Finite Group Databasebeta

← #14479189

Subgroups — #14479189

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D5×#41C211yesmaximal, characteristic
2#41×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C3×#41×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4#11756854C212yesmaximal, complemented
5#11756847C212yesmaximal, complemented
6#11756846C216yesmaximal, complemented
7#11756845C216yesmaximal, complemented
8#11756835C213yesmaximal, complemented
9D3×#4130C213yesmaximal, complemented
10AGL(1,𝔽5)×#235C213yesmaximal, complemented
11C2×#91909C213yesmaximal, complemented
12#10619412—31nomaximal, Hall
13#41×D15C411yescharacteristic, complemented
14C5×D3×#41C411yescharacteristic, complemented
15C3×D5×#41C2211yescharacteristic
16#92034C411yescharacteristic, complemented
17D3×#713C411yescharacteristic, complemented
18D5×#239C2211yescharacteristic
19D3×Q8×D5C2211yescharacteristic
20#92024C413yescomplemented
21D3×#711C413yescomplemented
22D5×#237C2213yes—
23D3×D4×D5C2213yes—
24#92016C413yescomplemented
25D3×#709C413yescomplemented
26D5×#235C2213yes—
27C2×C4×D3×D5C2213yes—
28Q8×ΓL(1,𝔽16)C2212yescomplemented
29D4×ΓL(1,𝔽16)C2216yescomplemented
30#91989C2213yescomplemented
31C2×C4×ΓL(1,𝔽16)C2213yescomplemented
32C3×Q8×AGL(1,𝔽5)C2212yescomplemented
33C3×D4×AGL(1,𝔽5)C2216yescomplemented
34C3×#4130C2213yescomplemented
35C2×C3×C4×AGL(1,𝔽5)C2213yescomplemented
36#67⋊AGL(1,𝔽5)C22112yescomplemented
37D3×C22⋊AGL(1,𝔽5)C2216yes—
38AGL(1,𝔽5)×#67C22112yescomplemented
39C2×Dic3⋊AGL(1,𝔽5)C2216yescomplemented
40C2×(C2×D3)⋊AGL(1,𝔽5)C2216yes—
41#91923C2216yescomplemented
42#91921C2216yescomplemented
43D3×C4⋊AGL(1,𝔽5)C2216yescomplemented
44AGL(1,𝔽5)×D12C2216yescomplemented
45C4×D3×AGL(1,𝔽5)C2216yescomplemented
46#91909C2211yescharacteristic
47#91909C2213yes—
48#91909C2216yes—
49#91909C2213yescomplemented
50#91909C2213yescomplemented
51#91909C2216yescomplemented
52ΓL(1,𝔽16)⋊Q8C2216yescomplemented
53#91907C2216yes—
54AGL(1,𝔽5)×Dic6C2216yescomplemented
55#85834—51nomaximal, Hall
56C2×D5×#41—31no—
57#66266—32no—
58#66266—36no—
59#41×AGL(1,𝔽5)—31no—
60#41×AGL(1,𝔽5)—33no—
61#41×AGL(1,𝔽5)—33no—
62#41×AGL(1,𝔽5)D311yescharacteristic, complemented
63#66262—32no—
64#66258—36no—
65C2×#4130—33no—
66C2×#4130—33no—
67C22×D3×D5C2313yes—
68C22×ΓL(1,𝔽16)C2316yes—
69C22×C3×AGL(1,𝔽5)C2316yes—
70C2×D3×AGL(1,𝔽5)C23112yes—
71C3×C5×#41C2×C411yescharacteristic, complemented
72#6821C2×C411yescharacteristic, complemented
73Q8×D15C2×C411yescharacteristic, complemented
74#6819C2×C413yescomplemented
75D4×D15C2×C413yescomplemented
76#6817C2×C413yescomplemented
77C2×C4×D15C2×C413yescomplemented
78C5×#239C2×C411yescharacteristic, complemented
79C5×D3×Q8C2×C411yescharacteristic, complemented
