Finite Group Databasebeta

← C3×#10615225 #14458612

Subgroups — C3×#10615225 #14458612

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic
2C3×#65875C211yesmaximal, characteristic, complemented
3C3×#65528C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5C3×#65507C211yesmaximal, characteristic, complemented
6C2×C3×#3964C211yesmaximal, characteristic, complemented
7C3×#65345C211yesmaximal, characteristic, complemented
8C3×#65343C211yesmaximal, characteristic, complemented
9C3×#65340C211yesmaximal, characteristic, complemented
10C3×#65332C211yesmaximal, characteristic, complemented
11C3×#65330C211yesmaximal, characteristic, complemented
12C3×#65324C211yesmaximal, characteristic, complemented
13C3×C4×#687C211yesmaximal, characteristic, complemented
14C3×D4×#168C211yesmaximal, characteristic, complemented
15C3×#65298C211yesmaximal, characteristic, complemented
16#10615225C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C3×C5×#123—21no—
21C3×C5×C22⋊Q8C2211yescharacteristic
22C3×C5×#121—21no—
23C3×C5×#121C2211yescharacteristic
24C3×C5×#120—21no—
25C3×C4×C5×D4C2211yescharacteristic
26C3×C4×C5×D4C2211yescharacteristic
27C2×C3×C5×C22⋊C4—21no—
28C2×C3×#689C2211yescharacteristic, complemented
29C3×#4081—21no—
30C2×C3×#687C2211yescharacteristic
31C2×C3×#687C2211yescharacteristic
32C3×#4072C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C3×#4070C2211yescharacteristic
35C3×#4070C2211yescharacteristic, complemented
36C22×C3×#168C2211yescharacteristic
37C22×C3×#168C2211yescharacteristic, complemented
38C3×#4035—21no—
39C3×#4025—21no—
40C3×#4023—21no—
41C3×#4016C2211yescharacteristic, complemented
42C3×C4×Dic10C2211yescharacteristic, complemented
43C3×#3967C2211yescharacteristic, complemented
44C3×#3967C2211yescharacteristic, complemented
45C3×#3967C2211yescharacteristic, complemented
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×#3964C2211yescharacteristic
50C3×#3964C2211yescharacteristic
51C3×#3964C2211yescharacteristic
52C3×C22⋊#168C2211yescharacteristic
53C3×C22⋊#168C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55C3×#3940C2211yescharacteristic, complemented
56C3×#3940C2211yescharacteristic, complemented
57C3×#3939C2211yescharacteristic, complemented
58C3×C4⋊#168C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3296—51nomaximal, Hall
61C5×#546C2×C311yescharacteristic
62#65875C2×C311yescharacteristic, complemented
63#65528C2×C311yescharacteristic, complemented
64#65522C2×C311yescharacteristic, complemented
65#65507C2×C311yescharacteristic, complemented
66C2×#3964C2×C311yescharacteristic, complemented
67#65345C2×C311yescharacteristic, complemented
68#65343C2×C311yescharacteristic, complemented
69#65340C2×C311yescharacteristic, complemented
70#65332C2×C311yescharacteristic, complemented
71#65330C2×C311yescharacteristic, complemented
72#65324C2×C311yescharacteristic, complemented
73C4×#687C2×C311yescharacteristic, complemented
74D4×#168C2×C311yescharacteristic, complemented
75#65298C2×C311yescharacteristic, complemented
76C24×C3×C5—21no—
77C3×C5×#41—22no—
78C3×C5×#41—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—41no—
85C2×C3×C5×D4D411yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×Dic5—21no—
93C2×C3×Dic10C2311yescharacteristic
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4D411yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C42×C5C2311yescharacteristic
105C3×C22⋊Dic5—21no—
106C3×C22⋊Dic5—21no—
107C3×C22⋊Dic5—21no—
108C3×#689—41no—
