Finite Group Databasebeta

← D5×#4774 #14431419

Subgroups — D5×#4774 #14431419

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#938C211yesmaximal, characteristic
2D3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3#11750875C211yesmaximal, characteristic, complemented
4C5×#4774C211yesmaximal, characteristic, complemented
5C3×D5×#102C211yesmaximal, characteristic, complemented
6#11748958C211yesmaximal, characteristic, complemented
7#11748954C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic, complemented
9D5×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
10#11747916C211yesmaximal, characteristic, complemented
11D5×#818C211yesmaximal, characteristic, complemented
12#11747571C211yesmaximal, characteristic, complemented
13D5×#807C211yesmaximal, characteristic, complemented
14#11747330C211yesmaximal, characteristic, complemented
15#11747318C211yesmaximal, characteristic, complemented
16D5×#480—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×D5×#67—21no—
19C2×C4×D3×D5—21no—
20C2×C4×D3×D5C2211yescharacteristic
21#91827C2211yescharacteristic
22C4⋊C4×D15C2211yescharacteristic, complemented
23C5×#938C2211yescharacteristic
24C5×D3×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C8×D5C2211yescharacteristic
26C3×D5×C4⋊C4C2211yescharacteristic
27#91565—21no—
28D5×#217—21no—
29#91533—21no—
30#91465C2211yescharacteristic
31#91456C2211yescharacteristic
32#91437C2211yescharacteristic, complemented
33D3×C4⋊Dic5C2211yescharacteristic, complemented
34D5×C4⋊Dic3C2211yescharacteristic
35D5×C4⋊Dic3C2211yescharacteristic
36#91404—21no—
37D3×#683—21no—
38D5×Dic3⋊C4—21no—
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#102C2211yescharacteristic, complemented
41#91116C2211yescharacteristic, complemented
42#91104C2211yescharacteristic, complemented
43#91102C2211yescharacteristic, complemented
44#91091C2211yescharacteristic, complemented
45C5×#832C2211yescharacteristic, complemented
46C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C5×#818C2211yescharacteristic, complemented
48C5×#807C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic, complemented
50C3×#3953C2211yescharacteristic, complemented
51C3×#3941C2211yescharacteristic, complemented
52#90990C2211yescharacteristic, complemented
53#90989C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90965C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58#90957C2211yescharacteristic, complemented
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60C2×#4774—51nomaximal, Hall
61D5×#121—31no—
62C2×D5×C4⋊C4—31no—
63C5×#480—31no—
64#65322—31no—
65#65256—31no—
66#65171—31no—
67#65171—31no—
68D5×#107—31no—
69D5×#107—31no—
70#65063—31no—
71#65063—31no—
72D5×#102—31no—
73D5×#102D311yescharacteristic, complemented
74#65025—31no—
75D5×C22⋊C8—31no—
76C23×C3×D5—21no—
77C22×D3×D5D411yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C2×#1220—21no—
80C2×C4×D15—21no—
81C2×C4×D15C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C3×D4×D5—22no—