80C5×#237C2×C413yescomplemented
81C5×D3×D4C2×C413yescomplemented
82C5×#235C2×C413yescomplemented
83C2×C4×C5×D3C2×C413yescomplemented
84C3×#713C2×C411yescharacteristic, complemented
85C3×Q8×D5C2311yescharacteristic
86C3×#711C2×C413yescomplemented
87C3×D4×D5C2313yes—
88C3×#709C2×C413yescomplemented
89C2×C3×C4×D5C2313yes—
90#6790C2×C416yescomplemented
91D3×C22⋊D5C2×C416yescomplemented
92D5×#67C2316yes—
93C2×#1200C2×C413yescomplemented
94#6782C2×C416yescomplemented
95C2×D3×Dic5C2×C413yescomplemented
96#6780C2×C416yescomplemented
97#6779C2×C416yescomplemented
98C2×D5×Dic3C2313yes—
99#6777C2×C413yescomplemented
100D3×D20C2×C413yescomplemented
101D5×D12C2313yes—
102C4×D3×D5C2×C413yescomplemented
103C4×D3×D5C2×C413yescomplemented
104C4×D3×D5C2×C413yescomplemented
105C4×D3×D5C2×C413yescomplemented
106C4×D3×D5C2313yes—
107C4×D3×D5C2311yescharacteristic
108C4×D3×D5C2313yes—
109C4×D3×D5C2313yes—
110#6773C2×C413yescomplemented
111#6772C2×C413yescomplemented
112#6771C2×C416yescomplemented
113D15⋊Q8C2×C413yescomplemented
114#6769C2×C413yescomplemented
115#6768C2×C413yescomplemented
116D3×Dic10C2×C413yescomplemented
117#6766C2×C413yescomplemented
118#6765C2×C413yescomplemented
119D5×Dic6C2313yes—
120#6763C2316yes—
121C4⋊ΓL(1,𝔽16)C2316yes—
122C4×ΓL(1,𝔽16)C2316yes—
123C4×ΓL(1,𝔽16)C2311yescharacteristic
124C4×ΓL(1,𝔽16)C2313yes—
125C3×C22⋊AGL(1,𝔽5)C2316yes—
126C3×C4⋊AGL(1,𝔽5)C2316yes—
127C3×C4×AGL(1,𝔽5)C2316yes—
128C3×C4×AGL(1,𝔽5)C2311yescharacteristic
129C3×C4×AGL(1,𝔽5)C2313yes—
130Dic3⋊AGL(1,𝔽5)C2316yes—
131Dic3⋊AGL(1,𝔽5)C2316yes—
132Dic3⋊AGL(1,𝔽5)C2312yes—
133Dic3⋊AGL(1,𝔽5)C2316yes—
134(C2×D3)⋊AGL(1,𝔽5)C2316yes—
135(C2×D3)⋊AGL(1,𝔽5)C2312yes—
136(C2×D3)⋊AGL(1,𝔽5)C2316yes—
137(C2×D3)⋊AGL(1,𝔽5)C2316yes—
138Dic3×AGL(1,𝔽5)C23112yes—
139C2×D3×#41—51no—
140C3×C4×#41—51no—
141Dic3×#41—51no—
142#5574—52no—
143#5572—52no—
144#5546—56no—
145#5545—56no—
146#5522—53no—
147D3×#117—53no—
148C4×#235—53no—
149C2×#872—53no—
150C2×C5×#41—31no—
151D5×#41—31no—
152D5×#41—31no—
153D5×#41—31no—
154D5×#41—33no—
155D5×#41—33no—
156D5×#41—33no—
157D5×#41—33no—
158D5×#41C2×D311yescharacteristic
159C2×#713—31no—
160C2×Q8×D5—31no—
161C2×#711—33no—
162C2×D4×D5—33no—
163C2×#709—33no—
164C22×C4×D5—33no—
165C2×C22⋊AGL(1,𝔽5)—36no—
166C2×C22⋊AGL(1,𝔽5)—36no—
167Q8×AGL(1,𝔽5)—32no—
168Q8×AGL(1,𝔽5)—36no—
169Q8×AGL(1,𝔽5)—36no—
170Q8×AGL(1,𝔽5)C2×D312yescomplemented
171D4×AGL(1,𝔽5)—312no—
172D4×AGL(1,𝔽5)—36no—
173D4×AGL(1,𝔽5)—312no—
174D4×AGL(1,𝔽5)—36no—
175D4×AGL(1,𝔽5)—36no—
176D4×AGL(1,𝔽5)C2×D316yescomplemented
177#4130—33no—
178#4130—36no—
179#4130—36no—
180#4130—33no—
181#4130—31no—
182#4130—36no—
183#4130—33no—
184#4130—33no—
185#4130—36no—
186#4130C2×D313yescomplemented
187C2×C4⋊AGL(1,𝔽5)—36no—
188C2×C4⋊AGL(1,𝔽5)—36no—
