Finite Group Databasebeta

← D3×#41×AGL(1,𝔽5) #14478943

Subgroups — D3×#41×AGL(1,𝔽5) #14478943

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 892 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
4AGL(1,𝔽5)×#239C212yesmaximal, complemented
5D3×Q8×AGL(1,𝔽5)C212yesmaximal, complemented
6AGL(1,𝔽5)×#237C216yesmaximal, complemented
7D3×D4×AGL(1,𝔽5)C216yesmaximal, complemented
8#11756835C213yesmaximal, complemented
9D3×#4130C213yesmaximal, complemented
10AGL(1,𝔽5)×#235C213yesmaximal, complemented
11C2×C4×D3×AGL(1,𝔽5)C213yesmaximal, complemented
12C2×#41×AGL(1,𝔽5)—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2216yes—
14#41×D15C411yescharacteristic, complemented
15C5×D3×#41C411yescharacteristic, complemented
16C3×D5×#41C2211yescharacteristic
17#92034C411yescharacteristic, complemented
18D3×#713C411yescharacteristic, complemented
19D5×#239C2211yescharacteristic
20D3×Q8×D5C2211yescharacteristic
21#92024C413yescomplemented
22D3×#711C413yescomplemented
23D5×#237C2213yes—
24D3×D4×D5C2213yes—
25#92016C413yescomplemented
26D3×#709C413yescomplemented
27D5×#235C2213yes—
28C2×C4×D3×D5C2213yes—
29Q8×ΓL(1,𝔽16)C2212yescomplemented
30D4×ΓL(1,𝔽16)C2216yescomplemented
31#91989C2213yescomplemented
32C2×C4×ΓL(1,𝔽16)C2213yescomplemented
33C3×Q8×AGL(1,𝔽5)C2212yescomplemented
34C3×D4×AGL(1,𝔽5)C2216yescomplemented
35C3×#4130C2213yescomplemented
36C2×C3×C4×AGL(1,𝔽5)C2213yescomplemented
37#67⋊AGL(1,𝔽5)C22112yescomplemented
38D3×C22⋊AGL(1,𝔽5)C2216yes—
39AGL(1,𝔽5)×#67C22112yescomplemented
40#91923C2216yescomplemented
41C2×Dic3×AGL(1,𝔽5)C2216yescomplemented
42#91921C2216yescomplemented
43D3×C4⋊AGL(1,𝔽5)C2216yes—
44AGL(1,𝔽5)×D12C2216yescomplemented
45C4×D3×AGL(1,𝔽5)C2211yescharacteristic
46C4×D3×AGL(1,𝔽5)C2213yes—
47C4×D3×AGL(1,𝔽5)C2216yes—
48C4×D3×AGL(1,𝔽5)C2213yescomplemented
49C4×D3×AGL(1,𝔽5)C2213yescomplemented
50C4×D3×AGL(1,𝔽5)C2216yescomplemented
51#91909C2216yescomplemented
52ΓL(1,𝔽16)⋊Q8C2216yescomplemented
53#91907C2216yescomplemented
54AGL(1,𝔽5)×Dic6C2216yescomplemented
55C4×D3×#41—51nomaximal, Hall
56C2×D5×#41—31no—
57#41×AGL(1,𝔽5)—31no—
58#41×AGL(1,𝔽5)—32no—
59#41×AGL(1,𝔽5)—36no—
60#41×AGL(1,𝔽5)—33no—
61#41×AGL(1,𝔽5)—33no—
62#41×AGL(1,𝔽5)D311yescharacteristic, direct product factor
63C2×Q8×AGL(1,𝔽5)—32no—
64C2×D4×AGL(1,𝔽5)—36no—
65C2×#4130—33no—
66C22×C4×AGL(1,𝔽5)—33no—
67C22×D3×D5C2313yes—
68C22×ΓL(1,𝔽16)C2316yes—
69C22×C3×AGL(1,𝔽5)C2316yes—
70C2×D3×AGL(1,𝔽5)—224no—
71C2×D3×AGL(1,𝔽5)C2316yes—
72C2×D3×AGL(1,𝔽5)C2316yes—
73C2×D3×AGL(1,𝔽5)C2316yes—
74C2×D3×AGL(1,𝔽5)C2312yes—
75C3×C5×#41C2×C411yescharacteristic, complemented
76#6821C2×C411yescharacteristic, complemented
77Q8×D15C2×C411yescharacteristic, complemented
78#6819C2×C413yescomplemented
79D4×D15C2×C413yescomplemented
80#6817C2×C413yescomplemented
81C2×C4×D15C2×C413yescomplemented
82C5×#239C2×C411yescharacteristic, complemented
83C5×D3×Q8C2×C411yescharacteristic, complemented
84C5×#237C2×C413yescomplemented