87C3×D4×D5—22no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91D5×#67—44no—
92C2×#1202—21no—
93C2×#1201—21no—
94C2×#1200—21no—
95C2×#1200D411yescharacteristic
96C2×D3×Dic5—21no—
97C2×D3×Dic5D411yescharacteristic
98C2×D5×Dic3—21no—
99C2×D5×Dic3—21no—
100C2×D5×Dic3D411yescharacteristic
101C4×D3×D5—22no—
102C4×D3×D5—22no—
103C4×D3×D5—44no—
104C2×C3×C5×C8C2311yescharacteristic
105C3×C5×C4⋊C4C2311yescharacteristic
106#6719—21no—
107C4⋊Dic15C2311yescharacteristic
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110C2×C3⋊#168C2311yescharacteristic
111C5×#217—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×Dic3⋊C4—21no—
115C2×C5×C3⋊C8C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C2×C3×#168C2311yescharacteristic
119C3×C8×D5—22no—
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123#6668—21no—
124#6665—21no—
125#6665—21no—
126D5×C3⋊C8—22no—
127C2×#938—51no—
128C2×D3×C4⋊C4—51no—
129C2×C3×#102—51no—
130C2×#832—51no—
131C2×(C2×D3)⋊C8—51no—
132C2×#818—51no—
133C2×#807—51no—
134#4774—51no—
135#4774—51no—
136#4774—51no—
137#4774—51no—
138#4774—51no—
139#4774—51no—
140#4774—51no—
141#4774D511yescharacteristic, direct product factor
142C2×D4×D5—61no—
143C2×D4×D5C2×D311yescharacteristic
144C22×C4×D5—31no—
145C22×C4×D5—61no—
146C5×#121—31no—
147C2×C5×C4⋊C4—31no—
148#4085—61no—
149#4084—31no—
150#4076—31no—
151C2×C4⋊Dic5—31no—
152C2×#683—61no—
153C2×C8×D5—31no—
154C2×C8×D5C2×D311yescharacteristic
155#4041—31no—
156D5×C4⋊C4—31no—
157D5×C4⋊C4—31no—
158D5×C4⋊C4—31no—
159D5×C4⋊C4—31no—
160D5×C4⋊C4—61no—
161D5×C4⋊C4—61no—
162D5×C4⋊C4C2×D311yescharacteristic
163#4030—61no—
164D5×C22⋊C4—61no—
165C5×#107—31no—
166C5×#107—31no—
167C5×#102—31no—
168C5×#102C2×D311yescharacteristic, complemented
169C5×C22⋊C8—31no—
170#3964—31no—
171#3964C2×D311yescharacteristic, complemented
172C22⋊#168—31no—
173#3953—31no—
174#3953C2×D311yescharacteristic, complemented
175#3952—31no—
176#3952—31no—
177#3950—31no—
178#3950—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic, complemented
181#3939—31no—
182#3939—31no—
183#3939—31no—
184#3939—31no—
185C2×#480—151noSylow
186C23×C3×C5—21no—
187C22×D15C2×D411yescharacteristic
188C22×C5×D3C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—42no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5C2×D411yescharacteristic
194C2×D3×D5—22no—
195C2×D3×D5—22no—
196C2×D3×D5D814yes—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201#1220—42no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15C2×D411yescharacteristic
205C4×D15—21no—
206C4×D15—21no—
207C4×D15—42no—
208C5×#67—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—21no—
213C4×C5×D3—21no—
214C4×C5×D3—42no—
215C3×C22⋊D5—42no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5C2×D411yescharacteristic
218C3×D20—21no—
219C3×D20—21no—
220C3×C4×D5—42no—
221C3×C4×D5#4112yes—
222C3×C4×D5#4112yes—
223#1202—42no—
224#1201—42no—
225#1200—22no—
226#1200—42no—
227D3×Dic5—22no—
228D3×Dic5—42no—
229D5×Dic3—22no—
230D5×Dic3—42no—
231D5×Dic3—42no—
232C3×C5×C8—21no—
233C3⋊#168—21no—
234C3×#168—21no—
