Finite Group Databasebeta

← D5×#4945 #14320518

Subgroups — D5×#4945 #14320518

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2C2×D5×#217C211yesmaximal, characteristic
3C2×D5×#217C211yesmaximal, characteristic
4C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
6#11751046C211yesmaximal, characteristic, complemented
7C5×#4945C211yesmaximal, characteristic, complemented
8#11749480C211yesmaximal, characteristic, complemented
9#11749479C211yesmaximal, characteristic, complemented
10D5×C3⋊#95C211yesmaximal, characteristic, complemented
11D5×C3⋊#95C211yesmaximal, characteristic, complemented
12#11748712C211yesmaximal, characteristic, complemented
13#11748709C211yesmaximal, characteristic, complemented
14#11748708C211yesmaximal, characteristic, complemented
15#11748706C211yesmaximal, characteristic, complemented
16D5×#388—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6712C2211yescharacteristic, complemented
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C5×#217C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C3×D5×C22⋊C4—24no—
37D5×#217—24no—
38D5×#217C418yescomplemented
39C2×Dic3⋊Dic5C2211yescharacteristic, complemented
40C2×#6669C2211yescharacteristic, complemented
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47D5×Dic3⋊C4—24no—
48C4×D5×Dic3—24no—
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C5×C3⋊#95C2211yescharacteristic, complemented
52C5×C3⋊#95C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57C2×#4945—51nomaximal, Hall
58C2×D5×C4⋊C4—31no—
59C2×D5×C22⋊C4—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4D311yescharacteristic
62C2×C42×D5—31no—
63C5×#388—31no—
64#65279—31no—
65#65240—31no—
66#65234—31no—
67#65233—31no—
68#65229—31no—
69#64959—31no—
70#64958—31no—
71D5×#95—31no—
72D5×#95—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5C2×C414yes—
81C23×C3×D5C2311yescharacteristic
82C23×C3×D5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5D414yes—
101C2×D5×Dic3—22no—
102C2×D5×Dic3—22no—
103C2×D5×Dic3—22no—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3—22no—
108C2×D5×Dic3—22no—
109C2×D5×Dic3—22no—
110C2×D5×Dic3C2×C414yes—
111C2×D5×Dic3C2×C414yes—
112C2×D5×Dic3D414yes—
113C3×C5×C22⋊C4—22no—
114#6719—22no—
115#6719C2×C414yescomplemented
116#6712—22no—
117C4×Dic15—22no—
118C5×#217—22no—
119C5×#217C2×C414yescomplemented
120C5×Dic3⋊C4—22no—
121C4×C5×Dic3—22no—
122C3×C22⋊Dic5—22no—
123C3×#685—22no—
124C3×#685—22no—
125Dic3⋊Dic5—22no—
126#6669—22no—
127#6665—22no—
128#6665—22no—
129#6665C2×C414yescomplemented
130#6665C2×C414yescomplemented
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C22×C3×C22⋊C4—51no—
134C22×#217—51no—
135C22×#217—51no—
136C22×Dic3⋊C4—51no—
137C22×C4×Dic3—51no—
138C2×C3⋊#95—51no—
139C2×C3⋊#95—51no—
140#4945—51no—
141#4945—51no—
142#4945—51no—
143#4945—51no—
144#4945—51no—
145#4945—51no—
146#4945—51no—
147#4945D511yescharacteristic, direct product factor
148C24×D5C2×D311yescharacteristic
149C22×C4×D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C22×C4×D5C2×D311yescharacteristic
154C22×C4×D5C2×D311yescharacteristic
155C2×C5×C4⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5C2×D311yescharacteristic
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685C2×D311yescharacteristic
168C2×#685C2×D311yescharacteristic
169C2×C4⋊Dic5—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175D5×C4⋊C4—64no—
