Finite Group Databasebeta

← D5⋊#5006 #14411964

Subgroups — D5⋊#5006 #14411964

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C2×#91989C211yesmaximal, characteristic, complemented
3C2×C3×#4130C211yesmaximal, characteristic, complemented
4D5⋊#806C214yesmaximal, complemented
5#11751817C212yesmaximal, complemented
6#11751816C212yesmaximal, complemented
7#11751815C214yesmaximal, complemented
8D5⋊#410—31nomaximal, Hall
9C2×#6817C411yescharacteristic, complemented
10C2×C5×#235C411yescharacteristic, complemented
11C22×C3×C4×D5C2211yescharacteristic
12C2×D5×#67C2212yes—
13C2×#6782C412yescomplemented
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×D12C411yescharacteristic, complemented
23C2×C4×D3×D5C412yescomplemented
24C2×#6773C2211yescharacteristic
25C2×#6772C2211yescharacteristic
26C2×#6771C2212yes—
27C2×D5×Dic6C411yescharacteristic, complemented
28C2×#6763C2212yes—
29#91989—21no—
30#91989—21no—
31#91989C2212yescomplemented
32#91989C2212yescomplemented
33C2×C4⋊ΓL(1,𝔽16)—21no—
34C2×C4×ΓL(1,𝔽16)—21no—
35C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
36C3×#4130—21no—
37C3×#4130—21no—
38C3×#4130C2212yescomplemented
39C3×#4130C2212yescomplemented
40C2×C3×C4⋊AGL(1,𝔽5)—21no—
41C2×C3×C4×AGL(1,𝔽5)—21no—
42#91173C2218yescomplemented
43#91172C2218yescomplemented
44C2×#5006—51nomaximal, Hall
45C2×D5×#41—31no—
46C2×#4130—31no—
47C2×#4130D311yescharacteristic, complemented
48#65785—32no—
49#65771—32no—
50D5⋊#99—34no—
51#65745—34no—
52C23×C3×D5C2311yescharacteristic
53C22×D3×D5C2×C412yes—
54C22×ΓL(1,𝔽16)—22no—
55C22×C3×AGL(1,𝔽5)—22no—
56C22×C3×C4×C5C2×C411yescharacteristic
57C2×#1220C2×C412yes—
58#6817—21no—
59#6817—21no—
60#6817—21no—
61#6817—21no—
62C2×D60C2×C411yescharacteristic, complemented
63C2×C4×D15C2×C412yescomplemented
64C2×Dic30C2×C411yescharacteristic, complemented
65C2×C5×#67C2×C412yes—
66C5×#235—21no—
67C5×#235—21no—
68C5×#235—21no—
69C5×#235—21no—
70C2×C5×D12C2×C411yescharacteristic, complemented
71C2×C4×C5×D3C2×C412yescomplemented
72C2×C5×Dic6C2×C411yescharacteristic, complemented
73C22×C3×Dic5C2×C411yescharacteristic
74C2×C3×C4×D5C2×C411yescharacteristic
75C2×C3×C4×D5C2×C411yescharacteristic
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×D5D411yescharacteristic
83C2×C3×C4×D5D411yescharacteristic
84C2×C3×C4×D5C2311yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86D5×#67—22no—
87D5×#67—22no—
88D5×#67—22no—
89D5×#67—22no—
90C2×#1204C2×C412yescomplemented
91C2×#1203C2×C412yescomplemented
92C2×#1202C2312yes—
93C2×#1201C2312yes—
94C2×#1200C2×C412yescomplemented
95#6782—22no—
96#6782—22no—
97#6782—22no—
98#6782—22no—
99C2×D3×Dic5C2×C412yescomplemented
100C2×D5×Dic3C2×C412yes—
101D5×D12—21no—
102D5×D12—21no—
103D5×D12—21no—
