Finite Group Databasebeta

← C3×#10613112 #14458621

Subgroups — C3×#10613112 #14458621

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×#65946C211yesmaximal, characteristic
2C3×#65863C211yesmaximal, characteristic, complemented
3C3×C5×#482C211yesmaximal, characteristic, complemented
4C3×#65330C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic, complemented
6C3×#65180C211yesmaximal, characteristic, complemented
7C3×#65176C211yesmaximal, characteristic, complemented
8C3×#65151C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65065C211yesmaximal, characteristic, complemented
11C3×D5×#102C211yesmaximal, characteristic, complemented
12C3×#65057C211yesmaximal, characteristic, complemented
13C3×#65056C211yesmaximal, characteristic, complemented
14C3×#65022C211yesmaximal, characteristic, complemented
15C3×#65014C211yesmaximal, characteristic, complemented
16#10613112C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C3×C5×#121C2211yescharacteristic
20C3×C5×#117C2211yescharacteristic, complemented
21C3×#4084—21no—
22C3×#4083—21no—
23C3×#4082C2211yescharacteristic
24C2×C3×#687C2211yescharacteristic
25C3×C4×C22⋊D5C2211yescharacteristic
26C3×#4070C2211yescharacteristic, complemented
27C22×C3×#168C2211yescharacteristic, complemented
28C2×C3×Dic20C2211yescharacteristic, complemented
29C2×C3×#677C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic
31C3×#4043C2211yescharacteristic
32C3×#4043C2211yescharacteristic
33C3×#4039C2211yescharacteristic
34C3×D5×C4⋊C4C2211yescharacteristic
35C3×#4036C2211yescharacteristic, complemented
36C3×#4033C2211yescharacteristic, complemented
37C3×#4029—21no—
38C3×#4029—21no—
39C3×D5×C22⋊C4—21no—
40C3×#4025—21no—
41C3×#4018—21no—
42C3×#4016—21no—
43C3×C5×#107C2211yescharacteristic, complemented
44C3×C5×#106C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic
46C3×C5×#102C2211yescharacteristic
47C3×C5×C22⋊C8C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3948C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3940C2211yescharacteristic, complemented
60C3×#3296—51nomaximal, Hall
61#65946C2×C311yescharacteristic
62#65863C2×C311yescharacteristic, complemented
63C5×#482C2×C311yescharacteristic, complemented
64#65330C2×C311yescharacteristic, complemented
65#65291C2×C311yescharacteristic, complemented
66#65180C2×C311yescharacteristic, complemented
67#65176C2×C311yescharacteristic, complemented
68#65151C2×C311yescharacteristic, complemented
69#65141C2×C311yescharacteristic, complemented
70#65065C2×C311yescharacteristic, complemented
71D5×#102C2×C311yescharacteristic, complemented
72#65057C2×C311yescharacteristic, complemented
73#65056C2×C311yescharacteristic, complemented
74#65022C2×C311yescharacteristic, complemented
75#65014C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5D411yescharacteristic
83C3×D4×D5—22no—
84C3×D4×D5—41no—
85C3×#709—22no—
86C3×#709—41no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C42×C5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×C22⋊Dic5—21no—
105C3×C22⋊Dic5D411yescharacteristic
106C3×#687—41no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685D411yescharacteristic
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683D411yescharacteristic
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168—41no—
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×Dic20—41no—
126C3×#677—22no—
127C3×C8×D5—41no—
