Finite Group Databasebeta

← C3×#10613073 #14458447

Subgroups — C3×#10613073 #14458447

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65943C211yesmaximal, characteristic
2C3×#65845C211yesmaximal, characteristic, complemented
3C3×C5×#481C211yesmaximal, characteristic, complemented
4C3×#65330C211yesmaximal, characteristic, complemented
5C2×C3×#3941C211yesmaximal, characteristic, complemented
6C3×#65159C211yesmaximal, characteristic, complemented
7C3×#65153C211yesmaximal, characteristic, complemented
8C3×#65152C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65065C211yesmaximal, characteristic, complemented
11C3×D5×#102C211yesmaximal, characteristic, complemented
12C3×#65051C211yesmaximal, characteristic, complemented
13C3×#65049C211yesmaximal, characteristic, complemented
14C3×#65020C211yesmaximal, characteristic, complemented
15C3×#65014C211yesmaximal, characteristic, complemented
16#10613073C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×D4×D5—21no—
18C2×C3×D4×D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
22C3×#4086C2211yescharacteristic
23C3×#4083—21no—
24C2×C3×#687C2211yescharacteristic, complemented
25C3×C4×C22⋊D5—21no—
26C3×C4×C22⋊D5C2211yescharacteristic
27C3×#4070—21no—
28C3×#4070C2211yescharacteristic, complemented
29C22×C3×#168C2211yescharacteristic, complemented
30C2×C3×#677C2211yescharacteristic
31C2×C3×#677C2211yescharacteristic, complemented
32C2×C3×C8×D5C2211yescharacteristic, complemented
33C3×#4043C2211yescharacteristic, complemented
34C3×#4042—21no—
35C3×#4041C2211yescharacteristic
36C3×#4039C2211yescharacteristic
37C3×D5×C4⋊C4C2211yescharacteristic, complemented
38C3×#4035—21no—
39C3×#4034C2211yescharacteristic, complemented
40C3×#4033C2211yescharacteristic, complemented
41C3×#4030—21no—
42C3×#4028—21no—
43C3×C5×#106C2211yescharacteristic, complemented
44C3×C5×#106C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic, complemented
46C3×C5×#102C2211yescharacteristic, complemented
47C3×C5×C22⋊C8C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic, complemented
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic, complemented
51C3×#3952C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3940C2211yescharacteristic, complemented
60C3×#3295—51nomaximal, Hall
61#65943C2×C311yescharacteristic
62#65845C2×C311yescharacteristic, complemented
63C5×#481C2×C311yescharacteristic, complemented
64#65330C2×C311yescharacteristic, complemented
65C2×#3941C2×C311yescharacteristic, complemented
66#65159C2×C311yescharacteristic, complemented
67#65153C2×C311yescharacteristic, complemented
68#65152C2×C311yescharacteristic, complemented
69#65141C2×C311yescharacteristic, complemented
70#65065C2×C311yescharacteristic, complemented
71D5×#102C2×C311yescharacteristic, complemented
72#65051C2×C311yescharacteristic, complemented
73#65049C2×C311yescharacteristic, complemented
74#65020C2×C311yescharacteristic, complemented
75#65014C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C23×C3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5D411yescharacteristic
86C3×D4×D5—22no—
87C3×D4×D5—41no—
88C3×D4×D5—44no—
89C2×C3×D20—22no—
90C2×C3×D20—21no—
91C2×C3×D20—21no—
92C2×C3×D20—41no—
93C2×C3×D20C2311yescharacteristic
94C2×C3×D20C2311yescharacteristic
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×Dic10—21no—
99C2×C3×Dic10C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C3×C5×C4⋊C4—21no—
