Finite Group Databasebeta

← C3×#10615226 #14458867

Subgroups — C3×#10615226 #14458867

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic, complemented
2C3×#65899C211yesmaximal, characteristic, complemented
3C3×#65527C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5C3×#65506C211yesmaximal, characteristic, complemented
6C2×C3×#3964C211yesmaximal, characteristic, complemented
7C3×#65346C211yesmaximal, characteristic, complemented
8C3×#65345C211yesmaximal, characteristic, complemented
9C3×#65337C211yesmaximal, characteristic, complemented
10C3×#65333C211yesmaximal, characteristic, complemented
11C3×#65327C211yesmaximal, characteristic, complemented
12C3×#65324C211yesmaximal, characteristic, complemented
13C3×C4×#686C211yesmaximal, characteristic, complemented
14C3×D4×#168C211yesmaximal, characteristic, complemented
15C3×#65298C211yesmaximal, characteristic, complemented
16#10615226C311yesmaximal, 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×#688C2211yescharacteristic, complemented
29C3×#4085—21no—
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076C2211yescharacteristic
33C3×#4076C2211yescharacteristic, complemented
34C3×#4072C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic5C2211yescharacteristic
36C22×C3×#168C2211yescharacteristic
37C22×C3×#168C2211yescharacteristic, complemented
38C3×#4044—21no—
39C3×#4029—21no—
40C3×#4027—21no—
41C3×C4×D20C2211yescharacteristic, complemented
42C3×#4016C2211yescharacteristic, 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×#3941C2211yescharacteristic, complemented
55C3×#3940C2211yescharacteristic, complemented
56C3×#3939C2211yescharacteristic, complemented
57C3×#3939C2211yescharacteristic, complemented
58C3×C4⋊#168C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3297—51nomaximal, Hall
61C5×#546C2×C311yescharacteristic, complemented
62#65899C2×C311yescharacteristic, complemented
63#65527C2×C311yescharacteristic, complemented
64#65522C2×C311yescharacteristic, complemented
65#65506C2×C311yescharacteristic, complemented
66C2×#3964C2×C311yescharacteristic, complemented
67#65346C2×C311yescharacteristic, complemented
68#65345C2×C311yescharacteristic, complemented
69#65337C2×C311yescharacteristic, complemented
70#65333C2×C311yescharacteristic, complemented
71#65327C2×C311yescharacteristic, complemented
72#65324C2×C311yescharacteristic, complemented
73C4×#686C2×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
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C22×C3×Dic5—21no—
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4D411yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C42×C5C2311yescharacteristic
108C3×C22⋊Dic5—21no—
109C3×#688—41no—
110C3×#686—22no—
111C3×#686—41no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—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×#553—51no—
129C3×#546D511yescharacteristic, complemented
130C3×#488—51no—
131C3×#484—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#466—51no—
135C3×#465—51no—
136C3×#463—51no—
137C3×#449—51no—
138C3×#447—51no—
139C3×C4×D8—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×#688C22×C311yescharacteristic, complemented
155#4085—21no—
156C2×#686C22×C311yescharacteristic
157C2×#686C22×C311yescharacteristic
158#4076C22×C311yescharacteristic
159#4076C22×C311yescharacteristic, complemented
160#4072C22×C311yescharacteristic, complemented
161C2×C4⋊Dic5C22×C311yescharacteristic
162C22×#168C22×C311yescharacteristic
163C22×#168C22×C311yescharacteristic, complemented
164#4044—21no—
165#4029—21no—
166#4027—21no—
167C4×D20C22×C311yescharacteristic, complemented
168#4016C22×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#3941C22×C311yescharacteristic, complemented
181#3940C22×C311yescharacteristic, complemented
182#3939C22×C311yescharacteristic, complemented
183#3939C22×C311yescharacteristic, complemented
184C4⋊#168C22×C311yescharacteristic, complemented
185C4×#168C22×C311yescharacteristic, complemented
186#3297—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
194C22×C3×D5—21no—
