Finite Group Databasebeta

← C3×#10604799 #14301024

Subgroups — C3×#10604799 #14301024

Order 1920.

876 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×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×C3×D5×D8C211yesmaximal, characteristic
3C3×#65780C211yesmaximal, characteristic, complemented
4C2×C3×#4007C211yesmaximal, characteristic, complemented
5C2×C3×#4007C211yesmaximal, characteristic, complemented
6C3×#64893C211yesmaximal, characteristic, complemented
7C3×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic, complemented
8#10604799C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×AGL(1,𝔽5)—21no—
10C2×C3×D4×D5C2211yescharacteristic
11C2×C3×D4×D5C2211yescharacteristic
12C2×C3×C22⋊AGL(1,𝔽5)—21no—
13C2×C3×C22⋊AGL(1,𝔽5)—21no—
14C2×C3×C22⋊AGL(1,𝔽5)—21no—
15C3×D4×AGL(1,𝔽5)—22no—
16C3×D4×AGL(1,𝔽5)—22no—
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×C3×D5⋊C8C2211yescharacteristic
21C2×C3×C5×D8C411yescharacteristic, complemented
22C2×C3×#686C411yescharacteristic, complemented
23C2×C3×#686C411yescharacteristic, complemented
24C3×D5×D8—22no—
25C3×D5×D8—22no—
26C2×C3×D40C411yescharacteristic, complemented
27C2×C3×C8×D5C2211yescharacteristic
28C3×#4007—22no—
29C3×#4007—22no—
30C3×#1879—51nomaximal, Hall
31C2×D4×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
32C2×D5×D8C2×C311yescharacteristic
33#65780C2×C311yescharacteristic, complemented
34C2×#4007C2×C311yescharacteristic, complemented
35C2×#4007C2×C311yescharacteristic, complemented
36#64893C2×C311yescharacteristic, complemented
37(C2×AGL(1,𝔽5))⋊C8C2×C311yescharacteristic, complemented
38C23×C3×D5—21no—
39C23×C3×D5—21no—
40C22×C3×AGL(1,𝔽5)—24no—
41C22×C3×AGL(1,𝔽5)—21no—
42C22×C3×AGL(1,𝔽5)—21no—
43C22×C3×AGL(1,𝔽5)—42no—
44C22×C3×AGL(1,𝔽5)—42no—
45C22×C3×AGL(1,𝔽5)D411yescharacteristic
46C22×C3×AGL(1,𝔽5)D411yescharacteristic
47C2×C3×C5×D4C2×C411yescharacteristic
48C2×C3×C5×D4C2×C411yescharacteristic, complemented
49C2×C3×C22⋊D5—21no—
50C2×C3×C22⋊D5—21no—
51C3×D4×D5—21no—
52C3×D4×D5—21no—
53C3×D4×D5—21no—
54C3×D4×D5—21no—
55C3×D4×D5—21no—
56C3×D4×D5—21no—
57C3×D4×D5D412yes—
58C3×D4×D5D412yes—
59C2×C3×D20C2×C411yescharacteristic
60C2×C3×D20C2×C411yescharacteristic, complemented
61C2×C3×C4×D5C2311yescharacteristic
62C3×C22⋊AGL(1,𝔽5)—24no—
63C3×C22⋊AGL(1,𝔽5)—42no—
64C3×C22⋊AGL(1,𝔽5)—42no—
65C2×C3×#170—21no—
66C3×C4⋊AGL(1,𝔽5)—21no—
67C3×C4⋊AGL(1,𝔽5)—21no—
68C3×C4⋊AGL(1,𝔽5)—21no—
69C3×C4⋊AGL(1,𝔽5)D412yes—
70C3×C4×AGL(1,𝔽5)—21no—
71C3×C4×AGL(1,𝔽5)—21no—
72C3×D5⋊C8—21no—
73C3×D5⋊C8—21no—
74C3×C5×D8—22no—
75C2×C3×C5×C8C2×C411yescharacteristic, complemented
76C3×#686—22no—
77C3×#686—22no—
78C2×C3×#168C2×C411yescharacteristic, complemented
79C3×D40—22no—
80C3×C8×D5—21no—
81C3×C8×D5—21no—
82C22×C3×D8—51no—
83C2×C3×C4×D4—51no—
84C2×C3×#102—51no—
85C2×C3×#102—51no—
86C3×#390—51no—
87C3×#340—51no—
88C3×#336—51no—
89C23×AGL(1,𝔽5)—21no—
