Finite Group Databasebeta

← #72230254

Subgroups — #72230254

Order 2880.

1428 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D32×D5C211yesmaximal, characteristic
2C4×ΓL(1,𝔽16)⋊D3C211yesmaximal, characteristic, complemented
3#13088694C212yesmaximal, complemented
4C4×C3⋊D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5C3×#91909C212yesmaximal, complemented
6#13088410C214yesmaximal, complemented
7#13088407C212yesmaximal, complemented
8#13088405C212yesmaximal
9D3×#4130—32nomaximal
10C2×D32×D5C2211yescharacteristic
11C2×ΓL(1,𝔽16)⋊D3C2212yes—
12C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
13C4×(C3⋊D3)⋊D5C411yescharacteristic, complemented
14C4×D3×D15C412yescomplemented
15C4×C5×D32C411yescharacteristic, complemented
16C4×D5×C3⋊D3C2211yescharacteristic
17C3×C4×D3×D5C2212yes—
18C4×C3⋊ΓL(1,𝔽16)C2211yescharacteristic, complemented
19C3×C4×ΓL(1,𝔽16)C2212yescomplemented
20C32×C4×AGL(1,𝔽5)C2211yescharacteristic, complemented
21#10624022C411yescharacteristic, complemented
22D3×#1200C412yescomplemented
23D32×Dic5C411yescharacteristic, complemented
24D5×#624C2211yescharacteristic
25D3×D5×Dic3C2212yes—
26ΓL(1,𝔽16)⋊Dic3C2212yescomplemented
27Dic3⋊ΓL(1,𝔽16)C2214yescomplemented
28(C2×D3)⋊ΓL(1,𝔽16)C2214yes—
29AGL(1,𝔽5)×C3⋊Dic3C2212yescomplemented
30C3×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
31C3×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
32#10593992—51nomaximal, Hall
33C2×C4×D3×D5—32no—
34#91989—32no—
35C3×#4130—32no—
36D3×C22⋊AGL(1,𝔽5)—34no—
37#91923—34no—
38D3×C4⋊AGL(1,𝔽5)—34no—
39C4×D3×AGL(1,𝔽5)—32no—
40C4×D3×AGL(1,𝔽5)—32no—
41C4×D3×AGL(1,𝔽5)—61no—
42#91909—32no—
43#91909D312yescomplemented
44#91907—34no—
45C2×(C3⋊D3)⋊D5C2×C411yescharacteristic
46C2×D3×D15C2×C412yes—
47C2×C5×D32C2×C411yescharacteristic
48C2×D5×C3⋊D3C2311yescharacteristic
49C2×C3×D3×D5C2312yes—
50C2×C3⋊ΓL(1,𝔽16)C2312yes—
51C2×C3×ΓL(1,𝔽16)C2314yes—
52C2×C32×AGL(1,𝔽5)C2312yes—
53D32×D5—24no—
54ΓL(1,𝔽16)⋊D3—24no—
55C3⋊D3×AGL(1,𝔽5)—24no—
56C4×C3⋊D15C2×C411yescharacteristic
57C4×C5×C3⋊D3C2×C411yescharacteristic
58C3×C4×D15C2×C412yescomplemented
59C3×C4×C5×D3C2×C412yescomplemented
60C32×C4×D5C2311yescharacteristic
61#67155C2×C411yescharacteristic
62#67154C2×C412yescomplemented
