Finite Group Databasebeta

← #72230326

Subgroups — #72230326

Order 2880.

1716 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3⋊D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×D5×#638C211yesmaximal, characteristic
3C2×#10624098C211yesmaximal, characteristic, complemented
4C2×C32×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5C2×(C2×AGL(1,𝔽5))⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6(C2×AGL(1,𝔽5))⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7(C2×AGL(1,𝔽5))⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11752055—34nomaximal
9C23×C32×D5C2211yescharacteristic
10C22×D5×C3⋊D3C2211yescharacteristic
11C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
12C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
13C22×C32×AGL(1,𝔽5)C2211yescharacteristic
14C22×C32×AGL(1,𝔽5)C2211yescharacteristic
15C2×C3⋊D3×AGL(1,𝔽5)—22no—
16C2×C3⋊D3×AGL(1,𝔽5)—22no—
17C2×C3⋊D3×AGL(1,𝔽5)—22no—
18C2×#67184C411yescharacteristic, complemented
19C2×C5×#638C411yescharacteristic, complemented
20D5×#638—22no—
21D5×#638—22no—
22C2×#67139C411yescharacteristic, complemented
23C2×#67138C411yescharacteristic, complemented
24C2×D5×C3⋊Dic3C2211yescharacteristic
25#10624098—22no—
26C32×C22⋊AGL(1,𝔽5)—22no—
27(C2×AGL(1,𝔽5))⋊(C3⋊D3)—22no—
28#10592655—51nomaximal, Hall
29C22×D3×AGL(1,𝔽5)—34no—
30C2×D5×#67—34no—
31C2×#6763—34no—
32C2×C3×C22⋊AGL(1,𝔽5)D314yescomplemented
33C2×(C2×D3)⋊AGL(1,𝔽5)—34no—
34(C2×AGL(1,𝔽5))⋊Dic3—34no—
35(C2×AGL(1,𝔽5))⋊Dic3—34no—
36C23×C32×C5C2×C411yescharacteristic, complemented
37C22×C3⋊D15C2×C411yescharacteristic
38C22×C5×C3⋊D3C2×C411yescharacteristic
39C22×C32×D5—21no—
40C22×C32×D5—21no—
41C22×C32×D5—21no—
42C22×C32×D5—21no—
43C22×C32×D5—21no—
44C22×C32×D5—21no—
45C22×C32×D5C2×C411yescharacteristic, complemented
46C22×C32×D5C2311yescharacteristic
47C2×D5×C3⋊D3—21no—
48C2×D5×C3⋊D3—21no—
49C2×D5×C3⋊D3—21no—
50C2×D5×C3⋊D3—21no—
51C2×D5×C3⋊D3D412yes—
52C2×D5×C3⋊D3D412yes—
53C2×C3⋊ΓL(1,𝔽16)—21no—
54C2×C3⋊ΓL(1,𝔽16)—21no—
55C2×C3⋊ΓL(1,𝔽16)—21no—
56C2×C3⋊ΓL(1,𝔽16)—21no—
57C2×C3⋊ΓL(1,𝔽16)—21no—
58C2×C3⋊ΓL(1,𝔽16)D412yescomplemented
59C2×C32×AGL(1,𝔽5)—21no—
60C2×C32×AGL(1,𝔽5)—21no—
61C2×C32×AGL(1,𝔽5)—21no—
62C2×C32×AGL(1,𝔽5)—21no—
63C2×C32×AGL(1,𝔽5)—21no—
64C2×C32×AGL(1,𝔽5)D412yescomplemented
