Finite Group Databasebeta

← C3×#10611507 #14417166

Subgroups — C3×#10611507 #14417166

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4061C211yesmaximal, characteristic
2C3×#65906C211yesmaximal, characteristic, complemented
3C3×#65880C211yesmaximal, characteristic
4C3×C5×#440C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6C3×C4×#689C211yesmaximal, characteristic, complemented
7C3×C4×#687C211yesmaximal, characteristic, complemented
8C3×#65170C211yesmaximal, characteristic, complemented
9C3×#65162C211yesmaximal, characteristic, complemented
10C3×D5×#103C211yesmaximal, characteristic, complemented
11C3×#65078C211yesmaximal, characteristic, complemented
12C3×#65061C211yesmaximal, characteristic
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×#65005C211yesmaximal, characteristic, complemented
15C3×#64997C211yesmaximal, characteristic, complemented
16#10611507C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C2×C3×#689C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C2×C3×#683—21no—
28C3×#4061C418yescomplemented
29C2×C3×Dic20C2211yescharacteristic
30C2×C3×#676C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic
32C3×#4038—21no—
33C3×#4038C2211yescharacteristic
34C3×D5×C4⋊C4C2211yescharacteristic
35C3×#4033—21no—
36C3×#4033C2211yescharacteristic
37C3×#4033C2211yescharacteristic
38C3×#4027—21no—
39C3×#4023—21no—
40C3×#4018—21no—
41C3×#4018C2211yescharacteristic
42C3×C4×Dic10—21no—
43C3×C4×Dic10C2211yescharacteristic
44C3×C4×Dic10C2211yescharacteristic
45C3×C5×#107C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×#102C2211yescharacteristic
48C3×C5×#97C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3964C2211yescharacteristic
51C3×#3949C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3947C2211yescharacteristic
55C3×C8×Dic5C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3942C2211yescharacteristic
58C3×#3940C2211yescharacteristic
59C3×#3939C2211yescharacteristic
60C3×C4×#168C2211yescharacteristic
61C3×#2947—51nomaximal, Hall
62C2×#4061C2×C311yescharacteristic
63#65906C2×C311yescharacteristic, complemented
64#65880C2×C311yescharacteristic
65C5×#440C2×C311yescharacteristic, complemented
66SD16×Dic5C2×C311yescharacteristic, complemented
67C4×#689C2×C311yescharacteristic, complemented
68C4×#687C2×C311yescharacteristic, complemented
69#65170C2×C311yescharacteristic, complemented
70#65162C2×C311yescharacteristic, complemented
71D5×#103C2×C311yescharacteristic, complemented
72#65078C2×C311yescharacteristic, complemented
73#65061C2×C311yescharacteristic
74#65046C2×C311yescharacteristic, complemented
75#65005C2×C311yescharacteristic, complemented
76#64997C2×C311yescharacteristic, complemented
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×C3×C22⋊D5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C3×Q8×D5—22no—
84C3×Q8×D5C2×C414yescomplemented
85C3×#711—22no—
86C3×#711C2×C414yes—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C2×C3×Dic10C2311yescharacteristic
93C3×C5×SD16C2×C414yescomplemented
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C42×C5—21no—
101C3×C42×C5C2311yescharacteristic
102C3×C22⋊Dic5—21no—
103C3×#689C2×C414yescomplemented
104C3×#687C2×C414yescomplemented
105C3×#685—21no—
106C3×#685D411yescharacteristic
107C3×#685D411yescharacteristic
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683D411yescharacteristic
117C3×#683D411yescharacteristic
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×Dic20C2×C414yescomplemented
