Finite Group Databasebeta

← #14458307

Subgroups — #14458307

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5611C211yesmaximal, characteristic, complemented
2#67×D20C211yesmaximal, characteristic, complemented
3#11751139C211yesmaximal, characteristic, complemented
4C3×#65325C211yesmaximal, characteristic, complemented
5#11749152C211yesmaximal, characteristic, complemented
6#11749099C211yesmaximal, characteristic, complemented
7#11749028C211yesmaximal, characteristic, complemented
8Dic3×#686C211yesmaximal, characteristic, complemented
9#67⋊#168C211yesmaximal, characteristic, complemented
10#11748462C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12D3×#3941C211yesmaximal, characteristic, complemented
13#11747403C211yesmaximal, characteristic, complemented
14#11747318C211yesmaximal, characteristic, complemented
15#11747245C211yesmaximal, characteristic, complemented
16#10615256—31nomaximal, Hall
17C2×C5×#237—21no—
18C22×C3×D20C2211yescharacteristic
19C2×D5×#67—21no—
20C2×D3×D20C2211yescharacteristic
21C3×C5×#121C2211yescharacteristic, complemented
22C2×#6715C2211yescharacteristic, complemented
23#91819C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic, complemented
25C5×#938C2211yescharacteristic, complemented
26C5×#935—21no—
27C5×D4×Dic3C2211yescharacteristic, complemented
28C4×C5×#67C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C5×D3×C4⋊C4C2211yescharacteristic, complemented
31C5×#888C2211yescharacteristic, complemented
32C5×#883—21no—
33C5×#878—21no—
34C2×C3×#686C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic, complemented
36#91564—21no—
37#91474—21no—
38#91458C2211yescharacteristic
39#91456C2211yescharacteristic
40Dic3×D20C2211yescharacteristic
41#91409—21no—
42C2×D3×#168C2211yescharacteristic, complemented
43#91116C2211yescharacteristic, complemented
44#91093C2211yescharacteristic, complemented
45#91091C2211yescharacteristic, complemented
46C3×C22⋊#168C2211yescharacteristic, complemented
47C3×#3941C2211yescharacteristic
48C3×#3941C2211yescharacteristic, complemented
49#90988C2211yescharacteristic, complemented
50#90988C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90969C2211yescharacteristic, complemented
53#90969C2211yescharacteristic, complemented
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56#90964C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#80014—51nomaximal, Hall
61C5×#547—31no—
62D4×D20—31no—
63#65377—31no—
64#65376—31no—
65#65327—31no—
66#65327—31no—
67#65325—31no—
68#65325D311yescharacteristic, complemented
69#65304—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65256—31no—
73#65256—31no—
74C2×#3941—31no—
75C2×#3941—31no—
76C23×C3×D5—21no—
77C22×D3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×D60C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×#67D411yescharacteristic
85C22×C5×Dic3—21no—
86C22×C5×Dic3—21no—
87C5×#237—44no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3C2311yescharacteristic
90C2×C5×Dic6—21no—
91C2×C3×D20—22no—
92C2×C3×D20—21no—
93C2×C3×D20—41no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×D20C2311yescharacteristic
96D5×#67—44no—
97C2×#1202—21no—
98C2×#1202—21no—
99C2×#1202—21no—
100C2×#1201—21no—
101C2×D5×Dic3—21no—
102D3×D20—22no—
103D3×D20—41no—
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106#6715—41no—
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C2×C3⋊#168—41no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217—21no—
113C5×#217—21no—
114C5×#217D411yescharacteristic
115C5×(C2×D3)⋊C4D411yescharacteristic
