Finite Group Databasebeta

← C3×#10613181 #14459116

Subgroups — C3×#10613181 #14459116

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65966C211yesmaximal, characteristic, complemented
2C3×#65841C211yesmaximal, characteristic
3C3×C5×#483C211yesmaximal, characteristic, complemented
4C3×#65337C211yesmaximal, characteristic, complemented
5C2×C3×#3942C211yesmaximal, characteristic, complemented
6C3×#65153C211yesmaximal, characteristic, complemented
7C3×#65151C211yesmaximal, characteristic, complemented
8C3×#65143C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65107C211yesmaximal, characteristic, complemented
11C3×#65095C211yesmaximal, characteristic, complemented
12C3×D5×#103C211yesmaximal, characteristic, complemented
13C3×#65081C211yesmaximal, characteristic, complemented
14C3×#65027C211yesmaximal, characteristic, complemented
15C3×#65014C211yesmaximal, characteristic, complemented
16#10613181C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×#709—21no—
19C22×C3×Dic10C2211yescharacteristic
20C3×C5×C22⋊Q8C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C3×#4090C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic
24C3×#4076C2211yescharacteristic
25C3×#4075—21no—
26C3×C4×C22⋊D5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28C2×C3×#677C2211yescharacteristic
29C2×C3×#677C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic
31C3×#4043C2211yescharacteristic
32C3×#4042—21no—
33C3×#4042—21no—
34C3×#4041C2211yescharacteristic
35C3×#4040—21no—
36C3×#4039C2211yescharacteristic
37C3×D5×C4⋊C4C2211yescharacteristic
38C3×#4034—21no—
39C3×#4034C2211yescharacteristic
40C3×#4033C2211yescharacteristic
41C3×#4027—21no—
42C3×#4024—21no—
43C3×C5×#106C2211yescharacteristic
44C3×C5×#106C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×C22⋊C8C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3948C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic
54C3×#3942C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3942C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3940C2211yescharacteristic
60C3×#3298—51nomaximal, Hall
61#65966C2×C311yescharacteristic, complemented
62#65841C2×C311yescharacteristic
63C5×#483C2×C311yescharacteristic, complemented
64#65337C2×C311yescharacteristic, complemented
65C2×#3942C2×C311yescharacteristic, complemented
66#65153C2×C311yescharacteristic, complemented
67#65151C2×C311yescharacteristic, complemented
68#65143C2×C311yescharacteristic, complemented
69#65141C2×C311yescharacteristic, complemented
70#65107C2×C311yescharacteristic, complemented
71#65095C2×C311yescharacteristic, complemented
72D5×#103C2×C311yescharacteristic, complemented
73#65081C2×C311yescharacteristic, complemented
74#65027C2×C311yescharacteristic, complemented
75#65014C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×C3×C22⋊D5—21no—
80C2×C3×C22⋊D5D411yescharacteristic
81C22×C3×Dic5—21no—
82C3×Q8×D5—22no—
83C3×Q8×D5—41no—
84C3×#709—44no—
85C2×C3×D20—21no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10—22no—
92C2×C3×Dic10—21no—
93C2×C3×Dic10—21no—
94C2×C3×Dic10—21no—
95C2×C3×Dic10—41no—
96C2×C3×Dic10C2311yescharacteristic
97C2×C3×Dic10C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4—21no—
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106C3×C22⋊Dic5D411yescharacteristic
107C3×#688—41no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685D411yescharacteristic
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