65C3⋊D3×AGL(1,𝔽5)—28no—
66#67184—22no—
67C2×C3⋊Dic15C2×C411yescharacteristic, complemented
68C5×#638—22no—
69C2×C5×C3⋊Dic3C2×C411yescharacteristic, complemented
70#67139—22no—
71#67138—22no—
72D5×C3⋊Dic3—21no—
73D5×C3⋊Dic3—21no—
74#65779—91noHall
75C22×#638—51no—
76C22×C4×C3⋊D3—51no—
77C2×C32×C22⋊C4—51no—
78C2×#3757—51no—
79C2×#3752—51no—
80#63658—51no—
81#63658—51no—
82C23×C3×D5C2×D314yes—
83C22×D3×D5—34no—
84C22×ΓL(1,𝔽16)—34no—
85C22×ΓL(1,𝔽16)—34no—
86C22×C3×AGL(1,𝔽5)C2×D314yes—
87C22×C3×AGL(1,𝔽5)C2×D314yes—
88C2×D3×AGL(1,𝔽5)—68no—
89C2×D3×AGL(1,𝔽5)—68no—
90C2×D3×AGL(1,𝔽5)—68no—
91C2×#1220—34no—
92C2×C5×#67—34no—
93D5×#67—68no—
94D5×#67—68no—
95C2×#1202—34no—
96C2×#1201—34no—
97C2×D5×Dic3—34no—
98#6763—68no—
99C3×C22⋊AGL(1,𝔽5)—28no—
100(C2×D3)⋊AGL(1,𝔽5)—68no—
101#4956—154no—
102C22×C32×C5—21no—
103C22×C32×C5—21no—
104C22×C32×C5—21no—
105C22×C32×C5C22×C411yescharacteristic
106C2×C3⋊D15—21no—
107C2×C3⋊D15—21no—
108C2×C3⋊D15C22⋊C412yescomplemented
109C2×C5×C3⋊D3—21no—
110C2×C5×C3⋊D3—21no—
111C2×C5×C3⋊D3C22⋊C412yescomplemented
112C2×C32×D5—21no—
113C2×C32×D5—21no—
114C2×C32×D5—21no—
115C2×C32×D5—41no—
116C2×C32×D5—41no—
117C2×C32×D5—41no—
118C2×C32×D5—41no—
119C2×C32×D5C2×D411yescharacteristic
120C2×C32×D5C2×D411yescharacteristic
121C2×C32×D5C2×D411yescharacteristic
122C2×C32×D5C2×D411yescharacteristic
123C2×C32×D5#4111yescharacteristic
124C2×C32×D5#4111yescharacteristic
125D5×C3⋊D3—22no—
126D5×C3⋊D3—22no—
127D5×C3⋊D3—22no—
128D5×C3⋊D3—22no—
129C3⋊ΓL(1,𝔽16)—22no—
130C3⋊ΓL(1,𝔽16)—41no—
131C32×AGL(1,𝔽5)—22no—
132C32×AGL(1,𝔽5)—41no—
133C3⋊Dic15—21no—
134C5×C3⋊Dic3—21no—
135C23×AGL(1,𝔽5)—91no—
136C2×D4×D5—91no—
137C2×C22⋊AGL(1,𝔽5)—91no—
138C2×C22⋊AGL(1,𝔽5)—91no—
139C2×C22⋊AGL(1,𝔽5)C3⋊D311yescharacteristic, complemented
140(C2×AGL(1,𝔽5))⋊C4—91no—
141(C2×AGL(1,𝔽5))⋊C4—91no—
142C24×C32—51no—
143C23×C3⋊D3—51no—
144C22×C32×C4—51no—
145C22×C32×C4—51no—
146C2×#638—51no—
147C2×#638—51no—
148C2×#638—51no—
149C2×#638—102no—
150C2×#638—102no—
151C2×#638AGL(1,𝔽5)11yescharacteristic, complemented
152C22×C3⋊Dic3—51no—
153C22×C3⋊Dic3—51no—
154C22×C3⋊Dic3—51no—
155C2×C4×C3⋊D3—102no—
156C2×C4×C3⋊D3—102no—
157C2×C4×C3⋊D3—102no—
158C32×C22⋊C4—102no—
159#3757—102no—
160#3752—102no—
161C23×C3×C5C4×D314yescomplemented
162C22×D15—34no—
163C22×C5×D3—34no—
