Finite Group Databasebeta

← #72230301

Subgroups — #72230301

Order 2880.

1556 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×C3⋊D3C211yesmaximal, characteristic
2C3×#91989C212yesmaximal, complemented
3#13088746C212yesmaximal
4#13088735C212yesmaximal, complemented
5#13088733C212yesmaximal, complemented
6C4×ΓL(1,𝔽16)⋊D3C212yesmaximal, complemented
7#13088724C212yesmaximal, complemented
8#13088723C212yesmaximal, complemented
9D3×#4130—32nomaximal
10C22×D5×C3⋊D3C2211yescharacteristic
11C2×ΓL(1,𝔽16)⋊D3C2214yes—
12C2×C4×C3⋊D15C411yescharacteristic, complemented
13C2×C4×C5×C3⋊D3C411yescharacteristic, complemented
14C2×C32×C4×D5C2211yescharacteristic
15C2×#67137C411yescharacteristic, complemented
16C2×C3⋊D3×Dic5C411yescharacteristic, complemented
17C2×D5×C3⋊Dic3C2211yescharacteristic
18C4×D5×C3⋊D3C411yescharacteristic, complemented
19C4×D5×C3⋊D3C411yescharacteristic, complemented
20C4×D5×C3⋊D3C411yescharacteristic, complemented
21C4×D5×C3⋊D3C411yescharacteristic, complemented
22C4×D5×C3⋊D3C2211yescharacteristic
23C4×D5×C3⋊D3C2211yescharacteristic
24C4×D5×C3⋊D3C2211yescharacteristic
25C4×D5×C3⋊D3C2211yescharacteristic
26C3×#6763C2214yes—
27C3×C4⋊ΓL(1,𝔽16)C2214yescomplemented
28C3×C4×ΓL(1,𝔽16)C2214yescomplemented
29#10623979C2214yescomplemented
30#10623978C2214yes—
31ΓL(1,𝔽16)⋊Dic3C2214yescomplemented
32#10594969—51nomaximal, Hall
33C2×C4×D3×D5—32no—
34C2×C4×D3×D5—61no—
35#91989D312yescomplemented
36C3×#4130—32no—
37D3×C22⋊AGL(1,𝔽5)—34no—
38#91923—34no—
39D3×C4⋊AGL(1,𝔽5)—34no—
40C4×D3×AGL(1,𝔽5)—34no—
41#91909—34no—
42#91907—34no—
43C22×C3⋊D15C2×C411yescharacteristic
44C22×C5×C3⋊D3C2×C411yescharacteristic
45C22×C32×D5C2311yescharacteristic
46C2×D5×C3⋊D3—24no—
47C2×D5×C3⋊D3C2×C411yescharacteristic
48C2×D5×C3⋊D3C2×C411yescharacteristic
49C2×D5×C3⋊D3C2311yescharacteristic
50C2×D5×C3⋊D3C2311yescharacteristic
51C2×C3×ΓL(1,𝔽16)C2318yes—
52ΓL(1,𝔽16)⋊D3—28no—
53C2×C32×C4×C5C2×C411yescharacteristic, complemented
54C2×C3⋊Dic15C2×C411yescharacteristic, complemented
55C4×C3⋊D15C2×C411yescharacteristic
56C4×C3⋊D15C2×C411yescharacteristic
57C4×C3⋊D15C2×C411yescharacteristic, complemented
58C4×C3⋊D15C2×C411yescharacteristic, complemented
59C2×C5×C3⋊Dic3C2×C411yescharacteristic, complemented
60C4×C5×C3⋊D3C2×C411yescharacteristic
61C4×C5×C3⋊D3C2×C411yescharacteristic
62C4×C5×C3⋊D3C2×C411yescharacteristic, complemented
63C4×C5×C3⋊D3C2×C411yescharacteristic, complemented
64C2×C32×Dic5C2×C411yescharacteristic, complemented
