Finite Group Databasebeta

← D3×#66266 #14479113

Subgroups — D3×#66266 #14479113

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 908 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
4#11756854C212yesmaximal, complemented
5D3×Q8×AGL(1,𝔽5)C212yesmaximal, complemented
6#11756846C216yesmaximal, complemented
7D3×D4×AGL(1,𝔽5)C216yesmaximal, complemented
8#11756838C213yesmaximal, complemented
9#11756836C213yesmaximal, complemented
10D3×#4130C213yesmaximal, complemented
11C2×D3×C4⋊AGL(1,𝔽5)C213yesmaximal, complemented
12C2×#66266—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
40C2×Dic3⋊AGL(1,𝔽5)C2216yescomplemented
41#91923C2216yescomplemented
42#91921C2216yescomplemented
43D3×C4⋊AGL(1,𝔽5)C2213yes—
44D3×C4⋊AGL(1,𝔽5)C2216yes—
45D3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
46D3×C4⋊AGL(1,𝔽5)C2216yescomplemented
47D3×C4⋊AGL(1,𝔽5)C2216yescomplemented
48AGL(1,𝔽5)×D12C2216yescomplemented
49C4×D3×AGL(1,𝔽5)C2216yes—
50#91909C2216yescomplemented
51ΓL(1,𝔽16)⋊Q8C2216yescomplemented
52#91907C2213yescomplemented
53#91907C2213yescomplemented
54AGL(1,𝔽5)×Dic6C2216yescomplemented
55D3×#520—51nomaximal, Hall
56C2×D5×#41—31no—
57#66266—31no—
58#66266—32no—
59#66266—36no—
60#66266—33no—
61#66266—33no—
62#66266D311yescharacteristic, 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)—412no—
71C2×D3×AGL(1,𝔽5)C2312yes—
72C2×D3×AGL(1,𝔽5)C2316yes—
73C2×D3×AGL(1,𝔽5)C23112yes—
74C3×C5×#41C2×C411yescharacteristic, complemented
75#6821C2×C411yescharacteristic, complemented
76Q8×D15C2×C411yescharacteristic, complemented
77#6819C2×C413yescomplemented
78D4×D15C2×C413yescomplemented
79#6817C2×C413yescomplemented
80C2×C4×D15C2×C413yescomplemented
81C5×#239C2×C411yescharacteristic, complemented
82C5×D3×Q8C2×C411yescharacteristic, complemented
83C5×#237C2×C413yescomplemented
84C5×D3×D4C2×C413yescomplemented
85C5×#235C2×C413yescomplemented
86C2×C4×C5×D3C2×C413yescomplemented
87C3×#713C2×C411yescharacteristic, complemented
88C3×Q8×D5C2311yescharacteristic
89C3×#711C2×C413yescomplemented
90C3×D4×D5C2313yes—
91C3×#709C2×C413yescomplemented
92C2×C3×C4×D5C2313yes—
93#6790C2×C416yescomplemented
94D3×C22⋊D5C2×C416yescomplemented
95D5×#67C2316yes—
96C2×#1200C2×C413yescomplemented
97#6782C2×C416yescomplemented
98C2×D3×Dic5C2×C413yescomplemented
99#6780C2×C416yescomplemented
100#6779C2×C416yescomplemented
101C2×D5×Dic3C2313yes—
102#6777C2×C413yescomplemented
103D3×D20C2×C413yescomplemented
104D5×D12C2313yes—
105C4×D3×D5C2×C413yescomplemented
