Finite Group Databasebeta

← #14479191

Subgroups — #14479191

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D5×#41C211yesmaximal, characteristic
2#11756995C211yesmaximal, characteristic, complemented
3C3×#66266C211yesmaximal, characteristic, complemented
4AGL(1,𝔽5)×#239C212yesmaximal, complemented
5#11756847C212yesmaximal, complemented
6#11756845C216yesmaximal, complemented
7AGL(1,𝔽5)×#237C216yesmaximal, complemented
8#11756838C213yesmaximal, complemented
9#11756836C213yesmaximal, complemented
10D3×#4130C213yesmaximal, complemented
11C2×#91907C213yesmaximal, 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×(C2×D3)⋊AGL(1,𝔽5)C2216yes—
40#91923C2216yescomplemented
41C2×Dic3×AGL(1,𝔽5)C2216yescomplemented
42#91921C2216yescomplemented
43D3×C4⋊AGL(1,𝔽5)C2213yescomplemented
44D3×C4⋊AGL(1,𝔽5)C2213yescomplemented
45AGL(1,𝔽5)×D12C2216yescomplemented
46C4×D3×AGL(1,𝔽5)C2216yescomplemented
47#91909C2216yes—
48ΓL(1,𝔽16)⋊Q8C2216yescomplemented
49#91907C2213yes—
50#91907C2216yes—
51#91907C2211yescharacteristic
52#91907C2216yescomplemented
53#91907C2216yescomplemented
54AGL(1,𝔽5)×Dic6C2216yescomplemented
55#85885—51nomaximal, Hall
56C2×D5×#41—31no—
57#66266—31no—
58#66266—33no—
59#66266—33no—
60#66266D311yescharacteristic, complemented
61#41×AGL(1,𝔽5)—32no—
62#41×AGL(1,𝔽5)—36no—
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)C2316yes—
71C2×D3×AGL(1,𝔽5)C2316yes—
72C3×C5×#41C2×C411yescharacteristic, complemented
73#6821C2×C411yescharacteristic, complemented
74Q8×D15C2×C411yescharacteristic, complemented
75#6819C2×C413yescomplemented
76D4×D15C2×C413yescomplemented
77#6817C2×C413yescomplemented
78C2×C4×D15C2×C413yescomplemented
79C5×#239C2×C411yescharacteristic, complemented
80C5×D3×Q8C2×C411yescharacteristic, complemented
81C5×#237C2×C413yescomplemented
82C5×D3×D4C2×C413yescomplemented
83C5×#235C2×C413yescomplemented
84C2×C4×C5×D3C2×C413yescomplemented
85C3×#713C2×C411yescharacteristic, complemented
86C3×Q8×D5C2311yescharacteristic
87C3×#711C2×C413yescomplemented
88C3×D4×D5C2313yes—
89C3×#709C2×C413yescomplemented
90C2×C3×C4×D5C2313yes—
91#6790C2×C416yescomplemented
92D3×C22⋊D5C2×C416yescomplemented
93D5×#67C2316yes—
94C2×#1200C2×C413yescomplemented
95#6782C2×C416yescomplemented
96C2×D3×Dic5C2×C413yescomplemented
97#6780C2×C416yescomplemented
98#6779C2×C416yescomplemented
99C2×D5×Dic3C2313yes—
100#6777C2×C413yescomplemented
101D3×D20C2×C413yescomplemented
102D5×D12C2313yes—
103C4×D3×D5C2×C413yescomplemented
104C4×D3×D5C2×C413yescomplemented