65C32×C4×D5C2×C411yescharacteristic, complemented
66C32×C4×D5C2×C411yescharacteristic, complemented
67C32×C4×D5C2311yescharacteristic
68C32×C4×D5C2311yescharacteristic
69#67137C2×C411yescharacteristic
70#67137C2×C411yescharacteristic
71#67137C2×C411yescharacteristic, complemented
72#67137C2×C411yescharacteristic, complemented
73C3⋊D3×Dic5C2×C411yescharacteristic
74C3⋊D3×Dic5C2×C411yescharacteristic
75C3⋊D3×Dic5C2×C411yescharacteristic, complemented
76C3⋊D3×Dic5C2×C411yescharacteristic, complemented
77D5×C3⋊Dic3C2×C411yescharacteristic, complemented
78D5×C3⋊Dic3C2×C411yescharacteristic, complemented
79D5×C3⋊Dic3C2311yescharacteristic
80D5×C3⋊Dic3C2311yescharacteristic
81C2×#4130—91noHall
82C22×C4×C3⋊D3—51no—
83C3×#926—52no—
84#63974—52no—
85#63957—52no—
86#63900—52no—
87C4×#624—52no—
88#63874—52no—
89#63849—52no—
90C22×D3×D5—32no—
91C22×D3×D5—61no—
92C2×D3×AGL(1,𝔽5)—38no—
93C2×C4×D15—32no—
94C2×C4×D15—61no—
95C2×C4×C5×D3—32no—
96C2×C4×C5×D3—61no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5C2×D312yes—
99C2×#1200—32no—
100C2×#1200—61no—
101C2×D3×Dic5—32no—
102C2×D3×Dic5—61no—
103C2×D5×Dic3—32no—
104C2×D5×Dic3—61no—
105C4×D3×D5—32no—
106C4×D3×D5—32no—
107C4×D3×D5—32no—
108C4×D3×D5—32no—
109C4×D3×D5—32no—
110C4×D3×D5—32no—
111C4×D3×D5—32no—
112C4×D3×D5—32no—
113C4×D3×D5—61no—
114C4×D3×D5—61no—
115C4×D3×D5—61no—
116C4×D3×D5—61no—
117C4×D3×D5—61no—
118C4×D3×D5—61no—
119C4×D3×D5—61no—
120C4×D3×D5—61no—
121#6763C2×D314yes—
122C4⋊ΓL(1,𝔽16)C2×D314yescomplemented
123C4×ΓL(1,𝔽16)C2×D314yescomplemented
124C3×C22⋊AGL(1,𝔽5)—34no—
125C3×C4⋊AGL(1,𝔽5)—34no—
126C3×C4×AGL(1,𝔽5)—34no—
127Dic3⋊AGL(1,𝔽5)—38no—
128(C2×D3)⋊AGL(1,𝔽5)—38no—
129Dic3×AGL(1,𝔽5)—38no—
130D3×#117—152no—
131C22×C32×C5C22×C411yescharacteristic
132C2×C3⋊D15—22no—
133C2×C3⋊D15C22×C411yescharacteristic
134C2×C3⋊D15C22×C411yescharacteristic
135C2×C5×C3⋊D3—22no—
136C2×C5×C3⋊D3C22×C411yescharacteristic
137C2×C5×C3⋊D3C22×C411yescharacteristic
138C2×C32×D5—22no—
139C2×C32×D5C22×C411yescharacteristic
140C2×C32×D5C2411yescharacteristic
141D5×C3⋊D3—22no—
142D5×C3⋊D3—22no—
143D5×C3⋊D3—22no—
144D5×C3⋊D3#4114yes—
145C3×ΓL(1,𝔽16)—28no—
146C32×C4×C5C22×C411yescharacteristic
147C32×C4×C5C22×C411yescharacteristic
148C3⋊Dic15C22×C411yescharacteristic
149C3⋊Dic15C22×C411yescharacteristic
150C5×C3⋊Dic3C22×C411yescharacteristic
151C5×C3⋊Dic3C22×C411yescharacteristic
152C32×Dic5C22×C411yescharacteristic
153C32×Dic5C22×C411yescharacteristic
