Finite Group Databasebeta

← #14326553

Subgroups — #14326553

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×#872C211yesmaximal, characteristic
2#11752349C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4#11751932C212yesmaximal
5D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
6AGL(1,𝔽5)×(C2×D3)⋊C4C212yesmaximal
7#11751853C211yesmaximal, characteristic
8#11751835C212yesmaximal, complemented
9#11751832C211yesmaximal, characteristic, complemented
10#11751746C211yesmaximal, characteristic, complemented
11#11751745C212yesmaximal, complemented
12#10617132—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C2×C4×D3×D5C2211yescharacteristic
15C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
16C2×C3×C4×AGL(1,𝔽5)C2212yes—
17C2×Dic3⋊AGL(1,𝔽5)C2212yes—
18C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
19C2×Dic3×AGL(1,𝔽5)C2212yes—
20#91761C411yescharacteristic, complemented
21C5×#872C411yescharacteristic, complemented
22C3×C42×D5C2211yescharacteristic
23D5×(C2×D3)⋊C4C2211yescharacteristic
24D5×(C2×D3)⋊C4C2211yescharacteristic
25#91402C411yescharacteristic, complemented
26#91402C411yescharacteristic, complemented
27#91398C411yescharacteristic, complemented
28#91398C411yescharacteristic, complemented
29D5×Dic3⋊C4C2211yescharacteristic
30D5×Dic3⋊C4C2211yescharacteristic
31C4×D5×Dic3C2211yescharacteristic
32#91386C411yescharacteristic, complemented
33#91371C411yescharacteristic, complemented
34#91235C2212yes—
35#91235C2211yescharacteristic
36#91235C2211yescharacteristic
37#91235C2212yes—
38C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
39C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
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#73766—51nomaximal, Hall
45D5×#117—31no—
46#65764—31no—
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)D311yescharacteristic, complemented
55#65686—31no—
56C22×D3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×ΓL(1,𝔽16)C2312yes—
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2312yes—
61C2×D3×AGL(1,𝔽5)—24no—
62C2×D3×AGL(1,𝔽5)—24no—
63C2×D3×AGL(1,𝔽5)—42no—
64C2×C4×D15C2×C411yescharacteristic
65C2×C4×C5×D3C2×C411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×#1200C2×C411yescharacteristic
70C2×D3×Dic5C2×C411yescharacteristic
71C2×D5×Dic3C2311yescharacteristic
72C2×D5×Dic3C2311yescharacteristic
73C2×D5×Dic3C2311yescharacteristic
74C4×D3×D5—24no—
75C3×C4⋊AGL(1,𝔽5)—24no—
76C3×C4×AGL(1,𝔽5)—42no—
77Dic3⋊AGL(1,𝔽5)—42no—
78(C2×D3)⋊AGL(1,𝔽5)—24no—
79Dic3×AGL(1,𝔽5)—24no—
80C3×C42×C5C2×C411yescharacteristic, complemented
81#6714C2×C411yescharacteristic
82#6714C2×C411yescharacteristic
83#6712C2×C411yescharacteristic, complemented
84#6712C2×C411yescharacteristic, complemented
85C4×Dic15C2×C411yescharacteristic, complemented
86C5×(C2×D3)⋊C4C2×C411yescharacteristic
87C5×(C2×D3)⋊C4C2×C411yescharacteristic
88C5×Dic3⋊C4C2×C411yescharacteristic, complemented
89C5×Dic3⋊C4C2×C411yescharacteristic, complemented
90C4×C5×Dic3C2×C411yescharacteristic, complemented
91C3×C4×Dic5C2×C411yescharacteristic, complemented
92C3×C4×Dic5C2×C411yescharacteristic, complemented
93C3×C4×Dic5C2×C411yescharacteristic, complemented
94Dic3⋊Dic5C2×C411yescharacteristic, complemented
95Dic3⋊Dic5C2×C411yescharacteristic, complemented
