Finite Group Databasebeta

← C3×#10611597 #14416995

Subgroups — C3×#10611597 #14416995

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4057C211yesmaximal, characteristic
2C3×#65880C211yesmaximal, characteristic, complemented
3C3×#65879C211yesmaximal, characteristic, complemented
4C3×C5×#442C211yesmaximal, characteristic, complemented
5C3×D8×Dic5C211yesmaximal, characteristic, complemented
6C3×C4×#687C211yesmaximal, characteristic, complemented
7C3×C4×#686C211yesmaximal, characteristic, complemented
8C3×#65150C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65074C211yesmaximal, characteristic, complemented
11C3×#65061C211yesmaximal, characteristic, complemented
12C3×D5×#102C211yesmaximal, characteristic, complemented
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×#64999C211yesmaximal, characteristic, complemented
15C3×#64997C211yesmaximal, characteristic, complemented
16#10611597C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×D8C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic, complemented
22C3×D4×Dic5C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic, complemented
24C2×C3×#687C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C3×C4×C22⋊D5—21no—
28C2×C3×#685—21no—
29C2×C3×#683—21no—
30C3×#4057C418yescomplemented
31C2×C3×#677C2211yescharacteristic
32C2×C3×#676C2211yescharacteristic
33C2×C3×C8×D5C2211yescharacteristic
34C3×#4039C2211yescharacteristic
35C3×#4038C2211yescharacteristic
36C3×D5×C4⋊C4C2211yescharacteristic
37C3×#4033C2211yescharacteristic, complemented
38C3×#4027—21no—
39C3×#4027—21no—
40C3×D5×C22⋊C4—21no—
41C3×#4023—21no—
42C3×C4×D20C2211yescharacteristic
43C3×#4018C2211yescharacteristic
44C3×C4×Dic10C2211yescharacteristic, complemented
45C3×C5×#106C2211yescharacteristic, complemented
46C3×C5×#102C2211yescharacteristic
47C3×C5×#102C2211yescharacteristic, complemented
48C3×C5×#97C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×#3964C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic
52C3×#3950C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3947C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×C4×#168C2211yescharacteristic, complemented
61C3×#2946—51nomaximal, Hall
62C2×#4057C2×C311yescharacteristic
63#65880C2×C311yescharacteristic, complemented
64#65879C2×C311yescharacteristic, complemented
65C5×#442C2×C311yescharacteristic, complemented
66D8×Dic5C2×C311yescharacteristic, complemented
67C4×#687C2×C311yescharacteristic, complemented
68C4×#686C2×C311yescharacteristic, complemented
69#65150C2×C311yescharacteristic, complemented
70#65141C2×C311yescharacteristic, complemented
71#65074C2×C311yescharacteristic, complemented
72#65061C2×C311yescharacteristic, complemented
73D5×#102C2×C311yescharacteristic, complemented
74#65046C2×C311yescharacteristic, complemented
75#64999C2×C311yescharacteristic, complemented
76#64997C2×C311yescharacteristic, complemented
77C23×C3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C22×C3×C4×C5—21no—
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C3×#711—22no—
88C3×#711C2×C414yescomplemented
89C3×D4×D5—22no—
90C3×D4×D5C2×C414yescomplemented
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5C2311yescharacteristic
96C2×C3×Dic10C2311yescharacteristic
97C3×C5×D8C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C22⋊Dic5—21no—
