Finite Group Databasebeta

← C3×#10617533 #14412552

Subgroups — C3×#10617533 #14412552

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×C3×#4130C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
4C3×#65794C214yesmaximal, complemented
5C3×#65793C214yesmaximal, complemented
6C3×#65782C212yesmaximal, complemented
7C3×#65767C212yesmaximal, complemented
8#10617533C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C411yescharacteristic, complemented
10C3×D5×#41—21no—
11C3×D5×#41—21no—
12C3×D5×#41—21no—
13C3×D5×#41—21no—
14C3×D5×#41C412yescomplemented
15C3×D5×#41C412yescomplemented
16C3×D5×#41C2212yes—
17C3×D5×#41C2212yes—
18C2×C3×#713C411yescharacteristic, complemented
19C2×C3×Q8×D5C2211yescharacteristic
20C2×C3×#711—21no—
21C2×C3×#711C411yescharacteristic, complemented
22C2×C3×D4×D5—21no—
23C2×C3×D4×D5C2211yescharacteristic
24C2×C3×#709—21no—
25C2×C3×#709C411yescharacteristic, complemented
26C22×C3×C4×D5—21no—
27C22×C3×C4×D5C2211yescharacteristic
28C2×C3×C22⋊AGL(1,𝔽5)—21no—
29C2×C3×#704—21no—
30C3×#4130—21no—
31C3×#4130—21no—
32C3×#4130C2212yes—
33C3×#4130C2212yescomplemented
34C2×C3×C4⋊AGL(1,𝔽5)C2212yescomplemented
35C2×C3×C4×AGL(1,𝔽5)—21no—
36C3×D5⋊M16—21no—
37C3×D5⋊M16—21no—
38C3×D5⋊M16C2212yes—
39C3×D5⋊M16C2212yescomplemented
40C2×C3×#700—21no—
41C2×C3×D5⋊C8C2212yescomplemented
42C3×#4009C2218yescomplemented
43C3×#4007C2218yescomplemented
44C3×#2896—51nomaximal, Hall
45C2×D5×#41C2×C311yescharacteristic
46C2×#4130C2×C311yescharacteristic, complemented
47C2×D5⋊M16C2×C311yescharacteristic, complemented
48#65794C2×C314yescomplemented
49#65793C2×C314yescomplemented
50#65782C2×C312yescomplemented
51#65767C2×C312yescomplemented
52C23×C3×D5—21no—
53C23×C3×D5D411yescharacteristic
54C22×C3×AGL(1,𝔽5)—22no—
55C3×C5×#41—21no—
56C3×C5×#41—21no—
57C3×C5×#41C2×C412yes—
58C3×C5×#41C2×C412yescomplemented
59C2×C3×C5×Q8C2×C411yescharacteristic, complemented
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2×C411yescharacteristic, complemented
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2×C411yescharacteristic
64C2×C3×C22⋊D5—21no—
65C2×C3×C22⋊D5—21no—
66C2×C3×C22⋊D5—21no—
67C22×C3×Dic5—21no—
68C22×C3×Dic5D411yescharacteristic
69C3×#713—21no—
70C3×#713—21no—
71C3×#713C2×C412yes—
72C3×#713C2×C412yescomplemented
73C3×Q8×D5—21no—
74C3×Q8×D5—21no—
75C3×Q8×D5C2×C412yescomplemented
76C3×Q8×D5C2312yes—
77C3×#711—22no—
78C3×#711—22no—
79C3×#711—22no—
80C3×#711—22no—
81C3×#711—21no—
82C3×#711—21no—
83C3×#711C2×C412yes—
84C3×#711C2×C412yescomplemented
85C3×D4×D5—22no—
86C3×D4×D5—22no—
87C3×D4×D5—22no—
88C3×D4×D5—22no—
89C3×D4×D5—21no—
90C3×D4×D5—21no—
91C3×D4×D5C2×C412yescomplemented
92C3×D4×D5C2312yes—
93C3×#709—21no—
94C3×#709—21no—
95C3×#709—22no—
96C3×#709—22no—
97C3×#709—22no—
98C3×#709—22no—
99C3×#709C2×C412yes—
100C3×#709C2×C412yescomplemented
101C2×C3×D20—21no—
102C2×C3×D20C2×C411yescharacteristic, complemented
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5—22no—
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5C2×C411yescharacteristic
111C2×C3×C4×D5C2×C411yescharacteristic
112C2×C3×C4×D5C2×C411yescharacteristic