96#6669C2×C411yescharacteristic, complemented
97#6669C2×C411yescharacteristic, complemented
98#6667C2×C411yescharacteristic
99#6667C2×C411yescharacteristic
100(C2×D3)⋊Dic5C2×C411yescharacteristic
101(C2×D3)⋊Dic5C2×C411yescharacteristic
102Dic3×Dic5C2×C411yescharacteristic, complemented
103Dic3×Dic5C2×C411yescharacteristic, complemented
104C2×#872—51no—
105C3×C4×C4⋊C4—51no—
106#4989—52no—
107#4978—52no—
108C4×(C2×D3)⋊C4—52no—
109#4937—51no—
110#4933—52no—
111#4664—51no—
112D3×#95—51no—
113#4650—51no—
114#4648—51no—
115C23×AGL(1,𝔽5)—32no—
116C22×C4×D5—31no—
117C2×C22⋊AGL(1,𝔽5)—32no—
118C2×C4⋊AGL(1,𝔽5)—32no—
119C2×C4⋊AGL(1,𝔽5)C2×D312yes—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)C2×D312yes—
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×D5C2×D311yescharacteristic
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))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
145(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
146#2343—151noSylow
147C22×D15C22×C411yescharacteristic
148C22×C5×D3C22×C411yescharacteristic
149C22×C3×D5C2411yescharacteristic
150C2×D3×D5—22no—
151C2×D3×D5—21no—
152C2×D3×D5—21no—
153C2×D3×D5#4114yes—
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)—22no—
160C2×C3×AGL(1,𝔽5)—22no—
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)#4114yes—
166D3×AGL(1,𝔽5)—48no—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×C3×C4×C5C22×C411yescharacteristic
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C411yescharacteristic
172C2×Dic15C22×C411yescharacteristic
173C4×D15—22no—
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C411yescharacteristic
176C2×C5×Dic3C22×C411yescharacteristic
177C4×C5×D3—22no—
178C2×C3×Dic5C22×C411yescharacteristic
179C2×C3×Dic5C22×C411yescharacteristic
180C2×C3×Dic5C22×C411yescharacteristic
181C3×C4×D5—22no—
182C3×C4×D5—22no—
183C3×C4×D5—21no—
184C3×C4×D5—21no—
185#1200—22no—
186D3×Dic5—22no—
187D5×Dic3—22no—
188D5×Dic3—22no—
189D5×Dic3—21no—
190D5×Dic3—21no—
191C22×C4×D3—51no—
192C22×C4×D3—52no—
193C2×C3×C4⋊C4—52no—
194C2×C3×C42—51no—
195C2×C3×C42—52no—
196C2×(C2×D3)⋊C4—51no—
197C2×(C2×D3)⋊C4—51no—
198C2×(C2×D3)⋊C4—52no—
199C2×Dic3⋊C4—51no—
200C2×Dic3⋊C4—51no—
201C2×Dic3⋊C4—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—52no—
204#872—51no—
205#872—51no—
206#872—51no—
207#872—51no—
208#872—51no—
209#872—51no—
210#872—51no—
211#872AGL(1,𝔽5)11yescharacteristic, complemented
212C3×#95—51no—
213C3×#95—51no—
214C3⋊#95—52no—
215C3⋊#95—52no—
216C3⋊#95—52no—
217C3⋊#95—52no—
218C3⋊#95—51no—
219C3⋊#95—51no—
220C3⋊#95—52no—
221C3⋊#95—52no—
222C23×D5—31no—
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×C5—31no—
231C22×Dic5—31no—
232C2×C4×D5—31no—
233C2×C4×D5—31no—
234C2×C4×D5—31no—
235C2×C4×D5—31no—
236C2×C4×D5—31no—
237C2×C4×D5—64no—
238C2×C4×D5C22×D311yescharacteristic
239C2×C4×D5C22×D311yescharacteristic
240C2×C4×D5C22×D311yescharacteristic
241C22⋊AGL(1,𝔽5)—64no—
242C4⋊AGL(1,𝔽5)—24no—
243C4⋊AGL(1,𝔽5)—122no—
244C4×AGL(1,𝔽5)—42no—
245C4×AGL(1,𝔽5)—64no—
246C5×C4⋊C4—31no—
247C5×C4⋊C4—31no—
248C5×C22⋊C4—31no—
249C5×C22⋊C4—31no—
250C42×C5—31no—
251C42×C5C4×D311yescharacteristic, complemented
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×Dic5C4×D311yescharacteristic, complemented