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×D4×Q8—51no—
130C3×#547—51no—
131C3×#487—51no—
132C3×#483—51no—
133C3×#483D511yescharacteristic, complemented
134C3×#475—51no—
135C3×#465—51no—
136C3×#465—51no—
137C3×#461—51no—
138C3×#448—51no—
139C3×#448—51no—
140C3×C4×SD16—51no—
141C3×C8×D4—51no—
142C2×C3×#103—51no—
143C2×C3×#103—51no—
144C2×Q8×D5C22×C311yescharacteristic
145C2×#709—21no—
146C22×Dic10C22×C311yescharacteristic
147C5×C22⋊Q8C22×C311yescharacteristic
148C2×C5×C4⋊C4C22×C311yescharacteristic
149#4090C22×C311yescharacteristic
150C2×#688C22×C311yescharacteristic
151#4076C22×C311yescharacteristic
152#4075—21no—
153C4×C22⋊D5C22×C311yescharacteristic
154C22×#168C22×C311yescharacteristic
155C2×#677C22×C311yescharacteristic
156C2×#677C22×C311yescharacteristic
157C2×C8×D5C22×C311yescharacteristic
158#4043C22×C311yescharacteristic
159#4042—21no—
160#4042—21no—
161#4041C22×C311yescharacteristic
162#4040—21no—
163#4039C22×C311yescharacteristic
164D5×C4⋊C4C22×C311yescharacteristic
165#4034—21no—
166#4034C22×C311yescharacteristic
167#4033C22×C311yescharacteristic
168#4027—21no—
169#4024—21no—
170C5×#106C22×C311yescharacteristic
171C5×#106C22×C311yescharacteristic
172C5×#103C22×C311yescharacteristic
173C5×#103C22×C311yescharacteristic
174C5×C22⋊C8C22×C311yescharacteristic
175#3967C22×C311yescharacteristic
176#3952C22×C311yescharacteristic
177#3948C22×C311yescharacteristic
178#3948C22×C311yescharacteristic
179#3946C22×C311yescharacteristic
180C8×Dic5C22×C311yescharacteristic
181#3942C22×C311yescharacteristic
182#3942C22×C311yescharacteristic
183#3942C22×C311yescharacteristic
184#3942C22×C311yescharacteristic
185#3941C22×C311yescharacteristic
186#3940C22×C311yescharacteristic
187#3298—51noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5C2×D411yescharacteristic
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—42no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C3×C22⋊D5—42no—
203C3×C22⋊D5SD1614yescomplemented
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—42no—
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C2×C3×Dic5C2×D411yescharacteristic
211C3×D20—21no—
212C3×D20—21no—
213C3×D20—42no—
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—42no—
217C3×C4×D5—42no—
218C3×C4×D5—42no—
219C3×Dic10—21no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222C3×Dic10—42no—
223C3×Dic10—42no—
224C3×Dic10—42no—
225C3×Dic10#4112yescomplemented
226C3×C5×C8—21no—
227C3×C5×C8—21no—
228C3×#168—21no—
229C3×#168—21no—
230C2×C3×#41—101no—
231C22×C3×Q8—51no—
232C22×C3×Q8—51no—
233C2×C3×SD16—51no—
234C2×C3×SD16—51no—
235C2×C3×SD16—51no—
236C22×C3×C8—51no—
237C22×C3×C8—51no—
238C3×C4⋊Q8—51no—
239C3×C4⋊Q8—51no—
240C3×C4⋊Q8—101no—
241C3×#123—101no—
242C3×#123—101no—
243C3×C22⋊Q8—51no—
244C3×C22⋊Q8—101no—
245C3×C22⋊Q8—101no—
246C3×C22⋊Q8—101no—
247C3×C22⋊Q8C2×D511yescharacteristic
248C3×#121—51no—
249C3×#121—51no—
250C3×C4×Q8—51no—
251C3×C4×D4—51no—
252C3×C4×D4—51no—
253C3×C4×D4—101no—
254C2×C3×C4⋊C4—51no—
255C2×C3×C4⋊C4C2×D511yescharacteristic
256C3×#106—51no—
257C3×#106C2×D511yescharacteristic
258C3×#106C2×D511yescharacteristic
259C3×C4⋊C8—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#103—51no—
263C3×#103—51no—
264C3×#103—51no—
265C3×#103—51no—
266C3×#103—51no—
267C3×#103C2×D511yescharacteristic
268C3×#103C2×D511yescharacteristic
269C3×#102—51no—
270C3×C22⋊C8—51no—
271C3×C22⋊C8C2×D511yescharacteristic