106C3×C22⋊Dic5—21no—
107C3×#687C2×C414yescomplemented
108C3×#686C2×C414yescomplemented
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685D411yescharacteristic
113C3×#685D411yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683D411yescharacteristic
120C3×#683D411yescharacteristic
121C3×C4×Dic5—21no—
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×#677C2×C414yescomplemented
128C3×#676C2×C414yescomplemented
129C3×C8×D5—22no—
130C2×C3×AGL(1,ℤ/8)—51no—
131C3×#520—51no—
132C3×#518—51no—
133C3×#442—51no—
134C3×#442D511yescharacteristic, complemented
135C3×#440—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×SD16—51no—
139C3×C4×D8—51no—
140C3×C4×D8—51no—
141C3×#428—51no—
142C3×#416—51no—
143C2×C3×#102—51no—
144C3×#405—51no—
145C2×#711C22×C311yescharacteristic
146C2×D4×D5C22×C311yescharacteristic
147C2×C5×D8C22×C311yescharacteristic
148C4×C5×D4C22×C311yescharacteristic
149C4×C5×D4C22×C311yescharacteristic, complemented
150D4×Dic5C22×C311yescharacteristic
151D4×Dic5C22×C311yescharacteristic, complemented
152C2×#687C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154C4×C22⋊D5—21no—
155C4×C22⋊D5—21no—
156C2×#685—21no—
157C2×#683—21no—
158#4057C3×C418yescomplemented
159C2×#677C22×C311yescharacteristic
160C2×#676C22×C311yescharacteristic
161C2×C8×D5C22×C311yescharacteristic
162#4039C22×C311yescharacteristic
163#4038C22×C311yescharacteristic
164D5×C4⋊C4C22×C311yescharacteristic
165#4033C22×C311yescharacteristic, complemented
166#4027—21no—
167#4027—21no—
168D5×C22⋊C4—21no—
169#4023—21no—
170C4×D20C22×C311yescharacteristic
171#4018C22×C311yescharacteristic
172C4×Dic10C22×C311yescharacteristic, complemented
173C5×#106C22×C311yescharacteristic, complemented
174C5×#102C22×C311yescharacteristic
175C5×#102C22×C311yescharacteristic, complemented
176C5×#97C22×C311yescharacteristic, complemented
177#3964C22×C311yescharacteristic
178#3964C22×C311yescharacteristic, complemented
179#3953C22×C311yescharacteristic
180#3950C22×C311yescharacteristic, complemented
181#3948C22×C311yescharacteristic, complemented
182#3947C22×C311yescharacteristic, complemented
183C8×Dic5C22×C311yescharacteristic, complemented
184#3942C22×C311yescharacteristic, complemented
185#3941C22×C311yescharacteristic
186#3940C22×C311yescharacteristic, complemented
187#3939C22×C311yescharacteristic, complemented
188C4×#168C22×C311yescharacteristic, complemented
189#2946—51noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—24no—
194C22×C3×D5—81no—
195C22×C3×D5—81no—
196C22×C3×D5C2×D411yescharacteristic
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C3×C5×D4C22×C412yes—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5—81no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208C3×C22⋊D5—24no—
209C3×C22⋊D5—24no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—24no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—81no—
215C2×C3×Dic5—81no—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×D20—21no—
220C3×D20C22×C412yes—
221C3×C4×D5—81no—
222C3×C4×D5—81no—
223C3×C4×D5—81no—
224C3×C4×D5C22×C412yes—
225C3×C4×D5#4112yes—
226C3×Dic10—21no—
227C3×Dic10C22×C412yes—
228C3×C5×C8—21no—
229C3×C5×C8C22×C412yes—
230C3×#168—21no—
231C3×#168C22×C412yes—
232C2×C3×#41—51no—
233C22×C3×D4—51no—
