Finite Group Databasebeta

← C3×#10614272 #14435584

Subgroups — C3×#10614272 #14435584

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#518C211yesmaximal, characteristic, complemented
2C3×#65868C211yesmaximal, characteristic, complemented
3C3×#65507C211yesmaximal, characteristic, complemented
4C3×#65506C211yesmaximal, characteristic
5C3×#65307C211yesmaximal, characteristic, complemented
6C3×C4×#687C211yesmaximal, characteristic, complemented
7C3×#65305C211yesmaximal, characteristic, complemented
8C3×#65305C211yesmaximal, characteristic, complemented
9C3×#65303C211yesmaximal, characteristic, complemented
10C3×C4×#686C211yesmaximal, characteristic, complemented
11C3×#65297C211yesmaximal, characteristic, complemented
12C3×#65296C211yesmaximal, characteristic, complemented
13C3×#65292C211yesmaximal, characteristic, complemented
14C3×#65289C211yesmaximal, characteristic, complemented
15C3×#65285C211yesmaximal, characteristic, complemented
16#10614272C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C3×C4×C5×D4—21no—
19C3×C4×C5×D4—21no—
20C3×C4×C5×D4C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24C3×C5×#117C2211yescharacteristic
25C3×C5×#117C2211yescharacteristic
26C2×C3×C5×C22⋊C4—21no—
27C2×C3×C5×C22⋊C4—21no—
28C2×C3×#687C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076C2211yescharacteristic
33C3×#4070C2211yescharacteristic
34C3×#4044—21no—
35C3×#4042—21no—
36C3×#4031—21no—
37C3×#4029—21no—
38C3×#4021C2211yescharacteristic, complemented
39C3×C4×D20C2211yescharacteristic, complemented
40C3×#4015C2211yescharacteristic, complemented
41C3×C4×Dic10C2211yescharacteristic, complemented
42C3×#3964C2211yescharacteristic
43C3×#3964C2211yescharacteristic
44C3×#3964C2211yescharacteristic
45C3×#3964C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic, complemented
49C3×#3942C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic, complemented
51C3×#3941C2211yescharacteristic, complemented
52C3×#3940C2211yescharacteristic, complemented
53C3×#3940C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55C3×#3939C2211yescharacteristic, complemented
56C3×C4⋊#168C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58C3×#3935C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61C5×#518C2×C311yescharacteristic, complemented
62#65868C2×C311yescharacteristic, complemented
63#65507C2×C311yescharacteristic, complemented
64#65506C2×C311yescharacteristic
65#65307C2×C311yescharacteristic, complemented
66C4×#687C2×C311yescharacteristic, complemented
67#65305C2×C311yescharacteristic, complemented
68#65305C2×C311yescharacteristic, complemented
69#65303C2×C311yescharacteristic, complemented
70C4×#686C2×C311yescharacteristic, complemented
71#65297C2×C311yescharacteristic, complemented
72#65296C2×C311yescharacteristic, complemented
73#65292C2×C311yescharacteristic, complemented
74#65289C2×C311yescharacteristic, complemented
75#65285C2×C311yescharacteristic, complemented
76C24×C3×C5—21no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4D411yescharacteristic
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C42×C5C2311yescharacteristic
106C3×C22⋊Dic5—21no—
107C3×#687—22no—
108C3×#687—22no—
109C3×#686—22no—
110C3×#686—22no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542—51no—
126C3×#518D511yescharacteristic, complemented
127C3×#485—51no—
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463—51no—
133C3×#450—51no—
134C3×#447—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C22×C5×D4C22×C311yescharacteristic
141C4×C5×D4—21no—
142C4×C5×D4—21no—
143C4×C5×D4C22×C311yescharacteristic
144C4×C5×D4C22×C311yescharacteristic
145C4×C5×D4C22×C311yescharacteristic
146C4×C5×D4C22×C311yescharacteristic
147C5×#117C22×C311yescharacteristic
148C5×#117C22×C311yescharacteristic
149C2×C5×C22⋊C4—21no—
150C2×C5×C22⋊C4—21no—
151C2×#687C22×C311yescharacteristic
152C2×#687C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154C2×#686C22×C311yescharacteristic
155#4076C22×C311yescharacteristic
156#4070C22×C311yescharacteristic
157#4044—21no—
158#4042—21no—
159#4031—21no—