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—22no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C3×C5×D4—42no—
202C3×C5×D4—42no—
203C3×C5×D4—81no—
204C3×C5×D4#4112yes—
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—21no—
211C2×C3×C4×C5—42no—
212C2×C3×C4×C5—81no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218C3×C22⋊D5—42no—
219C3×C22⋊D5—81no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—81no—
224C3×D20—21no—
225C3×D20—21no—
226C3×C4×D5—81no—
227C3×#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×C3×#41C2×D511yescharacteristic
232C22×C3×D4C2×D511yescharacteristic
233C2×C3×SD16—51no—
234C2×C3×D8—51no—
235C2×C3×D8—51no—
236C22×C3×C8—51no—
237C22×C3×C8—51no—
238C3×#126—101no—
239C3×#125—51no—
240C3×#124C2×D511yescharacteristic
241C3×#123—21no—
242C3×#123—101no—
243C3×C22⋊Q8C2×D511yescharacteristic
244C3×#121—21no—
245C3×#121—51no—
246C3×#121—51no—
247C3×#121—101no—
248C3×#121C2×D511yescharacteristic
249C3×#120—21no—
250C3×C4×D4—51no—
251C3×C4×D4—101no—
252C3×C4×D4C2×D511yescharacteristic
253C3×C4×D4C2×D511yescharacteristic
254C3×#117—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—21no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#106—51no—
260C3×C4⋊C8—51no—
261C3×#103—51no—
262C3×#103—51no—
263C3×#103—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102—51no—
271C3×C22⋊C8—51no—
272C3×C22⋊C8—51no—
273C3×C4×C8—51no—
274C24×C5—21no—
275C5×#41—22no—
276C5×#41—41no—
277C2×C5×Q8C23×C311yescharacteristic
278C2×C5×D4—22no—
279C2×C5×D4—21no—
280C2×C5×D4—21no—
281C2×C5×D4—21no—
282C2×C5×D4—41no—
283C2×C5×D4C3×D411yescharacteristic
284C2×C5×D4C23×C311yescharacteristic
285C2×C5×D4C23×C311yescharacteristic
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5C23×C311yescharacteristic
289C22×C4×C5C23×C311yescharacteristic
290C2×C22⋊D5—21no—
291C2×C22⋊D5—21no—
292C22×Dic5—21no—
293C2×D20C23×C311yescharacteristic
294C2×C4×D5—21no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4C3×D411yescharacteristic
297C5×C4⋊C4C23×C311yescharacteristic
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4C3×D411yescharacteristic
304C5×C22⋊C4C3×D411yescharacteristic
305C42×C5C23×C311yescharacteristic
306C22⋊Dic5—21no—
307#688—41no—
308#686—22no—
309#686—41no—
310#685—21no—
311#685—21no—
312#685—21no—
313C4⋊Dic5—21no—
314C4⋊Dic5C23×C311yescharacteristic
315C4⋊Dic5C23×C311yescharacteristic
316C4⋊Dic5C23×C311yescharacteristic
317#683—21no—
318#683—21no—
319C4×Dic5—21no—
320C2×#168—41no—
321C2×#168—41no—
322C2×#168C23×C311yescharacteristic
323C2×#168C23×C311yescharacteristic
324C2×#168C23×C311yescharacteristic
325C2×#168C23×C311yescharacteristic
326#553—51no—
327#546C3×D511yescharacteristic, complemented
328#488—51no—
329#484—51no—
330#482—51no—
331#478—51no—
332#466—51no—
333#465—51no—
334#463—51no—
335#449—51no—
336#447—51no—
337C4×D8—51no—
338C8×D4—51no—
339#416—51no—
340C2×#102—51no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—22no—
345C22×C3×C5—21no—
346C22×C3×C5—21no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—84no—
353C22×C3×C5#13512yes—
354C22×C3×C5C22×D411yescharacteristic
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×C4×C5C2×#4111yescharacteristic
365C3×C4×C5H(5,𝔽2)11yescharacteristic
366C3×Dic5—41no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C24×C3—21no—
370C3×#41—22no—
371C3×#41—41no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—41no—
378C2×C3×D4—51no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4C22⋊D511yescharacteristic
382C2×C3×D4C22×D511yescharacteristic
383C2×C3×D4C22×D511yescharacteristic
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4C22×D511yescharacteristic
389C22×C3×C4C22×D511yescharacteristic
390C3×SD16—201no—
391C3×D8—102no—
392C3×D8—201no—
393C2×C3×C8—51no—
394C2×C3×C8—51no—
395C2×C3×C8—51no—
396C2×C3×C8—51no—
397C2×C3×C8—201no—
398C2×C3×C8—201no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—51no—
403C3×C4⋊C4—101no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4C22⋊D511yescharacteristic
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C22⋊C4—101no—