106C4×D3×D5C2×C413yescomplemented
107C4×D3×D5C2×C413yescomplemented
108C4×D3×D5C2×C413yescomplemented
109C4×D3×D5C2313yes—
110C4×D3×D5C2311yescharacteristic
111C4×D3×D5C2313yes—
112C4×D3×D5C2313yes—
113#6773C2×C413yescomplemented
114#6772C2×C413yescomplemented
115#6771C2×C416yescomplemented
116D15⋊Q8C2×C413yescomplemented
117#6769C2×C413yescomplemented
118#6768C2×C413yescomplemented
119D3×Dic10C2×C413yescomplemented
120#6766C2×C413yescomplemented
121#6765C2×C413yescomplemented
122D5×Dic6C2313yes—
123#6763C2316yes—
124C4⋊ΓL(1,𝔽16)C2316yes—
125C4⋊ΓL(1,𝔽16)C2311yescharacteristic
126C4⋊ΓL(1,𝔽16)C2313yes—
127C4×ΓL(1,𝔽16)C2316yes—
128C3×C22⋊AGL(1,𝔽5)C2316yes—
129C3×C4⋊AGL(1,𝔽5)C2311yescharacteristic
130C3×C4⋊AGL(1,𝔽5)C2313yes—
131C3×C4⋊AGL(1,𝔽5)C2316yes—
132C3×C4×AGL(1,𝔽5)C2316yes—
133Dic3⋊AGL(1,𝔽5)C23112yes—
134Dic3⋊AGL(1,𝔽5)C2312yes—
135Dic3⋊AGL(1,𝔽5)C2316yes—
136(C2×D3)⋊AGL(1,𝔽5)C2316yes—
137(C2×D3)⋊AGL(1,𝔽5)C2316yes—
138Dic3×AGL(1,𝔽5)C2316yes—
139Dic3×AGL(1,𝔽5)C2316yes—
140C2×D3×#41—51no—
141C3×#520—51no—
142#5827—51no—
143#5574—52no—
144C4×D3×Q8—52no—
145#5546—56no—
146C4×D3×D4—56no—
147#5523—53no—
148D3×#117—53no—
149#5504—53no—
150C2×D3×C4⋊C4—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—33no—
181#4130—33no—
182#4130—36no—
183#4130C2×D313yescomplemented
184C2×C4⋊AGL(1,𝔽5)—36no—
185C2×C4⋊AGL(1,𝔽5)—33no—
186C2×C4⋊AGL(1,𝔽5)—33no—
187C2×C4⋊AGL(1,𝔽5)—36no—
188C2×C4⋊AGL(1,𝔽5)—31no—
189C2×C4⋊AGL(1,𝔽5)—36no—
190C2×C4⋊AGL(1,𝔽5)—36no—
191C2×C4⋊AGL(1,𝔽5)C2×D313yescomplemented
192C2×C4×AGL(1,𝔽5)—36no—
193C2×#520—151noSylow
194C22×D15C22×C413yes—
195C22×C5×D3C22×C413yes—
196C22×C3×D5C2413yes—
197C2×D3×D5—26no—
198C2×D3×D5—26no—
199C2×D3×D5C22×C413yes—
200C2×D3×D5C22×C413yes—
201C2×D3×D5C2413yes—
202C2×D3×D5C2411yescharacteristic
203C2×ΓL(1,𝔽16)—46no—
204C2×ΓL(1,𝔽16)C2412yes—
205C2×ΓL(1,𝔽16)C2416yes—
206C2×C3×AGL(1,𝔽5)—46no—
207C2×C3×AGL(1,𝔽5)C2412yes—
208C2×C3×AGL(1,𝔽5)C2416yes—
209D3×AGL(1,𝔽5)—212no—
210D3×AGL(1,𝔽5)—24no—
211D3×AGL(1,𝔽5)—412no—
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×D5C2413yes—
237C3×C4×D5C2411yescharacteristic
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×Dic3C2413yes—
254D5×Dic3C2411yescharacteristic
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, complemented
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×C4⋊C4—53no—
275Q8×Dic3—52no—
276D4×Dic3—56no—
277C4×#67—512no—
278#926—53no—
279C2×C4⋊Dic3—53no—
280C2×Dic3⋊C4—56no—
281#893—56no—
282#892—53no—