234C3×AGL(1,ℤ/8)—58no—
235C2×C3×SD16—51no—
236C2×C3×SD16—51no—
237C2×C3×D8—51no—
238C2×C3×D8C2×D511yescharacteristic
239C2×C3×M16—51no—
240C22×C3×C8—51no—
241C3×C4×Q8—51no—
242C3×C4×Q8—51no—
243C3×C4×D4—51no—
244C3×C4×D4—51no—
245C3×C4×D4—51no—
246C3×C4×D4—51no—
247C3×C4×D4—101no—
248C3×C4×D4—101no—
249C3×C4×D4—101no—
250C3×C4×D4—101no—
251C3×C4×D4C2×D511yescharacteristic
252C3×C4×D4C2×D511yescharacteristic, complemented
253C3×#117—51no—
254C3×#117—51no—
255C3×#117—101no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—101no—
258C2×C3×C22⋊C4—101no—
259C2×C3×C22⋊C4—101no—
260C3×#107—51no—
261C3×#107—51no—
262C3×#106—51no—
263C3×#106C2×D511yescharacteristic, complemented
264C3×#103—51no—
265C3×#103—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×#102C2×D511yescharacteristic
271C3×#102C2×D511yescharacteristic, complemented
272C3×#97—51no—
273C3×#97C2×D511yescharacteristic, complemented
274C3×C4×C8—51no—
275C3×C4×C8—51no—
276C23×D5—21no—
277C2×C5×D4C23×C311yescharacteristic
278C2×C5×D4C23×C311yescharacteristic
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C2×C22⋊D5—21no—
282C2×C22⋊D5—21no—
283C22×Dic5—21no—
284C22×Dic5—21no—
285C22×Dic5—21no—
286#711—22no—
287#711C2×C3×C414yescomplemented
288D4×D5—22no—
289D4×D5C2×C3×C414yescomplemented
290C2×D20C23×C311yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5C23×C311yescharacteristic
295C2×Dic10C23×C311yescharacteristic
296C5×D8C2×C3×C414yescomplemented
297C2×C5×C8C23×C311yescharacteristic
298C2×C5×C8C23×C311yescharacteristic
299C5×C4⋊C4C23×C311yescharacteristic
300C5×C4⋊C4C23×C311yescharacteristic
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C42×C5C23×C311yescharacteristic
304C22⋊Dic5—21no—
305C22⋊Dic5—21no—
306#687C2×C3×C414yescomplemented
307#686C2×C3×C414yescomplemented
308#685—21no—
309#685—21no—
310#685—21no—
311#685C3×D411yescharacteristic
312#685C3×D411yescharacteristic
313C4⋊Dic5C23×C311yescharacteristic
314C4⋊Dic5C23×C311yescharacteristic
315#683—21no—
316#683—21no—
317#683—21no—
318#683C3×D411yescharacteristic
319#683C3×D411yescharacteristic
320C4×Dic5—21no—
321C4×Dic5—21no—
322C4×Dic5—21no—
323C4×Dic5C23×C311yescharacteristic
324C2×#168C23×C311yescharacteristic
325C2×#168C23×C311yescharacteristic
326#677C2×C3×C414yescomplemented
327#676C2×C3×C414yescomplemented
328C8×D5—22no—
329C2×AGL(1,ℤ/8)—51no—
330#520—51no—
331#518—51no—
332#442—51no—
333#442C3×D511yescharacteristic, complemented
334#440—51no—
335#440—51no—
336C4×SD16—51no—
337C4×SD16—51no—
338C4×D8—51no—
339C4×D8—51no—
340#428—51no—
341#416—51no—
342C2×#102—51no—
343#405—51no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5C4×D412yes—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5—41no—
362C3×C4×C5C23×C411yescharacteristic
363C3×C4×C5C2×#4111yescharacteristic
364C3×Dic5—22no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5C4×D412yes—
370C24×C3—101no—
371C3×#41—54no—
372C3×#41—102no—
373C2×C3×Q8—51no—
374C2×C3×D4—54no—
375C2×C3×D4—51no—
376C2×C3×D4—102no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4C22×D511yescharacteristic
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4—21no—
382C22×C3×C4—21no—
383C22×C3×C4—51no—
384C22×C3×C4—101no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4—101no—
389C22×C3×C4—101no—
390C3×SD16—54no—
391C3×SD16—54no—
