Finite Group Databasebeta

← #72230196

Subgroups — #72230196

Order 2880.

1268 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3805C211yesmaximal, characteristic
2#13088735C211yesmaximal, characteristic, complemented
3#67⋊ΓL(1,𝔽16)C212yesmaximal, complemented
4C2×#10623965C211yesmaximal, characteristic, complemented
5C3×AGL(1,𝔽5)×#67C212yesmaximal, complemented
6#13088419C212yesmaximal, complemented
7#13088413C212yesmaximal, complemented
8#13088408C212yesmaximal, complemented
9D3×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
10#11756846—32nomaximal
11C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
12C22×C32×AGL(1,𝔽5)C2211yescharacteristic
13C2×D3×ΓL(1,𝔽16)C2212yes—
14C2×C3×D3×AGL(1,𝔽5)C2212yes—
15#10624229C411yescharacteristic, complemented
16#10624208C412yescomplemented
17C5×#3805C411yescharacteristic, complemented
18C2×D5×C3⋊Dic3C2211yescharacteristic
19C3×D5×#67C2212yes—
20C3×#6763C2212yes—
21#10624047C411yescharacteristic, complemented
22#10624046C411yescharacteristic, complemented
23#10624045C412yescomplemented
24D5×#627C2211yescharacteristic
25D5×#625C2211yescharacteristic
26D3×D5×Dic3C2212yes—
27#10623979C2211yescharacteristic
28#10623979C2211yescharacteristic
29ΓL(1,𝔽16)⋊Dic3C2212yes—
30Dic3⋊ΓL(1,𝔽16)C2212yes—
31(C2×D3)⋊ΓL(1,𝔽16)C2212yes—
32Dic3×ΓL(1,𝔽16)C2212yes—
33#10623965C2212yes—
34#10623965C2212yes—
35C3×Dic3⋊AGL(1,𝔽5)C2212yes—
36C3×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
37C3×Dic3×AGL(1,𝔽5)C2212yes—
38#10594876—51nomaximal, Hall
39D5×#237—32no—
40D4×ΓL(1,𝔽16)—32no—
41C3×D4×AGL(1,𝔽5)—32no—
42#67⋊AGL(1,𝔽5)—32no—
43#67⋊AGL(1,𝔽5)—32no—
44AGL(1,𝔽5)×#67—32no—
45AGL(1,𝔽5)×#67D312yescomplemented
46C2×Dic3⋊AGL(1,𝔽5)—32no—
47C2×Dic3⋊AGL(1,𝔽5)—32no—
48C2×Dic3⋊AGL(1,𝔽5)—61no—
49#91923—32no—
50#91923—32no—
51D3×C4⋊AGL(1,𝔽5)—32no—
52#91909—32no—
53ΓL(1,𝔽16)⋊Q8—32no—
54AGL(1,𝔽5)×Dic6—32no—
55C22×C32×D5C2311yescharacteristic
56C2×C3×D3×D5C2312yes—
57C2×C3⋊ΓL(1,𝔽16)—41no—
58C2×C3⋊ΓL(1,𝔽16)C2312yes—
59C2×C3×ΓL(1,𝔽16)C2312yes—
60C2×C3×ΓL(1,𝔽16)C2312yes—
61C2×C32×AGL(1,𝔽5)—41no—
62C2×C32×AGL(1,𝔽5)C2312yes—
63D3×ΓL(1,𝔽16)—42no—
64C3×D3×AGL(1,𝔽5)—42no—
65C2×C3⋊Dic15C2×C411yescharacteristic, complemented
66C2×C5×C3⋊Dic3C2×C411yescharacteristic, complemented
67C3×#1220C2×C412yescomplemented
68C3×C5×#67C2×C412yescomplemented
69#67158C2×C411yescharacteristic, complemented
70#67157C2×C411yescharacteristic, complemented
71#67154C2×C412yescomplemented
72#67153C2×C412yescomplemented
73#67150C2×C412yescomplemented
74D3×Dic15C2×C412yescomplemented