113C2×C3×C4×D5D411yescharacteristic
114C2×C3×C4×D5D411yescharacteristic
115C2×C3×C4×D5D411yescharacteristic
116C2×C3×C4×D5D411yescharacteristic
117C2×C3×C4×D5D411yescharacteristic
118C2×C3×C4×D5D411yescharacteristic
119C2×C3×C4×D5C2311yescharacteristic
120C2×C3×C4×D5C2311yescharacteristic
121C2×C3×C4×D5C2311yescharacteristic
122C2×C3×Dic10—21no—
123C2×C3×Dic10C2×C411yescharacteristic, complemented
124C3×C22⋊AGL(1,𝔽5)—22no—
125C3×C22⋊AGL(1,𝔽5)—22no—
126C3×#704—22no—
127C3×#704—22no—
128C2×C3×#170—22no—
129C3×C4⋊AGL(1,𝔽5)—22no—
130C3×C4⋊AGL(1,𝔽5)C2314yes—
131C3×C4×AGL(1,𝔽5)—22no—
132C3×C4×AGL(1,𝔽5)—22no—
133C3×#700—22no—
134C3×#700—22no—
135C3×D5⋊C8—22no—
136C3×D5⋊C8C2314yes—
137C22×C3×#41—51no—
138C22×C3×M16—51no—
139C2×C3×#117—51no—
140C3×#419—52no—
141C3×#418—52no—
142C3×#417—54no—
143C3×#416—54no—
144C2×C5×#41C3×C411yescharacteristic, complemented
145D5×#41—21no—
146D5×#41—21no—
147D5×#41—21no—
148D5×#41—21no—
149D5×#41C3×C412yescomplemented
150D5×#41C3×C412yescomplemented
151D5×#41C22×C312yes—
152D5×#41C22×C312yes—
153C2×#713C3×C411yescharacteristic, complemented
154C2×Q8×D5C22×C311yescharacteristic
155C2×#711—21no—
156C2×#711C3×C411yescharacteristic, complemented
157C2×D4×D5—21no—
158C2×D4×D5C22×C311yescharacteristic
159C2×#709—21no—
160C2×#709C3×C411yescharacteristic, complemented
161C22×C4×D5—21no—
162C22×C4×D5C22×C311yescharacteristic
163C2×C22⋊AGL(1,𝔽5)—21no—
164C2×#704—21no—
165#4130—21no—
166#4130—21no—
167#4130C22×C312yes—
168#4130C22×C312yescomplemented
169C2×C4⋊AGL(1,𝔽5)C22×C312yescomplemented
170C2×C4×AGL(1,𝔽5)—21no—
171D5⋊M16—21no—
172D5⋊M16—21no—
173D5⋊M16C22×C312yes—
174D5⋊M16C22×C312yescomplemented
175C2×#700—21no—
176C2×D5⋊C8C22×C312yescomplemented
177#4009C22×C318yescomplemented
178#4007C22×C318yescomplemented
179#2896—51noSylow
180C23×C3×C5—21no—
181C23×C3×C5C22⋊C411yescharacteristic
182C22×C3×D5—21no—
183C22×C3×D5—22no—
184C22×C3×D5—22no—
185C22×C3×D5—42no—
186C22×C3×D5—44no—
187C22×C3×D5C22⋊C411yescharacteristic
188C22×C3×D5C22⋊C411yescharacteristic
189C22×C3×D5C22⋊C411yescharacteristic
190C22×C3×D5C2×D411yescharacteristic
191C22×C3×D5C2×D411yescharacteristic
192C22×C3×D5C2×D411yescharacteristic
193C2×C3×AGL(1,𝔽5)—24no—
194C2×C3×AGL(1,𝔽5)—44no—
195C3×C5×Q8—21no—
196C3×C5×Q8C22×C412yes—
197C3×C5×D4—22no—
198C3×C5×D4—22no—
199C3×C5×D4—21no—
200C3×C5×D4C22×C412yes—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—22no—
203C2×C3×C4×C5—22no—
204C2×C3×C4×C5C22⋊C411yescharacteristic
205C2×C3×C4×C5C22⋊C411yescharacteristic
206C2×C3×C4×C5C22⋊C411yescharacteristic
207C2×C3×C4×C5C22×C411yescharacteristic
208C2×C3×C4×C5C22×C411yescharacteristic
209C2×C3×C4×C5C22×C411yescharacteristic
210C3×C22⋊D5—22no—
211C3×C22⋊D5—22no—
212C3×C22⋊D5—22no—
213C3×C22⋊D5—22no—
214C3×C22⋊D5—22no—
215C3×C22⋊D5—22no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—22no—
218C2×C3×Dic5—22no—
219C2×C3×Dic5C22⋊C411yescharacteristic
220C2×C3×Dic5C22⋊C411yescharacteristic
221C2×C3×Dic5C22⋊C411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C3×D20—22no—
226C3×D20—22no—
227C3×D20—21no—
228C3×D20C22×C412yes—
