Finite Group Databasebeta

← #14458965

Subgroups — #14458965

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5806C211yesmaximal, characteristic, complemented
2#11754512C211yesmaximal, characteristic, complemented
3C2×#91116C211yesmaximal, characteristic, complemented
4C3×#65506C211yesmaximal, characteristic, complemented
5#11749087C211yesmaximal, characteristic, complemented
6#11749035C211yesmaximal, characteristic, complemented
7#11749028C211yesmaximal, characteristic, complemented
8Dic3×#686C211yesmaximal, characteristic, complemented
9#11748982C211yesmaximal, characteristic, complemented
10#11748966C211yesmaximal, characteristic, complemented
11#11748965C211yesmaximal, characteristic, complemented
12#11748942C211yesmaximal, characteristic, complemented
13#11748545C211yesmaximal, characteristic, complemented
14#67⋊#168C211yesmaximal, characteristic, complemented
15#11748467C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C5×#237C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C5×#953—21no—
22C2×C5×#217—21no—
23C5×#939—21no—
24C5×#938C2211yescharacteristic
25C5×#936C2211yescharacteristic
26C5×#935—21no—
27C5×D4×Dic3C2211yescharacteristic
28C4×C5×#67C2211yescharacteristic
29C5×#924C2211yescharacteristic
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076C2211yescharacteristic
33#91571—21no—
34#91559—21no—
35#91456C2211yescharacteristic, complemented
36Dic3×D20C2211yescharacteristic, complemented
37#91414—21no—
38#91381C2211yescharacteristic, complemented
39#91362—21no—
40#91338C2211yescharacteristic, complemented
41C2×#6655C2211yescharacteristic, complemented
42C2×D3×#168C2211yescharacteristic, complemented
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45#91116C2211yescharacteristic
46#91116C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×C22⋊#168C2211yescharacteristic
50#90988C2211yescharacteristic, complemented
51#90988C2211yescharacteristic, complemented
52#90986C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90973C2211yescharacteristic, complemented
55#90973C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#80015—51nomaximal, Hall
61C5×#546—31no—
62#65899—31no—
63#65527—31no—
64#65522—31no—
65#65506D311yescharacteristic, complemented
66C2×#3964—31no—
67#65346—31no—
68#65345—31no—
69#65337—31no—
70#65333—31no—
71#65327—31no—
72#65324—31no—
73C4×#686—31no—
74D4×#168—31no—
75#65298—31no—
76C24×C3×C5—21no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4—41no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15—21no—
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C2×C5×#67D411yescharacteristic
87C22×C5×Dic3—21no—
88C22×C5×Dic3—21no—
89C5×#237—22no—
90C5×#237—41no—
91C2×C4×C5×D3C2311yescharacteristic
92C2×C5×Dic6C2311yescharacteristic
93C2×C3×C22⋊D5—21no—
94C2×C3×D20C2311yescharacteristic
95C2×#1201—21no—
96C2×D5×Dic3—21no—
97C4⋊Dic15—21no—
98C4⋊Dic15C2311yescharacteristic
99C4⋊Dic15C2311yescharacteristic
100C2×C3⋊#168—41no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#217—21no—
104C5×#217—21no—
105C5×#217—21no—
106C5×#217—21no—
107C5×#217—21no—
108C5×#217D411yescharacteristic
109C5×(C2×D3)⋊C4D411yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4D411yescharacteristic
113C4×C5×Dic3C2311yescharacteristic
114C3×#686—22no—
115C3×#686—41no—
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6669—21no—
121#6668—21no—
122(C2×D3)⋊Dic5—21no—
123#6665—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6655—41no—
127D3×#168—41no—
128#5806D511yescharacteristic, complemented
129#5618—51no—
130C3×#447—51no—
131C2×#832—51no—
132#5158—51no—
133#5157—51no—
134#5153—51no—
135Dic3×D8—51no—
136#5041—51no—
137#4784—51no—