164C22×C3×D5—24no—
165C22×C3×D5—24no—
166C22×C3×D5—24no—
167C22×C3×D5—24no—
168C22×C3×D5—24no—
169C22×C3×D5—24no—
170C22×C3×D5C4×D314yescomplemented
171C22×C3×D5C22×D314yes—
172C2×D3×D5—38no—
173C2×D3×D5—38no—
174C2×D3×D5—64no—
175C2×D3×D5—64no—
176C2×D3×D5—64no—
177C2×D3×D5—64no—
178C2×ΓL(1,𝔽16)—38no—
179C2×ΓL(1,𝔽16)—64no—
180C2×ΓL(1,𝔽16)—64no—
181C2×ΓL(1,𝔽16)—64no—
182C2×ΓL(1,𝔽16)—64no—
183C2×ΓL(1,𝔽16)—64no—
184C2×C3×AGL(1,𝔽5)—24no—
185C2×C3×AGL(1,𝔽5)—24no—
186C2×C3×AGL(1,𝔽5)—24no—
187C2×C3×AGL(1,𝔽5)—24no—
188C2×C3×AGL(1,𝔽5)—24no—
189C2×C3×AGL(1,𝔽5)#6718yescomplemented
190D3×AGL(1,𝔽5)—632no—
191#1220—68no—
192C2×Dic15—34no—
193C5×#67—68no—
194C2×C5×Dic3—34no—
195#1202—68no—
196#1201—68no—
197D5×Dic3—64no—
198D5×Dic3—64no—
199C22×#67—154no—
200C22×C4×D3—154no—
201C2×C3×C22⋊C4—54no—
202C2×#217—154no—
203C2×(C2×D3)⋊C4—154no—
204C3⋊#95—154no—
205C3⋊#95—154no—
206C2×C32×C5—41no—
207C2×C32×C5C2×C22⋊C411yescharacteristic
208C2×C32×C5C4×D411yescharacteristic
209C2×C32×C5C4×D411yescharacteristic
210C3⋊D15—22no—
211C5×C3⋊D3—22no—
212C32×D5—41no—
213C32×D5#12011yescharacteristic
214C32×D5#12111yescharacteristic
215C32×D5#12111yescharacteristic
216C32×D5#12311yescharacteristic
217C23×D5—91no—
218C23×D5C2×C3⋊D311yescharacteristic
219C22×AGL(1,𝔽5)—91no—
220C22×AGL(1,𝔽5)—91no—
221C22×AGL(1,𝔽5)—182no—
222C22×AGL(1,𝔽5)—182no—
223C22×AGL(1,𝔽5)—182no—
224C22×AGL(1,𝔽5)C2×C3⋊D311yescharacteristic
225C22×AGL(1,𝔽5)C2×C3⋊D311yescharacteristic
226C2×C5×D4—91no—
227C2×C22⋊D5—91no—
228C2×C22⋊D5—91no—
229D4×D5—182no—
230D4×D5—182no—
231C2×D20—91no—
232C2×C4×D5—91no—
233C22⋊AGL(1,𝔽5)—22no—
234C22⋊AGL(1,𝔽5)—182no—
235C22⋊AGL(1,𝔽5)—182no—
236C23×C32—51no—
237C23×C32—51no—
238C23×C32—101no—
239C23×C32—101no—
240C23×C32—101no—
241C23×C32—101no—
242C23×C32—101no—
243C23×C32—101no—
244C23×C32C2×AGL(1,𝔽5)11yescharacteristic, complemented
245C22×C3⋊D3—51no—
246C22×C3⋊D3—52no—
247C22×C3⋊D3—52no—
248C22×C3⋊D3—101no—
249C22×C3⋊D3—101no—
250C22×C3⋊D3—101no—
251C22×C3⋊D3—101no—
252C22×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
253C2×C32×C4—52no—
254C2×C32×C4—101no—
255C2×C32×C4—101no—
256C2×C32×C4—101no—
257C2×C32×C4—101no—
258C2×C32×C4—101no—
259#638—22no—
260#638—102no—
261#638—102no—
262#638—102no—
263C2×C3⋊Dic3—52no—
264C2×C3⋊Dic3—51no—