104D5×D12—21no—
105C4×D3×D5—22no—
106C4×D3×D5—22no—
107C4×D3×D5—22no—
108C4×D3×D5—22no—
109#6773—21no—
110#6773—21no—
111#6773—21no—
112#6773—21no—
113#6772—21no—
114#6772—21no—
115#6772—21no—
116#6772—21no—
117#6771—22no—
118#6771—22no—
119#6771—22no—
120#6771—22no—
121D5×Dic6—21no—
122D5×Dic6—21no—
123D5×Dic6—21no—
124D5×Dic6—21no—
125#6763—22no—
126#6763C2314yes—
127C4⋊ΓL(1,𝔽16)—22no—
128C4⋊ΓL(1,𝔽16)—22no—
129C4×ΓL(1,𝔽16)—22no—
130C4×ΓL(1,𝔽16)—22no—
131C3×C22⋊AGL(1,𝔽5)—22no—
132C3×C22⋊AGL(1,𝔽5)C2314yes—
133C3×C4⋊AGL(1,𝔽5)—22no—
134C3×C4⋊AGL(1,𝔽5)—22no—
135C3×C4×AGL(1,𝔽5)—22no—
136C3×C4×AGL(1,𝔽5)—22no—
137C22×#235—51no—
138C2×C3×#117—51no—
139C2×#926—51no—
140#5006—54no—
141#5006—52no—
142#5006—52no—
143C2×#806—54no—
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×C22⋊AGL(1,𝔽5)—32no—
164C2×C22⋊AGL(1,𝔽5)C2×D312yes—
165#4130—21no—
166#4130—21no—
167#4130—32no—
168#4130—32no—
169#4130—61no—
170#4130—61no—
171#4130C2×D312yescomplemented
172#4130C2×D312yescomplemented
173C2×C4⋊AGL(1,𝔽5)—21no—
174C2×C4⋊AGL(1,𝔽5)—61no—
175C2×C4×AGL(1,𝔽5)—21no—
176C2×C4×AGL(1,𝔽5)—61no—
177#4011—38no—
178#3999—38no—
179C2×#410—151noSylow
180C23×C3×C5C22×C411yescharacteristic
181C22×D15C22×C412yes—
182C22×C5×D3C22×C412yes—
183C22×C3×D5—42no—
184C22×C3×D5C22×C411yescharacteristic
185C22×C3×D5C2×D411yescharacteristic
186C22×C3×D5C2×D411yescharacteristic
187C22×C3×D5C2×D411yescharacteristic
188C22×C3×D5C2×D411yescharacteristic
189C22×C3×D5C2411yescharacteristic
190C2×D3×D5—22no—
191C2×D3×D5—22no—
192C2×D3×D5—44no—
193C2×ΓL(1,𝔽16)—24no—
194C2×ΓL(1,𝔽16)—44no—
195C2×C3×AGL(1,𝔽5)—24no—
196C2×C3×AGL(1,𝔽5)—44no—
197C2×C3×C4×C5C22⋊C411yescharacteristic
198C2×C3×C4×C5C22⋊C411yescharacteristic
199C2×C3×C4×C5C22⋊C411yescharacteristic
200C2×C3×C4×C5C22⋊C411yescharacteristic
201C2×C3×C4×C5C22×C411yescharacteristic
202C2×C3×C4×C5C22×C411yescharacteristic
203#1220—22no—
204#1220—22no—
205C2×Dic15C22×C412yes—
206D60—21no—
207D60—21no—
208C4×D15—22no—
209C4×D15—22no—
210Dic30—21no—
211Dic30—21no—
212C5×#67—22no—
213C5×#67—22no—
214C2×C5×Dic3C22×C412yes—
215C5×D12—21no—
216C5×D12—21no—
217C4×C5×D3—22no—
218C4×C5×D3—22no—
219C5×Dic6—21no—
220C5×Dic6—21no—
221C2×C3×Dic5C22⋊C411yescharacteristic
222C2×C3×Dic5C22⋊C411yescharacteristic
223C2×C3×Dic5C22⋊C411yescharacteristic
224C2×C3×Dic5C22⋊C411yescharacteristic
225C2×C3×Dic5C22×C411yescharacteristic
226C2×C3×Dic5C22×C411yescharacteristic
227C3×C4×D5C22⋊C411yescharacteristic
228C3×C4×D5C22⋊C411yescharacteristic
229C3×C4×D5C22⋊C411yescharacteristic
230C3×C4×D5C22⋊C411yescharacteristic
231C3×C4×D5C22⋊C411yescharacteristic
232C3×C4×D5C22⋊C411yescharacteristic
233C3×C4×D5C22⋊C411yescharacteristic
234C3×C4×D5C22⋊C411yescharacteristic