128C3×#552—51no—
129C3×#546—51no—
130C3×#488—51no—
131C3×#483—51no—
132C3×#482D511yescharacteristic, complemented
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×D4×D5C22×C311yescharacteristic
144C2×#709C22×C311yescharacteristic
145C5×#121C22×C311yescharacteristic
146C5×#117C22×C311yescharacteristic, complemented
147#4084—21no—
148#4083—21no—
149#4082C22×C311yescharacteristic
150C2×#687C22×C311yescharacteristic
151C4×C22⋊D5C22×C311yescharacteristic
152#4070C22×C311yescharacteristic, complemented
153C22×#168C22×C311yescharacteristic, complemented
154C2×Dic20C22×C311yescharacteristic, complemented
155C2×#677C22×C311yescharacteristic
156C2×C8×D5C22×C311yescharacteristic
157#4043C22×C311yescharacteristic
158#4043C22×C311yescharacteristic
159#4039C22×C311yescharacteristic
160D5×C4⋊C4C22×C311yescharacteristic
161#4036C22×C311yescharacteristic, complemented
162#4033C22×C311yescharacteristic, complemented
163#4029—21no—
164#4029—21no—
165D5×C22⋊C4—21no—
166#4025—21no—
167#4018—21no—
168#4016—21no—
169C5×#107C22×C311yescharacteristic, complemented
170C5×#106C22×C311yescharacteristic, complemented
171C5×#102C22×C311yescharacteristic
172C5×#102C22×C311yescharacteristic
173C5×C22⋊C8C22×C311yescharacteristic, complemented
174#3964C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3952C22×C311yescharacteristic
177#3948C22×C311yescharacteristic, complemented
178#3946C22×C311yescharacteristic, complemented
179C8×Dic5C22×C311yescharacteristic, complemented
180#3942C22×C311yescharacteristic, complemented
181#3942C22×C311yescharacteristic, complemented
182#3942C22×C311yescharacteristic, complemented
183#3941C22×C311yescharacteristic
184#3941C22×C311yescharacteristic
185#3940C22×C311yescharacteristic, complemented
186#3296—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—42no—
191C22×C3×D5—42no—
192C22×C3×D5—81no—
193C22×C3×D5C2×D411yescharacteristic
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4—81no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C3×C22⋊D5—22no—
205C3×C22⋊D5—42no—
206C3×C22⋊D5—42no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C3×D20—21no—
214C3×D20#4112yes—
215C3×C4×D5—21no—
216C3×C4×D5—21no—
217C3×C4×D5—42no—
218C3×C4×D5—42no—
219C3×C4×D5—81no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224C3×C5×C8—21no—
225C3×C5×C8—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41—51no—
229C22×C3×D4—51no—
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×#124—51no—
239C3×#123—101no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8—51no—
243C3×C22⋊Q8—51no—
244C3×#121—101no—
245C3×#121C2×D511yescharacteristic
246C3×#120—101no—
247C3×C4×Q8—51no—
248C3×C4×D4—51no—
249C3×C4×D4—51no—
250C3×#117—101no—
251C3×#117C2×D511yescharacteristic, complemented
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—101no—
254C3×#107C2×D511yescharacteristic, complemented
255C3×#106—51no—
256C3×#106C2×D511yescharacteristic, complemented
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×#102C2×D511yescharacteristic
267C3×#102C2×D511yescharacteristic
268C3×C22⋊C8—51no—
269C3×C22⋊C8C2×D511yescharacteristic, complemented
270C3×C4×C8—51no—
271C23×D5—21no—
272C2×C5×D4—21no—
273C2×C5×D4C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C2×C22⋊D5—21no—
276C2×C22⋊D5—21no—
277C2×C22⋊D5C3×D411yescharacteristic
278D4×D5—22no—
279D4×D5—41no—
280#709—22no—
281#709—41no—