105C4×D3×D5C2×C413yescomplemented
106C4×D3×D5C2×C413yescomplemented
107C4×D3×D5C2311yescharacteristic
108C4×D3×D5C2313yes—
109C4×D3×D5C2313yes—
110C4×D3×D5C2313yes—
111#6773C2×C413yescomplemented
112#6772C2×C413yescomplemented
113#6771C2×C416yescomplemented
114D15⋊Q8C2×C413yescomplemented
115#6769C2×C413yescomplemented
116#6768C2×C413yescomplemented
117D3×Dic10C2×C413yescomplemented
118#6766C2×C413yescomplemented
119#6765C2×C413yescomplemented
120D5×Dic6C2313yes—
121#6763C2316yes—
122C4⋊ΓL(1,𝔽16)C2316yes—
123C4⋊ΓL(1,𝔽16)C2313yes—
124C4⋊ΓL(1,𝔽16)C2311yescharacteristic
125C4×ΓL(1,𝔽16)C2316yes—
126C3×C22⋊AGL(1,𝔽5)C2316yes—
127C3×C4⋊AGL(1,𝔽5)C2313yes—
128C3×C4⋊AGL(1,𝔽5)C2316yes—
129C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
130C3×C4×AGL(1,𝔽5)C2316yes—
131Dic3⋊AGL(1,𝔽5)C2316yes—
132Dic3⋊AGL(1,𝔽5)C2316yes—
133(C2×D3)⋊AGL(1,𝔽5)C2316yes—
134(C2×D3)⋊AGL(1,𝔽5)C2312yes—
135(C2×D3)⋊AGL(1,𝔽5)C23112yes—
136Dic3×AGL(1,𝔽5)C23112yes—
137Dic3×AGL(1,𝔽5)C2316yes—
138Dic3×AGL(1,𝔽5)C2312yes—
139C2×D3×#41—51no—
140C3×#520—51no—
141#5827—51no—
142C4×#239—52no—
143#5572—52no—
144#5545—56no—
145C4×#237—56no—
146#5523—53no—
147D3×#117—53no—
148#5504—53no—
149C2×#892—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—31no—
180#4130—33no—
181#4130—36no—
182#4130—36no—
183#4130—36no—
184#4130—36no—
185#4130C2×D313yescomplemented
186C2×C4⋊AGL(1,𝔽5)—33no—
187C2×C4⋊AGL(1,𝔽5)—33no—
188C2×C4⋊AGL(1,𝔽5)—33no—
189C2×C4⋊AGL(1,𝔽5)C2×D313yescomplemented
190C2×C4×AGL(1,𝔽5)—36no—
191C2×C4×AGL(1,𝔽5)—36no—
192#3428—151noSylow
193C22×D15C22×C413yes—
194C22×C5×D3C22×C413yes—
195C22×C3×D5C2413yes—
196C2×D3×D5—43no—
197C2×D3×D5—43no—
198C2×D3×D5C22×C413yes—
199C2×D3×D5C22×C413yes—
200C2×D3×D5C2411yescharacteristic
201C2×D3×D5C2413yes—
202C2×ΓL(1,𝔽16)—46no—
203C2×ΓL(1,𝔽16)C2416yes—
204C2×ΓL(1,𝔽16)C2412yes—
205C2×C3×AGL(1,𝔽5)—46no—
206C2×C3×AGL(1,𝔽5)C2416yes—
207C2×C3×AGL(1,𝔽5)C2412yes—
208D3×AGL(1,𝔽5)—46no—
209D3×AGL(1,𝔽5)—46no—
210C3×C5×Q8C22×C411yescharacteristic
211C3×C5×D4C22×C413yes—
212C2×C3×C4×C5C22×C413yes—
213#1220C22×C416yes—
214C2×Dic15C22×C413yes—
215D60C22×C413yes—
216C4×D15C22×C413yes—
217C4×D15C22×C413yes—
218C4×D15C22×C413yes—
219C4×D15C22×C411yescharacteristic
220Dic30C22×C413yes—
221C5×#67C22×C416yes—
222C2×C5×Dic3C22×C413yes—
223C5×D12C22×C413yes—
224C4×C5×D3C22×C413yes—
225C4×C5×D3C22×C413yes—
226C4×C5×D3C22×C413yes—
227C4×C5×D3C22×C411yescharacteristic
228C5×Dic6C22×C413yes—
229C3×C22⋊D5C22×C416yes—
230C2×C3×Dic5C22×C413yes—
231C3×D20C22×C413yes—