268C4×Dic5C4×D311yescharacteristic, complemented
269C4×Dic5C4×D311yescharacteristic, complemented
270C2×#117—151no—
271#387—152no—
272#387—152no—
273#385—152no—
274#383—151no—
275#382—151no—
276#381—151no—
277C4×C4⋊C4—51no—
278C4×C22⋊C4—152no—
279#376—151no—
280C2×#95—151no—
281C22×C3×C5C23×C411yescharacteristic
282C2×D15—21no—
283C2×D15—21no—
284C2×D15#11712yes—
285C2×C5×D3—21no—
286C2×C5×D3—21no—
287C2×C5×D3#11712yes—
288C2×C3×D5C2×#4112yes—
289C2×C3×D5C2×#4112yes—
290C2×C3×D5H(5,𝔽2)11yescharacteristic
291C2×C3×D52−1+411yescharacteristic
292D3×D5—24no—
293D3×D5—24no—
294ΓL(1,𝔽16)—42no—
295ΓL(1,𝔽16)—42no—
296C3×AGL(1,𝔽5)—24no—
297C3×AGL(1,𝔽5)—42no—
298C3×C4×C5—21no—
299C3×C4×C5—21no—
300C3×C4×C5—21no—
301Dic15—21no—
302Dic15—21no—
303Dic15—21no—
304C3×Dic5—21no—
305C3×Dic5—21no—
306C3×Dic5—21no—
307C5×Dic3—21no—
308C5×Dic3—21no—
309C5×Dic3—21no—
310C23×D3—51no—
311C22×C3×C4—52no—
312C22×C3×C4—51no—
313C22×C3×C4—51no—
314C22×C3×C4—51no—
315C22×C3×C4—52no—
316C22×Dic3—51no—
317C22×Dic3—51no—
318C22×Dic3—51no—
319C22×Dic3—52no—
320C22×Dic3—52no—
321C2×C4×D3—51no—
322C2×C4×D3—51no—
323C2×C4×D3—51no—
324C2×C4×D3—104no—
325C2×C4×D3—104no—
326C2×C4×D3—104no—
327C2×C4×D3—202no—
328C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
329C3×C4⋊C4—104no—
330C3×C42—51no—
331C3×C42—51no—
332C3×C42—51no—
333C3×C42—202no—
334C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
335(C2×D3)⋊C4—51no—
336(C2×D3)⋊C4—51no—
337(C2×D3)⋊C4—51no—
338(C2×D3)⋊C4—51no—
339(C2×D3)⋊C4—51no—
340(C2×D3)⋊C4—51no—
341(C2×D3)⋊C4—104no—
342(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
343(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
344Dic3⋊C4—51no—
345Dic3⋊C4—51no—
346Dic3⋊C4—51no—
347Dic3⋊C4—51no—
348Dic3⋊C4—51no—
349Dic3⋊C4—51no—
350Dic3⋊C4—202no—
351Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
352Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
353C4×Dic3—51no—
354C4×Dic3—51no—
355C4×Dic3—51no—
356C4×Dic3—104no—
357C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
358C23×C5—31no—
359C22×D5—31no—
360C22×D5—34no—
361C22×D5—62no—
362C22×D5—61no—
363C22×D5—61no—
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)—62no—
371C2×AGL(1,𝔽5)—62no—
372C2×AGL(1,𝔽5)—62no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—62no—
375C2×AGL(1,𝔽5)—62no—
376C2×AGL(1,𝔽5)—128no—
377C2×AGL(1,𝔽5)#23514yes—
378C2×C4×C5—31no—
379C2×C4×C5—31no—
380C2×C4×C5—31no—
381C2×C4×C5—62no—
382C2×C4×C5C2×C4×D311yescharacteristic
383C2×C4×C5C2×C4×D311yescharacteristic
384C2×C4×C5C2×C4×D311yescharacteristic
385C2×Dic5—31no—
386C2×Dic5—31no—
387C2×Dic5—31no—
388C2×Dic5—62no—
389C2×Dic5C2×C4×D311yescharacteristic
390C2×Dic5C2×C4×D311yescharacteristic
391C2×Dic5C2×C4×D311yescharacteristic
392C4×D5—22no—
393C4×D5—21no—
394C4×D5—21no—
395C4×D5—22no—
396C4×D5—62no—
397C4×D5—62no—
398C4×D5—62no—
399C4×D5—61no—
400C4×D5—61no—
401C4×D5—62no—
402C23×C4—151no—
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—52no—
413C2×C4⋊C4—151no—
414C2×C4⋊C4—151no—
415C2×C4⋊C4—152no—
416C2×C22⋊C4—151no—
417C2×C22⋊C4—151no—
418C2×C22⋊C4—152no—
419C2×C42—51no—
420C2×C42—52no—
421C2×C42—151no—
422C2×C42—152no—
423#95—51no—
424#95—51no—
425#95—151no—
426#95—152no—
427#95—151no—
428#95—152no—
429#95—152no—