283#892—53no—
284D3×C4⋊C4—53no—
285D3×C4⋊C4—56no—
286D3×C4⋊C4—51no—
287D3×C4⋊C4—56no—
288D3×C4⋊C4—56no—
289#887—56no—
290#67⋊C4—512no—
291D3×C22⋊C4—56no—
292#877—56no—
293C4×D12—56no—
294#872—56no—
295C42×D3—56no—
296C4×Dic6—56no—
297C23×D5—33no—
298C22×AGL(1,𝔽5)—36no—
299C22×AGL(1,𝔽5)—32no—
300C22×AGL(1,𝔽5)—36no—
301C22×AGL(1,𝔽5)—312no—
302C22×AGL(1,𝔽5)—1212no—
303C22×AGL(1,𝔽5)C22×D316yes—
304C5×#41—31no—
305C5×#41—33no—
306C5×#41—33no—
307C5×#41C4×D311yescharacteristic, complemented
308C2×C5×Q8—31no—
309C2×C5×D4—33no—
310C22×C4×C5—33no—
311C2×C22⋊D5—36no—
312C22×Dic5—33no—
313#713—31no—
314#713—33no—
315#713—33no—
316#713C4×D311yescharacteristic, complemented
317Q8×D5—31no—
318Q8×D5—33no—
319Q8×D5—33no—
320Q8×D5C22×D311yescharacteristic
321#711—33no—
322#711—36no—
323#711—36no—
324#711—33no—
325#711—33no—
326#711C4×D313yescomplemented
327D4×D5—36no—
328D4×D5—33no—
329D4×D5—36no—
330D4×D5—33no—
331D4×D5—33no—
332D4×D5C22×D313yes—
333#709—33no—
334#709—36no—
335#709—33no—
336#709—36no—
337#709—33no—
338#709C4×D313yescomplemented
339C2×D20—33no—
340C2×C4×D5—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×D5C22×D313yes—
352C2×Dic10—33no—
353C22⋊AGL(1,𝔽5)—36no—
354C22⋊AGL(1,𝔽5)—36no—
355C22⋊AGL(1,𝔽5)—36no—
356C22⋊AGL(1,𝔽5)C22×D316yes—
357C4⋊AGL(1,𝔽5)—36no—
358C4⋊AGL(1,𝔽5)—312no—
359C4⋊AGL(1,𝔽5)—32no—
360C4⋊AGL(1,𝔽5)—33no—
361C4⋊AGL(1,𝔽5)—36no—
362C4⋊AGL(1,𝔽5)—31no—
363C4⋊AGL(1,𝔽5)C22×D313yes—
364C4⋊AGL(1,𝔽5)C22×D316yes—
365C4⋊AGL(1,𝔽5)C22×D311yescharacteristic
366C4×AGL(1,𝔽5)—36no—
367C4×AGL(1,𝔽5)—36no—
368C4×AGL(1,𝔽5)—36no—
369C4×AGL(1,𝔽5)C22×D316yes—
370C22×#41—151no—
371#520—51no—
372#520—153no—
373#520—153no—
374#520—156no—
375#520—152no—
376#520—151no—
377C2×C4×Q8—152no—
378C2×C4×D4—156no—
379C2×#117—153no—
380C22×C4⋊C4—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—23no—
389C2×C3×D5—23no—
390C2×C3×D5C23×C413yes—
391C2×C3×D5C2511yescharacteristic
392D3×D5—26no—
393D3×D5—23no—
394D3×D5—23no—
395D3×D5—26no—
396D3×D5H(5,𝔽2)12yes—
397D3×D52−1+412yes—
398ΓL(1,𝔽16)—26no—
399ΓL(1,𝔽16)—22no—
400C3×AGL(1,𝔽5)—26no—
401C3×AGL(1,𝔽5)—22no—
402C3×C4×C5C23×C413yes—
403C3×C4×C5C23×C411yescharacteristic
404Dic15C23×C411yescharacteristic
405Dic15C23×C413yes—
406C3×Dic5C23×C411yescharacteristic
407C3×Dic5C23×C413yes—
408C5×Dic3C23×C411yescharacteristic
409C5×Dic3C23×C413yes—
410C23×D3—53no—
411C3×#41—51no—
412C3×#41—53no—
413C3×#41—53no—
414C3×#41C2×AGL(1,𝔽5)11yescharacteristic, complemented
415C2×C3×Q8—51no—