232C3×C4×D5C22×C413yes—
233C3×C4×D5C22×C413yes—
234C3×C4×D5C2413yes—
235C3×C4×D5C2411yescharacteristic
236C3×Dic10C22×C413yes—
237#1204C22×C416yes—
238#1203C22×C416yes—
239#1202C22×C416yes—
240#1201C22×C416yes—
241#1200C22×C413yes—
242#1200C22×C413yes—
243#1200C22×C413yes—
244#1200C22×C411yescharacteristic
245D3×Dic5C22×C413yes—
246D3×Dic5C22×C413yes—
247D3×Dic5C22×C413yes—
248D3×Dic5C22×C411yescharacteristic
249D5×Dic3C22×C413yes—
250D5×Dic3C22×C413yes—
251D5×Dic3C2411yescharacteristic
252D5×Dic3C2413yes—
253C2×C3×#41—51no—
254D3×#41—51no—
255D3×#41—51no—
256D3×#41—51no—
257D3×#41—53no—
258D3×#41—53no—
259D3×#41—53no—
260D3×#41—53no—
261D3×#41AGL(1,𝔽5)11yescharacteristic, complemented
262C2×#239—51no—
263C2×D3×Q8—51no—
264C2×#237—53no—
265C2×D3×D4—53no—
266C2×#235—53no—
267C22×C4×D3—53no—
268C3×C4×Q8—52no—
269C3×C4×D4—56no—
270C3×#117—53no—
271C2×C3×C4⋊C4—53no—
272Q8×Dic3—52no—
273D4×Dic3—56no—
274C4×#67—512no—
275C2×(C2×D3)⋊C4—56no—
276#926—53no—
277C2×C4⋊Dic3—53no—
278C2×C4×Dic3—56no—
279#893—56no—
280#892—53no—
281#892—56no—
282#892—51no—
283#892—56no—
284#892—56no—
285D3×C4⋊C4—53no—
286D3×C4⋊C4—53no—
287#887—56no—
288#67⋊C4—512no—
289D3×C22⋊C4—56no—
290#877—56no—
291C4×D12—56no—
292#872—56no—
293C42×D3—56no—
294C4×Dic6—56no—
295C23×D5—33no—
296C22×AGL(1,𝔽5)—36no—
297C22×AGL(1,𝔽5)—36no—
298C22×AGL(1,𝔽5)—36no—
299C22×AGL(1,𝔽5)C22×D316yes—
300C5×#41—31no—
301C5×#41—33no—
302C5×#41—33no—
303C5×#41C4×D311yescharacteristic, complemented
304C2×C5×Q8—31no—
305C2×C5×D4—33no—
306C22×C4×C5—33no—
307C2×C22⋊D5—36no—
308C22×Dic5—33no—
309#713—31no—
310#713—33no—
311#713—33no—
312#713C4×D311yescharacteristic, complemented
313Q8×D5—31no—
314Q8×D5—33no—
315Q8×D5—33no—
316Q8×D5C22×D311yescharacteristic
317#711—33no—
318#711—36no—
319#711—36no—
320#711—33no—
321#711—33no—
322#711C4×D313yescomplemented
323D4×D5—36no—
324D4×D5—33no—
325D4×D5—36no—
326D4×D5—33no—
327D4×D5—33no—
328D4×D5C22×D313yes—
329#709—33no—
330#709—36no—
331#709—33no—
332#709—36no—
333#709—33no—
334#709C4×D313yescomplemented
335C2×D20—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—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—31no—
346C2×C4×D5—33no—
347C2×C4×D5C22×D313yes—
348C2×Dic10—33no—
349C22⋊AGL(1,𝔽5)—36no—
350C22⋊AGL(1,𝔽5)—36no—
351C22⋊AGL(1,𝔽5)—32no—
352C22⋊AGL(1,𝔽5)—312no—
353C22⋊AGL(1,𝔽5)C22×D316yes—
354C4⋊AGL(1,𝔽5)—36no—
355C4⋊AGL(1,𝔽5)—36no—
356C4⋊AGL(1,𝔽5)—33no—
357C4⋊AGL(1,𝔽5)—31no—
358C4⋊AGL(1,𝔽5)—36no—
359C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