235C5×C3⋊C8—21no—
236C22×C3×D4—51no—
237C22×#67—101no—
238C22×C4×D3—51no—
239C22×C4×D3—101no—
240C22×C3×C8—51no—
241C2×C3×C4⋊C4—51no—
242C2×#217—101no—
243#938—51no—
244#938—51no—
245#938—51no—
246#938—101no—
247#938—101no—
248#938C2×D511yescharacteristic
249C2×C4⋊Dic3—51no—
250C2×C4⋊Dic3—51no—
251C2×Dic3⋊C4—101no—
252C22×C3⋊C8—51no—
253D3×C4⋊C4—51no—
254D3×C4⋊C4—51no—
255D3×C4⋊C4—51no—
256D3×C4⋊C4—101no—
257D3×C4⋊C4—101no—
258D3×C4⋊C4C2×D511yescharacteristic, complemented
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic, complemented
263#832—51no—
264#832—51no—
265#832—51no—
266#832C2×D511yescharacteristic, complemented
267(C2×D3)⋊C8—51no—
268(C2×D3)⋊C8—51no—
269(C2×D3)⋊C8—51no—
270(C2×D3)⋊C8C2×D511yescharacteristic, complemented
271#818—51no—
272#818—51no—
273#818—51no—
274#818C2×D511yescharacteristic, complemented
275#807—51no—
276#807—51no—
277#807—51no—
278#807C2×D511yescharacteristic, complemented
279C23×D5—21no—
280C23×D5—31no—
281C2×C5×D4—61no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—31no—
284C22×C4×C5—61no—
285C2×C22⋊D5—21no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C22×Dic5—31no—
289C22×Dic5—61no—
290D4×D5—22no—
291D4×D5—22no—
292D4×D5—124no—
293C2×D20—61no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—21no—
296C2×C4×D5—31no—
297C2×C4×D5—31no—
298C2×C4×D5—31no—
299C2×C4×D5—62no—
300C2×C4×D5—62no—
301C2×C4×D5—61no—
302C2×C4×D5—61no—
303C2×C4×D5—61no—
304C2×C4×D5—61no—
305C2×C4×D5—124no—
306C2×C4×D5C22×D311yescharacteristic
307C2×C5×C8—31no—
308C2×C5×C8C22×D311yescharacteristic
309C5×C4⋊C4—31no—
310C5×C4⋊C4—31no—
311C5×C4⋊C4—61no—
312C5×C4⋊C4C22×D311yescharacteristic
313C5×C22⋊C4—61no—
314C22⋊Dic5—61no—
315#685—61no—
316#685—61no—
317C4⋊Dic5—31no—
318C4⋊Dic5—31no—
319C4⋊Dic5—61no—
320C4⋊Dic5C22×D311yescharacteristic
321#683—21no—
322#683—61no—
323#683—61no—
324#683—61no—
325#683—61no—
326C2×#168—31no—
327C2×#168C22×D311yescharacteristic
328C8×D5—22no—
329C8×D5—62no—
330C2×#121—151no—
331C22×C4⋊C4—151no—
332#480—31no—
333#480—151no—
334#480—151no—
335#480—151no—
336#480—151no—
337#480—151no—
338#480—151no—
339#480—151no—
340C2×#107—151no—
341C2×#107—151no—
342C2×#102—51no—
343C2×#102—151no—
344C2×C22⋊C8—151no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—21no—
350C2×D15—21no—
351C2×D15C2×D812yes—
352C2×C5×D3—21no—
353C2×C5×D3—21no—
354C2×C5×D3C2×D812yes—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C2×C3×D5—84no—
359C2×C3×D5#12312yes—
360C2×C3×D5C2×D812yes—
361C2×C3×D5#13712yes—
362D3×D5—28no—
363C3×C4×C5—41no—
364C3×C4×C5C2×#4111yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—21no—
367Dic15—41no—
368Dic15—41no—
369C3×Dic5—41no—
370C3×Dic5#12312yes—
371C5×Dic3—21no—
372C5×Dic3—41no—
373C5×Dic3—41no—
374C24×C3—101no—
375C23×D3—51no—
376C2×C3×D4—51no—
377C2×C3×D4—102no—
378C2×C3×D4—102no—
379C2×C3×D4—101no—
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4—51no—
382C22×C3×C4—101no—
383C2×#67—21no—
384C2×#67—101no—
385C2×#67—101no—
386C2×#67—101no—
387C2×#67—204no—
388C22×Dic3—51no—