176D5×C22⋊C4—24no—
177D5×C22⋊C4—38no—
178D5×C22⋊C4—64no—
179C42×D5—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188C2×#388—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5C22×C412yes—
196C23×C3×C5C2411yescharacteristic
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—28no—
204C22×C3×D5—28no—
205C22×C3×D5—28no—
206C22×C3×D5—44no—
207C22×C3×D5—44no—
208C22×C3×D5—44no—
209C22×C3×D5—44no—
210C22×C3×D5C22×C412yes—
211C22×C3×D5C22×C412yes—
212C22×C3×D5C2×D412yes—
213C22×C3×D5C2×D412yes—
214C22×C3×D5#4112yes—
215C22×C3×D5#4112yes—
216C22×C3×D5#4112yes—
217C22×C3×D5#4112yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15C22×C412yes—
234C2×Dic15C22×C412yes—
235C2×Dic15C2×D412yes—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3C22×C412yes—
246C2×C5×Dic3C22×C412yes—
247C2×C5×Dic3C2×D412yes—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5C2×D412yes—
254C3×C4×D5—28no—
255C3×C4×D5—44no—
256D5×Dic3—28no—
257D5×Dic3—28no—
258D5×Dic3—28no—
259D5×Dic3—44no—
260C25×C3—51no—
261C23×C3×C4—51no—
262C23×C3×C4—51no—
263C23×Dic3—51no—
264C23×Dic3—51no—
265C23×Dic3—51no—
266C23×Dic3—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—104no—
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—58no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217—51no—
279C2×#217—104no—
280C2×#217C2×D511yescharacteristic
281C2×#217C2×D511yescharacteristic
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4—104no—
286C2×Dic3⋊C4C2×D511yescharacteristic, complemented
287C2×C4×Dic3—51no—
288C2×C4×Dic3—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3—104no—
291C2×C4×Dic3C2×D511yescharacteristic, complemented
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic, complemented
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5C22×D311yescharacteristic
301C23×D5—22no—
302C23×D5—22no—
303C23×D5—22no—
304C23×D5—22no—
305C23×D5—22no—
306C23×D5—22no—
307C23×D5C4×D314yes—
308C23×D5C22×D311yescharacteristic
309C23×D5C22×D311yescharacteristic
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5—31no—
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×C4×D5—22no—
323C2×C4×D5—22no—
324C2×C4×D5—22no—
325C2×C4×D5—22no—
326C2×C4×D5—22no—
327C2×C4×D5—34no—
328C2×C4×D5—34no—
329C2×C4×D5—34no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—62no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—62no—
339C2×C4×D5#6714yes—
340C5×C4⋊C4—62no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—34no—
343C5×C22⋊C4—62no—
344C42×C5—62no—
345C22⋊Dic5—22no—
346C22⋊Dic5—34no—
347C22⋊Dic5—62no—
348#685—22no—
349#685—22no—
350#685—34no—
351#685—34no—
352#685—62no—
353#685—62no—
354C4⋊Dic5—62no—
355#683—62no—
356#683—62no—
357C4×Dic5—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×C4⋊C4—151no—
361C22×C22⋊C4—51no—
362C22×C22⋊C4—151no—
363C22×C22⋊C4—151no—
364C22×C42—151no—
365#388—31no—
366#388—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#388—151no—
372#388—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5C23×C411yescharacteristic
383C22×C3×C5C22×D411yescharacteristic
384C22×C3×C5C22×D411yescharacteristic
385C22×C3×C5C2×#4111yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—416no—
397C2×C3×D5#11714yes—
398C2×C3×D5C4×D414yes—
399C2×C3×D5C4×D414yes—
400C2×C3×D5#12114yes—
401C2×C3×D5#12314yes—
402C2×C3×D5#12414yes—
