Finite Group Databasebeta

← #14326556

Subgroups — #14326556

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#926C211yesmaximal, characteristic
2C2×#91235C211yesmaximal, characteristic
3C3×#65764C211yesmaximal, characteristic
4#11752029C212yesmaximal
5#11752021C212yesmaximal
6#11751840C212yesmaximal, complemented
7#11751839C212yesmaximal, complemented
8#11751834C211yesmaximal, characteristic, complemented
9#11751832C211yesmaximal, characteristic, complemented
10#11751750C211yesmaximal, characteristic, complemented
11#11751746C211yesmaximal, characteristic, complemented
12#10617132—31nomaximal, Hall
13C23×ΓL(1,𝔽16)C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
16C2×Dic3⋊AGL(1,𝔽5)C2212yes—
17C2×Dic3⋊AGL(1,𝔽5)C2212yes—
18C2×Dic3×AGL(1,𝔽5)C2212yes—
19C2×Dic3×AGL(1,𝔽5)C2212yes—
20#91815C411yescharacteristic, complemented
21C5×#926C411yescharacteristic, complemented
22D5×#217C2211yescharacteristic
23D5×#217C2211yescharacteristic
24#91528C411yescharacteristic, complemented
25#91528C411yescharacteristic, complemented
26D5×C4⋊Dic3C2211yescharacteristic
27D5×C4⋊Dic3C2211yescharacteristic
28C4×D5×Dic3C2211yescharacteristic
29C4×D5×Dic3C2211yescharacteristic
30#91358C411yescharacteristic, complemented
31#91358C411yescharacteristic, complemented
32#91357C411yescharacteristic, complemented
33#91357C411yescharacteristic, complemented
34#91235C2211yescharacteristic
35#91235C2211yescharacteristic
36#91235C2212yes—
37C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
38C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#74059—51nomaximal, Hall
45D5×#117—31no—
46#65764D311yescharacteristic
47C2×(C2×AGL(1,𝔽5))⋊C4—31no—
48#65711—32no—
49#65711—32no—
50#65699—32no—
51C22⋊C4×AGL(1,𝔽5)—32no—
52#65690—31no—
53#65689—31no—
54C4×C4⋊AGL(1,𝔽5)—31no—
55#65686—31no—
56C23×C3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)—24no—
58C22×ΓL(1,𝔽16)—24no—
59C22×ΓL(1,𝔽16)—42no—
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×AGL(1,𝔽5)C2312yes—
64C22×C3×C4×C5C2×C411yescharacteristic
65C22×C3×Dic5C2×C411yescharacteristic
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5C2×C411yescharacteristic
68C2×C3×C4×D5C2×C411yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×D5×Dic3C2311yescharacteristic
72C2×D5×Dic3C2311yescharacteristic
73C2×D5×Dic3C2311yescharacteristic
74C2×D5×Dic3C2311yescharacteristic
75C3×C22⋊AGL(1,𝔽5)—24no—
76Dic3⋊AGL(1,𝔽5)—24no—
77Dic3⋊AGL(1,𝔽5)—42no—
78Dic3×AGL(1,𝔽5)—24no—
79Dic3×AGL(1,𝔽5)—42no—
80#6719C2×C411yescharacteristic
81#6719C2×C411yescharacteristic
82C4⋊Dic15C2×C411yescharacteristic, complemented
83C4⋊Dic15C2×C411yescharacteristic, complemented
84C4×Dic15C2×C411yescharacteristic, complemented
85C4×Dic15C2×C411yescharacteristic, complemented
86C5×#217C2×C411yescharacteristic