90C2×D4×D5C22×C311yescharacteristic
91C2×D4×D5C22×C311yescharacteristic
92C2×C22⋊AGL(1,𝔽5)—21no—
93C2×C22⋊AGL(1,𝔽5)—21no—
94C2×C22⋊AGL(1,𝔽5)—21no—
95D4×AGL(1,𝔽5)—22no—
96D4×AGL(1,𝔽5)—22no—
97C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
98C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
99C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
100C2×D5⋊C8C22×C311yescharacteristic
101C2×C5×D8C3×C411yescharacteristic, complemented
102C2×#686C3×C411yescharacteristic, complemented
103C2×#686C3×C411yescharacteristic, complemented
104D5×D8—22no—
105D5×D8—22no—
106C2×D40C3×C411yescharacteristic, complemented
107C2×C8×D5C22×C311yescharacteristic
108#4007—22no—
109#4007—22no—
110#1879—51noSylow
111C23×C3×C5—21no—
112C23×C3×C5—21no—
113C22×C3×D5—21no—
114C22×C3×D5—22no—
115C22×C3×D5—22no—
116C22×C3×D5—21no—
117C22×C3×D5—41no—
118C22×C3×D5—41no—
119C22×C3×D5—41no—
120C22×C3×D5—41no—
121C22×C3×D5—41no—
122C22×C3×D5—41no—
123C22×C3×D5—41no—
124C22×C3×D5—41no—
125C22×C3×D5—41no—
126C22×C3×D5—41no—
127C22×C3×D5C2×D411yescharacteristic
128C2×C3×AGL(1,𝔽5)—21no—
129C2×C3×AGL(1,𝔽5)—21no—
130C2×C3×AGL(1,𝔽5)—21no—
131C2×C3×AGL(1,𝔽5)—22no—
132C2×C3×AGL(1,𝔽5)—21no—
133C2×C3×AGL(1,𝔽5)—21no—
134C2×C3×AGL(1,𝔽5)—48no—
135C2×C3×AGL(1,𝔽5)—41no—
136C2×C3×AGL(1,𝔽5)—41no—
137C2×C3×AGL(1,𝔽5)—41no—
138C2×C3×AGL(1,𝔽5)—41no—
139C2×C3×AGL(1,𝔽5)—41no—
140C2×C3×AGL(1,𝔽5)D812yescomplemented
141C3×C5×D4—21no—
142C3×C5×D4—21no—
143C3×C5×D4—21no—
144C3×C5×D4C22⋊C412yescomplemented
145C2×C3×C4×C5C22×C411yescharacteristic
146C3×C22⋊D5—22no—
147C3×C22⋊D5—22no—
148C3×C22⋊D5—41no—
149C3×C22⋊D5—41no—
150C2×C3×Dic5#4111yescharacteristic
151C3×D20—21no—
152C3×D20—21no—
153C3×D20—21no—
154C3×D20C22⋊C412yescomplemented
155C3×C4×D5C2×D411yescharacteristic
156C3×C4×D5C2×D411yescharacteristic
157C3×C4×D5C2×D411yescharacteristic
158C3×C4×D5#4111yescharacteristic
159C3×#170—41no—
160C3×C5×C8—21no—
161C3×#168—21no—
162C22×C3×D4—51no—
163C22×C3×D4—51no—
164C23×C3×C4—101no—
165C2×C3×D8—51no—
166C2×C3×D8—51no—
167C2×C3×D8—51no—
168C2×C3×D8—102no—
169C2×C3×D8—102no—
170C2×C3×D8AGL(1,𝔽5)11yescharacteristic, complemented
171C22×C3×C8—51no—
172C22×C3×C8—51no—
173C3×C4×D4—102no—
174C3×C4×D4—102no—
175C2×C3×C4⋊C4—51no—
176C2×C3×C4⋊C4—51no—
177C2×C3×C22⋊C4—101no—
178C2×C3×C22⋊C4—101no—
179C2×C3×C22⋊C4—101no—
180C2×C3×C42—51no—
181C3×#102—102no—
182C3×#102—102no—
183C23×D5—21no—
184C23×D5—21no—
185C22×AGL(1,𝔽5)—24no—
186C22×AGL(1,𝔽5)—21no—
187C22×AGL(1,𝔽5)—21no—
188C22×AGL(1,𝔽5)—42no—
189C22×AGL(1,𝔽5)—42no—
190C22×AGL(1,𝔽5)C3×D411yescharacteristic
191C22×AGL(1,𝔽5)C3×D411yescharacteristic
192C2×C5×D4C2×C3×C411yescharacteristic
193C2×C5×D4C2×C3×C411yescharacteristic, complemented
194C2×C22⋊D5—21no—
195C2×C22⋊D5—21no—
196D4×D5—21no—
197D4×D5—21no—
198D4×D5—21no—
199D4×D5—21no—
200D4×D5—21no—
201D4×D5—21no—
202D4×D5C3×D412yes—
203D4×D5C3×D412yes—