235C3×C4×D5C2×D411yescharacteristic
236C3×C4×D5C2×D411yescharacteristic
237C3×C4×D5C2×D411yescharacteristic
238C3×C4×D5C2×D411yescharacteristic
239C3×C4×D5C2×D411yescharacteristic
240C3×C4×D5C2×D411yescharacteristic
241C3×C4×D5C2×D411yescharacteristic
242C3×C4×D5C2×D411yescharacteristic
243#1204—22no—
244#1204—22no—
245#1203—22no—
246#1203—22no—
247#1202—22no—
248#1202—22no—
249#1201—22no—
250#1201—22no—
251#1200—22no—
252#1200—22no—
253D3×Dic5—22no—
254D3×Dic5—22no—
255D5×Dic3—22no—
256D5×Dic3—22no—
257C23×C3×C4—51no—
258C22×#67—52no—
259C2×#235—51no—
260C2×#235—52no—
261C2×#235—51no—
262C2×#235—52no—
263C2×#235—51no—
264C2×#235—101no—
265C2×#235—101no—
266C2×#235—101no—
267C2×#235—101no—
268C2×#235—101no—
269C2×#235—101no—
270C2×#235—101no—
271C2×#235—101no—
272C2×#235AGL(1,𝔽5)11yescharacteristic, complemented
273C22×D12—51no—
274C22×C4×D3—52no—
275C22×Dic6—51no—
276C3×#117—52no—
277C3×#117—52no—
278C3×#117—101no—
279C3×#117—101no—
280C2×C3×C4⋊C4—101no—
281C2×C3×C22⋊C4—52no—
282C2×C3×C42—101no—
283C2×#217—52no—
284#926—52no—
285#926—52no—
286#926—101no—
287#926—101no—
288C2×C4⋊Dic3—101no—
289C2×C4×Dic3—101no—
290#806—58no—
291#806—58no—
292C23×D5—32no—
293C23×D5C22×D311yescharacteristic
294C22×AGL(1,𝔽5)—22no—
295C22×AGL(1,𝔽5)—62no—
296C5×#41—61no—
297C5×#41—61no—
298C5×#41—61no—
299C5×#41—61no—
300C2×C5×Q8—31no—
301C2×C5×D4—32no—
302C2×C5×D4—31no—
303C22×C4×C5—32no—
304C22×C4×C5C4×D311yescharacteristic
305C2×C22⋊D5—32no—
306C2×C22⋊D5—32no—
307C2×C22⋊D5—32no—
308C22×Dic5—32no—
309C22×Dic5C4×D311yescharacteristic
310#713—61no—
311#713—61no—
312#713—61no—
313#713—61no—
314Q8×D5—61no—
315Q8×D5—61no—
316Q8×D5—61no—
317Q8×D5—61no—
318#711—62no—
319#711—62no—
320#711—62no—
321#711—62no—
322#711—61no—
323#711—61no—
324#711—61no—
325#711—61no—
326D4×D5—62no—
327D4×D5—62no—
328D4×D5—62no—
329D4×D5—62no—
330D4×D5—61no—
331D4×D5—61no—
332D4×D5—61no—
333D4×D5—61no—
334#709—61no—
335#709—61no—
336#709—61no—
337#709—61no—
338#709—62no—
339#709—62no—
340#709—62no—
341#709—62no—
342C2×D20—32no—
343C2×D20—31no—
344C2×C4×D5—32no—
345C2×C4×D5—32no—
346C2×C4×D5—32no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5C4×D311yescharacteristic
352C2×C4×D5C4×D311yescharacteristic
353C2×C4×D5D1211yescharacteristic
354C2×C4×D5D1211yescharacteristic
355C2×C4×D5D1211yescharacteristic
356C2×C4×D5D1211yescharacteristic
357C2×C4×D5#6711yescharacteristic
358C2×C4×D5#6711yescharacteristic
359C2×C4×D5#6711yescharacteristic
360C2×C4×D5#6711yescharacteristic
361C2×C4×D5C22×D311yescharacteristic
362C2×C4×D5C22×D311yescharacteristic
363C2×Dic10—31no—
364C2×Dic10—32no—
365C22⋊AGL(1,𝔽5)—22no—
366C22⋊AGL(1,𝔽5)—34no—
367C22⋊AGL(1,𝔽5)—62no—
368C22⋊AGL(1,𝔽5)C22×D314yes—
369C4⋊AGL(1,𝔽5)—22no—
