Finite Group Databasebeta

← D5⋊#4823 #14418001

Subgroups — D5⋊#4823 #14418001

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5⋊#948C211yesmaximal, characteristic, complemented
2D5⋊#907C211yesmaximal, characteristic, complemented
3D5×#950C211yesmaximal, characteristic
4C3×D5⋊#104C211yesmaximal, characteristic, complemented
5#11751982C212yesmaximal, complemented
6#11751980C212yesmaximal, complemented
7#11751958C212yesmaximal, complemented
8#11751956C212yesmaximal, complemented
9D5⋊#822C211yesmaximal, characteristic, complemented
10D5⋊#805C211yesmaximal, characteristic, complemented
11C2×#91149C211yesmaximal, characteristic, complemented
12D5⋊#444—31nomaximal, Hall
13C3×D5×#41C2211yescharacteristic
14D5×#235C2211yescharacteristic
15#91992C2212yescomplemented
16#91990—22no—
17#91990C2212yescomplemented
18D5⋊#208—21no—
19D5⋊#208C2211yescharacteristic
20C2×D5⋊(C3⋊C8)—21no—
21C2×D5⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C3×D5⋊M16C2211yescharacteristic
24#91929—22no—
25D5⋊ΓL(1,𝔽25)—21no—
26#91916C2212yescomplemented
27#91913C2212yescomplemented
28D3×D5⋊C8—21no—
29#91839C411yescharacteristic, complemented
30C5×#950C411yescharacteristic, complemented
31#91516C2211yescharacteristic
32#91514C2211yescharacteristic
33D5×#216C411yescharacteristic, complemented
34D5×#215C411yescharacteristic, complemented
35#91492C2211yescharacteristic
36#91490C2211yescharacteristic
37D5×#214C411yescharacteristic, complemented
38D5×#213C411yescharacteristic, complemented
39#91311C411yescharacteristic, complemented
40#91297C411yescharacteristic, complemented
41C2×D5×C3⋊C8C2211yescharacteristic
42C3×#4010C2212yescomplemented
43C3×#4008C2212yescomplemented
44#91162C2212yescomplemented
45#91161C2212yescomplemented
46#91158C2212yescomplemented
47#91156C2212yescomplemented
48#91149C2212yescomplemented
49#91149C2212yescomplemented
50C2×#4823—51nomaximal, Hall
51D5⋊#131—31no—
52D5⋊#131—31no—
53D5×#135—31no—
54D5⋊#104—31no—
55D5⋊#104D311yescharacteristic, complemented
56#65741—32no—
57#65737—32no—
58#65737—32no—
59#65733—32no—
60D5⋊#108—31no—
61C2×#3992—31no—
62C22×C3×AGL(1,𝔽5)—21no—
63C3×C5×#41C2×C411yescharacteristic
64#6817C2×C411yescharacteristic
65C5×#235C2×C411yescharacteristic
66C3×#713C2311yescharacteristic
67C3×Q8×D5C2×C411yescharacteristic
68C3×#711—21no—
69C3×#711C2311yescharacteristic
70C3×D4×D5—21no—
71C3×D4×D5C2×C411yescharacteristic
72C3×#709—21no—
73C3×#709C2×C411yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5C2311yescharacteristic
76D5×#67—21no—
77#6782—21no—
78D5×D12C2×C411yescharacteristic
79C4×D3×D5—21no—
80#6773C2311yescharacteristic
81#6772C2311yescharacteristic
82#6771—21no—
83D5×Dic6C2×C411yescharacteristic
84#6762—21no—
85#6762—22no—
86C2×C3⋊#170—22no—
87C2×C3⋊#170D412yes—
88#6758—22no—
89#6758C2312yes—
90D5⋊(C3⋊C8)—21no—
91D5⋊(C3⋊C8)—22no—
92D5⋊(C3⋊C8)D411yescharacteristic
93D5⋊(C3⋊C8)D411yescharacteristic
94D5⋊(C3⋊C8)C2312yes—
95C3×#704—21no—
96C3×C4×AGL(1,𝔽5)—21no—
97C3×C4×AGL(1,𝔽5)C2312yes—
98C3×#700C2312yes—
