Finite Group Databasebeta

← #72230286

Subgroups — #72230286

Order 2880.

1452 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
1C2×D5×#624C211yesmaximal, characteristic
2#13088746C211yesmaximal, characteristic
3#13088708C212yesmaximal, complemented
4C3⋊D3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
5C3×#91923C212yesmaximal, complemented
6#13088409C214yesmaximal, complemented
7#13088407C212yesmaximal, complemented
8AGL(1,𝔽5)×#624C212yesmaximal, complemented
9D3×#4130—32nomaximal
10C22×D5×C3⋊D3C2211yescharacteristic
11C2×ΓL(1,𝔽16)⋊D3C2212yes—
12C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
13C2×#67155C411yescharacteristic, complemented
14C2×#67149C412yescomplemented
15C2×C5×#624C411yescharacteristic, complemented
16C2×C3×D5×Dic3C2212yes—
17#10624098C2211yescharacteristic
18C3×#6763C2212yes—
19C32×C22⋊AGL(1,𝔽5)C2211yescharacteristic
20D5×#624C411yescharacteristic, complemented
21D5×#624C411yescharacteristic, complemented
22D5×#624C412yescomplemented
23D5×#624C2211yescharacteristic
24D5×#624C2211yescharacteristic
25D5×#624C2212yes—
26#10623978C2212yes—
27Dic3⋊ΓL(1,𝔽16)C2214yescomplemented
28Dic3×ΓL(1,𝔽16)C2214yescomplemented
29(C2×AGL(1,𝔽5))⋊(C3⋊D3)C2212yes—
30C3×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
31C3×Dic3×AGL(1,𝔽5)C2214yescomplemented
32#10594052—51nomaximal, Hall
33C2×C4×D3×D5—32no—
34#91989—32no—
35C3×#4130—32no—
36D3×C22⋊AGL(1,𝔽5)—32no—
37D3×C22⋊AGL(1,𝔽5)—32no—
38D3×C22⋊AGL(1,𝔽5)—61no—
39#91923—32no—
40#91923D312yescomplemented
41D3×C4⋊AGL(1,𝔽5)—34no—
42C4×D3×AGL(1,𝔽5)—34no—
43#91909—34no—
44#91907—34no—
45C22×C3⋊D15C2×C411yescharacteristic
46C22×C5×C3⋊D3C2×C411yescharacteristic
47C22×C32×D5C2311yescharacteristic
48C2×D5×C3⋊D3—24no—
49C2×D5×C3⋊D3C2×C411yescharacteristic
50C2×D5×C3⋊D3C2×C411yescharacteristic
51C2×D5×C3⋊D3C2311yescharacteristic
52C2×D5×C3⋊D3C2311yescharacteristic
53C2×C3⋊ΓL(1,𝔽16)C2312yes—
54C2×C3×ΓL(1,𝔽16)C2314yes—
55C2×C32×AGL(1,𝔽5)C2312yes—
56ΓL(1,𝔽16)⋊D3—24no—
57C3⋊D3×AGL(1,𝔽5)—24no—
58C2×C3×Dic15C2×C412yescomplemented
59C2×C3×C5×Dic3C2×C412yescomplemented
60#67155C2×C411yescharacteristic
61#67155C2×C411yescharacteristic
62#67155C2×C412yescomplemented
63#67149C2×C412yes—
64#67149C2×C412yes—
65#67149C2×C412yescomplemented
66#67149C2×C412yescomplemented