160#4029—21no—
161#4021C22×C311yescharacteristic, complemented
162C4×D20C22×C311yescharacteristic, complemented
163#4015C22×C311yescharacteristic, complemented
164C4×Dic10C22×C311yescharacteristic, complemented
165#3964C22×C311yescharacteristic
166#3964C22×C311yescharacteristic
167#3964C22×C311yescharacteristic
168#3964C22×C311yescharacteristic
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3942C22×C311yescharacteristic, complemented
172#3942C22×C311yescharacteristic, complemented
173#3941C22×C311yescharacteristic, complemented
174#3941C22×C311yescharacteristic, complemented
175#3940C22×C311yescharacteristic, complemented
176#3940C22×C311yescharacteristic, complemented
177#3939C22×C311yescharacteristic, complemented
178#3939C22×C311yescharacteristic, complemented
179C4⋊#168C22×C311yescharacteristic, complemented
180C4⋊#168C22×C311yescharacteristic, complemented
181#3935C22×C311yescharacteristic, complemented
182C4×#168C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5—24no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—81no—
188C23×C3×C5—81no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C3×D5—21no—
191C3×C5×D4—24no—
192C3×C5×D4—21no—
193C3×C5×D4—21no—
194C3×C5×D4#4112yes—
195C3×C5×D4#4112yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5—81no—
202C2×C3×C4×C5—81no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210C3×C22⋊D5—81no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C3×D20—21no—
215C3×D20—21no—
216C3×C4×D5—81no—
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—81no—
220C3×#168—21no—
221C3×#168—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×D4C2×D511yescharacteristic
225C2×C3×SD16—51no—
226C2×C3×SD16—51no—
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×C4⋊Q8—51no—
230C3×#126—101no—
231C3×#124—51no—
232C3×#124—101no—
233C3×#123—101no—
234C3×C22⋊Q8—51no—
235C3×C22⋊Q8—101no—
236C3×#121—51no—
237C3×C4×Q8—51no—
238C3×C4×D4—21no—
239C3×C4×D4—21no—
240C3×C4×D4—51no—
241C3×C4×D4C2×D511yescharacteristic
242C3×C4×D4C2×D511yescharacteristic
243C3×C4×D4C2×D511yescharacteristic
244C3×C4×D4C2×D511yescharacteristic
245C3×#117C2×D511yescharacteristic
246C3×#117C2×D511yescharacteristic
247C2×C3×C22⋊C4—21no—
248C2×C3×C22⋊C4—21no—
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106—51no—
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102—51no—
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×#97—51no—
266C3×C4×C8—51no—
267C24×C5—21no—
268C2×C5×D4—22no—
269C2×C5×D4—22no—
270C2×C5×D4—21no—
271C2×C5×D4C23×C311yescharacteristic
272C2×C5×D4C23×C311yescharacteristic
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5C23×C311yescharacteristic
278C2×C22⋊D5—21no—
279C2×D20C23×C311yescharacteristic
280C2×C4×D5—21no—
281C2×Dic10—21no—
282C2×Dic10C23×C311yescharacteristic
283C5×C4⋊C4C3×D411yescharacteristic
284C5×C4⋊C4C3×D411yescharacteristic
285C5×C4⋊C4C23×C311yescharacteristic
286C5×C4⋊C4C23×C311yescharacteristic
287C5×C22⋊C4—21no—
288C5×C22⋊C4—21no—
289C5×C22⋊C4—21no—
290C5×C22⋊C4—21no—
291C5×C22⋊C4—21no—
292C5×C22⋊C4C3×D411yescharacteristic
293C5×C22⋊C4C3×D411yescharacteristic
294C42×C5—21no—
295C42×C5C23×C311yescharacteristic
296C42×C5C23×C311yescharacteristic
297C22⋊Dic5—21no—
298#687—22no—
299#687—22no—
300#686—22no—
301#686—22no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5C23×C311yescharacteristic
308C4⋊Dic5C23×C311yescharacteristic
309#683—21no—
310#683—21no—
311C4×Dic5—21no—
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#542—51no—
317#518C3×D511yescharacteristic, complemented
318#485—51no—
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463—51no—
324#450—51no—
325#447—51no—
326#442—51no—
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—21no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—84no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—41no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5C2×#4111yescharacteristic
353C3×C4×C5C2×#4111yescharacteristic
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×Dic5—41no—
357C24×C3—21no—
358C2×C3×Q8—51no—