99C3×D5⋊C8—21no—
100#6740—22no—
101#6739—22no—
102#6738—22no—
103D3×#170—22no—
104#6718C2×C411yescharacteristic, complemented
105#6717C2×C411yescharacteristic, complemented
106#6716C2×C411yescharacteristic, complemented
107#6715C2×C411yescharacteristic, complemented
108C2×C3⋊#168C2×C411yescharacteristic
109C5×#216C2×C411yescharacteristic, complemented
110C5×#215C2×C411yescharacteristic, complemented
111C5×#214C2×C411yescharacteristic, complemented
112C5×#213C2×C411yescharacteristic, complemented
113C2×C5×C3⋊C8C2×C411yescharacteristic
114#6662C2×C411yescharacteristic, complemented
115#6661C2×C411yescharacteristic, complemented
116#6658C2×C411yescharacteristic, complemented
117#6657C2×C411yescharacteristic, complemented
118#6656C2×C411yescharacteristic, complemented
119#6655C2×C411yescharacteristic, complemented
120#6653C2×C411yescharacteristic, complemented
121#6652C2×C411yescharacteristic, complemented
122D5×C3⋊C8C2×C411yescharacteristic
123D5×C3⋊C8C2×C411yescharacteristic
124D5×C3⋊C8C2311yescharacteristic
125D5×C3⋊C8C2311yescharacteristic
126C2×#950—51no—
127C2×#948—51no—
128C2×#907—51no—
129C2×C3×#104—51no—
130C2×#822—51no—
131C2×#805—51no—
132C2×#803—51no—
133#4823—52no—
134#4823—52no—
135#4823—52no—
136#4823—52no—
137D5×#41—31no—
138D5×#41C2×D311yescharacteristic
139#4133—32no—
140#4133—32no—
141#4131—32no—
142#4131—32no—
143#4131—62no—
144#4131—62no—
145C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
146D5⋊M16—31no—
147D5⋊M16—61no—
148D5⋊M16—61no—
149D5⋊M16C2×D311yescharacteristic
150C2×D5⋊C8—31no—
151C2×D5⋊C8—61no—
152C2×D5⋊C8—61no—
153C5×#135—31no—
154#4096—31no—
155#4096—31no—
156#4065—31no—
157D5×Q16—31no—
158#4062—31no—
159#4062—31no—
160D5×SD16—31no—
161D5×SD16—31no—
162#4058—31no—
163D5×D8—31no—
164#4050—31no—
165C2×C8×D5—31no—
166#4010—32no—
167#4010C2×D312yescomplemented
168#4008—32no—
169#4008C2×D312yescomplemented
170#3996—32no—
171#3995—32no—
172#3992—32no—
173#3992—32no—
174C2×#444—151noSylow
175C22×C3×D5—21no—
176C22×C3×D5#4111yescharacteristic
177C2×D3×D5—21no—
178C2×C3×AGL(1,𝔽5)—22no—
179C2×C3×AGL(1,𝔽5)—42no—
180C3×C5×Q8C22×C411yescharacteristic
181C3×C5×D4—21no—
182C3×C5×D4C22×C411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5C22×C411yescharacteristic
185#1220—21no—
186D60C22×C411yescharacteristic
187C4×D15—21no—
188Dic30C22×C411yescharacteristic
189C5×#67—21no—
190C5×D12C22×C411yescharacteristic
191C4×C5×D3—21no—
192C5×Dic6C22×C411yescharacteristic
193C3×C22⋊D5—21no—
194C3×C22⋊D5—21no—
195C3×C22⋊D5—21no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5C2×D411yescharacteristic
198C3×D20—21no—
199C3×D20C22×C411yescharacteristic
200C3×C4×D5—21no—
201C3×C4×D5—21no—
202C3×C4×D5—21no—
203C3×C4×D5C22×C411yescharacteristic
204C3×C4×D5C2×D411yescharacteristic
205C3×C4×D5#4111yescharacteristic
206C3×C4×D5C2411yescharacteristic
207C3×Dic10—21no—
208C3×Dic10C22×C411yescharacteristic
209#1204—21no—
210#1203—21no—
211#1202—21no—
212#1201—21no—
213#1200—21no—
214D3×Dic5—21no—
215D5×Dic3—21no—
216C3⋊#170—22no—