360C4⋊AGL(1,𝔽5)C22×D313yes—
361C4⋊AGL(1,𝔽5)C22×D316yes—
362C4×AGL(1,𝔽5)—36no—
363C4×AGL(1,𝔽5)—32no—
364C4×AGL(1,𝔽5)—312no—
365C4×AGL(1,𝔽5)—36no—
366C4×AGL(1,𝔽5)C22×D316yes—
367C22×#41—151no—
368#520—51no—
369#520—153no—
370#520—153no—
371#520—151no—
372#519—152no—
373#518—156no—
374C4×#41—156no—
375C4×#41—152no—
376C2×#117—153no—
377C2×#117—153no—
378C22×C3×C5C23×C413yes—
379C2×D15—43no—
380C2×D15C23×C411yescharacteristic
381C2×D15C23×C413yes—
382C2×C5×D3—43no—
383C2×C5×D3C23×C411yescharacteristic
384C2×C5×D3C23×C413yes—
385C2×C3×D5—23no—
386C2×C3×D5—23no—
387C2×C3×D5C23×C413yes—
388C2×C3×D5C2511yescharacteristic
389D3×D5—23no—
390D3×D5—23no—
391D3×D5—21no—
392D3×D5—21no—
393D3×D5—43no—
394D3×D5—43no—
395ΓL(1,𝔽16)—22no—
396ΓL(1,𝔽16)—26no—
397C3×AGL(1,𝔽5)—22no—
398C3×AGL(1,𝔽5)—26no—
399C3×C4×C5C23×C413yes—
400C3×C4×C5C23×C411yescharacteristic
401Dic15C23×C411yescharacteristic
402Dic15C23×C413yes—
403C3×Dic5C23×C411yescharacteristic
404C3×Dic5C23×C413yes—
405C5×Dic3C23×C411yescharacteristic
406C5×Dic3C23×C413yes—
407C23×D3—53no—
408C3×#41—51no—
409C3×#41—53no—
410C3×#41—53no—
411C3×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
412C2×C3×Q8—51no—
413C2×C3×D4—53no—
414C22×C3×C4—53no—
415C22×C3×C4—56no—
416C2×#67—56no—
417C22×Dic3—53no—
418C22×Dic3—56no—
419#239—51no—
420#239—53no—
421#239—53no—
422#239C2×AGL(1,𝔽5)11yescharacteristic, complemented
423D3×Q8—51no—
424D3×Q8—53no—
425D3×Q8—53no—
426D3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
427#237—53no—
428#237—56no—
429#237—56no—
430#237—53no—
431#237—53no—
432#237C2×AGL(1,𝔽5)13yescomplemented
433D3×D4—56no—
434D3×D4—53no—
435D3×D4—56no—
436D3×D4—53no—
437D3×D4—53no—
438D3×D4C2×AGL(1,𝔽5)13yescomplemented
439#235—53no—
440#235—56no—
441#235—53no—
442#235—56no—
443#235—53no—
444#235C2×AGL(1,𝔽5)13yescomplemented
445C2×D12—53no—
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—53no—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—51no—
457C2×C4×D3—56no—
458C2×C4×D3—56no—
459C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
460C2×Dic6—53no—
461C3×C4⋊C4—56no—
462C3×C4⋊C4—51no—
463C3×C4⋊C4—53no—
464C3×C22⋊C4—56no—
465C3×C42—56no—
466#217—56no—
467(C2×D3)⋊C4—52no—
468(C2×D3)⋊C4—56no—
469(C2×D3)⋊C4—512no—
470C4⋊Dic3—56no—
471C4⋊Dic3—51no—
472C4⋊Dic3—53no—
473Dic3⋊C4—56no—
474Dic3⋊C4—56no—
475C4×Dic3—512no—
476C4×Dic3—52no—
477C4×Dic3—56no—
478C4×Dic3—56no—
479C23×C5—33no—
480C22×D5—33no—
481C22×D5—31no—
482C22×D5—33no—
483C22×D5—33no—
484C22×D5—33no—
485C22×D5—123no—
486C22×D5—123no—