389C22×Dic3—101no—
390C22×Dic3—101no—
391C2×C4×D3—21no—
392C2×C4×D3—51no—
393C2×C4×D3—51no—
394C2×C4×D3—51no—
395C2×C4×D3—102no—
396C2×C4×D3—102no—
397C2×C4×D3—101no—
398C2×C4×D3—101no—
399C2×C4×D3—101no—
400C2×C4×D3—204no—
401C2×C4×D3C22×D511yescharacteristic
402C2×C3×C8—51no—
403C2×C3×C8—102no—
404C2×C3×C8C22×D511yescharacteristic
405C3×C4⋊C4—51no—
406C3×C4⋊C4—101no—
407C3×C4⋊C4C22×D511yescharacteristic
408#217—21no—
409#217—101no—
410#217—101no—
411#217—101no—
412C4⋊Dic3—51no—
413C4⋊Dic3—51no—
414C4⋊Dic3—101no—
415C4⋊Dic3—101no—
416C4⋊Dic3C22×D511yescharacteristic
417C4⋊Dic3C22×D511yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—101no—
420Dic3⋊C4—101no—
421Dic3⋊C4—101no—
422C2×C3⋊C8—51no—
423C2×C3⋊C8—102no—
424C2×C3⋊C8C22×D511yescharacteristic
425C23×C5—21no—
426C23×C5—31no—
427C22×D5—21no—
428C22×D5—31no—
429C22×D5—34no—
430C22×D5—42no—
431C22×D5—42no—
432C22×D5—42no—
433C22×D5—62no—
434C22×D5—62no—
435C22×D5D3×D411yescharacteristic
436C5×D4—21no—
437C5×D4—21no—
438C5×D4—122no—
439C2×C4×C5—21no—
440C2×C4×C5—31no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—122no—
446C2×C4×C5C23×D311yescharacteristic
447C22⋊D5—42no—
448C22⋊D5—122no—
449C22⋊D5—122no—
450C2×Dic5—21no—
451C2×Dic5—31no—
452C2×Dic5—62no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—122no—
456C2×Dic5D3×D411yescharacteristic
457D20—21no—
458D20—21no—
459D20—122no—
460C4×D5—42no—
461C4×D5—62no—
462C4×D5—61no—
463C4×D5—61no—
464C4×D5—62no—
465C4×D5—122no—
466C4×D5—122no—
467C4×D5—122no—
468C4×D5—122no—
469C4×D5#23512yes—
470C4×D5#23712yes—
471C5×C8—21no—
472C5×C8—61no—
473#168—21no—
474#168—61no—
475C22×D4—51no—
476C22×D4—301no—
477C23×C4—151no—
478C23×C4—301no—
479C22×C8—51no—
480C22×C8—151no—
481#121—31no—
482#121—151no—
483#121—151no—
484#121—151no—
485#121—301no—
486#121—301no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—301no—
495C2×C4⋊C4—301no—
496C2×C4⋊C4—301no—
497C2×C22⋊C4—301no—
498#107—31no—
499#107—31no—
500#107—151no—
501#107—151no—
502#107—151no—
503#107—151no—
504#107—151no—
505#107—151no—
506#102—31no—
507#102—51no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102D3×D511yescharacteristic, complemented
514C22⋊C8—31no—
515C22⋊C8—151no—
516C22⋊C8—151no—
517C22⋊C8—151no—
518C2×C3×C5—81no—
519C2×C3×C5C2×#12311yescharacteristic
520C2×C3×C5C22×D811yescharacteristic
521C2×C3×C5C2×#13711yescharacteristic
522D15—22no—
523C3×D5—81no—
524C3×D5#48014yescomplemented
525C5×D3—22no—
526C23×C3—21no—
527C23×C3—51no—
528C23×C3—101no—
529C23×C3—202no—
530C23×C3—202no—
531C23×C3—202no—
532C22×D3—51no—
533C22×D3—54no—
534C22×D3—102no—
535C22×D3—102no—
536C22×D3D4×D511yescharacteristic
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—101no—
540C3×D4—101no—
541C3×D4—202no—
542C2×C3×C4—21no—
543C2×C3×C4—51no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—101no—
547C2×C3×C4—202no—
548C2×C3×C4C23×D511yescharacteristic
549#67—42no—
550#67—202no—
551#67—202no—
552#67—202no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—51no—