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C22⋊C4—21no—
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5D411yescharacteristic
109C3×#687—41no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683—21no—
120C3×#683D411yescharacteristic
121C3×C4×Dic5—21no—
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168—41no—
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C3×#677—22no—
127C3×#677—41no—
128C3×C8×D5—41no—
129C3×#554—51no—
130C3×D42—51no—
131C3×#486—51no—
132C3×#481—51no—
133C3×#481D511yescharacteristic, complemented
134C3×#476—51no—
135C3×#465—51no—
136C3×#465—51no—
137C3×#460—51no—
138C3×#450—51no—
139C3×#450—51no—
140C3×C4×SD16—51no—
141C3×C8×D4—51no—
142C2×C3×#102—51no—
143C2×C3×#102—51no—
144C2×D4×D5—21no—
145C2×D4×D5C22×C311yescharacteristic
146C22×D20C22×C311yescharacteristic
147C5×#121C22×C311yescharacteristic
148C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
149#4086C22×C311yescharacteristic
150#4083—21no—
151C2×#687C22×C311yescharacteristic, complemented
152C4×C22⋊D5—21no—
153C4×C22⋊D5C22×C311yescharacteristic
154#4070—21no—
155#4070C22×C311yescharacteristic, complemented
156C22×#168C22×C311yescharacteristic, complemented
157C2×#677C22×C311yescharacteristic
158C2×#677C22×C311yescharacteristic, complemented
159C2×C8×D5C22×C311yescharacteristic, complemented
160#4043C22×C311yescharacteristic, complemented
161#4042—21no—
162#4041C22×C311yescharacteristic
163#4039C22×C311yescharacteristic
164D5×C4⋊C4C22×C311yescharacteristic, complemented
165#4035—21no—
166#4034C22×C311yescharacteristic, complemented
167#4033C22×C311yescharacteristic, complemented
168#4030—21no—
169#4028—21no—
170C5×#106C22×C311yescharacteristic, complemented
171C5×#106C22×C311yescharacteristic, complemented
172C5×#102C22×C311yescharacteristic, complemented
173C5×#102C22×C311yescharacteristic, complemented
174C5×C22⋊C8C22×C311yescharacteristic, complemented
175#3964C22×C311yescharacteristic, complemented
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic, complemented
178#3952C22×C311yescharacteristic, complemented
179#3946C22×C311yescharacteristic, complemented
180C8×Dic5C22×C311yescharacteristic, complemented
181#3942C22×C311yescharacteristic, complemented
182#3941C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3941C22×C311yescharacteristic, complemented
185#3941C22×C311yescharacteristic, complemented
186#3940C22×C311yescharacteristic, complemented
187#3295—51noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—42no—
195C22×C3×D5—42no—
196C22×C3×D5—81no—
197C22×C3×D5—81no—
198C22×C3×D5C2×D411yescharacteristic
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C3×C5×D4—42no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—81no—
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210C3×C22⋊D5—42no—
211C3×C22⋊D5—42no—
212C3×C22⋊D5—81no—
213C3×C22⋊D5SD1614yescomplemented
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—21no—
222C3×D20—42no—
223C3×D20—42no—
224C3×D20#4112yes—
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227C3×C4×D5—42no—
228C3×C4×D5—81no—
229C3×Dic10—21no—
230C3×Dic10—21no—
231C3×Dic10—81no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C3×#168—21no—
235C3×#168—21no—
236C22×C3×D4—51no—
237C22×C3×D4—51no—
238C22×C3×D4—101no—
239C2×C3×SD16—51no—
240C2×C3×SD16—51no—
241C2×C3×SD16—51no—
242C22×C3×C8—51no—
243C22×C3×C8—51no—
244C3×C4⋊Q8—51no—
245C3×#127—51no—