109C3×#687—22no—
110C3×#687—41no—
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
122C2×C3×#168—41no—
123C2×C3×#168—41no—
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C3×#552—51no—
129C3×#546D511yescharacteristic
130C3×#488—51no—
131C3×#483—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#467—51no—
135C3×#465—51no—
136C3×#464—51no—
137C3×#452—51no—
138C3×#450—51no—
139C3×C4×SD16—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×C5×#41C22×C311yescharacteristic
144C22×C5×D4C22×C311yescharacteristic
145C5×#124C22×C311yescharacteristic
146C5×#123—21no—
147C5×C22⋊Q8C22×C311yescharacteristic
148C5×#121—21no—
149C5×#121C22×C311yescharacteristic
150C5×#120—21no—
151C4×C5×D4C22×C311yescharacteristic
152C4×C5×D4C22×C311yescharacteristic
153C2×C5×C22⋊C4—21no—
154C2×#689C22×C311yescharacteristic, complemented
155#4081—21no—
156C2×#687C22×C311yescharacteristic
157C2×#687C22×C311yescharacteristic
158#4072C22×C311yescharacteristic, complemented
159C2×C4⋊Dic5C22×C311yescharacteristic
160#4070C22×C311yescharacteristic
161#4070C22×C311yescharacteristic, complemented
162C22×#168C22×C311yescharacteristic
163C22×#168C22×C311yescharacteristic, complemented
164#4035—21no—
165#4025—21no—
166#4023—21no—
167#4016C22×C311yescharacteristic, complemented
168C4×Dic10C22×C311yescharacteristic, complemented
169#3967C22×C311yescharacteristic, complemented
170#3967C22×C311yescharacteristic, complemented
171#3967C22×C311yescharacteristic, complemented
172#3964C22×C311yescharacteristic
173#3964C22×C311yescharacteristic
174#3964C22×C311yescharacteristic
175#3964C22×C311yescharacteristic
176#3964C22×C311yescharacteristic
177#3964C22×C311yescharacteristic
178C22⋊#168C22×C311yescharacteristic
179C22⋊#168C22×C311yescharacteristic, complemented
180#3942C22×C311yescharacteristic, complemented
181#3940C22×C311yescharacteristic, complemented
182#3940C22×C311yescharacteristic, complemented
183#3939C22×C311yescharacteristic, complemented
184C4⋊#168C22×C311yescharacteristic, complemented
185C4×#168C22×C311yescharacteristic, complemented
186#3296—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—42no—
190C23×C3×C5—42no—
191C23×C3×C5—81no—
192C23×C3×C5C2×D411yescharacteristic
193C23×C3×C5C2×D411yescharacteristic
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×D4—22no—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—42no—
201C3×C5×D4—42no—
202C3×C5×D4—81no—
203C3×C5×D4#4112yes—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—42no—
211C2×C3×C4×C5—81no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2411yescharacteristic
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—42no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224C3×#168—21no—
225C3×#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41C2×D511yescharacteristic
229C22×C3×D4C2×D511yescharacteristic
230C2×C3×Q16—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×#126—101no—
236C3×#125—51no—
237C3×#125—101no—
238C3×#124C2×D511yescharacteristic
239C3×#123—21no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8—51no—
243C3×C22⋊Q8C2×D511yescharacteristic
244C3×#121—21no—
245C3×#121C2×D511yescharacteristic
246C3×#120—21no—
247C3×C4×Q8—51no—
248C3×C4×D4C2×D511yescharacteristic
249C3×C4×D4C2×D511yescharacteristic
250C3×#117—51no—
251C3×#117—101no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—21no—
254C3×#107—51no—
255C3×#106—51no—
256C3×#106—51no—