359C2×C3×Q8—101no—
360C2×C3×D4—22no—
361C2×C3×D4—22no—
362C2×C3×D4—21no—
363C2×C3×D4—51no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C3×SD16—102no—
374C3×SD16—102no—
375C3×D8—102no—
376C3×D8—102no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8—51no—
381C3×C4⋊C4—51no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—101no—
384C3×C4⋊C4—101no—
385C3×C4⋊C4—101no—
386C3×C4⋊C4C22⋊D511yescharacteristic
387C3×C4⋊C4C22⋊D511yescharacteristic
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4C22⋊D511yescharacteristic
401C3×C22⋊C4C22⋊D511yescharacteristic
402C3×C42—21no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405C3×C42C22×D511yescharacteristic
406C23×C5—24no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—81no—
410C23×C5—81no—
411C23×C5C2×C3×D411yescharacteristic
412C22×D5—21no—
413C5×D4—24no—
414C5×D4—21no—
415C5×D4—21no—
416C5×D4C3×#4112yes—
417C5×D4C3×#4112yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—81no—
423C2×C4×C5—81no—
424C2×C4×C5—81no—
425C2×C4×C5—81no—
426C2×C4×C5C2×C3×D411yescharacteristic
427C2×C4×C5C2×C3×D411yescharacteristic
428C2×C4×C5C2×C3×D411yescharacteristic
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C2×C3×D411yescharacteristic
431C2×C4×C5C24×C311yescharacteristic
432C22⋊D5—81no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436D20—21no—
437D20—21no—
438C4×D5—81no—
439Dic10—21no—
440Dic10—21no—
441Dic10—81no—
442#168—21no—
443#168—21no—
444#168—21no—
445#168—21no—
446C22×D4C2×C3×D511yescharacteristic
447C2×SD16—51no—
448C2×SD16—51no—
449C2×D8—51no—
450C2×D8—51no—
451C4⋊Q8—51no—
452#126—101no—
453#124—51no—
454#124—101no—
455#123—101no—
456C22⋊Q8—51no—
457C22⋊Q8—101no—
458#121—51no—
459C4×Q8—51no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—51no—
463C4×D4C2×C3×D511yescharacteristic
464C4×D4C2×C3×D511yescharacteristic
465C4×D4C2×C3×D511yescharacteristic
466C4×D4C2×C3×D511yescharacteristic
467#117C2×C3×D511yescharacteristic
468#117C2×C3×D511yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471#107—51no—
472#107—51no—
473#106—51no—
474#106—51no—
475C4⋊C8—51no—
476C4⋊C8—51no—
477#103—51no—
478#103—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102—51no—
484#102—51no—
485C22⋊C8—51no—
486C22⋊C8—51no—
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—41no—
490C2×C3×C5—42no—
491C2×C3×C5—42no—
492C2×C3×C5#52511yescharacteristic
493C2×C3×C5#57611yescharacteristic
494C2×C3×C5#57711yescharacteristic
495C3×D5—81no—
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3—101no—
502C23×C3C2×C22⋊D511yescharacteristic
503C3×Q8—101no—
504C3×Q8—101no—
505C3×Q8—401no—
506C3×D4—24no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—101no—
510C3×D4—101no—
511C3×D4—401no—
512C3×D4#70912yes—
513C3×D4#70912yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—81no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—81no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—401no—
526C2×C3×C4C2×C22⋊D511yescharacteristic
527C2×C3×C4C2×C22⋊D511yescharacteristic
528C2×C3×C4C2×C22⋊D511yescharacteristic
529C2×C3×C4C2×C22⋊D511yescharacteristic
530C2×C3×C4C2×C22⋊D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—101no—
533C3×C8—101no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—84no—
546C22×C5C22×C3×D411yescharacteristic
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—41no—
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5C2×C3×#4111yescharacteristic
558C4×C5C2×C3×#4111yescharacteristic
559Dic5—41no—
560Dic5—41no—
561Dic5—41no—
562C24—21no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—51no—
569C2×D4—101no—
570C2×D4C22×C3×D511yescharacteristic
571C2×D4C22×C3×D511yescharacteristic
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—102no—
579SD16—102no—
580D8—102no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8—51no—
585C2×C8—51no—
586C4⋊C4—51no—
587C4⋊C4—51no—
588C4⋊C4—101no—
589C4⋊C4—101no—
590C4⋊C4—101no—
591C4⋊C4C3×C22⋊D511yescharacteristic
592C4⋊C4C3×C22⋊D511yescharacteristic
593C4⋊C4C22×C3×D511yescharacteristic
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4C3×C22⋊D511yescharacteristic