63#67149C2×C412yes—
64D3×Dic15C2×C412yescomplemented
65Dic3×D15C2×C412yescomplemented
66C5×#624C2×C411yescharacteristic
67C5×D3×Dic3C2×C412yescomplemented
68#67137C2×C411yescharacteristic
69C3⋊D3×Dic5C2×C411yescharacteristic
70D5×C3⋊Dic3C2311yescharacteristic
71C3×#1200C2×C412yescomplemented
72C3×D3×Dic5C2×C412yescomplemented
73C3×D5×Dic3C2312yes—
74C2×#4130—91noHall
75C2×C4×D32—51no—
76C42×C3⋊D3—51no—
77C3×#872—52no—
78#63921—52no—
79#63883—52no—
80C4×#624—51no—
81#63878—54no—
82#63855—52no—
83C22×D3×D5—32no—
84C2×D3×AGL(1,𝔽5)—34no—
85C2×D3×AGL(1,𝔽5)—34no—
86C2×D3×AGL(1,𝔽5)—62no—
87C2×C4×D15—32no—
88C2×C4×C5×D3—32no—
89C2×C3×C4×D5—32no—
90C2×#1200—32no—
91C2×D3×Dic5—32no—
92C2×D5×Dic3—32no—
93C4×D3×D5—32no—
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—61no—
101C4×D3×D5C2×D312yes—
102#6763—34no—
103C4⋊ΓL(1,𝔽16)—34no—
104C4×ΓL(1,𝔽16)—32no—
105C4×ΓL(1,𝔽16)—61no—
106C4×ΓL(1,𝔽16)C2×D312yescomplemented
107C3×C22⋊AGL(1,𝔽5)—34no—
108C3×C4⋊AGL(1,𝔽5)—34no—
109C3×C4×AGL(1,𝔽5)—21no—
110C3×C4×AGL(1,𝔽5)—32no—
111C3×C4×AGL(1,𝔽5)C2×D312yescomplemented
112Dic3⋊AGL(1,𝔽5)—34no—
113Dic3⋊AGL(1,𝔽5)C2×D314yescomplemented
114(C2×D3)⋊AGL(1,𝔽5)—34no—
115(C2×D3)⋊AGL(1,𝔽5)C2×D314yes—
116Dic3×AGL(1,𝔽5)—34no—
117Dic3×AGL(1,𝔽5)—34no—
118Dic3×AGL(1,𝔽5)—62no—
119D3×#117—152no—
120C2×C3⋊D15C22×C411yescharacteristic
121C2×C5×C3⋊D3C22×C411yescharacteristic
122C2×C3×D15C22×C412yes—
123C2×C3×C5×D3C22×C412yes—
124C2×C32×D5C2411yescharacteristic
125(C3⋊D3)⋊D5—22no—
126D3×D15—24no—
127C5×D32—22no—
128D5×C3⋊D3#4114yes—
129C3×D3×D5—24no—
130C3⋊ΓL(1,𝔽16)—22no—
131C3×ΓL(1,𝔽16)—24no—
132C32×AGL(1,𝔽5)—22no—
133C32×C4×C5C22×C411yescharacteristic
134C3⋊Dic15C22×C411yescharacteristic
135C5×C3⋊Dic3C22×C411yescharacteristic
136C3×Dic15C22×C412yes—
137C3×C5×Dic3C22×C412yes—
138C32×Dic5C22×C411yescharacteristic
139C22×C4×D5—91no—
140C2×C22⋊AGL(1,𝔽5)—92no—
141#4130—32no—
142#4130—92no—
143#4130—94no—
144C2×C4⋊AGL(1,𝔽5)—92no—
145C2×C4×AGL(1,𝔽5)—91no—
146C2×C4×AGL(1,𝔽5)—91no—
147C22×D32—51no—
148C2×C4×C3⋊D3—51no—
149C2×C4×C3⋊D3—52no—
150C2×C3×C4×D3—52no—
151C2×#624—51no—
152C2×#624—52no—
153C2×D3×Dic3—52no—
154C4×D32—51no—
155C4×D32—51no—
156C4×D32—52no—
157C4×D32—51no—
158C4×D32—52no—
159C4×D32AGL(1,𝔽5)11yescharacteristic, complemented