87C5×#217C2×C411yescharacteristic
88C5×C4⋊Dic3C2×C411yescharacteristic, complemented
89C5×C4⋊Dic3C2×C411yescharacteristic, complemented
90C4×C5×Dic3C2×C411yescharacteristic, complemented
91C4×C5×Dic3C2×C411yescharacteristic, complemented
92#6668C2×C411yescharacteristic, complemented
93#6668C2×C411yescharacteristic, complemented
94#6668C2×C411yescharacteristic, complemented
95#6668C2×C411yescharacteristic, complemented
96#6665C2×C411yescharacteristic
97#6665C2×C411yescharacteristic
98#6665C2×C411yescharacteristic
99#6665C2×C411yescharacteristic
100Dic3×Dic5C2×C411yescharacteristic, complemented
101Dic3×Dic5C2×C411yescharacteristic, complemented
102Dic3×Dic5C2×C411yescharacteristic, complemented
103Dic3×Dic5C2×C411yescharacteristic, complemented
104C2×#926—51no—
105C3×#381—51no—
106C2×C3⋊#95—51no—
107#4946—52no—
108Dic3×C22⋊C4—52no—
109#4654—52no—
110#4653—52no—
111#4651—51no—
112#4650—51no—
113#4649—51no—
114#4648—51no—
115C23×AGL(1,𝔽5)—32no—
116C22×C4×D5C2×D311yescharacteristic
117C2×C22⋊AGL(1,𝔽5)C2×D312yes—
118C2×C4⋊AGL(1,𝔽5)—32no—
119C2×C4⋊AGL(1,𝔽5)—32no—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)—32no—
122C5×#117—31no—
123#4072—31no—
124#4038—31no—
125#4038—31no—
126D5×C4⋊C4—31no—
127D5×C4⋊C4—31no—
128D5×C22⋊C4—31no—
129D5×C22⋊C4—31no—
130#4023—31no—
131#4023—31no—
132#4018—31no—
133#4018—31no—
134C42×D5—31no—
135C42×D5—31no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4—32no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4—32no—
140(C2×AGL(1,𝔽5))⋊C4—31no—
141(C2×AGL(1,𝔽5))⋊C4—31no—
142(C2×AGL(1,𝔽5))⋊C4—32no—
143(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
144(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
145(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
146#2343—151noSylow
147C23×C3×C5C22×C411yescharacteristic
148C22×C3×D5—22no—
149C22×C3×D5—21no—
150C22×C3×D5—21no—
151C22×C3×D5C22×C411yescharacteristic
152C22×C3×D5#4114yes—
153C22×C3×D5C2411yescharacteristic
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—22no—
157C2×ΓL(1,𝔽16)—22no—
158C2×ΓL(1,𝔽16)—22no—
159C2×ΓL(1,𝔽16)—48no—
160C2×ΓL(1,𝔽16)#4114yes—
161C2×C3×AGL(1,𝔽5)—22no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—22no—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×C3×C4×C5C22×C411yescharacteristic
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C411yescharacteristic
172C2×Dic15C22×C411yescharacteristic
173C2×Dic15C22×C411yescharacteristic
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C411yescharacteristic
176C2×C5×Dic3C22×C411yescharacteristic
177C2×C5×Dic3C22×C411yescharacteristic
178C2×C3×Dic5—22no—
179C2×C3×Dic5C22×C411yescharacteristic
180C2×C3×Dic5C22×C411yescharacteristic
181C3×C4×D5—22no—
182C3×C4×D5—22no—
183C3×C4×D5—22no—
184C3×C4×D5—22no—
185D5×Dic3—22no—
186D5×Dic3—22no—