189C2×C4×AGL(1,𝔽5)—33no—
190C2×C4×AGL(1,𝔽5)—36no—
191C2×C4×AGL(1,𝔽5)C2×D313yescomplemented
192#3428—151noSylow
193C22×D15C22×C413yes—
194C22×C5×D3C22×C413yes—
195C22×C3×D5C2413yes—
196C2×D3×D5—46no—
197C2×D3×D5C22×C413yes—
198C2×D3×D5C22×C413yes—
199C2×D3×D5C2411yescharacteristic
200C2×D3×D5C2413yes—
201C2×ΓL(1,𝔽16)—46no—
202C2×ΓL(1,𝔽16)C2416yes—
203C2×ΓL(1,𝔽16)C2412yes—
204C2×C3×AGL(1,𝔽5)—46no—
205C2×C3×AGL(1,𝔽5)C2416yes—
206C2×C3×AGL(1,𝔽5)C2412yes—
207D3×AGL(1,𝔽5)—412no—
208C3×C5×Q8C22×C411yescharacteristic
209C3×C5×D4C22×C413yes—
210C2×C3×C4×C5C22×C413yes—
211#1220C22×C416yes—
212C2×Dic15C22×C413yes—
213D60C22×C413yes—
214C4×D15C22×C413yes—
215C4×D15C22×C413yes—
216C4×D15C22×C413yes—
217C4×D15C22×C411yescharacteristic
218Dic30C22×C413yes—
219C5×#67C22×C416yes—
220C2×C5×Dic3C22×C413yes—
221C5×D12C22×C413yes—
222C4×C5×D3C22×C413yes—
223C4×C5×D3C22×C413yes—
224C4×C5×D3C22×C413yes—
225C4×C5×D3C22×C411yescharacteristic
226C5×Dic6C22×C413yes—
227C3×C22⋊D5C22×C416yes—
228C2×C3×Dic5C22×C413yes—
229C3×D20C22×C413yes—
230C3×C4×D5C22×C413yes—
231C3×C4×D5C22×C413yes—
232C3×C4×D5C2411yescharacteristic
233C3×C4×D5C2413yes—
234C3×Dic10C22×C413yes—
235#1204C22×C416yes—
236#1203C22×C416yes—
237#1202C22×C416yes—
238#1201C22×C416yes—
239#1200C22×C413yes—
240#1200C22×C413yes—
241#1200C22×C413yes—
242#1200C22×C411yescharacteristic
243D3×Dic5C22×C413yes—
244D3×Dic5C22×C413yes—
245D3×Dic5C22×C413yes—
246D3×Dic5C22×C411yescharacteristic
247D5×Dic3C22×C413yes—
248D5×Dic3C22×C413yes—
249D5×Dic3C2413yes—
250D5×Dic3C2411yescharacteristic
251C2×C3×#41—51no—
252D3×#41—51no—
253D3×#41—51no—
254D3×#41—51no—
255D3×#41—53no—
256D3×#41—53no—
257D3×#41—53no—
258D3×#41—53no—
259D3×#41AGL(1,𝔽5)11yescharacteristic, complemented
260C2×#239—51no—
261C2×D3×Q8—51no—
262C2×#237—53no—
263C2×D3×D4—53no—
264C2×#235—53no—
265C22×C4×D3—53no—
266C3×C4×Q8—52no—
267C3×C4×D4—56no—
268C3×#117—53no—
269C2×C3×C42—53no—
270Q8×Dic3—52no—
271D4×Dic3—56no—
272C4×#67—512no—
273C2×(C2×D3)⋊C4—56no—
274#926—53no—
275C2×Dic3⋊C4—56no—
276C2×C4×Dic3—53no—
277#893—56no—
278#892—56no—
279D3×C4⋊C4—56no—
280#887—56no—
281#67⋊C4—512no—
282D3×C22⋊C4—56no—
283#877—56no—
284C4×D12—56no—
285#872—51no—
286#872—53no—
287#872—56no—
288#872—53no—
289#872—53no—
290#872—56no—
291C42×D3—56no—
292C4×Dic6—56no—
293C23×D5—33no—
294C22×AGL(1,𝔽5)—36no—
295C22×AGL(1,𝔽5)—312no—
296C22×AGL(1,𝔽5)C22×D316yes—
297C5×#41—31no—
298C5×#41—33no—
299C5×#41—33no—
300C5×#41C4×D311yescharacteristic, complemented
301C2×C5×Q8—31no—
302C2×C5×D4—33no—
303C22×C4×C5—33no—
304C2×C22⋊D5—36no—
305C22×Dic5—33no—
306#713—31no—
307#713—33no—
308#713—33no—
309#713C4×D311yescharacteristic, complemented
310Q8×D5—31no—
311Q8×D5—33no—
312Q8×D5—33no—
313Q8×D5C22×D311yescharacteristic