416C3×C22⋊C4—101no—
417C3×C22⋊C4C22⋊D511yescharacteristic
418C3×C22⋊C4C22⋊D511yescharacteristic
419C3×C42—101no—
420C3×C42C22×D511yescharacteristic
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—42no—
424C23×C5—42no—
425C23×C5—81no—
426C23×C5C2×C3×D411yescharacteristic
427C23×C5C2×C3×D411yescharacteristic
428C22×D5—21no—
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—22no—
432C5×D4—21no—
433C5×D4—21no—
434C5×D4—21no—
435C5×D4—42no—
436C5×D4—42no—
437C5×D4—81no—
438C5×D4C3×#4112yes—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—42no—
446C2×C4×C5—81no—
447C2×C4×C5C2×C3×D411yescharacteristic
448C2×C4×C5C2×C3×D411yescharacteristic
449C2×C4×C5C2×C3×D411yescharacteristic
450C2×C4×C5C2×C3×D411yescharacteristic
451C2×C4×C5C24×C311yescharacteristic
452C22⋊D5—42no—
453C22⋊D5—81no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—81no—
458D20—21no—
459D20—21no—
460C4×D5—81no—
461#168—21no—
462#168—21no—
463#168—21no—
464#168—21no—
465C2×#41C2×C3×D511yescharacteristic
466C22×D4C2×C3×D511yescharacteristic
467C2×SD16—51no—
468C2×D8—51no—
469C2×D8—51no—
470C22×C8—51no—
471C22×C8—51no—
472#126—101no—
473#125—51no—
474#124C2×C3×D511yescharacteristic
475#123—21no—
476#123—101no—
477C22⋊Q8C2×C3×D511yescharacteristic
478#121—21no—
479#121—51no—
480#121—51no—
481#121—101no—
482#121C2×C3×D511yescharacteristic
483#120—21no—
484C4×D4—51no—
485C4×D4—101no—
486C4×D4C2×C3×D511yescharacteristic
487C4×D4C2×C3×D511yescharacteristic
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—21no—
491#107—51no—
492#107—51no—
493#106—51no—
494C4⋊C8—51no—
495#103—51no—
496#103—51no—
497#103—51no—
498#102—51no—
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102—51no—
504#102—51no—
505C22⋊C8—51no—
506C22⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5—42no—
511C2×C3×C5—81no—
512C2×C3×C5#54611yescharacteristic
513C2×C3×C5C2×#13511yescharacteristic
514C2×C3×C5#57611yescharacteristic
515C3×D5—81no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—42no—
519C23×C3—42no—
520C23×C3—81no—
521C23×C3—101no—
522C23×C3C2×C22⋊D511yescharacteristic
523C23×C3C2×C22⋊D511yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—22no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—42no—
531C3×D4—42no—
532C3×D4—81no—
533C3×D4—101no—
534C3×D4—101no—
535C3×D4—202no—
536C3×D4—401no—
537C3×D4#71112yes—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—42no—
545C2×C3×C4—81no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—401no—
550C2×C3×C4—401no—
551C2×C3×C4C2×C22⋊D511yescharacteristic
552C2×C3×C4C2×C22⋊D511yescharacteristic
553C2×C3×C4C2×C22⋊D511yescharacteristic
554C2×C3×C4C2×C22⋊D511yescharacteristic
555C2×C3×C4C23×D511yescharacteristic
556C3×C8—101no—
557C3×C8—101no—
558C3×C8—101no—
559C3×C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—22no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—84no—
572C22×C5C3×#13512yes—
573C22×C5C22×C3×D411yescharacteristic
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5C2×C3×#4111yescharacteristic
584C4×C5C3×H(5,𝔽2)11yescharacteristic
585Dic5—41no—
586Dic5—41no—
587Dic5—41no—
588C24—21no—
589#41—22no—
590#41—41no—
591C2×Q8C22×C3×D511yescharacteristic
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—51no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4C3×C22⋊D511yescharacteristic
601C2×D4C22×C3×D511yescharacteristic
602C2×D4C22×C3×D511yescharacteristic
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4C22×C3×D511yescharacteristic
608C22×C4C22×C3×D511yescharacteristic
609SD16—201no—
610D8—102no—
611D8—201no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—51no—
615C2×C8—51no—
616C2×C8—201no—
617C2×C8—201no—
618C4⋊C4—21no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4C3×C22⋊D511yescharacteristic
626C4⋊C4C22×C3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4C3×C22⋊D511yescharacteristic
637C22⋊C4C3×C22⋊D511yescharacteristic
638C42—101no—
639C42C22×C3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—84no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3#409612yes—