67C5×#624C2×C411yescharacteristic
68C5×#624C2×C411yescharacteristic
69C5×#624C2×C412yescomplemented
70C3×D5×Dic3C2×C412yescomplemented
71C3×D5×Dic3C2×C412yescomplemented
72C3×D5×Dic3C2312yes—
73C3×D5×Dic3C2312yes—
74C2×#4130—91noHall
75C22×#624—51no—
76C22⋊C4×C3⋊D3—51no—
77C3×#877—52no—
78#63974—51no—
79#63955—52no—
80#63883—52no—
81C4×#624—52no—
82#63836—54no—
83C22×D3×D5—32no—
84C22×D3×D5—61no—
85C2×D3×AGL(1,𝔽5)—34no—
86C2×D3×AGL(1,𝔽5)—34no—
87C2×D3×AGL(1,𝔽5)—62no—
88C2×C4×D15—32no—
89C2×C4×C5×D3—32no—
90C2×C3×C4×D5—32no—
91C2×#1200—32no—
92C2×D3×Dic5—32no—
93C2×D5×Dic3C2×D312yes—
94C4×D3×D5—32no—
95C4×D3×D5—32no—
96C4×D3×D5—32no—
97C4×D3×D5—32no—
98C4×D3×D5—32no—
99C4×D3×D5—32no—
100C4×D3×D5—32no—
101C4×D3×D5—32no—
102#6763—32no—
103#6763—61no—
104#6763C2×D312yes—
105C4⋊ΓL(1,𝔽16)—34no—
106C4×ΓL(1,𝔽16)—34no—
107C3×C22⋊AGL(1,𝔽5)—21no—
108C3×C22⋊AGL(1,𝔽5)—32no—
109C3×C22⋊AGL(1,𝔽5)C2×D312yes—
110C3×C4⋊AGL(1,𝔽5)—34no—
111C3×C4×AGL(1,𝔽5)—34no—
112Dic3⋊AGL(1,𝔽5)—34no—
113Dic3⋊AGL(1,𝔽5)C2×D314yescomplemented
114(C2×D3)⋊AGL(1,𝔽5)—34no—
115(C2×D3)⋊AGL(1,𝔽5)—34no—
116(C2×D3)⋊AGL(1,𝔽5)—62no—
117Dic3×AGL(1,𝔽5)—34no—
118Dic3×AGL(1,𝔽5)C2×D314yescomplemented
119D3×#117—152no—
120C22×C32×C5C22×C411yescharacteristic
121C2×C3⋊D15—22no—
122C2×C3⋊D15C22×C411yescharacteristic
123C2×C3⋊D15C22×C411yescharacteristic
124C2×C5×C3⋊D3—22no—
125C2×C5×C3⋊D3C22×C411yescharacteristic
126C2×C5×C3⋊D3C22×C411yescharacteristic
127C2×C32×D5—22no—
128C2×C32×D5C22×C411yescharacteristic
129C2×C32×D5C2411yescharacteristic
130D5×C3⋊D3—22no—
131D5×C3⋊D3—22no—
132D5×C3⋊D3—22no—
133D5×C3⋊D3#4114yes—
134C3⋊ΓL(1,𝔽16)—22no—
135C3×ΓL(1,𝔽16)—24no—
136C32×AGL(1,𝔽5)—22no—
137C3×Dic15C22×C412yes—
138C3×Dic15C22×C412yes—
139C3×C5×Dic3C22×C412yes—
140C3×C5×Dic3C22×C412yes—
141C22×C4×D5—91no—
142C2×C22⋊AGL(1,𝔽5)—91no—
143C2×C22⋊AGL(1,𝔽5)—91no—
144#4130—32no—
145#4130—94no—
146#4130—92no—
147C2×C4⋊AGL(1,𝔽5)—92no—
148C2×C4×AGL(1,𝔽5)—92no—
149C23×C3⋊D3—51no—
150C2×C4×C3⋊D3—52no—
151C22×C3×Dic3—52no—
152C2×#624—51no—
153C2×#624—52no—
154C2×#624—51no—
155C2×#624—51no—
156C2×#624—51no—
157C2×#624—51no—
158C2×#624—52no—
159C2×#624—52no—
160C2×#624—52no—
161C2×#624AGL(1,𝔽5)11yescharacteristic, complemented
162C32×C22⋊C4—51no—
163#3757—51no—
164#3752—52no—