229C3×C4×D5—22no—
230C3×C4×D5—22no—
231C3×C4×D5—22no—
232C3×C4×D5—22no—
233C3×C4×D5—22no—
234C3×C4×D5—22no—
235C3×C4×D5C22⋊C411yescharacteristic
236C3×C4×D5C22⋊C411yescharacteristic
237C3×C4×D5C22⋊C411yescharacteristic
238C3×C4×D5C22⋊C411yescharacteristic
239C3×C4×D5C22⋊C411yescharacteristic
240C3×C4×D5C22⋊C411yescharacteristic
241C3×C4×D5C22×C411yescharacteristic
242C3×C4×D5C22×C411yescharacteristic
243C3×C4×D5C22×C411yescharacteristic
244C3×C4×D5C2×D411yescharacteristic
245C3×C4×D5C2×D411yescharacteristic
246C3×C4×D5C2×D411yescharacteristic
247C3×C4×D5C2×D411yescharacteristic
248C3×C4×D5C2×D411yescharacteristic
249C3×C4×D5C2×D411yescharacteristic
250C3×C4×D5C2411yescharacteristic
251C3×Dic10—21no—
252C3×Dic10—22no—
253C3×Dic10—22no—
254C3×Dic10C22×C412yes—
255C3×#170—24no—
256C2×C3×#41—52no—
257C2×C3×#41—52no—
258C2×C3×#41—52no—
259C2×C3×#41—52no—
260C2×C3×#41—51no—
261C2×C3×#41—51no—
262C2×C3×#41—51no—
263C2×C3×#41—101no—
264C2×C3×#41—101no—
265C2×C3×#41—101no—
266C2×C3×#41—101no—
267C2×C3×#41—101no—
268C2×C3×#41—101no—
269C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
270C22×C3×Q8—51no—
271C22×C3×D4—51no—
272C22×C3×D4—101no—
273C23×C3×C4—51no—
274C23×C3×C4—101no—
275C2×C3×M16—52no—
276C2×C3×M16—52no—
277C2×C3×M16—101no—
278C2×C3×M16—101no—
279C2×C3×M16—101no—
280C2×C3×M16—101no—
281C22×C3×C8—52no—
282C3×#117—52no—
283C3×#117—52no—
284C3×#117—101no—
285C3×#117—101no—
286C2×C3×C4⋊C4—52no—
287C2×C3×C22⋊C4—101no—
288C2×C3×C42—101no—
289C3×#103—58no—
290C3×#102—58no—
291C23×D5—21no—
292C23×D5C3×D411yescharacteristic
293C22×AGL(1,𝔽5)—22no—
294C5×#41—21no—
295C5×#41—21no—
296C5×#41C2×C3×C412yes—
297C5×#41C2×C3×C412yescomplemented
298C2×C5×Q8C2×C3×C411yescharacteristic, complemented
299C2×C5×D4—21no—
300C2×C5×D4C2×C3×C411yescharacteristic, complemented
301C22×C4×C5—21no—
302C22×C4×C5C2×C3×C411yescharacteristic
303C2×C22⋊D5—21no—
304C2×C22⋊D5—21no—
305C2×C22⋊D5—21no—
306C22×Dic5—21no—
307C22×Dic5C3×D411yescharacteristic
308#713—21no—
309#713—21no—
310#713C2×C3×C412yes—
311#713C2×C3×C412yescomplemented
312Q8×D5—21no—
313Q8×D5—21no—
314Q8×D5C2×C3×C412yescomplemented
315Q8×D5C23×C312yes—
316#711—22no—
317#711—22no—
318#711—22no—
319#711—22no—
320#711—21no—
321#711—21no—
322#711C2×C3×C412yes—
323#711C2×C3×C412yescomplemented
324D4×D5—22no—
325D4×D5—22no—
326D4×D5—22no—
327D4×D5—22no—
328D4×D5—21no—
329D4×D5—21no—
330D4×D5C2×C3×C412yescomplemented
331D4×D5C23×C312yes—
332#709—21no—
333#709—21no—
334#709—22no—
335#709—22no—
336#709—22no—
337#709—22no—
338#709C2×C3×C412yes—
339#709C2×C3×C412yescomplemented
340C2×D20—21no—
341C2×D20C2×C3×C411yescharacteristic, complemented
342C2×C4×D5—21no—
343C2×C4×D5—21no—
344C2×C4×D5—21no—
345C2×C4×D5—22no—
346C2×C4×D5—22no—
347C2×C4×D5—22no—
348C2×C4×D5—22no—
349C2×C4×D5C2×C3×C411yescharacteristic
350C2×C4×D5C2×C3×C411yescharacteristic
351C2×C4×D5C2×C3×C411yescharacteristic
352C2×C4×D5C3×D411yescharacteristic
353C2×C4×D5C3×D411yescharacteristic
354C2×C4×D5C3×D411yescharacteristic
355C2×C4×D5C3×D411yescharacteristic
356C2×C4×D5C3×D411yescharacteristic
357C2×C4×D5C3×D411yescharacteristic