246C3×#125—101no—
247C3×C22⋊Q8—51no—
248C3×C22⋊Q8—51no—
249C3×C22⋊Q8—101no—
250C3×C22⋊Q8—101no—
251C3×#121—51no—
252C3×#121—101no—
253C3×#121C2×D511yescharacteristic
254C3×#120—101no—
255C3×#120—101no—
256C3×C4×Q8—51no—
257C3×C4×D4—51no—
258C3×C4×D4—51no—
259C3×C4×D4—101no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
262C3×#106—51no—
263C3×#106C2×D511yescharacteristic, complemented
264C3×#106C2×D511yescharacteristic, complemented
265C3×C4⋊C8—51no—
266C3×#103—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102—51no—
271C3×#102—51no—
272C3×#102—51no—
273C3×#102—51no—
274C3×#102C2×D511yescharacteristic, complemented
275C3×#102C2×D511yescharacteristic, complemented
276C3×C22⋊C8—51no—
277C3×C22⋊C8C2×D511yescharacteristic, complemented
278C3×C4×C8—51no—
279C23×D5—21no—
280C23×D5—21no—
281C2×C5×D4—21no—
282C2×C5×D4C23×C311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5C23×C311yescharacteristic
285C2×C22⋊D5—21no—
286C2×C22⋊D5—21no—
287C2×C22⋊D5—21no—
288C2×C22⋊D5C3×D411yescharacteristic
289D4×D5—22no—
290D4×D5—41no—
291D4×D5—44no—
292C2×D20—22no—
293C2×D20—21no—
294C2×D20—21no—
295C2×D20—41no—
296C2×D20C23×C311yescharacteristic
297C2×D20C23×C311yescharacteristic
298C2×C4×D5—21no—
299C2×C4×D5—21no—
300C2×C4×D5C23×C311yescharacteristic
301C2×Dic10—21no—
302C2×Dic10C23×C311yescharacteristic
303C2×C5×C8C23×C311yescharacteristic
304C2×C5×C8C23×C311yescharacteristic
305C5×C4⋊C4—21no—
306C5×C4⋊C4C23×C311yescharacteristic
307C5×C4⋊C4C23×C311yescharacteristic
308C5×C4⋊C4C23×C311yescharacteristic
309C5×C22⋊C4—21no—
310C22⋊Dic5—21no—
311C22⋊Dic5C3×D411yescharacteristic
312#687—41no—
313#685—21no—
314#685—21no—
315#685—21no—
316#685C3×D411yescharacteristic
317C4⋊Dic5—21no—
318C4⋊Dic5C23×C311yescharacteristic
319#683—21no—
320#683—21no—
321#683—21no—
322#683—21no—
323#683C3×D411yescharacteristic
324C4×Dic5—21no—
325C4×Dic5C23×C311yescharacteristic
326C2×#168—41no—
327C2×#168C23×C311yescharacteristic
328C2×#168C23×C311yescharacteristic
329#677—22no—
330#677—41no—
331C8×D5—41no—
332#554—51no—
333D42—51no—
334#486—51no—
335#481—51no—
336#481C3×D511yescharacteristic, complemented
337#476—51no—
338#465—51no—
339#465—51no—
340#460—51no—
341#450—51no—
342#450—51no—
343C4×SD16—51no—
344C8×D4—51no—
345C2×#102—51no—
346C2×#102—51no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5C2×SD1612yes—
353C22×C3×C5C22×D411yescharacteristic
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5—22no—
357C2×C3×D5—41no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—84no—
363C2×C3×D5—84no—
364C2×C3×D5C2×SD1612yes—
365C3×C4×C5—21no—
366C3×C4×C5—41no—
367C3×C4×C5—41no—
368C3×C4×C5—41no—
369C3×C4×C5C2×#4111yescharacteristic
370C3×C4×C5H(5,𝔽2)11yescharacteristic
371C3×Dic5—21no—
372C3×Dic5—21no—
373C3×Dic5—41no—
374C3×Dic5—41no—
375C3×Dic5C2×SD1612yes—
376C24×C3—101no—
377C24×C3—101no—
378C2×C3×Q8—51no—
379C2×C3×Q8—101no—
380C2×C3×D4—21no—
381C2×C3×D4—51no—
382C2×C3×D4—51no—
383C2×C3×D4—51no—
384C2×C3×D4—102no—
385C2×C3×D4—101no—
386C2×C3×D4—101no—
387C2×C3×D4—101no—
388C2×C3×D4—101no—
389C2×C3×D4—102no—
390C2×C3×D4—101no—
391C2×C3×D4—201no—
392C2×C3×D4—201no—
393C2×C3×D4—204no—
394C2×C3×D4C22×D511yescharacteristic
395C22×C3×C4—21no—
396C22×C3×C4—51no—
397C22×C3×C4—101no—
398C22×C3×C4—101no—
399C22×C3×C4C22×D511yescharacteristic
400C3×SD16—102no—
401C3×SD16—201no—
402C3×SD16—201no—
403C2×C3×C8—51no—
404C2×C3×C8—51no—
405C2×C3×C8—201no—