314#711—33no—
315#711—36no—
316#711—36no—
317#711—33no—
318#711—33no—
319#711C4×D313yescomplemented
320D4×D5—36no—
321D4×D5—33no—
322D4×D5—36no—
323D4×D5—33no—
324D4×D5—33no—
325D4×D5C22×D313yes—
326#709—33no—
327#709—36no—
328#709—33no—
329#709—36no—
330#709—33no—
331#709C4×D313yescomplemented
332C2×D20—33no—
333C2×C4×D5—33no—
334C2×C4×D5—33no—
335C2×C4×D5—33no—
336C2×C4×D5—33no—
337C2×C4×D5—33no—
338C2×C4×D5—33no—
339C2×C4×D5—33no—
340C2×C4×D5—33no—
341C2×C4×D5—33no—
342C2×C4×D5—31no—
343C2×C4×D5—33no—
344C2×C4×D5C22×D313yes—
345C2×Dic10—33no—
346C22⋊AGL(1,𝔽5)—36no—
347C22⋊AGL(1,𝔽5)—36no—
348C22⋊AGL(1,𝔽5)—32no—
349C22⋊AGL(1,𝔽5)—36no—
350C22⋊AGL(1,𝔽5)—36no—
351C22⋊AGL(1,𝔽5)C22×D316yes—
352C4⋊AGL(1,𝔽5)—36no—
353C4⋊AGL(1,𝔽5)—32no—
354C4⋊AGL(1,𝔽5)—36no—
355C4⋊AGL(1,𝔽5)—36no—
356C4⋊AGL(1,𝔽5)—36no—
357C4⋊AGL(1,𝔽5)C22×D316yes—
358C4×AGL(1,𝔽5)—312no—
359C4×AGL(1,𝔽5)—31no—
360C4×AGL(1,𝔽5)—33no—
361C4×AGL(1,𝔽5)—36no—
362C4×AGL(1,𝔽5)C22×D313yes—
363C4×AGL(1,𝔽5)C22×D311yescharacteristic
364C4×AGL(1,𝔽5)C22×D316yes—
365C22×#41—151no—
366#520—156no—
367#520—152no—
368#519—152no—
369#518—156no—
370C4×#41—51no—
371C4×#41—153no—
372C4×#41—153no—
373C4×#41—151no—
374C2×#117—153no—
375C2×#117—153no—
376C22×C3×C5C23×C413yes—
377C2×D15—43no—
378C2×D15C23×C411yescharacteristic
379C2×D15C23×C413yes—
380C2×C5×D3—43no—
381C2×C5×D3C23×C411yescharacteristic
382C2×C5×D3C23×C413yes—
383C2×C3×D5—26no—
384C2×C3×D5C23×C413yes—
385C2×C3×D5C2511yescharacteristic
386D3×D5—26no—
387D3×D5—22no—
388D3×D5—43no—
389D3×D5—43no—
390ΓL(1,𝔽16)—26no—
391ΓL(1,𝔽16)—22no—
392C3×AGL(1,𝔽5)—26no—
393C3×AGL(1,𝔽5)—22no—
394C3×C4×C5C23×C413yes—
395C3×C4×C5C23×C411yescharacteristic
396Dic15C23×C411yescharacteristic
397Dic15C23×C413yes—
398C3×Dic5C23×C411yescharacteristic
399C3×Dic5C23×C413yes—
400C5×Dic3C23×C411yescharacteristic
401C5×Dic3C23×C413yes—
402C23×D3—53no—
403C3×#41—51no—
404C3×#41—53no—
405C3×#41—53no—
406C3×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
407C2×C3×Q8—51no—
408C2×C3×D4—53no—
409C22×C3×C4—53no—
410C22×C3×C4—56no—
411C2×#67—56no—
412C22×Dic3—53no—
413C22×Dic3—56no—
414#239—51no—
415#239—53no—
416#239—53no—
417#239C2×AGL(1,𝔽5)11yescharacteristic, complemented
418D3×Q8—51no—
419D3×Q8—53no—
420D3×Q8—53no—
421D3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
422#237—53no—
423#237—56no—
424#237—56no—
425#237—53no—
426#237—53no—
427#237C2×AGL(1,𝔽5)13yescomplemented
428D3×D4—56no—
429D3×D4—53no—
430D3×D4—56no—
431D3×D4—53no—
432D3×D4—53no—
433D3×D4C2×AGL(1,𝔽5)13yescomplemented
434#235—53no—
435#235—56no—
436#235—53no—
437#235—56no—
438#235—53no—
439#235C2×AGL(1,𝔽5)13yescomplemented
440C2×D12—53no—
441C2×C4×D3—53no—
442C2×C4×D3—53no—
443C2×C4×D3—53no—
444C2×C4×D3—53no—
