Finite Group Databasebeta

← C3×D5×#485 #14431597

Subgroups — C3×D5×#485 #14431597

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C22⋊Q8C211yesmaximal, characteristic
2C3×D5×#117C211yesmaximal, characteristic
3C3×C5×#485C211yesmaximal, characteristic, complemented
4C3×#65334C211yesmaximal, characteristic, complemented
5C3×#65285C211yesmaximal, characteristic, complemented
6C3×#65177C211yesmaximal, characteristic, complemented
7C3×D5×#107C211yesmaximal, characteristic, complemented
8C3×#65156C211yesmaximal, characteristic, complemented
9C3×D5×#106C211yesmaximal, characteristic, complemented
10C3×#65104C211yesmaximal, characteristic, complemented
11C3×#65103C211yesmaximal, characteristic, complemented
12C3×D5×#103C211yesmaximal, characteristic, complemented
13C3×D5×#103C211yesmaximal, characteristic, complemented
14C3×D5×C22⋊C8C211yesmaximal, characteristic
15C3×#65012C211yesmaximal, characteristic, complemented
16D5×#485C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C3×C5×#117C2211yescharacteristic
21C3×#4092C2211yescharacteristic
22C3×#4072C2211yescharacteristic
23C3×#4070C2211yescharacteristic
24C2×C3×C8×D5C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26C3×#4043C2211yescharacteristic
27C3×#4042—21no—
28C3×#4038C2211yescharacteristic
29C3×#4038C2211yescharacteristic
30C3×D5×C4⋊C4—21no—
31C3×D5×C4⋊C4C2211yescharacteristic
32C3×D5×C4⋊C4C2211yescharacteristic
33C3×D5×C4⋊C4C2211yescharacteristic
34C3×D5×C22⋊C4—21no—
35C3×D5×C22⋊C4—21no—
36C3×#4024—21no—
37C3×#4023—21no—
38C3×#4018—21no—
39C3×C42×D5—21no—
40C3×C5×#107C2211yescharacteristic, complemented
41C3×C5×#106C2211yescharacteristic, complemented
42C3×C5×#103C2211yescharacteristic, complemented
43C3×C5×#103C2211yescharacteristic, complemented
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×#3967C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×C22⋊#168C2211yescharacteristic
48C3×#3952C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3950C2211yescharacteristic, complemented
51C3×#3949C2211yescharacteristic, complemented
52C3×#3948C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3940C2211yescharacteristic, complemented
57C3×#3940C2211yescharacteristic, complemented
58C3×#3939C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C2×C3×#485—51nomaximal, Hall
61D5×C22⋊Q8C2×C311yescharacteristic
62D5×#117C2×C311yescharacteristic
63C5×#485C2×C311yescharacteristic, complemented
64#65334C2×C311yescharacteristic, complemented
65#65285C2×C311yescharacteristic, complemented
66#65177C2×C311yescharacteristic, complemented
67D5×#107C2×C311yescharacteristic, complemented
68#65156C2×C311yescharacteristic, complemented
69D5×#106C2×C311yescharacteristic, complemented
70#65104C2×C311yescharacteristic, complemented
71#65103C2×C311yescharacteristic, complemented
72D5×#103C2×C311yescharacteristic, complemented
73D5×#103C2×C311yescharacteristic, complemented
74D5×C22⋊C8C2×C311yescharacteristic
75#65012C2×C311yescharacteristic, complemented
76C23×C3×D5D411yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×Dic5D411yescharacteristic
80C3×Q8×D5—22no—
81C3×Q8×D5—22no—
82C2×C3×C4×D5—22no—
83C2×C3×C4×D5—22no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10—21no—
93C2×C3×Dic10C2311yescharacteristic
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C42×C5—21no—
103C3×C22⋊Dic5—21no—
104C3×C22⋊Dic5—21no—
105C3×#685—21no—
106C3×#685—21no—
107C3×#685—21no—
108C3×#685—21no—
109C3×C4⋊Dic5—21no—
110C3×C4⋊Dic5C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C3×C8×D5—22no—
124C3×C8×D5—22no—
125C2×C3×C22⋊Q8—51no—