85C5×D3×D4C2×C413yescomplemented
86C5×#235C2×C413yescomplemented
87C2×C4×C5×D3C2×C413yescomplemented
88C3×#713C2×C411yescharacteristic, complemented
89C3×Q8×D5C2311yescharacteristic
90C3×#711C2×C413yescomplemented
91C3×D4×D5C2313yes—
92C3×#709C2×C413yescomplemented
93C2×C3×C4×D5C2313yes—
94#6790C2×C416yescomplemented
95D3×C22⋊D5C2×C416yescomplemented
96D5×#67C2316yes—
97C2×#1200C2×C413yescomplemented
98#6782C2×C416yescomplemented
99C2×D3×Dic5C2×C413yescomplemented
100#6780C2×C416yescomplemented
101#6779C2×C416yescomplemented
102C2×D5×Dic3C2313yes—
103#6777C2×C413yescomplemented
104D3×D20C2×C413yescomplemented
105D5×D12C2313yes—
106C4×D3×D5C2×C413yescomplemented
107C4×D3×D5C2×C413yescomplemented
108C4×D3×D5C2×C413yescomplemented
109C4×D3×D5C2×C413yescomplemented
110C4×D3×D5C2311yescharacteristic
111C4×D3×D5C2313yes—
112C4×D3×D5C2313yes—
113C4×D3×D5C2313yes—
114#6773C2×C413yescomplemented
115#6772C2×C413yescomplemented
116#6771C2×C416yescomplemented
117D15⋊Q8C2×C413yescomplemented
118#6769C2×C413yescomplemented
119#6768C2×C413yescomplemented
120D3×Dic10C2×C413yescomplemented
121#6766C2×C413yescomplemented
122#6765C2×C413yescomplemented
123D5×Dic6C2313yes—
124#6763C2316yes—
125C4⋊ΓL(1,𝔽16)C2316yes—
126C4×ΓL(1,𝔽16)C2316yes—
127C4×ΓL(1,𝔽16)C2313yes—
128C4×ΓL(1,𝔽16)C2311yescharacteristic
129C3×C22⋊AGL(1,𝔽5)C2316yes—
130C3×C4⋊AGL(1,𝔽5)C2316yes—
131C3×C4×AGL(1,𝔽5)C2316yes—
132C3×C4×AGL(1,𝔽5)C2313yes—
133C3×C4×AGL(1,𝔽5)C2311yescharacteristic
134Dic3⋊AGL(1,𝔽5)C23112yes—
135(C2×D3)⋊AGL(1,𝔽5)C23112yes—
136Dic3×AGL(1,𝔽5)C2316yes—
137Dic3×AGL(1,𝔽5)C2316yes—
138Dic3×AGL(1,𝔽5)C2316yes—
139Dic3×AGL(1,𝔽5)C2312yes—
140C2×D3×#41—51no—
141C3×C4×#41—51no—
142Dic3×#41—51no—
143C4×#239—52no—
144C4×D3×Q8—52no—
145C4×D3×D4—56no—
146C4×#237—56no—
147#5522—53no—
148D3×#117—53no—
149C4×#235—53no—
150C2×C42×D3—53no—
151C23×AGL(1,𝔽5)—36no—
152C2×C5×#41—31no—
153D5×#41—31no—
154D5×#41—31no—
155D5×#41—31no—
156D5×#41—33no—
157D5×#41—33no—
158D5×#41—33no—
159D5×#41—33no—
160D5×#41C2×D311yescharacteristic
161C2×#713—31no—
162C2×Q8×D5—31no—
163C2×#711—33no—
164C2×D4×D5—33no—
165C2×#709—33no—
166C22×C4×D5—33no—
167C2×C22⋊AGL(1,𝔽5)—36no—
168Q8×AGL(1,𝔽5)—32no—
169Q8×AGL(1,𝔽5)—36no—
170Q8×AGL(1,𝔽5)—36no—
171Q8×AGL(1,𝔽5)C2×D312yescomplemented
172D4×AGL(1,𝔽5)—312no—
173D4×AGL(1,𝔽5)—36no—
174D4×AGL(1,𝔽5)—312no—
175D4×AGL(1,𝔽5)—36no—
176D4×AGL(1,𝔽5)—36no—
177D4×AGL(1,𝔽5)C2×D316yescomplemented
178#4130—33no—
179#4130—36no—
180#4130—36no—
181#4130—36no—
182#4130C2×D313yescomplemented
183C2×C4⋊AGL(1,𝔽5)—36no—
184C2×C4×AGL(1,𝔽5)—36no—
185C2×C4×AGL(1,𝔽5)—33no—
186C2×C4×AGL(1,𝔽5)—31no—
187C2×C4×AGL(1,𝔽5)—33no—
188C2×C4×AGL(1,𝔽5)—36no—
189C2×C4×AGL(1,𝔽5)—36no—
190C2×C4×AGL(1,𝔽5)—33no—
191C2×C4×AGL(1,𝔽5)—33no—
192C2×C4×AGL(1,𝔽5)C2×D313yescomplemented
193C2×C4×#41—151noSylow
194C22×D15C22×C413yes—
195C22×C5×D3C22×C413yes—
196C22×C3×D5C2413yes—
197C2×D3×D5—212no—
198C2×D3×D5C22×C413yes—