75Dic3×D15C2×C412yescomplemented
76C5×#627C2×C411yescharacteristic, complemented
77C5×#625C2×C411yescharacteristic, complemented
78C5×D3×Dic3C2×C412yescomplemented
79D5×C3⋊Dic3C2×C411yescharacteristic, complemented
80D5×C3⋊Dic3C2×C411yescharacteristic, complemented
81D5×C3⋊Dic3C2311yescharacteristic
82D5×C3⋊Dic3C2311yescharacteristic
83C3×#1202C2×C412yescomplemented
84C3×#1201C2×C412yescomplemented
85C3×D5×Dic3C2312yes—
86#66266—91noHall
87C2×#3805—51no—
88C2×#3750—51no—
89C3×C4×#67—52no—
90#67⋊Dic3—52no—
91#63957—51no—
92#63879—52no—
93#63877—52no—
94D3×Dic3⋊C4—52no—
95#63837—52no—
96C22×ΓL(1,𝔽16)—32no—
97C22×ΓL(1,𝔽16)—32no—
98C22×ΓL(1,𝔽16)—61no—
99C22×C3×AGL(1,𝔽5)—21no—
100C22×C3×AGL(1,𝔽5)—32no—
101C22×C3×AGL(1,𝔽5)C2×D312yes—
102C2×D3×AGL(1,𝔽5)—32no—
103C2×D3×AGL(1,𝔽5)C2×D312yes—
104#6819—32no—
105C5×#237—32no—
106C3×D4×D5—32no—
107D5×#67—32no—
108D5×#67C2×D312yes—
109#6780—32no—
110#6780—32no—
111#6779—32no—
112#6779—32no—
113C2×D5×Dic3—32no—
114C2×D5×Dic3—32no—
115C2×D5×Dic3—61no—
116C4×D3×D5—32no—
117#6766—32no—
118#6765—32no—
119D5×Dic6—32no—
120#6763—32no—
121#6763C2×D312yes—
122C4⋊ΓL(1,𝔽16)—32no—
123C4×ΓL(1,𝔽16)—32no—
124C3×C22⋊AGL(1,𝔽5)—32no—
125C3×C22⋊AGL(1,𝔽5)—32no—
126C3×C4⋊AGL(1,𝔽5)—32no—
127C3×C4×AGL(1,𝔽5)—32no—
128Dic3⋊AGL(1,𝔽5)—32no—
129Dic3⋊AGL(1,𝔽5)—32no—
130Dic3⋊AGL(1,𝔽5)—32no—
131Dic3⋊AGL(1,𝔽5)—32no—
132Dic3⋊AGL(1,𝔽5)—32no—
133Dic3⋊AGL(1,𝔽5)—32no—
134Dic3⋊AGL(1,𝔽5)—32no—
135Dic3⋊AGL(1,𝔽5)—62no—
136Dic3⋊AGL(1,𝔽5)—62no—
137Dic3⋊AGL(1,𝔽5)C2×D312yes—
138(C2×D3)⋊AGL(1,𝔽5)—32no—
139(C2×D3)⋊AGL(1,𝔽5)C2×D312yes—
140Dic3×AGL(1,𝔽5)—32no—
141Dic3×AGL(1,𝔽5)—32no—
142Dic3×AGL(1,𝔽5)—32no—
143Dic3×AGL(1,𝔽5)C2×D312yes—
144#5546—152no—
145C22×C32×C5C22×C411yescharacteristic
146C2×C3×D15C22×C412yes—
147C2×C3×C5×D3C22×C412yes—
148C2×C32×D5—21no—
149C2×C32×D5—21no—
150C2×C32×D5C22×C411yescharacteristic
151C2×C32×D5C2411yescharacteristic
152C3×D3×D5—22no—
153C3×D3×D5—22no—
154C3⋊ΓL(1,𝔽16)—22no—
155C3×ΓL(1,𝔽16)—22no—
156C3×ΓL(1,𝔽16)—22no—
157C32×AGL(1,𝔽5)—22no—
158C3⋊Dic15C22×C411yescharacteristic
159C3⋊Dic15C22×C411yescharacteristic
160C5×C3⋊Dic3C22×C411yescharacteristic
161C5×C3⋊Dic3C22×C411yescharacteristic
162C3×Dic15C22×C412yes—
163C3×C5×Dic3C22×C412yes—
164D5×#41—91no—
165Q8×AGL(1,𝔽5)—92no—
166D4×AGL(1,𝔽5)—32no—
167D4×AGL(1,𝔽5)—92no—
168D4×AGL(1,𝔽5)—92no—
169#4130—92no—
170#4130—91no—
171C2×C4⋊AGL(1,𝔽5)—92no—
172C2×C4⋊AGL(1,𝔽5)—91no—
173C22×C32×C4—51no—
174C22×C3⋊Dic3—51no—
175C22×C3⋊Dic3—51no—
176C2×C3×#67—52no—
177C2×C3×C4×D3—52no—
178C2×#627—51no—
179C2×#625—51no—