370C4⋊AGL(1,𝔽5)—22no—
371C4⋊AGL(1,𝔽5)—62no—
372C4⋊AGL(1,𝔽5)—62no—
373C4×AGL(1,𝔽5)—22no—
374C4×AGL(1,𝔽5)—22no—
375C4×AGL(1,𝔽5)—62no—
376C4×AGL(1,𝔽5)—62no—
377C22×#41—151no—
378C2×#117—51no—
379C2×#117—151no—
380#410—154no—
381#410—152no—
382#410—152no—
383C2×#99—154no—
384C22×C3×C5—41no—
385C22×C3×C5C2×C22⋊C411yescharacteristic
386C22×C3×C5C2×C22⋊C411yescharacteristic
387C22×C3×C5C23×C411yescharacteristic
388C2×D15—22no—
389C2×D15—42no—
390C2×C5×D3—22no—
391C2×C5×D3—42no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5C2×C22⋊C411yescharacteristic
399C2×C3×D5C2×C22⋊C411yescharacteristic
400C2×C3×D5C22×D411yescharacteristic
401C2×C3×D5C22×D411yescharacteristic
402D3×D5—44no—
403D3×D5—44no—
404ΓL(1,𝔽16)—44no—
405C3×AGL(1,𝔽5)—44no—
406C3×C4×C5C2×C22⋊C411yescharacteristic
407C3×C4×C5C2×C22⋊C411yescharacteristic
408C3×C4×C5C2×C22⋊C411yescharacteristic
409C3×C4×C5C2×C22⋊C411yescharacteristic
410Dic15—22no—
411C3×Dic5C2×C22⋊C411yescharacteristic
412C3×Dic5C2×C22⋊C411yescharacteristic
413C3×Dic5C2×C22⋊C411yescharacteristic
414C3×Dic5C2×C22⋊C411yescharacteristic
415C5×Dic3—22no—
416C24×C3—51no—
417C23×D3—52no—
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×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—102no—
432C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
433C2×#67—52no—
434C2×#67—52no—
435C2×#67—52no—
436C2×#67—102no—
437C2×#67—102no—
438C2×#67—102no—
439C2×#67—102no—
440C2×#67C2×AGL(1,𝔽5)12yes—
441C22×Dic3—52no—
442C22×Dic3—102no—
443#235—21no—
444#235—21no—
445#235—21no—
446#235—21no—
447#235—101no—
448#235—101no—
449#235—101no—
450#235—101no—
451#235—102no—
452#235—102no—
453#235—102no—
454#235—102no—
455#235—101no—
456#235—101no—
457#235—101no—
458#235—101no—
459#235—102no—
460#235—102no—
461#235—102no—
462#235—102no—
463#235—101no—
464#235—101no—
465#235—101no—
466#235—101no—
467C2×D12—52no—
468C2×D12—51no—
469C2×D12—101no—
470C2×D12—101no—
471C2×D12—101no—
472C2×D12—101no—
473C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
474C2×C4×D3—52no—
475C2×C4×D3—52no—
476C2×C4×D3—52no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3C2×AGL(1,𝔽5)12yescomplemented
482C2×Dic6—51no—
483C2×Dic6—52no—
484C2×Dic6—101no—
485C2×Dic6—101no—
486C2×Dic6—101no—
487C2×Dic6—101no—
488C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
489C3×C4⋊C4—102no—
490C3×C4⋊C4—102no—
491C3×C22⋊C4—54no—
492C3×C22⋊C4—102no—
493C3×C42—102no—
494C3×C42—102no—
495#217—54no—
496#217—102no—
497C4⋊Dic3—102no—
498C4⋊Dic3—102no—
499C4×Dic3—102no—
500C4×Dic3—102no—
501C23×C5—32no—
502C23×C5C2×C4×D311yescharacteristic
503C22×D5—32no—
504C22×D5—42no—
505C22×D5—62no—
506C22×D5—62no—
507C22×D5—124no—
508C22×D5C2×C4×D311yescharacteristic
509C22×D5C2×D1211yescharacteristic