199C2×D3×D5C22×C413yes—
200C2×D3×D5C2413yes—
201C2×D3×D5C2411yescharacteristic
202C2×ΓL(1,𝔽16)—212no—
203C2×ΓL(1,𝔽16)C2416yes—
204C2×ΓL(1,𝔽16)C2412yes—
205C2×C3×AGL(1,𝔽5)—212no—
206C2×C3×AGL(1,𝔽5)C2416yes—
207C2×C3×AGL(1,𝔽5)C2412yes—
208D3×AGL(1,𝔽5)—212no—
209D3×AGL(1,𝔽5)—212no—
210D3×AGL(1,𝔽5)—212no—
211D3×AGL(1,𝔽5)#4118yesdirect product factor
212C3×C5×Q8C22×C411yescharacteristic, complemented
213C3×C5×D4C22×C413yescomplemented
214C2×C3×C4×C5C22×C413yescomplemented
215#1220C22×C416yescomplemented
216C2×Dic15C22×C413yescomplemented
217D60C22×C413yescomplemented
218C4×D15C22×C413yes—
219C4×D15C22×C411yescharacteristic
220C4×D15C22×C413yescomplemented
221C4×D15C22×C413yescomplemented
222Dic30C22×C413yescomplemented
223C5×#67C22×C416yescomplemented
224C2×C5×Dic3C22×C413yescomplemented
225C5×D12C22×C413yescomplemented
226C4×C5×D3C22×C413yes—
227C4×C5×D3C22×C411yescharacteristic
228C4×C5×D3C22×C413yescomplemented
229C4×C5×D3C22×C413yescomplemented
230C5×Dic6C22×C413yescomplemented
231C3×C22⋊D5C22×C416yescomplemented
232C2×C3×Dic5C22×C413yescomplemented
233C3×D20C22×C413yescomplemented
234C3×C4×D5C22×C413yescomplemented
235C3×C4×D5C22×C413yescomplemented
236C3×C4×D5C2411yescharacteristic
237C3×C4×D5C2413yes—
238C3×Dic10C22×C413yescomplemented
239#1204C22×C416yescomplemented
240#1203C22×C416yescomplemented
241#1202C22×C416yescomplemented
242#1201C22×C416yescomplemented
243#1200C22×C413yes—
244#1200C22×C411yescharacteristic
245#1200C22×C413yescomplemented
246#1200C22×C413yescomplemented
247D3×Dic5C22×C413yes—
248D3×Dic5C22×C411yescharacteristic
249D3×Dic5C22×C413yescomplemented
250D3×Dic5C22×C413yescomplemented
251D5×Dic3C22×C413yescomplemented
252D5×Dic3C22×C413yescomplemented
253D5×Dic3C2411yescharacteristic
254D5×Dic3C2413yes—
255C2×C3×#41—51no—
256D3×#41—51no—
257D3×#41—51no—
258D3×#41—51no—
259D3×#41—53no—
260D3×#41—53no—
261D3×#41—53no—
262D3×#41—53no—
263D3×#41AGL(1,𝔽5)11yescharacteristic, direct product factor
264C2×#239—51no—
265C2×D3×Q8—51no—
266C2×#237—53no—
267C2×D3×D4—53no—
268C2×#235—53no—
269C22×C4×D3—53no—
270C22×C4×D3—56no—
271C3×C4×Q8—52no—
272C3×C4×D4—56no—
273C3×#117—53no—
274C2×C3×C42—53no—
275Q8×Dic3—52no—
276D4×Dic3—56no—
277C4×#67—512no—
278#926—53no—
279C2×C4×Dic3—56no—
280C2×C4×Dic3—53no—
281#893—56no—
282#892—56no—
283D3×C4⋊C4—56no—
284#887—56no—
285#67⋊C4—512no—
286D3×C22⋊C4—56no—
287#877—56no—
288C4×D12—56no—
289#872—56no—
290C42×D3—51no—
291C42×D3—53no—
292C42×D3—56no—
293C42×D3—53no—
294C42×D3—53no—
295C42×D3—56no—
296C4×Dic6—56no—
297C23×D5—33no—
298C22×AGL(1,𝔽5)—32no—
299C22×AGL(1,𝔽5)—36no—
300C22×AGL(1,𝔽5)—36no—
301C22×AGL(1,𝔽5)—36no—
302C22×AGL(1,𝔽5)—36no—
303C22×AGL(1,𝔽5)—624no—
304C22×AGL(1,𝔽5)C22×D316yes—
305C5×#41—31no—
306C5×#41—33no—
307C5×#41—33no—
308C5×#41C4×D311yescharacteristic, complemented
309C2×C5×Q8—31no—
310C2×C5×D4—33no—
311C22×C4×C5—33no—
312C2×C22⋊D5—36no—
313C22×Dic5—33no—
314#713—31no—
315#713—33no—
