Finite Group Databasebeta

← #14326877

Subgroups — #14326877

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#872C211yesmaximal, characteristic
2#11752345C211yesmaximal, characteristic, complemented
3C3×#65689C211yesmaximal, characteristic, complemented
4#11751856C212yesmaximal
5#11751854C211yesmaximal, characteristic
6#11751848C211yesmaximal, characteristic
7#11751837C212yesmaximal, complemented
8#11751836C212yesmaximal
9#11751833C212yesmaximal, complemented
10#11751832C211yesmaximal, characteristic, complemented
11#11751746C211yesmaximal, characteristic, complemented
12#10617133—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×C4×ΓL(1,𝔽16)C2212yes—
15C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
16C2×Dic3⋊AGL(1,𝔽5)C2212yes—
17C2×Dic3⋊AGL(1,𝔽5)C2212yes—
18C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
19C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
20C2×Dic3×AGL(1,𝔽5)C2212yes—
21C2×Dic3×AGL(1,𝔽5)C2212yes—
22#91761C411yescharacteristic, complemented
23C5×#872C411yescharacteristic, complemented
24C3×C42×D5C2211yescharacteristic
25D5×(C2×D3)⋊C4C2211yescharacteristic
26D5×(C2×D3)⋊C4C2211yescharacteristic
27#91402C411yescharacteristic, complemented
28#91402C411yescharacteristic, complemented
29#91398C411yescharacteristic, complemented
30#91398C411yescharacteristic, complemented
31D5×Dic3⋊C4C2211yescharacteristic
32D5×Dic3⋊C4C2211yescharacteristic
33C4×D5×Dic3C2211yescharacteristic
34#91386C411yescharacteristic, complemented
35#91371C411yescharacteristic, complemented
36#91235C2211yescharacteristic
37#91235C2211yescharacteristic
38#91235C2212yes—
39C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
40C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#74156—51nomaximal, Hall
45D5×#117—31no—
46#65765—31no—
47C4×C22⋊AGL(1,𝔽5)—31no—
48#65712—32no—
49C4⋊C4×AGL(1,𝔽5)—32no—
50#65700—32no—
51#65700—32no—
52#65689—31no—
53#65689D311yescharacteristic, complemented
54#65686—31no—
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×C4×D15C2×C411yescharacteristic
62C2×C4×C5×D3C2×C411yescharacteristic
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×C4×D5C2311yescharacteristic
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1200C2×C411yescharacteristic
67C2×D3×Dic5C2×C411yescharacteristic
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2311yescharacteristic
70C2×D5×Dic3C2311yescharacteristic
71C4×D3×D5—24no—
72C4×ΓL(1,𝔽16)—24no—
73C3×C4⋊AGL(1,𝔽5)—42no—
74Dic3⋊AGL(1,𝔽5)—24no—
75Dic3⋊AGL(1,𝔽5)—42no—
76(C2×D3)⋊AGL(1,𝔽5)—24no—
77(C2×D3)⋊AGL(1,𝔽5)—42no—
78Dic3×AGL(1,𝔽5)—24no—
79Dic3×AGL(1,𝔽5)—24no—
80C3×C42×C5C2×C411yescharacteristic
81#6714C2×C411yescharacteristic
82#6714C2×C411yescharacteristic
83#6712C2×C411yescharacteristic
84#6712C2×C411yescharacteristic
85C4×Dic15C2×C411yescharacteristic
86C5×(C2×D3)⋊C4C2×C411yescharacteristic
87C5×(C2×D3)⋊C4C2×C411yescharacteristic
88C5×Dic3⋊C4C2×C411yescharacteristic
89C5×Dic3⋊C4C2×C411yescharacteristic
90C4×C5×Dic3C2×C411yescharacteristic
91C3×C4×Dic5C2×C411yescharacteristic
92C3×C4×Dic5C2×C411yescharacteristic