487C22×D5C23×D313yes—
488C2×AGL(1,𝔽5)—32no—
489C2×AGL(1,𝔽5)—36no—
490C2×AGL(1,𝔽5)—46no—
491C2×AGL(1,𝔽5)—126no—
492C2×AGL(1,𝔽5)—126no—
493C2×AGL(1,𝔽5)—126no—
494C2×AGL(1,𝔽5)C23×D316yes—
495C2×AGL(1,𝔽5)C23×D312yes—
496C5×Q8—33no—
497C5×Q8C2×C4×D311yescharacteristic
498C5×D4—36no—
499C5×D4—33no—
500C5×D4C2×C4×D313yes—
501C2×C4×C5—33no—
502C2×C4×C5—33no—
503C2×C4×C5—31no—
504C2×C4×C5—33no—
505C2×C4×C5—33no—
506C2×C4×C5C2×C4×D313yes—
507C22⋊D5—36no—
508C22⋊D5—36no—
509C22⋊D5—36no—
510C22⋊D5C2×C4×D316yes—
511C2×Dic5—33no—
512C2×Dic5—33no—
513C2×Dic5—31no—
514C2×Dic5—33no—
515C2×Dic5—33no—
516C2×Dic5C2×C4×D313yes—
517D20—36no—
518D20—33no—
519D20C2×C4×D313yes—
520C4×D5—33no—
521C4×D5—33no—
522C4×D5—31no—
523C4×D5—33no—
524C4×D5—31no—
525C4×D5—33no—
526C4×D5—33no—
527C4×D5—33no—
528C4×D5—31no—
529C4×D5—33no—
530C4×D5—33no—
531C4×D5—33no—
532C4×D5C2×C4×D313yes—
533C4×D5C2×C4×D313yes—
534C4×D5C23×D313yes—
535C4×D5C23×D311yescharacteristic
536Dic10—33no—
537Dic10—36no—
538Dic10C2×C4×D313yes—
539C2×#41—31no—
540C2×#41—51no—
541C2×#41—153no—
542C2×#41—153no—
543C2×#41—153no—
544C2×#41—153no—
545C2×#41—151no—
546C2×#41—151no—
547C2×#41—151no—
548C2×#41—153no—
549C2×#41—153no—
550C2×#41—151no—
551C22×Q8—151no—
552C22×D4—153no—
553C23×C4—153no—
554C4×Q8—52no—
555C4×Q8—156no—
556C4×Q8—156no—
557C4×Q8—152no—
558C4×D4—56no—
559C4×D4—156no—
560C4×D4—1512no—
561C4×D4—156no—
562C4×D4—1512no—
563C4×D4—156no—
564#117—53no—
565#117—156no—
566#117—156no—
567#117—153no—
568#117—151no—
569#117—156no—
570#117—156no—
571#117—156no—
572#117—153no—
573C2×C4⋊C4—53no—
574C2×C4⋊C4—153no—
575C2×C4⋊C4—153no—
576C2×C4⋊C4—153no—
577C2×C22⋊C4—156no—
578C2×C22⋊C4—156no—
579C2×C42—156no—
580C2×C42—156no—
581C2×C3×C5—23no—
582C2×C3×C5C24×C411yescharacteristic
583D15—21no—
584D15—23no—
585C3×D5—23no—
586C3×D5#58511yescharacteristic
587C3×D5#58511yescharacteristic
588C5×D3—21no—
589C5×D3—23no—
590C23×C3—53no—
591C22×D3—53no—
592C22×D3—51no—
593C22×D3—53no—
594C22×D3—53no—
595C22×D3—53no—
596C22×D3—203no—
597C22×D3—203no—
598C22×D3C22×AGL(1,𝔽5)13yes—
599C3×Q8—53no—
600C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
601C3×D4—56no—
602C3×D4—53no—
603C3×D4C22×AGL(1,𝔽5)13yes—
604C2×C3×C4—53no—
605C2×C3×C4—53no—
606C2×C3×C4—53no—
607C2×C3×C4—53no—
608C2×C3×C4—51no—
609C2×C3×C4—56no—
610C2×C3×C4—52no—
611C2×C3×C4—206no—
612C2×C3×C4C22×AGL(1,𝔽5)13yes—
613#67—56no—
614#67—56no—
615#67—56no—
616#67C22×AGL(1,𝔽5)16yes—
617C2×Dic3—53no—
618C2×Dic3—53no—
619C2×Dic3—53no—
620C2×Dic3—51no—