138#4772—51no—
139#4768—51no—
140#4766—51no—
141#67⋊C8—51no—
142#4722—51no—
143C2×C5×#41—31no—
144C22×C5×D4C2×D311yescharacteristic
145C5×#124—31no—
146C5×#123—61no—
147C5×C22⋊Q8—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C2×C5×C22⋊C4—61no—
154C2×#688—31no—
155#4085—61no—
156C2×#686C2×D311yescharacteristic
157C2×#686C2×D311yescharacteristic
158#4076—31no—
159#4076C2×D311yescharacteristic
160#4072—31no—
161C2×C4⋊Dic5—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4044—61no—
165#4029—61no—
166#4027—61no—
167C4×D20—31no—
168#4016—31no—
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964C2×D311yescharacteristic
177#3964C2×D311yescharacteristic
178C22⋊#168—31no—
179C22⋊#168C2×D311yescharacteristic
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—42no—
190C23×C3×C5—42no—
191C23×C3×C5—81no—
192C23×C3×C5C2×D411yescharacteristic
193C22×C5×D3C2×D411yescharacteristic
194C22×C3×D5—21no—
195C3×C5×D4—21no—
196C3×C5×D4—21no—
197C3×C5×D4—21no—
198C3×C5×D4—42no—
199C3×C5×D4#4112yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—81no—
207C5×#67—22no—
208C5×#67—42no—
209C5×#67—81no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—42no—
213C2×C5×Dic3—81no—
214C2×C5×Dic3C2×D411yescharacteristic
215C2×C5×Dic3C2×D411yescharacteristic
216C2×C5×Dic3C2×D411yescharacteristic
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C5×Dic6—21no—
220C5×Dic6—21no—
221C3×C22⋊D5—42no—
222C2×C3×Dic5—21no—
223C3×D20—21no—
224C3×D20—21no—
225#1201—81no—
226D5×Dic3—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C22×C3×D4C2×D511yescharacteristic
232C2×#237C2×D511yescharacteristic
233C2×C3×D8—51no—
234C2×C3×D8—51no—
235C3×#121—51no—
236#953—21no—
237C2×#217—21no—
238#939—21no—
239#939—101no—
240#938—51no—
241#938C2×D511yescharacteristic
242#936C2×D511yescharacteristic
243#935—21no—
244D4×Dic3—51no—
245D4×Dic3—101no—
246D4×Dic3C2×D511yescharacteristic
247C2×#214—51no—
248C4×#67C2×D511yescharacteristic
249C2×C4⋊Dic3—51no—
250#924C2×D511yescharacteristic
251C22×C3⋊C8—51no—
252C2×D3×C8—51no—
253#892—51no—
254#890—51no—
255#886—101no—
256#879—101no—
257C3×#102—51no—
258C3×#102—51no—
259C3×C22⋊C8—51no—
260#832—51no—
261#832—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265(C2×D3)⋊C8—51no—
266#818—51no—
267#818—51no—
268#816—51no—
269#816—51no—
270Dic3⋊C8—51no—
271C8×Dic3—51no—
272#810—51no—
273#808—51no—
274C24×C5—21no—
275C5×#41—62no—
276C5×#41—121no—
277C2×C5×Q8—31no—
278C2×C5×D4—22no—
279C2×C5×D4—21no—
280C2×C5×D4—31no—
281C2×C5×D4—41no—
282C2×C5×D4—61no—
283C2×C5×D4—61no—
284C2×C5×D4C22×D311yescharacteristic
285C2×C5×D4C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—61no—
288C22×C4×C5—61no—
289C22×C4×C5C22×D311yescharacteristic
290C2×C22⋊D5—21no—
291C2×C22⋊D5—61no—
292C22×Dic5—61no—
293C2×D20C22×D311yescharacteristic
294C2×C4×D5—61no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—61no—
298C5×C22⋊C4—31no—
299C5×C22⋊C4—31no—
300C5×C22⋊C4—61no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C5×C22⋊C4—61no—
305C42×C5—31no—
306C22⋊Dic5—61no—
307#688—121no—
308#686—22no—
309#686—41no—
310#685—21no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5C22×D311yescharacteristic
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—151no—
327#546—31no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—51no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—22no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—84no—
350C22×C3×C5#13512yes—
351C22×C3×C5C22×D411yescharacteristic
352C2×C5×D3—21no—
353C2×C5×D3—21no—
354C2×C5×D3—21no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—21no—
359C3×C4×C5C2×#4111yescharacteristic
360C3×C4×C5H(5,𝔽2)11yescharacteristic