403C2×C3×D5#12614yes—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—22no—
408Dic15—22no—
409Dic15—41no—
410C3×Dic5—22no—
411C3×Dic5—41no—
412C5×Dic3—22no—
413C5×Dic3—22no—
414C5×Dic3—22no—
415C5×Dic3—41no—
416C24×C3—51no—
417C24×C3—54no—
418C24×C3—51no—
419C24×C3—102no—
420C24×C3—102no—
421C24×C3—102no—
422C24×C3—102no—
423C24×C3—102no—
424C24×C3—102no—
425C24×C3C22×D511yescharacteristic
426C22×C3×C4—51no—
427C22×C3×C4—54no—
428C22×C3×C4—51no—
429C22×C3×C4—102no—
430C22×C3×C4—102no—
431C22×C3×C4—102no—
432C22×C3×C4—102no—
433C22×C3×C4—102no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×Dic3—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3—54no—
440C22×Dic3—54no—
441C22×Dic3—54no—
442C22×Dic3—51no—
443C22×Dic3—102no—
444C22×Dic3—102no—
445C22×Dic3—102no—
446C22×Dic3—102no—
447C22×Dic3—102no—
448C22×Dic3—102no—
449C22×Dic3—102no—
450C22×Dic3—102no—
451C22×Dic3—102no—
452C22×Dic3C22×D511yescharacteristic
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C3×C22⋊C4—22no—
457C3×C22⋊C4—102no—
458C3×C22⋊C4—102no—
459C3×C22⋊C4—102no—
460#217—22no—
461#217—54no—
462#217—54no—
463#217—54no—
464#217—102no—
465#217—102no—
466#217—102no—
467#217C4×D514yescomplemented
468Dic3⋊C4—22no—
469Dic3⋊C4—102no—
470Dic3⋊C4—102no—
471Dic3⋊C4—102no—
472C4×Dic3—22no—
473C4×Dic3—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5C2×C4×D312yes—
483C23×C5C23×D311yescharacteristic
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—28no—
491C22×D5—28no—
492C22×D5—28no—
493C22×D5—44no—
494C22×D5—44no—
495C22×D5—44no—
496C22×D5—44no—
497C22×D5C2×C4×D312yes—
498C22×D5C2×C4×D312yes—
499C22×D5#23512yes—
500C22×D5D3×D412yes—
501C22×D5#23712yes—
502C22×D5#23712yes—
503C22×D5#23712yes—
504C22×D5C2×#6712yes—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5—61no—
522C2×C4×C5C2×#6712yes—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—32no—
529C2×Dic5—32no—
530C2×Dic5—32no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5C2×#6712yes—
541C4×D5—28no—
542C4×D5—44no—
543C4×D5—68no—
544C4×D5—68no—
545C4×D5—68no—
546C4×D5—124no—
547C25—51no—
548C23×C4—51no—
549C23×C4—51no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553C23×C4—151no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—151no—
556C2×C4⋊C4—151no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—304no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—104no—
565C2×C22⋊C4—158no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C22⋊C4—151no—
572C2×C22⋊C4—304no—
573C2×C22⋊C4D3×D511yescharacteristic
574C2×C42—31no—
575C2×C42—151no—
576C2×C42—151no—
577C2×C42—151no—
578C2×C42—304no—
579#95—31no—
580#95—31no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95—151no—
585#95—151no—
586#95—151no—
587C2×C3×C5—42no—
588C2×C3×C5C2×#11711yescharacteristic
589C2×C3×C5C2×C4×D411yescharacteristic
590C2×C3×C5C2×C4×D411yescharacteristic
591C2×C3×C5C2×#12111yescharacteristic
592C2×C3×C5C2×#12311yescharacteristic
593C2×C3×C5C2×#12411yescharacteristic
594C2×C3×C5C2×#12611yescharacteristic
595C3×D5—42no—
596C3×D5#38818yescomplemented
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—52no—
604C23×C3—52no—
605C23×C3—52no—
606C23×C3—52no—
607C23×C3—52no—
608C23×C3—52no—
609C23×C3—52no—
610C23×C3—52no—
611C23×C3—108no—
612C23×C3—108no—
613C23×C3—108no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3—101no—