165C3×#217—52no—
166C3×Dic3⋊C4—54no—
167C3×C4×Dic3—54no—
168Dic3⋊Dic3—54no—
169#3722—52no—
170Dic32—54no—
171C22×D15—32no—
172C22×D15—61no—
173C22×C5×D3—32no—
174C22×C5×D3—61no—
175C22×C3×D5—21no—
176C22×C3×D5C22×D312yes—
177C2×D3×D5—32no—
178C2×D3×D5—32no—
179C2×D3×D5—32no—
180C2×D3×D5—32no—
181C2×D3×D5—68no—
182C2×D3×D5—61no—
183C2×D3×D5—61no—
184C2×D3×D5—61no—
185C2×D3×D5—61no—
186C2×D3×D5—124no—
187C2×ΓL(1,𝔽16)—34no—
188C2×ΓL(1,𝔽16)—62no—
189C2×ΓL(1,𝔽16)C22×D314yes—
190C2×C3×AGL(1,𝔽5)—22no—
191C2×C3×AGL(1,𝔽5)—34no—
192C2×C3×AGL(1,𝔽5)C22×D314yes—
193D3×AGL(1,𝔽5)—68no—
194D3×AGL(1,𝔽5)—68no—
195D3×AGL(1,𝔽5)—124no—
196C2×C3×C4×C5—32no—
197C2×Dic15C4×D312yescomplemented
198C4×D15—32no—
199C4×D15—32no—
200C4×D15—32no—
201C4×D15—32no—
202C2×C5×Dic3C4×D312yescomplemented
203C4×C5×D3—32no—
204C4×C5×D3—32no—
205C4×C5×D3—32no—
206C4×C5×D3—32no—
207C2×C3×Dic5—32no—
208C3×C4×D5—32no—
209C3×C4×D5—32no—
210C3×C4×D5—32no—
211C3×C4×D5—32no—
212#1200—32no—
213#1200—32no—
214#1200—32no—
215#1200—32no—
216D3×Dic5—32no—
217D3×Dic5—32no—
218D3×Dic5—32no—
219D3×Dic5—32no—
220D5×Dic3C4×D312yescomplemented
221D5×Dic3C4×D312yescomplemented
222D5×Dic3C22×D312yes—
223D5×Dic3C22×D312yes—
224C22×C4×D3—152no—
225C3×#117—152no—
226#926—152no—
227#892—154no—
228D3×C4⋊C4—154no—
229D3×C22⋊C4—152no—
230D3×C22⋊C4—152no—
231D3×C22⋊C4—301no—
232#877—52no—
233#877—152no—
234#872—154no—
235C42×D3—154no—
236C2×C32×C5—21no—
237C2×C32×C5C23×C411yescharacteristic
238C3⋊D15—21no—
239C3⋊D15#11712yescomplemented
240C5×C3⋊D3—21no—
241C5×C3⋊D3#11712yescomplemented
242C32×D5—21no—
243C32×D5C2×#4112yes—
244C23×D5—91no—
245C22×AGL(1,𝔽5)—92no—
246C22×AGL(1,𝔽5)—92no—
247C22×C4×C5—91no—
248C22×Dic5—91no—
249C2×C4×D5—32no—
250C2×C4×D5—91no—
251C2×C4×D5—91no—
252C2×C4×D5—92no—
253C2×C4×D5—92no—
254C2×C4×D5—91no—
255C2×C4×D5—91no—
256C2×C4×D5—92no—
257C22⋊AGL(1,𝔽5)—32no—
258C22⋊AGL(1,𝔽5)—92no—
259C22⋊AGL(1,𝔽5)—91no—
260C22⋊AGL(1,𝔽5)—92no—
261C22⋊AGL(1,𝔽5)D3211yescharacteristic
262C4⋊AGL(1,𝔽5)—34no—
263C4⋊AGL(1,𝔽5)—94no—
264C4×AGL(1,𝔽5)—34no—
265C4×AGL(1,𝔽5)—94no—
266C23×C32—51no—
267C22×C3⋊D3—51no—
268C22×C3⋊D3—51no—
269C22×C3⋊D3—51no—
270C22×C3⋊D3—51no—
271C22×C3⋊D3—51no—
272C22×C3⋊D3—104no—
273C22×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