406C2×C3×C8—201no—
407C2×C3×C8C22×D511yescharacteristic
408C2×C3×C8C22×D511yescharacteristic
409C3×C4⋊C4—21no—
410C3×C4⋊C4—51no—
411C3×C4⋊C4—51no—
412C3×C4⋊C4—101no—
413C3×C4⋊C4—101no—
414C3×C4⋊C4—101no—
415C3×C4⋊C4—101no—
416C3×C4⋊C4—101no—
417C3×C4⋊C4C22×D511yescharacteristic
418C3×C4⋊C4C22×D511yescharacteristic
419C3×C4⋊C4C22×D511yescharacteristic
420C3×C22⋊C4—21no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C22⋊C4—101no—
424C3×C22⋊C4—101no—
425C3×C22⋊C4—101no—
426C3×C22⋊C4—101no—
427C3×C42—51no—
428C3×C42—101no—
429C23×C5—21no—
430C23×C5C2×C3×D411yescharacteristic
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—42no—
434C22×D5—42no—
435C22×D5—42no—
436C22×D5—42no—
437C22×D5—81no—
438C22×D5—81no—
439C22×D5C2×C3×D411yescharacteristic
440C5×D4—21no—
441C5×D4—21no—
442C5×D4—42no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—81no—
449C2×C4×C5C2×C3×D411yescharacteristic
450C2×C4×C5C24×C311yescharacteristic
451C22⋊D5—42no—
452C22⋊D5—42no—
453C22⋊D5—81no—
454C22⋊D5C3×SD1614yescomplemented
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5C2×C3×D411yescharacteristic
458C2×Dic5C2×C3×D411yescharacteristic
459C2×Dic5C2×C3×D411yescharacteristic
460D20—21no—
461D20—21no—
462D20—21no—
463D20—42no—
464D20—42no—
465D20C3×#4112yes—
466C4×D5—21no—
467C4×D5—21no—
468C4×D5—42no—
469C4×D5—81no—
470Dic10—21no—
471Dic10—21no—
472Dic10—81no—
473C5×C8—21no—
474C5×C8—21no—
475#168—21no—
476#168—21no—
477C22×D4—51no—
478C22×D4—51no—
479C22×D4—101no—
480C2×SD16—51no—
481C2×SD16—51no—
482C2×SD16—51no—
483C22×C8—51no—
484C22×C8—51no—
485C4⋊Q8—51no—
486#127—51no—
487#125—101no—
488C22⋊Q8—51no—
489C22⋊Q8—51no—
490C22⋊Q8—101no—
491C22⋊Q8—101no—
492#121—51no—
493#121—101no—
494#121C2×C3×D511yescharacteristic
495#120—101no—
496#120—101no—
497C4×Q8—51no—
498C4×D4—51no—
499C4×D4—51no—
500C4×D4—101no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
503#106—51no—
504#106C2×C3×D511yescharacteristic, complemented
505#106C2×C3×D511yescharacteristic, complemented
506C4⋊C8—51no—
507#103—51no—
508#102—51no—
509#102—51no—
510#102—51no—
511#102—51no—
512#102—51no—
513#102—51no—
514#102—51no—
515#102C2×C3×D511yescharacteristic, complemented
516#102C2×C3×D511yescharacteristic, complemented
517C22⋊C8—51no—
518C22⋊C8C2×C3×D511yescharacteristic, complemented
519C4×C8—51no—
520C2×C3×C5—22no—
521C2×C3×C5—81no—
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5C22×SD1611yescharacteristic
524C2×C3×C5#57611yescharacteristic
525C3×D5—22no—
526C3×D5—42no—
527C3×D5—81no—
528C23×C3—21no—
529C23×C3—51no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3—202no—
533C23×C3—202no—
534C23×C3—202no—
535C23×C3—202no—
536C23×C3—401no—
537C23×C3—401no—
538C23×C3D4×D511yescharacteristic
539C3×Q8—101no—
540C3×Q8—101no—
541C3×Q8—401no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—42no—
545C3×D4—54no—
546C3×D4—52no—
547C3×D4—101no—
548C3×D4—101no—
549C3×D4—101no—
550C3×D4—202no—
551C3×D4—202no—
552C3×D4—202no—
553C3×D4—202no—
554C3×D4—401no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—51no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—81no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—202no—
569C2×C3×C4—401no—
570C2×C3×C4D4×D511yescharacteristic
571C2×C3×C4C23×D511yescharacteristic
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—101no—
575C3×C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5C2×C3×SD1612yes—