361Dic15—41no—
362Dic15—41no—
363C3×Dic5—41no—
364C5×Dic3—21no—
365C5×Dic3—21no—
366C5×Dic3—21no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C24×C3—21no—
370C2×C3×D4—22no—
371C2×C3×D4—21no—
372C2×C3×D4—41no—
373C2×C3×D4—51no—
374C2×C3×D4—101no—
375C2×C3×D4C22×D511yescharacteristic
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—101no—
381C2×#67C22⋊D511yescharacteristic
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—101no—
385C22×Dic3—101no—
386#237—22no—
387#237—41no—
388C2×C4×D3C22×D511yescharacteristic
389C2×Dic6C22×D511yescharacteristic
390C3×D8—102no—
391C3×D8—201no—
392C2×C3×C8—51no—
393C2×C3×C8—51no—
394C3×C4⋊C4—51no—
395C3×C22⋊C4—101no—
396#217—21no—
397#217—21no—
398#217—21no—
399#217—21no—
400#217—21no—
401#217—101no—
402#217—101no—
403#217C22⋊D511yescharacteristic
404#214—201no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4C22⋊D511yescharacteristic
407C4⋊Dic3—51no—
408C4⋊Dic3—51no—
409C4⋊Dic3—101no—
410C4⋊Dic3—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—101no—
414Dic3⋊C4C22⋊D511yescharacteristic
415C4×Dic3—101no—
416C4×Dic3C22×D511yescharacteristic
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420D3×C8—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—31no—
424C23×C5—42no—
425C23×C5—42no—
426C23×C5—81no—
427C23×C5D3×D411yescharacteristic
428C22×D5—21no—
429C5×Q8—61no—
430C5×Q8—61no—
431C5×D4—21no—
432C5×D4—21no—
433C5×D4—21no—
434C5×D4—42no—
435C5×D4—62no—
436C5×D4—122no—
437C5×D4—241no—
438C5×D4#23712yes—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—31no—
442C2×C4×C5—31no—
443C2×C4×C5—31no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—122no—
449C2×C4×C5—241no—
450C2×C4×C5D3×D411yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—42no—
453C22⋊D5—241no—
454C2×Dic5—21no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—21no—
459D20—21no—
460C4×D5—241no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—31no—
466C22×D4D3×D511yescharacteristic
467C2×SD16—151no—
468C2×D8—51no—
469C2×D8—51no—
470C22×C8—151no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124—31no—
475#123—61no—
476#123—301no—
477C22⋊Q8—31no—
478#121—31no—
479#121—51no—
480#121—61no—
481#121—151no—
482#121—301no—
483#120—61no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—61no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—51no—
499#102—51no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—51no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5—42no—
510C2×C3×C5—81no—
511C2×C3×C5#54611yescharacteristic
512C2×C3×C5C2×#13511yescharacteristic
513C2×C3×C5#57611yescharacteristic
514C3×D5—81no—
515C5×D3—41no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—42no—
519C23×C3—42no—
520C23×C3—81no—
521C23×C3—101no—
522C23×C3C2×C22⋊D511yescharacteristic
523C22×D3C2×C22⋊D511yescharacteristic
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—42no—
528C3×D4—101no—
529C3×D4—101no—
530C3×D4—202no—
531C3×D4#71112yes—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—101no—
535C2×C3×C4C2×C22⋊D511yescharacteristic
536C2×C3×C4C23×D511yescharacteristic
537#67—22no—
538#67—42no—
539#67—81no—
540#67—401no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—42no—
544C2×Dic3—81no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—401no—
548C2×Dic3—401no—
549C2×Dic3C2×C22⋊D511yescharacteristic
550C2×Dic3C2×C22⋊D511yescharacteristic
551C2×Dic3C2×C22⋊D511yescharacteristic
552C4×D3—21no—
553C4×D3—21no—
554Dic6—21no—
555Dic6—21no—
556C3×C8—101no—
557C3×C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—22no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—61no—
569C22×C5—61no—
570C22×C5—61no—