128C3×#676C2×C414yescomplemented
129C3×C8×D5—22no—
130C2×C3×#137—51no—
131C3×#520—51no—
132C3×#519—51no—
133C3×#441—51no—
134C3×#441—51no—
135C3×#440—51no—
136C3×#440D511yescharacteristic, complemented
137C3×C4×Q16—51no—
138C3×C4×Q16—51no—
139C3×C4×SD16—51no—
140C3×C4×SD16—51no—
141C3×#428—51no—
142C3×#416—51no—
143C2×C3×#103—51no—
144C3×#405—51no—
145C2×Q8×D5C22×C311yescharacteristic
146C2×#711C22×C311yescharacteristic
147C2×C5×SD16C22×C311yescharacteristic
148C4×C5×Q8C22×C311yescharacteristic
149C4×C5×D4C22×C311yescharacteristic
150Q8×Dic5C22×C311yescharacteristic
151C2×#689C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153C2×#687C22×C311yescharacteristic
154C4×C22⋊D5—21no—
155C2×#683—21no—
156#4061C3×C418yescomplemented
157C2×Dic20C22×C311yescharacteristic
158C2×#676C22×C311yescharacteristic
159C2×C8×D5C22×C311yescharacteristic
160#4038—21no—
161#4038C22×C311yescharacteristic
162D5×C4⋊C4C22×C311yescharacteristic
163#4033—21no—
164#4033C22×C311yescharacteristic
165#4033C22×C311yescharacteristic
166#4027—21no—
167#4023—21no—
168#4018—21no—
169#4018C22×C311yescharacteristic
170C4×Dic10—21no—
171C4×Dic10C22×C311yescharacteristic
172C4×Dic10C22×C311yescharacteristic
173C5×#107C22×C311yescharacteristic
174C5×#103C22×C311yescharacteristic
175C5×#102C22×C311yescharacteristic
176C5×#97C22×C311yescharacteristic
177#3967C22×C311yescharacteristic
178#3964C22×C311yescharacteristic
179#3949C22×C311yescharacteristic
180#3948C22×C311yescharacteristic
181#3948C22×C311yescharacteristic
182#3947C22×C311yescharacteristic
183C8×Dic5C22×C311yescharacteristic
184#3942C22×C311yescharacteristic
185#3942C22×C311yescharacteristic
186#3940C22×C311yescharacteristic
187#3939C22×C311yescharacteristic
188C4×#168C22×C311yescharacteristic
189#2947—51noSylow
190C23×C3×C5—21no—
191C22×C3×D5C2×D411yescharacteristic
192C3×C5×Q8—21no—
193C3×C5×Q8C22×C412yes—
194C3×C5×D4—21no—
195C3×C5×D4C22×C412yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C3×C22⋊D5—24no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—24no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C3×C4×D5—24no—
214C3×C4×D5—81no—
215C3×C4×D5C22×C412yes—
216C3×C4×D5#4112yes—
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—24no—
220C3×Dic10C22×C412yes—
221C3×Dic10C22×C412yes—
222C3×C5×C8—21no—
223C3×C5×C8C22×C412yes—
224C3×#168—21no—
225C3×#168C22×C412yes—
226C2×C3×#41—51no—
227C22×C3×Q8—51no—
228C3×#137—58no—
229C2×C3×Q16—51no—
230C2×C3×Q16—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16C2×D511yescharacteristic
233C2×C3×M16—51no—
234C22×C3×C8—51no—
235C3×C4×Q8—51no—
236C3×C4×Q8—51no—
237C3×C4×Q8—51no—
238C3×C4×Q8—51no—
239C3×C4×Q8—51no—
240C3×C4×Q8—101no—
241C3×C4×Q8—101no—
242C3×C4×Q8C2×D511yescharacteristic
243C3×C4×D4—51no—
244C3×C4×D4—101no—
245C3×C4×D4—101no—
246C3×C4×D4C2×D511yescharacteristic
247C3×#117—51no—
248C3×#117—51no—
249C3×#117—101no—
250C3×#117—101no—
251C3×#117—101no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C4⋊C4—101no—
254C3×#107—51no—
255C3×#107C2×D511yescharacteristic
256C3×#106—51no—
257C3×#106—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#103—51no—
263C3×#103C2×D511yescharacteristic
264C3×#102—51no—
265C3×#102C2×D511yescharacteristic
266C3×#97—51no—
267C3×#97C2×D511yescharacteristic
268C3×C4×C8—51no—
269C3×C4×C8—51no—
270C2×C5×Q8C23×C311yescharacteristic
271C2×C5×D4C23×C311yescharacteristic
272C22×C4×C5—21no—
273C2×C22⋊D5—21no—
274C22×Dic5—21no—