272C3×C4×C8—51no—
273C2×C5×Q8C23×C311yescharacteristic
274C22×C4×C5—21no—
275C22×C4×C5C23×C311yescharacteristic
276C2×C22⋊D5—21no—
277C2×C22⋊D5C3×D411yescharacteristic
278C22×Dic5—21no—
279Q8×D5—22no—
280Q8×D5—41no—
281#709—44no—
282C2×D20—21no—
283C2×D20C23×C311yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×C4×D5C23×C311yescharacteristic
288C2×Dic10—22no—
289C2×Dic10—21no—
290C2×Dic10—21no—
291C2×Dic10—21no—
292C2×Dic10—41no—
293C2×Dic10C23×C311yescharacteristic
294C2×Dic10C23×C311yescharacteristic
295C2×C5×C8C23×C311yescharacteristic
296C2×C5×C8C23×C311yescharacteristic
297C5×C4⋊C4—21no—
298C5×C4⋊C4—21no—
299C5×C4⋊C4C23×C311yescharacteristic
300C5×C4⋊C4C23×C311yescharacteristic
301C5×C4⋊C4C23×C311yescharacteristic
302C5×C22⋊C4—21no—
303C22⋊Dic5C3×D411yescharacteristic
304#688—41no—
305#685—21no—
306#685—21no—
307#685—21no—
308#685—21no—
309#685C3×D411yescharacteristic
310C4⋊Dic5—21no—
311C4⋊Dic5C23×C311yescharacteristic
312#683—21no—
313#683—21no—
314#683—21no—
315#683—21no—
316#683—21no—
317#683C3×D411yescharacteristic
318C4×Dic5—21no—
319C4×Dic5C23×C311yescharacteristic
320C2×#168—41no—
321C2×#168C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323#677—22no—
324#677—41no—
325C8×D5—41no—
326D4×Q8—51no—
327#547—51no—
328#487—51no—
329#483—51no—
330#483C3×D511yescharacteristic, complemented
331#475—51no—
332#465—51no—
333#465—51no—
334#461—51no—
335#448—51no—
336#448—51no—
337C4×SD16—51no—
338C8×D4—51no—
339C2×#103—51no—
340C2×#103—51no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5C2×SD1612yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—41no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5C2×SD1612yes—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358C3×Dic5—22no—
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5C2×SD1612yes—
364C3×#41—204no—
365C2×C3×Q8—51no—
366C2×C3×Q8—51no—
367C2×C3×Q8—101no—
368C2×C3×Q8—101no—
369C2×C3×Q8—102no—
370C2×C3×Q8—101no—
371C2×C3×Q8—102no—
372C2×C3×Q8—201no—
373C2×C3×Q8—201no—
374C2×C3×Q8C22×D511yescharacteristic
375C2×C3×D4—51no—
376C2×C3×D4—51no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C22×C3×C4—21no—
380C22×C3×C4—51no—
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C22×C3×C4—101no—
384C22×C3×C4—101no—
385C22×C3×C4C22×D511yescharacteristic
386C3×SD16—102no—
387C3×SD16—201no—
388C3×SD16—201no—
389C2×C3×C8—51no—
390C2×C3×C8—51no—
391C2×C3×C8—201no—
392C2×C3×C8—201no—
393C2×C3×C8C22×D511yescharacteristic
394C2×C3×C8C22×D511yescharacteristic
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—51no—
398C3×C4⋊C4—51no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4—101no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4—101no—
403C3×C4⋊C4—101no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4C22×D511yescharacteristic
406C3×C4⋊C4C22×D511yescharacteristic
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—51no—
410C3×C22⋊C4—51no—
411C3×C22⋊C4—101no—
412C3×C22⋊C4—101no—
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C42—51no—
416C3×C42—101no—
417C23×C5C2×C3×D411yescharacteristic
418C22×D5—21no—
419C22×D5C2×C3×D411yescharacteristic
420C5×Q8—21no—
421C5×Q8—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—42no—
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C24×C311yescharacteristic
431C22⋊D5—42no—
432C22⋊D5C3×SD1614yescomplemented
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—42no—
437C2×Dic5C2×C3×D411yescharacteristic