274C2×C32×C4—52no—
275C2×C3⋊Dic3—52no—
276C4×C3⋊D3—104no—
277C2×C3×Dic3—52no—
278C2×C3×Dic3—52no—
279C2×C3×Dic3—52no—
280C2×C3×Dic3—52no—
281C2×C3×Dic3—52no—
282C2×C3×Dic3—54no—
283C2×C3×Dic3C2×AGL(1,𝔽5)12yescomplemented
284#624—51no—
285#624—51no—
286#624—52no—
287#624—52no—
288#624—52no—
289#624—52no—
290#624—52no—
291#624—104no—
292#624C2×AGL(1,𝔽5)11yescharacteristic
293#624C2×AGL(1,𝔽5)11yescharacteristic
294#624C2×AGL(1,𝔽5)12yescomplemented
295C2×#117—451noSylow
296C22×C3×C5—21no—
297C22×C3×C5C2×C4×D312yes—
298C2×D15—32no—
299C2×D15—32no—
300C2×D15—61no—
301C2×D15—61no—
302C2×D15—64no—
303C2×D15—122no—
304C2×C5×D3—32no—
305C2×C5×D3—32no—
306C2×C5×D3—61no—
307C2×C5×D3—61no—
308C2×C5×D3—64no—
309C2×C5×D3—122no—
310C2×C3×D5—24no—
311C2×C3×D5—21no—
312C2×C3×D5—21no—
313C2×C3×D5—42no—
314C2×C3×D5C2×C4×D312yes—
315C2×C3×D5C23×D312yes—
316D3×D5—38no—
317D3×D5—64no—
318D3×D5—64no—
319D3×D5—64no—
320D3×D5—64no—
321D3×D5—122no—
322D3×D5—122no—
323D3×D5—122no—
324ΓL(1,𝔽16)—24no—
325ΓL(1,𝔽16)—64no—
326ΓL(1,𝔽16)—122no—
327C3×AGL(1,𝔽5)—24no—
328C3×AGL(1,𝔽5)—42no—
329C3×AGL(1,𝔽5)—64no—
330C3×C4×C5—32no—
331C3×C4×C5—32no—
332Dic15C2×C4×D312yes—
333Dic15C2×C4×D312yes—
334C3×Dic5—32no—
335C3×Dic5—32no—
336C5×Dic3C2×C4×D312yes—
337C5×Dic3C2×C4×D312yes—
338C23×D3—152no—
339C23×D3—301no—
340C22×C3×C4—152no—
341C22×Dic3—52no—
342C2×C4×D3—32no—
343C2×C4×D3—152no—
344C2×C4×D3—152no—
345C2×C4×D3—152no—
346C2×C4×D3—152no—
347C2×C4×D3—152no—
348C2×C4×D3—152no—
349C2×C4×D3—152no—
350C2×C4×D3—152no—
351C2×C4×D3—152no—
352C2×C4×D3—152no—
353C2×C4×D3—152no—
354C2×C4×D3—154no—
355C2×C4×D3—154no—
356C2×C4×D3—302no—
357C3×C4⋊C4—154no—
358C3×C22⋊C4—52no—
359C3×C22⋊C4—101no—
360C3×C22⋊C4—152no—
361C3×C42—154no—
362#217—52no—
363#217—152no—
364#217—301no—
365(C2×D3)⋊C4—154no—
366(C2×D3)⋊C4—154no—
367(C2×D3)⋊C4—302no—
368C4⋊Dic3—154no—
369Dic3⋊C4—54no—
370Dic3⋊C4—154no—
371C4×Dic3—54no—
372C4×Dic3—154no—
373C4×Dic3—154no—
374C32×C5C2×#11711yescharacteristic, complemented, Hall
375C23×C5—91no—
376C22×D5—91no—
377C22×D5—91no—
378C22×D5—91no—
379C22×D5—91no—
380C22×D5—91no—
381C22×D5—184no—
382C22×D5C2×D3211yescharacteristic
383C2×AGL(1,𝔽5)—34no—
384C2×AGL(1,𝔽5)—92no—
385C2×AGL(1,𝔽5)—184no—
386C2×AGL(1,𝔽5)—184no—
387C2×AGL(1,𝔽5)C2×D3212yes—