282C2×D20C23×C311yescharacteristic
283C2×C4×D5—21no—
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5C23×C311yescharacteristic
287C2×Dic10C23×C311yescharacteristic
288C2×Dic10C23×C311yescharacteristic
289C2×C5×C8C23×C311yescharacteristic
290C2×C5×C8C23×C311yescharacteristic
291C5×C4⋊C4C23×C311yescharacteristic
292C5×C4⋊C4C23×C311yescharacteristic
293C5×C4⋊C4C23×C311yescharacteristic
294C5×C22⋊C4—21no—
295C5×C22⋊C4—21no—
296C42×C5—21no—
297C22⋊Dic5—21no—
298C22⋊Dic5—21no—
299C22⋊Dic5—21no—
300C22⋊Dic5C3×D411yescharacteristic
301#687—41no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685C3×D411yescharacteristic
306C4⋊Dic5—21no—
307C4⋊Dic5—21no—
308C4⋊Dic5—21no—
309C4⋊Dic5C23×C311yescharacteristic
310#683—21no—
311#683—21no—
312#683—21no—
313#683—21no—
314#683C3×D411yescharacteristic
315C4×Dic5—21no—
316C4×Dic5C23×C311yescharacteristic
317C2×#168—41no—
318C2×#168C23×C311yescharacteristic
319C2×#168C23×C311yescharacteristic
320Dic20—41no—
321#677—22no—
322C8×D5—41no—
323#552—51no—
324#546—51no—
325#488—51no—
326#483—51no—
327#482C3×D511yescharacteristic, complemented
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—41no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—22no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—84no—
351C2×C3×D5#13512yes—
352C3×C4×C5—21no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358C3×Dic5—21no—
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C24×C3—101no—
365C3×#41—102no—
366C3×#41—201no—
367C2×C3×Q8—51no—
368C2×C3×Q8—51no—
369C2×C3×D4—21no—
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—101no—
373C2×C3×D4—102no—
374C2×C3×D4—101no—
375C2×C3×D4—201no—
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C22×C3×C4C22×D511yescharacteristic
382C3×Q16—201no—
383C3×SD16—102no—
384C3×SD16—201no—
385C2×C3×C8—51no—
386C2×C3×C8—51no—
387C2×C3×C8—201no—
388C2×C3×C8—201no—
389C2×C3×C8C22×D511yescharacteristic
390C2×C3×C8C22×D511yescharacteristic
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—51no—
406C3×C22⋊C4—51no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4—101no—
412C3×C22⋊C4—101no—
413C3×C42—21no—
414C3×C42—51no—
415C3×C42—101no—
416C23×C5—21no—
417C23×C5C2×C3×D411yescharacteristic
418C22×D5—21no—
419C22×D5—42no—
420C22×D5—42no—
421C22×D5—81no—
422C22×D5C2×C3×D411yescharacteristic
423C5×D4—21no—
424C5×D4—21no—
425C5×D4—81no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5C2×C3×D411yescharacteristic
432C2×C4×C5C24×C311yescharacteristic
433C22⋊D5—22no—
434C22⋊D5—42no—
435C22⋊D5—42no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5C2×C3×D411yescharacteristic
440C2×Dic5C2×C3×D411yescharacteristic
441C2×Dic5C2×C3×D411yescharacteristic
442D20—21no—
443D20C3×#4112yes—
444C4×D5—21no—
445C4×D5—21no—
446C4×D5—42no—
447C4×D5—42no—
448C4×D5—81no—
449Dic10—21no—
450Dic10—21no—
451Dic10—21no—
452Dic10—21no—
453C5×C8—21no—
454C5×C8—21no—
455#168—21no—
456#168—21no—
457C2×#41—51no—
458C22×D4—51no—
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#124—51no—
468#123—101no—
469#123—101no—
470C22⋊Q8—51no—
471C22⋊Q8—51no—
472C22⋊Q8—51no—
473#121—101no—
474#121C2×C3×D511yescharacteristic
475#120—101no—
476C4×Q8—51no—
477C4×D4—51no—
478C4×D4—51no—
479#117—101no—
480#117C2×C3×D511yescharacteristic, complemented
481C2×C4⋊C4—51no—
482C2×C22⋊C4—101no—
483#107C2×C3×D511yescharacteristic, complemented
484#106—51no—