445C2×C4×D3—51no—
446C2×C4×D3—53no—
447C2×C4×D3—53no—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—53no—
452C2×C4×D3—512no—
453C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
454C2×Dic6—53no—
455C3×C4⋊C4—56no—
456C3×C22⋊C4—56no—
457C3×C42—56no—
458C3×C42—53no—
459C3×C42—51no—
460#217—56no—
461(C2×D3)⋊C4—52no—
462(C2×D3)⋊C4—56no—
463(C2×D3)⋊C4—56no—
464(C2×D3)⋊C4—56no—
465C4⋊Dic3—56no—
466Dic3⋊C4—56no—
467Dic3⋊C4—52no—
468Dic3⋊C4—56no—
469Dic3⋊C4—56no—
470C4×Dic3—512no—
471C4×Dic3—53no—
472C4×Dic3—51no—
473C4×Dic3—56no—
474C23×C5—33no—
475C22×D5—33no—
476C22×D5—31no—
477C22×D5—33no—
478C22×D5—33no—
479C22×D5—33no—
480C22×D5—126no—
481C22×D5C23×D313yes—
482C2×AGL(1,𝔽5)—36no—
483C2×AGL(1,𝔽5)—32no—
484C2×AGL(1,𝔽5)—46no—
485C2×AGL(1,𝔽5)—1212no—
486C2×AGL(1,𝔽5)—126no—
487C2×AGL(1,𝔽5)C23×D316yes—
488C2×AGL(1,𝔽5)C23×D312yes—
489C5×Q8—33no—
490C5×Q8C2×C4×D311yescharacteristic
491C5×D4—36no—
492C5×D4—33no—
493C5×D4C2×C4×D313yes—
494C2×C4×C5—33no—
495C2×C4×C5—33no—
496C2×C4×C5—31no—
497C2×C4×C5—33no—
498C2×C4×C5—33no—
499C2×C4×C5C2×C4×D313yes—
500C22⋊D5—36no—
501C22⋊D5—36no—
502C22⋊D5—36no—
503C22⋊D5C2×C4×D316yes—
504C2×Dic5—33no—
505C2×Dic5—33no—
506C2×Dic5—31no—
507C2×Dic5—33no—
508C2×Dic5—33no—
509C2×Dic5C2×C4×D313yes—
510D20—36no—
511D20—33no—
512D20C2×C4×D313yes—
513C4×D5—33no—
514C4×D5—33no—
515C4×D5—33no—
516C4×D5—31no—
517C4×D5—31no—
518C4×D5—33no—
519C4×D5—33no—
520C4×D5—33no—
521C4×D5—31no—
522C4×D5—33no—
523C4×D5—33no—
524C4×D5—33no—
525C4×D5C2×C4×D313yes—
526C4×D5C2×C4×D313yes—
527C4×D5C23×D311yescharacteristic
528C4×D5C23×D313yes—
529Dic10—33no—
530Dic10—36no—
531Dic10C2×C4×D313yes—
532C2×#41—31no—
533C2×#41—51no—
534C2×#41—153no—
535C2×#41—153no—
536C2×#41—153no—
537C2×#41—153no—
538C2×#41—151no—
539C2×#41—151no—
540C2×#41—151no—
541C2×#41—153no—
542C2×#41—153no—
543C2×#41—151no—
544C22×Q8—151no—
545C22×D4—153no—
546C23×C4—153no—
547C4×Q8—52no—
548C4×Q8—156no—
549C4×Q8—156no—
550C4×Q8—152no—
551C4×D4—56no—
552C4×D4—156no—
553C4×D4—1512no—
554C4×D4—156no—
555C4×D4—1512no—
556C4×D4—156no—
557#117—53no—
558#117—151no—
559#117—153no—
560#117—153no—
561#117—153no—
562#117—156no—
563#117—156no—
564#117—156no—
565#117—156no—
566#117—153no—
567C2×C4⋊C4—156no—
568C2×C4⋊C4—156no—
569C2×C22⋊C4—156no—
570C2×C22⋊C4—156no—
571C2×C42—53no—
572C2×C42—156no—
573C2×C42—153no—
574C2×C3×C5—23no—
575C2×C3×C5C24×C411yescharacteristic
576D15—21no—
577D15—23no—
578C3×D5—23no—
579C3×D5#58512yes—
580C5×D3—21no—
581C5×D3—23no—
582C23×C3—53no—
583C22×D3—53no—
584C22×D3—51no—
585C22×D3—53no—
586C22×D3—53no—
587C22×D3—53no—
588C22×D3—206no—
589C22×D3C22×AGL(1,𝔽5)13yes—
590C3×Q8—53no—
591C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
592C3×D4—56no—
593C3×D4—53no—