204C2×D20C2×C3×C411yescharacteristic
205C2×D20C2×C3×C411yescharacteristic, complemented
206C2×C4×D5C23×C311yescharacteristic
207C22⋊AGL(1,𝔽5)—24no—
208C22⋊AGL(1,𝔽5)—42no—
209C22⋊AGL(1,𝔽5)—42no—
210C2×#170—21no—
211C4⋊AGL(1,𝔽5)—21no—
212C4⋊AGL(1,𝔽5)—21no—
213C4⋊AGL(1,𝔽5)—21no—
214C4⋊AGL(1,𝔽5)C3×D412yes—
215C4×AGL(1,𝔽5)—21no—
216C4×AGL(1,𝔽5)—21no—
217D5⋊C8—21no—
218D5⋊C8—21no—
219C5×D8—22no—
220C2×C5×C8C2×C3×C411yescharacteristic, complemented
221#686—22no—
222#686—22no—
223C2×#168C2×C3×C411yescharacteristic, complemented
224D40—22no—
225C8×D5—21no—
226C8×D5—21no—
227C22×D8—51no—
228C2×C4×D4—51no—
229C2×#102—51no—
230C2×#102—51no—
231#390—51no—
232#340—51no—
233#336—51no—
234C22×C3×C5—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5C4×D411yescharacteristic
241C2×C3×D5—22no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C2×C3×D5—42no—
245C2×C3×D5—42no—
246C2×C3×D5—42no—
247C2×C3×D5—42no—
248C2×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C2×C3×D5—81no—
252C2×C3×D5—81no—
253C2×C3×D5—81no—
254C2×C3×D5—81no—
255C2×C3×D5#12011yescharacteristic
256C2×C3×D5#12111yescharacteristic
257C2×C3×D5C2×D811yescharacteristic
258C2×C3×D5#13511yescharacteristic
259C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
260C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
261C3×AGL(1,𝔽5)—22no—
262C3×AGL(1,𝔽5)—42no—
263C3×AGL(1,𝔽5)—41no—
264C3×AGL(1,𝔽5)—81no—
265C3×C4×C5C2×C22⋊C411yescharacteristic
266C3×C4×C5C4×D411yescharacteristic
267C3×Dic5#12111yescharacteristic
268C3×Dic5#12311yescharacteristic
269C24×C3—101no—
270C24×C3—101no—
271C2×C3×D4—52no—
272C2×C3×D4—52no—
273C2×C3×D4—51no—
274C2×C3×D4—51no—
275C2×C3×D4—101no—
276C2×C3×D4—101no—
277C2×C3×D4—101no—
278C2×C3×D4—101no—
279C2×C3×D4—101no—
280C2×C3×D4—101no—
281C2×C3×D4—101no—
282C2×C3×D4—101no—
283C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
284C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—101no—
289C22×C3×C4—104no—
290C22×C3×C4—101no—
291C22×C3×C4—202no—
292C22×C3×C4—202no—
293C3×D8—22no—
294C3×D8—102no—
295C3×D8—102no—
296C3×D8—102no—
297C2×C3×C8—51no—
298C2×C3×C8—101no—
299C2×C3×C8—101no—
300C2×C3×C8—101no—
301C2×C3×C8—101no—
302C2×C3×C8—101no—
303C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic, complemented
304C3×C4⋊C4—52no—
305C3×C4⋊C4—101no—
306C3×C4⋊C4—101no—
307C3×C4⋊C4—101no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—202no—
310C3×C22⋊C4—202no—
311C3×C42—101no—
312C3×C42—101no—
313C23×C5—21no—
314C23×C5—21no—
315C22×D5—21no—
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—21no—
319C22×D5—41no—
320C22×D5—41no—
321C22×D5—41no—
322C22×D5—41no—
323C22×D5—41no—
324C22×D5—41no—
325C22×D5—41no—
326C22×D5—41no—
327C22×D5—41no—
328C22×D5—41no—
329C22×D5C2×C3×D411yescharacteristic
330C2×AGL(1,𝔽5)—21no—
331C2×AGL(1,𝔽5)—21no—
332C2×AGL(1,𝔽5)—21no—
333C2×AGL(1,𝔽5)—22no—
334C2×AGL(1,𝔽5)—21no—