485#106C2×C3×D511yescharacteristic, complemented
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#102C2×C3×D511yescharacteristic
496#102C2×C3×D511yescharacteristic
497C22⋊C8—51no—
498C22⋊C8C2×C3×D511yescharacteristic, complemented
499C4×C8—51no—
500C2×C3×C5—41no—
501C2×C3×C5—81no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C3×D5—22no—
506C3×D5—42no—
507C23×C3—21no—
508C23×C3—51no—
509C23×C3—101no—
510C23×C3—202no—
511C23×C3—202no—
512C23×C3—401no—
513C23×C3D4×D511yescharacteristic
514C3×Q8—101no—
515C3×Q8—101no—
516C3×Q8—101no—
517C3×Q8—101no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—52no—
521C3×D4—81no—
522C3×D4—102no—
523C3×D4—101no—
524C3×D4—202no—
525C3×D4—202no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—51no—
532C2×C3×C4—51no—
533C2×C3×C4—51no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—202no—
540C2×C3×C4—202no—
541C2×C3×C4—401no—
542C2×C3×C4D4×D511yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—101no—
547C3×C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—41no—
552C22×C5—41no—
553C22×C5—41no—
554C22×C5C22×C3×D411yescharacteristic
555C2×D5—21no—
556C2×D5—21no—
557C2×D5—22no—
558C2×D5—41no—
559C2×D5—41no—
560C2×D5—84no—
561C2×D5C3×#13512yes—
562C4×C5—21no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5—41no—
566C4×C5C2×C3×#4111yescharacteristic
567C4×C5C3×H(5,𝔽2)11yescharacteristic
568Dic5—21no—
569Dic5—21no—
570Dic5—21no—
571Dic5—41no—
572Dic5—41no—
573Dic5—41no—
574C24—101no—
575#41—102no—
576#41—201no—
577C2×Q8—51no—
578C2×Q8—51no—
579C2×D4—21no—
580C2×D4—51no—
581C2×D4—51no—
582C2×D4—101no—
583C2×D4—102no—
584C2×D4—101no—
585C2×D4—201no—
586C2×D4C22×C3×D511yescharacteristic
587C22×C4—51no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4C22×C3×D511yescharacteristic
592Q16—201no—
593SD16—102no—
594SD16—201no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—201no—
598C2×C8—201no—
599C2×C8C22×C3×D511yescharacteristic
600C2×C8C22×C3×D511yescharacteristic
601C4⋊C4—51no—
602C4⋊C4—51no—
603C4⋊C4—101no—
604C4⋊C4—101no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4C22×C3×D511yescharacteristic
611C4⋊C4C22×C3×D511yescharacteristic
612C4⋊C4C22×C3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—51no—
616C22⋊C4—51no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C22⋊C4—101no—
622C22⋊C4—101no—
623C42—21no—
624C42—51no—
625C42—101no—
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—52no—
634C22×C3—101no—
635C22×C3—101no—
636C22×C3—102no—
637C22×C3—201no—
638C22×C3—201no—
639C22×C3—404no—
640C22×C3C2×D4×D511yescharacteristic
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—101no—
646C3×C4—101no—
647C3×C4—101no—
648C3×C4—201no—
649C3×C4—201no—
650C3×C4—201no—
651C3×C4D5×#4111yescharacteristic
652C3×C4#414911yescharacteristic
653C2×C5—41no—
654C2×C5—81no—
655C2×C5C3×#54611yescharacteristic
656C2×C5C2×C3×#13511yescharacteristic
657C2×C5C3×#57711yescharacteristic
658D5—22no—
659D5—42no—
660C23—21no—
661C23—51no—
662C23—101no—
663C23—202no—
664C23—202no—
665C23—401no—
666C23C3×D4×D511yescharacteristic
667Q8—101no—
668Q8—101no—
669Q8—101no—
670Q8—101no—
671D4—21no—
672D4—21no—
673D4—52no—
674D4—81no—
675D4—102no—
676D4—101no—
677D4—202no—
678D4—202no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—51no—
685C2×C4—51no—
686C2×C4—51no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—202no—
693C2×C4—202no—
694C2×C4—401no—