510C22×D5C2×D1211yescharacteristic
511C22×D5C2×#6711yescharacteristic
512C22×D5C2×#6711yescharacteristic
513C22×D5C23×D311yescharacteristic
514C2×AGL(1,𝔽5)—24no—
515C2×AGL(1,𝔽5)—44no—
516C2×AGL(1,𝔽5)—64no—
517C2×AGL(1,𝔽5)—124no—
518C5×Q8—61no—
519C5×Q8—61no—
520C5×D4—62no—
521C5×D4—62no—
522C5×D4—61no—
523C5×D4—61no—
524C2×C4×C5—32no—
525C2×C4×C5—62no—
526C2×C4×C5—62no—
527C2×C4×C5(C2×D3)⋊C411yescharacteristic
528C2×C4×C5(C2×D3)⋊C411yescharacteristic
529C2×C4×C5(C2×D3)⋊C411yescharacteristic
530C2×C4×C5(C2×D3)⋊C411yescharacteristic
531C2×C4×C5C2×C4×D311yescharacteristic
532C2×C4×C5C2×C4×D311yescharacteristic
533C22⋊D5—62no—
534C22⋊D5—62no—
535C22⋊D5—62no—
536C22⋊D5—62no—
537C22⋊D5—62no—
538C22⋊D5—62no—
539C2×Dic5—32no—
540C2×Dic5—62no—
541C2×Dic5—62no—
542C2×Dic5(C2×D3)⋊C411yescharacteristic
543C2×Dic5(C2×D3)⋊C411yescharacteristic
544C2×Dic5(C2×D3)⋊C411yescharacteristic
545C2×Dic5(C2×D3)⋊C411yescharacteristic
546C2×Dic5C2×C4×D311yescharacteristic
547C2×Dic5C2×C4×D311yescharacteristic
548D20—62no—
549D20—62no—
550D20—61no—
551D20—61no—
552C4×D5—62no—
553C4×D5—62no—
554C4×D5—62no—
555C4×D5—62no—
556C4×D5—62no—
557C4×D5—62no—
558C4×D5(C2×D3)⋊C411yescharacteristic
559C4×D5(C2×D3)⋊C411yescharacteristic
560C4×D5(C2×D3)⋊C411yescharacteristic
561C4×D5(C2×D3)⋊C411yescharacteristic
562C4×D5(C2×D3)⋊C411yescharacteristic
563C4×D5(C2×D3)⋊C411yescharacteristic
564C4×D5(C2×D3)⋊C411yescharacteristic
565C4×D5(C2×D3)⋊C411yescharacteristic
566C4×D5C2×D1211yescharacteristic
567C4×D5C2×D1211yescharacteristic
568C4×D5C2×D1211yescharacteristic
569C4×D5C2×D1211yescharacteristic
570C4×D5C2×#6711yescharacteristic
571C4×D5C2×#6711yescharacteristic
572C4×D5C2×#6711yescharacteristic
573C4×D5C2×#6711yescharacteristic
574Dic10—61no—
575Dic10—61no—
576Dic10—62no—
577Dic10—62no—
578C2×#41—31no—
579C2×#41—152no—
580C2×#41—151no—
581C2×#41—152no—
582C2×#41—151no—
583C2×#41—151no—
584C2×#41—301no—
585C2×#41—301no—
586C2×#41—301no—
587C2×#41—301no—
588C2×#41—301no—
589C2×#41—301no—
590C2×#41—301no—
591C2×#41—301no—
592C22×Q8—151no—
593C22×D4—151no—
594C22×D4—152no—
595C23×C4—51no—
596C23×C4—152no—
597#117—52no—
598#117—52no—
599#117—101no—
600#117—101no—
601#117—152no—
602#117—152no—
603#117—301no—
604#117—301no—
605C2×C4⋊C4—101no—
606C2×C4⋊C4—301no—
607C2×C22⋊C4—52no—
608C2×C22⋊C4—152no—
609C2×C42—101no—
610C2×C42—301no—
611#99—158no—
612#99—158no—
613C2×C3×C5—21no—
614C2×C3×C5—21no—
615C2×C3×C5—21no—
616C2×C3×C5C22×C22⋊C411yescharacteristic
617D15—42no—
618C3×D5—21no—
619C3×D5—21no—
620C3×D5—21no—
621C3×D5#41012yescomplemented
622C5×D3—42no—
623C23×C3—51no—
624C23×C3—51no—
625C23×C3—51no—
626C23×C3—51no—
627C23×C3—51no—
628C23×C3—51no—
629C23×C3—202no—
630C23×C3C22×AGL(1,𝔽5)11yescharacteristic