416C2×C3×D4—53no—
417C22×C3×C4—53no—
418C22×C3×C4—56no—
419C2×#67—56no—
420C22×Dic3—53no—
421C22×Dic3—56no—
422#239—51no—
423#239—53no—
424#239—53no—
425#239C2×AGL(1,𝔽5)11yescharacteristic, complemented
426D3×Q8—51no—
427D3×Q8—53no—
428D3×Q8—53no—
429D3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
430#237—53no—
431#237—56no—
432#237—56no—
433#237—53no—
434#237—53no—
435#237C2×AGL(1,𝔽5)13yescomplemented
436D3×D4—56no—
437D3×D4—53no—
438D3×D4—56no—
439D3×D4—53no—
440D3×D4—53no—
441D3×D4C2×AGL(1,𝔽5)13yescomplemented
442#235—53no—
443#235—56no—
444#235—53no—
445#235—56no—
446#235—53no—
447#235C2×AGL(1,𝔽5)13yescomplemented
448C2×D12—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—51no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—53no—
459C2×C4×D3—53no—
460C2×C4×D3—52no—
461C2×C4×D3—56no—
462C2×C4×D3—512no—
463C2×C4×D3—2012no—
464C2×C4×D3C2×AGL(1,𝔽5)13yescomplemented
465C2×Dic6—53no—
466C3×C4⋊C4—56no—
467C3×C4⋊C4—53no—
468C3×C4⋊C4—51no—
469C3×C22⋊C4—56no—
470C3×C42—56no—
471#217—56no—
472(C2×D3)⋊C4—56no—
473(C2×D3)⋊C4—56no—
474C4⋊Dic3—56no—
475C4⋊Dic3—53no—
476C4⋊Dic3—51no—
477Dic3⋊C4—512no—
478Dic3⋊C4—52no—
479Dic3⋊C4—56no—
480C4×Dic3—56no—
481C4×Dic3—56no—
482C4×Dic3—56no—
483C23×C5—33no—
484C22×D5—31no—
485C22×D5—33no—
486C22×D5—33no—
487C22×D5—33no—
488C22×D5—33no—
489C22×D5—66no—
490C22×D5—66no—
491C22×D5C23×D313yes—
492C2×AGL(1,𝔽5)—32no—
493C2×AGL(1,𝔽5)—36no—
494C2×AGL(1,𝔽5)—46no—
495C2×AGL(1,𝔽5)—64no—
496C2×AGL(1,𝔽5)—612no—
497C2×AGL(1,𝔽5)—1212no—
498C2×AGL(1,𝔽5)—126no—
499C2×AGL(1,𝔽5)C23×D312yes—
500C2×AGL(1,𝔽5)C23×D316yes—
501C5×Q8—33no—
502C5×Q8C2×C4×D311yescharacteristic, complemented
503C5×D4—36no—
504C5×D4—33no—
505C5×D4C2×C4×D313yescomplemented
506C2×C4×C5—33no—
507C2×C4×C5—33no—
508C2×C4×C5—31no—
509C2×C4×C5—33no—
510C2×C4×C5—33no—
511C2×C4×C5C2×C4×D313yescomplemented
512C22⋊D5—36no—
513C22⋊D5—36no—
514C22⋊D5—36no—
515C22⋊D5C2×C4×D316yescomplemented
516C2×Dic5—33no—
517C2×Dic5—33no—
518C2×Dic5—31no—
519C2×Dic5—33no—
520C2×Dic5—33no—
521C2×Dic5C2×C4×D313yescomplemented
522D20—36no—
523D20—33no—
524D20C2×C4×D313yescomplemented
525C4×D5—33no—
526C4×D5—33no—
527C4×D5—33no—
528C4×D5—31no—
529C4×D5—31no—
530C4×D5—33no—
531C4×D5—33no—
532C4×D5—33no—
533C4×D5—31no—
534C4×D5—33no—
535C4×D5—33no—
536C4×D5—33no—
537C4×D5C2×C4×D313yescomplemented
538C4×D5C2×C4×D313yescomplemented
539C4×D5C23×D313yes—
540C4×D5C23×D311yescharacteristic
541Dic10—33no—
542Dic10—36no—
543Dic10C2×C4×D313yescomplemented