217C3⋊#170C2×D412yes—
218C3⋊#170C2×D412yes—
219C3×#170—22no—
220C3⋊#168C22×C411yescharacteristic
221C3⋊#168C22×C411yescharacteristic
222C5×C3⋊C8C22×C411yescharacteristic
223C5×C3⋊C8C22×C411yescharacteristic
224C2×C3×#41—51no—
225C2×#235—51no—
226C2×C3×M16—51no—
227C2×C3×C42—51no—
228#950—51no—
229#950—51no—
230#950—51no—
231#950—51no—
232#950—51no—
233#950—51no—
234#950—51no—
235#950AGL(1,𝔽5)11yescharacteristic, complemented
236#948—52no—
237#948—52no—
238#948—102no—
239C2×#216—51no—
240C2×#215—51no—
241C2×#214—51no—
242C2×#213—51no—
243C2×#208—51no—
244C2×#208—101no—
245C22×C3⋊C8—51no—
246C22×C3⋊C8—51no—
247C22×C3⋊C8—101no—
248#907—52no—
249#907—52no—
250#907—102no—
251C2×ΓL(1,𝔽25)—101no—
252C2×D3×C8—101no—
253C3×#104—52no—
254C3×#104—52no—
255#822—52no—
256#822—52no—
257#805—52no—
258#805—52no—
259#803—52no—
260#803—52no—
261C22×AGL(1,𝔽5)—21no—
262C5×#41—31no—
263C5×#41C4×D311yescharacteristic
264#713—31no—
265#713C22×D311yescharacteristic
266Q8×D5—31no—
267Q8×D5C4×D311yescharacteristic
268#711—21no—
269#711—31no—
270#711—61no—
271#711C22×D311yescharacteristic
272D4×D5—21no—
273D4×D5—31no—
274D4×D5—61no—
275D4×D5C4×D311yescharacteristic
276#709—21no—
277#709—31no—
278#709—61no—
279#709C4×D311yescharacteristic
280C2×C4×D5—21no—
281C2×C4×D5—61no—
282C2×C4×D5C22×D311yescharacteristic
283#704—21no—
284#704—62no—
285#704—62no—
286#704—61no—
287C2×#170—32no—
288C2×#170—62no—
289C2×#170—62no—
290C4×AGL(1,𝔽5)—21no—
291C4×AGL(1,𝔽5)C22×D312yes—
292#700—32no—
293#700—62no—
294#700—62no—
295#700C22×D312yes—
296D5⋊C8—21no—
297D5⋊C8—31no—
298D5⋊C8—31no—
299D5⋊C8—32no—
300D5⋊C8—62no—
301D5⋊C8—62no—
302D5⋊C8—61no—
303C5×Q16—31no—
304C5×SD16—31no—
305C5×SD16—31no—
306C5×D8—31no—
307C2×C5×C8—31no—
308#689—31no—
309#689—31no—
310#688—31no—
311#688—31no—
312#687—31no—
313#687—31no—
314#686—31no—
315#686—31no—
316C2×#168—31no—
317Dic20—31no—
318D40—31no—
319#677—31no—
320#677—31no—
321C8×D5—31no—
322C8×D5—31no—
323C8×D5—31no—
324C8×D5—31no—
325C2×#135—151no—
326C2×#131—151no—
327C2×#131—151no—
328#444—152no—
329#444—152no—
330#444—152no—
331#444—152no—
332C2×#108—151no—
333C2×#104—51no—
334C2×#104—151no—
335C2×#97—151no—
336C22×C3×C5—21no—
337C22×C3×C5C4×D411yescharacteristic
338C2×D15—21no—
339C2×C5×D3—21no—
340C2×C3×D5—22no—
341C2×C3×D5—21no—
342C2×C3×D5—42no—
343C2×C3×D5C4×D411yescharacteristic
344C2×C3×D5C2×#4111yescharacteristic
345D3×D5—42no—
346C3×AGL(1,𝔽5)—42no—
347C3×C4×C5—21no—
348C3×C4×C5C4×D411yescharacteristic
349C3×C4×C5C23×C411yescharacteristic
350Dic15—21no—
351C3×Dic5—21no—
352C3×Dic5C4×D411yescharacteristic
353C3×Dic5C22×D411yescharacteristic
354C5×Dic3—21no—
355C3×#41—51no—
356C3×#41—51no—
357C3×#41—51no—
358C3×#41—101no—
359C3×#41—101no—
360C3×#41C2×AGL(1,𝔽5)11yescharacteristic
361C2×C3×Q8—51no—
362C2×C3×D4—51no—
363C2×C3×D4—101no—
364C22×C3×C4—51no—
365C22×C3×C4—101no—
366C22×C3×C4—101no—
367C2×#67—101no—
368#235—51no—
369#235—51no—
370#235—51no—
371#235—101no—
372#235—101no—
373#235C2×AGL(1,𝔽5)11yescharacteristic
374C2×D12—51no—