438C2×Dic5C2×C3×D411yescharacteristic
439C2×Dic5C2×C3×D411yescharacteristic
440D20—21no—
441D20—21no—
442D20—42no—
443C4×D5—21no—
444C4×D5—21no—
445C4×D5—42no—
446C4×D5—42no—
447C4×D5—42no—
448Dic10—21no—
449Dic10—21no—
450Dic10—21no—
451Dic10—42no—
452Dic10—42no—
453Dic10—42no—
454Dic10C3×#4112yescomplemented
455C5×C8—21no—
456C5×C8—21no—
457#168—21no—
458#168—21no—
459C2×#41—101no—
460C22×Q8—51no—
461C22×Q8—51no—
462C2×SD16—51no—
463C2×SD16—51no—
464C2×SD16—51no—
465C22×C8—51no—
466C22×C8—51no—
467C4⋊Q8—51no—
468C4⋊Q8—51no—
469C4⋊Q8—101no—
470#123—101no—
471#123—101no—
472C22⋊Q8—51no—
473C22⋊Q8—101no—
474C22⋊Q8—101no—
475C22⋊Q8—101no—
476C22⋊Q8C2×C3×D511yescharacteristic
477#121—51no—
478#121—51no—
479C4×Q8—51no—
480C4×D4—51no—
481C4×D4—51no—
482C4×D4—101no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4C2×C3×D511yescharacteristic
485#106—51no—
486#106C2×C3×D511yescharacteristic
487#106C2×C3×D511yescharacteristic
488C4⋊C8—51no—
489#103—51no—
490#103—51no—
491#103—51no—
492#103—51no—
493#103—51no—
494#103—51no—
495#103—51no—
496#103C2×C3×D511yescharacteristic
497#103C2×C3×D511yescharacteristic
498#102—51no—
499C22⋊C8—51no—
500C22⋊C8C2×C3×D511yescharacteristic
501C4×C8—51no—
502C2×C3×C5—22no—
503C2×C3×C5#54611yescharacteristic
504C2×C3×C5C22×SD1611yescharacteristic
505C2×C3×C5#57811yescharacteristic
506C3×D5—22no—
507C3×D5—81no—
508C23×C3—51no—
509C23×C3—101no—
510C23×C3D4×D511yescharacteristic
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—52no—
514C3×Q8—101no—
515C3×Q8—101no—
516C3×Q8—101no—
517C3×Q8—202no—
518C3×Q8—202no—
519C3×Q8—202no—
520C3×D4—54no—
521C3×D4—101no—
522C3×D4—101no—
523C3×D4—202no—
524C3×D4—202no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—42no—
532C2×C3×C4—51no—
533C2×C3×C4—51no—
534C2×C3×C4—51no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4—202no—
541C2×C3×C4—202no—
542C2×C3×C4—202no—
543C2×C3×C4—202no—
544C2×C3×C4D4×D511yescharacteristic
545C2×C3×C4C23×D511yescharacteristic
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—101no—
549C3×C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5C2×C3×SD1612yes—
553C22×C5C22×C3×D411yescharacteristic
554C2×D5—21no—
555C2×D5—21no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—41no—
559C2×D5C2×C3×SD1612yes—
560C4×C5—21no—
561C4×C5—41no—
562C4×C5—41no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5C2×C3×#4111yescharacteristic
566C4×C5C3×H(5,𝔽2)11yescharacteristic
567Dic5—21no—
568Dic5—22no—
569Dic5—21no—
570Dic5—41no—
571Dic5—41no—
572Dic5C2×C3×SD1612yes—
573#41—204no—
574C2×Q8—51no—
575C2×Q8—51no—
576C2×Q8—101no—
577C2×Q8—101no—
578C2×Q8—102no—
579C2×Q8—101no—
580C2×Q8—102no—
581C2×Q8—201no—
582C2×Q8—201no—
583C2×Q8C22×C3×D511yescharacteristic
584C2×D4—51no—
585C2×D4—51no—
586C2×D4—101no—
587C2×D4—101no—
588C22×C4—21no—
589C22×C4—51no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4C22×C3×D511yescharacteristic
595SD16—102no—
596SD16—201no—
597SD16—201no—
598C2×C8—51no—
599C2×C8—51no—
600C2×C8—201no—
601C2×C8—201no—
602C2×C8C22×C3×D511yescharacteristic
603C2×C8C22×C3×D511yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—51no—
607C4⋊C4—51no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4—101no—
612C4⋊C4—101no—
613C4⋊C4—101no—
614C4⋊C4C22×C3×D511yescharacteristic
615C4⋊C4C22×C3×D511yescharacteristic
616C4⋊C4C22×C3×D511yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—51no—
619C22⋊C4—51no—
620C22⋊C4—101no—
621C22⋊C4—101no—