335C2×AGL(1,𝔽5)—21no—
336C2×AGL(1,𝔽5)—48no—
337C2×AGL(1,𝔽5)—41no—
338C2×AGL(1,𝔽5)—41no—
339C2×AGL(1,𝔽5)—41no—
340C2×AGL(1,𝔽5)—41no—
341C2×AGL(1,𝔽5)—41no—
342C2×AGL(1,𝔽5)C3×D812yescomplemented
343C5×D4—21no—
344C5×D4—21no—
345C5×D4—21no—
346C5×D4C3×C22⋊C412yescomplemented
347C2×C4×C5C22×C3×C411yescharacteristic
348C22⋊D5—22no—
349C22⋊D5—22no—
350C22⋊D5—41no—
351C22⋊D5—41no—
352C2×Dic5C3×#4111yescharacteristic
353D20—21no—
354D20—21no—
355D20—21no—
356D20C3×C22⋊C412yescomplemented
357C4×D5C2×C3×D411yescharacteristic
358C4×D5C2×C3×D411yescharacteristic
359C4×D5C2×C3×D411yescharacteristic
360C4×D5C3×#4111yescharacteristic
361#170—41no—
362C5×C8—21no—
363#168—21no—
364C22×D4—51no—
365C22×D4—51no—
366C23×C4—101no—
367C2×D8—51no—
368C2×D8—51no—
369C2×D8—51no—
370C2×D8—102no—
371C2×D8—102no—
372C2×D8C3×AGL(1,𝔽5)11yescharacteristic, complemented
373C22×C8—51no—
374C22×C8—51no—
375C4×D4—102no—
376C4×D4—102no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—51no—
379C2×C22⋊C4—101no—
380C2×C22⋊C4—101no—
381C2×C22⋊C4—101no—
382C2×C42—51no—
383#102—102no—
384#102—102no—
385C2×C3×C5—42no—
386C2×C3×C5—81no—
387C2×C3×C5#38611yescharacteristic
388C2×C3×C5C4×D811yescharacteristic
389C2×C3×C5#44211yescharacteristic
390C3×D5—42no—
391C3×D5—81no—
392C3×D5#44711yescharacteristic
393C3×D5#44911yescharacteristic
394C3×D5#45911yescharacteristic
395C3×D5#46311yescharacteristic
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—51no—
399C23×C3—102no—
400C23×C3—102no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—201no—
404C23×C3—201no—
405C23×C3—201no—
406C23×C3—201no—
407C23×C3—201no—
408C23×C3—201no—
409C23×C3—201no—
410C23×C3—201no—
411C23×C3—201no—
412C23×C3—201no—
413C3×D4—21no—
414C3×D4—21no—
415C3×D4—21no—
416C3×D4—52no—
417C3×D4—102no—
418C3×D4—102no—
419C3×D4—101no—
420C3×D4—101no—
421C3×D4—101no—
422C3×D4—201no—
423C3×D4—201no—
424C3×D4C22⋊AGL(1,𝔽5)12yescomplemented
425C2×C3×C4—51no—
426C2×C3×C4—51no—
427C2×C3×C4—51no—
428C2×C3×C4—51no—
429C2×C3×C4—51no—
430C2×C3×C4—52no—
431C2×C3×C4—101no—
432C2×C3×C4—101no—
433C2×C3×C4—101no—
434C2×C3×C4—102no—
435C2×C3×C4—101no—
436C2×C3×C4—101no—
437C2×C3×C4—208no—
438C2×C3×C4—201no—
439C2×C3×C4—201no—
440C2×C3×C4—201no—
441C2×C3×C4—201no—
442C2×C3×C4—201no—
443C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
444C3×C8—21no—
445C3×C8—101no—
446C3×C8—201no—
447C22×C5—22no—
448C22×C5—41no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5C3×C4×D411yescharacteristic
454C2×D5—22no—
455C2×D5—41no—
456C2×D5—41no—
457C2×D5—42no—
458C2×D5—42no—
459C2×D5—42no—
460C2×D5—42no—
461C2×D5—41no—
462C2×D5—41no—
463C2×D5—41no—
464C2×D5—81no—
465C2×D5—81no—
466C2×D5—81no—
467C2×D5—81no—
468C2×D5C3×#12011yescharacteristic
469C2×D5C3×#12111yescharacteristic
470C2×D5C2×C3×D811yescharacteristic
471C2×D5C3×#13511yescharacteristic
472C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