160C32×C42—51no—
161C4×C3⋊Dic3—51no—
162C4×C3⋊Dic3—52no—
163C3×(C2×D3)⋊C4—54no—
164C3×Dic3⋊C4—54no—
165C3×C4×Dic3—52no—
166Dic3⋊Dic3—54no—
167(C2×D3)⋊Dic3—54no—
168Dic32—52no—
169C22×D15—32no—
170C22×C5×D3—32no—
171C22×C3×D5—32no—
172C2×D3×D5—32no—
173C2×D3×D5—32no—
174C2×D3×D5—32no—
175C2×D3×D5—68no—
176C2×D3×D5—61no—
177C2×D3×D5C22×D312yes—
178C2×ΓL(1,𝔽16)—34no—
179C2×ΓL(1,𝔽16)—62no—
180C2×ΓL(1,𝔽16)C22×D314yes—
181C2×C3×AGL(1,𝔽5)—22no—
182C2×C3×AGL(1,𝔽5)—34no—
183C2×C3×AGL(1,𝔽5)C22×D314yes—
184D3×AGL(1,𝔽5)—68no—
185D3×AGL(1,𝔽5)—64no—
186D3×AGL(1,𝔽5)—64no—
187D3×AGL(1,𝔽5)—68no—
188C2×C3×C4×C5—32no—
189C2×Dic15—32no—
190C4×D15—32no—
191C4×D15—32no—
192C4×D15—32no—
193C4×D15—61no—
194C4×D15C4×D312yescomplemented
195C2×C5×Dic3—32no—
196C4×C5×D3—32no—
197C4×C5×D3—32no—
198C4×C5×D3—32no—
199C4×C5×D3—61no—
200C4×C5×D3C4×D312yescomplemented
201C2×C3×Dic5—32no—
202C3×C4×D5—21no—
203C3×C4×D5—32no—
204C3×C4×D5—32no—
205C3×C4×D5—32no—
206C3×C4×D5C22×D312yes—
207#1200—32no—
208#1200—32no—
209#1200—32no—
210#1200—61no—
211#1200C4×D312yescomplemented
212D3×Dic5—32no—
213D3×Dic5—32no—
214D3×Dic5—32no—
215D3×Dic5—61no—
216D3×Dic5C4×D312yescomplemented
217D5×Dic3—32no—
218D5×Dic3—32no—
219D5×Dic3—32no—
220D5×Dic3—61no—
221D5×Dic3C22×D312yes—
222C22×C4×D3—152no—
223C3×#117—152no—
224#926—152no—
225#892—154no—
226D3×C4⋊C4—154no—
227D3×C22⋊C4—154no—
228#877—154no—
229#872—52no—
230#872—152no—
231C42×D3—152no—
232C42×D3—152no—
233C42×D3—301no—
234C2×C32×C5C23×C411yescharacteristic
235C3⋊D15#11712yescomplemented
236C5×C3⋊D3#11712yescomplemented
237C3×D15—22no—
238C3×C5×D3—22no—
239C32×D5C2×#4112yes—
240C23×D5—91no—
241C22×AGL(1,𝔽5)—92no—
242C22×AGL(1,𝔽5)—92no—
243C22×C4×C5—91no—
244C22×Dic5—91no—
245C2×C4×D5—32no—
246C2×C4×D5—91no—
247C2×C4×D5—91no—
248C2×C4×D5—91no—
249C2×C4×D5—92no—
250C2×C4×D5—92no—
251C2×C4×D5—92no—
252C2×C4×D5—91no—
253C22⋊AGL(1,𝔽5)—34no—
254C22⋊AGL(1,𝔽5)—94no—
255C4⋊AGL(1,𝔽5)—34no—
256C4⋊AGL(1,𝔽5)—94no—
257C4×AGL(1,𝔽5)—32no—
258C4×AGL(1,𝔽5)—92no—
259C4×AGL(1,𝔽5)—92no—
260C4×AGL(1,𝔽5)—91no—
261C4×AGL(1,𝔽5)D3211yescharacteristic, complemented
262C22×C3⋊D3—51no—
263C22×C3×D3—52no—
264C2×D32—51no—
265C2×D32—52no—
266C2×D32—104no—
267C2×D32C2×AGL(1,𝔽5)11yescharacteristic