388C2×C4×C5—32no—
389C2×C4×C5—91no—
390C2×C4×C5—91no—
391C2×C4×C5—92no—
392C2×Dic5—32no—
393C2×Dic5—91no—
394C2×Dic5—91no—
395C2×Dic5—92no—
396C4×D5—32no—
397C4×D5—32no—
398C4×D5—32no—
399C4×D5—32no—
400C4×D5—92no—
401C4×D5—92no—
402C4×D5—92no—
403C4×D5—92no—
404C22×C32—51no—
405C22×C32—51no—
406C22×C32—102no—
407C22×C32C22×AGL(1,𝔽5)11yescharacteristic
408C2×C3⋊D3—22no—
409C2×C3⋊D3—51no—
410C2×C3⋊D3—54no—
411C2×C3⋊D3—51no—
412C2×C3⋊D3—102no—
413C2×C3⋊D3—102no—
414C2×C3⋊D3—102no—
415C2×C3⋊D3—102no—
416C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
417C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
418C32×C4—102no—
419C3⋊Dic3—102no—
420C3×Dic3—52no—
421C3×Dic3—52no—
422C3×Dic3—104no—
423C3×Dic3C22×AGL(1,𝔽5)12yes—
424C3×Dic3C22×AGL(1,𝔽5)12yes—
425C23×C4—451no—
426#117—152no—
427#117—454no—
428#117—452no—
429C2×C4⋊C4—452no—
430C2×C22⋊C4—451no—
431C2×C22⋊C4—451no—
432C2×C42—452no—
433C2×C3×C5—22no—
434C2×C3×C5—21no—
435C2×C3×C5—41no—
436C2×C3×C5C22×C4×D312yes—
437D15—34no—
438D15—62no—
439D15—62no—
440D15—121no—
441C3×D5—22no—
442C3×D5—22no—
443C3×D5—41no—
444C3×D5D3×#4114yes—
445C5×D3—34no—
446C5×D3—62no—
447C5×D3—62no—
448C5×D3—121no—
449C23×C3—52no—
450C23×C3—101no—
451C22×D3—32no—
452C22×D3—61no—
453C22×D3—152no—
454C22×D3—152no—
455C22×D3—152no—
456C22×D3—152no—
457C22×D3—152no—
458C22×D3—301no—
459C22×D3—301no—
460C22×D3—301no—
461C22×D3—301no—
462C22×D3—301no—
463C22×D3—308no—
464C22×D3—604no—
465C2×C3×C4—32no—
466C2×C3×C4—54no—
467C2×C3×C4—102no—
468C2×C3×C4—152no—
469C2×C3×C4—152no—
470C2×C3×C4—152no—
471C2×C3×C4—152no—
472C2×C3×C4—152no—
473C2×C3×C4—154no—
474C2×Dic3—52no—
475C2×Dic3—52no—
476C2×Dic3—52no—
477C2×Dic3—52no—
478C2×Dic3—52no—
479C2×Dic3—54no—
480C2×Dic3—154no—
481C2×Dic3—302no—
482C2×Dic3D3×AGL(1,𝔽5)12yescomplemented
483C4×D3—32no—
484C4×D3—32no—
485C4×D3—32no—
486C4×D3—32no—
487C4×D3—152no—
488C4×D3—152no—
489C4×D3—152no—
490C4×D3—152no—
491C4×D3—152no—
492C4×D3—152no—
493C4×D3—152no—
494C4×D3—152no—
495C4×D3—152no—
496C4×D3—152no—
497C4×D3—152no—
498C4×D3—152no—
499C4×D3—308no—
500C4×D3—308no—
501C4×D3—604no—
502C22×C5—91no—
503C22×C5—91no—
504C22×C5—182no—
505C22×C5C4×D3211yescharacteristic
506C2×D5—22no—
507C2×D5—91no—
508C2×D5—94no—
509C2×D5—91no—
510C2×D5—182no—
511C2×D5—182no—