617C23×C3—101no—
618C23×C3—101no—
619C23×C3—101no—
620C23×C3—204no—
621C23×C3—204no—
622C23×C3—204no—
623C23×C3—204no—
624C23×C3C2×C4×D512yes—
625C23×C3C23×D511yescharacteristic
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—52no—
632C2×C3×C4—108no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—204no—
639C2×C3×C4D4×D512yes—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—52no—
650C2×Dic3—52no—
651C2×Dic3—52no—
652C2×Dic3—108no—
653C2×Dic3—108no—
654C2×Dic3—108no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—204no—
665C2×Dic3C2×C4×D512yes—
666C2×Dic3C2×C4×D512yes—
667C2×Dic3D4×D512yes—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—41no—
672C22×C5—41no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5C22×C4×D311yescharacteristic
676C22×C5C2×#23511yescharacteristic
677C22×C5C2×D3×D411yescharacteristic
678C22×C5C2×#23711yescharacteristic
679C22×C5C2×#23711yescharacteristic
680C22×C5C2×#23711yescharacteristic
681C22×C5C22×#6711yescharacteristic
682C2×D5—22no—
683C2×D5—22no—
684C2×D5—22no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—41no—
688C2×D5—41no—
689C2×D5—416no—
690C2×D5#87714yes—
691C2×D5#87914yes—
692C2×D5#67⋊C414yes—
693C2×D5#88314yes—
694C2×D5C4×#6714yes—
695C2×D5#93614yes—
696C2×D5#93914yes—
697C4×C5—22no—
698C4×C5—41no—
699C4×C5—62no—
700C4×C5—62no—
701C4×C5—62no—
702C4×C5—121no—
703Dic5—22no—
704Dic5—41no—
705Dic5—62no—
706Dic5—62no—
707Dic5—62no—
708Dic5—121no—
709C24—51no—
710C24—54no—
711C24—51no—
712C24—102no—
713C24—102no—
714C24—102no—
715C24—102no—
716C24—102no—
717C24—102no—
718C24C2×D3×D511yescharacteristic
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—51no—
724C22×C4—54no—
725C22×C4—51no—
726C22×C4—102no—
727C22×C4—102no—
728C22×C4—102no—
729C22×C4—102no—
730C22×C4—102no—
731C22×C4—154no—
732C22×C4—154no—
733C22×C4—154no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4C2×D3×D511yescharacteristic
748C22×C4C2×D3×D511yescharacteristic
749C4⋊C4—62no—
750C4⋊C4—302no—
751C4⋊C4—302no—
752C4⋊C4—302no—
753C22⋊C4—22no—
754C22⋊C4—34no—
755C22⋊C4—62no—
756C22⋊C4—102no—
757C22⋊C4—102no—
758C22⋊C4—102no—
759C22⋊C4—154no—
760C22⋊C4—154no—
761C22⋊C4—154no—
762C22⋊C4—302no—
763C22⋊C4—302no—
764C22⋊C4—302no—
765C42—62no—
766C42—302no—
767C42—302no—
768C42—302no—
769C3×C5C2×#38811yescharacteristic, complemented, Hall
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—54no—
778C22×C3—54no—
779C22×C3—54no—
780C22×C3—54no—
781C22×C3—54no—
782C22×C3—54no—
783C22×C3—54no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—2016no—
788C22×C3—201no—
789C22×C3—201no—
790C22×C3—201no—
791C22×C3—201no—
792C22×C3C22×C4×D511yescharacteristic
793C22×C3C2×D4×D511yescharacteristic
794C22×C3C2×D4×D511yescharacteristic
795C22×C3D5×#4111yescharacteristic
796C22×C3D5×#4111yescharacteristic
797C22×C3D5×#4111yescharacteristic
798C22×C3D5×#4111yescharacteristic
799C3×C4—22no—
800C3×C4—41no—
801C3×C4—102no—
802C3×C4—201no—
803Dic3—22no—
804Dic3—22no—
805Dic3—22no—
806Dic3—41no—
807Dic3—102no—
808Dic3—102no—
809Dic3—102no—
810Dic3—201no—
811C2×C5—42no—
812C2×C5C2×#87711yescharacteristic
813C2×C5C2×#87911yescharacteristic
814C2×C5C2×#67⋊C411yescharacteristic
815C2×C5C2×#88311yescharacteristic
816C2×C5C2×C4×#6711yescharacteristic
817C2×C5C2×#93611yescharacteristic
818C2×C5C2×#93911yescharacteristic
819D5—42no—
820D5#494518yesdirect product factor