392C3×D8—54no—
393C3×D8C4×D514yescomplemented
394C3×M16—54no—
395C2×C3×C8—51no—
396C2×C3×C8—51no—
397C2×C3×C8—102no—
398C2×C3×C8C22×D511yescharacteristic
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—51no—
403C3×C4⋊C4—51no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4—101no—
407C3×C4⋊C4C22×D511yescharacteristic
408C3×C4⋊C4C22×D511yescharacteristic
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—51no—
412C3×C22⋊C4—51no—
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C22⋊C4—101no—
416C3×C22⋊C4—101no—
417C3×C22⋊C4—101no—
418C3×C42—51no—
419C3×C42—101no—
420C3×C42—101no—
421C3×C42—101no—
422C3×C42C22×D511yescharacteristic
423C23×C5—21no—
424C23×C5—21no—
425C22×D5—21no—
426C22×D5—24no—
427C22×D5—81no—
428C22×D5—81no—
429C22×D5C2×C3×D411yescharacteristic
430C5×D4—21no—
431C5×D4—21no—
432C5×D4C22×C3×C412yes—
433C5×D4C22×C3×C412yes—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—81no—
437C2×C4×C5—81no—
438C2×C4×C5C2×C3×D411yescharacteristic
439C2×C4×C5C2×C3×D411yescharacteristic
440C2×C4×C5C24×C311yescharacteristic
441C22⋊D5—24no—
442C22⋊D5—24no—
443C2×Dic5—21no—
444C2×Dic5—24no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—81no—
448C2×Dic5—81no—
449C2×Dic5C2×C3×D411yescharacteristic
450C2×Dic5C2×C3×D411yescharacteristic
451C2×Dic5C2×C3×D411yescharacteristic
452D20—21no—
453D20C22×C3×C412yes—
454C4×D5—81no—
455C4×D5—81no—
456C4×D5—81no—
457C4×D5C22×C3×C412yes—
458C4×D5C3×#4112yes—
459Dic10—21no—
460Dic10C22×C3×C412yes—
461C5×C8—21no—
462C5×C8C22×C3×C412yes—
463#168—21no—
464#168C22×C3×C412yes—
465C2×#41—51no—
466C22×D4—51no—
467AGL(1,ℤ/8)—58no—
468C2×SD16—51no—
469C2×SD16—51no—
470C2×D8—51no—
471C2×D8C2×C3×D511yescharacteristic
472C2×M16—51no—
473C22×C8—51no—
474C4×Q8—51no—
475C4×Q8—51no—
476C4×D4—51no—
477C4×D4—51no—
478C4×D4—51no—
479C4×D4—51no—
480C4×D4—101no—
481C4×D4—101no—
482C4×D4—101no—
483C4×D4—101no—
484C4×D4C2×C3×D511yescharacteristic
485C4×D4C2×C3×D511yescharacteristic, complemented
486#117—51no—
487#117—51no—
488#117—101no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493#107—51no—
494#107—51no—
495#106—51no—
496#106C2×C3×D511yescharacteristic, complemented
497#103—51no—
498#103—51no—
499#102—51no—
500#102—51no—
501#102—51no—
502#102—51no—
503#102C2×C3×D511yescharacteristic
504#102C2×C3×D511yescharacteristic, complemented
505#97—51no—
506#97C2×C3×D511yescharacteristic, complemented
507C4×C8—51no—
508C4×C8—51no—
509C2×C3×C5—42no—
510C2×C3×C5—42no—
511C2×C3×C5C2×C4×D411yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C2×C3×C5#57711yescharacteristic
514C3×D5—22no—
515C3×D5—42no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—51no—
519C23×C3—104no—
520C23×C3—101no—
521C23×C3—401no—
522C23×C3—401no—
523C3×Q8—52no—
524C3×Q8—101no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—52no—
528C3×D4—104no—
529C3×D4—104no—
530C3×D4—101no—
531C3×D4C2×C4×D512yes—
532C3×D4C2×C4×D512yes—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—51no—
536C2×C3×C4—52no—
537C2×C3×C4—52no—
538C2×C3×C4—51no—
539C2×C3×C4—51no—
540C2×C3×C4—81no—
541C2×C3×C4—81no—
542C2×C3×C4—104no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—401no—
547C2×C3×C4—401no—
548C2×C3×C4—401no—
549C2×C3×C4—401no—
550C2×C3×C4—401no—
551C2×C3×C4D4×D511yescharacteristic