621C2×Dic3—53no—
622C2×Dic3—52no—
623C2×Dic3—56no—
624C2×Dic3—206no—
625C2×Dic3C22×AGL(1,𝔽5)13yes—
626D12—56no—
627D12—53no—
628D12C22×AGL(1,𝔽5)13yes—
629C4×D3—51no—
630C4×D3—53no—
631C4×D3—53no—
632C4×D3—53no—
633C4×D3—51no—
634C4×D3—53no—
635C4×D3—53no—
636C4×D3—53no—
637C4×D3—51no—
638C4×D3—53no—
639C4×D3—53no—
640C4×D3—53no—
641C4×D3—206no—
642C4×D3—206no—
643C4×D3C22×AGL(1,𝔽5)11yescharacteristic
644C4×D3C22×AGL(1,𝔽5)13yes—
645C4×D3C22×AGL(1,𝔽5)13yes—
646C4×D3C22×AGL(1,𝔽5)13yes—
647Dic6—53no—
648Dic6—56no—
649Dic6C22×AGL(1,𝔽5)13yes—
650C22×C5—31no—
651C22×C5—33no—
652C22×C5—123no—
653C22×C5C22×C4×D313yes—
654C2×D5—23no—
655C2×D5—23no—
656C2×D5—31no—
657C2×D5—33no—
658C2×D5—63no—
659C2×D5—61no—
660C2×D5—63no—
661C2×D5—61no—
662C2×D5—123no—
663C2×D5—123no—
664C2×D5—123no—
665C2×D5C22×C4×D313yes—
666C2×D5C24×D311yescharacteristic
667AGL(1,𝔽5)—26no—
668AGL(1,𝔽5)—22no—
669AGL(1,𝔽5)—62no—
670AGL(1,𝔽5)—66no—
671C4×C5—33no—
672C4×C5—31no—
673C4×C5C22×C4×D313yes—
674C4×C5C22×C4×D311yescharacteristic
675Dic5—33no—
676Dic5—31no—
677Dic5C22×C4×D313yes—
678Dic5C22×C4×D311yescharacteristic
679C24—153no—
680#41—31no—
681#41—33no—
682#41—33no—
683#41—51no—
684#41—53no—
685#41—53no—
686#41—156no—
687#41—156no—
688#41—153no—
689#41—153no—
690#41—156no—
691#41—153no—
692#41—153no—
693#41—156no—
694#41—153no—
695#41—153no—
696#41—151no—
697#41—153no—
698#41—153no—
699#41D3×AGL(1,𝔽5)11yescharacteristic, complemented
700C2×Q8—31no—
701C2×Q8—51no—
702C2×Q8—153no—
703C2×Q8—153no—
704C2×Q8—153no—
705C2×Q8—151no—
706C2×D4—33no—
707C2×D4—53no—
708C2×D4—153no—
709C2×D4—153no—
710C2×D4—156no—
711C2×D4—153no—
712C2×D4—156no—
713C2×D4—156no—
714C2×D4—153no—
715C22×C4—33no—
716C22×C4—53no—
717C22×C4—56no—
718C22×C4—153no—
719C22×C4—153no—
720C22×C4—151no—
721C22×C4—153no—
722C22×C4—153no—
723C22×C4—153no—
724C22×C4—153no—
725C22×C4—153no—
726C22×C4—153no—
727C22×C4—153no—
728C22×C4—153no—
729C22×C4—156no—
730C22×C4—156no—
731C22×C4—153no—
732C22×C4—156no—
733C4⋊C4—53no—
734C4⋊C4—56no—
735C4⋊C4—51no—
736C4⋊C4—151no—
737C4⋊C4—153no—
738C4⋊C4—156no—
739C4⋊C4—156no—
740C4⋊C4—156no—
741C22⋊C4—56no—
742C22⋊C4—152no—
743C22⋊C4—156no—
744C22⋊C4—1512no—
745C22⋊C4—156no—
746C42—56no—
747C42—152no—
748C42—156no—
749C42—156no—
750C42—1512no—
751C3×C5#342811yescharacteristic, complemented, Hall
752C22×C3—51no—
753C22×C3—53no—
754C22×C3—103no—
755C22×C3—103no—
756C22×C3C23×AGL(1,𝔽5)13yes—
757C2×D3—43no—
758C2×D3—51no—
759C2×D3—53no—
760C2×D3—103no—
761C2×D3—103no—
762C2×D3—101no—