358C2×C4×D5C23×C311yescharacteristic
359C2×C4×D5C23×C311yescharacteristic
360C2×C4×D5C23×C311yescharacteristic
361C2×Dic10—21no—
362C2×Dic10C2×C3×C411yescharacteristic, complemented
363C22⋊AGL(1,𝔽5)—22no—
364C22⋊AGL(1,𝔽5)—22no—
365#704—22no—
366#704—22no—
367C2×#170—22no—
368C4⋊AGL(1,𝔽5)—22no—
369C4⋊AGL(1,𝔽5)C23×C314yes—
370C4×AGL(1,𝔽5)—22no—
371C4×AGL(1,𝔽5)—22no—
372#700—22no—
373#700—22no—
374D5⋊C8—22no—
375D5⋊C8C23×C314yes—
376C22×#41—51no—
377C22×M16—51no—
378C2×#117—51no—
379#419—52no—
380#418—52no—
381#417—54no—
382#416—54no—
383C22×C3×C5—22no—
384C22×C3×C5—41no—
385C22×C3×C5—42no—
386C22×C3×C5C2×C22⋊C411yescharacteristic
387C22×C3×C5C2×C22⋊C411yescharacteristic
388C22×C3×C5C2×C22⋊C411yescharacteristic
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—44no—
397C2×C3×D5—42no—
398C2×C3×D5—44no—
399C2×C3×D5C2×C22⋊C411yescharacteristic
400C2×C3×D5C2×C22⋊C411yescharacteristic
401C2×C3×D5C2×C22⋊C411yescharacteristic
402C2×C3×D5C22×D411yescharacteristic
403C3×AGL(1,𝔽5)—44no—
404C3×C4×C5—22no—
405C3×C4×C5C2×C22⋊C411yescharacteristic
406C3×C4×C5C2×C22⋊C411yescharacteristic
407C3×C4×C5C2×C22⋊C411yescharacteristic
408C3×C4×C5C23×C411yescharacteristic
409C3×Dic5—22no—
410C3×Dic5C2×C22⋊C411yescharacteristic
411C3×Dic5C2×C22⋊C411yescharacteristic
412C3×Dic5C2×C22⋊C411yescharacteristic
413C3×Dic5C22×D411yescharacteristic
414C24×C3—51no—
415C24×C3—101no—
416C3×#41—21no—
417C3×#41—21no—
418C3×#41—52no—
419C3×#41—52no—
420C3×#41—52no—
421C3×#41—52no—
422C3×#41—52no—
423C3×#41—52no—
424C3×#41—102no—
425C3×#41—102no—
426C3×#41—102no—
427C3×#41—102no—
428C3×#41—102no—
429C3×#41—102no—
430C3×#41—102no—
431C3×#41—102no—
432C3×#41—101no—
433C3×#41—101no—
434C3×#41—101no—
435C3×#41—101no—
436C3×#41—101no—
437C3×#41—101no—
438C3×#41C2×AGL(1,𝔽5)12yes—
439C3×#41C2×AGL(1,𝔽5)12yescomplemented
440C2×C3×Q8—52no—
441C2×C3×Q8—52no—
442C2×C3×Q8—51no—
443C2×C3×Q8—101no—
444C2×C3×Q8—101no—
445C2×C3×Q8—101no—
446C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
447C2×C3×D4—21no—
448C2×C3×D4—52no—
449C2×C3×D4—52no—
450C2×C3×D4—51no—
451C2×C3×D4—101no—
452C2×C3×D4—101no—
453C2×C3×D4—101no—
454C2×C3×D4—101no—
455C2×C3×D4—102no—
456C2×C3×D4—102no—
457C2×C3×D4—102no—
458C2×C3×D4—102no—
459C2×C3×D4—101no—
460C2×C3×D4—101no—
461C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
462C22×C3×C4—21no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—51no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—101no—
477C22×C3×C4—102no—
478C22×C3×C4—102no—
479C22×C3×C4—102no—
480C22×C3×C4—102no—
481C22×C3×C4—101no—
482C22×C3×C4—101no—
483C22×C3×C4—101no—
484C22×C3×C4—102no—
485C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
486C3×M16—102no—
487C3×M16—102no—
488C3×M16—102no—
489C3×M16—102no—
490C2×C3×C8—54no—
491C2×C3×C8—102no—
492C2×C3×C8—102no—
493C3×C4⋊C4—54no—
494C3×C4⋊C4—102no—
495C3×C22⋊C4—102no—
496C3×C22⋊C4—102no—
497C3×C42—102no—
498C3×C42—102no—
499C23×C5—21no—
500C23×C5C3×C22⋊C411yescharacteristic
501C22×D5—21no—
502C22×D5—22no—
503C22×D5—22no—
504C22×D5—42no—
505C22×D5—44no—
506C22×D5C3×C22⋊C411yescharacteristic
