845D5—21no—
846D5—122no—
847D5#513212yescomplemented
848C23—32no—
849C23—51no—
850C23—51no—
851C23—51no—
852C23—51no—
853C23—51no—
854C23—51no—
855C23—152no—
856C23—202no—
857C23—302no—
858C23—302no—
859C23—604no—
860C23C2×D3×AGL(1,𝔽5)11yescharacteristic
861Q8—61no—
862Q8—61no—
863Q8—302no—
864Q8—302no—
865Q8—301no—
866Q8—301no—
867D4—62no—
868D4—62no—
869D4—61no—
870D4—61no—
871D4—302no—
872D4—302no—
873D4—302no—
874D4—302no—
875D4—302no—
876D4—302no—
877D4—302no—
878D4—302no—
879D4—301no—
880D4—301no—
881C2×C4—32no—
882C2×C4—51no—
883C2×C4—51no—
884C2×C4—51no—
885C2×C4—51no—
886C2×C4—51no—
887C2×C4—51no—
888C2×C4—51no—
889C2×C4—51no—
890C2×C4—51no—
891C2×C4—51no—
892C2×C4—51no—
893C2×C4—51no—
894C2×C4—51no—
895C2×C4—51no—
896C2×C4—51no—
897C2×C4—51no—
898C2×C4—51no—
899C2×C4—51no—
900C2×C4—51no—
901C2×C4—51no—
902C2×C4—51no—
903C2×C4—51no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—152no—
907C2×C4—302no—
908C2×C4—302no—
909C2×C4—302no—
910C2×C4—302no—
911C2×C4—302no—
912C2×C4—302no—
913C2×C4—302no—
914C2×C4—302no—
915C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
916C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
917C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
918C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
919C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
920C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
921C8—104no—
922C8—304no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—52no—
927C2×C3—101no—
928C2×C3—101no—
929C2×C3—101no—
930C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
931D3—42no—
932D3—202no—
933C5C2×#513211yescharacteristic, complemented, Sylow
934C22—41no—
935C22—51no—
936C22—51no—
937C22—51no—
938C22—51no—
939C22—62no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—122no—
944C22—201no—
945C22—201no—
946C22—201no—
947C22—302no—
948C22—602no—
949C22—604no—
950C22—604no—
951C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
952C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
953C22C22×D3×AGL(1,𝔽5)11yescharacteristic
954C4—51no—
955C4—51no—
956C4—51no—
957C4—51no—
958C4—62no—
959C4—302no—
960C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
961C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
962C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
963C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
964C3D5⋊#41311yescharacteristic, complemented, Sylow
965C2—21no—
966C2—21no—
967C2—21no—
968C2—52no—
969C2—101no—
970C2—101no—
971C2—101no—
972C2—122no—
973C2—602no—
974C2C22×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×D5×#235C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#413
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5⋊#208C2semidirect
3. C2×C3×D5⋊M16C2semidirect
4. #11752008C2semidirect
5. D5⋊#824C2semidirect
6. D5⋊#823C2semidirect
7. #11751818C2semidirect
28. C2×#6762C22semidirect
32. D5⋊#208C22semidirect
35. C2×C3×#704C22semidirect
39. C3×D5⋊M16C22semidirect
42. #91175C22semidirect
43. #91174C22semidirect
47. C2×D5⋊M16D3semidirect
164. C2×#704C2×D3semidirect
172. D5⋊M16C2×D3semidirect
615. C3×D5#413semidirect
807. C3×C5C2×#413semidirect
847. D5#5132semidirect
933. C5C2×#5132semidirect
964. C3D5⋊#413semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C2×D5⋊#2082
C2×C3×D5⋊M162
#117520082
D5⋊#8242
D5⋊#8232
#117518182
D5⋊#4133
C2×#51325