582C22×C5C22×C3×D411yescharacteristic
583C2×D5—21no—
584C2×D5—21no—
585C2×D5—22no—
586C2×D5—41no—
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—41no—
590C2×D5—41no—
591C2×D5—84no—
592C2×D5—84no—
593C2×D5C2×C3×SD1612yes—
594C4×C5—21no—
595C4×C5—41no—
596C4×C5—41no—
597C4×C5—41no—
598C4×C5C2×C3×#4111yescharacteristic
599C4×C5C3×H(5,𝔽2)11yescharacteristic
600Dic5—21no—
601Dic5—21no—
602Dic5—41no—
603Dic5—41no—
604Dic5C2×C3×SD1612yes—
605C24—101no—
606C24—101no—
607C2×Q8—51no—
608C2×Q8—101no—
609C2×D4—21no—
610C2×D4—51no—
611C2×D4—51no—
612C2×D4—51no—
613C2×D4—102no—
614C2×D4—101no—
615C2×D4—101no—
616C2×D4—101no—
617C2×D4—101no—
618C2×D4—102no—
619C2×D4—101no—
620C2×D4—201no—
621C2×D4—201no—
622C2×D4—204no—
623C2×D4C22×C3×D511yescharacteristic
624C22×C4—21no—
625C22×C4—51no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4C22×C3×D511yescharacteristic
629SD16—102no—
630SD16—201no—
631SD16—201no—
632C2×C8—51no—
633C2×C8—51no—
634C2×C8—201no—
635C2×C8—201no—
636C2×C8C22×C3×D511yescharacteristic
637C2×C8C22×C3×D511yescharacteristic
638C4⋊C4—21no—
639C4⋊C4—51no—
640C4⋊C4—51no—
641C4⋊C4—101no—
642C4⋊C4—101no—
643C4⋊C4—101no—
644C4⋊C4—101no—
645C4⋊C4—101no—
646C4⋊C4C22×C3×D511yescharacteristic
647C4⋊C4C22×C3×D511yescharacteristic
648C4⋊C4C22×C3×D511yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—51no—
651C22⋊C4—51no—
652C22⋊C4—101no—
653C22⋊C4—101no—
654C22⋊C4—101no—
655C22⋊C4—101no—
656C42—51no—
657C42—101no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—52no—
665C22×C3—101no—
666C22×C3—101no—
667C22×C3—102no—
668C22×C3—201no—
669C22×C3—201no—
670C22×C3—201no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3—404no—
674C22×C3—404no—
675C22×C3D5×SD1612yes—
676C22×C3C2×D4×D511yescharacteristic
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—52no—
682C3×C4—101no—
683C3×C4—101no—
684C3×C4—201no—
685C3×C4—201no—
686C3×C4D5×#4111yescharacteristic
687C3×C4#414911yescharacteristic
688C2×C5—22no—
689C2×C5—81no—
690C2×C5C3×#54611yescharacteristic
691C2×C5C22×C3×SD1611yescharacteristic
692C2×C5C3×#57611yescharacteristic
693D5—22no—
694D5—42no—
695D5—81no—
696C23—21no—
697C23—51no—
698C23—101no—
699C23—101no—
700C23—202no—
701C23—202no—
702C23—202no—
703C23—202no—
704C23—401no—
705C23—401no—
706C23C3×D4×D511yescharacteristic
707Q8—101no—
708Q8—101no—
709Q8—401no—
710D4—21no—
711D4—21no—
712D4—42no—
713D4—54no—
714D4—52no—
715D4—101no—
716D4—101no—
717D4—101no—
718D4—202no—
719D4—202no—
720D4—202no—
721D4—202no—
722D4—401no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—51no—
729C2×C4—51no—
730C2×C4—51no—
731C2×C4—81no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—202no—
737C2×C4—401no—
738C2×C4C3×D4×D511yescharacteristic
739C2×C4C23×C3×D511yescharacteristic
740C8—21no—
741C8—21no—
742C8—101no—
743C8—101no—
744C2×C3—22no—
745C2×C3—81no—
746C2×C3—102no—
747C2×C3—202no—
748C2×C3—401no—
749C2×C3#6598811yescharacteristic
750C2×C3C2×D5×SD1611yescharacteristic
751C2×C3#6610811yescharacteristic
752C5C3×#329511yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—52no—
759C22—101no—
760C22—101no—
761C22—102no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—201no—
767C22—404no—
768C22—404no—
769C22C3×D5×SD1612yes—
770C22C2×C3×D4×D511yescharacteristic
771C4—21no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—52no—
776C4—101no—
777C4—101no—
778C4—201no—
779C4—201no—
780C4C3×D5×#4111yescharacteristic