316#713—33no—
317#713C4×D311yescharacteristic, complemented
318Q8×D5—31no—
319Q8×D5—33no—
320Q8×D5—33no—
321Q8×D5C22×D311yescharacteristic
322#711—33no—
323#711—36no—
324#711—36no—
325#711—33no—
326#711—33no—
327#711C4×D313yescomplemented
328D4×D5—36no—
329D4×D5—33no—
330D4×D5—36no—
331D4×D5—33no—
332D4×D5—33no—
333D4×D5C22×D313yes—
334#709—33no—
335#709—36no—
336#709—33no—
337#709—36no—
338#709—33no—
339#709C4×D313yescomplemented
340C2×D20—33no—
341C2×C4×D5—33no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—33no—
348C2×C4×D5—31no—
349C2×C4×D5—33no—
350C2×C4×D5—33no—
351C2×C4×D5—33no—
352C2×C4×D5C22×D313yes—
353C2×Dic10—33no—
354C22⋊AGL(1,𝔽5)—36no—
355C22⋊AGL(1,𝔽5)—312no—
356C22⋊AGL(1,𝔽5)C22×D316yes—
357C4⋊AGL(1,𝔽5)—312no—
358C4⋊AGL(1,𝔽5)—36no—
359C4⋊AGL(1,𝔽5)C22×D316yes—
360C4×AGL(1,𝔽5)—32no—
361C4×AGL(1,𝔽5)—36no—
362C4×AGL(1,𝔽5)—36no—
363C4×AGL(1,𝔽5)—36no—
364C4×AGL(1,𝔽5)—31no—
365C4×AGL(1,𝔽5)—33no—
366C4×AGL(1,𝔽5)—36no—
367C4×AGL(1,𝔽5)C22×D311yescharacteristic
368C4×AGL(1,𝔽5)C22×D313yes—
369C4×AGL(1,𝔽5)C22×D316yes—
370C22×#41—151no—
371C4×#41—51no—
372C4×#41—153no—
373C4×#41—153no—
374C4×#41—156no—
375C4×#41—152no—
376C4×#41—151no—
377C2×C4×Q8—152no—
378C2×C4×D4—156no—
379C2×#117—153no—
380C22×C42—153no—
381C22×C3×C5C23×C413yes—
382C2×D15—26no—
383C2×D15C23×C413yes—
384C2×D15C23×C411yescharacteristic
385C2×C5×D3—26no—
386C2×C5×D3C23×C413yes—
387C2×C5×D3C23×C411yescharacteristic
388C2×C3×D5—26no—
389C2×C3×D5C23×C413yes—
390C2×C3×D5C2511yescharacteristic
391D3×D5—26no—
392D3×D5—26no—
393D3×D5—26no—
394D3×D5C2×#4114yes—
395ΓL(1,𝔽16)—26no—
396ΓL(1,𝔽16)C2×#4114yescomplemented
397C3×AGL(1,𝔽5)—26no—
398C3×AGL(1,𝔽5)C2×#4114yescomplemented
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—52no—
447C2×C4×D3—53no—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—51no—
451C2×C4×D3—53no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—56no—
459C2×C4×D3—56no—
460C2×C4×D3—56no—
461C2×C4×D3—1024no—
462C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
463C2×Dic6—53no—
464C3×C4⋊C4—56no—
465C3×C22⋊C4—56no—
466C3×C42—56no—
467C3×C42—51no—
468C3×C42—53no—
469#217—56no—
470(C2×D3)⋊C4—512no—
471C4⋊Dic3—56no—
472Dic3⋊C4—512no—
473C4×Dic3—56no—
474C4×Dic3—52no—
475C4×Dic3—56no—
476C4×Dic3—56no—
477C4×Dic3—51no—
478C4×Dic3—53no—
479C4×Dic3—56no—
480C23×C5—33no—
481C22×D5—31no—
482C22×D5—33no—
483C22×D5—33no—
484C22×D5—33no—
485C22×D5—33no—
486C22×D5—612no—
487C22×D5C23×D313yes—
488C2×AGL(1,𝔽5)—212no—
489C2×AGL(1,𝔽5)—32no—
490C2×AGL(1,𝔽5)—38no—
491C2×AGL(1,𝔽5)—36no—
492C2×AGL(1,𝔽5)—612no—
493C2×AGL(1,𝔽5)—612no—
494C2×AGL(1,𝔽5)—612no—
495C2×AGL(1,𝔽5)—612no—
496C2×AGL(1,𝔽5)C23×D316yes—
497C2×AGL(1,𝔽5)C23×D312yes—
498C5×Q8—33no—
499C5×Q8C2×C4×D311yescharacteristic, complemented
500C5×D4—36no—
501C5×D4—33no—
502C5×D4C2×C4×D313yescomplemented
503C2×C4×C5—33no—
504C2×C4×C5—33no—
505C2×C4×C5—31no—
506C2×C4×C5—33no—
507C2×C4×C5—33no—
508C2×C4×C5C2×C4×D313yescomplemented