265C2×C3⋊Dic3—101no—
266C2×C3⋊Dic3—101no—
267C2×C3⋊Dic3—101no—
268C2×C3⋊Dic3—101no—
269C2×C3⋊Dic3—101no—
270C2×C3⋊Dic3—101no—
271C2×C3⋊Dic3—101no—
272C2×C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
273C4×C3⋊D3—108no—
274#386—451noSylow
275C22×C3×C5—24no—
276C22×C3×C5—24no—
277C22×C3×C5—24no—
278C22×C3×C5C2×C4×D314yes—
279C2×D15—38no—
280C2×D15—64no—
281C2×D15—64no—
282C2×C5×D3—38no—
283C2×C5×D3—64no—
284C2×C5×D3—64no—
285C2×C3×D5—24no—
286C2×C3×D5—24no—
287C2×C3×D5—24no—
288C2×C3×D5—44no—
289C2×C3×D5—44no—
290C2×C3×D5—44no—
291C2×C3×D5—44no—
292C2×C3×D5#23514yes—
293C2×C3×D5D3×D414yes—
294C2×C3×D5D3×D414yes—
295C2×C3×D5D3×D414yes—
296C2×C3×D5#23714yes—
297C2×C3×D5C2×#6714yes—
298D3×D5—68no—
299D3×D5—68no—
300D3×D5—68no—
301D3×D5—68no—
302ΓL(1,𝔽16)—68no—
303ΓL(1,𝔽16)—124no—
304C3×AGL(1,𝔽5)—28no—
305C3×AGL(1,𝔽5)—44no—
306Dic15—64no—
307C5×Dic3—64no—
308C24×C3—54no—
309C23×D3—154no—
310C22×C3×C4—54no—
311C22×C3×C4—54no—
312C2×#67—34no—
313C2×#67—154no—
314C2×#67—154no—
315C2×#67—154no—
316C2×#67—308no—
317C2×#67—308no—
318C22×Dic3—154no—
319C22×Dic3—154no—
320C22×Dic3—154no—
321C2×C4×D3—308no—
322C2×C4×D3—308no—
323C2×C4×D3—308no—
324C3×C22⋊C4—108no—
325#217—308no—
326(C2×D3)⋊C4—308no—
327C32×C5#38611yescharacteristic, complemented, Hall
328C23×C5—91no—
329C23×C5C4×C3⋊D311yescharacteristic, complemented
330C22×D5—21no—
331C22×D5—21no—
332C22×D5—21no—
333C22×D5—21no—
334C22×D5—21no—
335C22×D5—21no—
336C22×D5—91no—
337C22×D5—92no—
338C22×D5—92no—
339C22×D5—181no—
340C22×D5—181no—
341C22×D5—181no—
342C22×D5—181no—
343C22×D5C4×C3⋊D311yescharacteristic, complemented
344C22×D5C22×C3⋊D311yescharacteristic
345C2×AGL(1,𝔽5)—21no—
346C2×AGL(1,𝔽5)—21no—
347C2×AGL(1,𝔽5)—21no—
348C2×AGL(1,𝔽5)—21no—
349C2×AGL(1,𝔽5)—21no—
350C2×AGL(1,𝔽5)—92no—
351C2×AGL(1,𝔽5)—188no—
352C2×AGL(1,𝔽5)—181no—
353C2×AGL(1,𝔽5)—181no—
354C2×AGL(1,𝔽5)—181no—
355C2×AGL(1,𝔽5)—181no—
356C2×AGL(1,𝔽5)—181no—
357C2×AGL(1,𝔽5)#63812yescomplemented
358C5×D4—182no—
359C2×C4×C5—91no—
360C22⋊D5—182no—
361C22⋊D5—182no—
362C2×Dic5—91no—
363D20—182no—
364C4×D5—181no—
365C4×D5—181no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—51no—
370C22×C32—51no—
371C22×C32—51no—
372C22×C32—51no—
373C22×C32—51no—
374C22×C32—51no—
375C22×C32—101no—
376C22×C32—101no—
377C22×C32—101no—
