Finite Group Databasebeta

← #14417442

Subgroups — #14417442

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×SD16C211yesmaximal, characteristic
2#11755140C211yesmaximal, characteristic, complemented
3#11754910C211yesmaximal, characteristic
4SD16×Dic15C211yesmaximal, characteristic, complemented
5C5×Dic3×SD16C211yesmaximal, characteristic, complemented
6#11749241C211yesmaximal, characteristic, complemented
7#11749234C211yesmaximal, characteristic, complemented
8#11749208C211yesmaximal, characteristic, complemented
9#11749018C211yesmaximal, characteristic, complemented
10#11749010C211yesmaximal, characteristic, complemented
11#11748962C211yesmaximal, characteristic
12#11747806C211yesmaximal, characteristic, complemented
13Dic3×#677C211yesmaximal, characteristic, complemented
14#11747671C211yesmaximal, characteristic, complemented
15#11747645C211yesmaximal, characteristic, complemented
16#10611380—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic, complemented
21D4×Dic15C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic, complemented
23C5×D4×Dic3C2211yescharacteristic
24C2×C3×#688C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×D5×SD16C418yescomplemented
27C2×C3×#677C2211yescharacteristic
28C2×C3×C8×D5C2211yescharacteristic
29#91559—21no—
30Dic3×C22⋊D5—21no—
31D5×#217—21no—
32C2×#6665—21no—
33#91434C2211yescharacteristic
34Dic3×D20C2211yescharacteristic
35#91358—21no—
36#91358C2211yescharacteristic
37#91358C2211yescharacteristic
38#91357—21no—
39#91357C2211yescharacteristic
40#91331—21no—
41#91331C2211yescharacteristic, complemented
42Dic3×Dic10—21no—
43Dic3×Dic10C2211yescharacteristic, complemented
44C2×#6649C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91101C2211yescharacteristic, complemented
48C8×Dic15C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#832C2211yescharacteristic
51C5×#817C2211yescharacteristic, complemented
52C5×C8×Dic3C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55#90971C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60#90953C2211yescharacteristic, complemented
61#83843—51nomaximal, Hall
62C2×D5×SD16D311yescharacteristic
63#65906—31no—
64#65879—31no—
65C4×C5×SD16—31no—
66SD16×Dic5—31no—
67#65315—31no—
68#65307—31no—
69#65149—31no—
70#65141—31no—
71#65106—31no—
72#65091—31no—
73#65059—31no—
74#65046—31no—
75C4×#677—31no—
76#64978—31no—
77C23×C3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×Dic15—21no—
81C22×C5×Dic3—21no—
82C2×C3×C22⋊D5—21no—
83C3×Q8×D5—22no—
84C3×Q8×D5C2×C414yescomplemented
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yes—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C2×D5×Dic3—21no—
93C2×D5×Dic3—21no—
94C3×C5×SD16C2×C414yescomplemented
95C2×C3×C5×C8C2311yescharacteristic
96#6719—21no—
97C4⋊Dic15—21no—
98C4⋊Dic15C2311yescharacteristic
99C4⋊Dic15C2311yescharacteristic
100C4×Dic15—21no—
101C4×Dic15C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#217—21no—
104C5×C4⋊Dic3—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C5×C4⋊Dic3C2311yescharacteristic
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C3×#688C2×C414yescomplemented
111C3×#687C2×C414yescomplemented
112C2×C3×#168C2311yescharacteristic
113C3×#677C2×C414yescomplemented
114C3×C8×D5C2×C414yescomplemented
115#6668—21no—
116#6668—21no—
117#6668D411yescharacteristic
118#6668D411yescharacteristic
119#6665—21no—
120#6665—21no—
121#6665—21no—
122#6665—21no—
123#6665D411yescharacteristic
124#6665D411yescharacteristic
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5—21no—
129#6649—22no—
130C22×C3×SD16—51no—
131#5812—51no—
132#5798—51no—
133#5225—51no—
134#5215—51no—
135#5164—51no—
136#5164—51no—
137#5164—51no—
138#5164—51no—
139Dic3×SD16—51no—
140Dic3×SD16—51no—
141Dic3×SD16—51no—
142Dic3×SD16D511yescharacteristic, complemented
143#5106—51no—
144#5101—51no—
145C2×Q8×D5C2×D311yescharacteristic
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×SD16C2×D311yescharacteristic
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#688C2×D311yescharacteristic
152D4×Dic5—31no—
153C2×#687C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C2×#685—61no—
156D5×SD16Dic318yescomplemented
157C2×#677C2×D311yescharacteristic
158C2×#676—31no—
159C2×C8×D5C2×D311yescharacteristic