509C22⋊D5—36no—
510C22⋊D5—36no—
511C22⋊D5—36no—
512C22⋊D5C2×C4×D316yescomplemented
513C2×Dic5—33no—
514C2×Dic5—33no—
515C2×Dic5—31no—
516C2×Dic5—33no—
517C2×Dic5—33no—
518C2×Dic5C2×C4×D313yescomplemented
519D20—36no—
520D20—33no—
521D20C2×C4×D313yescomplemented
522C4×D5—33no—
523C4×D5—33no—
524C4×D5—31no—
525C4×D5—33no—
526C4×D5—31no—
527C4×D5—33no—
528C4×D5—33no—
529C4×D5—33no—
530C4×D5—31no—
531C4×D5—33no—
532C4×D5—33no—
533C4×D5—33no—
534C4×D5C2×C4×D313yescomplemented
535C4×D5C2×C4×D313yescomplemented
536C4×D5C23×D311yescharacteristic
537C4×D5C23×D313yes—
538Dic10—33no—
539Dic10—36no—
540Dic10C2×C4×D313yescomplemented
541C2×#41—31no—
542C2×#41—51no—
543C2×#41—153no—
544C2×#41—153no—
545C2×#41—153no—
546C2×#41—153no—
547C2×#41—151no—
548C2×#41—151no—
549C2×#41—151no—
550C2×#41—153no—
551C2×#41—153no—
552C2×#41—151no—
553C22×Q8—151no—
554C22×D4—153no—
555C23×C4—153no—
556C23×C4—156no—
557C4×Q8—52no—
558C4×Q8—156no—
559C4×Q8—156no—
560C4×Q8—152no—
561C4×D4—56no—
562C4×D4—156no—
563C4×D4—1512no—
564C4×D4—156no—
565C4×D4—1512no—
566C4×D4—156no—
567#117—53no—
568#117—156no—
569#117—156no—
570#117—156no—
571#117—153no—
572C2×C4⋊C4—156no—
573C2×C22⋊C4—156no—
574C2×C42—53no—
575C2×C42—153no—
576C2×C42—156no—
577C2×C42—153no—
578C2×C42—153no—
579C2×C42—156no—
580C2×C42—151no—
581C2×C42—153no—
582C2×C42—156no—
583C2×C3×C5—23no—
584C2×C3×C5C24×C411yescharacteristic
585D15—23no—
586D15C4×#4112yescomplemented
587C3×D5—23no—
588C3×D5C22×#4112yes—
589C5×D3—23no—
590C5×D3C4×#4112yescomplemented
591C23×C3—53no—
592C22×D3—51no—
593C22×D3—53no—
594C22×D3—53no—
595C22×D3—53no—
596C22×D3—53no—
597C22×D3—1012no—
598C22×D3C22×AGL(1,𝔽5)13yes—
599C3×Q8—53no—
600C3×Q8C22×AGL(1,𝔽5)11yescharacteristic, complemented
601C3×D4—56no—
602C3×D4—53no—
603C3×D4C22×AGL(1,𝔽5)13yescomplemented
604C2×C3×C4—52no—
605C2×C3×C4—53no—
606C2×C3×C4—53no—
607C2×C3×C4—53no—
608C2×C3×C4—51no—
609C2×C3×C4—53no—
610C2×C3×C4—56no—
611C2×C3×C4—1012no—
612C2×C3×C4C22×AGL(1,𝔽5)13yescomplemented
613#67—56no—
614#67—56no—
615#67—56no—
616#67C22×AGL(1,𝔽5)16yescomplemented
617C2×Dic3—52no—
618C2×Dic3—53no—
619C2×Dic3—53no—
620C2×Dic3—53no—
621C2×Dic3—51no—
622C2×Dic3—53no—
623C2×Dic3—56no—
624C2×Dic3—1012no—
625C2×Dic3C22×AGL(1,𝔽5)13yescomplemented
626D12—56no—
627D12—53no—
628D12C22×AGL(1,𝔽5)13yescomplemented
629C4×D3—58no—
630C4×D3—51no—
631C4×D3—53no—
632C4×D3—53no—
633C4×D3—53no—
634C4×D3—51no—
635C4×D3—53no—
636C4×D3—53no—
637C4×D3—53no—
638C4×D3—51no—
639C4×D3—53no—
640C4×D3—53no—
641C4×D3—53no—
642C4×D3—1012no—
643C4×D3—1012no—
644C4×D3—1012no—
645C4×D3C22×AGL(1,𝔽5)11yescharacteristic
646C4×D3C22×AGL(1,𝔽5)13yes—
647C4×D3C22×AGL(1,𝔽5)13yescomplemented
648C4×D3C22×AGL(1,𝔽5)13yescomplemented
649Dic6—53no—
650Dic6—56no—
651Dic6C22×AGL(1,𝔽5)13yescomplemented
652C22×C5—31no—
653C22×C5—33no—
654C22×C5—66no—
655C22×C5C22×C4×D313yes—
656C2×D5—26no—
657C2×D5—31no—
658C2×D5—34no—
659C2×D5—33no—