154C22×C4×D5—91no—
155C2×C22⋊AGL(1,𝔽5)—92no—
156#4130—32no—
157#4130—92no—
158#4130—92no—
159#4130—92no—
160C2×C4⋊AGL(1,𝔽5)—92no—
161C2×C4×AGL(1,𝔽5)—92no—
162C23×C3⋊D3—51no—
163C22×C32×C4—51no—
164C22×C3⋊Dic3—51no—
165C2×C4×C3⋊D3—51no—
166C2×C4×C3⋊D3—51no—
167C2×C4×C3⋊D3—51no—
168C2×C4×C3⋊D3—51no—
169C2×C4×C3⋊D3—51no—
170C2×C4×C3⋊D3—51no—
171C2×C4×C3⋊D3—51no—
172C2×C4×C3⋊D3—51no—
173C2×C4×C3⋊D3—51no—
174C2×C4×C3⋊D3—51no—
175C2×C4×C3⋊D3—51no—
176C2×C4×C3⋊D3AGL(1,𝔽5)11yescharacteristic, complemented
177C2×#624—54no—
178C3×#217—54no—
179C3×C4⋊Dic3—54no—
180C3×C4×Dic3—54no—
181#3724—54no—
182#3722—54no—
183Dic32—54no—
184C22×D15—32no—
185C22×D15—61no—
186C22×C5×D3—32no—
187C22×C5×D3—61no—
188C22×C3×D5—21no—
189C22×C3×D5C22×D312yes—
190C2×D3×D5—32no—
191C2×D3×D5—32no—
192C2×D3×D5—32no—
193C2×D3×D5—32no—
194C2×D3×D5—68no—
195C2×D3×D5—61no—
196C2×D3×D5—64no—
197C2×D3×D5—64no—
198C2×D3×D5—61no—
199C2×D3×D5—61no—
200C2×D3×D5—61no—
201C2×ΓL(1,𝔽16)C22×D318yes—
202C2×C3×AGL(1,𝔽5)—38no—
203D3×AGL(1,𝔽5)—616no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5C4×D312yescomplemented
206C2×Dic15—32no—
207C2×Dic15—61no—
208C4×D15—32no—
209C4×D15—32no—
210C4×D15—32no—
211C4×D15—32no—
212C4×D15—61no—
213C4×D15—61no—
214C4×D15—61no—
215C4×D15—61no—
216C2×C5×Dic3—32no—
217C2×C5×Dic3—61no—
218C4×C5×D3—32no—
219C4×C5×D3—32no—
220C4×C5×D3—32no—
221C4×C5×D3—32no—
222C4×C5×D3—61no—
223C4×C5×D3—61no—
224C4×C5×D3—61no—
225C4×C5×D3—61no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5C4×D312yescomplemented
228C3×C4×D5—21no—
229C3×C4×D5—21no—
230C3×C4×D5—21no—
231C3×C4×D5—21no—
232C3×C4×D5C4×D312yescomplemented
233C3×C4×D5C4×D312yescomplemented
234C3×C4×D5C22×D312yes—
235C3×C4×D5C22×D312yes—
236#1200—32no—
237#1200—32no—
238#1200—32no—
239#1200—32no—
240#1200—61no—
241#1200—61no—
242#1200—61no—
243#1200—61no—
244D3×Dic5—32no—
245D3×Dic5—32no—
246D3×Dic5—32no—
247D3×Dic5—32no—
248D3×Dic5—61no—
249D3×Dic5—61no—
250D3×Dic5—61no—
251D3×Dic5—61no—
252D5×Dic3—32no—
253D5×Dic3—32no—
254D5×Dic3—32no—
255D5×Dic3—32no—
256D5×Dic3—61no—
257D5×Dic3—61no—
258D5×Dic3—61no—
259D5×Dic3—61no—
260C22×C4×D3—152no—
261C22×C4×D3—301no—
262C3×#117—152no—
263#926—52no—
264#892—154no—
265D3×C4⋊C4—154no—
266D3×C22⋊C4—154no—
267#877—154no—
268#872—154no—
269C42×D3—154no—
270C2×C32×C5—21no—
271C2×C32×C5C23×C411yescharacteristic
272C3⋊D15—21no—
273C3⋊D15#11712yescomplemented
274C5×C3⋊D3—21no—
275C5×C3⋊D3#11712yescomplemented
276C32×D5—21no—