631C22×D3—52no—
632C22×D3—102no—
633C22×D3—102no—
634C22×D3—204no—
635C22×D3C22×AGL(1,𝔽5)12yes—
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×C4—51no—
653C2×C3×C4—51no—
654C2×C3×C4—51no—
655C2×C3×C4—51no—
656C2×C3×C4—51no—
657C2×C3×C4—51no—
658C2×C3×C4—104no—
659C2×C3×C4—204no—
660C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
661C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
662C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
663C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
664C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
665C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
666#67—22no—
667#67—22no—
668#67—102no—
669#67—102no—
670#67—102no—
671#67—102no—
672#67—102no—
673#67—102no—
674C2×Dic3—52no—
675C2×Dic3—102no—
676C2×Dic3—102no—
677C2×Dic3—104no—
678C2×Dic3—204no—
679C2×Dic3C22×AGL(1,𝔽5)12yes—
680D12—21no—
681D12—21no—
682D12—102no—
683D12—102no—
684D12—101no—
685D12—101no—
686C4×D3—22no—
687C4×D3—22no—
688C4×D3—102no—
689C4×D3—102no—
690C4×D3—102no—
691C4×D3—102no—
692C4×D3—102no—
693C4×D3—102no—
694Dic6—21no—
695Dic6—21no—
696Dic6—102no—
697Dic6—102no—
698Dic6—101no—
699Dic6—101no—
700C22×C5—41no—
701C22×C5—62no—
702C22×C5—122no—
703C22×C5C2×(C2×D3)⋊C411yescharacteristic
704C22×C5C2×(C2×D3)⋊C411yescharacteristic
705C22×C5C22×C4×D311yescharacteristic
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—22no—
709C2×D5—41no—
710C2×D5—41no—
711C2×D5—41no—
712C2×D5—62no—
713C2×D5—124no—
714C2×D5—124no—
715C2×D5—122no—
716C2×D5C2×(C2×D3)⋊C411yescharacteristic
717C2×D5C2×(C2×D3)⋊C411yescharacteristic
718C2×D5C22×D1211yescharacteristic
719C2×D5C22×#6711yescharacteristic
720AGL(1,𝔽5)—44no—
721AGL(1,𝔽5)—124no—
722C4×C5—62no—
723C4×C5C2×(C2×D3)⋊C411yescharacteristic
724C4×C5C2×(C2×D3)⋊C411yescharacteristic
725C4×C5C2×(C2×D3)⋊C411yescharacteristic
726C4×C5C2×(C2×D3)⋊C411yescharacteristic
727Dic5—62no—
728Dic5C2×(C2×D3)⋊C411yescharacteristic
729Dic5C2×(C2×D3)⋊C411yescharacteristic
730Dic5C2×(C2×D3)⋊C411yescharacteristic
731Dic5C2×(C2×D3)⋊C411yescharacteristic
732C24—51no—
733C24—152no—
734#41—61no—
735#41—61no—
736#41—61no—
737#41—61no—
738#41—302no—
739#41—302no—
740#41—302no—
741#41—302no—
742#41—302no—
743#41—302no—
744#41—302no—
745#41—302no—
746#41—301no—
747#41—301no—
748#41—301no—
749#41—301no—
750#41—301no—
751#41—301no—
752#41—301no—
753#41—301no—
754#41—301no—
755#41—301no—
756#41—301no—
757#41—301no—
758C2×Q8—31no—
759C2×Q8—152no—
760C2×Q8—151no—
761C2×Q8—301no—
762C2×Q8—301no—
763C2×Q8—301no—
764C2×Q8—301no—
765C2×D4—32no—
766C2×D4—31no—
767C2×D4—152no—
768C2×D4—152no—
769C2×D4—152no—
770C2×D4—152no—
771C2×D4—151no—
772C2×D4—301no—
773C2×D4—301no—
774C2×D4—301no—