507C22×D5C3×C22⋊C411yescharacteristic
508C22×D5C3×C22⋊C411yescharacteristic
509C22×D5C2×C3×D411yescharacteristic
510C22×D5C2×C3×D411yescharacteristic
511C22×D5C2×C3×D411yescharacteristic
512C2×AGL(1,𝔽5)—24no—
513C2×AGL(1,𝔽5)—44no—
514C5×Q8—21no—
515C5×Q8C22×C3×C412yes—
516C5×D4—22no—
517C5×D4—22no—
518C5×D4—21no—
519C5×D4C22×C3×C412yes—
520C2×C4×C5—21no—
521C2×C4×C5—22no—
522C2×C4×C5—22no—
523C2×C4×C5C3×C22⋊C411yescharacteristic
524C2×C4×C5C3×C22⋊C411yescharacteristic
525C2×C4×C5C3×C22⋊C411yescharacteristic
526C2×C4×C5C22×C3×C411yescharacteristic
527C2×C4×C5C22×C3×C411yescharacteristic
528C2×C4×C5C22×C3×C411yescharacteristic
529C22⋊D5—22no—
530C22⋊D5—22no—
531C22⋊D5—22no—
532C22⋊D5—22no—
533C22⋊D5—22no—
534C22⋊D5—22no—
535C2×Dic5—21no—
536C2×Dic5—22no—
537C2×Dic5—22no—
538C2×Dic5C3×C22⋊C411yescharacteristic
539C2×Dic5C3×C22⋊C411yescharacteristic
540C2×Dic5C3×C22⋊C411yescharacteristic
541C2×Dic5C2×C3×D411yescharacteristic
542C2×Dic5C2×C3×D411yescharacteristic
543C2×Dic5C2×C3×D411yescharacteristic
544D20—22no—
545D20—22no—
546D20—21no—
547D20C22×C3×C412yes—
548C4×D5—22no—
549C4×D5—22no—
550C4×D5—22no—
551C4×D5—22no—
552C4×D5—22no—
553C4×D5—22no—
554C4×D5C3×C22⋊C411yescharacteristic
555C4×D5C3×C22⋊C411yescharacteristic
556C4×D5C3×C22⋊C411yescharacteristic
557C4×D5C3×C22⋊C411yescharacteristic
558C4×D5C3×C22⋊C411yescharacteristic
559C4×D5C3×C22⋊C411yescharacteristic
560C4×D5C22×C3×C411yescharacteristic
561C4×D5C22×C3×C411yescharacteristic
562C4×D5C22×C3×C411yescharacteristic
563C4×D5C2×C3×D411yescharacteristic
564C4×D5C2×C3×D411yescharacteristic
565C4×D5C2×C3×D411yescharacteristic
566C4×D5C2×C3×D411yescharacteristic
567C4×D5C2×C3×D411yescharacteristic
568C4×D5C2×C3×D411yescharacteristic
569C4×D5C24×C311yescharacteristic
570Dic10—21no—
571Dic10—22no—
572Dic10—22no—
573Dic10C22×C3×C412yes—
574#170—24no—
575C2×#41—52no—
576C2×#41—52no—
577C2×#41—52no—
578C2×#41—52no—
579C2×#41—51no—
580C2×#41—51no—
581C2×#41—51no—
582C2×#41—101no—
583C2×#41—101no—
584C2×#41—101no—
585C2×#41—101no—
586C2×#41—101no—
587C2×#41—101no—
588C2×#41C3×AGL(1,𝔽5)11yescharacteristic, complemented
589C22×Q8—51no—
590C22×D4—51no—
591C22×D4—101no—
592C23×C4—51no—
593C23×C4—101no—
594C2×M16—52no—
595C2×M16—52no—
596C2×M16—101no—
597C2×M16—101no—
598C2×M16—101no—
599C2×M16—101no—
600C22×C8—52no—
601#117—52no—
602#117—52no—
603#117—101no—
604#117—101no—
605C2×C4⋊C4—52no—
606C2×C22⋊C4—101no—
607C2×C42—101no—
608#103—58no—
609#102—58no—
610C2×C3×C5—21no—
611C2×C3×C5—21no—
612C2×C3×C5—21no—
613C2×C3×C5—42no—
614C2×C3×C5C22×C22⋊C411yescharacteristic
615C3×D5—21no—
616C3×D5—21no—
617C3×D5—21no—
618C3×D5—42no—
619C3×D5#57512yes—
620C23×C3—21no—
621C23×C3—51no—
622C23×C3—51no—
623C23×C3—51no—
624C23×C3—51no—
625C23×C3—51no—
626C23×C3—51no—
627C23×C3—102no—
628C23×C3—102no—
629C23×C3—101no—
630C23×C3—202no—
631C23×C3—204no—
632C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
633C3×Q8—21no—
634C3×Q8—52no—
635C3×Q8—102no—
636C3×Q8—102no—
637C3×Q8—101no—
638C3×Q8C22×AGL(1,𝔽5)12yes—
639C3×D4—22no—
640C3×D4—22no—
641C3×D4—21no—
642C3×D4—52no—
643C3×D4—102no—
644C3×D4—102no—