126C2×C3×#117—51no—
127C3×#485—51no—
128C3×#485—51no—
129C3×#485—51no—
130C3×#485—51no—
131C3×#485—51no—
132C3×#485—51no—
133C3×#485—51no—
134C3×#485D511yescharacteristic, direct product factor
135C2×C3×#107—51no—
136C2×C3×#106—51no—
137C2×C3×#103—51no—
138C2×C3×#103—51no—
139C2×C3×C22⋊C8—51no—
140C2×Q8×D5C22×C311yescharacteristic
141C22×C4×D5C22×C311yescharacteristic
142C5×C22⋊Q8C22×C311yescharacteristic
143C5×#117C22×C311yescharacteristic
144#4092C22×C311yescharacteristic
145#4072C22×C311yescharacteristic
146#4070C22×C311yescharacteristic
147C2×C8×D5C22×C311yescharacteristic
148C2×C8×D5C22×C311yescharacteristic
149#4043C22×C311yescharacteristic
150#4042—21no—
151#4038C22×C311yescharacteristic
152#4038C22×C311yescharacteristic
153D5×C4⋊C4—21no—
154D5×C4⋊C4C22×C311yescharacteristic
155D5×C4⋊C4C22×C311yescharacteristic
156D5×C4⋊C4C22×C311yescharacteristic
157D5×C22⋊C4—21no—
158D5×C22⋊C4—21no—
159#4024—21no—
160#4023—21no—
161#4018—21no—
162C42×D5—21no—
163C5×#107C22×C311yescharacteristic, complemented
164C5×#106C22×C311yescharacteristic, complemented
165C5×#103C22×C311yescharacteristic, complemented
166C5×#103C22×C311yescharacteristic, complemented
167C5×C22⋊C8C22×C311yescharacteristic
168#3967C22×C311yescharacteristic, complemented
169#3967C22×C311yescharacteristic, complemented
170C22⋊#168C22×C311yescharacteristic
171#3952C22×C311yescharacteristic
172#3952C22×C311yescharacteristic
173#3950C22×C311yescharacteristic, complemented
174#3949C22×C311yescharacteristic, complemented
175#3948C22×C311yescharacteristic, complemented
176#3948C22×C311yescharacteristic, complemented
177#3942C22×C311yescharacteristic, complemented
178#3942C22×C311yescharacteristic, complemented
179#3940C22×C311yescharacteristic, complemented
180#3940C22×C311yescharacteristic, complemented
181#3939C22×C311yescharacteristic, complemented
182#3939C22×C311yescharacteristic, complemented
183C2×#485—51noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—22no—
186C22×C3×D5—22no—
187C22×C3×D5—22no—
188C22×C3×D5C2×D411yescharacteristic
189C22×C3×D5C2×D411yescharacteristic
190C3×C5×Q8—21no—
191C3×C5×Q8—21no—
192C2×C3×C4×C5—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×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×C3×Dic5—22no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×C4×D5—22no—
208C3×C4×D5—21no—
209C3×C4×D5—21no—
210C3×C4×D5—22no—
211C3×C4×D5—42no—
212C3×C4×D5—42no—
213C3×C4×D5—42no—
214C3×C4×D5—42no—
215C3×C4×D5#4112yes—
216C3×C4×D5#4112yes—
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—42no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×Q8—51no—
225C23×C3×C4—51no—
226C22×C3×C8—51no—
227C22×C3×C8—51no—
228C3×C22⋊Q8—51no—
229C3×C22⋊Q8—51no—
230C3×C22⋊Q8—51no—
231C3×C22⋊Q8—101no—
232C3×C22⋊Q8—101no—
233C3×C22⋊Q8C2×D511yescharacteristic
234C3×#117—51no—
235C3×#117—51no—
236C3×#117—51no—
237C3×#117—101no—
238C3×#117—101no—
239C3×#117C2×D511yescharacteristic
240C2×C3×C4⋊C4—51no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—101no—
244C2×C3×C22⋊C4—101no—
245C2×C3×C22⋊C4—101no—
246C2×C3×C42—101no—
247C3×#107—51no—
248C3×#107—51no—
249C3×#107—51no—
250C3×#107C2×D511yescharacteristic, complemented
251C3×#106—51no—
252C3×#106—51no—
253C3×#106—51no—
254C3×#106C2×D511yescharacteristic, complemented
255C3×#103—51no—
256C3×#103—51no—
257C3×#103—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103C2×D511yescharacteristic, complemented
262C3×#103C2×D511yescharacteristic, complemented
263C3×C22⋊C8—51no—
264C3×C22⋊C8—51no—
265C3×C22⋊C8—51no—
266C3×C22⋊C8C2×D511yescharacteristic