775C2×D4—301no—
776C2×D4—302no—
777C2×D4—302no—
778C2×D4—302no—
779C2×D4—302no—
780C22×C4—32no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—51no—
790C22×C4—51no—
791C22×C4—51no—
792C22×C4—51no—
793C22×C4—51no—
794C22×C4—102no—
795C22×C4—152no—
796C22×C4—152no—
797C22×C4—152no—
798C22×C4—152no—
799C22×C4—302no—
800C22×C4—302no—
801C22×C4—302no—
802C22×C4—302no—
803C22×C4—302no—
804C22×C4D3×AGL(1,𝔽5)11yescharacteristic
805C4⋊C4—102no—
806C4⋊C4—102no—
807C4⋊C4—302no—
808C4⋊C4—302no—
809C22⋊C4—54no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—302no—
813C42—102no—
814C42—102no—
815C42—302no—
816C42—302no—
817C3×C5C2×#41011yescharacteristic, complemented, Hall
818C22×C3—41no—
819C22×C3—51no—
820C22×C3—51no—
821C22×C3—51no—
822C22×C3—51no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—201no—
827C22×C3—201no—
828C22×C3—201no—
829C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
830C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
831C22×C3C23×AGL(1,𝔽5)11yescharacteristic
832C2×D3—22no—
833C2×D3—42no—
834C2×D3—102no—
835C2×D3—204no—
836C2×D3—204no—
837C2×D3—202no—
838C3×C4—51no—
839C3×C4—51no—
840C3×C4—51no—
841C3×C4—51no—
842C3×C4—204no—
843C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
844C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
845C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
846C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
847Dic3—22no—
848Dic3—102no—
849Dic3—204no—
850C2×C5—21no—
851C2×C5—21no—
852C2×C5—21no—
853C2×C5—122no—
854C2×C5C22×(C2×D3)⋊C411yescharacteristic
855D5—21no—
856D5—21no—
857D5—21no—
858D5—122no—
859D5#500612yescomplemented
860C23—32no—
861C23—51no—
862C23—51no—
863C23—51no—
864C23—51no—
865C23—51no—
866C23—51no—
867C23—152no—
868C23—202no—
869C23—302no—
870C23—302no—
871C23—604no—
872C23C2×D3×AGL(1,𝔽5)11yescharacteristic
873Q8—61no—
874Q8—61no—
875Q8—302no—
876Q8—302no—
877Q8—301no—
878Q8—301no—
879D4—62no—
880D4—62no—
881D4—61no—
882D4—61no—
883D4—302no—
884D4—302no—
885D4—302no—
886D4—302no—
887D4—302no—
888D4—302no—
889D4—302no—
890D4—302no—
891D4—301no—
892D4—301no—
893C2×C4—32no—
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—51no—
905C2×C4—51no—
906C2×C4—51no—
907C2×C4—51no—
908C2×C4—51no—
909C2×C4—51no—
910C2×C4—51no—
911C2×C4—51no—
912C2×C4—51no—
913C2×C4—51no—
914C2×C4—51no—
915C2×C4—51no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—104no—
919C2×C4—152no—
920C2×C4—204no—
921C2×C4—302no—
922C2×C4—302no—
923C2×C4—302no—
924C2×C4—302no—
925C2×C4—302no—
926C2×C4—302no—
927C2×C4—302no—
928C2×C4—302no—
929C2×C4—304no—
930C2×C4—604no—
931C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
932C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