257C3×C4⋊C8—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×#102—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×C22⋊C8—51no—
269C3×C22⋊C8—51no—
270C3×C4×C8—51no—
271C24×C5—21no—
272C5×#41—22no—
273C5×#41—41no—
274C2×C5×Q8C23×C311yescharacteristic
275C2×C5×D4—22no—
276C2×C5×D4—21no—
277C2×C5×D4—21no—
278C2×C5×D4—21no—
279C2×C5×D4—41no—
280C2×C5×D4C3×D411yescharacteristic
281C2×C5×D4C23×C311yescharacteristic
282C2×C5×D4C23×C311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5C23×C311yescharacteristic
286C22×C4×C5C23×C311yescharacteristic
287C22×Dic5—21no—
288C2×Dic10C23×C311yescharacteristic
289C5×C4⋊C4—21no—
290C5×C4⋊C4C3×D411yescharacteristic
291C5×C4⋊C4C23×C311yescharacteristic
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4—21no—
296C5×C22⋊C4—21no—
297C5×C22⋊C4C3×D411yescharacteristic
298C5×C22⋊C4C3×D411yescharacteristic
299C42×C5C23×C311yescharacteristic
300C22⋊Dic5—21no—
301C22⋊Dic5—21no—
302C22⋊Dic5—21no—
303#689—41no—
304#687—22no—
305#687—41no—
306C4⋊Dic5—21no—
307C4⋊Dic5C23×C311yescharacteristic
308C4⋊Dic5C23×C311yescharacteristic
309C4⋊Dic5C23×C311yescharacteristic
310#683—21no—
311#683—21no—
312#683—21no—
313#683—21no—
314#683—21no—
315C4×Dic5—21no—
316C4×Dic5—21no—
317C2×#168—41no—
318C2×#168—41no—
319C2×#168C23×C311yescharacteristic
320C2×#168C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323#552—51no—
324#546C3×D511yescharacteristic
325#488—51no—
326#483—51no—
327#482—51no—
328#478—51no—
329#467—51no—
330#465—51no—
331#464—51no—
332#452—51no—
333#450—51no—
334C4×SD16—51no—
335C8×D4—51no—
336#416—51no—
337C2×#102—51no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—22no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—84no—
350C22×C3×C5#13512yes—
351C22×C3×C5C22×D411yescharacteristic
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5—41no—
357C3×C4×C5—41no—
358C3×C4×C5C2×#4111yescharacteristic
359C3×C4×C5H(5,𝔽2)11yescharacteristic
360C3×Dic5—41no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C24×C3—21no—
365C3×#41—22no—
366C3×#41—41no—
367C2×C3×Q8—51no—
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—22no—
370C2×C3×D4—21no—
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—41no—
374C2×C3×D4C22⋊D511yescharacteristic
375C2×C3×D4C22×D511yescharacteristic
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—101no—
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C3×Q16—201no—
383C3×SD16—102no—
384C3×SD16—201no—
385C2×C3×C8—51no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—51no—
389C2×C3×C8—201no—
390C2×C3×C8—201no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4—101no—
401C3×C4⋊C4C22⋊D511yescharacteristic
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4C22⋊D511yescharacteristic
412C3×C22⋊C4C22⋊D511yescharacteristic
413C3×C42—101no—
414C3×C42—101no—
415C3×C42C22×D511yescharacteristic
416C23×C5—21no—
417C23×C5—21no—
418C23×C5—42no—
419C23×C5—42no—
420C23×C5—81no—
421C23×C5C2×C3×D411yescharacteristic
422C23×C5C2×C3×D411yescharacteristic
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—22no—
426C5×D4—21no—
427C5×D4—21no—
428C5×D4—21no—
429C5×D4—42no—
430C5×D4—42no—
431C5×D4—81no—
432C5×D4C3×#4112yes—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—42no—
440C2×C4×C5—81no—
441C2×C4×C5C2×C3×D411yescharacteristic
442C2×C4×C5C2×C3×D411yescharacteristic
443C2×C4×C5C2×C3×D411yescharacteristic
444C2×C4×C5C2×C3×D411yescharacteristic
445C2×C4×C5C24×C311yescharacteristic
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—42no—
451Dic10—21no—