544C2×#41—31no—
545C2×#41—51no—
546C2×#41—153no—
547C2×#41—153no—
548C2×#41—153no—
549C2×#41—153no—
550C2×#41—151no—
551C2×#41—151no—
552C2×#41—151no—
553C2×#41—153no—
554C2×#41—153no—
555C2×#41—151no—
556C22×Q8—151no—
557C22×D4—153no—
558C23×C4—153no—
559C23×C4—156no—
560C4×Q8—52no—
561C4×Q8—156no—
562C4×Q8—156no—
563C4×Q8—152no—
564C4×D4—56no—
565C4×D4—156no—
566C4×D4—1512no—
567C4×D4—156no—
568C4×D4—1512no—
569C4×D4—156no—
570#117—53no—
571#117—156no—
572#117—156no—
573#117—153no—
574#117—153no—
575#117—153no—
576C2×C4⋊C4—53no—
577C2×C4⋊C4—153no—
578C2×C4⋊C4—156no—
579C2×C4⋊C4—156no—
580C2×C4⋊C4—156no—
581C2×C4⋊C4—151no—
582C2×C4⋊C4—156no—
583C2×C4⋊C4—153no—
584C2×C22⋊C4—156no—
585C2×C42—156no—
586C2×C3×C5—23no—
587C2×C3×C5C24×C411yescharacteristic
588D15—23no—
589D15#52012yescomplemented
590C3×D5—23no—
591C3×D5C2×H(5,𝔽2)11yescharacteristic
592C3×D5C2×2−1+411yescharacteristic
593C5×D3—23no—
594C5×D3#52012yescomplemented
595C23×C3—53no—
596C22×D3—51no—
597C22×D3—53no—
598C22×D3—53no—
599C22×D3—53no—
600C22×D3—53no—
601C22×D3—106no—
602C22×D3—106no—
603C22×D3C22×AGL(1,𝔽5)13yes—
604C3×Q8—53no—
605C3×Q8C22×AGL(1,𝔽5)11yescharacteristic, complemented
606C3×D4—56no—
607C3×D4—53no—
608C3×D4C22×AGL(1,𝔽5)13yescomplemented
609C2×C3×C4—53no—
610C2×C3×C4—53no—
611C2×C3×C4—53no—
612C2×C3×C4—53no—
613C2×C3×C4—51no—
614C2×C3×C4—52no—
615C2×C3×C4—56no—
616C2×C3×C4—206no—
617C2×C3×C4C22×AGL(1,𝔽5)13yescomplemented
618#67—56no—
619#67—56no—
620#67—56no—
621#67C22×AGL(1,𝔽5)16yescomplemented
622C2×Dic3—53no—
623C2×Dic3—53no—
624C2×Dic3—53no—
625C2×Dic3—53no—
626C2×Dic3—51no—
627C2×Dic3—52no—
628C2×Dic3—56no—
629C2×Dic3—206no—
630C2×Dic3C22×AGL(1,𝔽5)13yescomplemented
631D12—56no—
632D12—53no—
633D12C22×AGL(1,𝔽5)13yescomplemented
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—51no—
643C4×D3—53no—
644C4×D3—53no—
645C4×D3—53no—
646C4×D3—104no—
647C4×D3—1012no—
648C4×D3—2012no—
649C4×D3C22×AGL(1,𝔽5)11yescharacteristic
650C4×D3C22×AGL(1,𝔽5)13yes—
651C4×D3C22×AGL(1,𝔽5)13yescomplemented
652C4×D3C22×AGL(1,𝔽5)13yescomplemented
653Dic6—53no—
654Dic6—56no—
655Dic6C22×AGL(1,𝔽5)13yescomplemented
656C22×C5—31no—
657C22×C5—33no—
658C22×C5—66no—
659C22×C5C22×C4×D313yes—
660C2×D5—23no—
661C2×D5—23no—
662C2×D5—31no—
663C2×D5—32no—
664C2×D5—32no—
665C2×D5—33no—
666C2×D5—66no—
667C2×D5—66no—
668C2×D5—66no—
669C2×D5—63no—
670C2×D5—63no—
671C2×D5C22×C4×D313yes—
672C2×D5C24×D311yescharacteristic
673AGL(1,𝔽5)—26no—
674AGL(1,𝔽5)—22no—
675AGL(1,𝔽5)—66no—