187D5×Dic3—21no—
188D5×Dic3—21no—
189D5×Dic3—21no—
190D5×Dic3—21no—
191C23×C3×C4—51no—
192C23×Dic3—52no—
193C2×C3×C22⋊C4—52no—
194C2×#217—51no—
195C2×#217—51no—
196#926—51no—
197#926—51no—
198#926—51no—
199#926—51no—
200#926—51no—
201#926—51no—
202#926—51no—
203#926AGL(1,𝔽5)11yescharacteristic, complemented
204C2×C4⋊Dic3—51no—
205C2×C4⋊Dic3—51no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4—52no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—52no—
211C2×C4×Dic3—52no—
212C3×#95—51no—
213C3×#95—51no—
214C3×#95—52no—
215C3⋊#95—52no—
216C3⋊#95—52no—
217C3⋊#95—52no—
218C3⋊#95—52no—
219C3⋊#95—51no—
220C3⋊#95—51no—
221C3⋊#95—52no—
222C23×D5C22×D311yescharacteristic
223C22×AGL(1,𝔽5)—32no—
224C22×AGL(1,𝔽5)—32no—
225C22×AGL(1,𝔽5)—64no—
226C22×AGL(1,𝔽5)—64no—
227C22×AGL(1,𝔽5)—122no—
228C22×AGL(1,𝔽5)C22×D312yes—
229C22×AGL(1,𝔽5)C22×D312yes—
230C22×C4×C5C4×D311yescharacteristic
231C22×Dic5C4×D311yescharacteristic
232C2×C4×D5—24no—
233C2×C4×D5—31no—
234C2×C4×D5—31no—
235C2×C4×D5—31no—
236C2×C4×D5—31no—
237C2×C4×D5C4×D311yescharacteristic
238C2×C4×D5C4×D311yescharacteristic
239C2×C4×D5C22×D311yescharacteristic
240C2×C4×D5C22×D311yescharacteristic
241C22⋊AGL(1,𝔽5)—24no—
242C4⋊AGL(1,𝔽5)—64no—
243C4⋊AGL(1,𝔽5)—122no—
244C4×AGL(1,𝔽5)—64no—
245C4×AGL(1,𝔽5)—122no—
246C5×C4⋊C4—31no—
247C5×C4⋊C4—31no—
248C5×C22⋊C4—31no—
249C5×C22⋊C4—31no—
250C42×C5—31no—
251C42×C5—31no—
252C22⋊Dic5—31no—
253C22⋊Dic5—31no—
254#685—31no—
255#685—31no—
256#685—31no—
257#685—31no—
258C4⋊Dic5—31no—
259C4⋊Dic5—31no—
260#683—31no—
261#683—31no—
262#683—31no—
263#683—31no—
264C4×Dic5—31no—
265C4×Dic5—31no—
266C4×Dic5—31no—
267C4×Dic5—31no—
268C4×Dic5—31no—
269C4×Dic5—31no—
270C2×#117—151no—
271#387—152no—
272#387—152no—
273#385—152no—
274#383—151no—
275#382—151no—
276#381—51no—
277C4×C4⋊C4—151no—
278C4×C22⋊C4—152no—
279#376—151no—
280C2×#95—151no—
281C22×C3×C5—21no—
282C22×C3×C5—21no—
283C22×C3×C5#11712yes—
284C22×C3×C5C23×C411yescharacteristic
285C2×C3×D5—21no—
286C2×C3×D5—21no—
287C2×C3×D5—24no—
288C2×C3×D5—24no—
289C2×C3×D5#11712yes—
290C2×C3×D5C2×#4112yes—
291C2×C3×D5C2×#4112yes—
292C2×C3×D5H(5,𝔽2)11yescharacteristic
293C2×C3×D52−1+411yescharacteristic
294ΓL(1,𝔽16)—24no—
295ΓL(1,𝔽16)—42no—
296C3×AGL(1,𝔽5)—42no—
297C3×AGL(1,𝔽5)—42no—
298C3×C4×C5—21no—
299C3×C4×C5—21no—
300Dic15—21no—
301Dic15—21no—
302Dic15—21no—
303Dic15—21no—
304C3×Dic5—21no—
305C3×Dic5—21no—
306C5×Dic3—21no—
307C5×Dic3—21no—
308C5×Dic3—21no—
309C5×Dic3—21no—
310C24×C3—51no—
311C22×C3×C4—51no—
312C22×C3×C4—51no—
313C22×C3×C4—51no—
314C22×C3×C4—51no—
315C22×C3×C4—51no—
316C22×C3×C4—52no—
317C22×C3×C4—52no—
318C22×C3×C4—104no—
319C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
320C22×Dic3—52no—
321C22×Dic3—51no—
322C22×Dic3—51no—
323C22×Dic3—51no—
324C22×Dic3—51no—