93C3×C4×Dic5C2×C411yescharacteristic
94Dic3⋊Dic5C2×C411yescharacteristic
95Dic3⋊Dic5C2×C411yescharacteristic
96#6669C2×C411yescharacteristic
97#6669C2×C411yescharacteristic
98#6667C2×C411yescharacteristic
99#6667C2×C411yescharacteristic
100(C2×D3)⋊Dic5C2×C411yescharacteristic
101(C2×D3)⋊Dic5C2×C411yescharacteristic
102Dic3×Dic5C2×C411yescharacteristic
103Dic3×Dic5C2×C411yescharacteristic
104C2×#872—51no—
105C3×#382—51no—
106#4990—52no—
107#4976—52no—
108#4932—51no—
109#4669—52no—
110#4667—51no—
111#4666—51no—
112#4650—51no—
113#4649—52no—
114#4648—51no—
115C22×C4×D5—31no—
116C2×C22⋊AGL(1,𝔽5)—32no—
117C2×C22⋊AGL(1,𝔽5)—32no—
118C2×C4⋊AGL(1,𝔽5)—32no—
119C2×C4⋊AGL(1,𝔽5)—32no—
120C2×C4⋊AGL(1,𝔽5)C2×D312yes—
121C2×C4×AGL(1,𝔽5)—32no—
122C2×C4×AGL(1,𝔽5)—32no—
123C2×C4×AGL(1,𝔽5)—32no—
124C5×#117—31no—
125#4072—31no—
126#4038—31no—
127#4038—31no—
128D5×C4⋊C4—31no—
129D5×C4⋊C4—31no—
130D5×C22⋊C4—31no—
131D5×C22⋊C4—31no—
132#4023—31no—
133#4023—31no—
134#4018—31no—
135#4018—31no—
136C42×D5—31no—
137C42×D5C2×D311yescharacteristic
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#2346—151noSylow
147C22×D15C22×C411yescharacteristic
148C22×C5×D3C22×C411yescharacteristic
149C22×C3×D5C2411yescharacteristic
150C2×D3×D5—22no—
151C2×D3×D5—22no—
152C2×D3×D5—21no—
153C2×D3×D5—21no—
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)#4114yes—
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)—22no—
166C2×C3×C4×C5C22×C411yescharacteristic
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×Dic15C22×C411yescharacteristic
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C411yescharacteristic
172C4×D15—22no—
173C2×C5×Dic3C22×C411yescharacteristic
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C411yescharacteristic
176C4×C5×D3—22no—
177C2×C3×Dic5C22×C411yescharacteristic
178C2×C3×Dic5C22×C411yescharacteristic
179C2×C3×Dic5C22×C411yescharacteristic
180C3×C4×D5—22no—
181C3×C4×D5—22no—
182C3×C4×D5—21no—
183C3×C4×D5—21no—
184#1200—22no—
185D3×Dic5—22no—
186D5×Dic3—22no—
187D5×Dic3—21no—
188D5×Dic3—21no—
189D5×Dic3#4114yes—
190C22×C4×D3—51no—
191C2×C3×C4⋊C4—52no—
192C2×C3×C42—51no—
193C2×(C2×D3)⋊C4—51no—
194C2×(C2×D3)⋊C4—51no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4—52no—
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—52no—
205#872—51no—
206#872—51no—
207#872—51no—
208#872—51no—
209#872—51no—
210#872—51no—
211#872—51no—
212#872AGL(1,𝔽5)11yescharacteristic, complemented
213C3×#95—51no—
214C3×#95—52no—
215C3×#95—51no—
216C3⋊#95—52no—
217C3⋊#95—52no—
218C3⋊#95—51no—
219C3⋊#95—51no—
220C3⋊#95—52no—
221C23×D5—31no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)—32no—
224C22×AGL(1,𝔽5)C22×D312yes—
225C22×AGL(1,𝔽5)C22×D312yes—
226C22×C4×C5—31no—
227C22×Dic5—31no—
228C2×C4×D5—31no—
229C2×C4×D5—31no—
230C2×C4×D5—31no—
231C2×C4×D5—31no—
232C2×C4×D5—31no—
233C2×C4×D5—64no—
234C2×C4×D5C22×D311yescharacteristic
235C2×C4×D5C22×D311yescharacteristic
236C2×C4×D5C22×D311yescharacteristic
237C22⋊AGL(1,𝔽5)—64no—
238C22⋊AGL(1,𝔽5)—122no—
239C4⋊AGL(1,𝔽5)—42no—
240C4⋊AGL(1,𝔽5)—64no—