180#3805—51no—
181#3805—52no—
182#3805—51no—
183#3805—51no—
184#3805—52no—
185#3805AGL(1,𝔽5)11yescharacteristic, complemented
186C2×D3×Dic3—52no—
187C2×D3×Dic3—52no—
188#3750—52no—
189#3750—52no—
190C3×#217—52no—
191C3×(C2×D3)⋊C4—52no—
192C3×Dic3⋊C4—52no—
193C3×C4×Dic3—52no—
194#3724—51no—
195#3724—51no—
196Dic3⋊Dic3—52no—
197(C2×D3)⋊Dic3—52no—
198Dic32—52no—
199Dic32—52no—
200C22×C3×D5—21no—
201C22×C3×D5—32no—
202C22×C3×D5C22×D312yes—
203C2×D3×D5C22×D312yes—
204C2×ΓL(1,𝔽16)—32no—
205C2×ΓL(1,𝔽16)—32no—
206C2×ΓL(1,𝔽16)—62no—
207C2×ΓL(1,𝔽16)—122no—
208C2×ΓL(1,𝔽16)—122no—
209C2×ΓL(1,𝔽16)—121no—
210C2×ΓL(1,𝔽16)—121no—
211C2×ΓL(1,𝔽16)C22×D312yes—
212C2×ΓL(1,𝔽16)C22×D312yes—
213C2×C3×AGL(1,𝔽5)—22no—
214C2×C3×AGL(1,𝔽5)—32no—
215C2×C3×AGL(1,𝔽5)—32no—
216C2×C3×AGL(1,𝔽5)—42no—
217C2×C3×AGL(1,𝔽5)—41no—
218C2×C3×AGL(1,𝔽5)—41no—
219C2×C3×AGL(1,𝔽5)—122no—
220C2×C3×AGL(1,𝔽5)C22×D312yes—
221C2×C3×AGL(1,𝔽5)C22×D312yes—
222D3×AGL(1,𝔽5)—42no—
223D3×AGL(1,𝔽5)—122no—
224C3×C5×D4—32no—
225#1220—32no—
226#1220C4×D312yescomplemented
227C2×Dic15—32no—
228C2×Dic15—32no—
229C2×Dic15—61no—
230C4×D15—32no—
231Dic30—32no—
232C5×#67—32no—
233C5×#67C4×D312yescomplemented
234C2×C5×Dic3—32no—
235C2×C5×Dic3—32no—
236C2×C5×Dic3—61no—
237C4×C5×D3—32no—
238C5×Dic6—32no—
239C3×C22⋊D5—32no—
240C3×C22⋊D5—32no—
241C3×D20—32no—
242C3×C4×D5—32no—
243#1204—32no—
244#1204—32no—
245#1202—32no—
246#1202C4×D312yescomplemented
247#1201—32no—
248#1201C4×D312yescomplemented
249#1200—32no—
250D3×Dic5—32no—
251D5×Dic3—32no—
252D5×Dic3—32no—
253D5×Dic3—32no—
254D5×Dic3—32no—
255D5×Dic3—32no—
256D5×Dic3—32no—
257D5×Dic3—61no—
258D5×Dic3—61no—
259D5×Dic3—61no—
260D5×Dic3—61no—
261D5×Dic3C22×D312yes—
262C2×#237—152no—
263C3×C4×D4—152no—
264D4×Dic3—152no—
265C4×#67—52no—
266C4×#67—152no—
267C2×Dic3⋊C4—152no—
268C2×Dic3⋊C4—152no—
269C2×Dic3⋊C4—301no—
270D3×C4⋊C4—152no—
271#887—152no—
272#67⋊C4—152no—
273#67⋊C4—152no—
274#877—152no—
275#877—152no—
276#872—152no—
277C4×Dic6—152no—
278C2×C32×C5—21no—
279C2×C32×C5C23×C411yescharacteristic
280C3×D15—22no—
281C3×C5×D3—22no—
282C32×D5—21no—
283C32×D5H(5,𝔽2)11yescharacteristic
284C32×D52−1+411yescharacteristic
285C22×AGL(1,𝔽5)—32no—
286C22×AGL(1,𝔽5)—92no—
287C22×AGL(1,𝔽5)—91no—
288C22×AGL(1,𝔽5)D3211yescharacteristic
289C5×#41—91no—
290#713—91no—
291Q8×D5—91no—
292#711—91no—
293#711—92no—
294D4×D5—32no—
295D4×D5—91no—
296#709—92no—
297#709—91no—
298C2×C4×D5—92no—
299C2×C4×D5—91no—
300C22⋊AGL(1,𝔽5)—32no—
301C22⋊AGL(1,𝔽5)—32no—
302C22⋊AGL(1,𝔽5)—92no—
303C4⋊AGL(1,𝔽5)—32no—