277C32×D5C2×#4112yes—
278C23×D5—91no—
279C22×AGL(1,𝔽5)—94no—
280C22×C4×C5—91no—
281C22×Dic5—91no—
282C2×C4×D5—91no—
283C2×C4×D5—91no—
284C2×C4×D5—91no—
285C2×C4×D5—91no—
286C2×C4×D5—91no—
287C2×C4×D5—91no—
288C2×C4×D5—91no—
289C2×C4×D5—91no—
290C2×C4×D5—91no—
291C2×C4×D5—91no—
292C2×C4×D5—91no—
293C2×C4×D5D3211yescharacteristic
294C22⋊AGL(1,𝔽5)—34no—
295C22⋊AGL(1,𝔽5)—94no—
296C4⋊AGL(1,𝔽5)—34no—
297C4⋊AGL(1,𝔽5)—94no—
298C4×AGL(1,𝔽5)—34no—
299C4×AGL(1,𝔽5)—94no—
300C23×C32—51no—
301C22×C3⋊D3—51no—
302C22×C3⋊D3—51no—
303C22×C3⋊D3—51no—
304C22×C3⋊D3—51no—
305C22×C3⋊D3—51no—
306C22×C3⋊D3—104no—
307C22×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
308C2×C32×C4—51no—
309C2×C32×C4—51no—
310C2×C32×C4—51no—
311C2×C32×C4—51no—
312C2×C32×C4—51no—
313C2×C32×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
314C2×C3⋊Dic3—51no—
315C2×C3⋊Dic3—51no—
316C2×C3⋊Dic3—51no—
317C2×C3⋊Dic3—51no—
318C2×C3⋊Dic3—51no—
319C2×C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
320C4×C3⋊D3—51no—
321C4×C3⋊D3—51no—
322C4×C3⋊D3—51no—
323C4×C3⋊D3—51no—
324C4×C3⋊D3—51no—
325C4×C3⋊D3—51no—
326C4×C3⋊D3—51no—
327C4×C3⋊D3—51no—
328C4×C3⋊D3—51no—
329C4×C3⋊D3—51no—
330C4×C3⋊D3—51no—
331C4×C3⋊D3—51no—
332C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
333C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
334C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
335C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
336C2×C3×Dic3—58no—
337#624—108no—
338C2×#117—451noSylow
339C22×C3×C5—21no—
340C22×C3×C5C2×C4×D312yes—
341C2×D15—32no—
342C2×D15—32no—
343C2×D15—61no—
344C2×D15—61no—
345C2×D15—64no—
346C2×D15—62no—
347C2×D15—62no—
348C2×C5×D3—32no—
349C2×C5×D3—32no—
350C2×C5×D3—61no—
351C2×C5×D3—61no—
352C2×C5×D3—64no—
353C2×C5×D3—62no—
354C2×C5×D3—62no—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5—24no—
358C2×C3×D5—21no—
359C2×C3×D5—21no—
360C2×C3×D5C2×C4×D312yes—
361C2×C3×D5C23×D312yes—
362D3×D5—38no—
363D3×D5—64no—
364D3×D5—64no—
365D3×D5—64no—
366D3×D5—62no—
367D3×D5—62no—
368D3×D5—62no—
369D3×D5—62no—
370D3×D5—62no—
371D3×D5—62no—
372D3×D5—64no—
373ΓL(1,𝔽16)—28no—
374C3×AGL(1,𝔽5)—68no—
375C3×C4×C5—21no—
376C3×C4×C5—21no—
377C3×C4×C5C2×C4×D312yes—
378C3×C4×C5C2×C4×D312yes—
379Dic15—32no—
380Dic15—32no—
381Dic15—61no—
382Dic15—61no—
383C3×Dic5—21no—
384C3×Dic5—21no—
385C3×Dic5C2×C4×D312yes—
386C3×Dic5C2×C4×D312yes—
387C5×Dic3—32no—
388C5×Dic3—32no—
389C5×Dic3—61no—
390C5×Dic3—61no—
391C23×D3—152no—