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—52no—
828C23—52no—
829C23—52no—
830C23—52no—
831C23—52no—
832C23—52no—
833C23—52no—
834C23—52no—
835C23—108no—
836C23—108no—
837C23—108no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—204no—
845C23—204no—
846C23—204no—
847C23—204no—
848C23C4×D3×D512yes—
849C23C22×D3×D511yescharacteristic
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—52no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—108no—
869C2×C4—101no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—152no—
875C2×C4—152no—
876C2×C4—152no—
877C2×C4—204no—
878C2×C4—308no—
879C2×C4—308no—
880C2×C4—308no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—604no—
891C2×C4D5×#6712yes—
892C2×C3—42no—
893C2×C3—58no—
894C2×C3—202no—
895C2×C3D5×#11711yescharacteristic
896C2×C3C4×D4×D511yescharacteristic
897C2×C3C4×D4×D511yescharacteristic
898C2×C3D5×#12111yescharacteristic
899C2×C3D5×#12311yescharacteristic
900C2×C3D5×#12411yescharacteristic
901C2×C3D5×#12611yescharacteristic
902C5C2×#494511yescharacteristic, complemented, Sylow
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—54no—
911C22—54no—
912C22—54no—
913C22—54no—
914C22—54no—
915C22—54no—
916C22—54no—
917C22—102no—
918C22—102no—
919C22—102no—
920C22—2016no—
921C22—201no—
922C22—201no—
923C22—201no—
924C22—201no—
925C22C2×C4×D3×D511yescharacteristic
926C22D5×#23511yescharacteristic
927C22D3×D4×D511yescharacteristic
928C22D5×#23711yescharacteristic
929C22D5×#23711yescharacteristic
930C22D5×#23711yescharacteristic
931C22C2×D5×#6711yescharacteristic
932C4—22no—
933C4—41no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—102no—
938C4—121no—
939C4—201no—
940C4—302no—
941C4—302no—
942C4—302no—
943C4—601no—
944C3D5×#38811yescharacteristic, complemented, Sylow
945C2—42no—
946C2—58no—
947C2—202no—
948C2D5×#87711yescharacteristic
949C2D5×#87911yescharacteristic
950C2D5×#67⋊C411yescharacteristic
951C2D5×#88311yescharacteristic
952C2C4×D5×#6711yescharacteristic
953C2D5×#93611yescharacteristic
954C2D5×#93911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×D5×Dic3⋊C4C2semidirect
5. C2×C4×D5×Dic3C2semidirect
6. #11751046C2semidirect
7. C5×#4945C2semidirect
8. #11749480C2semidirect
9. #11749479C2semidirect
10. D5×C3⋊#95C2semidirect
11. D5×C3⋊#95C2semidirect
12. #11748712C2semidirect
13. #11748709C2semidirect
14. #11748708C2semidirect
15. #11748706C2semidirect
27. C2×#6712C22semidirect
28. C2×C4×Dic15C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
32. C2×C4×C5×Dic3C22semidirect
38. D5×#217C4semidirect
39. C2×Dic3⋊Dic5C22semidirect
40. C2×#6669C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. C5×C3⋊#95C22semidirect
52. C5×C3⋊#95C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
115. #6719C2×C4semidirect
119. C5×#217C2×C4semidirect
129. #6665C2×C4semidirect
130. #6665C2×C4semidirect
147. #4945D5direct (N × H)
286. C2×Dic3⋊C4C2×D5semidirect
291. C2×C4×Dic3C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
467. #217C4×D5semidirect
596. C3×D5#388semidirect
769. C3×C5C2×#388semidirect
820. D5#4945direct (N × H)
902. C5C2×#4945semidirect
944. C3D5×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C2×D5×#2172
C2×D5×Dic3⋊C42
C2×C4×D5×Dic32
#117510462
C5×#49452
#117494802
#117494792
D5×C3⋊#952
#117487122
#117487092
#117487082
#117487062
D5×#3883
C2×#49455