304C4⋊AGL(1,𝔽5)—92no—
305C4⋊AGL(1,𝔽5)—91no—
306C4⋊AGL(1,𝔽5)—91no—
307C4⋊AGL(1,𝔽5)—92no—
308C4⋊AGL(1,𝔽5)—92no—
309C4×AGL(1,𝔽5)—32no—
310C4×AGL(1,𝔽5)—92no—
311C4×AGL(1,𝔽5)—92no—
312C23×C32—51no—
313C22×C3×D3—52no—
314C2×C32×C4—52no—
315C2×C32×C4—201no—
316C2×C3⋊Dic3—51no—
317C2×C3⋊Dic3—51no—
318C2×C3⋊Dic3—51no—
319C2×C3⋊Dic3—51no—
320C2×C3⋊Dic3—51no—
321C2×C3⋊Dic3—52no—
322C2×C3⋊Dic3—201no—
323C2×C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
324C3×#67—52no—
325C3×#67—52no—
326C3×#67—52no—
327C3×#67C2×AGL(1,𝔽5)12yescomplemented
328C2×C3×Dic3—52no—
329C2×C3×Dic3—52no—
330C2×C3×Dic3—52no—
331C3×C4×D3—202no—
332#627—51no—
333#627—52no—
334#627C2×AGL(1,𝔽5)11yescharacteristic, complemented
335#625—52no—
336#625—51no—
337#625C2×AGL(1,𝔽5)11yescharacteristic, complemented
338D3×Dic3—52no—
339D3×Dic3—52no—
340D3×Dic3—52no—
341D3×Dic3—202no—
342D3×Dic3C2×AGL(1,𝔽5)12yescomplemented
343#520—451noSylow
344C22×C3×C5—21no—
345C22×C3×C5—32no—
346C22×C3×C5C2×C4×D312yes—
347C2×D15C2×C4×D312yes—
348C2×C5×D3C2×C4×D312yes—
349C2×C3×D5—21no—
350C2×C3×D5—21no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—22no—
354C2×C3×D5—22no—
355C2×C3×D5—21no—
356C2×C3×D5—21no—
357C2×C3×D5—32no—
358C2×C3×D5—62no—
359C2×C3×D5—62no—
360C2×C3×D5C2×C4×D312yes—
361C2×C3×D5C23×D312yes—
362D3×D5—22no—
363D3×D5—22no—
364ΓL(1,𝔽16)—22no—
365ΓL(1,𝔽16)—22no—
366ΓL(1,𝔽16)—62no—
367ΓL(1,𝔽16)—62no—
368ΓL(1,𝔽16)—122no—
369C3×AGL(1,𝔽5)—22no—
370C3×AGL(1,𝔽5)—22no—
371C3×AGL(1,𝔽5)—42no—
372C3×AGL(1,𝔽5)—62no—
373C3×AGL(1,𝔽5)—62no—
374C3×C4×C5—32no—
375Dic15—32no—
376Dic15—32no—
377Dic15—61no—
378Dic15—61no—
379Dic15C2×C4×D312yes—
380C3×Dic5—32no—
381C5×Dic3—32no—
382C5×Dic3—32no—
383C5×Dic3—61no—
384C5×Dic3—61no—
385C5×Dic3C2×C4×D312yes—
386C2×C3×D4—152no—
387C22×C3×C4—52no—
388C22×C3×C4—101no—
389C22×C3×C4—152no—
390C2×#67—52no—
391C2×#67—152no—
392C22×Dic3—152no—
393C22×Dic3—152no—
394C22×Dic3—152no—
395C22×Dic3—152no—
396C22×Dic3—301no—
397C22×Dic3—301no—
398#237—32no—
399#237—152no—
400#237—152no—
401#237—152no—
402#237—152no—
403#237—152no—
404#237—152no—
405#237—152no—
406C2×C4×D3—52no—
407C2×C4×D3—152no—
408C2×C4×D3—152no—
409C2×Dic6—152no—
410C3×C4⋊C4—152no—
411C3×C22⋊C4—152no—
412C3×C22⋊C4—152no—
413C3×C42—152no—
414#217—52no—
415#217—152no—
416(C2×D3)⋊C4—52no—
417(C2×D3)⋊C4—152no—
418C4⋊Dic3—152no—
419Dic3⋊C4—52no—
420Dic3⋊C4—152no—
421Dic3⋊C4—152no—
422Dic3⋊C4—152no—
423Dic3⋊C4—152no—
424Dic3⋊C4—152no—
425Dic3⋊C4—152no—
426Dic3⋊C4—152no—
427Dic3⋊C4—302no—
428Dic3⋊C4—302no—
429C4×Dic3—52no—
430C4×Dic3—152no—