763C2×D3—101no—
764C2×D3—203no—
765C2×D3—203no—
766C2×D3—203no—
767C2×D3C23×AGL(1,𝔽5)11yescharacteristic
768C2×D3C23×AGL(1,𝔽5)13yes—
769C3×C4—53no—
770C3×C4—51no—
771C3×C4—102no—
772C3×C4—106no—
773C3×C4C23×AGL(1,𝔽5)13yes—
774C3×C4C23×AGL(1,𝔽5)11yescharacteristic
775Dic3—53no—
776Dic3—51no—
777Dic3—102no—
778Dic3—106no—
779Dic3C23×AGL(1,𝔽5)13yes—
780Dic3C23×AGL(1,𝔽5)11yescharacteristic
781C2×C5—23no—
782C2×C5—61no—
783C2×C5—63no—
784C2×C5C23×C4×D311yescharacteristic
785D5—23no—
786D5—61no—
787D5—63no—
788D5#596611yescharacteristic
789D5#596811yescharacteristic
790C23—33no—
791C23—53no—
792C23—151no—
793C23—153no—
794C23—153no—
795C23—153no—
796C23—153no—
797C23—603no—
798C23—603no—
799Q8—33no—
800Q8—53no—
801Q8—156no—
802Q8—153no—
803Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
804D4—36no—
805D4—33no—
806D4—56no—
807D4—53no—
808D4—156no—
809D4—156no—
810D4—156no—
811D4—156no—
812D4—153no—
813D4C2×D3×AGL(1,𝔽5)13yes—
814C2×C4—33no—
815C2×C4—31no—
816C2×C4—33no—
817C2×C4—33no—
818C2×C4—33no—
819C2×C4—53no—
820C2×C4—53no—
821C2×C4—51no—
822C2×C4—53no—
823C2×C4—53no—
824C2×C4—52no—
825C2×C4—56no—
826C2×C4—151no—
827C2×C4—153no—
828C2×C4—153no—
829C2×C4—153no—
830C2×C4—151no—
831C2×C4—153no—
832C2×C4—153no—
833C2×C4—153no—
834C2×C4—151no—
835C2×C4—153no—
836C2×C4—153no—
837C2×C4—153no—
838C2×C4—153no—
839C2×C4—151no—
840C2×C4—153no—
841C2×C4—153no—
842C2×C4—153no—
843C2×C4—156no—
844C2×C4—152no—
845C2×C4—206no—
846C2×C4—606no—
847C2×C4—606no—
848C2×C4—606no—
849C2×C4C2×D3×AGL(1,𝔽5)13yes—
850C2×C3—23no—
851C2×C3—51no—
852C2×C3—51no—
853C2×C3—103no—
854C2×C3C24×AGL(1,𝔽5)11yescharacteristic
855D3—21no—
856D3—23no—
857D3—101no—
858D3—103no—
859C5#8588511yescharacteristic, complemented, Sylow
860C22—31no—
861C22—33no—
862C22—51no—
863C22—53no—
864C22—103no—
865C22—103no—
866C22—123no—
867C22—151no—
868C22—153no—
869C22—303no—
870C22—303no—
871C22—301no—
872C22—301no—
873C22—603no—
874C22—603no—
875C22—603no—
876C22C22×D3×AGL(1,𝔽5)13yes—
877C4—31no—
878C4—33no—
879C4—51no—
880C4—53no—
881C4—106no—
882C4—102no—
883C4—151no—
884C4—153no—
885C4—302no—
886C4—306no—
887C4C22×D3×AGL(1,𝔽5)11yescharacteristic
888C4C22×D3×AGL(1,𝔽5)13yes—
889C3#1061941211yescharacteristic, complemented, Sylow
890C2—23no—
891C2—51no—
892C2—51no—
893C2—61no—
894C2—63no—
895C2—103no—
896C2—301no—
897C2—303no—
898C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
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 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