375C2×C4×D3—101no—
376C2×Dic6—51no—
377C3×M16—52no—
378C3×M16—101no—
379C2×C3×C8—101no—
380C3×C42—52no—
381C3×C42—101no—
382#216—51no—
383#216—51no—
384#216—51no—
385#216C2×AGL(1,𝔽5)11yescharacteristic, complemented
386#215—51no—
387#215—51no—
388#215—51no—
389#215C2×AGL(1,𝔽5)11yescharacteristic, complemented
390#214—51no—
391#214—51no—
392#214—51no—
393#214C2×AGL(1,𝔽5)11yescharacteristic, complemented
394#213—51no—
395#213—51no—
396#213—51no—
397#213C2×AGL(1,𝔽5)11yescharacteristic, complemented
398#208—52no—
399#208—102no—
400#208—102no—
401#208—101no—
402C2×C3⋊C8—52no—
403C2×C3⋊C8—51no—
404C2×C3⋊C8—51no—
405C2×C3⋊C8—52no—
406C2×C3⋊C8—51no—
407C2×C3⋊C8—51no—
408C2×C3⋊C8—51no—
409C2×C3⋊C8—51no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8—102no—
412C2×C3⋊C8—102no—
413C2×C3⋊C8—101no—
414C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
415ΓL(1,𝔽25)—102no—
416ΓL(1,𝔽25)—102no—
417D3×C8—102no—
418D3×C8—102no—
419C22×D5—21no—
420C22×D5—61no—
421C22×D5#23711yescharacteristic
422C2×AGL(1,𝔽5)—22no—
423C2×AGL(1,𝔽5)—42no—
424C5×Q8—31no—
425C5×Q8C2×C4×D311yescharacteristic
426C5×D4—21no—
427C5×D4—31no—
428C5×D4—61no—
429C5×D4C2×C4×D311yescharacteristic
430C2×C4×C5—21no—
431C2×C4×C5—61no—
432C2×C4×C5C2×C4×D311yescharacteristic
433C22⋊D5—21no—
434C22⋊D5—21no—
435C22⋊D5—21no—
436C22⋊D5—61no—
437C22⋊D5—61no—
438C22⋊D5—61no—
439C2×Dic5—21no—
440C2×Dic5—61no—
441C2×Dic5D3×D411yescharacteristic
442D20—21no—
443D20—31no—
444D20—61no—
445D20C2×C4×D311yescharacteristic
446C4×D5—21no—
447C4×D5—21no—
448C4×D5—21no—
449C4×D5—61no—
450C4×D5—61no—
451C4×D5—61no—
452C4×D5C2×C4×D311yescharacteristic
453C4×D5D3×D411yescharacteristic
454C4×D5#23711yescharacteristic
455C4×D5C23×D311yescharacteristic
456Dic10—21no—
457Dic10—31no—
458Dic10—61no—
459Dic10C2×C4×D311yescharacteristic
460#170—22no—
461#170—32no—
462#170—32no—
463#170—62no—
464C5×C8—31no—
465C5×C8—31no—
466#168—31no—
467#168—31no—
468C2×#41—51no—
469C2×#41—151no—
470#135—31no—
471#135—151no—
472#135—151no—
473#135—151no—
474#135—151no—
475#135—151no—
476#135—151no—
477#135—151no—
478C2×Q16—151no—
479C2×SD16—151no—
480C2×SD16—151no—
481C2×D8—151no—
482#131—152no—
483#131—152no—
484#131—152no—
485#131—152no—
486#131—302no—
487#131—302no—
488C2×M16—51no—
489C2×M16—151no—
490C2×M16—301no—
491C2×M16—301no—
492C22×C8—151no—
493C22×C8—151no—
494C22×C8—301no—
495C22×C8—301no—
496C2×C42—51no—
497#108—152no—
498#108—152no—
499#104—52no—
500#104—52no—
501#104—152no—
502#104—152no—
503#97—152no—
504#97—152no—
505C2×C3×C5—21no—
506C2×C3×C5—41no—
507C2×C3×C5C2×C4×D411yescharacteristic
508D15—41no—
509C3×D5—21no—
510C3×D5—41no—
511C3×D5#44412yescomplemented
512C5×D3—41no—
513C23×C3—51no—
514C23×C3—101no—
515C22×D3—101no—
516C3×Q8—51no—
517C3×Q8—101no—
518C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
519C3×D4—21no—
520C3×D4—51no—
521C3×D4—101no—
522C3×D4—101no—
523C3×D4—101no—
524C3×D4—101no—
525C3×D4C22×AGL(1,𝔽5)11yescharacteristic
526C2×C3×C4—21no—
527C2×C3×C4—51no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—51no—