325C22×Dic3—52no—
326C22×Dic3—104no—
327C22×Dic3—104no—
328C22×Dic3—202no—
329C3×C22⋊C4—104no—
330#217—51no—
331#217—51no—
332#217—51no—
333#217—51no—
334#217—51no—
335#217—51no—
336#217C2×AGL(1,𝔽5)11yescharacteristic
337#217C2×AGL(1,𝔽5)11yescharacteristic
338C4⋊Dic3—51no—
339C4⋊Dic3—51no—
340C4⋊Dic3—51no—
341C4⋊Dic3—51no—
342C4⋊Dic3—51no—
343C4⋊Dic3—51no—
344C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
345C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
346Dic3⋊C4—104no—
347Dic3⋊C4—202no—
348C4×Dic3—51no—
349C4×Dic3—51no—
350C4×Dic3—51no—
351C4×Dic3—51no—
352C4×Dic3—51no—
353C4×Dic3—51no—
354C4×Dic3—104no—
355C4×Dic3—202no—
356C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
357C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
358C23×C5C2×C4×D311yescharacteristic
359C22×D5—22no—
360C22×D5—21no—
361C22×D5—21no—
362C22×D5C2×C4×D311yescharacteristic
363C22×D5#23714yes—
364C22×D5C23×D311yescharacteristic
365C2×AGL(1,𝔽5)—22no—
366C2×AGL(1,𝔽5)—22no—
367C2×AGL(1,𝔽5)—22no—
368C2×AGL(1,𝔽5)—22no—
369C2×AGL(1,𝔽5)—22no—
370C2×AGL(1,𝔽5)—22no—
371C2×AGL(1,𝔽5)—34no—
372C2×AGL(1,𝔽5)—62no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—62no—
375C2×AGL(1,𝔽5)—62no—
376C2×AGL(1,𝔽5)—62no—
377C2×AGL(1,𝔽5)—128no—
378C2×C4×C5—22no—
379C2×C4×C5—31no—
380C2×C4×C5—31no—
381C2×C4×C5—31no—
382C2×C4×C5—31no—
383C2×C4×C5C2×C4×D311yescharacteristic
384C2×C4×C5C2×C4×D311yescharacteristic
385C2×Dic5—22no—
386C2×Dic5—31no—
387C2×Dic5—31no—
388C2×Dic5—31no—
389C2×Dic5—31no—
390C2×Dic5C2×C4×D311yescharacteristic
391C2×Dic5C2×C4×D311yescharacteristic
392C4×D5—22no—
393C4×D5—22no—
394C4×D5—22no—
395C4×D5—22no—
396C4×D5—62no—
397C4×D5—62no—
398C4×D5—61no—
399C4×D5—61no—
400C4×D5—61no—
401C4×D5—61no—
402C23×C4—51no—
403C23×C4—152no—
404#117—31no—
405#117—151no—
406#117—151no—
407#117—151no—
408#117—151no—
409#117—151no—
410#117—151no—
411#117—151no—
412C2×C4⋊C4—151no—
413C2×C4⋊C4—151no—
414C2×C4⋊C4—152no—
415C2×C4⋊C4—152no—
416C2×C22⋊C4—52no—
417C2×C22⋊C4—151no—
418C2×C22⋊C4—151no—
419C2×C42—151no—
420C2×C42—151no—
421C2×C42—152no—
422C2×C42—152no—
423#95—51no—
424#95—51no—
425#95—52no—
426#95—151no—
427#95—151no—
428#95—152no—
429#95—152no—
430#95—152no—
431#95—152no—
432#95—152no—
433C2×C3×C5—22no—
434C2×C3×C5C2×#11711yescharacteristic
435C2×C3×C5C4×#4111yescharacteristic
436C2×C3×C5#52011yescharacteristic
437C3×D5—22no—
438C3×D5#55112yes—
439C3×D5#55212yes—
440C23×C3—51no—
441C23×C3—54no—
442C23×C3—51no—
443C23×C3—102no—
444C23×C3—101no—
445C23×C3—101no—
446C23×C3C22×AGL(1,𝔽5)11yescharacteristic
447C2×C3×C4—22no—
448C2×C3×C4—51no—
449C2×C3×C4—51no—
450C2×C3×C4—102no—
451C2×C3×C4—102no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—102no—
457C2×C3×C4—102no—
458C2×C3×C4—102no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