431C4×Dic3—152no—
432C4×Dic3—152no—
433C4×Dic3—152no—
434C32×C5#52011yescharacteristic, complemented, Hall
435C22×D5—32no—
436C22×D5C2×D3211yescharacteristic
437C2×AGL(1,𝔽5)—32no—
438C2×AGL(1,𝔽5)—32no—
439C2×AGL(1,𝔽5)—41no—
440C2×AGL(1,𝔽5)—92no—
441C2×AGL(1,𝔽5)—122no—
442C2×AGL(1,𝔽5)—362no—
443C2×AGL(1,𝔽5)—361no—
444C2×AGL(1,𝔽5)C2×D3212yes—
445C5×Q8—91no—
446C5×D4—32no—
447C5×D4—91no—
448C2×C4×C5—92no—
449C2×C4×C5—91no—
450C22⋊D5—32no—
451C22⋊D5—32no—
452C22⋊D5—92no—
453C2×Dic5—92no—
454C2×Dic5—91no—
455D20—32no—
456D20—91no—
457C4×D5—32no—
458C4×D5—92no—
459C4×D5—92no—
460C4×D5—91no—
461C4×D5—91no—
462C4×D5—91no—
463C4×D5—91no—
464Dic10—91no—
465Dic10—92no—
466C22×C32—51no—
467C22×C32—51no—
468C22×C32—101no—
469C22×C32—101no—
470C22×C32C22×AGL(1,𝔽5)11yescharacteristic
471C2×C3×D3—52no—
472C2×C3×D3—102no—
473C2×C3×D3—102no—
474C2×C3×D3C22×AGL(1,𝔽5)12yes—
475C32×C4—102no—
476C3⋊Dic3—51no—
477C3⋊Dic3—51no—
478C3⋊Dic3—102no—
479C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
480C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
481C3×Dic3—52no—
482C3×Dic3—102no—
483C3×Dic3—102no—
484C3×Dic3C22×AGL(1,𝔽5)12yes—
485C2×#41—451no—
486C4×Q8—452no—
487C4×D4—152no—
488C4×D4—452no—
489C4×D4—452no—
490#117—452no—
491#117—451no—
492C2×C4⋊C4—452no—
493C2×C4⋊C4—451no—
494C2×C3×C5—21no—
495C2×C3×C5—21no—
496C2×C3×C5—22no—
497C2×C3×C5—21no—
498C2×C3×C5—62no—
499C2×C3×C5C22×C4×D312yes—
500D15—22no—
501C3×D5—21no—
502C3×D5—21no—
503C3×D5—22no—
504C3×D5—21no—
505C3×D5—21no—
506C3×D5—62no—
507C3×D5#100412yes—
508C3×D5#101012yes—
509C5×D3—22no—
510C23×C3—52no—
511C23×C3—101no—
512C23×C3—152no—
513C22×D3—52no—
514C3×D4—32no—
515C3×D4—152no—
516C3×D4—152no—
517C3×D4—152no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—102no—
521C2×C3×C4—152no—
522C2×C3×C4—152no—
523C2×C3×C4—152no—
524C2×C3×C4—202no—
525C2×C3×C4—201no—
526C2×C3×C4—201no—
527C2×C3×C4—602no—
528#67—32no—
529#67—52no—
530#67—52no—
531#67—52no—
532#67—152no—
533#67—152no—
534#67—152no—
535#67D3×AGL(1,𝔽5)12yescomplemented
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—52no—
539C2×Dic3—52no—
540C2×Dic3—52no—
541C2×Dic3—61no—
542C2×Dic3—152no—
543C2×Dic3—152no—
544C2×Dic3—152no—
545C2×Dic3—152no—
546C2×Dic3—152no—
547C2×Dic3—152no—
548C2×Dic3—152no—
549C2×Dic3—152no—
550C2×Dic3—152no—
551C2×Dic3—152no—
552C2×Dic3—301no—
553C2×Dic3—301no—
554C2×Dic3—301no—
555C2×Dic3—301no—
556C2×Dic3—301no—
557C2×Dic3—302no—
558C2×Dic3—602no—
559C2×Dic3—602no—
560C2×Dic3—601no—
561C2×Dic3—601no—
562C4×D3—32no—
563C4×D3—152no—