695C2×C4C3×D4×D511yescharacteristic
696C2×C4C23×C3×D511yescharacteristic
697C8—21no—
698C8—21no—
699C8—101no—
700C8—101no—
701C2×C3—41no—
702C2×C3—81no—
703C2×C3—102no—
704C2×C3—202no—
705C2×C3#6598811yescharacteristic
706C2×C3D5×#13511yescharacteristic
707C2×C3#6610911yescharacteristic
708C5C3×#329611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—52no—
716C22—101no—
717C22—101no—
718C22—102no—
719C22—201no—
720C22—201no—
721C22—404no—
722C22C2×C3×D4×D511yescharacteristic
723C4—21no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—101no—
728C4—101no—
729C4—101no—
730C4—201no—
731C4—201no—
732C4—201no—
733C4C3×D5×#4111yescharacteristic
734C4C3×#414911yescharacteristic
735C3#1061311211yescharacteristic, direct product factor, Sylow
736C2—41no—
737C2—81no—
738C2—102no—
739C2—202no—
740C2C3×#6598811yescharacteristic
741C2C3×D5×#13511yescharacteristic
742C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#482C2
socleC22×C3×C5C22×D4
prime radicalC3×#65946C2
hypercenterC3×#482D5
hypocenterC5C3×#3296
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#482

Complements

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

NH ≅ G/Ntype
2. C3×#65863C2semidirect
3. C3×C5×#482C2semidirect
4. C3×#65330C2semidirect
5. C3×#65291C2semidirect
6. C3×#65180C2semidirect
7. C3×#65176C2semidirect
8. C3×#65151C2semidirect
9. C3×#65141C2semidirect
10. C3×#65065C2semidirect
11. C3×D5×#102C2semidirect
12. C3×#65057C2semidirect
13. C3×#65056C2semidirect
14. C3×#65022C2semidirect
15. C3×#65014C2semidirect
16. #10613112C3direct (N × H)
20. C3×C5×#117C22semidirect
26. C3×#4070C22semidirect
27. C22×C3×#168C22semidirect
28. C2×C3×Dic20C22semidirect
35. C3×#4036C22semidirect
36. C3×#4033C22semidirect
43. C3×C5×#107C22semidirect
44. C3×C5×#106C22semidirect
47. C3×C5×C22⋊C8C22semidirect
51. C3×#3948C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3942C22semidirect
55. C3×#3942C22semidirect
56. C3×#3942C22semidirect
59. C3×#3940C22semidirect
62. #65863C2×C3semidirect
63. C5×#482C2×C3semidirect
64. #65330C2×C3semidirect
65. #65291C2×C3semidirect
66. #65180C2×C3semidirect
67. #65176C2×C3semidirect
68. #65151C2×C3semidirect
69. #65141C2×C3semidirect
70. #65065C2×C3semidirect
71. D5×#102C2×C3semidirect
72. #65057C2×C3semidirect
73. #65056C2×C3semidirect
74. #65022C2×C3semidirect
75. #65014C2×C3semidirect
132. C3×#482D5semidirect
146. C5×#117C22×C3semidirect
152. #4070C22×C3semidirect
153. C22×#168C22×C3semidirect
154. C2×Dic20C22×C3semidirect
161. #4036C22×C3semidirect
162. #4033C22×C3semidirect
169. C5×#107C22×C3semidirect
170. C5×#106C22×C3semidirect
173. C5×C22⋊C8C22×C3semidirect
177. #3948C22×C3semidirect
178. #3946C22×C3semidirect
179. C8×Dic5C22×C3semidirect
180. #3942C22×C3semidirect
181. #3942C22×C3semidirect
182. #3942C22×C3semidirect
185. #3940C22×C3semidirect
251. C3×#117C2×D5semidirect
254. C3×#107C2×D5semidirect
256. C3×#106C2×D5semidirect
269. C3×C22⋊C8C2×D5semidirect
327. #482C3×D5semidirect
480. #117C2×C3×D5semidirect
483. #107C2×C3×D5semidirect
485. #106C2×C3×D5semidirect
498. C22⋊C8C2×C3×D5semidirect
626. C3×C5#3296semidirect
708. C5C3×#3296semidirect
735. C3#10613112direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659462
C3×#658632
C3×C5×#4822
C3×#653302
C3×#652912
C3×#651802
C3×#651762
C3×#651512
C3×#651412
C3×#650652
C3×D5×#1022
C3×#650572
C3×#650562
C3×#650222
C3×#650142
#106131123
C3×#32965