378C22×C32—201no—
379C22×C32—201no—
380C22×C32—201no—
381C22×C32—201no—
382C22×C32C22×AGL(1,𝔽5)11yescharacteristic
383C2×C3⋊D3—21no—
384C2×C3⋊D3—21no—
385C2×C3⋊D3—52no—
386C2×C3⋊D3—102no—
387C2×C3⋊D3—102no—
388C2×C3⋊D3—102no—
389C2×C3⋊D3—102no—
390C2×C3⋊D3—101no—
391C2×C3⋊D3—101no—
392C2×C3⋊D3C22⋊AGL(1,𝔽5)12yescomplemented
393C32×C4—102no—
394C32×C4—201no—
395C3⋊Dic3—21no—
396C3⋊Dic3—102no—
397C3⋊Dic3—101no—
398C3⋊Dic3—201no—
399C22×D4—451no—
400C23×C4—451no—
401C2×C22⋊C4—51no—
402C2×C22⋊C4—451no—
403C2×C22⋊C4—451no—
404#95—451no—
405#95—451no—
406C2×C3×C5—44no—
407C2×C3×C5D3×C22⋊C414yes—
408C2×C3×C5#67⋊C414yes—
409C2×C3×C5C4×#6714yes—
410D15—68no—
411C3×D5—44no—
412C3×D5#88314yes—
413C3×D5#88414yes—
414C3×D5#93714yes—
415C3×D5#93814yes—
416C5×D3—68no—
417C23×C3—54no—
418C23×C3—54no—
419C23×C3—104no—
420C23×C3—104no—
421C23×C3—104no—
422C23×C3—104no—
423C23×C3—104no—
424C23×C3—104no—
425C23×C3D3×AGL(1,𝔽5)14yescomplemented
426C22×D3—34no—
427C22×D3—158no—
428C22×D3—158no—
429C22×D3—154no—
430C22×D3—304no—
431C22×D3—304no—
432C22×D3—304no—
433C22×D3—304no—
434C2×C3×C4—58no—
435C2×C3×C4—104no—
436C2×C3×C4—104no—
437C2×C3×C4—104no—
438C2×C3×C4—104no—
439C2×C3×C4—104no—
440#67—68no—
441#67—308no—
442#67—308no—
443#67—308no—
444C2×Dic3—34no—
445C2×Dic3—158no—
446C2×Dic3—154no—
447C2×Dic3—304no—
448C2×Dic3—304no—
449C2×Dic3—304no—
450C2×Dic3—304no—
451C2×Dic3—304no—
452C2×Dic3—304no—
453C2×Dic3—304no—
454C4×D3—3032no—
455C22×C5—21no—
456C22×C5—21no—
457C22×C5—21no—
458C22×C5—92no—
459C22×C5—181no—
460C22×C5—181no—
461C22×C5C2×C4×C3⋊D311yescharacteristic
462C2×D5—21no—
463C2×D5—21no—
464C2×D5—21no—
465C2×D5—41no—
466C2×D5—41no—
467C2×D5—41no—
468C2×D5—41no—
469C2×D5—92no—
470C2×D5—181no—
471C2×D5—181no—
472C2×D5—182no—
473C2×D5—182no—
474C2×D5—182no—
475C2×D5—182no—
476C2×D5#382811yescharacteristic
477C2×D5D4×C3⋊D311yescharacteristic
478C2×D5D4×C3⋊D311yescharacteristic
479C2×D5D4×C3⋊D311yescharacteristic
480C2×D5#383011yescharacteristic
481C2×D5C2×#63811yescharacteristic
482AGL(1,𝔽5)—22no—
483AGL(1,𝔽5)—41no—
484AGL(1,𝔽5)—182no—
485AGL(1,𝔽5)—361no—
486C4×C5—181no—
487Dic5—181no—
488C2×C32—41no—
489C2×C32—51no—
490C2×C32—51no—
491C2×C32—51no—
492C2×C32—51no—
493C2×C32—201no—
494C2×C32D4×AGL(1,𝔽5)11yescharacteristic