512C2×D5—182no—
513C2×D5—182no—
514C2×D5C4×D3211yescharacteristic
515C2×D5C22×D3211yescharacteristic
516AGL(1,𝔽5)—22no—
517AGL(1,𝔽5)—64no—
518AGL(1,𝔽5)—182no—
519C4×C5—32no—
520C4×C5—32no—
521Dic5—32no—
522Dic5—32no—
523C2×C32—21no—
524C2×C32—52no—
525C2×C32—101no—
526C2×C32C23×AGL(1,𝔽5)11yescharacteristic
527C3⋊D3—21no—
528C3⋊D3—52no—
529C3⋊D3—101no—
530C3⋊D3#413012yescomplemented
531C24—451no—
532C22×C4—91no—
533C22×C4—152no—
534C22×C4—452no—
535C22×C4—452no—
536C22×C4—451no—
537C22×C4—451no—
538C22×C4—452no—
539C22×C4—451no—
540C22×C4—451no—
541C22×C4—452no—
542C22×C4—451no—
543C22×C4—452no—
544C4⋊C4—154no—
545C4⋊C4—454no—
546C22⋊C4—51no—
547C22⋊C4—152no—
548C22⋊C4—452no—
549C22⋊C4—452no—
550C22⋊C4—451no—
551C42—154no—
552C42—454no—
553C3×C5—21no—
554C3×C5D3×#11712yescomplemented
555C22×C3—21no—
556C22×C3—52no—
557C22×C3—52no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3—104no—
561C22×C3—202no—
562C22×C3C2×D3×AGL(1,𝔽5)12yes—
563C2×D3—32no—
564C2×D3—32no—
565C2×D3—61no—
566C2×D3—61no—
567C2×D3—64no—
568C2×D3—122no—
569C2×D3—158no—
570C2×D3—152no—
571C2×D3—152no—
572C2×D3—304no—
573C2×D3—301no—
574C2×D3—301no—
575C2×D3—304no—
576C2×D3—304no—
577C2×D3—304no—
578C2×D3—304no—
579C2×D3—602no—
580C2×D3—602no—
581C2×D3—602no—
582C2×D3—602no—
583C3×C4—32no—
584C3×C4—32no—
585C3×C4—104no—
586C3×C4—152no—
587C3×C4—152no—
588C3×C4—202no—
589C3×C4—304no—
590Dic3—52no—
591Dic3—52no—
592Dic3—104no—
593Dic3—304no—
594Dic3—602no—
595Dic3C2×D3×AGL(1,𝔽5)12yes—
596Dic3C2×D3×AGL(1,𝔽5)12yes—
597C2×C5—21no—
598C2×C5—92no—
599C2×C5—181no—
600C2×C5C2×C4×D3211yescharacteristic
601D5—21no—
602D5—92no—
603D5—181no—
604D5#6431212yes—
605C32C2×#413011yescharacteristic, complemented, Sylow
606C23—51no—
607C23—91no—
608C23—451no—
609C23—451no—
610C23—451no—
611C23—451no—
612C23—451no—
613C23—904no—
614C2×C4—32no—
615C2×C4—52no—
616C2×C4—91no—
617C2×C4—91no—
618C2×C4—92no—
619C2×C4—152no—
620C2×C4—152no—
621C2×C4—152no—
622C2×C4—152no—
623C2×C4—152no—
624C2×C4—154no—
625C2×C4—452no—
626C2×C4—452no—
627C2×C4—452no—
628C2×C4—452no—
629C2×C4—451no—
630C2×C4—451no—
631C2×C4—452no—
632C2×C4—452no—
633C2×C4—904no—
634C2×C4—904no—
635C2×C3—22no—
636C2×C3—21no—
637C2×C3—41no—
638C2×C3—54no—
639C2×C3—102no—
640C2×C3—102no—
641C2×C3—201no—