267C23×D5C3×D411yescharacteristic
268C2×C5×Q8C23×C311yescharacteristic
269C22×C4×C5C23×C311yescharacteristic
270C22×Dic5C3×D411yescharacteristic
271Q8×D5—22no—
272Q8×D5—22no—
273C2×C4×D5—22no—
274C2×C4×D5—22no—
275C2×C4×D5—21no—
276C2×C4×D5—21no—
277C2×C4×D5—21no—
278C2×C4×D5—21no—
279C2×C4×D5C3×D411yescharacteristic
280C2×C4×D5C3×D411yescharacteristic
281C2×C4×D5C23×C311yescharacteristic
282C2×C4×D5C23×C311yescharacteristic
283C2×Dic10—21no—
284C2×Dic10C23×C311yescharacteristic
285C2×C5×C8C23×C311yescharacteristic
286C2×C5×C8C23×C311yescharacteristic
287C5×C4⋊C4—21no—
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C22⋊C4—21no—
292C5×C22⋊C4—21no—
293C42×C5—21no—
294C22⋊Dic5—21no—
295C22⋊Dic5—21no—
296#685—21no—
297#685—21no—
298#685—21no—
299#685—21no—
300C4⋊Dic5—21no—
301C4⋊Dic5C23×C311yescharacteristic
302C4⋊Dic5C23×C311yescharacteristic
303C4⋊Dic5C23×C311yescharacteristic
304#683—21no—
305#683—21no—
306#683—21no—
307#683—21no—
308#683—21no—
309C4×Dic5—21no—
310C4×Dic5—21no—
311C4×Dic5—21no—
312C2×#168C23×C311yescharacteristic
313C2×#168C23×C311yescharacteristic
314C8×D5—22no—
315C8×D5—22no—
316C2×C22⋊Q8—51no—
317C2×#117—51no—
318#485—51no—
319#485—51no—
320#485—51no—
321#485—51no—
322#485—51no—
323#485—51no—
324#485—51no—
325#485C3×D511yescharacteristic, direct product factor
326C2×#107—51no—
327C2×#106—51no—
328C2×#103—51no—
329C2×#103—51no—
330C2×C22⋊C8—51no—
331C22×C3×C5—21no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5C22×D411yescharacteristic
335C2×C3×D5—21no—
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5—44no—
339C2×C3×D5#12312yes—
340C2×C3×D5#13512yes—
341C2×C3×D5#13712yes—
342C3×C4×C5—21no—
343C3×C4×C5—41no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347C3×C4×C5C2×#4111yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349C3×Dic5—21no—
350C3×Dic5—41no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C3×Dic5#12312yes—
355C24×C3—51no—
356C2×C3×Q8—51no—
357C2×C3×Q8—101no—
358C2×C3×Q8—102no—
359C2×C3×Q8—102no—
360C2×C3×Q8C22×D511yescharacteristic
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—102no—
367C22×C3×C4—102no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C2×C3×C8—51no—
374C2×C3×C8—51no—
375C2×C3×C8—102no—
376C2×C3×C8—102no—
377C2×C3×C8C22×D511yescharacteristic
378C2×C3×C8C22×D511yescharacteristic
379C3×C4⋊C4—21no—
380C3×C4⋊C4—51no—
381C3×C4⋊C4—51no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—101no—
384C3×C4⋊C4—101no—
385C3×C4⋊C4—101no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C4⋊C4C22×D511yescharacteristic
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C42—21no—
401C3×C42—101no—
402C3×C42—101no—
403C3×C42—101no—
404C23×C5C2×C3×D411yescharacteristic
405C22×D5—22no—
406C22×D5—22no—
407C22×D5—22no—
408C22×D5C2×C3×D411yescharacteristic
409C22×D5C2×C3×D411yescharacteristic
410C5×Q8—21no—
411C5×Q8—21no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5C2×C3×D411yescharacteristic
419C2×C4×C5C24×C311yescharacteristic
420C2×Dic5—22no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5C2×C3×D411yescharacteristic
426C2×Dic5C2×C3×D411yescharacteristic
427C4×D5—22no—
428C4×D5—21no—
429C4×D5—21no—
430C4×D5—22no—
431C4×D5—42no—
432C4×D5—42no—
433C4×D5—42no—
434C4×D5—42no—
435C4×D5C3×#4112yes—
436C4×D5C3×#4112yes—
437Dic10—21no—
438Dic10—21no—
439Dic10—42no—
440C5×C8—21no—
441C5×C8—21no—
442#168—21no—
443#168—21no—
444C22×Q8—51no—
445C23×C4—51no—
446C22×C8—51no—
447C22×C8—51no—
448C22⋊Q8—51no—
449C22⋊Q8—51no—
450C22⋊Q8—51no—
451C22⋊Q8—101no—
452C22⋊Q8—101no—
453C22⋊Q8C2×C3×D511yescharacteristic