392C23×D3—301no—
393C22×C3×C4—52no—
394C22×C3×C4—101no—
395C22×Dic3—152no—
396C22×Dic3—301no—
397C2×C4×D3—32no—
398C2×C4×D3—61no—
399C2×C4×D3—152no—
400C2×C4×D3—152no—
401C2×C4×D3—152no—
402C2×C4×D3—152no—
403C2×C4×D3—152no—
404C2×C4×D3—152no—
405C2×C4×D3—152no—
406C2×C4×D3—152no—
407C2×C4×D3—152no—
408C2×C4×D3—152no—
409C2×C4×D3—152no—
410C2×C4×D3—158no—
411C2×C4×D3—301no—
412C2×C4×D3—301no—
413C2×C4×D3—301no—
414C2×C4×D3—301no—
415C2×C4×D3—301no—
416C2×C4×D3—301no—
417C2×C4×D3—301no—
418C2×C4×D3—301no—
419C2×C4×D3—301no—
420C2×C4×D3—301no—
421C2×C4×D3—301no—
422C3×C4⋊C4—154no—
423C3×C22⋊C4—154no—
424C3×C42—154no—
425#217—54no—
426(C2×D3)⋊C4—158no—
427C4⋊Dic3—54no—
428Dic3⋊C4—158no—
429C4×Dic3—54no—
430C4×Dic3—158no—
431C32×C5C2×#11711yescharacteristic, complemented, Hall
432C23×C5—91no—
433C22×D5—91no—
434C22×D5—91no—
435C22×D5—91no—
436C22×D5—91no—
437C22×D5—91no—
438C22×D5—184no—
439C22×D5C2×D3211yescharacteristic
440C2×AGL(1,𝔽5)—38no—
441C2×AGL(1,𝔽5)—188no—
442C2×C4×C5—91no—
443C2×C4×C5—91no—
444C2×C4×C5—91no—
445C2×C4×C5—91no—
446C2×C4×C5—91no—
447C2×C4×C5#62411yescharacteristic, complemented
448C2×Dic5—91no—
449C2×Dic5—91no—
450C2×Dic5—91no—
451C2×Dic5—91no—
452C2×Dic5—91no—
453C2×Dic5#62411yescharacteristic, complemented
454C4×D5—91no—
455C4×D5—91no—
456C4×D5—91no—
457C4×D5—91no—
458C4×D5—91no—
459C4×D5—91no—
460C4×D5—91no—
461C4×D5—91no—
462C4×D5—91no—
463C4×D5—91no—
464C4×D5—91no—
465C4×D5—91no—
466C4×D5#62411yescharacteristic, complemented
467C4×D5#62411yescharacteristic, complemented
468C4×D5C2×D3211yescharacteristic
469C4×D5C2×D3211yescharacteristic
470C22×C32—51no—
471C22×C32—51no—
472C22×C32—102no—
473C22×C32C22×AGL(1,𝔽5)11yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—51no—
476C2×C3⋊D3—54no—
477C2×C3⋊D3—51no—
478C2×C3⋊D3—102no—
479C2×C3⋊D3—102no—
480C2×C3⋊D3—102no—
481C2×C3⋊D3—102no—
482C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
483C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
484C32×C4—51no—
485C32×C4—51no—
486C32×C4C22×AGL(1,𝔽5)11yescharacteristic
487C32×C4C22×AGL(1,𝔽5)11yescharacteristic
488C3⋊Dic3—51no—
489C3⋊Dic3—51no—
490C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
491C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
492C3×Dic3—108no—
493C23×C4—451no—
494#117—152no—
495#117—452no—
496#117—452no—
497#117—452no—
498C2×C4⋊C4—452no—
499C2×C22⋊C4—452no—
500C2×C42—452no—
501C2×C3×C5—21no—
502C2×C3×C5—21no—
503C2×C3×C5—22no—