676AGL(1,𝔽5)—62no—
677C4×C5—33no—
678C4×C5—31no—
679C4×C5C22×C4×D313yes—
680C4×C5C22×C4×D311yescharacteristic
681Dic5—33no—
682Dic5—31no—
683Dic5C22×C4×D313yes—
684Dic5C22×C4×D311yescharacteristic
685C24—153no—
686#41—31no—
687#41—33no—
688#41—33no—
689#41—51no—
690#41—53no—
691#41—53no—
692#41—156no—
693#41—156no—
694#41—153no—
695#41—153no—
696#41—156no—
697#41—153no—
698#41—153no—
699#41—156no—
700#41—153no—
701#41—153no—
702#41—151no—
703#41—153no—
704#41—153no—
705#41D3×AGL(1,𝔽5)11yescharacteristic, complemented
706C2×Q8—31no—
707C2×Q8—51no—
708C2×Q8—153no—
709C2×Q8—153no—
710C2×Q8—153no—
711C2×Q8—151no—
712C2×D4—33no—
713C2×D4—53no—
714C2×D4—153no—
715C2×D4—153no—
716C2×D4—156no—
717C2×D4—153no—
718C2×D4—156no—
719C2×D4—156no—
720C2×D4—153no—
721C22×C4—33no—
722C22×C4—53no—
723C22×C4—56no—
724C22×C4—153no—
725C22×C4—151no—
726C22×C4—153no—
727C22×C4—153no—
728C22×C4—153no—
729C22×C4—153no—
730C22×C4—153no—
731C22×C4—153no—
732C22×C4—153no—
733C22×C4—153no—
734C22×C4—153no—
735C22×C4—152no—
736C22×C4—156no—
737C22×C4—1512no—
738C22×C4—153no—
739C22×C4—156no—
740C22×C4—6012no—
741C4⋊C4—53no—
742C4⋊C4—56no—
743C4⋊C4—51no—
744C4⋊C4—156no—
745C4⋊C4—153no—
746C4⋊C4—1512no—
747C4⋊C4—156no—
748C4⋊C4—152no—
749C4⋊C4—151no—
750C22⋊C4—56no—
751C22⋊C4—156no—
752C22⋊C4—156no—
753C22⋊C4—156no—
754C42—56no—
755C42—156no—
756C42—156no—
757C42—156no—
758C3×C5C2×#52011yescharacteristic, complemented, Hall
759C22×C3—51no—
760C22×C3—53no—
761C22×C3—103no—
762C22×C3—103no—
763C22×C3C23×AGL(1,𝔽5)13yes—
764C2×D3—26no—
765C2×D3—51no—
766C2×D3—52no—
767C2×D3—52no—
768C2×D3—53no—
769C2×D3—106no—
770C2×D3—103no—
771C2×D3—103no—
772C2×D3—106no—
773C2×D3—106no—
774C2×D3C23×AGL(1,𝔽5)13yes—
775C2×D3C23×AGL(1,𝔽5)11yescharacteristic
776C3×C4—53no—
777C3×C4—51no—
778C3×C4—106no—
779C3×C4—102no—
780C3×C4C23×AGL(1,𝔽5)13yes—
781C3×C4C23×AGL(1,𝔽5)11yescharacteristic
782Dic3—53no—
783Dic3—51no—
784Dic3—106no—
785Dic3—102no—
786Dic3C23×AGL(1,𝔽5)13yes—
787Dic3C23×AGL(1,𝔽5)11yescharacteristic
788C2×C5—23no—
789C2×C5—32no—
790C2×C5—63no—
791C2×C5C23×C4×D311yescharacteristic
792D5—23no—
793D5—32no—
794D5—63no—
795D5D3×H(5,𝔽2)11yescharacteristic
796D5D3×2−1+411yescharacteristic
797C23—33no—
798C23—53no—
799C23—151no—
800C23—153no—
801C23—153no—
802C23—153no—
803C23—153no—
804C23—306no—
805C23—306no—
806Q8—33no—
807Q8—53no—
808Q8—156no—
809Q8—153no—
810Q8C2×D3×AGL(1,𝔽5)11yescharacteristic, complemented
811D4—36no—
812D4—33no—
813D4—56no—
814D4—53no—