241C4⋊AGL(1,𝔽5)—122no—
242C4×AGL(1,𝔽5)—64no—
243C4×AGL(1,𝔽5)—64no—
244C4×AGL(1,𝔽5)—64no—
245C5×C4⋊C4—31no—
246C5×C4⋊C4—31no—
247C5×C22⋊C4—31no—
248C5×C22⋊C4—31no—
249C42×C5—31no—
250C42×C5C4×D311yescharacteristic
251C22⋊Dic5—31no—
252C22⋊Dic5—31no—
253#685—31no—
254#685—31no—
255#685—31no—
256#685—31no—
257C4⋊Dic5—31no—
258C4⋊Dic5—31no—
259#683—31no—
260#683—31no—
261#683—31no—
262#683—31no—
263C4×Dic5—31no—
264C4×Dic5—31no—
265C4×Dic5—31no—
266C4×Dic5C4×D311yescharacteristic
267C4×Dic5C4×D311yescharacteristic
268C4×Dic5C4×D311yescharacteristic
269C2×#117—151no—
270#389—152no—
271#388—152no—
272#388—152no—
273#382—51no—
274#382—151no—
275#380—151no—
276C4×C4⋊C4—152no—
277C4×C22⋊C4—151no—
278#376—151no—
279#376—151no—
280C22×C3×C5C23×C411yescharacteristic
281C2×D15—21no—
282C2×D15—21no—
283C2×D15—21no—
284C2×C5×D3—21no—
285C2×C5×D3—21no—
286C2×C5×D3—21no—
287C2×C3×D5C2×#4112yes—
288C2×C3×D5C2×#4112yes—
289C2×C3×D5H(5,𝔽2)11yescharacteristic
290C2×C3×D52−1+411yescharacteristic
291D3×D5—42no—
292D3×D5—42no—
293ΓL(1,𝔽16)—24no—
294ΓL(1,𝔽16)—42no—
295C3×AGL(1,𝔽5)—42no—
296C3×AGL(1,𝔽5)—42no—
297C3×C4×C5—21no—
298C3×C4×C5—21no—
299C3×C4×C5—21no—
300Dic15—21no—
301Dic15—21no—
302Dic15#11712yes—
303C3×Dic5—21no—
304C3×Dic5—21no—
305C3×Dic5—21no—
306C5×Dic3—21no—
307C5×Dic3—21no—
308C5×Dic3#11712yes—
309C23×D3—51no—
310C22×C3×C4—51no—
311C22×C3×C4—51no—
312C22×C3×C4—51no—
313C22×C3×C4—52no—
314C22×C3×C4—52no—
315C22×Dic3—51no—
316C22×Dic3—52no—
317C22×Dic3—51no—
318C22×Dic3—51no—
319C22×Dic3—52no—
320C2×C4×D3—51no—
321C2×C4×D3—51no—
322C2×C4×D3—51no—
323C2×C4×D3—104no—
324C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
325C3×C4⋊C4—202no—
326C3×C42—51no—
327C3×C42—51no—
328C3×C42—51no—
329C3×C42C2×AGL(1,𝔽5)11yescharacteristic
330(C2×D3)⋊C4—51no—
331(C2×D3)⋊C4—51no—
332(C2×D3)⋊C4—51no—
333(C2×D3)⋊C4—51no—
334(C2×D3)⋊C4—51no—
335(C2×D3)⋊C4—51no—
336(C2×D3)⋊C4—104no—
337(C2×D3)⋊C4—202no—
338(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
339(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
340Dic3⋊C4—51no—
341Dic3⋊C4—51no—
342Dic3⋊C4—51no—
343Dic3⋊C4—51no—
344Dic3⋊C4—51no—
345Dic3⋊C4—51no—
346Dic3⋊C4—104no—
347Dic3⋊C4—202no—
348Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
349Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
350C4×Dic3—51no—
351C4×Dic3—51no—
352C4×Dic3—51no—
353C4×Dic3—104no—
354C4×Dic3—104no—
355C4×Dic3—104no—
356C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
357C23×C5—31no—
358C22×D5—31no—
359C22×D5—61no—
360C22×D5—61no—
361C22×D5—62no—
362C22×D5—62no—
363C22×D5C23×D311yescharacteristic
364C2×AGL(1,𝔽5)—22no—
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)—34no—
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×C4×C5—31no—
377C2×C4×C5—31no—
378C2×C4×C5—31no—
379C2×C4×C5—62no—
380C2×C4×C5C2×C4×D311yescharacteristic
381C2×C4×C5C2×C4×D311yescharacteristic
382C2×C4×C5C2×C4×D311yescharacteristic
383C2×Dic5—31no—
384C2×Dic5—31no—
385C2×Dic5—31no—
386C2×Dic5—62no—
387C2×Dic5C2×C4×D311yescharacteristic
388C2×Dic5C2×C4×D311yescharacteristic