504C2×C3×C5—21no—
505C2×C3×C5C22×C4×D312yes—
506D15—34no—
507D15—62no—
508D15—61no—
509D15—61no—
510D15—62no—
511C3×D5—21no—
512C3×D5—21no—
513C3×D5—22no—
514C3×D5—22no—
515C3×D5D3×#4114yes—
516C5×D3—34no—
517C5×D3—62no—
518C5×D3—61no—
519C5×D3—61no—
520C5×D3—62no—
521C23×C3—52no—
522C23×C3—101no—
523C22×D3—32no—
524C22×D3—61no—
525C22×D3—152no—
526C22×D3—152no—
527C22×D3—152no—
528C22×D3—152no—
529C22×D3—152no—
530C22×D3—301no—
531C22×D3—301no—
532C22×D3—301no—
533C22×D3—301no—
534C22×D3—301no—
535C22×D3—308no—
536C22×D3—304no—
537C22×D3—304no—
538C2×C3×C4—21no—
539C2×C3×C4—52no—
540C2×C3×C4—52no—
541C2×C3×C4—52no—
542C2×C3×C4—52no—
543C2×C3×C4—52no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—158no—
550C2×C3×C4D3×AGL(1,𝔽5)12yescomplemented
551C2×Dic3—32no—
552C2×Dic3—58no—
553C2×Dic3—61no—
554C2×Dic3—152no—
555C2×Dic3—152no—
556C2×Dic3—152no—
557C2×Dic3—152no—
558C2×Dic3—152no—
559C2×Dic3—301no—
560C2×Dic3—301no—
561C2×Dic3—301no—
562C2×Dic3—301no—
563C2×Dic3—301no—
564C4×D3—32no—
565C4×D3—32no—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—152no—
573C4×D3—152no—
574C4×D3—152no—
575C4×D3—152no—
576C4×D3—152no—
577C4×D3—152no—
578C4×D3—152no—
579C4×D3—152no—
580C4×D3—152no—
581C4×D3—152no—
582C4×D3—152no—
583C4×D3—152no—
584C4×D3—301no—
585C4×D3—301no—
586C4×D3—301no—
587C4×D3—301no—
588C4×D3—301no—
589C4×D3—301no—
590C4×D3—301no—
591C4×D3—301no—
592C4×D3—301no—
593C4×D3—301no—
594C4×D3—301no—
595C4×D3—301no—
596C4×D3—3016no—
597C22×C5—91no—
598C22×C5—91no—
599C22×C5—182no—
600C22×C5C2×#62411yescharacteristic
601C2×D5—22no—
602C2×D5—91no—
603C2×D5—94no—
604C2×D5—91no—
605C2×D5—182no—
606C2×D5—182no—
607C2×D5—182no—
608C2×D5—182no—
609C2×D5C2×#62411yescharacteristic
610C2×D5C22×D3211yescharacteristic
611AGL(1,𝔽5)—68no—
612C4×C5—91no—
613C4×C5—91no—
614C4×C5C2×#62411yescharacteristic
615C4×C5C2×#62411yescharacteristic
616Dic5—91no—
617Dic5—91no—
618Dic5C2×#62411yescharacteristic
619Dic5C2×#62411yescharacteristic
620C2×C32—21no—
621C2×C32—52no—
622C2×C32—101no—
623C2×C32C23×AGL(1,𝔽5)11yescharacteristic
624C3⋊D3—21no—
625C3⋊D3—52no—
626C3⋊D3—101no—
627C3⋊D3#413012yescomplemented
628C24—451no—
629C22×C4—51no—
630C22×C4—91no—
631C22×C4—451no—
632C22×C4—451no—
633C22×C4—451no—
634C22×C4—451no—
635C22×C4—451no—
636C22×C4—451no—
637C22×C4—451no—
638C22×C4—451no—
639C22×C4—451no—
640C22×C4—451no—
641C22×C4—451no—
642C22×C4—454no—
643C22×C4—451no—
644C4⋊C4—154no—
645C4⋊C4—454no—