660C2×D5—66no—
661C2×D5—66no—
662C2×D5—66no—
663C2×D5—66no—
664C2×D5C22×C4×D313yes—
665C2×D5C24×D311yescharacteristic
666AGL(1,𝔽5)—26no—
667AGL(1,𝔽5)—34no—
668AGL(1,𝔽5)—66no—
669AGL(1,𝔽5)D3×#4114yesdirect product factor
670C4×C5—33no—
671C4×C5—31no—
672C4×C5C22×C4×D313yes—
673C4×C5C22×C4×D311yescharacteristic
674Dic5—33no—
675Dic5—31no—
676Dic5C22×C4×D313yes—
677Dic5C22×C4×D311yescharacteristic
678C24—153no—
679#41—31no—
680#41—33no—
681#41—33no—
682#41—51no—
683#41—53no—
684#41—53no—
685#41—156no—
686#41—156no—
687#41—153no—
688#41—153no—
689#41—156no—
690#41—153no—
691#41—153no—
692#41—156no—
693#41—153no—
694#41—153no—
695#41—151no—
696#41—153no—
697#41—153no—
698#41D3×AGL(1,𝔽5)11yescharacteristic, direct product factor
699C2×Q8—31no—
700C2×Q8—51no—
701C2×Q8—153no—
702C2×Q8—153no—
703C2×Q8—153no—
704C2×Q8—151no—
705C2×D4—33no—
706C2×D4—53no—
707C2×D4—153no—
708C2×D4—153no—
709C2×D4—156no—
710C2×D4—153no—
711C2×D4—156no—
712C2×D4—156no—
713C2×D4—153no—
714C22×C4—33no—
715C22×C4—53no—
716C22×C4—56no—
717C22×C4—151no—
718C22×C4—153no—
719C22×C4—153no—
720C22×C4—153no—
721C22×C4—153no—
722C22×C4—153no—
723C22×C4—153no—
724C22×C4—153no—
725C22×C4—153no—
726C22×C4—153no—
727C22×C4—153no—
728C22×C4—152no—
729C22×C4—156no—
730C22×C4—156no—
731C22×C4—156no—
732C22×C4—153no—
733C22×C4—156no—
734C22×C4—3024no—
735C4⋊C4—56no—
736C4⋊C4—1512no—
737C4⋊C4—156no—
738C22⋊C4—56no—
739C22⋊C4—1512no—
740C22⋊C4—156no—
741C42—51no—
742C42—53no—
743C42—56no—
744C42—152no—
745C42—151no—
746C42—153no—
747C42—156no—
748C42—156no—
749C42—156no—
750C42—156no—
751C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
752C22×C3—51no—
753C22×C3—53no—
754C22×C3—106no—
755C22×C3C23×AGL(1,𝔽5)13yes—
756C2×D3—26no—
757C2×D3—51no—
758C2×D3—54no—
759C2×D3—53no—
760C2×D3—106no—
761C2×D3—106no—
762C2×D3—106no—
763C2×D3—106no—
764C2×D3C23×AGL(1,𝔽5)13yes—
765C2×D3C23×AGL(1,𝔽5)11yescharacteristic
766C3×C4—54no—
767C3×C4—53no—
768C3×C4—51no—
769C3×C4—106no—
770C3×C4C23×AGL(1,𝔽5)13yes—
771C3×C4C23×AGL(1,𝔽5)11yescharacteristic
772Dic3—54no—
773Dic3—53no—
774Dic3—51no—
775Dic3—106no—
776Dic3C23×AGL(1,𝔽5)13yes—
777Dic3C23×AGL(1,𝔽5)11yescharacteristic
778C2×C5—23no—
779C2×C5—32no—
780C2×C5—63no—
781C2×C5C23×C4×D311yescharacteristic
782D5—23no—
783D5—32no—
784D5—63no—
785D5C2×D3×#4112yes—
786C23—33no—
787C23—53no—
788C23—151no—
789C23—153no—
790C23—153no—
791C23—153no—
792C23—153no—
793C23—3012no—
794Q8—33no—
795Q8—53no—
796Q8—156no—
797Q8—153no—
798Q8C2×D3×AGL(1,𝔽5)11yescharacteristic, complemented
799D4—36no—
800D4—33no—
801D4—56no—
802D4—53no—
803D4—156no—
804D4—156no—
805D4—156no—
806D4—156no—
807D4—153no—
808D4C2×D3×AGL(1,𝔽5)13yescomplemented
809C2×C4—33no—
810C2×C4—33no—
811C2×C4—33no—
812C2×C4—31no—
813C2×C4—33no—
814C2×C4—52no—
815C2×C4—53no—
816C2×C4—53no—
817C2×C4—53no—
818C2×C4—51no—
819C2×C4—53no—
820C2×C4—56no—
821C2×C4—1012no—
822C2×C4—151no—
823C2×C4—153no—
824C2×C4—153no—