564C4×D3—152no—
565C4×D3—152no—
566C4×D3—202no—
567C4×D3—602no—
568Dic6—32no—
569Dic6—152no—
570Dic6—152no—
571Dic6—152no—
572C22×C5—32no—
573C22×C5C4×D3211yescharacteristic
574C2×D5—21no—
575C2×D5—21no—
576C2×D5—32no—
577C2×D5—62no—
578C2×D5—62no—
579C2×D5C4×D3211yescharacteristic
580C2×D5C22×D3211yescharacteristic
581AGL(1,𝔽5)—22no—
582AGL(1,𝔽5)—62no—
583AGL(1,𝔽5)—62no—
584AGL(1,𝔽5)—182no—
585C4×C5—32no—
586C4×C5—91no—
587C4×C5—91no—
588Dic5—32no—
589Dic5—91no—
590Dic5—91no—
591C2×C32—21no—
592C2×C32—51no—
593C2×C32—51no—
594C2×C32—101no—
595C2×C32C23×AGL(1,𝔽5)11yescharacteristic
596C3×D3—22no—
597C3×D3—102no—
598#41—91no—
599#41—452no—
600#41—451no—
601#41—452no—
602#41—451no—
603#41—451no—
604C2×Q8—451no—
605C2×D4—152no—
606C2×D4—451no—
607C22×C4—51no—
608C22×C4—152no—
609C22×C4—452no—
610C22×C4—451no—
611C22×C4—452no—
612C22×C4—451no—
613C4⋊C4—152no—
614C4⋊C4—452no—
615C4⋊C4—452no—
616C4⋊C4—451no—
617C4⋊C4—452no—
618C4⋊C4—451no—
619C22⋊C4—152no—
620C22⋊C4—152no—
621C22⋊C4—452no—
622C42—152no—
623C42—452no—
624C42—452no—
625C3×C5—21no—
626C3×C5#554612yescomplemented
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—52no—
630C22×C3—52no—
631C22×C3—101no—
632C22×C3—101no—
633C22×C3—102no—
634C22×C3—102no—
635C22×C3—101no—
636C22×C3—101no—
637C22×C3—101no—
638C22×C3—101no—
639C22×C3—152no—
640C22×C3—302no—
641C22×C3—302no—
642C22×C3C2×D3×AGL(1,𝔽5)12yes—
643C2×D3—52no—
644C2×D3—102no—
645C2×D3—102no—
646C2×D3C2×D3×AGL(1,𝔽5)12yes—
647C3×C4—32no—
648C3×C4—102no—
649C3×C4—102no—
650C3×C4—152no—
651C3×C4—202no—
652C3×C4—302no—
653C3×C4—302no—
654Dic3—32no—
655Dic3—32no—
656Dic3—52no—
657Dic3—61no—
658Dic3—61no—
659Dic3—102no—
660Dic3—102no—
661Dic3—152no—
662Dic3—152no—
663Dic3—301no—
664Dic3—301no—
665Dic3—302no—
666Dic3—302no—
667Dic3—602no—
668Dic3C2×D3×AGL(1,𝔽5)12yes—
669C2×C5—21no—
670C2×C5—62no—
671C2×C5C2×C4×D3211yescharacteristic
672D5—21no—
673D5—62no—
674D5#6429811yescharacteristic
675D5#6433011yescharacteristic
676C32#6626611yescharacteristic, complemented, Sylow
677C23—51no—
678C23—152no—
679Q8—91no—
680Q8—452no—
681Q8—451no—
682D4—32no—
683D4—91no—
684D4—152no—
685D4—152no—
686D4—152no—
687D4—451no—
688D4—452no—
689C2×C4—52no—
690C2×C4—92no—
691C2×C4—91no—
692C2×C4—152no—
693C2×C4—152no—
694C2×C4—152no—
695C2×C4—201no—
696C2×C4—452no—
697C2×C4—452no—
698C2×C4—451no—
699C2×C4—451no—
700C2×C4—451no—
701C2×C4—451no—
702C2×C4—452no—
703C2×C4—451no—
704C2×C4—452no—
705C2×C4—602no—
706C2×C4—1802no—
707C2×C4—1801no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—22no—