268C2×C32×C4—51no—
269C2×C32×C4—52no—
270C2×C3⋊Dic3—51no—
271C2×C3⋊Dic3—52no—
272C4×C3⋊D3—51no—
273C4×C3⋊D3—51no—
274C4×C3⋊D3—51no—
275C4×C3⋊D3—104no—
276C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
277C2×C3×Dic3—52no—
278C2×C3×Dic3—54no—
279C3×C4×D3—52no—
280C3×C4×D3—52no—
281C3×C4×D3—52no—
282C3×C4×D3C2×AGL(1,𝔽5)12yescomplemented
283#624—51no—
284#624—52no—
285#624—104no—
286#624C2×AGL(1,𝔽5)11yescharacteristic
287D3×Dic3—52no—
288D3×Dic3—52no—
289D3×Dic3—52no—
290D3×Dic3C2×AGL(1,𝔽5)12yescomplemented
291C2×#117—451noSylow
292C22×C3×C5—32no—
293C2×D15—32no—
294C2×D15—61no—
295C2×D15—64no—
296C2×D15C2×C4×D312yes—
297C2×C5×D3—32no—
298C2×C5×D3—61no—
299C2×C5×D3—64no—
300C2×C5×D3C2×C4×D312yes—
301C2×C3×D5—21no—
302C2×C3×D5—32no—
303C2×C3×D5—64no—
304C2×C3×D5C23×D312yes—
305D3×D5—24no—
306D3×D5—38no—
307D3×D5—64no—
308D3×D5—64no—
309D3×D5—64no—
310ΓL(1,𝔽16)—24no—
311ΓL(1,𝔽16)—62no—
312ΓL(1,𝔽16)—62no—
313ΓL(1,𝔽16)—64no—
314C3×AGL(1,𝔽5)—22no—
315C3×AGL(1,𝔽5)—22no—
316C3×AGL(1,𝔽5)—24no—
317C3×AGL(1,𝔽5)—64no—
318C3×C4×C5—21no—
319C3×C4×C5—32no—
320C3×C4×C5C2×C4×D312yes—
321Dic15—32no—
322Dic15—61no—
323Dic15C2×C4×D312yes—
324C3×Dic5—21no—
325C3×Dic5—32no—
326C3×Dic5C2×C4×D312yes—
327C5×Dic3—32no—
328C5×Dic3—61no—
329C5×Dic3C2×C4×D312yes—
330C23×D3—152no—
331C22×C3×C4—152no—
332C22×Dic3—152no—
333C2×C4×D3—32no—
334C2×C4×D3—52no—
335C2×C4×D3—152no—
336C2×C4×D3—152no—
337C2×C4×D3—152no—
338C2×C4×D3—152no—
339C2×C4×D3—152no—
340C2×C4×D3—152no—
341C2×C4×D3—152no—
342C2×C4×D3—152no—
343C2×C4×D3—152no—
344C2×C4×D3—152no—
345C2×C4×D3—154no—
346C2×C4×D3—154no—
347C2×C4×D3—301no—
348C2×C4×D3—302no—
349C3×C4⋊C4—154no—
350C3×C22⋊C4—154no—
351C3×C42—52no—
352C3×C42—101no—
353C3×C42—152no—
354#217—154no—
355(C2×D3)⋊C4—54no—
356(C2×D3)⋊C4—154no—
357C4⋊Dic3—154no—
358Dic3⋊C4—54no—
359Dic3⋊C4—154no—
360C4×Dic3—52no—
361C4×Dic3—154no—
362C4×Dic3—154no—
363C4×Dic3—152no—
364C4×Dic3—302no—
365C4×Dic3—301no—
366C32×C5C2×#11711yescharacteristic, complemented, Hall
367C23×C5—91no—
368C22×D5—32no—
369C22×D5—91no—
370C22×D5—92no—
371C22×D5—91no—
372C22×D5—184no—
373C2×AGL(1,𝔽5)—34no—
374C2×AGL(1,𝔽5)—92no—
375C2×AGL(1,𝔽5)—184no—
376C2×AGL(1,𝔽5)—184no—
377C2×AGL(1,𝔽5)C2×D3212yes—
378C2×C4×C5—32no—