781C4C3×#414911yescharacteristic
782C3#1061307311yescharacteristic, direct product factor, Sylow
783C2—22no—
784C2—81no—
785C2—102no—
786C2—202no—
787C2—401no—
788C2C3×#6598811yescharacteristic
789C2C2×C3×D5×SD1611yescharacteristic
790C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#481C2
socleC22×C3×C5C22×D4
prime radicalC3×#65943C2
hypercenterC3×#481D5
hypocenterC5C3×#3295
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#481

Complements

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

NH ≅ G/Ntype
2. C3×#65845C2semidirect
3. C3×C5×#481C2semidirect
4. C3×#65330C2semidirect
5. C2×C3×#3941C2semidirect
6. C3×#65159C2semidirect
7. C3×#65153C2semidirect
8. C3×#65152C2semidirect
9. C3×#65141C2semidirect
10. C3×#65065C2semidirect
11. C3×D5×#102C2semidirect
12. C3×#65051C2semidirect
13. C3×#65049C2semidirect
14. C3×#65020C2semidirect
15. C3×#65014C2semidirect
16. #10613073C3direct (N × H)
21. C2×C3×C5×C4⋊C4C22semidirect
24. C2×C3×#687C22semidirect
28. C3×#4070C22semidirect
29. C22×C3×#168C22semidirect
31. C2×C3×#677C22semidirect
32. C2×C3×C8×D5C22semidirect
33. C3×#4043C22semidirect
37. C3×D5×C4⋊C4C22semidirect
39. C3×#4034C22semidirect
40. C3×#4033C22semidirect
43. C3×C5×#106C22semidirect
44. C3×C5×#106C22semidirect
45. C3×C5×#102C22semidirect
46. C3×C5×#102C22semidirect
47. C3×C5×C22⋊C8C22semidirect
48. C3×#3964C22semidirect
50. C3×#3953C22semidirect
51. C3×#3952C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3942C22semidirect
57. C3×#3941C22semidirect
58. C3×#3941C22semidirect
59. C3×#3940C22semidirect
62. #65845C2×C3semidirect
63. C5×#481C2×C3semidirect
64. #65330C2×C3semidirect
65. C2×#3941C2×C3semidirect
66. #65159C2×C3semidirect
67. #65153C2×C3semidirect
68. #65152C2×C3semidirect
69. #65141C2×C3semidirect
70. #65065C2×C3semidirect
71. D5×#102C2×C3semidirect
72. #65051C2×C3semidirect
73. #65049C2×C3semidirect
74. #65020C2×C3semidirect
75. #65014C2×C3semidirect
133. C3×#481D5semidirect
148. C2×C5×C4⋊C4C22×C3semidirect
151. C2×#687C22×C3semidirect
155. #4070C22×C3semidirect
156. C22×#168C22×C3semidirect
158. C2×#677C22×C3semidirect
159. C2×C8×D5C22×C3semidirect
160. #4043C22×C3semidirect
164. D5×C4⋊C4C22×C3semidirect
166. #4034C22×C3semidirect
167. #4033C22×C3semidirect
170. C5×#106C22×C3semidirect
171. C5×#106C22×C3semidirect
172. C5×#102C22×C3semidirect
173. C5×#102C22×C3semidirect
174. C5×C22⋊C8C22×C3semidirect
175. #3964C22×C3semidirect
177. #3953C22×C3semidirect
178. #3952C22×C3semidirect
179. #3946C22×C3semidirect
180. C8×Dic5C22×C3semidirect
181. #3942C22×C3semidirect
184. #3941C22×C3semidirect
185. #3941C22×C3semidirect
186. #3940C22×C3semidirect
213. C3×C22⋊D5SD16semidirect
261. C2×C3×C4⋊C4C2×D5semidirect
263. C3×#106C2×D5semidirect
264. C3×#106C2×D5semidirect
274. C3×#102C2×D5semidirect
275. C3×#102C2×D5semidirect
277. C3×C22⋊C8C2×D5semidirect
336. #481C3×D5semidirect
454. C22⋊D5C3×SD16semidirect
502. C2×C4⋊C4C2×C3×D5semidirect
504. #106C2×C3×D5semidirect
505. #106C2×C3×D5semidirect
515. #102C2×C3×D5semidirect
516. #102C2×C3×D5semidirect
518. C22⋊C8C2×C3×D5semidirect
658. C3×C5#3295semidirect
752. C5C3×#3295semidirect
782. C3#10613073direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659432
C3×#658452
C3×C5×#4812
C3×#653302
C2×C3×#39412
C3×#651592
C3×#651532
C3×#651522
C3×#651412
C3×#650652
C3×D5×#1022
C3×#650512
C3×#650492
C3×#650202
C3×#650142
#106130733
C3×#32955