594C3×D4C22×AGL(1,𝔽5)13yes—
595C2×C3×C4—53no—
596C2×C3×C4—53no—
597C2×C3×C4—53no—
598C2×C3×C4—51no—
599C2×C3×C4—53no—
600C2×C3×C4—56no—
601C2×C3×C4—52no—
602C2×C3×C4—206no—
603C2×C3×C4C22×AGL(1,𝔽5)13yes—
604#67—56no—
605#67—56no—
606#67—56no—
607#67C22×AGL(1,𝔽5)16yes—
608C2×Dic3—53no—
609C2×Dic3—53no—
610C2×Dic3—53no—
611C2×Dic3—53no—
612C2×Dic3—51no—
613C2×Dic3—52no—
614C2×Dic3—56no—
615C2×Dic3—206no—
616C2×Dic3C22×AGL(1,𝔽5)13yes—
617D12—56no—
618D12—53no—
619D12C22×AGL(1,𝔽5)13yes—
620C4×D3—51no—
621C4×D3—53no—
622C4×D3—53no—
623C4×D3—53no—
624C4×D3—51no—
625C4×D3—53no—
626C4×D3—53no—
627C4×D3—53no—
628C4×D3—51no—
629C4×D3—53no—
630C4×D3—53no—
631C4×D3—53no—
632C4×D3—2012no—
633C4×D3C22×AGL(1,𝔽5)11yescharacteristic
634C4×D3C22×AGL(1,𝔽5)13yes—
635C4×D3C22×AGL(1,𝔽5)13yes—
636C4×D3C22×AGL(1,𝔽5)13yes—
637Dic6—53no—
638Dic6—56no—
639Dic6C22×AGL(1,𝔽5)13yes—
640C22×C5—31no—
641C22×C5—33no—
642C22×C5—123no—
643C22×C5C22×C4×D313yes—
644C2×D5—26no—
645C2×D5—31no—
646C2×D5—33no—
647C2×D5—66no—
648C2×D5—62no—
649C2×D5—123no—
650C2×D5—123no—
651C2×D5—123no—
652C2×D5C22×C4×D313yes—
653C2×D5C24×D311yescharacteristic
654AGL(1,𝔽5)—22no—
655AGL(1,𝔽5)—26no—
656AGL(1,𝔽5)—66no—
657AGL(1,𝔽5)—62no—
658C4×C5—33no—
659C4×C5—31no—
660C4×C5C22×C4×D313yes—
661C4×C5C22×C4×D311yescharacteristic
662Dic5—33no—
663Dic5—31no—
664Dic5C22×C4×D313yes—
665Dic5C22×C4×D311yescharacteristic
666C24—153no—
667#41—31no—
668#41—33no—
669#41—33no—
670#41—51no—
671#41—53no—
672#41—53no—
673#41—156no—
674#41—156no—
675#41—153no—
676#41—153no—
677#41—156no—
678#41—153no—
679#41—153no—
680#41—156no—
681#41—153no—
682#41—153no—
683#41—151no—
684#41—153no—
685#41—153no—
686#41D3×AGL(1,𝔽5)11yescharacteristic, complemented
687C2×Q8—31no—
688C2×Q8—51no—
689C2×Q8—153no—
690C2×Q8—153no—
691C2×Q8—153no—
692C2×Q8—151no—
693C2×D4—33no—
694C2×D4—53no—
695C2×D4—153no—
696C2×D4—153no—
697C2×D4—156no—
698C2×D4—153no—
699C2×D4—156no—
700C2×D4—156no—
701C2×D4—153no—
702C22×C4—33no—
703C22×C4—53no—
704C22×C4—56no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—151no—
708C22×C4—153no—
709C22×C4—153no—
710C22×C4—153no—
711C22×C4—153no—
712C22×C4—153no—
713C22×C4—153no—
714C22×C4—153no—
715C22×C4—153no—
716C22×C4—1512no—
717C22×C4—153no—
718C22×C4—156no—
719C4⋊C4—56no—
720C4⋊C4—152no—
721C4⋊C4—156no—
722C4⋊C4—156no—
723C4⋊C4—156no—
724C4⋊C4—156no—
725C22⋊C4—56no—
726C22⋊C4—152no—
727C22⋊C4—156no—
728C22⋊C4—156no—
729C22⋊C4—156no—
730C22⋊C4—156no—
731C42—51no—
732C42—53no—
733C42—56no—
734C42—153no—
735C42—151no—
736C42—156no—
737C42—1512no—
738C3×C5#342811yescharacteristic, complemented, Hall
739C22×C3—51no—
740C22×C3—53no—
741C22×C3—106no—
742C22×C3C23×AGL(1,𝔽5)13yes—
743C2×D3—43no—
744C2×D3—51no—
745C2×D3—53no—