646C22⋊C4—154no—
647C22⋊C4—454no—
648C42—154no—
649C42—454no—
650C3×C5—21no—
651C3×C5D3×#11712yescomplemented
652C22×C3—21no—
653C22×C3—52no—
654C22×C3—52no—
655C22×C3—101no—
656C22×C3—101no—
657C22×C3—104no—
658C22×C3—102no—
659C22×C3—102no—
660C22×C3C2×D3×AGL(1,𝔽5)12yes—
661C2×D3—32no—
662C2×D3—32no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—64no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—158no—
669C2×D3—152no—
670C2×D3—152no—
671C2×D3—304no—
672C2×D3—301no—
673C2×D3—301no—
674C2×D3—304no—
675C2×D3—304no—
676C2×D3—304no—
677C2×D3—302no—
678C2×D3—302no—
679C2×D3—302no—
680C2×D3—302no—
681C2×D3—302no—
682C2×D3—302no—
683C2×D3—304no—
684C2×D3—302no—
685C2×D3—302no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—52no—
689C3×C4—52no—
690C3×C4—101no—
691C3×C4—101no—
692C3×C4—308no—
693C3×C4C2×D3×AGL(1,𝔽5)12yes—
694C3×C4C2×D3×AGL(1,𝔽5)12yes—
695Dic3—32no—
696Dic3—32no—
697Dic3—61no—
698Dic3—61no—
699Dic3—108no—
700Dic3—152no—
701Dic3—152no—
702Dic3—301no—
703Dic3—301no—
704C2×C5—21no—
705C2×C5—92no—
706C2×C5—181no—
707C2×C5C22×#62411yescharacteristic
708D5—21no—
709D5—92no—
710D5—181no—
711D5#6430612yes—
712C32C2×#413011yescharacteristic, complemented, Sylow
713C23—51no—
714C23—91no—
715C23—451no—
716C23—451no—
717C23—451no—
718C23—451no—
719C23—451no—
720C23—904no—
721C2×C4—51no—
722C2×C4—51no—
723C2×C4—51no—
724C2×C4—51no—
725C2×C4—51no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—158no—
732C2×C4—451no—
733C2×C4—451no—
734C2×C4—451no—
735C2×C4—451no—
736C2×C4—451no—
737C2×C4—451no—
738C2×C4—451no—
739C2×C4—451no—
740C2×C4—451no—
741C2×C4—451no—
742C2×C4—451no—
743C2×C4—451no—
744C2×C4—451no—
745C2×C4—451no—
746C2×C4—451no—
747C2×C4—451no—
748C2×C4—451no—
749C2×C4—908no—
750C2×C4ΓL(1,𝔽16)⋊D311yescharacteristic, complemented
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—54no—
756C2×C3—102no—
757C2×C3—101no—
758C2×C3—101no—
759C2×C3—102no—
760C2×C3C22×D3×AGL(1,𝔽5)12yes—
761D3—34no—
762D3—62no—
763D3—61no—
764D3—61no—
765D3—62no—
766D3—154no—
767D3—302no—
768D3—301no—
769D3—301no—
770D3—302no—
771C5#1059496911yescharacteristic, complemented, Sylow
772C22—51no—
773C22—51no—
774C22—91no—
775C22—91no—
776C22—102no—
777C22—182no—
778C22—454no—
779C22—451no—
780C22—451no—
781C22—902no—
782C22—902no—
783C22—902no—
784C22—902no—
785C22C2×ΓL(1,𝔽16)⋊D311yescharacteristic
786C4—51no—
787C4—51no—
788C4—91no—
789C4—91no—
790C4—308no—
791C4—451no—
792C4—451no—