473C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
474AGL(1,𝔽5)—22no—
475AGL(1,𝔽5)—42no—
476AGL(1,𝔽5)—41no—
477AGL(1,𝔽5)—81no—
478C4×C5C2×C3×C22⋊C411yescharacteristic
479C4×C5C3×C4×D411yescharacteristic
480Dic5C3×#12111yescharacteristic
481Dic5C3×#12311yescharacteristic
482C24—101no—
483C24—101no—
484C2×D4—52no—
485C2×D4—52no—
486C2×D4—51no—
487C2×D4—51no—
488C2×D4—101no—
489C2×D4—101no—
490C2×D4—101no—
491C2×D4—101no—
492C2×D4—101no—
493C2×D4—101no—
494C2×D4—101no—
495C2×D4—101no—
496C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
497C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
498C22×C4—51no—
499C22×C4—51no—
500C22×C4—51no—
501C22×C4—101no—
502C22×C4—104no—
503C22×C4—101no—
504C22×C4—202no—
505C22×C4—202no—
506D8—22no—
507D8—102no—
508D8—102no—
509D8—102no—
510C2×C8—51no—
511C2×C8—101no—
512C2×C8—101no—
513C2×C8—101no—
514C2×C8—101no—
515C2×C8—101no—
516C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
517C4⋊C4—52no—
518C4⋊C4—101no—
519C4⋊C4—101no—
520C4⋊C4—101no—
521C22⋊C4—104no—
522C22⋊C4—202no—
523C22⋊C4—202no—
524C42—101no—
525C42—101no—
526C3×C5#187911yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—51no—
534C22×C3—51no—
535C22×C3—51no—
536C22×C3—51no—
537C22×C3—51no—
538C22×C3—51no—
539C22×C3—102no—
540C22×C3—202no—
541C22×C3—202no—
542C22×C3—202no—
543C22×C3—202no—
544C22×C3—201no—
545C22×C3—201no—
546C22×C3—201no—
547C22×C3—201no—
548C22×C3—201no—
549C22×C3—401no—
550C22×C3—401no—
551C22×C3—401no—
552C22×C3—401no—
553C22×C3D4×AGL(1,𝔽5)11yescharacteristic
554C3×C4—51no—
555C3×C4—51no—
556C3×C4—102no—
557C3×C4—201no—
558C3×C4—202no—
559C3×C4—401no—
560C3×C4D4×AGL(1,𝔽5)11yescharacteristic
561C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
562C2×C5—42no—
563C2×C5—81no—
564C2×C5C3×#38611yescharacteristic
565C2×C5C3×C4×D811yescharacteristic
566C2×C5C3×#44211yescharacteristic
567D5—42no—
568D5—81no—
569D5C3×#44711yescharacteristic
570D5C3×#44911yescharacteristic
571D5C3×#45911yescharacteristic
572D5C3×#46311yescharacteristic
573C23—21no—
574C23—21no—
575C23—51no—
576C23—102no—
577C23—102no—
578C23—101no—
579C23—101no—
580C23—201no—
581C23—201no—
582C23—201no—
583C23—201no—
584C23—201no—
585C23—201no—
586C23—201no—
587C23—201no—
588C23—201no—
589C23—201no—
590D4—21no—
591D4—21no—
592D4—21no—
593D4—52no—
594D4—102no—
595D4—102no—
596D4—101no—
597D4—101no—
598D4—101no—
599D4—201no—
600D4—201no—
601D4C3×C22⋊AGL(1,𝔽5)12yescomplemented
602C2×C4—51no—
603C2×C4—51no—
604C2×C4—51no—
605C2×C4—51no—
606C2×C4—51no—
607C2×C4—52no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—102no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—208no—
615C2×C4—201no—
616C2×C4—201no—
617C2×C4—201no—
618C2×C4—201no—
619C2×C4—201no—
620C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
621C8—21no—
622C8—101no—
623C8—201no—
624C2×C3—42no—