452Dic10—21no—
453#168—21no—
454#168—21no—
455#168—21no—
456#168—21no—
457C2×#41C2×C3×D511yescharacteristic
458C22×D4C2×C3×D511yescharacteristic
459C2×Q16—51no—
460C2×SD16—51no—
461C2×SD16—51no—
462C22×C8—51no—
463C22×C8—51no—
464#126—101no—
465#125—51no—
466#125—101no—
467#124C2×C3×D511yescharacteristic
468#123—21no—
469#123—101no—
470C22⋊Q8—51no—
471C22⋊Q8—51no—
472C22⋊Q8C2×C3×D511yescharacteristic
473#121—21no—
474#121C2×C3×D511yescharacteristic
475#120—21no—
476C4×Q8—51no—
477C4×D4C2×C3×D511yescharacteristic
478C4×D4C2×C3×D511yescharacteristic
479#117—51no—
480#117—101no—
481C2×C4⋊C4—51no—
482C2×C22⋊C4—21no—
483#107—51no—
484#106—51no—
485#106—51no—
486C4⋊C8—51no—
487#103—51no—
488#103—51no—
489#103—51no—
490#103—51no—
491#102—51no—
492#102—51no—
493#102—51no—
494#102—51no—
495#102—51no—
496#102—51no—
497C22⋊C8—51no—
498C22⋊C8—51no—
499C4×C8—51no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5—42no—
503C2×C3×C5—81no—
504C2×C3×C5#54611yescharacteristic
505C2×C3×C5C2×#13511yescharacteristic
506C2×C3×C5#57711yescharacteristic
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—42no—
510C23×C3—42no—
511C23×C3—81no—
512C23×C3C2×C22⋊D511yescharacteristic
513C23×C3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—101no—
517C3×Q8—101no—
518C3×D4—22no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—42no—
523C3×D4—42no—
524C3×D4—81no—
525C3×D4#71112yes—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—42no—
533C2×C3×C4—81no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—202no—
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—101no—
545C3×C8—101no—
546C3×C8—101no—
547C3×C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5—22no—
554C22×C5—41no—
555C22×C5—41no—
556C22×C5—41no—
557C22×C5—41no—
558C22×C5—41no—
559C22×C5—84no—
560C22×C5C3×#13512yes—
561C22×C5C22×C3×D411yescharacteristic
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—41no—
567C4×C5—41no—
568C4×C5C2×C3×#4111yescharacteristic
569C4×C5C3×H(5,𝔽2)11yescharacteristic
570Dic5—41no—
571Dic5—41no—
572Dic5—41no—
573Dic5—41no—
574C24—21no—
575#41—22no—
576#41—41no—
577C2×Q8—51no—
578C2×Q8C22×C3×D511yescharacteristic
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4C3×C22⋊D511yescharacteristic
585C2×D4C22×C3×D511yescharacteristic
586C2×D4C22×C3×D511yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—101no—
590C22×C4C22×C3×D511yescharacteristic
591C22×C4C22×C3×D511yescharacteristic
592Q16—201no—
593SD16—102no—
594SD16—201no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—51no—
598C2×C8—51no—
599C2×C8—201no—
600C2×C8—201no—
601C4⋊C4—21no—
602C4⋊C4—51no—
603C4⋊C4—51no—
604C4⋊C4—51no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4C3×C22⋊D511yescharacteristic
612C4⋊C4C22×C3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C22⋊C4C3×C22⋊D511yescharacteristic
622C22⋊C4C3×C22⋊D511yescharacteristic
623C42—101no—
624C42—101no—
625C42C22×C3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—84no—
639C22×C3#409612yes—
640C22×C3C22×C22⋊D511yescharacteristic
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—201no—
648C3×C4—201no—
649C3×C4—201no—
650C3×C4—201no—
651C3×C4C2×#71111yescharacteristic
652C3×C4#414411yescharacteristic
653C2×C5—22no—
654C2×C5—41no—
655C2×C5—42no—
656C2×C5—81no—
657C2×C5C3×#54611yescharacteristic
658C2×C5C2×C3×#13511yescharacteristic
659C2×C5C3×#57711yescharacteristic
660C23—21no—
661C23—21no—
662C23—42no—
663C23—42no—
664C23—81no—