711C2×C3—21no—
712C2×C3—52no—
713C2×C3—52no—
714C2×C3—62no—
715C2×C3—101no—
716C2×C3—101no—
717C2×C3—101no—
718C2×C3—101no—
719C2×C3—102no—
720C2×C3—302no—
721C2×C3C22×D3×AGL(1,𝔽5)12yes—
722D3—22no—
723D3—102no—
724C5#1059487611yescharacteristic, complemented, Sylow
725C22—32no—
726C22—51no—
727C22—51no—
728C22—101no—
729C22—101no—
730C22—152no—
731C22—302no—
732C22—302no—
733C22D32×AGL(1,𝔽5)11yescharacteristic
734C4—32no—
735C4—91no—
736C4—91no—
737C4—102no—
738C4—152no—
739C4—302no—
740C4—302no—
741C4—451no—
742C4—451no—
743C4—902no—
744C3—21no—
745C3#1175684612yescomplemented
746C2—21no—
747C2—51no—
748C2—51no—
749C2—62no—
750C2—101no—
751C2—302no—
752C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC22×C32×C5C22×C4
prime radicalD5×#3805C2
cosocleC2×C32×D5C24
hypercenterC22D32×AGL(1,𝔽5)
hypocenterC32×C5#520
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #13088735C2semidirect
3. #67⋊ΓL(1,𝔽16)C2semidirect
4. C2×#10623965C2semidirect
5. C3×AGL(1,𝔽5)×#67C2semidirect
6. #13088419C2semidirect
7. #13088413C2semidirect
8. #13088408C2semidirect
9. D3×Dic3⋊AGL(1,𝔽5)C2semidirect
15. #10624229C4semidirect
16. #10624208C4semidirect
17. C5×#3805C4semidirect
21. #10624047C4semidirect
22. #10624046C4semidirect
23. #10624045C4semidirect
45. AGL(1,𝔽5)×#67D3semidirect
65. C2×C3⋊Dic15C2×C4semidirect
66. C2×C5×C3⋊Dic3C2×C4semidirect
67. C3×#1220C2×C4semidirect
68. C3×C5×#67C2×C4semidirect
69. #67158C2×C4semidirect
70. #67157C2×C4semidirect
71. #67154C2×C4semidirect
72. #67153C2×C4semidirect
73. #67150C2×C4semidirect
74. D3×Dic15C2×C4semidirect
75. Dic3×D15C2×C4semidirect
76. C5×#627C2×C4semidirect
77. C5×#625C2×C4semidirect
78. C5×D3×Dic3C2×C4semidirect
79. D5×C3⋊Dic3C2×C4semidirect
80. D5×C3⋊Dic3C2×C4semidirect
83. C3×#1202C2×C4semidirect
84. C3×#1201C2×C4semidirect
185. #3805AGL(1,𝔽5)semidirect
226. #1220C4×D3semidirect
233. C5×#67C4×D3semidirect
246. #1202C4×D3semidirect
248. #1201C4×D3semidirect
323. C2×C3⋊Dic3C2×AGL(1,𝔽5)semidirect
327. C3×#67C2×AGL(1,𝔽5)semidirect
334. #627C2×AGL(1,𝔽5)semidirect
337. #625C2×AGL(1,𝔽5)semidirect
342. D3×Dic3C2×AGL(1,𝔽5)semidirect
434. C32×C5#520semidirect
535. #67D3×AGL(1,𝔽5)semidirect
626. C3×C5#5546semidirect
676. C32#66266semidirect
724. C5#10594876semidirect
745. C3#11756846semidirect

Maximal subgroups

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

subgroupindex
D5×#38052
#130887352
#67⋊ΓL(1,𝔽16)2
C2×#106239652
C3×AGL(1,𝔽5)×#672
#130884192
#130884132
#130884082
D3×Dic3⋊AGL(1,𝔽5)2
#117568463
#105948765