622C22⋊C4—101no—
623C22⋊C4—101no—
624C42—51no—
625C42—101no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—52no—
630C22×C3—101no—
631C22×C3—101no—
632C22×C3—201no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3D5×SD1612yes—
636C22×C3C2×D4×D511yescharacteristic
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—52no—
643C3×C4—101no—
644C3×C4—101no—
645C3×C4—102no—
646C3×C4—201no—
647C3×C4—201no—
648C3×C4D5×#4111yescharacteristic
649C3×C4#414911yescharacteristic
650C2×C5—22no—
651C2×C5C3×#54611yescharacteristic
652C2×C5C22×C3×SD1611yescharacteristic
653C2×C5C3×#57811yescharacteristic
654D5—22no—
655D5—81no—
656C23—51no—
657C23—101no—
658C23C3×D4×D511yescharacteristic
659Q8—21no—
660Q8—21no—
661Q8—52no—
662Q8—101no—
663Q8—101no—
664Q8—101no—
665Q8—202no—
666Q8—202no—
667Q8—202no—
668D4—54no—
669D4—101no—
670D4—101no—
671D4—202no—
672D4—202no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—42no—
680C2×C4—51no—
681C2×C4—51no—
682C2×C4—51no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4C3×D4×D511yescharacteristic
693C2×C4C23×C3×D511yescharacteristic
694C8—21no—
695C8—21no—
696C8—101no—
697C8—101no—
698C2×C3—22no—
699C2×C3—102no—
700C2×C3—401no—
701C2×C3#6598811yescharacteristic
702C2×C3C2×D5×SD1611yescharacteristic
703C2×C3#6611311yescharacteristic
704C5C3×#329811yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—52no—
708C22—101no—
709C22—101no—
710C22—201no—
711C22—201no—
712C22—201no—
713C22C3×D5×SD1612yes—
714C22C2×C3×D4×D511yescharacteristic
715C4—21no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—52no—
721C4—101no—
722C4—101no—
723C4—102no—
724C4—201no—
725C4—201no—
726C4C3×D5×#4111yescharacteristic
727C4C3×#414911yescharacteristic
728C3#1061318111yescharacteristic, direct product factor, Sylow
729C2—22no—
730C2—102no—
731C2—401no—
732C2C3×#6598811yescharacteristic
733C2C2×C3×D5×SD1611yescharacteristic
734C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#483C2
socleC22×C3×C5C22×D4
prime radicalC3×#65841C2
hypercenterC3×#483D5
hypocenterC5C3×#3298
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#483

Complements

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

NH ≅ G/Ntype
1. C3×#65966C2semidirect
3. C3×C5×#483C2semidirect
4. C3×#65337C2semidirect
5. C2×C3×#3942C2semidirect
6. C3×#65153C2semidirect
7. C3×#65151C2semidirect
8. C3×#65143C2semidirect
9. C3×#65141C2semidirect
10. C3×#65107C2semidirect
11. C3×#65095C2semidirect
12. C3×D5×#103C2semidirect
13. C3×#65081C2semidirect
14. C3×#65027C2semidirect
15. C3×#65014C2semidirect
16. #10613181C3direct (N × H)
61. #65966C2×C3semidirect
63. C5×#483C2×C3semidirect
64. #65337C2×C3semidirect
65. C2×#3942C2×C3semidirect
66. #65153C2×C3semidirect
67. #65151C2×C3semidirect
68. #65143C2×C3semidirect
69. #65141C2×C3semidirect
70. #65107C2×C3semidirect
71. #65095C2×C3semidirect
72. D5×#103C2×C3semidirect
73. #65081C2×C3semidirect
74. #65027C2×C3semidirect
75. #65014C2×C3semidirect
133. C3×#483D5semidirect
203. C3×C22⋊D5SD16semidirect
225. C3×Dic10#41semidirect
330. #483C3×D5semidirect
432. C22⋊D5C3×SD16semidirect
454. Dic10C3×#41semidirect
626. C3×C5#3298semidirect
704. C5C3×#3298semidirect
728. C3#10613181direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659662
C3×#658412
C3×C5×#4832
C3×#653372
C2×C3×#39422
C3×#651532
C3×#651512
C3×#651432
C3×#651412
C3×#651072
C3×#650952
C3×D5×#1032
C3×#650812
C3×#650272
C3×#650142
#106131813
C3×#32985