116C5×C4⋊Dic3—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×C4⋊Dic3C2311yescharacteristic
119C5×Dic3⋊C4—21no—
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4D411yescharacteristic
122C4×C5×Dic3C2311yescharacteristic
123C3×#686—22no—
124C3×#686—41no—
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127#6665—21no—
128#6665—21no—
129D3×#168—41no—
130D4×#67—51no—
131#5611D511yescharacteristic, complemented
132C3×#447—51no—
133C2×#832—51no—
134#5157—51no—
135#5156—51no—
136#5150—51no—
137Dic3×D8—51no—
138#5038—51no—
139#4774—51no—
140D3×#102—51no—
141#4760—51no—
142#4759—51no—
143#4736—51no—
144#67⋊C8—51no—
145C2×C5×#41—61no—
146C2×D4×D5—61no—
147C22×D20—31no—
148C22×D20C2×D311yescharacteristic
149C5×C4⋊Q8—31no—
150C5×#123—61no—
151C5×#123—61no—
152C5×C22⋊Q8—61no—
153C5×#121—31no—
154C5×#121C2×D311yescharacteristic, complemented
155C4×C5×D4—31no—
156C4×C5×D4—31no—
157C2×C5×C4⋊C4—31no—
158C2×C5×C4⋊C4—31no—
159C2×#686—31no—
160C2×#686C2×D311yescharacteristic
161C2×#686C2×D311yescharacteristic, complemented
162#4076—31no—
163#4076—31no—
164C22×#168—31no—
165C22×#168—31no—
166#4041—61no—
167#4028—61no—
168#4028—61no—
169#4020—31no—
170C4×D20—31no—
171#3964—31no—
172C22⋊#168—31no—
173C22⋊#168C2×D311yescharacteristic, complemented
174#3941—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941—31no—
181#3941C2×D311yescharacteristic
182#3941C2×D311yescharacteristic, complemented
183#3939—31no—
184#3939—31no—
185#3939—31no—
186C4⋊#168—31no—
187C4×#168—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5C2×D411yescharacteristic
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—42no—
196C22×C3×D5—42no—
197C22×C3×D5—81no—
198C2×D3×D5—42no—
199C2×D3×D5—42no—
200C2×D3×D5—81no—
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—42no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209#1220—42no—
210C2×Dic15—21no—
211D60—21no—
212D60—21no—
213C5×#67—42no—
214C5×#67D814yescomplemented
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—42no—
218C2×C5×Dic3—42no—
219C2×C5×Dic3C2×D411yescharacteristic
220C2×C5×Dic3C2×D411yescharacteristic
221C2×C5×Dic3C2×D411yescharacteristic
222C4×C5×D3—21no—
223C4×C5×D3—21no—
224C4×C5×D3—42no—
225C5×Dic6—42no—
226C3×D20—21no—
227C3×D20—21no—
228C3×D20—21no—
229C3×D20—42no—
230C3×D20#4112yescomplemented
231#1202—42no—
232#1202—42no—
233#1202—81no—
234#1201—42no—
235D5×Dic3—42no—
236C3⋊#168—21no—
237C3⋊#168—21no—
238C3×#168—21no—
239C3×#168—21no—
240C22×C3×D4—51no—
241C22×#67—101no—
242C2×#237—21no—
243C2×D3×D4—51no—
244C2×C3×D8—51no—
245C2×C3×D8—51no—
246C3×#121C2×D511yescharacteristic, complemented
247#953—101no—
248#940—51no—
249#939—101no—
250#938—51no—
251#938C2×D511yescharacteristic, complemented
252#937—101no—
253#935—21no—
254D4×Dic3—51no—
255D4×Dic3C2×D511yescharacteristic, complemented
256C2×#213—51no—
257#930—51no—
258C4×#67C2×D511yescharacteristic
259C2×C4⋊Dic3C2×D511yescharacteristic, complemented
260C22×C3⋊C8—51no—
261C2×D3×C8—51no—
262D3×C4⋊C4C2×D511yescharacteristic, complemented
263#888C2×D511yescharacteristic, complemented
264#883—21no—
265#878—21no—
266C3×#102—51no—
267C3×#102—51no—
268C3×C22⋊C8—51no—
269#832—51no—
270#832—51no—
271#832—51no—
272#832—51no—
273#832—51no—
274#821—51no—
275#821—51no—
276(C2×D3)⋊C8—51no—
277#818—51no—
278#818—51no—
279Dic3⋊C8—51no—
280C8×Dic3—51no—
281#809—51no—
282#807—51no—
283C23×D5—21no—
284C23×D5—61no—
285C5×#41—124no—
286C2×C5×Q8—61no—
287C2×C5×D4—21no—
288C2×C5×D4—31no—
289C2×C5×D4—61no—
290C2×C5×D4C22×D311yescharacteristic
291C22×C4×C5—31no—
292C22×C4×C5—61no—
293C22×C4×C5—61no—
294C22×C4×C5—61no—
295C22×C4×C5C22×D311yescharacteristic