552C2×C3×C4D4×D511yescharacteristic
553C2×C3×C4C23×D511yescharacteristic
554C3×C8—21no—
555C3×C8—52no—
556C3×C8—101no—
557C3×C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—41no—
563C22×C5—41no—
564C22×C5C22×C3×D411yescharacteristic
565C2×D5—21no—
566C2×D5—21no—
567C2×D5—22no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—84no—
571C2×D5C3×C4×D412yes—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—41no—
575C4×C5—41no—
576C4×C5C23×C3×C411yescharacteristic
577C4×C5C2×C3×#4111yescharacteristic
578Dic5—21no—
579Dic5—21no—
580Dic5—22no—
581Dic5—41no—
582Dic5—41no—
583Dic5C3×C4×D412yes—
584C24—101no—
585#41—54no—
586#41—102no—
587C2×Q8—51no—
588C2×D4—54no—
589C2×D4—51no—
590C2×D4—102no—
591C2×D4—101no—
592C2×D4—101no—
593C2×D4C22×C3×D511yescharacteristic
594C2×D4C22×C3×D511yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—51no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604SD16—54no—
605SD16—54no—
606D8—54no—
607D8C3×C4×D514yescomplemented
608M16—54no—
609C2×C8—51no—
610C2×C8—51no—
611C2×C8—102no—
612C2×C8C22×C3×D511yescharacteristic
613C2×C8C22×C3×D511yescharacteristic
614C4⋊C4—51no—
615C4⋊C4—51no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—101no—
619C4⋊C4—101no—
620C4⋊C4—101no—
621C4⋊C4C22×C3×D511yescharacteristic
622C4⋊C4C22×C3×D511yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—51no—
626C22⋊C4—51no—
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C42—51no—
633C42—101no—
634C42—101no—
635C42—101no—
636C42C22×C3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—52no—
645C22×C3—101no—
646C22×C3—101no—
647C22×C3—102no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—404no—
651C22×C3C2×D4×D511yescharacteristic
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—52no—
657C3×C4—101no—
658C3×C4—101no—
659C3×C4—102no—
660C3×C4—201no—
661C3×C4—201no—
662C3×C4C22×C4×D511yescharacteristic
663C3×C4D5×#4111yescharacteristic
664C2×C5—42no—
665C2×C5—42no—
666C2×C5C2×C3×C4×D411yescharacteristic
667C2×C5C3×#57611yescharacteristic
668C2×C5C3×#57711yescharacteristic
669D5—22no—
670D5—42no—
671C23—21no—
672C23—21no—
673C23—51no—
674C23—104no—
675C23—101no—
676C23—401no—
677C23—401no—
678Q8—52no—
679Q8—101no—
680D4—21no—
681D4—21no—
682D4—52no—
683D4—104no—
684D4—104no—
685D4—101no—
686D4C2×C3×C4×D512yes—
687D4C2×C3×C4×D512yes—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—51no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—51no—
694C2×C4—51no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—104no—
698C2×C4—101no—
699C2×C4—101no—
700C2×C4—101no—
701C2×C4—401no—
702C2×C4—401no—
703C2×C4—401no—
704C2×C4—401no—
705C2×C4—401no—
706C2×C4C3×D4×D511yescharacteristic
707C2×C4C3×D4×D511yescharacteristic
708C2×C4C23×C3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—101no—
712C8C2×C3×C4×D512yes—
713C2×C3—42no—
714C2×C3—42no—
715C2×C3—102no—
716C2×C3—202no—
717C2×C3C4×D4×D511yescharacteristic
718C2×C3#6610811yescharacteristic
719C2×C3#6610911yescharacteristic
720C5C3×#294611yescharacteristic, complemented, Sylow
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—52no—
728C22—101no—
729C22—101no—
730C22—102no—
731C22—201no—
732C22—201no—
733C22—404no—
734C22C2×C3×D4×D511yescharacteristic
735C4—21no—
736C4—21no—
737C4—41no—
738C4—41no—
739C4—52no—
740C4—101no—
741C4—101no—