430#95—152no—
431#95—152no—
432#95—152no—
433C2×C3×C5C2×#11711yescharacteristic
434C2×C3×C5C4×#4111yescharacteristic
435C2×C3×C5#52011yescharacteristic
436D15—22no—
437C3×D5#55112yes—
438C3×D5#55212yes—
439C5×D3—22no—
440C23×C3—51no—
441C22×D3—51no—
442C22×D3—54no—
443C22×D3—102no—
444C22×D3—101no—
445C22×D3—101no—
446C22×D3C22×AGL(1,𝔽5)11yescharacteristic
447C2×C3×C4—54no—
448C2×C3×C4—51no—
449C2×C3×C4—51no—
450C2×C3×C4—51no—
451C2×C3×C4—101no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—101no—
455C2×C3×C4—102no—
456C2×C3×C4—102no—
457C2×C3×C4—102no—
458C2×C3×C4—102no—
459C2×C3×C4—102no—
460C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
461C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
462C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
463C2×Dic3—51no—
464C2×Dic3—51no—
465C2×Dic3—51no—
466C2×Dic3—102no—
467C2×Dic3—101no—
468C2×Dic3—102no—
469C2×Dic3—101no—
470C2×Dic3—102no—
471C2×Dic3—102no—
472C2×Dic3—102no—
473C2×Dic3—102no—
474C2×Dic3—102no—
475C2×Dic3—102no—
476C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
477C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
478C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
479C4×D3—22no—
480C4×D3—102no—
481C4×D3—102no—
482C4×D3—102no—
483C4×D3—208no—
484C22×C5—32no—
485C22×C5—61no—
486C22×C5—61no—
487C22×C5C22×C4×D311yescharacteristic
488C2×D5—32no—
489C2×D5—61no—
490C2×D5—61no—
491C2×D5—64no—
492C2×D5—64no—
493C2×D5C2×#23512yes—
494C2×D5#100411yescharacteristic
495C2×D5#100711yescharacteristic
496C2×D5D3×#4112yes—
497AGL(1,𝔽5)—24no—
498AGL(1,𝔽5)—42no—
499AGL(1,𝔽5)—122no—
500AGL(1,𝔽5)—122no—
501C4×C5—21no—
502C4×C5—21no—
503C4×C5—21no—
504C4×C5—61no—
505C4×C5—61no—
506C4×C5—61no—
507Dic5—21no—
508Dic5—21no—
509Dic5—21no—
510Dic5—61no—
511Dic5—61no—
512Dic5—61no—
513C24—151no—
514C22×C4—31no—
515C22×C4—52no—
516C22×C4—51no—
517C22×C4—51no—
518C22×C4—51no—
519C22×C4—52no—
520C22×C4—151no—
521C22×C4—151no—
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—304no—
531C22×C4—602no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—104no—
535C4⋊C4—151no—
536C4⋊C4—151no—
537C4⋊C4—151no—
538C4⋊C4—151no—
539C4⋊C4—151no—
540C4⋊C4—151no—
541C4⋊C4—602no—
542C22⋊C4—31no—
543C22⋊C4—31no—
544C22⋊C4—151no—
545C22⋊C4—151no—
546C22⋊C4—151no—
547C22⋊C4—151no—
548C22⋊C4—151no—
549C22⋊C4—151no—
550C22⋊C4—304no—
551C42—31no—
552C42—51no—
553C42—51no—
554C42—51no—
555C42—151no—
556C42—151no—
557C42—151no—
558C42—202no—
559C42—304no—
560C42D3×AGL(1,𝔽5)11yescharacteristic, complemented
561C3×C5#234311yescharacteristic, complemented, Hall
562C22×C3—52no—
563C22×C3—52no—
564C22×C3—51no—
565C22×C3—51no—
566C22×C3C23×AGL(1,𝔽5)11yescharacteristic
567C2×D3—21no—
568C2×D3—21no—
569C2×D3—52no—
570C2×D3—104no—
571C2×D3—104no—
572C2×D3—101no—
573C2×D3—101no—
574C2×D3#413012yes—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—104no—
579C3×C4—101no—
580C3×C4—101no—
581C3×C4—101no—
582C3×C4—202no—
583Dic3—21no—
584Dic3—21no—
585Dic3—21no—
586Dic3—101no—
587Dic3—101no—
588Dic3—101no—
589Dic3—202no—
590Dic3—202no—
591C2×C5—62no—
592C2×C5C4×#23511yescharacteristic
593C2×C5#550411yescharacteristic
594C2×C5D3×#11711yescharacteristic
595D5—62no—
596D5#555612yes—
597D5#558112yes—
598C23—31no—
599C23—51no—