556C2×Dic3—102no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—202no—
560C2×Dic3—202no—
561C2×Dic3D4×D511yescharacteristic
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—42no—
565C4×D3—102no—
566C4×D3—102no—
567C4×D3—101no—
568C4×D3—101no—
569C4×D3—202no—
570C4×D3—202no—
571C4×D3—202no—
572C3×C8—21no—
573C3×C8—101no—
574C3⋊C8—21no—
575C3⋊C8—101no—
576C22×C5—32no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5—61no—
581C22×C5—61no—
582C22×C5C2×D3×D411yescharacteristic
583C2×D5—32no—
584C2×D5—41no—
585C2×D5—41no—
586C2×D5—41no—
587C2×D5—61no—
588C2×D5—61no—
589C2×D5—68no—
590C2×D5—84no—
591C2×D5#88312yes—
592C2×D5D3×D812yes—
593C2×D5#91512yes—
594C4×C5—41no—
595C4×C5—61no—
596C4×C5—121no—
597C4×C5—121no—
598C4×C5C2×#23511yescharacteristic
599C4×C5C2×#23711yescharacteristic
600Dic5—41no—
601Dic5—61no—
602Dic5—121no—
603Dic5—121no—
604Dic5#88312yes—
605C24—101no—
606C24—151no—
607C2×D4—51no—
608C2×D4—61no—
609C2×D4—102no—
610C2×D4—102no—
611C2×D4—101no—
612C2×D4—301no—
613C2×D4—301no—
614C2×D4—301no—
615C2×D4—604no—
616C2×D4C2×D3×D511yescharacteristic
617C22×C4—31no—
618C22×C4—51no—
619C22×C4—61no—
620C22×C4—101no—
621C22×C4—151no—
622C22×C4—151no—
623C22×C4—151no—
624C22×C4—151no—
625C22×C4—301no—
626C22×C4—302no—
627C22×C4—302no—
628C22×C4—301no—
629C22×C4—301no—
630C22×C4—301no—
631C22×C4—301no—
632C22×C4—604no—
633C2×C8—31no—
634C2×C8—51no—
635C2×C8—102no—
636C2×C8—151no—
637C2×C8—302no—
638C2×C8C2×D3×D511yescharacteristic
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—51no—
642C4⋊C4—61no—
643C4⋊C4—101no—
644C4⋊C4—151no—
645C4⋊C4—151no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C4⋊C4—301no—
650C4⋊C4—301no—
651C4⋊C4C2×D3×D511yescharacteristic
652C22⋊C4—61no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C3×C5C2×#48011yescharacteristic, complemented, Hall
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—52no—
661C22×C3—52no—
662C22×C3—52no—
663C22×C3—201no—
664C22×C3—201no—
665C22×C3—201no—
666C22×C3—404no—
667C22×C3C2×D4×D511yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—52no—
671C2×D3—108no—
672C2×D3—101no—
673C2×D3—101no—
674C2×D3D5×D812yes—
675C3×C4—41no—
676C3×C4—52no—
677C3×C4—201no—
678C3×C4D5×#4111yescharacteristic
679C3×C4D5×#4111yescharacteristic
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—101no—
684Dic3—201no—
685Dic3—201no—
686C2×C5—62no—
687C2×C5—81no—
688C2×C5C2×#88311yescharacteristic
689C2×C5C2×D3×D811yescharacteristic
690C2×C5C2×#91511yescharacteristic
691D5—62no—
692D5—81no—
693D5#477414yesdirect product factor
694C23—21no—
695C23—31no—
696C23—51no—
697C23—101no—
698C23—154no—
699C23—151no—
700C23—202no—
701C23—202no—
702C23—202no—
703C23—302no—
704C23—302no—
705D4—21no—
706D4—21no—
707D4—101no—
708D4—101no—
709D4—122no—
710D4—202no—
711D4—602no—
712D4—602no—
713D4—602no—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—51no—
717C2×C4—52no—
718C2×C4—52no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—101no—
724C2×C4—122no—
725C2×C4—151no—
726C2×C4—202no—
727C2×C4—302no—