746C2×D3—106no—
747C2×D3—102no—
748C2×D3—203no—
749C2×D3—203no—
750C2×D3—203no—
751C2×D3C23×AGL(1,𝔽5)11yescharacteristic
752C2×D3C23×AGL(1,𝔽5)13yes—
753C3×C4—53no—
754C3×C4—51no—
755C3×C4—106no—
756C3×C4—102no—
757C3×C4C23×AGL(1,𝔽5)13yes—
758C3×C4C23×AGL(1,𝔽5)11yescharacteristic
759Dic3—53no—
760Dic3—51no—
761Dic3—106no—
762Dic3—102no—
763Dic3C23×AGL(1,𝔽5)13yes—
764Dic3C23×AGL(1,𝔽5)11yescharacteristic
765C2×C5—23no—
766C2×C5—61no—
767C2×C5—63no—
768C2×C5C23×C4×D311yescharacteristic
769D5—23no—
770D5—61no—
771D5—63no—
772D5#596412yes—
773C23—33no—
774C23—53no—
775C23—151no—
776C23—153no—
777C23—153no—
778C23—153no—
779C23—153no—
780C23—606no—
781Q8—33no—
782Q8—53no—
783Q8—156no—
784Q8—153no—
785Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
786D4—36no—
787D4—33no—
788D4—56no—
789D4—53no—
790D4—156no—
791D4—156no—
792D4—156no—
793D4—156no—
794D4—153no—
795D4C2×D3×AGL(1,𝔽5)13yes—
796C2×C4—33no—
797C2×C4—33no—
798C2×C4—33no—
799C2×C4—31no—
800C2×C4—33no—
801C2×C4—53no—
802C2×C4—53no—
803C2×C4—53no—
804C2×C4—51no—
805C2×C4—53no—
806C2×C4—52no—
807C2×C4—56no—
808C2×C4—151no—
809C2×C4—153no—
810C2×C4—153no—
811C2×C4—153no—
812C2×C4—153no—
813C2×C4—151no—
814C2×C4—153no—
815C2×C4—153no—
816C2×C4—151no—
817C2×C4—153no—
818C2×C4—153no—
819C2×C4—153no—
820C2×C4—153no—
821C2×C4—153no—
822C2×C4—153no—
823C2×C4—151no—
824C2×C4—153no—
825C2×C4—152no—
826C2×C4—156no—
827C2×C4—206no—
828C2×C4—6012no—
829C2×C4—606no—
830C2×C4C2×D3×AGL(1,𝔽5)13yes—
831C2×C3—23no—
832C2×C3—52no—
833C2×C3—103no—
834C2×C3C24×AGL(1,𝔽5)11yescharacteristic
835D3—21no—
836D3—23no—
837D3—101no—
838D3—103no—
839C5#8583411yescharacteristic, complemented, Sylow
840C22—31no—
841C22—33no—
842C22—51no—
843C22—53no—
844C22—106no—
845C22—123no—
846C22—151no—
847C22—153no—
848C22—306no—
849C22—302no—
850C22—603no—
851C22—603no—
852C22—603no—
853C22C22×D3×AGL(1,𝔽5)13yes—
854C4—31no—
855C4—33no—
856C4—51no—
857C4—53no—
858C4—102no—
859C4—106no—
860C4—151no—
861C4—153no—
862C4—306no—
863C4—302no—
864C4C22×D3×AGL(1,𝔽5)13yes—
865C4C22×D3×AGL(1,𝔽5)11yescharacteristic
866C3#1061941211yescharacteristic, complemented, Sylow
867C2—23no—
868C2—52no—
869C2—61no—
870C2—63no—
871C2—103no—
872C2—301no—
873C2—303no—
874C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4C22×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
prime radicalD3×D5×#41C2
cosocleC2×C3×D5C25
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. #41×ΓL(1,𝔽16)C2semidirect
3. C3×#41×AGL(1,𝔽5)C2semidirect
4. #11756854C2semidirect
5. #11756847C2semidirect
6. #11756846C2semidirect
7. #11756845C2semidirect
8. #11756835C2semidirect
9. D3×#4130C2semidirect
10. AGL(1,𝔽5)×#235C2semidirect
11. C2×#91909C2semidirect
13. #41×D15C4semidirect
14. C5×D3×#41C4semidirect