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298D4×D5—124no—
299C2×D20—22no—
300C2×D20—21no—
301C2×D20—31no—
302C2×D20—41no—
303C2×D20—62no—
304C2×D20—61no—
305C2×D20—61no—
306C2×D20—61no—
307C2×D20—121no—
308C2×D20C22×D311yescharacteristic
309C2×D20C22×D311yescharacteristic
310C2×C4×D5—61no—
311C5×C4⋊C4—31no—
312C5×C4⋊C4—31no—
313C5×C4⋊C4—31no—
314C5×C4⋊C4—61no—
315C5×C4⋊C4—61no—
316C5×C4⋊C4—61no—
317C5×C4⋊C4C22×D311yescharacteristic
318C5×C22⋊C4—21no—
319C5×C22⋊C4—31no—
320C5×C22⋊C4—31no—
321C5×C22⋊C4—61no—
322C5×C22⋊C4—61no—
323C42×C5—31no—
324#686—22no—
325#686—41no—
326#686—121no—
327#685—61no—
328#685—61no—
329#685—61no—
330C4⋊Dic5—31no—
331C2×#168—31no—
332C2×#168—31no—
333C2×#168—121no—
334C2×#168—121no—
335C2×#168C22×D311yescharacteristic
336C2×#168C22×D311yescharacteristic
337#547—31no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—51no—
347#447—151no—
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—41no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5C2×D812yes—
358C22×C3×C5C22×D411yescharacteristic
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×C5×D3—21no—
363C2×C5×D3—21no—
364C2×C5×D3C2×D812yes—
365C2×C3×D5—22no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—41no—
371C2×C3×D5—84no—
372D3×D5—84no—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5C2×#4111yescharacteristic
376C3×C4×C5H(5,𝔽2)11yescharacteristic
377Dic15—41no—
378C5×Dic3—21no—
379C5×Dic3—21no—
380C5×Dic3—41no—
381C5×Dic3—41no—
382C5×Dic3C2×D812yes—
383C24×C3—101no—
384C23×D3—101no—
385C2×C3×D4—21no—
386C2×C3×D4—51no—
387C2×C3×D4—51no—
388C2×C3×D4—102no—
389C2×C3×D4—101no—
390C2×C3×D4—201no—
391C2×C3×D4C22×D511yescharacteristic
392C22×C3×C4C22×D511yescharacteristic
393C2×#67—21no—
394C2×#67—101no—
395C2×#67—101no—
396C2×#67—101no—
397C2×#67—101no—
398C2×#67—101no—
399C2×#67—204no—
400C2×#67C22⋊D511yescharacteristic
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3—101no—
404#237—44no—
405D3×D4—102no—
406D3×D4—201no—
407C2×D12—51no—
408C2×C4×D3—21no—
409C2×C4×D3C22×D511yescharacteristic
410C2×Dic6—21no—
411C3×D8—102no—
412C3×D8—201no—
413C2×C3×C8—51no—
414C2×C3×C8—51no—
415C3×C4⋊C4C22×D511yescharacteristic
416C3×C22⋊C4—21no—
417#217—21no—
418#217—21no—
419#217—101no—
420#217—101no—
421#217C22⋊D511yescharacteristic
422#213—201no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4C22⋊D511yescharacteristic
425C4⋊Dic3—21no—
426C4⋊Dic3—51no—
427C4⋊Dic3C22×D511yescharacteristic
428C4⋊Dic3C22×D511yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431Dic3⋊C4C22⋊D511yescharacteristic
432C4×Dic3C22×D511yescharacteristic
433C2×C3⋊C8—51no—
434C2×C3⋊C8—51no—
435C2×C3⋊C8—201no—
436D3×C8—201no—
437C23×C5—21no—
438C23×C5—31no—
439C23×C5D3×D411yescharacteristic
440C22×D5—21no—
441C22×D5—21no—
442C22×D5—42no—
443C22×D5—42no—
444C22×D5—61no—
445C22×D5—81no—
446C22×D5—122no—
447C22×D5—122no—
448C22×D5—241no—
449C5×Q8—122no—
450C5×D4—21no—
451C5×D4—21no—
452C5×D4—34no—
453C5×D4—42no—
454C5×D4—122no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—31no—
459C2×C4×C5—31no—
460C2×C4×C5—31no—
461C2×C4×C5—61no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—122no—
466C2×C4×C5—122no—
467C2×C4×C5—122no—
468C2×C4×C5D3×D411yescharacteristic
469C2×C4×C5C23×D311yescharacteristic
470C22⋊D5—122no—
471C22⋊D5—122no—
472C2×Dic5—61no—
473D20—21no—
474D20—21no—
475D20—21no—
476D20—42no—
477D20—61no—
478D20—61no—
479D20—122no—
480D20—122no—
481D20—241no—
482D20#23712yescomplemented
483C4×D5—122no—
484#168—21no—
485#168—21no—
486#168—61no—
487#168—61no—
488C2×#41—61no—