665C23C2×C3×C22⋊D511yescharacteristic
666C23C2×C3×C22⋊D511yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—101no—
670Q8—101no—
671D4—22no—
672D4—21no—
673D4—21no—
674D4—21no—
675D4—42no—
676D4—42no—
677D4—81no—
678D4C3×#71112yes—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—42no—
686C2×C4—81no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—202no—
692C2×C4C2×C3×C22⋊D511yescharacteristic
693C2×C4C2×C3×C22⋊D511yescharacteristic
694C2×C4C2×C3×C22⋊D511yescharacteristic
695C2×C4C2×C3×C22⋊D511yescharacteristic
696C2×C4C23×C3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—101no—
700C8—101no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3—42no—
704C2×C3—81no—
705C2×C3#6614011yescharacteristic
706C2×C3C2×#409611yescharacteristic
707C2×C3#6617011yescharacteristic
708C5C3×#329611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—84no—
721C22C3×#409612yes—
722C22C22×C3×C22⋊D511yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—201no—
730C4—201no—
731C4—201no—
732C4—201no—
733C4C2×C3×#71111yescharacteristic
734C4C3×#414411yescharacteristic
735C3#1061522511yescharacteristic, direct product factor, Sylow
736C2—22no—
737C2—41no—
738C2—42no—
739C2—81no—
740C2C3×#6614011yescharacteristic
741C2C2×C3×#409611yescharacteristic
742C2C3×#6617011yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenterC3×#546D5
hypocenterC5C3×#3296
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#546

Complements

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

NH ≅ G/Ntype
2. C3×#65875C2semidirect
3. C3×#65528C2semidirect
4. C3×#65522C2semidirect
5. C3×#65507C2semidirect
6. C2×C3×#3964C2semidirect
7. C3×#65345C2semidirect
8. C3×#65343C2semidirect
9. C3×#65340C2semidirect
10. C3×#65332C2semidirect
11. C3×#65330C2semidirect
12. C3×#65324C2semidirect
13. C3×C4×#687C2semidirect
14. C3×D4×#168C2semidirect
15. C3×#65298C2semidirect
16. #10615225C3direct (N × H)
28. C2×C3×#689C22semidirect
32. C3×#4072C22semidirect
35. C3×#4070C22semidirect
37. C22×C3×#168C22semidirect
41. C3×#4016C22semidirect
42. C3×C4×Dic10C22semidirect
43. C3×#3967C22semidirect
44. C3×#3967C22semidirect
45. C3×#3967C22semidirect
53. C3×C22⋊#168C22semidirect
54. C3×#3942C22semidirect
55. C3×#3940C22semidirect
56. C3×#3940C22semidirect
57. C3×#3939C22semidirect
58. C3×C4⋊#168C22semidirect
59. C3×C4×#168C22semidirect
62. #65875C2×C3semidirect
63. #65528C2×C3semidirect
64. #65522C2×C3semidirect
65. #65507C2×C3semidirect
66. C2×#3964C2×C3semidirect
67. #65345C2×C3semidirect
68. #65343C2×C3semidirect
69. #65340C2×C3semidirect
70. #65332C2×C3semidirect
71. #65330C2×C3semidirect
72. #65324C2×C3semidirect
73. C4×#687C2×C3semidirect
74. D4×#168C2×C3semidirect
75. #65298C2×C3semidirect
154. C2×#689C22×C3semidirect
158. #4072C22×C3semidirect
161. #4070C22×C3semidirect
163. C22×#168C22×C3semidirect
167. #4016C22×C3semidirect
168. C4×Dic10C22×C3semidirect
169. #3967C22×C3semidirect
170. #3967C22×C3semidirect
171. #3967C22×C3semidirect
179. C22⋊#168C22×C3semidirect
180. #3942C22×C3semidirect
181. #3940C22×C3semidirect
182. #3940C22×C3semidirect
183. #3939C22×C3semidirect
184. C4⋊#168C22×C3semidirect
185. C4×#168C22×C3semidirect
626. C3×C5#3296semidirect
708. C5C3×#3296semidirect
735. C3#10615225direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5462
C3×#658752
C3×#655282
C3×#655222
C3×#655072
C2×C3×#39642
C3×#653452
C3×#653432
C3×#653402
C3×#653322
C3×#653302
C3×#653242
C3×C4×#6872
C3×D4×#1682
C3×#652982
#106152253
C3×#32965