379C2×C4×C5—91no—
380C2×C4×C5—92no—
381C2×C4×C5—91no—
382C2×Dic5—32no—
383C2×Dic5—91no—
384C2×Dic5—92no—
385C2×Dic5—91no—
386C4×D5—32no—
387C4×D5—32no—
388C4×D5—32no—
389C4×D5—92no—
390C4×D5—92no—
391C4×D5—92no—
392C4×D5—91no—
393C4×D5—91no—
394C4×D5—91no—
395C4×D5C2×D3211yescharacteristic
396C22×C32—51no—
397C2×C3⋊D3—51no—
398C2×C3⋊D3—54no—
399C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
400C2×C3×D3—52no—
401C2×C3×D3—104no—
402C2×C3×D3C22×AGL(1,𝔽5)12yes—
403D32—22no—
404D32—104no—
405D32—102no—
406C32×C4—51no—
407C32×C4—102no—
408C32×C4C22×AGL(1,𝔽5)11yescharacteristic
409C3⋊Dic3—51no—
410C3⋊Dic3—102no—
411C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
412C3×Dic3—52no—
413C3×Dic3—104no—
414C3×Dic3C22×AGL(1,𝔽5)12yes—
415C23×C4—451no—
416#117—152no—
417#117—452no—
418#117—454no—
419C2×C4⋊C4—452no—
420C2×C22⋊C4—452no—
421C2×C42—451no—
422C2×C42—451no—
423C2×C3×C5—21no—
424C2×C3×C5—62no—
425C2×C3×C5C22×C4×D312yes—
426D15—22no—
427D15—34no—
428D15—62no—
429C3×D5—22no—
430C3×D5—62no—
431C3×D5D3×#4114yes—
432C5×D3—22no—
433C5×D3—34no—
434C5×D3—62no—
435C23×C3—152no—
436C22×D3—32no—
437C22×D3—52no—
438C22×D3—152no—
439C22×D3—152no—
440C22×D3—152no—
441C22×D3—152no—
442C22×D3—301no—
443C22×D3—308no—
444C2×C3×C4—32no—
445C2×C3×C4—52no—
446C2×C3×C4—54no—
447C2×C3×C4—101no—
448C2×C3×C4—102no—
449C2×C3×C4—152no—
450C2×C3×C4—152no—
451C2×C3×C4—152no—
452C2×C3×C4—152no—
453C2×C3×C4—154no—
454C2×Dic3—32no—
455C2×Dic3—52no—
456C2×Dic3—54no—
457C2×Dic3—152no—
458C2×Dic3—152no—
459C2×Dic3—152no—
460C2×Dic3—152no—
461C2×Dic3—154no—
462C2×Dic3—301no—
463C2×Dic3—302no—
464C4×D3—32no—
465C4×D3—32no—
466C4×D3—32no—
467C4×D3—52no—
468C4×D3—52no—
469C4×D3—52no—
470C4×D3—61no—
471C4×D3—152no—
472C4×D3—152no—
473C4×D3—152no—
474C4×D3—152no—
475C4×D3—152no—
476C4×D3—152no—
477C4×D3—152no—
478C4×D3—152no—
479C4×D3—152no—
480C4×D3—301no—
481C4×D3—301no—
482C4×D3—301no—
483C4×D3—308no—
484C4×D3—308no—
485C4×D3—304no—
486C4×D3—304no—
487C4×D3D3×AGL(1,𝔽5)12yescomplemented
488C22×C5—32no—
489C22×C5—91no—
490C22×C5—182no—
491C2×D5—32no—
492C2×D5—64no—
493C2×D5—91no—
494C2×D5—94no—
495C2×D5—182no—
496C2×D5—184no—
497C2×D5C22×D3211yescharacteristic
498AGL(1,𝔽5)—22no—
499AGL(1,𝔽5)—64no—