389C2×Dic5C2×C4×D311yescharacteristic
390C4×D5—21no—
391C4×D5—21no—
392C4×D5—22no—
393C4×D5—22no—
394C4×D5—34no—
395C4×D5—62no—
396C4×D5—62no—
397C4×D5—61no—
398C4×D5—61no—
399C4×D5—62no—
400C23×C4—151no—
401#117—31no—
402#117—151no—
403#117—151no—
404#117—151no—
405#117—151no—
406#117—151no—
407#117—151no—
408#117—151no—
409C2×C4⋊C4—52no—
410C2×C4⋊C4—151no—
411C2×C4⋊C4—151no—
412C2×C4⋊C4—152no—
413C2×C4⋊C4—152no—
414C2×C22⋊C4—151no—
415C2×C22⋊C4—151no—
416C2×C22⋊C4—152no—
417C2×C22⋊C4—152no—
418C2×C42—51no—
419C2×C42—151no—
420C2×C42—152no—
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—
431C2×C3×C5C2×#11711yescharacteristic
432C2×C3×C5C4×#4111yescharacteristic
433C2×C3×C5#52011yescharacteristic
434D15—41no—
435C3×D5#55212yes—
436C3×D5#55512yes—
437C5×D3—41no—
438C23×C3—51no—
439C22×D3—51no—
440C22×D3—102no—
441C22×D3—101no—
442C22×D3—102no—
443C22×D3—101no—
444C22×D3C22×AGL(1,𝔽5)11yescharacteristic
445C2×C3×C4—51no—
446C2×C3×C4—51no—
447C2×C3×C4—51no—
448C2×C3×C4—102no—
449C2×C3×C4—101no—
450C2×C3×C4—102no—
451C2×C3×C4—101no—
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×C4C22×AGL(1,𝔽5)11yescharacteristic
459C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
460C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
461C2×Dic3—51no—
462C2×Dic3—54no—
463C2×Dic3—54no—
464C2×Dic3—51no—
465C2×Dic3—51no—
466C2×Dic3—102no—
467C2×Dic3—101no—
468C2×Dic3—101no—
469C2×Dic3—102no—
470C2×Dic3—102no—
471C2×Dic3—102no—
472C2×Dic3—102no—
473C2×Dic3—102no—
474C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
475C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
476C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
477C4×D3—22no—
478C4×D3—102no—
479C4×D3—102no—
480C4×D3—102no—
481C22×C5—61no—
482C22×C5—61no—
483C22×C5—61no—
484C22×C5C22×C4×D311yescharacteristic
485C2×D5—61no—
486C2×D5—61no—
487C2×D5—61no—
488C2×D5—122no—
489C2×D5—122no—
490C2×D5#100411yescharacteristic
491C2×D5#100711yescharacteristic
492C2×D5D3×#4112yes—
493C2×D5D3×#4112yes—
494AGL(1,𝔽5)—42no—
495AGL(1,𝔽5)—42no—
496AGL(1,𝔽5)—64no—
497AGL(1,𝔽5)—122no—
498C4×C5—21no—
499C4×C5—21no—
500C4×C5—21no—
501C4×C5—32no—
502C4×C5—61no—
503C4×C5—61no—
504Dic5—21no—
505Dic5—21no—
506Dic5—21no—
507Dic5—32no—
508Dic5—61no—
509Dic5—61no—
510C24—151no—
511C22×C4—31no—
512C22×C4—51no—
513C22×C4—51no—
514C22×C4—51no—
515C22×C4—52no—
516C22×C4—52no—
517C22×C4—151no—
518C22×C4—151no—
519C22×C4—151no—
520C22×C4—151no—
521C22×C4—151no—
522C22×C4—152no—
523C22×C4—151no—
524C22×C4—152no—
525C22×C4—304no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—151no—
529C4⋊C4—151no—
530C4⋊C4—151no—
531C4⋊C4—151no—
532C4⋊C4—151no—
533C4⋊C4—151no—
534C4⋊C4—202no—
535C4⋊C4—304no—
536C4⋊C4—602no—
537C22⋊C4—31no—
538C22⋊C4—31no—
539C22⋊C4—151no—
540C22⋊C4—151no—
541C22⋊C4—151no—
542C22⋊C4—151no—
543C22⋊C4—151no—
544C22⋊C4—151no—
545C22⋊C4—304no—
546C22⋊C4—602no—
547C42—31no—
548C42—51no—
549C42—51no—
550C42—51no—
551C42—151no—
552C42—151no—
553C42—151no—
554C42—304no—
555C42—304no—
556C42—304no—
557C42D3×AGL(1,𝔽5)11yescharacteristic