571C22×C5—84no—
572C22×C5#91212yes—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—61no—
579C4×C5—61no—
580C4×C5—61no—
581C4×C5—121no—
582C4×C5—121no—
583C4×C5C2×#23711yescharacteristic
584C4×C5#100411yescharacteristic
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—21no—
589#41—62no—
590#41—121no—
591C2×Q8—31no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—31no—
595C2×D4—41no—
596C2×D4—51no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—101no—
600C2×D4—301no—
601C2×D4C2×D3×D511yescharacteristic
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—102no—
611D8—201no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—51no—
621C4⋊C4—61no—
622C4⋊C4—151no—
623C4⋊C4—151no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4—301no—
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—31no—
639C42—301no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—84no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3#409612yes—
654C22×C3C22×C22⋊D511yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C3×C4—21no—
659C3×C4—201no—
660C3×C4C2×#71111yescharacteristic
661C3×C4#414411yescharacteristic
662Dic3—21no—
663Dic3—21no—
664Dic3—21no—
665Dic3—41no—
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—42no—
671C2×C5—81no—
672C2×C5—121no—
673C2×C5#559111yescharacteristic
674C2×C5C2×#91211yescharacteristic
675C2×C5#577411yescharacteristic
676D5—81no—
677C23—21no—
678C23—21no—
679C23—31no—
680C23—42no—
681C23—42no—
682C23—81no—
683C23—101no—
684C23D3×C22⋊D511yescharacteristic
685Q8—61no—
686Q8—61no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—62no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—202no—
696D4—241no—
697D4—1201no—
698D4#678012yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—101no—
709C2×C4—122no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—42no—
723C2×C3—81no—
724C2×C3—401no—
725C2×C3#6614011yescharacteristic
726C2×C3C2×#409611yescharacteristic
727C2×C3#6616911yescharacteristic
728D3—41no—
729C5#8001511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—84no—
742C22—201no—
743C22—201no—
744C22—201no—
745C22#9149312yes—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—61no—
749C4—61no—
750C4—61no—
751C4—121no—
752C4—121no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4C2×#678011yescharacteristic
757C4#9204911yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—42no—
761C2—81no—
762C2—121no—
763C2—401no—
764C2#1175469811yescharacteristic
765C2C2×#9149311yescharacteristic
766C2#1175539011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5806C2semidirect
2. #11754512C2semidirect
3. C2×#91116C2semidirect
4. C3×#65506C2semidirect
5. #11749087C2semidirect
6. #11749035C2semidirect
7. #11749028C2semidirect
8. Dic3×#686C2semidirect
9. #11748982C2semidirect
10. #11748966C2semidirect
11. #11748965C2semidirect
12. #11748942C2semidirect
13. #11748545C2semidirect
14. #67⋊#168C2semidirect
15. #11748467C2semidirect
35. #91456C22semidirect
36. Dic3×D20C22semidirect
38. #91381C22semidirect
40. #91338C22semidirect
41. C2×#6655C22semidirect
42. C2×D3×#168C22semidirect
50. #90988C22semidirect
51. #90988C22semidirect
52. #90986C22semidirect
53. Dic3⋊#168C22semidirect
54. #90973C22semidirect
55. #90973C22semidirect
56. #90972C22semidirect
57. #90964C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
65. #65506D3semidirect
128. #5806D5semidirect
640. C3×C5#3297semidirect
729. C5#80015semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
C5×#58062
#117545122
C2×#911162
C3×#655062
#117490872
#117490352
#117490282
Dic3×#6862
#117489822
#117489662
#117489652
#117489422
#117485452
#67⋊#1682
#117484672
#106152263
#800155