825C2×C4—153no—
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—158no—
835C2×C4—152no—
836C2×C4—153no—
837C2×C4—153no—
838C2×C4—153no—
839C2×C4—151no—
840C2×C4—153no—
841C2×C4—156no—
842C2×C4—3012no—
843C2×C4—3012no—
844C2×C4—3012no—
845C2×C4—3012no—
846C2×C4C2×D3×AGL(1,𝔽5)13yescomplemented
847C2×C3—23no—
848C2×C3—52no—
849C2×C3—103no—
850C2×C3C24×AGL(1,𝔽5)11yescharacteristic
851D3—23no—
852D3—52no—
853D3—103no—
854D3#41×AGL(1,𝔽5)12yesdirect product factor
855C5C4×D3×#4111yescharacteristic, complemented, Sylow
856C22—31no—
857C22—33no—
858C22—51no—
859C22—53no—
860C22—66no—
861C22—106no—
862C22—154no—
863C22—151no—
864C22—153no—
865C22—306no—
866C22—306no—
867C22—306no—
868C22—306no—
869C22C22×D3×AGL(1,𝔽5)13yes—
870C4—31no—
871C4—33no—
872C4—54no—
873C4—51no—
874C4—53no—
875C4—106no—
876C4—154no—
877C4—151no—
878C4—153no—
879C4—306no—
880C4C22×D3×AGL(1,𝔽5)13yes—
881C4C22×D3×AGL(1,𝔽5)11yescharacteristic
882C3C2×#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
883C2—23no—
884C2—32no—
885C2—52no—
886C2—63no—
887C2—103no—
888C2—152no—
889C2—303no—
890C2C23×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×C5C2×C4×#41
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. AGL(1,𝔽5)×#239C2semidirect
5. D3×Q8×AGL(1,𝔽5)C2semidirect
6. AGL(1,𝔽5)×#237C2semidirect
7. D3×D4×AGL(1,𝔽5)C2semidirect
8. #11756835C2semidirect
9. D3×#4130C2semidirect
10. AGL(1,𝔽5)×#235C2semidirect
11. C2×C4×D3×AGL(1,𝔽5)C2semidirect
14. #41×D15C4semidirect
15. C5×D3×#41C4semidirect
17. #92034C4semidirect
18. D3×#713C4semidirect
21. #92024C4semidirect
22. D3×#711C4semidirect
25. #92016C4semidirect
26. D3×#709C4semidirect
29. Q8×ΓL(1,𝔽16)C22semidirect
30. D4×ΓL(1,𝔽16)C22semidirect
31. #91989C22semidirect
32. C2×C4×ΓL(1,𝔽16)C22semidirect
33. C3×Q8×AGL(1,𝔽5)C22semidirect
34. C3×D4×AGL(1,𝔽5)C22semidirect
35. C3×#4130C22semidirect
36. C2×C3×C4×AGL(1,𝔽5)C22semidirect
37. #67⋊AGL(1,𝔽5)C22semidirect
39. AGL(1,𝔽5)×#67C22semidirect
40. #91923C22semidirect
41. C2×Dic3×AGL(1,𝔽5)C22semidirect
42. #91921C22semidirect
44. AGL(1,𝔽5)×D12C22semidirect
48. C4×D3×AGL(1,𝔽5)C22semidirect
49. C4×D3×AGL(1,𝔽5)C22semidirect
50. C4×D3×AGL(1,𝔽5)C22semidirect
51. #91909C22semidirect
52. ΓL(1,𝔽16)⋊Q8C22semidirect
53. #91907C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
62. #41×AGL(1,𝔽5)D3direct (N × H)
75. C3×C5×#41C2×C4semidirect
76. #6821C2×C4semidirect
77. Q8×D15C2×C4semidirect
78. #6819C2×C4semidirect
79. D4×D15C2×C4semidirect
80. #6817C2×C4semidirect
81. C2×C4×D15C2×C4semidirect
82. C5×#239C2×C4semidirect
83. C5×D3×Q8C2×C4semidirect
84. C5×#237C2×C4semidirect
85. C5×D3×D4C2×C4semidirect
86. C5×#235C2×C4semidirect
87. C2×C4×C5×D3C2×C4semidirect
88. C3×#713C2×C4semidirect
90. C3×#711C2×C4semidirect
92. C3×#709C2×C4semidirect
94. #6790C2×C4semidirect
95. D3×C22⋊D5C2×C4semidirect
97. C2×#1200C2×C4semidirect
98. #6782C2×C4semidirect
99. C2×D3×Dic5C2×C4semidirect
100. #6780C2×C4semidirect