742C4—102no—
743C4—201no—
744C4—201no—
745C4C22×C3×C4×D511yescharacteristic
746C4C3×D5×#4111yescharacteristic
747C3#1061159711yescharacteristic, direct product factor, Sylow
748C2—42no—
749C2—42no—
750C2—102no—
751C2—202no—
752C2C3×C4×D4×D511yescharacteristic
753C2C3×#6610811yescharacteristic
754C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#442C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4057C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#442D5
hypocenterC5C3×#2946
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
2. C3×#65880C2semidirect
3. C3×#65879C2semidirect
4. C3×C5×#442C2semidirect
5. C3×D8×Dic5C2semidirect
6. C3×C4×#687C2semidirect
7. C3×C4×#686C2semidirect
8. C3×#65150C2semidirect
9. C3×#65141C2semidirect
10. C3×#65074C2semidirect
11. C3×#65061C2semidirect
12. C3×D5×#102C2semidirect
13. C3×#65046C2semidirect
14. C3×#64999C2semidirect
15. C3×#64997C2semidirect
16. #10611597C3direct (N × H)
21. C3×C4×C5×D4C22semidirect
23. C3×D4×Dic5C22semidirect
30. C3×#4057C4semidirect
37. C3×#4033C22semidirect
44. C3×C4×Dic10C22semidirect
45. C3×C5×#106C22semidirect
47. C3×C5×#102C22semidirect
48. C3×C5×#97C22semidirect
50. C3×#3964C22semidirect
52. C3×#3950C22semidirect
53. C3×#3948C22semidirect
54. C3×#3947C22semidirect
55. C3×C8×Dic5C22semidirect
56. C3×#3942C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
60. C3×C4×#168C22semidirect
63. #65880C2×C3semidirect
64. #65879C2×C3semidirect
65. C5×#442C2×C3semidirect
66. D8×Dic5C2×C3semidirect
67. C4×#687C2×C3semidirect
68. C4×#686C2×C3semidirect
69. #65150C2×C3semidirect
70. #65141C2×C3semidirect
71. #65074C2×C3semidirect
72. #65061C2×C3semidirect
73. D5×#102C2×C3semidirect
74. #65046C2×C3semidirect
75. #64999C2×C3semidirect
76. #64997C2×C3semidirect
88. C3×#711C2×C4semidirect
90. C3×D4×D5C2×C4semidirect
97. C3×C5×D8C2×C4semidirect
107. C3×#687C2×C4semidirect
108. C3×#686C2×C4semidirect
127. C3×#677C2×C4semidirect
128. C3×#676C2×C4semidirect
134. C3×#442D5semidirect
149. C4×C5×D4C22×C3semidirect
151. D4×Dic5C22×C3semidirect
158. #4057C3×C4semidirect
165. #4033C22×C3semidirect
172. C4×Dic10C22×C3semidirect
173. C5×#106C22×C3semidirect
175. C5×#102C22×C3semidirect
176. C5×#97C22×C3semidirect
178. #3964C22×C3semidirect
180. #3950C22×C3semidirect
181. #3948C22×C3semidirect
182. #3947C22×C3semidirect
183. C8×Dic5C22×C3semidirect
184. #3942C22×C3semidirect
186. #3940C22×C3semidirect
187. #3939C22×C3semidirect
188. C4×#168C22×C3semidirect
252. C3×C4×D4C2×D5semidirect
263. C3×#106C2×D5semidirect
271. C3×#102C2×D5semidirect
273. C3×#97C2×D5semidirect
287. #711C2×C3×C4semidirect
289. D4×D5C2×C3×C4semidirect
296. C5×D8C2×C3×C4semidirect
306. #687C2×C3×C4semidirect
307. #686C2×C3×C4semidirect
326. #677C2×C3×C4semidirect
327. #676C2×C3×C4semidirect
333. #442C3×D5semidirect
393. C3×D8C4×D5semidirect
485. C4×D4C2×C3×D5semidirect
496. #106C2×C3×D5semidirect
504. #102C2×C3×D5semidirect
506. #97C2×C3×D5semidirect
607. D8C3×C4×D5semidirect
637. C3×C5#2946semidirect
720. C5C3×#2946semidirect
747. C3#10611597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40572
C3×#658802
C3×#658792
C3×C5×#4422
C3×D8×Dic52
C3×C4×#6872
C3×C4×#6862
C3×#651502
C3×#651412
C3×#650742
C3×#650612
C3×D5×#1022
C3×#650462
C3×#649992
C3×#649972
#106115973
C3×#29465