558C3×C5#234611yescharacteristic, complemented, Hall
559C22×C3—52no—
560C22×C3—52no—
561C22×C3—51no—
562C22×C3—51no—
563C22×C3C23×AGL(1,𝔽5)11yescharacteristic
564C2×D3—21no—
565C2×D3—21no—
566C2×D3—21no—
567C2×D3—101no—
568C2×D3—101no—
569C2×D3—101no—
570C2×D3—202no—
571C2×D3—202no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—101no—
576C3×C4—101no—
577C3×C4—101no—
578C3×C4—202no—
579C3×C4—202no—
580Dic3—21no—
581Dic3—21no—
582Dic3—52no—
583Dic3—104no—
584Dic3—101no—
585Dic3—101no—
586Dic3—202no—
587Dic3#413012yes—
588C2×C5—121no—
589C2×C5#550411yescharacteristic
590C2×C5D3×#11711yescharacteristic
591C2×C5#552211yescharacteristic
592D5—121no—
593D5#567012yes—
594D5#569312yes—
595C23—31no—
596C23—51no—
597C23—151no—
598C23—302no—
599C23—301no—
600C23—302no—
601C23—301no—
602C2×C4—31no—
603C2×C4—31no—
604C2×C4—31no—
605C2×C4—51no—
606C2×C4—51no—
607C2×C4—51no—
608C2×C4—62no—
609C2×C4—102no—
610C2×C4—101no—
611C2×C4—102no—
612C2×C4—101no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—154no—
620C2×C4—151no—
621C2×C4—154no—
622C2×C4—151no—
623C2×C4—151no—
624C2×C4—302no—
625C2×C4—302no—
626C2×C4—302no—
627C2×C4—301no—
628C2×C4—301no—
629C2×C4—302no—
630C2×C4—302no—
631C2×C4—302no—
632C2×C4—302no—
633C2×C4—302no—
634C2×C4—302no—
635C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
636C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
637C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
638C2×C3—52no—
639C2×C3—52no—
640C2×C3C2×#413011yescharacteristic
641C2×C3#41×AGL(1,𝔽5)11yescharacteristic
642C2×C3#6626611yescharacteristic
643D3—41no—
644D3—201no—
645C5#7415611yescharacteristic, complemented, Sylow
646C22—52no—
647C22—52no—
648C22—51no—
649C22—51no—
650C22—61no—
651C22—61no—
652C22—61no—
653C22—301no—
654C22—301no—
655C22—301no—
656C22—602no—
657C22—602no—
658C22C22×D3×AGL(1,𝔽5)11yescharacteristic
659C4—21no—
660C4—21no—
661C4—21no—
662C4—32no—
663C4—61no—
664C4—61no—
665C4—101no—
666C4—101no—
667C4—101no—
668C4—152no—
669C4—202no—
670C4—202no—
671C4—304no—
672C4—301no—
673C4—301no—
674C4—602no—
675C3#1061713311yescharacteristic, complemented, Sylow
676C2—52no—
677C2—52no—
678C2—121no—
679C2—601no—
680C2D3×#413011yescharacteristic
681C2#1175683511yescharacteristic
682C2#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#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752345C2semidirect
3. C3×#65689C2semidirect
7. #11751837C2semidirect
9. #11751833C2semidirect
10. #11751832C2semidirect
11. #11751746C2semidirect
22. #91761C4semidirect
23. C5×#872C4semidirect
27. #91402C4semidirect
28. #91402C4semidirect
29. #91398C4semidirect
30. #91398C4semidirect
34. #91386C4semidirect
35. #91371C4semidirect
53. #65689D3semidirect
212. #872AGL(1,𝔽5)semidirect
558. C3×C5#2346semidirect
645. C5#74156semidirect
675. C3#10617133semidirect

Maximal subgroups

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

subgroupindex
D5×#8722
#117523452
C3×#656892
#117518562
#117518542
#117518482
#117518372
#117518362
#117518332
#117518322
#117517462
#106171333
#741565