600C23—154no—
601C23—151no—
602C23—302no—
603C23—301no—
604C23—301no—
605C2×C4—31no—
606C2×C4—31no—
607C2×C4—31no—
608C2×C4—54no—
609C2×C4—51no—
610C2×C4—51no—
611C2×C4—51no—
612C2×C4—62no—
613C2×C4—101no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—101no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—151no—
623C2×C4—151no—
624C2×C4—151no—
625C2×C4—302no—
626C2×C4—302no—
627C2×C4—302no—
628C2×C4—301no—
629C2×C4—302no—
630C2×C4—301no—
631C2×C4—302no—
632C2×C4—302no—
633C2×C4—302no—
634C2×C4—302no—
635C2×C4—302no—
636C2×C4—302no—
637C2×C4—302no—
638C2×C4—608no—
639C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
640C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
641C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
642C2×C3—52no—
643C2×C3—52no—
644C2×C3C2×#413011yescharacteristic
645C2×C3#41×AGL(1,𝔽5)11yescharacteristic
646C2×C3#6626611yescharacteristic
647D3—22no—
648D3—102no—
649C5#7376611yescharacteristic, complemented, Sylow
650C22—32no—
651C22—52no—
652C22—52no—
653C22—51no—
654C22—51no—
655C22—61no—
656C22—61no—
657C22—152no—
658C22—304no—
659C22—304no—
660C22—301no—
661C22—301no—
662C22C22×D3×AGL(1,𝔽5)11yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—61no—
667C4—61no—
668C4—61no—
669C4—104no—
670C4—101no—
671C4—101no—
672C4—101no—
673C4—202no—
674C4—301no—
675C4—301no—
676C4—301no—
677C4—602no—
678C4—602no—
679C3#1061713211yescharacteristic, complemented, Sylow
680C2—52no—
681C2—52no—
682C2—62no—
683C2—302no—
684C2AGL(1,𝔽5)×#23511yescharacteristic
685C2D3×#413011yescharacteristic
686C2#1175683611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C42×C5C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752349C2semidirect
3. C3×C4×C4⋊AGL(1,𝔽5)C2semidirect
8. #11751835C2semidirect
9. #11751832C2semidirect
10. #11751746C2semidirect
11. #11751745C2semidirect
20. #91761C4semidirect
21. C5×#872C4semidirect
25. #91402C4semidirect
26. #91402C4semidirect
27. #91398C4semidirect
28. #91398C4semidirect
32. #91386C4semidirect
33. #91371C4semidirect
54. C4×C4⋊AGL(1,𝔽5)D3semidirect
80. C3×C42×C5C2×C4semidirect
83. #6712C2×C4semidirect
84. #6712C2×C4semidirect
85. C4×Dic15C2×C4semidirect
88. C5×Dic3⋊C4C2×C4semidirect
89. C5×Dic3⋊C4C2×C4semidirect
90. C4×C5×Dic3C2×C4semidirect
91. C3×C4×Dic5C2×C4semidirect
92. C3×C4×Dic5C2×C4semidirect
93. C3×C4×Dic5C2×C4semidirect
94. Dic3⋊Dic5C2×C4semidirect
95. Dic3⋊Dic5C2×C4semidirect
96. #6669C2×C4semidirect
97. #6669C2×C4semidirect
102. Dic3×Dic5C2×C4semidirect
103. Dic3×Dic5C2×C4semidirect
211. #872AGL(1,𝔽5)semidirect
251. C42×C5C4×D3semidirect
267. C4×Dic5C4×D3semidirect
268. C4×Dic5C4×D3semidirect
269. C4×Dic5C4×D3semidirect
334. C3×C42C2×AGL(1,𝔽5)semidirect
351. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
352. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
357. C4×Dic3C2×AGL(1,𝔽5)semidirect
560. C42D3×AGL(1,𝔽5)semidirect
561. C3×C5#2343semidirect
649. C5#73766semidirect
679. C3#10617132semidirect

Maximal subgroups

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

subgroupindex
D5×#8722
#117523492
C3×C4×C4⋊AGL(1,𝔽5)2
#117519322
D3×(C2×AGL(1,𝔽5))⋊C42
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518532
#117518352
#117518322
#117517462
#117517452
#106171323
#737665