489C22×D4—51no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—51no—
493C2×D8—51no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—31no—
498#127—151no—
499#123—61no—
500#123—61no—
501C22⋊Q8—61no—
502#121—31no—
503#121—151no—
504#121—151no—
505#121—301no—
506#121D3×D511yescharacteristic, complemented
507#120—301no—
508#120—301no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—151no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—31no—
514#107—151no—
515#107—151no—
516#107—151no—
517C4⋊C8—151no—
518#102—51no—
519#102—51no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102—151no—
527#102—151no—
528C22⋊C8—51no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—81no—
533C2×C3×C5#54611yescharacteristic
534C2×C3×C5C22×D811yescharacteristic
535C2×C3×C5#57711yescharacteristic
536D15—81no—
537C3×D5—42no—
538C3×D5—81no—
539C5×D3—22no—
540C23×C3—21no—
541C23×C3—101no—
542C23×C3—101no—
543C23×C3—202no—
544C23×C3—202no—
545C23×C3—401no—
546C23×C3C2×C22⋊D511yescharacteristic
547C22×D3—101no—
548C22×D3—202no—
549C22×D3—202no—
550C22×D3—401no—
551C22×D3C2×C22⋊D511yescharacteristic
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—42no—
555C3×D4—52no—
556C3×D4—101no—
557C3×D4—101no—
558C3×D4—101no—
559C3×D4—202no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4C2×C22⋊D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—42no—
566#67—202no—
567#67—202no—
568#67—202no—
569#67—202no—
570#67—401no—
571#67#68614yescomplemented
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—42no—
575C2×Dic3—42no—
576C2×Dic3—101no—
577C2×Dic3—202no—
578C2×Dic3C2×C22⋊D511yescharacteristic
579C2×Dic3C2×C22⋊D511yescharacteristic
580C2×Dic3C2×C22⋊D511yescharacteristic
581D12—101no—
582D12—101no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—42no—
586Dic6—42no—
587C3×C8—101no—
588C3×C8—101no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—32no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—61no—
598C22×C5—61no—
599C22×C5D3×D812yes—
600C22×C5C2×D3×D411yescharacteristic
601C2×D5—22no—
602C2×D5—41no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C2×D5—84no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—121no—
611C2×D5—244no—
612C4×C5—21no—
613C4×C5—32no—
614C4×C5—41no—
615C4×C5—61no—
616C4×C5—61no—
617C4×C5—121no—
618C4×C5—121no—
619C4×C5C2×#23711yescharacteristic
620C4×C5#100411yescharacteristic
621Dic5—121no—
622C24—101no—
623C24—301no—
624#41—124no—
625C2×Q8—61no—
626C2×D4—21no—
627C2×D4—31no—
628C2×D4—51no—
629C2×D4—51no—
630C2×D4—61no—
631C2×D4—102no—
632C2×D4—101no—
633C2×D4—151no—
634C2×D4—201no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—302no—
639C2×D4—301no—
640C2×D4—301no—
641C2×D4—601no—
642C2×D4—604no—
643C2×D4C2×D3×D511yescharacteristic
644C22×C4—31no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—102no—
651D8—201no—
652D8—601no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—151no—
656C2×C8—151no—
657C2×C8—601no—
658C2×C8—601no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—151no—
666C4⋊C4C2×D3×D511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—31no—
669C22⋊C4—31no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—31no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—102no—
683C22×C3—201no—
684C22×C3—201no—
685C22×C3—201no—
686C22×C3—201no—
687C22×C3—201no—
688C22×C3—404no—
689C22×C3C2×#68612yes—
690C22×C3C22×C22⋊D511yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—201no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—404no—
697C2×D3C2×#68612yes—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4D5×#4111yescharacteristic