495C2×C32D4×AGL(1,𝔽5)11yescharacteristic
496C2×C32C2×C22⋊AGL(1,𝔽5)11yescharacteristic
497C3⋊D3—22no—
498C3⋊D3—102no—
499C24—51no—
500C24—451no—
501C2×D4—91no—
502C2×D4—451no—
503C2×D4—451no—
504C2×D4—451no—
505C2×D4—902no—
506C2×D4—902no—
507C22×C4—51no—
508C22×C4—51no—
509C22×C4—451no—
510C22×C4—451no—
511C22×C4—451no—
512C22×C4—902no—
513C22×C4—902no—
514C22×C4—902no—
515C22⋊C4—102no—
516C22⋊C4—902no—
517C22⋊C4—902no—
518C3×C5#495614yescomplemented
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—54no—
523C22×C3—54no—
524C22×C3—54no—
525C22×C3—54no—
526C22×C3—54no—
527C22×C3—54no—
528C22×C3—104no—
529C22×C3—104no—
530C22×C3—104no—
531C22×C3—204no—
532C22×C3—204no—
533C22×C3—204no—
534C22×C3—204no—
535C22×C3C2×D3×AGL(1,𝔽5)14yes—
536C2×D3—38no—
537C2×D3—64no—
538C2×D3—64no—
539C2×D3—158no—
540C2×D3—308no—
541C2×D3—308no—
542C2×D3—308no—
543C2×D3—308no—
544C2×D3—304no—
545C2×D3—304no—
546C3×C4—108no—
547C3×C4—204no—
548Dic3—64no—
549Dic3—308no—
550Dic3—304no—
551Dic3—604no—
552C2×C5—41no—
553C2×C5—182no—
554C2×C5C22⋊C4×C3⋊D311yescharacteristic
555C2×C5#6409011yescharacteristic
556C2×C5C4×#63811yescharacteristic
557D5—41no—
558D5—182no—
559D5#6409211yescharacteristic
560D5#6409311yescharacteristic
561D5#6414611yescharacteristic
562D5#6414711yescharacteristic
563C32#6577911yescharacteristic, complemented, Sylow
564C23—51no—
565C23—51no—
566C23—91no—
567C23—101no—
568C23—101no—
569C23—101no—
570C23—101no—
571C23—101no—
572C23—101no—
573C23—452no—
574C23—452no—
575C23—451no—
576C23—901no—
577C23—901no—
578C23—901no—
579C23—901no—
580C23C3⋊D3×AGL(1,𝔽5)11yescharacteristic, complemented
581D4—182no—
582D4—902no—
583D4—902no—
584D4—902no—
585C2×C4—52no—
586C2×C4—91no—
587C2×C4—101no—
588C2×C4—101no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—452no—
593C2×C4—451no—
594C2×C4—908no—
595C2×C4—901no—
596C2×C4—901no—
597C2×C4—901no—
598C2×C4—901no—
599C2×C4—901no—
600C2×C4—901no—
601C2×C4—901no—
602C2×C3—44no—
603C2×C3—54no—
604C2×C3—54no—
605C2×C3—54no—
606C2×C3—54no—
607C2×C3—204no—
608C2×C3AGL(1,𝔽5)×#6714yes—
609C2×C3D3×C22⋊AGL(1,𝔽5)14yes—
610C2×C3#67⋊AGL(1,𝔽5)14yes—
611D3—68no—
612D3—308no—
613C5#1059265511yescharacteristic, complemented, Sylow
614C22—21no—
615C22—21no—
616C22—21no—
617C22—51no—
618C22—51no—
619C22—51no—