815D4—156no—
816D4—156no—
817D4—156no—
818D4—156no—
819D4—153no—
820D4C2×D3×AGL(1,𝔽5)13yescomplemented
821C2×C4—33no—
822C2×C4—31no—
823C2×C4—33no—
824C2×C4—33no—
825C2×C4—33no—
826C2×C4—53no—
827C2×C4—53no—
828C2×C4—51no—
829C2×C4—53no—
830C2×C4—53no—
831C2×C4—52no—
832C2×C4—56no—
833C2×C4—151no—
834C2×C4—153no—
835C2×C4—153no—
836C2×C4—153no—
837C2×C4—153no—
838C2×C4—151no—
839C2×C4—153no—
840C2×C4—153no—
841C2×C4—151no—
842C2×C4—153no—
843C2×C4—153no—
844C2×C4—153no—
845C2×C4—153no—
846C2×C4—151no—
847C2×C4—153no—
848C2×C4—153no—
849C2×C4—153no—
850C2×C4—152no—
851C2×C4—156no—
852C2×C4—206no—
853C2×C4—3012no—
854C2×C4—304no—
855C2×C4—6012no—
856C2×C4—606no—
857C2×C4C2×D3×AGL(1,𝔽5)13yescomplemented
858C2×C3—23no—
859C2×C3—51no—
860C2×C3—51no—
861C2×C3—103no—
862C2×C3C24×AGL(1,𝔽5)11yescharacteristic
863D3—23no—
864D3—52no—
865D3—103no—
866D3#6626612yesdirect product factor
867C5D3×#52011yescharacteristic, complemented, Sylow
868C22—31no—
869C22—33no—
870C22—51no—
871C22—53no—
872C22—66no—
873C22—103no—
874C22—103no—
875C22—152no—
876C22—152no—
877C22—151no—
878C22—153no—
879C22—306no—
880C22—306no—
881C22—303no—
882C22—303no—
883C22—306no—
884C22C22×D3×AGL(1,𝔽5)13yes—
885C4—31no—
886C4—33no—
887C4—51no—
888C4—53no—
889C4—106no—
890C4—102no—
891C4—151no—
892C4—153no—
893C4—306no—
894C4—302no—
895C4C22×D3×AGL(1,𝔽5)11yescharacteristic
896C4C22×D3×AGL(1,𝔽5)13yes—
897C3C2×#6626611yescharacteristic, complemented, Sylow
898C2—23no—
899C2—32no—
900C2—51no—
901C2—51no—
902C2—63no—
903C2—103no—
904C2—152no—
905C2—303no—
906C2C23×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×C5C2×#520
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. #11756854C2semidirect
5. D3×Q8×AGL(1,𝔽5)C2semidirect
6. #11756846C2semidirect
7. D3×D4×AGL(1,𝔽5)C2semidirect
8. #11756838C2semidirect
9. #11756836C2semidirect
10. D3×#4130C2semidirect
11. C2×D3×C4⋊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. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
41. #91923C22semidirect
42. #91921C22semidirect
46. D3×C4⋊AGL(1,𝔽5)C22semidirect
47. D3×C4⋊AGL(1,𝔽5)C22semidirect
48. AGL(1,𝔽5)×D12C22semidirect
50. #91909C22semidirect
51. ΓL(1,𝔽16)⋊Q8C22semidirect
52. #91907C22semidirect
53. #91907C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
62. #66266D3direct (N × H)
74. C3×C5×#41C2×C4semidirect
75. #6821C2×C4semidirect
76. Q8×D15C2×C4semidirect
77. #6819C2×C4semidirect
78. D4×D15C2×C4semidirect
79. #6817C2×C4semidirect