793C4C2×ΓL(1,𝔽16)⋊D311yescharacteristic
794C4C2×ΓL(1,𝔽16)⋊D311yescharacteristic
795C3—21no—
796C3D3×#413012yescomplemented
797C2—21no—
798C2—52no—
799C2—92no—
800C2—101no—
801C2—181no—
802C2—452no—
803C2—901no—
804C2C22×ΓL(1,𝔽16)⋊D311yescharacteristic
subgroupG/H
centerC4C2×ΓL(1,𝔽16)⋊D3
commutator, socleC2×C32×C5C23×C4
FrattiniC2C22×ΓL(1,𝔽16)⋊D3
FittingC2×C32×C4×C5C2×C4
prime radicalC22×D5×C3⋊D3C22
cosocleC2×C32×D5C24
hypercenterC2×C4ΓL(1,𝔽16)⋊D3
hypocenterC32×C5C2×#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C3×#91989C2semidirect
4. #13088735C2semidirect
5. #13088733C2semidirect
6. C4×ΓL(1,𝔽16)⋊D3C2semidirect
7. #13088724C2semidirect
8. #13088723C2semidirect
12. C2×C4×C3⋊D15C4semidirect
13. C2×C4×C5×C3⋊D3C4semidirect
15. C2×#67137C4semidirect
16. C2×C3⋊D3×Dic5C4semidirect
18. C4×D5×C3⋊D3C4semidirect
19. C4×D5×C3⋊D3C4semidirect
20. C4×D5×C3⋊D3C4semidirect
21. C4×D5×C3⋊D3C4semidirect
27. C3×C4⋊ΓL(1,𝔽16)C22semidirect
28. C3×C4×ΓL(1,𝔽16)C22semidirect
29. #10623979C22semidirect
31. ΓL(1,𝔽16)⋊Dic3C22semidirect
35. #91989D3semidirect
53. C2×C32×C4×C5C2×C4semidirect
54. C2×C3⋊Dic15C2×C4semidirect
57. C4×C3⋊D15C2×C4semidirect
58. C4×C3⋊D15C2×C4semidirect
59. C2×C5×C3⋊Dic3C2×C4semidirect
62. C4×C5×C3⋊D3C2×C4semidirect
63. C4×C5×C3⋊D3C2×C4semidirect
64. C2×C32×Dic5C2×C4semidirect
65. C32×C4×D5C2×C4semidirect
66. C32×C4×D5C2×C4semidirect
71. #67137C2×C4semidirect
72. #67137C2×C4semidirect
75. C3⋊D3×Dic5C2×C4semidirect
76. C3⋊D3×Dic5C2×C4semidirect
77. D5×C3⋊Dic3C2×C4semidirect
78. D5×C3⋊Dic3C2×C4semidirect
122. C4⋊ΓL(1,𝔽16)C2×D3semidirect
123. C4×ΓL(1,𝔽16)C2×D3semidirect
176. C2×C4×C3⋊D3AGL(1,𝔽5)semidirect
205. C2×C3×C4×C5C4×D3semidirect
227. C2×C3×Dic5C4×D3semidirect
232. C3×C4×D5C4×D3semidirect
233. C3×C4×D5C4×D3semidirect
273. C3⋊D15#117semidirect
275. C5×C3⋊D3#117semidirect
313. C2×C32×C4C2×AGL(1,𝔽5)semidirect
319. C2×C3⋊Dic3C2×AGL(1,𝔽5)semidirect
334. C4×C3⋊D3C2×AGL(1,𝔽5)semidirect
335. C4×C3⋊D3C2×AGL(1,𝔽5)semidirect
431. C32×C5C2×#117semidirect
447. C2×C4×C5#624semidirect
453. C2×Dic5#624semidirect
466. C4×D5#624semidirect
467. C4×D5#624semidirect
550. C2×C3×C4D3×AGL(1,𝔽5)semidirect
627. C3⋊D3#4130semidirect
651. C3×C5D3×#117semidirect
712. C32C2×#4130semidirect
750. C2×C4ΓL(1,𝔽16)⋊D3semidirect
771. C5#10594969semidirect
796. C3D3×#4130semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×C3⋊D32
C3×#919892
#130887462
#130887352
#130887332
C4×ΓL(1,𝔽16)⋊D32
#130887242
#130887232
D3×#41303
#105949695