728C2×C4—302no—
729C2×C4—302no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—602no—
735C2×C4—602no—
736C2×C4—602no—
737C2×C4—602no—
738C2×C4—602no—
739C2×C4C22×D3×D511yescharacteristic
740C8—21no—
741C8—61no—
742C8—101no—
743C8—301no—
744C2×C3—54no—
745C2×C3—81no—
746C2×C3—401no—
747C2×C3D5×#12311yescharacteristic
748C2×C3C2×D5×D811yescharacteristic
749C2×C3D5×#13711yescharacteristic
750D3—22no—
751D3—102no—
752C5C2×#477411yescharacteristic, complemented, Sylow
753C22—32no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—52no—
758C22—52no—
759C22—52no—
760C22—61no—
761C22—61no—
762C22—152no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—308no—
767C22—301no—
768C22—301no—
769C22—404no—
770C22D3×D4×D511yescharacteristic
771C4—41no—
772C4—52no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—201no—
777C4—301no—
778C4—601no—
779C4—601no—
780C4D5×#23511yescharacteristic
781C4D5×#23711yescharacteristic
782C3D5×#48011yescharacteristic, complemented, Sylow
783C2—54no—
784C2—62no—
785C2—81no—
786C2—302no—
787C2—401no—
788C2D5×#88311yescharacteristic
789C2D3×D5×D811yescharacteristic
790C2D5×#91511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalD5×#938C2
hypercenter#102D3×D5
hypocenterC3×C5C2×#480
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D3×D5×C4⋊C4C2semidirect
3. #11750875C2semidirect
4. C5×#4774C2semidirect
5. C3×D5×#102C2semidirect
6. #11748958C2semidirect
7. #11748954C2semidirect
8. D5×#832C2semidirect
9. D5×(C2×D3)⋊C8C2semidirect
10. #11747916C2semidirect
11. D5×#818C2semidirect
12. #11747571C2semidirect
13. D5×#807C2semidirect
14. #11747330C2semidirect
15. #11747318C2semidirect
22. C4⋊C4×D15C22semidirect
24. C5×D3×C4⋊C4C22semidirect
32. #91437C22semidirect
33. D3×C4⋊Dic5C22semidirect
40. C3×C5×#102C22semidirect
41. #91116C22semidirect
42. #91104C22semidirect
43. #91102C22semidirect
44. #91091C22semidirect
45. C5×#832C22semidirect
46. C5×(C2×D3)⋊C8C22semidirect
47. C5×#818C22semidirect
48. C5×#807C22semidirect
49. C3×#3964C22semidirect
50. C3×#3953C22semidirect
51. C3×#3941C22semidirect
52. #90990C22semidirect
53. #90989C22semidirect
54. #90988C22semidirect
55. #90988C22semidirect
56. #90965C22semidirect
57. #90964C22semidirect
58. #90957C22semidirect
59. (C2×D3)⋊#168C22semidirect
73. D5×#102D3semidirect
141. #4774D5direct (N × H)
168. C5×#102C2×D3semidirect
171. #3964C2×D3semidirect
174. #3953C2×D3semidirect
180. #3941C2×D3semidirect
258. D3×C4⋊C4C2×D5semidirect
262. C3×#102C2×D5semidirect
266. #832C2×D5semidirect
270. (C2×D3)⋊C8C2×D5semidirect
274. #818C2×D5semidirect
278. #807C2×D5semidirect
513. #102D3×D5semidirect
524. C3×D5#480semidirect
656. C3×C5C2×#480semidirect
693. D5#4774direct (N × H)
752. C5C2×#4774semidirect
782. C3D5×#480semidirect

Maximal subgroups

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

subgroupindex
D5×#9382
D3×D5×C4⋊C42
#117508752
C5×#47742
C3×D5×#1022
#117489582
#117489542
D5×#8322
D5×(C2×D3)⋊C82
#117479162
D5×#8182
#117475712
D5×#8072
#117473302
#117473182
D5×#4803
C2×#47745