620C22—51no—
621C22—51no—
622C22—51no—
623C22—92no—
624C22—101no—
625C22—101no—
626C22—101no—
627C22—181no—
628C22—181no—
629C22—201no—
630C22—201no—
631C22—201no—
632C22—201no—
633C22—452no—
634C22—902no—
635C22—902no—
636C22—902no—
637C22—902no—
638C22—901no—
639C22—901no—
640C22C2×C3⋊D3×AGL(1,𝔽5)11yescharacteristic
641C4—102no—
642C4—181no—
643C4—201no—
644C4—902no—
645C4—901no—
646C4—1801no—
647C3#1175205514yescomplemented
648C2—41no—
649C2—51no—
650C2—51no—
651C2—51no—
652C2—51no—
653C2—182no—
654C2—201no—
655C2—902no—
656C2AGL(1,𝔽5)×#63811yescharacteristic
657C2C3⋊D3×C22⋊AGL(1,𝔽5)11yescharacteristic
658C2#1308869011yescharacteristic
subgroupG/H
center, FrattiniC22C2×C3⋊D3×AGL(1,𝔽5)
commutator, socleC22×C32×C5C22×C4
FittingC23×C32×C5C2×C4
prime radicalC2×D5×#638C2
cosocleC22×C32×D5C23
hypercenterC23C3⋊D3×AGL(1,𝔽5)
hypocenterC32×C5#386
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊D3×AGL(1,𝔽5)C2semidirect
3. C2×#10624098C2semidirect
4. C2×C32×C22⋊AGL(1,𝔽5)C2semidirect
5. C2×(C2×AGL(1,𝔽5))⋊(C3⋊D3)C2semidirect
6. (C2×AGL(1,𝔽5))⋊(C3⋊Dic3)C2semidirect
7. (C2×AGL(1,𝔽5))⋊(C3⋊Dic3)C2semidirect
18. C2×#67184C4semidirect
19. C2×C5×#638C4semidirect
22. C2×#67139C4semidirect
23. C2×#67138C4semidirect
32. C2×C3×C22⋊AGL(1,𝔽5)D3semidirect
36. C23×C32×C5C2×C4semidirect
45. C22×C32×D5C2×C4semidirect
58. C2×C3⋊ΓL(1,𝔽16)D4semidirect
64. C2×C32×AGL(1,𝔽5)D4semidirect
67. C2×C3⋊Dic15C2×C4semidirect
69. C2×C5×C3⋊Dic3C2×C4semidirect
108. C2×C3⋊D15C22⋊C4semidirect
111. C2×C5×C3⋊D3C22⋊C4semidirect
139. C2×C22⋊AGL(1,𝔽5)C3⋊D3semidirect
151. C2×#638AGL(1,𝔽5)semidirect
161. C23×C3×C5C4×D3semidirect
170. C22×C3×D5C4×D3semidirect
189. C2×C3×AGL(1,𝔽5)#67semidirect
244. C23×C32C2×AGL(1,𝔽5)semidirect
272. C2×C3⋊Dic3C2×AGL(1,𝔽5)semidirect
327. C32×C5#386semidirect
329. C23×C5C4×C3⋊D3semidirect
343. C22×D5C4×C3⋊D3semidirect
357. C2×AGL(1,𝔽5)#638semidirect
392. C2×C3⋊D3C22⋊AGL(1,𝔽5)semidirect
425. C23×C3D3×AGL(1,𝔽5)semidirect
518. C3×C5#4956semidirect
563. C32#65779semidirect
580. C23C3⋊D3×AGL(1,𝔽5)semidirect
613. C5#10592655semidirect
647. C3#11752055semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊D3×AGL(1,𝔽5)2
C2×D5×#6382
C2×#106240982
C2×C32×C22⋊AGL(1,𝔽5)2
C2×(C2×AGL(1,𝔽5))⋊(C3⋊D3)2
(C2×AGL(1,𝔽5))⋊(C3⋊Dic3)2
#117520553
#105926555