16. #92034C4semidirect
17. D3×#713C4semidirect
20. #92024C4semidirect
21. D3×#711C4semidirect
24. #92016C4semidirect
25. D3×#709C4semidirect
28. Q8×ΓL(1,𝔽16)C22semidirect
29. D4×ΓL(1,𝔽16)C22semidirect
30. #91989C22semidirect
31. C2×C4×ΓL(1,𝔽16)C22semidirect
32. C3×Q8×AGL(1,𝔽5)C22semidirect
33. C3×D4×AGL(1,𝔽5)C22semidirect
34. C3×#4130C22semidirect
35. C2×C3×C4×AGL(1,𝔽5)C22semidirect
36. #67⋊AGL(1,𝔽5)C22semidirect
38. AGL(1,𝔽5)×#67C22semidirect
39. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
41. #91923C22semidirect
42. #91921C22semidirect
43. D3×C4⋊AGL(1,𝔽5)C22semidirect
44. AGL(1,𝔽5)×D12C22semidirect
45. C4×D3×AGL(1,𝔽5)C22semidirect
49. #91909C22semidirect
50. #91909C22semidirect
51. #91909C22semidirect
52. ΓL(1,𝔽16)⋊Q8C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
62. #41×AGL(1,𝔽5)D3semidirect
71. C3×C5×#41C2×C4semidirect
72. #6821C2×C4semidirect
73. Q8×D15C2×C4semidirect
74. #6819C2×C4semidirect
75. D4×D15C2×C4semidirect
76. #6817C2×C4semidirect
77. C2×C4×D15C2×C4semidirect
78. C5×#239C2×C4semidirect
79. C5×D3×Q8C2×C4semidirect
80. C5×#237C2×C4semidirect
81. C5×D3×D4C2×C4semidirect
82. C5×#235C2×C4semidirect
83. C2×C4×C5×D3C2×C4semidirect
84. C3×#713C2×C4semidirect
86. C3×#711C2×C4semidirect
88. C3×#709C2×C4semidirect
90. #6790C2×C4semidirect
91. D3×C22⋊D5C2×C4semidirect
93. C2×#1200C2×C4semidirect
94. #6782C2×C4semidirect
95. C2×D3×Dic5C2×C4semidirect
96. #6780C2×C4semidirect
97. #6779C2×C4semidirect
99. #6777C2×C4semidirect
100. D3×D20C2×C4semidirect
102. C4×D3×D5C2×C4semidirect
103. C4×D3×D5C2×C4semidirect
104. C4×D3×D5C2×C4semidirect
105. C4×D3×D5C2×C4semidirect
110. #6773C2×C4semidirect
111. #6772C2×C4semidirect
112. #6771C2×C4semidirect
113. D15⋊Q8C2×C4semidirect
114. #6769C2×C4semidirect
115. #6768C2×C4semidirect
116. D3×Dic10C2×C4semidirect
117. #6766C2×C4semidirect
118. #6765C2×C4semidirect
170. Q8×AGL(1,𝔽5)C2×D3semidirect
176. D4×AGL(1,𝔽5)C2×D3semidirect
186. #4130C2×D3semidirect
191. C2×C4×AGL(1,𝔽5)C2×D3semidirect
259. D3×#41AGL(1,𝔽5)semidirect
300. C5×#41C4×D3semidirect
309. #713C4×D3semidirect
319. #711C4×D3semidirect
331. #709C4×D3semidirect
406. C3×#41C2×AGL(1,𝔽5)semidirect
417. #239C2×AGL(1,𝔽5)semidirect
421. D3×Q8C2×AGL(1,𝔽5)semidirect
427. #237C2×AGL(1,𝔽5)semidirect
433. D3×D4C2×AGL(1,𝔽5)semidirect
439. #235C2×AGL(1,𝔽5)semidirect
453. C2×C4×D3C2×AGL(1,𝔽5)semidirect
686. #41D3×AGL(1,𝔽5)semidirect
738. C3×C5#3428semidirect
839. C5#85834semidirect
866. C3#10619412semidirect

Maximal subgroups

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

subgroupindex
D3×D5×#412
#41×ΓL(1,𝔽16)2
C3×#41×AGL(1,𝔽5)2
#117568542
#117568472
#117568462
#117568452
#117568352
D3×#41302
AGL(1,𝔽5)×#2352
C2×#919092
#106194123
#858345