657C22×C3C22×C22⋊D511yescharacteristic
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—201no—
665C3×C4—201no—
666C3×C4—201no—
667C3×C4C2×#71111yescharacteristic
668C3×C4#414411yescharacteristic
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—42no—
672C2×C5—81no—
673C2×C5C3×#54611yescharacteristic
674C2×C5C2×C3×#13511yescharacteristic
675C2×C5C3×#57611yescharacteristic
676D5—81no—
677C23—21no—
678C23—21no—
679C23—42no—
680C23—42no—
681C23—81no—
682C23—101no—
683C23C2×C3×C22⋊D511yescharacteristic
684C23C2×C3×C22⋊D511yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—22no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—101no—
695D4—101no—
696D4—202no—
697D4—401no—
698D4C3×#71112yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—42no—
706C2×C4—81no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—401no—
711C2×C4—401no—
712C2×C4C2×C3×C22⋊D511yescharacteristic
713C2×C4C2×C3×C22⋊D511yescharacteristic
714C2×C4C2×C3×C22⋊D511yescharacteristic
715C2×C4C2×C3×C22⋊D511yescharacteristic
716C2×C4C23×C3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—101no—
720C8—101no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—42no—
724C2×C3—81no—
725C2×C3—401no—
726C2×C3#6614011yescharacteristic
727C2×C3C2×#409611yescharacteristic
728C2×C3#6616911yescharacteristic
729C5C3×#329711yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—201no—
743C22—201no—
744C22—201no—
745C22C3×#409612yes—
746C22C22×C3×C22⋊D511yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—41no—
753C4—201no—
754C4—201no—
755C4—201no—
756C4C2×C3×#71111yescharacteristic
757C4C3×#414411yescharacteristic
758C3#1061522611yescharacteristic, direct product factor, Sylow
759C2—22no—
760C2—41no—
761C2—42no—
762C2—81no—
763C2—401no—
764C2C3×#6614011yescharacteristic
765C2C2×C3×#409611yescharacteristic
766C2C3×#6616911yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenterC3×#546D5
hypocenterC5C3×#3297
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
1. C3×C5×#546C2semidirect
2. C3×#65899C2semidirect
3. C3×#65527C2semidirect
4. C3×#65522C2semidirect
5. C3×#65506C2semidirect
6. C2×C3×#3964C2semidirect
7. C3×#65346C2semidirect
8. C3×#65345C2semidirect
9. C3×#65337C2semidirect
10. C3×#65333C2semidirect
11. C3×#65327C2semidirect
12. C3×#65324C2semidirect
13. C3×C4×#686C2semidirect
14. C3×D4×#168C2semidirect
15. C3×#65298C2semidirect
16. #10615226C3direct (N × H)
28. C2×C3×#688C22semidirect
33. C3×#4076C22semidirect
34. C3×#4072C22semidirect
37. C22×C3×#168C22semidirect
41. C3×C4×D20C22semidirect
42. C3×#4016C22semidirect
43. C3×#3967C22semidirect
44. C3×#3967C22semidirect
45. C3×#3967C22semidirect
53. C3×C22⋊#168C22semidirect
54. C3×#3941C22semidirect
55. C3×#3940C22semidirect
56. C3×#3939C22semidirect
57. C3×#3939C22semidirect
58. C3×C4⋊#168C22semidirect
59. C3×C4×#168C22semidirect
61. C5×#546C2×C3semidirect
62. #65899C2×C3semidirect
63. #65527C2×C3semidirect
64. #65522C2×C3semidirect
65. #65506C2×C3semidirect
66. C2×#3964C2×C3semidirect
67. #65346C2×C3semidirect
68. #65345C2×C3semidirect
69. #65337C2×C3semidirect
70. #65333C2×C3semidirect
71. #65327C2×C3semidirect
72. #65324C2×C3semidirect
73. C4×#686C2×C3semidirect
74. D4×#168C2×C3semidirect
75. #65298C2×C3semidirect
129. C3×#546D5semidirect
154. C2×#688C22×C3semidirect
159. #4076C22×C3semidirect
160. #4072C22×C3semidirect
163. C22×#168C22×C3semidirect
167. C4×D20C22×C3semidirect
168. #4016C22×C3semidirect
169. #3967C22×C3semidirect
170. #3967C22×C3semidirect
171. #3967C22×C3semidirect
179. C22⋊#168C22×C3semidirect
180. #3941C22×C3semidirect
181. #3940C22×C3semidirect
182. #3939C22×C3semidirect
183. #3939C22×C3semidirect
184. C4⋊#168C22×C3semidirect
185. C4×#168C22×C3semidirect
327. #546C3×D5semidirect
640. C3×C5#3297semidirect
729. C5C3×#3297semidirect
758. C3#10615226direct (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×#658992
C3×#655272
C3×#655222
C3×#655062
C2×C3×#39642
C3×#653462
C3×#653452
C3×#653372
C3×#653332
C3×#653272
C3×#653242
C3×C4×#6862
C3×D4×#1682
C3×#652982
#106152263
C3×#32975