645C3×D4—102no—
646C3×D4—102no—
647C3×D4—102no—
648C3×D4—102no—
649C3×D4—102no—
650C3×D4—102no—
651C3×D4—101no—
652C3×D4C22×AGL(1,𝔽5)12yes—
653C2×C3×C4—21no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—51no—
657C2×C3×C4—51no—
658C2×C3×C4—51no—
659C2×C3×C4—51no—
660C2×C3×C4—51no—
661C2×C3×C4—51no—
662C2×C3×C4—51no—
663C2×C3×C4—51no—
664C2×C3×C4—51no—
665C2×C3×C4—51no—
666C2×C3×C4—51no—
667C2×C3×C4—51no—
668C2×C3×C4—51no—
669C2×C3×C4—51no—
670C2×C3×C4—51no—
671C2×C3×C4—51no—
672C2×C3×C4—51no—
673C2×C3×C4—51no—
674C2×C3×C4—51no—
675C2×C3×C4—51no—
676C2×C3×C4—51no—
677C2×C3×C4—51no—
678C2×C3×C4—102no—
679C2×C3×C4—102no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4—102no—
684C2×C3×C4—101no—
685C2×C3×C4—102no—
686C2×C3×C4—102no—
687C2×C3×C4—104no—
688C2×C3×C4—204no—
689C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
690C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
691C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
692C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
693C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
694C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
695C3×C8—104no—
696C22×C5—22no—
697C22×C5—41no—
698C22×C5—42no—
699C22×C5C2×C3×C22⋊C411yescharacteristic
700C22×C5C2×C3×C22⋊C411yescharacteristic
701C22×C5C2×C3×C22⋊C411yescharacteristic
702C2×D5—22no—
703C2×D5—22no—
704C2×D5—22no—
705C2×D5—22no—
706C2×D5—41no—
707C2×D5—41no—
708C2×D5—41no—
709C2×D5—44no—
710C2×D5—42no—
711C2×D5—44no—
712C2×D5C2×C3×C22⋊C411yescharacteristic
713C2×D5C2×C3×C22⋊C411yescharacteristic
714C2×D5C2×C3×C22⋊C411yescharacteristic
715C2×D5C22×C3×D411yescharacteristic
716AGL(1,𝔽5)—44no—
717C4×C5—22no—
718C4×C5C2×C3×C22⋊C411yescharacteristic
719C4×C5C2×C3×C22⋊C411yescharacteristic
720C4×C5C2×C3×C22⋊C411yescharacteristic
721C4×C5C23×C3×C411yescharacteristic
722Dic5—22no—
723Dic5C2×C3×C22⋊C411yescharacteristic
724Dic5C2×C3×C22⋊C411yescharacteristic
725Dic5C2×C3×C22⋊C411yescharacteristic
726Dic5C22×C3×D411yescharacteristic
727C24—51no—
728C24—101no—
729#41—21no—
730#41—21no—
731#41—52no—
732#41—52no—
733#41—52no—
734#41—52no—
735#41—52no—
736#41—52no—
737#41—102no—
738#41—102no—
739#41—102no—
740#41—102no—
741#41—102no—
742#41—102no—
743#41—102no—
744#41—102no—
745#41—101no—
746#41—101no—
747#41—101no—
748#41—101no—
749#41—101no—
750#41—101no—
751#41C2×C3×AGL(1,𝔽5)12yes—
752#41C2×C3×AGL(1,𝔽5)12yescomplemented
753C2×Q8—52no—
754C2×Q8—52no—
755C2×Q8—51no—
756C2×Q8—101no—
757C2×Q8—101no—
758C2×Q8—101no—
759C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
760C2×D4—21no—
761C2×D4—52no—
762C2×D4—52no—
763C2×D4—51no—
764C2×D4—101no—
765C2×D4—101no—
766C2×D4—101no—
767C2×D4—101no—
768C2×D4—102no—
769C2×D4—102no—
770C2×D4—102no—
771C2×D4—102no—
772C2×D4—101no—
773C2×D4—101no—
774C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
775C22×C4—21no—
776C22×C4—51no—
777C22×C4—51no—
778C22×C4—51no—
779C22×C4—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—101no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—102no—
794C22×C4—101no—
795C22×C4—101no—
796C22×C4—101no—
797C22×C4—102no—