101. #6779C2×C4semidirect
103. #6777C2×C4semidirect
104. D3×D20C2×C4semidirect
106. C4×D3×D5C2×C4semidirect
107. C4×D3×D5C2×C4semidirect
108. C4×D3×D5C2×C4semidirect
109. C4×D3×D5C2×C4semidirect
114. #6773C2×C4semidirect
115. #6772C2×C4semidirect
116. #6771C2×C4semidirect
117. D15⋊Q8C2×C4semidirect
118. #6769C2×C4semidirect
119. #6768C2×C4semidirect
120. D3×Dic10C2×C4semidirect
121. #6766C2×C4semidirect
122. #6765C2×C4semidirect
171. Q8×AGL(1,𝔽5)C2×D3semidirect
177. D4×AGL(1,𝔽5)C2×D3semidirect
182. #4130C2×D3semidirect
192. C2×C4×AGL(1,𝔽5)C2×D3semidirect
211. D3×AGL(1,𝔽5)#41direct (N × H)
212. C3×C5×Q8C22×C4semidirect
213. C3×C5×D4C22×C4semidirect
214. C2×C3×C4×C5C22×C4semidirect
215. #1220C22×C4semidirect
216. C2×Dic15C22×C4semidirect
217. D60C22×C4semidirect
220. C4×D15C22×C4semidirect
221. C4×D15C22×C4semidirect
222. Dic30C22×C4semidirect
223. C5×#67C22×C4semidirect
224. C2×C5×Dic3C22×C4semidirect
225. C5×D12C22×C4semidirect
228. C4×C5×D3C22×C4semidirect
229. C4×C5×D3C22×C4semidirect
230. C5×Dic6C22×C4semidirect
231. C3×C22⋊D5C22×C4semidirect
232. C2×C3×Dic5C22×C4semidirect
233. C3×D20C22×C4semidirect
234. C3×C4×D5C22×C4semidirect
235. C3×C4×D5C22×C4semidirect
238. C3×Dic10C22×C4semidirect
239. #1204C22×C4semidirect
240. #1203C22×C4semidirect
241. #1202C22×C4semidirect
242. #1201C22×C4semidirect
245. #1200C22×C4semidirect
246. #1200C22×C4semidirect
249. D3×Dic5C22×C4semidirect
250. D3×Dic5C22×C4semidirect
251. D5×Dic3C22×C4semidirect
252. D5×Dic3C22×C4semidirect
263. D3×#41AGL(1,𝔽5)direct (N × H)
308. C5×#41C4×D3semidirect
317. #713C4×D3semidirect
327. #711C4×D3semidirect
339. #709C4×D3semidirect
396. ΓL(1,𝔽16)C2×#41semidirect
398. C3×AGL(1,𝔽5)C2×#41semidirect
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
462. C2×C4×D3C2×AGL(1,𝔽5)semidirect
499. C5×Q8C2×C4×D3semidirect
502. C5×D4C2×C4×D3semidirect
508. C2×C4×C5C2×C4×D3semidirect
512. C22⋊D5C2×C4×D3semidirect
518. C2×Dic5C2×C4×D3semidirect
521. D20C2×C4×D3semidirect
534. C4×D5C2×C4×D3semidirect
535. C4×D5C2×C4×D3semidirect
540. Dic10C2×C4×D3semidirect
586. D15C4×#41semidirect
590. C5×D3C4×#41semidirect
600. C3×Q8C22×AGL(1,𝔽5)semidirect
603. C3×D4C22×AGL(1,𝔽5)semidirect
612. C2×C3×C4C22×AGL(1,𝔽5)semidirect
616. #67C22×AGL(1,𝔽5)semidirect
625. C2×Dic3C22×AGL(1,𝔽5)semidirect
628. D12C22×AGL(1,𝔽5)semidirect
647. C4×D3C22×AGL(1,𝔽5)semidirect
648. C4×D3C22×AGL(1,𝔽5)semidirect
651. Dic6C22×AGL(1,𝔽5)semidirect
669. AGL(1,𝔽5)D3×#41direct (N × H)
698. #41D3×AGL(1,𝔽5)direct (N × H)
751. C3×C5C2×C4×#41semidirect
798. Q8C2×D3×AGL(1,𝔽5)semidirect
808. D4C2×D3×AGL(1,𝔽5)semidirect
846. C2×C4C2×D3×AGL(1,𝔽5)semidirect
854. D3#41×AGL(1,𝔽5)direct (N × H)
855. C5C4×D3×#41semidirect
882. C3C2×#41×AGL(1,𝔽5)semidirect

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
AGL(1,𝔽5)×#2392
D3×Q8×AGL(1,𝔽5)2
AGL(1,𝔽5)×#2372
D3×D4×AGL(1,𝔽5)2
#117568352
D3×#41302
AGL(1,𝔽5)×#2352
C2×C4×D3×AGL(1,𝔽5)2
C2×#41×AGL(1,𝔽5)3
C4×D3×#415