642C2×C3C22×D3×AGL(1,𝔽5)12yes—
643D3—34no—
644D3—62no—
645D3—62no—
646D3—121no—
647D3—154no—
648D3—302no—
649D3—302no—
650D3—601no—
651C5#1059405211yescharacteristic, complemented, Sylow
652C22—51no—
653C22—51no—
654C22—91no—
655C22—91no—
656C22—102no—
657C22—182no—
658C22—454no—
659C22—451no—
660C22—451no—
661C22—902no—
662C22—902no—
663C22—902no—
664C22—902no—
665C22D32×AGL(1,𝔽5)11yescharacteristic
666C4—32no—
667C4—32no—
668C4—102no—
669C4—152no—
670C4—152no—
671C4—304no—
672C4—902no—
673C3—21no—
674C3D3×#413012yescomplemented
675C2—21no—
676C2—52no—
677C2—92no—
678C2—101no—
679C2—181no—
680C2—452no—
681C2—901no—
682C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC22×C32×C5C22×C4
prime radicalC22×D5×C3⋊D3C22
cosocleC2×C32×D5C24
hypercenterC22D32×AGL(1,𝔽5)
hypocenterC32×C5C2×#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
3. #13088708C2semidirect
5. C3×#91923C2semidirect
6. #13088409C2semidirect
7. #13088407C2semidirect
8. AGL(1,𝔽5)×#624C2semidirect
13. C2×#67155C4semidirect
14. C2×#67149C4semidirect
15. C2×C5×#624C4semidirect
20. D5×#624C4semidirect
21. D5×#624C4semidirect
22. D5×#624C4semidirect
27. Dic3⋊ΓL(1,𝔽16)C22semidirect
28. Dic3×ΓL(1,𝔽16)C22semidirect
30. C3×Dic3⋊AGL(1,𝔽5)C22semidirect
31. C3×Dic3×AGL(1,𝔽5)C22semidirect
40. #91923D3semidirect
58. C2×C3×Dic15C2×C4semidirect
59. C2×C3×C5×Dic3C2×C4semidirect
62. #67155C2×C4semidirect
65. #67149C2×C4semidirect
66. #67149C2×C4semidirect
69. C5×#624C2×C4semidirect
70. C3×D5×Dic3C2×C4semidirect
71. C3×D5×Dic3C2×C4semidirect
113. Dic3⋊AGL(1,𝔽5)C2×D3semidirect
118. Dic3×AGL(1,𝔽5)C2×D3semidirect
161. C2×#624AGL(1,𝔽5)semidirect
197. C2×Dic15C4×D3semidirect
202. C2×C5×Dic3C4×D3semidirect
220. D5×Dic3C4×D3semidirect
221. D5×Dic3C4×D3semidirect
239. C3⋊D15#117semidirect
241. C5×C3⋊D3#117semidirect
283. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
294. #624C2×AGL(1,𝔽5)semidirect
374. C32×C5C2×#117semidirect
482. C2×Dic3D3×AGL(1,𝔽5)semidirect
530. C3⋊D3#4130semidirect
554. C3×C5D3×#117semidirect
605. C32C2×#4130semidirect
651. C5#10594052semidirect
674. C3D3×#4130semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#6242
#130887462
#130887082
C3⋊D3×C22⋊AGL(1,𝔽5)2
C3×#919232
#130884092
#130884072
AGL(1,𝔽5)×#6242
D3×#41303
#105940525