531C2×C3×C4—51no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—102no—
537C2×C3×C4—202no—
538C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
539#67—21no—
540#67—101no—
541#67—101no—
542#67—101no—
543C2×Dic3—101no—
544D12—51no—
545D12—101no—
546D12C22×AGL(1,𝔽5)11yescharacteristic
547C4×D3—21no—
548C4×D3—101no—
549C4×D3—101no—
550C4×D3—101no—
551Dic6—51no—
552Dic6—101no—
553Dic6C22×AGL(1,𝔽5)11yescharacteristic
554C3×C8—102no—
555C3⋊C8—52no—
556C3⋊C8—52no—
557C3⋊C8—51no—
558C3⋊C8—51no—
559C3⋊C8—102no—
560C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
561C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
562C22×C5—21no—
563C22×C5—61no—
564C22×C5#67⋊C411yescharacteristic
565C2×D5—22no—
566C2×D5—21no—
567C2×D5—42no—
568C2×D5—61no—
569C2×D5—122no—
570C2×D5#67⋊C411yescharacteristic
571C2×D5C2×#23711yescharacteristic
572AGL(1,𝔽5)—42no—
573C4×C5—21no—
574C4×C5—61no—
575C4×C5#67⋊C411yescharacteristic
576C4×C5C22×C4×D311yescharacteristic
577Dic5—21no—
578Dic5—61no—
579Dic5#67⋊C411yescharacteristic
580Dic5C2×D3×D411yescharacteristic
581#41—31no—
582#41—51no—
583#41—51no—
584#41—51no—
585#41—101no—
586#41—101no—
587#41—151no—
588#41—151no—
589#41—151no—
590#41—301no—
591#41—301no—
592#41D3×AGL(1,𝔽5)11yescharacteristic
593C2×Q8—51no—
594C2×Q8—151no—
595C2×D4—51no—
596C2×D4—101no—
597C2×D4—151no—
598C2×D4—301no—
599C22×C4—51no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—301no—
603Q16—31no—
604Q16—151no—
605Q16—151no—
606Q16—151no—
607SD16—31no—
608SD16—31no—
609SD16—151no—
610SD16—151no—
611SD16—151no—
612SD16—151no—
613SD16—151no—
614SD16—151no—
615D8—31no—
616D8—151no—
617D8—151no—
618D8—151no—
619M16—52no—
620M16—101no—
621M16—152no—
622M16—302no—
623M16—302no—
624M16—302no—
625M16—302no—
626M16—301no—
627C2×C8—31no—
628C2×C8—101no—
629C2×C8—151no—
630C2×C8—151no—
631C2×C8—151no—
632C2×C8—151no—
633C2×C8—152no—
634C2×C8—151no—
635C2×C8—151no—
636C2×C8—152no—
637C2×C8—151no—
638C2×C8—302no—
639C2×C8—302no—
640C2×C8—302no—
641C2×C8—302no—
642C2×C8—301no—
643C42—52no—
644C42—101no—
645C3×C5C2×#44411yescharacteristic, complemented, Hall
646C22×C3—21no—
647C22×C3—51no—
648C22×C3—51no—
649C22×C3—102no—
650C22×C3—101no—
651C22×C3—202no—
652C22×C3D4×AGL(1,𝔽5)11yescharacteristic
653C2×D3—21no—
654C2×D3—101no—
655C2×D3—202no—
656C3×C4—21no—
657C3×C4—51no—
658C3×C4—51no—
659C3×C4—101no—
660C3×C4—202no—
661C3×C4D4×AGL(1,𝔽5)11yescharacteristic
662C3×C4C23×AGL(1,𝔽5)11yescharacteristic
663Dic3—21no—
664Dic3—101no—
665C2×C5—21no—
666C2×C5—41no—
667C2×C5—121no—
668C2×C5C2×#67⋊C411yescharacteristic
669D5—21no—
670D5—41no—
671D5—121no—
672D5#482312yescomplemented
673C23—51no—
674C23—101no—
675C23—301no—
676Q8—31no—
677Q8—51no—
678Q8—101no—
679Q8—151no—
680Q8—301no—
681Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
682D4—21no—
683D4—31no—
684D4—51no—
685D4—61no—
686D4—101no—
687D4—101no—
688D4—101no—
689D4—101no—
690D4—151no—
691D4—301no—
692D4—301no—
693D4—301no—
694D4—301no—