500AGL(1,𝔽5)—182no—
501C4×C5—32no—
502C4×C5—91no—
503C4×C5C4×D3211yescharacteristic
504Dic5—32no—
505Dic5—91no—
506Dic5C4×D3211yescharacteristic
507C2×C32—52no—
508C2×C32C23×AGL(1,𝔽5)11yescharacteristic
509C3⋊D3—52no—
510C3⋊D3#413012yescomplemented
511C3×D3—22no—
512C3×D3—102no—
513C24—451no—
514C22×C4—91no—
515C22×C4—152no—
516C22×C4—452no—
517C22×C4—451no—
518C22×C4—452no—
519C22×C4—451no—
520C22×C4—451no—
521C22×C4—452no—
522C22×C4—451no—
523C22×C4—452no—
524C22×C4—451no—
525C22×C4—452no—
526C4⋊C4—154no—
527C4⋊C4—454no—
528C22⋊C4—154no—
529C22⋊C4—454no—
530C42—51no—
531C42—152no—
532C42—451no—
533C42—452no—
534C42—452no—
535C3×C5—21no—
536C3×C5D3×#11712yescomplemented
537C22×C3—32no—
538C22×C3—52no—
539C22×C3—101no—
540C22×C3—152no—
541C22×C3—304no—
542C2×D3—32no—
543C2×D3—52no—
544C2×D3—61no—
545C2×D3—64no—
546C2×D3—104no—
547C2×D3—158no—
548C2×D3—152no—
549C2×D3—304no—
550C2×D3—301no—
551C2×D3—304no—
552C2×D3—304no—
553C2×D3—304no—
554C2×D3C2×D3×AGL(1,𝔽5)12yes—
555C3×C4—21no—
556C3×C4—32no—
557C3×C4—52no—
558C3×C4—101no—
559C3×C4—104no—
560C3×C4—102no—
561C3×C4—102no—
562C3×C4—152no—
563C3×C4—304no—
564C3×C4C2×D3×AGL(1,𝔽5)12yes—
565Dic3—32no—
566Dic3—52no—
567Dic3—61no—
568Dic3—104no—
569Dic3—152no—
570Dic3—301no—
571Dic3—304no—
572Dic3—302no—
573Dic3—302no—
574Dic3C2×D3×AGL(1,𝔽5)12yes—
575C2×C5—62no—
576C2×C5—92no—
577C2×C5C2×C4×D3211yescharacteristic
578D5—62no—
579D5—92no—
580D5#6430612yes—
581C32C2×#413011yescharacteristic, complemented, Sylow
582C23—91no—
583C23—152no—
584C23—452no—
585C23—451no—
586C23—451no—
587C23—904no—
588C2×C4—32no—
589C2×C4—51no—
590C2×C4—52no—
591C2×C4—91no—
592C2×C4—92no—
593C2×C4—91no—
594C2×C4—152no—
595C2×C4—152no—
596C2×C4—152no—
597C2×C4—152no—
598C2×C4—154no—
599C2×C4—452no—
600C2×C4—452no—
601C2×C4—451no—
602C2×C4—451no—
603C2×C4—452no—
604C2×C4—451no—
605C2×C4—451no—
606C2×C4—452no—
607C2×C4—451no—
608C2×C4—452no—
609C2×C4—904no—
610C2×C4—904no—
611C2×C3—21no—
612C2×C3—54no—
613C2×C3—62no—
614C2×C3—102no—
615C2×C3—302no—
616C2×C3C22×D3×AGL(1,𝔽5)12yes—
617D3—22no—
618D3—34no—
619D3—62no—
620D3—102no—
621D3—154no—
622D3—302no—
623C5#1059399211yescharacteristic, complemented, Sylow
624C22—32no—
625C22—51no—
626C22—91no—
627C22—152no—
628C22—182no—