462C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
463C2×Dic3—54no—
464C2×Dic3—51no—
465C2×Dic3—51no—
466C2×Dic3—51no—
467C2×Dic3—51no—
468C2×Dic3—102no—
469C2×Dic3—101no—
470C2×Dic3—102no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474C2×Dic3—102no—
475C2×Dic3—102no—
476C2×Dic3—102no—
477C2×Dic3—102no—
478C2×Dic3—102no—
479C2×Dic3—208no—
480C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
481C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
482C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
483C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
484C22×C5—21no—
485C22×C5—21no—
486C22×C5#87712yes—
487C22×C5C22×C4×D311yescharacteristic
488C2×D5—21no—
489C2×D5—21no—
490C2×D5—24no—
491C2×D5—24no—
492C2×D5#87712yes—
493C2×D5C2×#23712yes—
494C2×D5D3×#4112yes—
495C2×D5#100911yescharacteristic
496C2×D5#101011yescharacteristic
497AGL(1,𝔽5)—42no—
498AGL(1,𝔽5)—42no—
499AGL(1,𝔽5)—64no—
500AGL(1,𝔽5)—122no—
501C4×C5—21no—
502C4×C5—21no—
503C4×C5—61no—
504C4×C5—61no—
505C4×C5—61no—
506C4×C5—61no—
507Dic5—21no—
508Dic5—21no—
509Dic5—61no—
510Dic5—61no—
511Dic5—61no—
512Dic5—61no—
513C24—51no—
514C22×C4—51no—
515C22×C4—51no—
516C22×C4—51no—
517C22×C4—51no—
518C22×C4—51no—
519C22×C4—52no—
520C22×C4—52no—
521C22×C4—104no—
522C22×C4—151no—
523C22×C4—151no—
524C22×C4—151no—
525C22×C4—151no—
526C22×C4—152no—
527C22×C4—152no—
528C22×C4—304no—
529C22×C4—304no—
530C22×C4—602no—
531C22×C4D3×AGL(1,𝔽5)11yescharacteristic
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—151no—
535C4⋊C4—151no—
536C4⋊C4—151no—
537C4⋊C4—151no—
538C4⋊C4—151no—
539C4⋊C4—151no—
540C4⋊C4—304no—
541C4⋊C4—602no—
542C22⋊C4—31no—
543C22⋊C4—31no—
544C22⋊C4—104no—
545C22⋊C4—151no—
546C22⋊C4—151no—
547C22⋊C4—151no—
548C22⋊C4—151no—
549C22⋊C4—151no—
550C22⋊C4—151no—
551C42—31no—
552C42—31no—
553C42—151no—
554C42—151no—
555C42—151no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—304no—
560C42—602no—
561C3×C5#234311yescharacteristic, complemented, Hall
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—52no—
565C22×C3—52no—
566C22×C3—51no—
567C22×C3—51no—
568C22×C3—52no—
569C22×C3—104no—
570C22×C3—104no—
571C22×C3—101no—
572C22×C3—101no—
573C22×C3#413012yes—
574C22×C3C23×AGL(1,𝔽5)11yescharacteristic
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—101no—
578C3×C4—101no—
579C3×C4—202no—
580C3×C4—202no—
581Dic3—21no—
582Dic3—21no—
583Dic3—21no—
584Dic3—21no—
585Dic3—104no—
586Dic3—101no—
587Dic3—101no—
588Dic3—101no—
589Dic3—101no—
590Dic3—202no—
591C2×C5—22no—
592C2×C5C2×#87711yescharacteristic
593C2×C5#552211yescharacteristic
594C2×C5#552311yescharacteristic
595D5—22no—
596D5#565012yes—
597D5#565812yes—
598C23—51no—
599C23—54no—
600C23—51no—
601C23—102no—
602C23—101no—
603C23—101no—