275C22×Dic5—21no—
276Q8×D5—22no—
277Q8×D5C2×C3×C414yescomplemented
278#711—22no—
279#711C2×C3×C414yes—
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5C23×C311yescharacteristic
283C2×Dic10—21no—
284C2×Dic10C23×C311yescharacteristic
285C2×Dic10C23×C311yescharacteristic
286C5×SD16C2×C3×C414yescomplemented
287C2×C5×C8C23×C311yescharacteristic
288C2×C5×C8C23×C311yescharacteristic
289C5×C4⋊C4—21no—
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C4⋊C4C23×C311yescharacteristic
292C5×C22⋊C4—21no—
293C42×C5—21no—
294C42×C5C23×C311yescharacteristic
295C22⋊Dic5—21no—
296#689C2×C3×C414yescomplemented
297#687C2×C3×C414yescomplemented
298#685—21no—
299#685C3×D411yescharacteristic
300#685C3×D411yescharacteristic
301C4⋊Dic5—21no—
302C4⋊Dic5C23×C311yescharacteristic
303C4⋊Dic5C23×C311yescharacteristic
304#683—21no—
305#683—21no—
306#683—21no—
307#683—21no—
308#683—21no—
309#683C3×D411yescharacteristic
310#683C3×D411yescharacteristic
311C4×Dic5—21no—
312C4×Dic5—21no—
313C4×Dic5—21no—
314C4×Dic5—21no—
315C4×Dic5—21no—
316C4×Dic5—21no—
317C4×Dic5C23×C311yescharacteristic
318C2×#168C23×C311yescharacteristic
319C2×#168C23×C311yescharacteristic
320Dic20C2×C3×C414yescomplemented
321#676C2×C3×C414yescomplemented
322C8×D5—22no—
323C2×#137—51no—
324#520—51no—
325#519—51no—
326#441—51no—
327#441—51no—
328#440—51no—
329#440C3×D511yescharacteristic, complemented
330C4×Q16—51no—
331C4×Q16—51no—
332C4×SD16—51no—
333C4×SD16—51no—
334#428—51no—
335#416—51no—
336C2×#103—51no—
337#405—51no—
338C22×C3×C5—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C3×D5—21no—
343C2×C3×D5—21no—
344C2×C3×D5C4×D412yes—
345C3×C4×C5—22no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—41no—
349C3×C4×C5—41no—
350C3×C4×C5C23×C411yescharacteristic
351C3×C4×C5C2×#4111yescharacteristic
352C3×Dic5—22no—
353C3×Dic5—22no—
354C3×Dic5—21no—
355C3×Dic5—21no—
356C3×Dic5—41no—
357C3×Dic5—41no—
358C3×Dic5C4×D412yes—
359C3×#41—54no—
360C3×#41—102no—
361C2×C3×Q8—54no—
362C2×C3×Q8—51no—
363C2×C3×Q8—51no—
364C2×C3×Q8—101no—
365C2×C3×Q8—102no—
366C2×C3×Q8C22×D511yescharacteristic
367C2×C3×D4—101no—
368C2×C3×D4C22×D511yescharacteristic
369C22×C3×C4—21no—
370C22×C3×C4—51no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C22×C3×C4—101no—
375C3×Q16—54no—
376C3×Q16—54no—
377C3×SD16—54no—
378C3×SD16C4×D514yescomplemented
379C3×M16—54no—
380C2×C3×C8—51no—
381C2×C3×C8—51no—
382C2×C3×C8—102no—
383C2×C3×C8C22×D511yescharacteristic
384C2×C3×C8C22×D511yescharacteristic
385C3×C4⋊C4—21no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4—51no—
388C3×C4⋊C4—51no—
389C3×C4⋊C4—51no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4—101no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C4⋊C4C22×D511yescharacteristic
398C3×C22⋊C4—21no—
399C3×C22⋊C4—51no—
400C3×C22⋊C4—51no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C42—21no—
404C3×C42—51no—
405C3×C42—101no—
406C3×C42—101no—
407C3×C42—101no—
408C3×C42—101no—
409C3×C42—101no—
410C3×C42—101no—
411C3×C42C22×D511yescharacteristic
412C23×C5—21no—
413C22×D5C2×C3×D411yescharacteristic
414C5×Q8—21no—
415C5×Q8C22×C3×C412yes—
416C5×D4—21no—
417C5×D4C22×C3×C412yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—81no—
422C2×C4×C5C2×C3×D411yescharacteristic
423C2×C4×C5C2×C3×D411yescharacteristic
424C2×C4×C5C24×C311yescharacteristic
425C22⋊D5—24no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—24no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—81no—
432C2×Dic5C2×C3×D411yescharacteristic