454#117—51no—
455#117—51no—
456#117—51no—
457#117—101no—
458#117—101no—
459#117C2×C3×D511yescharacteristic
460C2×C4⋊C4—51no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—101no—
464C2×C22⋊C4—101no—
465C2×C22⋊C4—101no—
466C2×C42—101no—
467#107—51no—
468#107—51no—
469#107—51no—
470#107C2×C3×D511yescharacteristic, complemented
471#106—51no—
472#106—51no—
473#106—51no—
474#106C2×C3×D511yescharacteristic, complemented
475#103—51no—
476#103—51no—
477#103—51no—
478#103—51no—
479#103—51no—
480#103—51no—
481#103C2×C3×D511yescharacteristic, complemented
482#103C2×C3×D511yescharacteristic, complemented
483C22⋊C8—51no—
484C22⋊C8—51no—
485C22⋊C8—51no—
486C22⋊C8C2×C3×D511yescharacteristic
487C2×C3×C5—41no—
488C2×C3×C5C2×#12311yescharacteristic
489C2×C3×C5C2×#13511yescharacteristic
490C2×C3×C5C2×#13711yescharacteristic
491C3×D5—41no—
492C3×D5#48514yesdirect product factor
493C23×C3—51no—
494C23×C3—51no—
495C23×C3—102no—
496C23×C3—102no—
497C23×C3—102no—
498C23×C3D4×D511yescharacteristic
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—101no—
502C3×Q8—101no—
503C3×Q8—202no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—51no—
511C2×C3×C4—52no—
512C2×C3×C4—52no—
513C2×C3×C4—51no—
514C2×C3×C4—102no—
515C2×C3×C4—102no—
516C2×C3×C4—102no—
517C2×C3×C4—101no—
518C2×C3×C4—101no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—202no—
524C2×C3×C4—202no—
525C2×C3×C4—202no—
526C2×C3×C4—202no—
527C2×C3×C4D4×D511yescharacteristic
528C2×C3×C4C23×D511yescharacteristic
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—101no—
532C3×C8—101no—
533C22×C5—21no—
534C22×C5—21no—
535C22×C5—21no—
536C22×C5C22×C3×D411yescharacteristic
537C2×D5—21no—
538C2×D5—21no—
539C2×D5—21no—
540C2×D5—44no—
541C2×D5C3×#12312yes—
542C2×D5C3×#13512yes—
543C2×D5C3×#13712yes—
544C4×C5—21no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5C2×C3×#4111yescharacteristic
550C4×C5C2×C3×#4111yescharacteristic
551Dic5—21no—
552Dic5—41no—
553Dic5—41no—
554Dic5—41no—
555Dic5—41no—
556Dic5C3×#12312yes—
557C24—51no—
558C2×Q8—51no—
559C2×Q8—101no—
560C2×Q8—102no—
561C2×Q8—102no—
562C2×Q8C22×C3×D511yescharacteristic
563C22×C4—51no—
564C22×C4—51no—
565C22×C4—51no—
566C22×C4—51no—
567C22×C4—51no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4C22×C3×D511yescharacteristic
575C2×C8—51no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8—102no—
579C2×C8C22×C3×D511yescharacteristic
580C2×C8C22×C3×D511yescharacteristic
581C4⋊C4—21no—
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
593C4⋊C4C22×C3×D511yescharacteristic
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—101no—
597C22⋊C4—101no—
598C22⋊C4—101no—
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C42—21no—
603C42—101no—
604C42—101no—
605C42—101no—
606C3×C5C2×#48511yescharacteristic, complemented, Hall
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—52no—
611C22×C3—52no—
612C22×C3—52no—
613C22×C3—101no—
614C22×C3—101no—
615C22×C3—101no—
616C22×C3—204no—
617C22×C3C2×D4×D511yescharacteristic
618C3×C4—21no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—52no—
624C3×C4—101no—
625C3×C4—201no—
626C3×C4—201no—
627C3×C4—201no—
628C3×C4—201no—
629C3×C4D5×#4111yescharacteristic
630C3×C4D5×#4111yescharacteristic
631C2×C5—41no—
632C2×C5C2×C3×#12311yescharacteristic
633C2×C5C2×C3×#13511yescharacteristic
634C2×C5C2×C3×#13711yescharacteristic
635D5—41no—
636D5C3×#48514yesdirect product factor
637C23—51no—
638C23—51no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23C3×D4×D511yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—101no—