80. C2×C4×D15C2×C4semidirect
81. C5×#239C2×C4semidirect
82. C5×D3×Q8C2×C4semidirect
83. C5×#237C2×C4semidirect
84. C5×D3×D4C2×C4semidirect
85. C5×#235C2×C4semidirect
86. C2×C4×C5×D3C2×C4semidirect
87. C3×#713C2×C4semidirect
89. C3×#711C2×C4semidirect
91. C3×#709C2×C4semidirect
93. #6790C2×C4semidirect
94. D3×C22⋊D5C2×C4semidirect
96. C2×#1200C2×C4semidirect
97. #6782C2×C4semidirect
98. C2×D3×Dic5C2×C4semidirect
99. #6780C2×C4semidirect
100. #6779C2×C4semidirect
102. #6777C2×C4semidirect
103. D3×D20C2×C4semidirect
105. C4×D3×D5C2×C4semidirect
106. C4×D3×D5C2×C4semidirect
107. C4×D3×D5C2×C4semidirect
108. C4×D3×D5C2×C4semidirect
113. #6773C2×C4semidirect
114. #6772C2×C4semidirect
115. #6771C2×C4semidirect
116. D15⋊Q8C2×C4semidirect
117. #6769C2×C4semidirect
118. #6768C2×C4semidirect
119. D3×Dic10C2×C4semidirect
120. #6766C2×C4semidirect
121. #6765C2×C4semidirect
171. Q8×AGL(1,𝔽5)C2×D3semidirect
177. D4×AGL(1,𝔽5)C2×D3semidirect
183. #4130C2×D3semidirect
191. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
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)semidirect
307. C5×#41C4×D3semidirect
316. #713C4×D3semidirect
326. #711C4×D3semidirect
338. #709C4×D3semidirect
414. C3×#41C2×AGL(1,𝔽5)semidirect
425. #239C2×AGL(1,𝔽5)semidirect
429. D3×Q8C2×AGL(1,𝔽5)semidirect
435. #237C2×AGL(1,𝔽5)semidirect
441. D3×D4C2×AGL(1,𝔽5)semidirect
447. #235C2×AGL(1,𝔽5)semidirect
464. C2×C4×D3C2×AGL(1,𝔽5)semidirect
502. C5×Q8C2×C4×D3semidirect
505. C5×D4C2×C4×D3semidirect
511. C2×C4×C5C2×C4×D3semidirect
515. C22⋊D5C2×C4×D3semidirect
521. C2×Dic5C2×C4×D3semidirect
524. D20C2×C4×D3semidirect
537. C4×D5C2×C4×D3semidirect
538. C4×D5C2×C4×D3semidirect
543. Dic10C2×C4×D3semidirect
589. D15#520semidirect
594. C5×D3#520semidirect
605. C3×Q8C22×AGL(1,𝔽5)semidirect
608. C3×D4C22×AGL(1,𝔽5)semidirect
617. C2×C3×C4C22×AGL(1,𝔽5)semidirect
621. #67C22×AGL(1,𝔽5)semidirect
630. C2×Dic3C22×AGL(1,𝔽5)semidirect
633. D12C22×AGL(1,𝔽5)semidirect
651. C4×D3C22×AGL(1,𝔽5)semidirect
652. C4×D3C22×AGL(1,𝔽5)semidirect
655. Dic6C22×AGL(1,𝔽5)semidirect
705. #41D3×AGL(1,𝔽5)semidirect
758. C3×C5C2×#520semidirect
810. Q8C2×D3×AGL(1,𝔽5)semidirect
820. D4C2×D3×AGL(1,𝔽5)semidirect
857. C2×C4C2×D3×AGL(1,𝔽5)semidirect
866. D3#66266direct (N × H)
867. C5D3×#520semidirect
897. C3C2×#66266semidirect

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
#117568542
D3×Q8×AGL(1,𝔽5)2
#117568462
D3×D4×AGL(1,𝔽5)2
#117568382
#117568362
D3×#41302
C2×D3×C4⋊AGL(1,𝔽5)2
C2×#662663
D3×#5205