798C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
799M16—102no—
800M16—102no—
801M16—102no—
802M16—102no—
803C2×C8—54no—
804C2×C8—102no—
805C2×C8—102no—
806C4⋊C4—54no—
807C4⋊C4—102no—
808C22⋊C4—102no—
809C22⋊C4—102no—
810C42—102no—
811C42—102no—
812C3×C5#289611yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—41no—
815C22×C3—42no—
816C22×C3—51no—
817C22×C3—51no—
818C22×C3—51no—
819C22×C3—51no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—201no—
825C22×C3—201no—
826C22×C3—201no—
827C22×C3—202no—
828C22×C3—204no—
829C22×C3—204no—
830C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
831C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
832C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
833C3×C4—22no—
834C3×C4—51no—
835C3×C4—51no—
836C3×C4—51no—
837C3×C4—51no—
838C3×C4—102no—
839C3×C4—204no—
840C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
841C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
842C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
843C3×C4C23×AGL(1,𝔽5)11yescharacteristic
844C2×C5—21no—
845C2×C5—21no—
846C2×C5—21no—
847C2×C5—42no—
848C2×C5C22×C3×C22⋊C411yescharacteristic
849D5—21no—
850D5—21no—
851D5—21no—
852D5—42no—
853D5C3×#57512yes—
854C23—21no—
855C23—51no—
856C23—51no—
857C23—51no—
858C23—51no—
859C23—51no—
860C23—51no—
861C23—102no—
862C23—102no—
863C23—101no—
864C23—202no—
865C23—204no—
866C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
867Q8—21no—
868Q8—52no—
869Q8—102no—
870Q8—102no—
871Q8—101no—
872Q8C22×C3×AGL(1,𝔽5)12yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—52no—
877D4—102no—
878D4—102no—
879D4—102no—
880D4—102no—
881D4—102no—
882D4—102no—
883D4—102no—
884D4—102no—
885D4—101no—
886D4C22×C3×AGL(1,𝔽5)12yes—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—51no—
891C2×C4—51no—
892C2×C4—51no—
893C2×C4—51no—
894C2×C4—51no—
895C2×C4—51no—
896C2×C4—51no—
897C2×C4—51no—
898C2×C4—51no—
899C2×C4—51no—
900C2×C4—51no—
901C2×C4—51no—
902C2×C4—51no—
903C2×C4—51no—
904C2×C4—51no—
905C2×C4—51no—
906C2×C4—51no—
907C2×C4—51no—
908C2×C4—51no—
909C2×C4—51no—
910C2×C4—51no—
911C2×C4—51no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—102no—
916C2×C4—102no—
917C2×C4—102no—
918C2×C4—101no—
919C2×C4—102no—
920C2×C4—102no—
921C2×C4—104no—
922C2×C4—204no—
923C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
924C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
925C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
926C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
927C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
928C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
929C8—104no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—42no—
934C2×C3—52no—
935C2×C3—101no—
936C2×C3—101no—
937C2×C3—101no—
938C2×C3—202no—
939C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
940C5C3×#289611yescharacteristic, complemented, Sylow
941C22—22no—
942C22—41no—
943C22—42no—
944C22—51no—
945C22—51no—
946C22—51no—
947C22—51no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—201no—
953C22—201no—
954C22—201no—