646Q8—101no—
647Q8—202no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—51no—
655C2×C4—52no—
656C2×C4—52no—
657C2×C4—51no—
658C2×C4—102no—
659C2×C4—102no—
660C2×C4—102no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—202no—
668C2×C4—202no—
669C2×C4—202no—
670C2×C4—202no—
671C2×C4C3×D4×D511yescharacteristic
672C2×C4C23×C3×D511yescharacteristic
673C8—21no—
674C8—21no—
675C8—101no—
676C8—101no—
677C2×C3—41no—
678C2×C3—54no—
679C2×C3—201no—
680C2×C3D5×#12311yescharacteristic
681C2×C3D5×#13511yescharacteristic
682C2×C3D5×#13711yescharacteristic
683C5C2×C3×#48511yescharacteristic, complemented, Sylow
684C22—21no—
685C22—21no—
686C22—21no—
687C22—52no—
688C22—52no—
689C22—52no—
690C22—101no—
691C22—101no—
692C22—101no—
693C22—204no—
694C22C2×C3×D4×D511yescharacteristic
695C4—21no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—52no—
701C4—101no—
702C4—201no—
703C4—201no—
704C4—201no—
705C4—201no—
706C4C3×D5×#4111yescharacteristic
707C4C3×D5×#4111yescharacteristic
708C3D5×#48511yescharacteristic, direct product factor, Sylow
709C2—41no—
710C2—54no—
711C2—201no—
712C2C3×D5×#12311yescharacteristic
713C2C3×D5×#13511yescharacteristic
714C2C3×D5×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#485C2
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
hypercenterC3×#485D5
hypocenterC5C2×C3×#485
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
3. C3×C5×#485C2semidirect
4. C3×#65334C2semidirect
5. C3×#65285C2semidirect
6. C3×#65177C2semidirect
7. C3×D5×#107C2semidirect
8. C3×#65156C2semidirect
9. C3×D5×#106C2semidirect
10. C3×#65104C2semidirect
11. C3×#65103C2semidirect
12. C3×D5×#103C2semidirect
13. C3×D5×#103C2semidirect
15. C3×#65012C2semidirect
16. D5×#485C3direct (N × H)
40. C3×C5×#107C22semidirect
41. C3×C5×#106C22semidirect
42. C3×C5×#103C22semidirect
43. C3×C5×#103C22semidirect
45. C3×#3967C22semidirect
46. C3×#3967C22semidirect
50. C3×#3950C22semidirect
51. C3×#3949C22semidirect
52. C3×#3948C22semidirect
53. C3×#3948C22semidirect
54. C3×#3942C22semidirect
55. C3×#3942C22semidirect
56. C3×#3940C22semidirect
57. C3×#3940C22semidirect
58. C3×#3939C22semidirect
59. C3×#3939C22semidirect
63. C5×#485C2×C3semidirect
64. #65334C2×C3semidirect
65. #65285C2×C3semidirect
66. #65177C2×C3semidirect
67. D5×#107C2×C3semidirect
68. #65156C2×C3semidirect
69. D5×#106C2×C3semidirect
70. #65104C2×C3semidirect
71. #65103C2×C3semidirect
72. D5×#103C2×C3semidirect
73. D5×#103C2×C3semidirect
75. #65012C2×C3semidirect
134. C3×#485D5direct (N × H)
163. C5×#107C22×C3semidirect
164. C5×#106C22×C3semidirect
165. C5×#103C22×C3semidirect
166. C5×#103C22×C3semidirect
168. #3967C22×C3semidirect
169. #3967C22×C3semidirect
173. #3950C22×C3semidirect
174. #3949C22×C3semidirect
175. #3948C22×C3semidirect
176. #3948C22×C3semidirect
177. #3942C22×C3semidirect
178. #3942C22×C3semidirect
179. #3940C22×C3semidirect
180. #3940C22×C3semidirect
181. #3939C22×C3semidirect
182. #3939C22×C3semidirect
250. C3×#107C2×D5semidirect
254. C3×#106C2×D5semidirect
261. C3×#103C2×D5semidirect
262. C3×#103C2×D5semidirect
325. #485C3×D5direct (N × H)
470. #107C2×C3×D5semidirect
474. #106C2×C3×D5semidirect
481. #103C2×C3×D5semidirect
482. #103C2×C3×D5semidirect
492. C3×D5#485direct (N × H)
606. C3×C5C2×#485semidirect
636. D5C3×#485direct (N × H)
683. C5C2×C3×#485semidirect
708. C3D5×#485direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C22⋊Q82
C3×D5×#1172
C3×C5×#4852
C3×#653342
C3×#652852
C3×#651772
C3×D5×#1072
C3×#651562
C3×D5×#1062
C3×#651042
C3×#651032
C3×D5×#1032
C3×D5×C22⋊C82
C3×#650122
D5×#4853
C2×C3×#4855