606C22⋊C4C3×C22⋊D511yescharacteristic
607C42—21no—
608C42—101no—
609C42C22×C3×D511yescharacteristic
610C42C22×C3×D511yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—84no—
622C22×C3—201no—
623C22×C3—201no—
624C22×C3—201no—
625C22×C3C22×C22⋊D511yescharacteristic
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—201no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4C2×#70911yescharacteristic
637C3×C4C2×#70911yescharacteristic
638C2×C5—41no—
639C2×C5—42no—
640C2×C5—42no—
641C2×C5C3×#52511yescharacteristic
642C2×C5C3×#57611yescharacteristic
643C2×C5C3×#57711yescharacteristic
644D5—81no—
645C23—24no—
646C23—21no—
647C23—21no—
648C23—81no—
649C23—81no—
650C23—101no—
651C23C2×C3×C22⋊D511yescharacteristic
652Q8—101no—
653Q8—101no—
654Q8—401no—
655D4—24no—
656D4—21no—
657D4—21no—
658D4—101no—
659D4—101no—
660D4—401no—
661D4C3×#70912yes—
662D4C3×#70912yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—401no—
675C2×C4C2×C3×C22⋊D511yescharacteristic
676C2×C4C2×C3×C22⋊D511yescharacteristic
677C2×C4C2×C3×C22⋊D511yescharacteristic
678C2×C4C2×C3×C22⋊D511yescharacteristic
679C2×C4C2×C3×C22⋊D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—101no—
682C8—101no—
683C8—101no—
684C8—101no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—401no—
689C2×C3#6612511yescharacteristic
690C2×C3#6616911yescharacteristic
691C2×C3#6617011yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—21no—
694C22—22no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—84no—
703C22—201no—
704C22—201no—
705C22—201no—
706C22C22×C3×C22⋊D511yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—201no—
715C4—201no—
716C4—201no—
717C4C2×C3×#70911yescharacteristic
718C4C2×C3×#70911yescharacteristic
719C3#1061427211yescharacteristic, direct product factor, Sylow
720C2—41no—
721C2—42no—
722C2—42no—
723C2—401no—
724C2C3×#6612511yescharacteristic
725C2C3×#6616911yescharacteristic
726C2C3×#6617011yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#518C2
socleC22×C3×C5C22×D4
prime radicalC3×#65506C2
hypercenterC3×#518D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
2. C3×#65868C2semidirect
3. C3×#65507C2semidirect
5. C3×#65307C2semidirect
6. C3×C4×#687C2semidirect
7. C3×#65305C2semidirect
8. C3×#65305C2semidirect
9. C3×#65303C2semidirect
10. C3×C4×#686C2semidirect
11. C3×#65297C2semidirect
12. C3×#65296C2semidirect
13. C3×#65292C2semidirect
14. C3×#65289C2semidirect
15. C3×#65285C2semidirect
16. #10614272C3direct (N × H)
38. C3×#4021C22semidirect
39. C3×C4×D20C22semidirect
40. C3×#4015C22semidirect
41. C3×C4×Dic10C22semidirect
48. C3×#3942C22semidirect
49. C3×#3942C22semidirect
50. C3×#3941C22semidirect
51. C3×#3941C22semidirect
52. C3×#3940C22semidirect
53. C3×#3940C22semidirect
54. C3×#3939C22semidirect
55. C3×#3939C22semidirect
56. C3×C4⋊#168C22semidirect
57. C3×C4⋊#168C22semidirect
58. C3×#3935C22semidirect
59. C3×C4×#168C22semidirect
61. C5×#518C2×C3semidirect
62. #65868C2×C3semidirect
63. #65507C2×C3semidirect
65. #65307C2×C3semidirect
66. C4×#687C2×C3semidirect
67. #65305C2×C3semidirect
68. #65305C2×C3semidirect
69. #65303C2×C3semidirect
70. C4×#686C2×C3semidirect
71. #65297C2×C3semidirect
72. #65296C2×C3semidirect
73. #65292C2×C3semidirect
74. #65289C2×C3semidirect
75. #65285C2×C3semidirect
126. C3×#518D5semidirect
161. #4021C22×C3semidirect
162. C4×D20C22×C3semidirect
163. #4015C22×C3semidirect
164. C4×Dic10C22×C3semidirect
171. #3942C22×C3semidirect
172. #3942C22×C3semidirect
173. #3941C22×C3semidirect
174. #3941C22×C3semidirect
175. #3940C22×C3semidirect
176. #3940C22×C3semidirect
177. #3939C22×C3semidirect
178. #3939C22×C3semidirect
179. C4⋊#168C22×C3semidirect
180. C4⋊#168C22×C3semidirect
181. #3935C22×C3semidirect
182. C4×#168C22×C3semidirect
317. #518C3×D5semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10614272direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C3×#658682
C3×#655072
C3×#655062
C3×#653072
C3×C4×#6872
C3×#653052
C3×#653032
C3×C4×#6862
C3×#652972
C3×#652962
C3×#652922
C3×#652892
C3×#652852
#106142723
C3×#31185