604C23C2×D3×AGL(1,𝔽5)11yescharacteristic
605C2×C4—22no—
606C2×C4—31no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—51no—
611C2×C4—51no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—102no—
623C2×C4—154no—
624C2×C4—151no—
625C2×C4—151no—
626C2×C4—151no—
627C2×C4—151no—
628C2×C4—302no—
629C2×C4—301no—
630C2×C4—302no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—301no—
634C2×C4—302no—
635C2×C4—302no—
636C2×C4—302no—
637C2×C4—302no—
638C2×C4—302no—
639C2×C4—608no—
640C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
641C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
642C2×C3—22no—
643C2×C3—52no—
644C2×C3—52no—
645C2×C3—102no—
646C2×C3C2×#413011yescharacteristic
647C2×C3#41×AGL(1,𝔽5)11yescharacteristic
648C2×C3#6626611yescharacteristic
649C5#7405911yescharacteristic, complemented, Sylow
650C22—21no—
651C22—21no—
652C22—52no—
653C22—51no—
654C22—51no—
655C22—52no—
656C22—52no—
657C22—104no—
658C22—104no—
659C22—101no—
660C22—101no—
661C22#9192312yes—
662C22C22×D3×AGL(1,𝔽5)11yescharacteristic
663C4—21no—
664C4—21no—
665C4—61no—
666C4—61no—
667C4—61no—
668C4—61no—
669C4—101no—
670C4—101no—
671C4—202no—
672C4—202no—
673C4—304no—
674C4—301no—
675C4—301no—
676C4—301no—
677C4—301no—
678C4—602no—
679C3#1061713211yescharacteristic, complemented, Sylow
680C2—22no—
681C2—52no—
682C2—52no—
683C2—102no—
684C2#1175683511yescharacteristic
685C2#1175683811yescharacteristic
686C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751840C2semidirect
7. #11751839C2semidirect
8. #11751834C2semidirect
9. #11751832C2semidirect
10. #11751750C2semidirect
11. #11751746C2semidirect
20. #91815C4semidirect
21. C5×#926C4semidirect
24. #91528C4semidirect
25. #91528C4semidirect
30. #91358C4semidirect
31. #91358C4semidirect
32. #91357C4semidirect
33. #91357C4semidirect
82. C4⋊Dic15C2×C4semidirect
83. C4⋊Dic15C2×C4semidirect
84. C4×Dic15C2×C4semidirect
85. C4×Dic15C2×C4semidirect
88. C5×C4⋊Dic3C2×C4semidirect
89. C5×C4⋊Dic3C2×C4semidirect
90. C4×C5×Dic3C2×C4semidirect
91. C4×C5×Dic3C2×C4semidirect
92. #6668C2×C4semidirect
93. #6668C2×C4semidirect
94. #6668C2×C4semidirect
95. #6668C2×C4semidirect
100. Dic3×Dic5C2×C4semidirect
101. Dic3×Dic5C2×C4semidirect
102. Dic3×Dic5C2×C4semidirect
103. Dic3×Dic5C2×C4semidirect
203. #926AGL(1,𝔽5)semidirect
344. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
345. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
356. C4×Dic3C2×AGL(1,𝔽5)semidirect
357. C4×Dic3C2×AGL(1,𝔽5)semidirect
561. C3×C5#2343semidirect
649. C5#74059semidirect
679. C3#10617132semidirect

Maximal subgroups

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

subgroupindex
D5×#9262
C2×#912352
C3×#657642
#117520292
#117520212
#117518402
#117518392
#117518342
#117518322
#117517502
#117517462
#106171323
#740595