695D4C2×D3×AGL(1,𝔽5)11yescharacteristic
696C2×C4—21no—
697C2×C4—51no—
698C2×C4—51no—
699C2×C4—51no—
700C2×C4—51no—
701C2×C4—51no—
702C2×C4—61no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—102no—
708C2×C4—202no—
709C2×C4—301no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
714C8—31no—
715C8—31no—
716C8—102no—
717C8—152no—
718C8—152no—
719C8—151no—
720C8—151no—
721C8—302no—
722C2×C3—21no—
723C2×C3—41no—
724C2×C3—52no—
725C2×C3—101no—
726C2×C3—201no—
727C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
728D3—41no—
729D3—201no—
730C5C2×#482311yescharacteristic, complemented, Sylow
731C22—21no—
732C22—51no—
733C22—51no—
734C22—61no—
735C22—102no—
736C22—101no—
737C22—202no—
738C22—301no—
739C22—602no—
740C22#67⋊AGL(1,𝔽5)11yescharacteristic
741C4—21no—
742C4—51no—
743C4—51no—
744C4—61no—
745C4—101no—
746C4—202no—
747C4—301no—
748C4#67⋊AGL(1,𝔽5)11yescharacteristic
749C4C22×D3×AGL(1,𝔽5)11yescharacteristic
750C3D5⋊#44411yescharacteristic, complemented, Sylow
751C2—21no—
752C2—41no—
753C2—52no—
754C2—101no—
755C2—121no—
756C2—201no—
757C2—601no—
758C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4#67⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#950C2
cosocleC3×C4×D5C24
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. D5⋊#948C2semidirect
2. D5⋊#907C2semidirect
4. C3×D5⋊#104C2semidirect
5. #11751982C2semidirect
6. #11751980C2semidirect
7. #11751958C2semidirect
8. #11751956C2semidirect
9. D5⋊#822C2semidirect
10. D5⋊#805C2semidirect
11. C2×#91149C2semidirect
15. #91992C22semidirect
17. #91990C22semidirect
26. #91916C22semidirect
27. #91913C22semidirect
29. #91839C4semidirect
30. C5×#950C4semidirect
33. D5×#216C4semidirect
34. D5×#215C4semidirect
37. D5×#214C4semidirect
38. D5×#213C4semidirect
39. #91311C4semidirect
40. #91297C4semidirect
42. C3×#4010C22semidirect
43. C3×#4008C22semidirect
44. #91162C22semidirect
45. #91161C22semidirect
46. #91158C22semidirect
47. #91156C22semidirect
48. #91149C22semidirect
49. #91149C22semidirect
55. D5⋊#104D3semidirect
104. #6718C2×C4semidirect
105. #6717C2×C4semidirect
106. #6716C2×C4semidirect
107. #6715C2×C4semidirect
109. C5×#216C2×C4semidirect
110. C5×#215C2×C4semidirect
111. C5×#214C2×C4semidirect
112. C5×#213C2×C4semidirect
114. #6662C2×C4semidirect
115. #6661C2×C4semidirect
116. #6658C2×C4semidirect
117. #6657C2×C4semidirect
118. #6656C2×C4semidirect
119. #6655C2×C4semidirect
120. #6653C2×C4semidirect
121. #6652C2×C4semidirect
167. #4010C2×D3semidirect
169. #4008C2×D3semidirect
235. #950AGL(1,𝔽5)semidirect
385. #216C2×AGL(1,𝔽5)semidirect
389. #215C2×AGL(1,𝔽5)semidirect
393. #214C2×AGL(1,𝔽5)semidirect
397. #213C2×AGL(1,𝔽5)semidirect
511. C3×D5#444semidirect
645. C3×C5C2×#444semidirect
672. D5#4823semidirect
730. C5C2×#4823semidirect
750. C3D5⋊#444semidirect

Maximal subgroups

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

subgroupindex
D5⋊#9482
D5⋊#9072
D5×#9502
C3×D5⋊#1042
#117519822
#117519802
#117519582
#117519562
D5⋊#8222
D5⋊#8052
C2×#911492
D5⋊#4443
C2×#48235