625C2×C3—51no—
626C2×C3—51no—
627C2×C3—51no—
628C2×C3—51no—
629C2×C3—81no—
630C2×C3—202no—
631C2×C3—401no—
632C2×C3D8×AGL(1,𝔽5)11yescharacteristic
633C2×C3#6573111yescharacteristic
634C2×C3#6577911yescharacteristic
635C5C3×#187911yescharacteristic, complemented, Sylow
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—51no—
643C22—51no—
644C22—51no—
645C22—51no—
646C22—51no—
647C22—51no—
648C22—102no—
649C22—202no—
650C22—202no—
651C22—202no—
652C22—202no—
653C22—201no—
654C22—201no—
655C22—201no—
656C22—201no—
657C22—201no—
658C22—401no—
659C22—401no—
660C22—401no—
661C22—401no—
662C22C3×D4×AGL(1,𝔽5)11yescharacteristic
663C4—51no—
664C4—51no—
665C4—102no—
666C4—201no—
667C4—202no—
668C4—401no—
669C4C3×D4×AGL(1,𝔽5)11yescharacteristic
670C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
671C3#1060479911yescharacteristic, direct product factor, Sylow
672C2—42no—
673C2—51no—
674C2—51no—
675C2—51no—
676C2—51no—
677C2—81no—
678C2—202no—
679C2—401no—
680C2C3×D8×AGL(1,𝔽5)11yescharacteristic
681C2C3×#6573111yescharacteristic
682C2C3×#6577911yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×D8C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D5×D8C2
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×D8AGL(1,𝔽5)
hypocenterC5C3×#1879
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×AGL(1,𝔽5)C2semidirect
3. C3×#65780C2semidirect
4. C2×C3×#4007C2semidirect
5. C2×C3×#4007C2semidirect
6. C3×#64893C2semidirect
7. C3×(C2×AGL(1,𝔽5))⋊C8C2semidirect
8. #10604799C3direct (N × H)
21. C2×C3×C5×D8C4semidirect
22. C2×C3×#686C4semidirect
23. C2×C3×#686C4semidirect
26. C2×C3×D40C4semidirect
31. C2×D4×AGL(1,𝔽5)C2×C3semidirect
33. #65780C2×C3semidirect
34. C2×#4007C2×C3semidirect
35. C2×#4007C2×C3semidirect
36. #64893C2×C3semidirect
37. (C2×AGL(1,𝔽5))⋊C8C2×C3semidirect
48. C2×C3×C5×D4C2×C4semidirect
60. C2×C3×D20C2×C4semidirect
75. C2×C3×C5×C8C2×C4semidirect
78. C2×C3×#168C2×C4semidirect
101. C2×C5×D8C3×C4semidirect
102. C2×#686C3×C4semidirect
103. C2×#686C3×C4semidirect
106. C2×D40C3×C4semidirect
140. C2×C3×AGL(1,𝔽5)D8semidirect
144. C3×C5×D4C22⋊C4semidirect
154. C3×D20C22⋊C4semidirect
170. C2×C3×D8AGL(1,𝔽5)semidirect
193. C2×C5×D4C2×C3×C4semidirect
205. C2×D20C2×C3×C4semidirect
220. C2×C5×C8C2×C3×C4semidirect
223. C2×#168C2×C3×C4semidirect
284. C2×C3×D4C2×AGL(1,𝔽5)semidirect
303. C2×C3×C8C2×AGL(1,𝔽5)semidirect
342. C2×AGL(1,𝔽5)C3×D8semidirect
346. C5×D4C3×C22⋊C4semidirect
356. D20C3×C22⋊C4semidirect
372. C2×D8C3×AGL(1,𝔽5)semidirect
424. C3×D4C22⋊AGL(1,𝔽5)semidirect
497. C2×D4C2×C3×AGL(1,𝔽5)semidirect
516. C2×C8C2×C3×AGL(1,𝔽5)semidirect
526. C3×C5#1879semidirect
601. D4C3×C22⋊AGL(1,𝔽5)semidirect
635. C5C3×#1879semidirect
671. C3#10604799direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×AGL(1,𝔽5)2
C2×C3×D5×D82
C3×#657802
C2×C3×#40072
C3×#648932
C3×(C2×AGL(1,𝔽5))⋊C82
#106047993
C3×#18795