701C3×C4#414911yescharacteristic
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—201no—
707Dic3C2×#68612yes—
708C2×C5—22no—
709C2×C5—62no—
710C2×C5—81no—
711C2×C5#559111yescharacteristic
712C2×C5C2×D3×D811yescharacteristic
713C2×C5#577511yescharacteristic
714D5—42no—
715D5—81no—
716D5—241no—
717C23—21no—
718C23—31no—
719C23—101no—
720C23—101no—
721C23—202no—
722C23—202no—
723C23—301no—
724C23—401no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D3×C22⋊D511yescharacteristic
729Q8—122no—
730D4—21no—
731D4—21no—
732D4—34no—
733D4—42no—
734D4—52no—
735D4—101no—
736D4—101no—
737D4—101no—
738D4—122no—
739D4—202no—
740D4—301no—
741D4—301no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—602no—
746D4—1201no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4D3×C22⋊D511yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—101no—
765C8—101no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—81no—
770C2×C3—202no—
771C2×C3—401no—
772C2×C3C22×#68611yescharacteristic
773C2×C3#6616311yescharacteristic
774C2×C3#6617111yescharacteristic
775D3—22no—
776D3—401no—
777C5#8001411yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—61no—
785C22—61no—
786C22—102no—
787C22—201no—
788C22—201no—
789C22—201no—
790C22—201no—
791C22—201no—
792C22—404no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D3×#68612yes—
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—32no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—121no—
806C4—601no—
807C4D5×#23711yescharacteristic
808C4#9202611yescharacteristic
809C3#1061525611yescharacteristic, complemented, Sylow
810C2—22no—
811C2—62no—
812C2—81no—
813C2—202no—
814C2—401no—
815C2—1201no—
816C2C2×D3×#68611yescharacteristic
817C2#1175506611yescharacteristic
818C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C5×#5611C2semidirect
2. #67×D20C2semidirect
3. #11751139C2semidirect
4. C3×#65325C2semidirect
5. #11749152C2semidirect
6. #11749099C2semidirect
7. #11749028C2semidirect
8. Dic3×#686C2semidirect
9. #67⋊#168C2semidirect
10. #11748462C2semidirect
11. C2×#90964C2semidirect
12. D3×#3941C2semidirect
13. #11747403C2semidirect
14. #11747318C2semidirect
15. #11747245C2semidirect
21. C3×C5×#121C22semidirect
22. C2×#6715C22semidirect
24. C22×C3⋊#168C22semidirect
25. C5×#938C22semidirect
27. C5×D4×Dic3C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C5×D3×C4⋊C4C22semidirect
31. C5×#888C22semidirect
35. C2×C3×#686C22semidirect
42. C2×D3×#168C22semidirect
43. #91116C22semidirect
44. #91093C22semidirect
45. #91091C22semidirect
46. C3×C22⋊#168C22semidirect
48. C3×#3941C22semidirect
49. #90988C22semidirect
50. #90988C22semidirect
51. Dic3⋊#168C22semidirect
52. #90969C22semidirect
53. #90969C22semidirect
56. #90964C22semidirect
57. #90964C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
68. #65325D3semidirect
131. #5611D5semidirect
154. C5×#121C2×D3semidirect
161. C2×#686C2×D3semidirect
173. C22⋊#168C2×D3semidirect
182. #3941C2×D3semidirect
214. C5×#67D8semidirect
230. C3×D20#41semidirect
246. C3×#121C2×D5semidirect
251. #938C2×D5semidirect
255. D4×Dic3C2×D5semidirect
259. C2×C4⋊Dic3C2×D5semidirect
262. D3×C4⋊C4C2×D5semidirect
263. #888C2×D5semidirect
482. D20#237semidirect
506. #121D3×D5semidirect
571. #67#686semidirect
676. C3×C5#3294semidirect
777. C5#80014semidirect
809. C3#10615256semidirect

Maximal subgroups

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

subgroupindex
C5×#56112
#67×D202
#117511392
C3×#653252
#117491522
#117490992
#117490282
Dic3×#6862
#67⋊#1682
#117484622
C2×#909642
D3×#39412
#117474032
#117473182
#117472452
#106152563
#800145