933C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
934C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
935C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
936C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—52no—
941C2×C3—101no—
942C2×C3—101no—
943C2×C3—101no—
944C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
945D3—42no—
946D3—202no—
947C5C2×#500611yescharacteristic, complemented, Sylow
948C22—41no—
949C22—51no—
950C22—51no—
951C22—51no—
952C22—51no—
953C22—62no—
954C22—102no—
955C22—102no—
956C22—102no—
957C22—122no—
958C22—201no—
959C22—201no—
960C22—201no—
961C22—302no—
962C22—602no—
963C22—604no—
964C22—604no—
965C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
966C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
967C22C22×D3×AGL(1,𝔽5)11yescharacteristic
968C4—51no—
969C4—51no—
970C4—51no—
971C4—51no—
972C4—62no—
973C4—204no—
974C4—302no—
975C4—604no—
976C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
977C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
978C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
979C4C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
980C3D5⋊#41011yescharacteristic, complemented, Sylow
981C2—21no—
982C2—21no—
983C2—21no—
984C2—52no—
985C2—101no—
986C2—101no—
987C2—101no—
988C2—122no—
989C2—602no—
990C2C22×(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
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#410
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×#91989C2semidirect
3. C2×C3×#4130C2semidirect
4. D5⋊#806C2semidirect
5. #11751817C2semidirect
6. #11751816C2semidirect
7. #11751815C2semidirect
9. C2×#6817C4semidirect
10. C2×C5×#235C4semidirect
13. C2×#6782C4semidirect
22. C2×D5×D12C4semidirect
23. C2×C4×D3×D5C4semidirect
27. C2×D5×Dic6C4semidirect
31. #91989C22semidirect
32. #91989C22semidirect
38. C3×#4130C22semidirect
39. C3×#4130C22semidirect
42. #91173C22semidirect
43. #91172C22semidirect
47. C2×#4130D3semidirect
62. C2×D60C2×C4semidirect
63. C2×C4×D15C2×C4semidirect
64. C2×Dic30C2×C4semidirect
70. C2×C5×D12C2×C4semidirect
71. C2×C4×C5×D3C2×C4semidirect
72. C2×C5×Dic6C2×C4semidirect
90. C2×#1204C2×C4semidirect
91. C2×#1203C2×C4semidirect
94. C2×#1200C2×C4semidirect
99. C2×D3×Dic5C2×C4semidirect
171. #4130C2×D3semidirect
172. #4130C2×D3semidirect
272. C2×#235AGL(1,𝔽5)semidirect
473. C2×D12C2×AGL(1,𝔽5)semidirect
481. C2×C4×D3C2×AGL(1,𝔽5)semidirect
488. C2×Dic6C2×AGL(1,𝔽5)semidirect
621. C3×D5#410semidirect
817. C3×C5C2×#410semidirect
859. D5#5006semidirect
947. C5C2×#5006semidirect
980. C3D5⋊#410semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C2×#919892
C2×C3×#41302
D5⋊#8062
#117518172
#117518162
#117518152
D5⋊#4103
C2×#50065