433C2×Dic5C2×C3×D411yescharacteristic
434C2×Dic5C2×C3×D411yescharacteristic
435C4×D5—24no—
436C4×D5—81no—
437C4×D5C22×C3×C412yes—
438C4×D5C3×#4112yes—
439Dic10—21no—
440Dic10—21no—
441Dic10—24no—
442Dic10C22×C3×C412yes—
443Dic10C22×C3×C412yes—
444C5×C8—21no—
445C5×C8C22×C3×C412yes—
446#168—21no—
447#168C22×C3×C412yes—
448C2×#41—51no—
449C22×Q8—51no—
450#137—58no—
451C2×Q16—51no—
452C2×Q16—51no—
453C2×SD16—51no—
454C2×SD16C2×C3×D511yescharacteristic
455C2×M16—51no—
456C22×C8—51no—
457C4×Q8—51no—
458C4×Q8—51no—
459C4×Q8—51no—
460C4×Q8—51no—
461C4×Q8—51no—
462C4×Q8—101no—
463C4×Q8—101no—
464C4×Q8C2×C3×D511yescharacteristic
465C4×D4—51no—
466C4×D4—101no—
467C4×D4—101no—
468C4×D4C2×C3×D511yescharacteristic
469#117—51no—
470#117—51no—
471#117—101no—
472#117—101no—
473#117—101no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—101no—
476#107—51no—
477#107C2×C3×D511yescharacteristic
478#106—51no—
479#106—51no—
480#103—51no—
481#103—51no—
482#103—51no—
483#103—51no—
484#103—51no—
485#103C2×C3×D511yescharacteristic
486#102—51no—
487#102C2×C3×D511yescharacteristic
488#97—51no—
489#97C2×C3×D511yescharacteristic
490C4×C8—51no—
491C4×C8—51no—
492C2×C3×C5—42no—
493C2×C3×C5C2×C4×D411yescharacteristic
494C2×C3×C5#57711yescharacteristic
495C2×C3×C5#57811yescharacteristic
496C3×D5—22no—
497C23×C3—21no—
498C23×C3—51no—
499C3×Q8—21no—
500C3×Q8—52no—
501C3×Q8—52no—
502C3×Q8—104no—
503C3×Q8—101no—
504C3×Q8—101no—
505C3×Q8C2×C4×D512yes—
506C3×D4—21no—
507C3×D4—104no—
508C3×D4C2×C4×D512yes—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—51no—
513C2×C3×C4—52no—
514C2×C3×C4—52no—
515C2×C3×C4—51no—
516C2×C3×C4—51no—
517C2×C3×C4—81no—
518C2×C3×C4—104no—
519C2×C3×C4—104no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—401no—
525C2×C3×C4—401no—
526C2×C3×C4D4×D511yescharacteristic
527C2×C3×C4D4×D511yescharacteristic
528C2×C3×C4C23×D511yescharacteristic
529C3×C8—21no—
530C3×C8—52no—
531C3×C8—101no—
532C3×C8C2×C4×D512yes—
533C22×C5—22no—
534C22×C5—41no—
535C22×C5—41no—
536C22×C5C22×C3×D411yescharacteristic
537C2×D5—21no—
538C2×D5—21no—
539C2×D5C3×C4×D412yes—
540C4×C5—21no—
541C4×C5—21no—
542C4×C5—22no—
543C4×C5—41no—
544C4×C5—41no—
545C4×C5C23×C3×C411yescharacteristic
546C4×C5C2×C3×#4111yescharacteristic
547Dic5—21no—
548Dic5—21no—
549Dic5—22no—
550Dic5—22no—
551Dic5—41no—
552Dic5—41no—
553Dic5C3×C4×D412yes—
554#41—54no—
555#41—102no—
556C2×Q8—54no—
557C2×Q8—51no—
558C2×Q8—51no—
559C2×Q8—101no—
560C2×Q8—102no—
561C2×Q8C22×C3×D511yescharacteristic
562C2×D4—101no—
563C2×D4C22×C3×D511yescharacteristic
564C22×C4—21no—
565C22×C4—51no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570Q16—54no—
571Q16—54no—
572SD16—54no—
573SD16C3×C4×D514yescomplemented
574M16—54no—
575C2×C8—51no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8C22×C3×D511yescharacteristic
579C2×C8C22×C3×D511yescharacteristic
580C4⋊C4—21no—
581C4⋊C4—51no—
582C4⋊C4—51no—
583C4⋊C4—51no—
584C4⋊C4—51no—
585C4⋊C4—101no—
586C4⋊C4—101no—
587C4⋊C4—101no—
588C4⋊C4—101no—
589C4⋊C4—101no—
590C4⋊C4—101no—
591C4⋊C4C22×C3×D511yescharacteristic
592C4⋊C4C22×C3×D511yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—51no—
595C22⋊C4—51no—
596C22⋊C4—101no—
597C22⋊C4—101no—
598C42—21no—
599C42—51no—
600C42—101no—
601C42—101no—
602C42—101no—
603C42—101no—
604C42—101no—
605C42—101no—
606C42C22×C3×D511yescharacteristic
607C3×C5#294711yescharacteristic, complemented, Hall
608C22×C3—22no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—52no—