955C22—202no—
956C22—204no—
957C22—204no—
958C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
959C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
960C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
961C4—22no—
962C4—51no—
963C4—51no—
964C4—51no—
965C4—51no—
966C4—102no—
967C4—204no—
968C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
969C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
970C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
971C4C23×C3×AGL(1,𝔽5)11yescharacteristic
972C3#1061753311yescharacteristic, direct product factor, Sylow
973C2—21no—
974C2—21no—
975C2—21no—
976C2—42no—
977C2—52no—
978C2—101no—
979C2—101no—
980C2—101no—
981C2—202no—
982C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC3×C4C2×C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC4×D5C24×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C3×#2896
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4130C2semidirect
3. C2×C3×D5⋊M16C2semidirect
4. C3×#65794C2semidirect
5. C3×#65793C2semidirect
6. C3×#65782C2semidirect
7. C3×#65767C2semidirect
8. #10617533C3direct (N × H)
9. C2×C3×C5×#41C4semidirect
14. C3×D5×#41C4semidirect
15. C3×D5×#41C4semidirect
18. C2×C3×#713C4semidirect
21. C2×C3×#711C4semidirect
25. C2×C3×#709C4semidirect
33. C3×#4130C22semidirect
34. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
39. C3×D5⋊M16C22semidirect
41. C2×C3×D5⋊C8C22semidirect
42. C3×#4009C22semidirect
43. C3×#4007C22semidirect
46. C2×#4130C2×C3semidirect
47. C2×D5⋊M16C2×C3semidirect
48. #65794C2×C3semidirect
49. #65793C2×C3semidirect
50. #65782C2×C3semidirect
51. #65767C2×C3semidirect
58. C3×C5×#41C2×C4semidirect
59. C2×C3×C5×Q8C2×C4semidirect
61. C2×C3×C5×D4C2×C4semidirect
72. C3×#713C2×C4semidirect
75. C3×Q8×D5C2×C4semidirect
84. C3×#711C2×C4semidirect
91. C3×D4×D5C2×C4semidirect
100. C3×#709C2×C4semidirect
102. C2×C3×D20C2×C4semidirect
123. C2×C3×Dic10C2×C4semidirect
144. C2×C5×#41C3×C4semidirect
149. D5×#41C3×C4semidirect
150. D5×#41C3×C4semidirect
153. C2×#713C3×C4semidirect
156. C2×#711C3×C4semidirect
160. C2×#709C3×C4semidirect
168. #4130C22×C3semidirect
169. C2×C4⋊AGL(1,𝔽5)C22×C3semidirect
174. D5⋊M16C22×C3semidirect
176. C2×D5⋊C8C22×C3semidirect
177. #4009C22×C3semidirect
178. #4007C22×C3semidirect
269. C2×C3×#41AGL(1,𝔽5)semidirect
297. C5×#41C2×C3×C4semidirect
298. C2×C5×Q8C2×C3×C4semidirect
300. C2×C5×D4C2×C3×C4semidirect
311. #713C2×C3×C4semidirect
314. Q8×D5C2×C3×C4semidirect
323. #711C2×C3×C4semidirect
330. D4×D5C2×C3×C4semidirect
339. #709C2×C3×C4semidirect
341. C2×D20C2×C3×C4semidirect
362. C2×Dic10C2×C3×C4semidirect
439. C3×#41C2×AGL(1,𝔽5)semidirect
446. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
461. C2×C3×D4C2×AGL(1,𝔽5)semidirect
588. C2×#41C3×AGL(1,𝔽5)semidirect
752. #41C2×C3×AGL(1,𝔽5)semidirect
759. C2×Q8C2×C3×AGL(1,𝔽5)semidirect
774. C2×D4C2×C3×AGL(1,𝔽5)semidirect
812. C3×C5#2896semidirect
940. C5C3×#2896semidirect
972. C3#10617533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×C3×#41302
C2×C3×D5⋊M162
C3×#657942
C3×#657932
C3×#657822
C3×#657672
#106175333
C3×#28965