2. #11756995C2semidirect
3. C3×#66266C2semidirect
4. AGL(1,𝔽5)×#239C2semidirect
5. #11756847C2semidirect
6. #11756845C2semidirect
7. AGL(1,𝔽5)×#237C2semidirect
8. #11756838C2semidirect
9. #11756836C2semidirect
10. D3×#4130C2semidirect
11. C2×#91907C2semidirect
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
40. #91923C22semidirect
41. C2×Dic3×AGL(1,𝔽5)C22semidirect
42. #91921C22semidirect
43. D3×C4⋊AGL(1,𝔽5)C22semidirect
44. D3×C4⋊AGL(1,𝔽5)C22semidirect
45. AGL(1,𝔽5)×D12C22semidirect
46. C4×D3×AGL(1,𝔽5)C22semidirect
48. ΓL(1,𝔽16)⋊Q8C22semidirect
52. #91907C22semidirect
53. #91907C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
60. #66266D3semidirect
72. C3×C5×#41C2×C4semidirect
73. #6821C2×C4semidirect
74. Q8×D15C2×C4semidirect
75. #6819C2×C4semidirect
76. D4×D15C2×C4semidirect
77. #6817C2×C4semidirect
78. C2×C4×D15C2×C4semidirect
79. C5×#239C2×C4semidirect
80. C5×D3×Q8C2×C4semidirect
81. C5×#237C2×C4semidirect
82. C5×D3×D4C2×C4semidirect
83. C5×#235C2×C4semidirect
84. C2×C4×C5×D3C2×C4semidirect
85. C3×#713C2×C4semidirect
87. C3×#711C2×C4semidirect
89. C3×#709C2×C4semidirect
91. #6790C2×C4semidirect
92. D3×C22⋊D5C2×C4semidirect
94. C2×#1200C2×C4semidirect
95. #6782C2×C4semidirect
96. C2×D3×Dic5C2×C4semidirect
97. #6780C2×C4semidirect
98. #6779C2×C4semidirect
100. #6777C2×C4semidirect
101. D3×D20C2×C4semidirect
103. C4×D3×D5C2×C4semidirect
104. C4×D3×D5C2×C4semidirect
105. C4×D3×D5C2×C4semidirect
106. C4×D3×D5C2×C4semidirect
111. #6773C2×C4semidirect
112. #6772C2×C4semidirect
113. #6771C2×C4semidirect
114. D15⋊Q8C2×C4semidirect
115. #6769C2×C4semidirect
116. #6768C2×C4semidirect
117. D3×Dic10C2×C4semidirect
118. #6766C2×C4semidirect
119. #6765C2×C4semidirect
170. Q8×AGL(1,𝔽5)C2×D3semidirect
176. D4×AGL(1,𝔽5)C2×D3semidirect
185. #4130C2×D3semidirect
189. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
261. D3×#41AGL(1,𝔽5)semidirect
303. C5×#41C4×D3semidirect
312. #713C4×D3semidirect
322. #711C4×D3semidirect
334. #709C4×D3semidirect
411. C3×#41C2×AGL(1,𝔽5)semidirect
422. #239C2×AGL(1,𝔽5)semidirect
426. D3×Q8C2×AGL(1,𝔽5)semidirect
432. #237C2×AGL(1,𝔽5)semidirect
438. D3×D4C2×AGL(1,𝔽5)semidirect
444. #235C2×AGL(1,𝔽5)semidirect
459. C2×C4×D3C2×AGL(1,𝔽5)semidirect
699. #41D3×AGL(1,𝔽5)semidirect
751. C3×C5#3428semidirect
859. C5#85885semidirect
889. 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
#117569952
C3×#662662
AGL(1,𝔽5)×#2392
#117568472
#117568452
AGL(1,𝔽5)×#2372
#117568382
#117568362
D3×#41302
C2×#919072
#106194123
#858855