612C22×C3—101no—
613C22×C3—101no—
614C22×C3C2×D4×D511yescharacteristic
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—22no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—52no—
621C3×C4—101no—
622C3×C4—101no—
623C3×C4—102no—
624C3×C4—102no—
625C3×C4—201no—
626C3×C4—201no—
627C3×C4C22×C4×D511yescharacteristic
628C3×C4D5×#4111yescharacteristic
629C2×C5—42no—
630C2×C5C2×C3×C4×D411yescharacteristic
631C2×C5C3×#57711yescharacteristic
632C2×C5C3×#57811yescharacteristic
633D5—22no—
634C23—21no—
635C23—51no—
636Q8—21no—
637Q8—52no—
638Q8—52no—
639Q8—104no—
640Q8—101no—
641Q8—101no—
642Q8C2×C3×C4×D512yes—
643D4—21no—
644D4—104no—
645D4C2×C3×C4×D512yes—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—51no—
650C2×C4—52no—
651C2×C4—52no—
652C2×C4—51no—
653C2×C4—51no—
654C2×C4—81no—
655C2×C4—104no—
656C2×C4—104no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—401no—
662C2×C4—401no—
663C2×C4C3×D4×D511yescharacteristic
664C2×C4C3×D4×D511yescharacteristic
665C2×C4C23×C3×D511yescharacteristic
666C8—21no—
667C8—52no—
668C8—101no—
669C8C2×C3×C4×D512yes—
670C2×C3—42no—
671C2×C3—102no—
672C2×C3C4×D4×D511yescharacteristic
673C2×C3#6610911yescharacteristic
674C2×C3#6611311yescharacteristic
675C5C3×#294711yescharacteristic, complemented, Sylow
676C22—22no—
677C22—41no—
678C22—41no—
679C22—52no—
680C22—101no—
681C22—101no—
682C22C2×C3×D4×D511yescharacteristic
683C4—21no—
684C4—21no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—52no—
689C4—101no—
690C4—101no—
691C4—102no—
692C4—102no—
693C4—201no—
694C4—201no—
695C4C22×C3×C4×D511yescharacteristic
696C4C3×D5×#4111yescharacteristic
697C3#1061150711yescharacteristic, direct product factor, Sylow
698C2—42no—
699C2—102no—
700C2C3×C4×D4×D511yescharacteristic
701C2C3×#6610911yescharacteristic
702C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
cosocleC2×C4×C5C24×C3
hypercenterC3×#440D5
hypocenterC5C3×#2947
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×#65906C2semidirect
4. C3×C5×#440C2semidirect
5. C3×SD16×Dic5C2semidirect
6. C3×C4×#689C2semidirect
7. C3×C4×#687C2semidirect
8. C3×#65170C2semidirect
9. C3×#65162C2semidirect
10. C3×D5×#103C2semidirect
11. C3×#65078C2semidirect
13. C3×#65046C2semidirect
14. C3×#65005C2semidirect
15. C3×#64997C2semidirect
16. #10611507C3direct (N × H)
28. C3×#4061C4semidirect
63. #65906C2×C3semidirect
65. C5×#440C2×C3semidirect
66. SD16×Dic5C2×C3semidirect
67. C4×#689C2×C3semidirect
68. C4×#687C2×C3semidirect
69. #65170C2×C3semidirect
70. #65162C2×C3semidirect
71. D5×#103C2×C3semidirect
72. #65078C2×C3semidirect
74. #65046C2×C3semidirect
75. #65005C2×C3semidirect
76. #64997C2×C3semidirect
84. C3×Q8×D5C2×C4semidirect
93. C3×C5×SD16C2×C4semidirect
103. C3×#689C2×C4semidirect
104. C3×#687C2×C4semidirect
127. C3×Dic20C2×C4semidirect
128. C3×#676C2×C4semidirect
136. C3×#440D5semidirect
156. #4061C3×C4semidirect
277. Q8×D5C2×C3×C4semidirect
286. C5×SD16C2×C3×C4semidirect
296. #689C2×C3×C4semidirect
297. #687C2×C3×C4semidirect
320. Dic20C2×C3×C4semidirect
321. #676C2×C3×C4semidirect
329. #440C3×D5semidirect
378. C3×SD16C4×D5semidirect
573. SD16C3×C4×D5semidirect
607. C3×C5#2947semidirect
675. C5C3×#2947semidirect
697. C3#10611507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40612
C3×#659062
C3×#658802
C3×C5×#4402
C3×SD16×Dic52
C3×C4×#6892
C3×C4×#6872
C3×#651702
C3×#651622
C3×D5×#1032
C3×#650782
C3×#650612
C3×#650462
C3×#650052
C3×#649972
#106115073
C3×#29475