629C22—304no—
630C22—454no—
631C22—451no—
632C22—904no—
633C22—902no—
634C4—32no—
635C4—51no—
636C4—91no—
637C4—102no—
638C4—152no—
639C4—304no—
640C4—451no—
641C4—902no—
642C4D32×AGL(1,𝔽5)11yescharacteristic
643C3—21no—
644C3D3×#413012yescomplemented
645C2—52no—
646C2—62no—
647C2—92no—
648C2—302no—
649C2—452no—
650C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC4D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FrattiniC2C2×D32×AGL(1,𝔽5)
FittingC32×C4×C5C22×C4
prime radicalC2×D32×D5C22
cosocleC2×C32×D5C24
hypocenterC32×C5C2×#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×ΓL(1,𝔽16)⋊D3C2semidirect
3. #13088694C2semidirect
4. C4×C3⋊D3×AGL(1,𝔽5)C2semidirect
5. C3×#91909C2semidirect
6. #13088410C2semidirect
7. #13088407C2semidirect
13. C4×(C3⋊D3)⋊D5C4semidirect
14. C4×D3×D15C4semidirect
15. C4×C5×D32C4semidirect
18. C4×C3⋊ΓL(1,𝔽16)C22semidirect
19. C3×C4×ΓL(1,𝔽16)C22semidirect
20. C32×C4×AGL(1,𝔽5)C22semidirect
21. #10624022C4semidirect
22. D3×#1200C4semidirect
23. D32×Dic5C4semidirect
26. ΓL(1,𝔽16)⋊Dic3C22semidirect
27. Dic3⋊ΓL(1,𝔽16)C22semidirect
29. AGL(1,𝔽5)×C3⋊Dic3C22semidirect
30. C3×Dic3⋊AGL(1,𝔽5)C22semidirect
43. #91909D3semidirect
58. C3×C4×D15C2×C4semidirect
59. C3×C4×C5×D3C2×C4semidirect
62. #67154C2×C4semidirect
64. D3×Dic15C2×C4semidirect
65. Dic3×D15C2×C4semidirect
67. C5×D3×Dic3C2×C4semidirect
71. C3×#1200C2×C4semidirect
72. C3×D3×Dic5C2×C4semidirect
106. C4×ΓL(1,𝔽16)C2×D3semidirect
111. C3×C4×AGL(1,𝔽5)C2×D3semidirect
113. Dic3⋊AGL(1,𝔽5)C2×D3semidirect
159. C4×D32AGL(1,𝔽5)semidirect
194. C4×D15C4×D3semidirect
200. C4×C5×D3C4×D3semidirect
211. #1200C4×D3semidirect
216. D3×Dic5C4×D3semidirect
235. C3⋊D15#117semidirect
236. C5×C3⋊D3#117semidirect
261. C4×AGL(1,𝔽5)D32semidirect
282. C3×C4×D3C2×AGL(1,𝔽5)semidirect
290. D3×Dic3C2×AGL(1,𝔽5)semidirect
366. C32×C5C2×#117semidirect
487. C4×D3D3×AGL(1,𝔽5)semidirect
510. C3⋊D3#4130semidirect
536. C3×C5D3×#117semidirect
581. C32C2×#4130semidirect
623. C5#10593992semidirect
644. C3D3×#4130semidirect

Maximal subgroups

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

subgroupindex
C4×D32×D52
C4×ΓL(1,𝔽16)⋊D32
#130886942
C4×C3⋊D3×AGL(1,𝔽5)2
C3×#919092
#130884102
#130884072
#130884052
D3×#41303
#105939925