160#4039—31no—
161#4038—31no—
162#4038—31no—
163#4038—61no—
164#4033—31no—
165#4033—61no—
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—31no—
169#4018—31no—
170#4018—61no—
171C4×Dic10—31no—
172C4×Dic10—61no—
173C5×#106—31no—
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3949—31no—
181#3948—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3941—31no—
186#3939—31no—
187#3939—31no—
188#3935—31no—
189#2949—151noSylow
190C23×C3×C5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—24no—
193C22×C3×D5—81no—
194C22×C3×D5—81no—
195C22×C3×D5C2×D411yescharacteristic
196C3×C5×Q8—21no—
197C3×C5×Q8C22×C412yes—
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—81no—
205C2×Dic15C2×D411yescharacteristic
206C2×Dic15C2×D411yescharacteristic
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—81no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C3×C22⋊D5—24no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C3×D20—21no—
216C3×D20C22×C412yes—
217C3×C4×D5—24no—
218C3×C4×D5C22×C412yes—
219C3×C4×D5#4112yes—
220C3×Dic10—21no—
221C3×Dic10—24no—
222C3×Dic10C22×C412yes—
223D5×Dic3—81no—
224D5×Dic3—81no—
225C3×C5×C8C22×C412yes—
226C3⋊#168—21no—
227C3×#168C22×C412yes—
228C5×C3⋊C8—21no—
229C22×C3×Q8—51no—
230C22×C3×D4—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C2×C3×SD16—58no—
234C2×C3×SD16—51no—
235C2×C3×SD16C2×D511yescharacteristic
236C22×C3×C8—51no—
237C2×#217—101no—
238C2×#217—101no—
239Q8×Dic3—51no—
240Q8×Dic3—51no—
241Q8×Dic3—51no—
242Q8×Dic3—101no—
243Q8×Dic3—101no—
244Q8×Dic3C2×D511yescharacteristic, complemented
245D4×Dic3—51no—
246D4×Dic3—51no—
247D4×Dic3—51no—
248D4×Dic3—101no—
249D4×Dic3—101no—
250D4×Dic3C2×D511yescharacteristic
251#926—51no—
252#926—51no—
253#926—51no—
254#926—101no—
255#926—101no—
256C2×#208—51no—
257#835—51no—
258#835—51no—
259#835—51no—
260#835C2×D511yescharacteristic, complemented
261#832—51no—
262#832—51no—
263#832—51no—
264#832C2×D511yescharacteristic
265#818—51no—
266#818—51no—
267#817—51no—
268#817C2×D511yescharacteristic, complemented
269#815—51no—
270#815—51no—
271C8×Dic3—51no—
272C8×Dic3C2×D511yescharacteristic, complemented
273C23×D5—21no—
274C2×C5×Q8C22×D311yescharacteristic
275C2×C5×D4C22×D311yescharacteristic
276C22×C4×C5—61no—
277C2×C22⋊D5—21no—
278C22×Dic5—61no—
279Q8×D5—22no—
280Q8×D5C2×Dic314yescomplemented
281D4×D5—22no—
282D4×D5C2×Dic314yes—
283C2×D20C22×D311yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—21no—
289C2×Dic10C22×D311yescharacteristic
290C5×SD16C2×Dic314yescomplemented
291C2×C5×C8—31no—
292C2×C5×C8C22×D311yescharacteristic
293C5×C4⋊C4—31no—
294C5×C4⋊C4—31no—
295C5×C4⋊C4—61no—
296C5×C22⋊C4—61no—
297C42×C5—31no—
298C42×C5—61no—
299C22⋊Dic5—61no—
300#688C2×Dic314yescomplemented
301#687C2×Dic314yescomplemented
302#685—31no—
303#685—31no—
304#685—61no—
305#685—61no—
306#685—61no—
307#685—61no—
308C4⋊Dic5—31no—
309C4⋊Dic5—31no—
310C4⋊Dic5—61no—
311#683—31no—
312#683—31no—
313#683—61no—
314#683—61no—
315C4×Dic5—31no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C4×Dic5—61no—
321C2×#168—31no—
322C2×#168C22×D311yescharacteristic
323#677C2×Dic314yescomplemented
324#676—62no—
325C8×D5C2×Dic314yescomplemented
326C22×SD16—51no—
327#519—151no—
328#518—151no—
329#440—151no—
330#440—151no—
331#440—151no—
332#440—151no—
333C4×SD16—31no—
334C4×SD16—151no—
335C4×SD16—151no—
336C4×SD16—151no—
337#427—151no—
338#419—151no—
339#418—151no—
340#405—151no—
341C22×C3×C5—22no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—22no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—84no—
351C2×C3×D5C4×D412yes—
352C3×C4×C5—22no—
353C3×C4×C5C23×C411yescharacteristic
354C3×C4×C5C2×#4111yescharacteristic
355Dic15—21no—
356Dic15—21no—
357Dic15—41no—
358Dic15—41no—
359C3×Dic5—22no—
360C3×Dic5C4×D412yes—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C5×Dic3—41no—
365C24×C3—101no—
366C2×C3×Q8—54no—
367C2×C3×Q8—51no—
368C2×C3×Q8—101no—
369C2×C3×Q8—102no—
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4—54no—
372C2×C3×D4—51no—
373C2×C3×D4—102no—
374C2×C3×D4—101no—
375C2×C3×D4C22×D511yescharacteristic
376C22×C3×C4—51no—
377C22×C3×C4—101no—
378C22×Dic3—21no—
379C22×Dic3—101no—
380C22×Dic3—101no—
381C22×Dic3—101no—
382C3×SD16—54no—
383C3×SD16—54no—
384C3×SD16—54no—
385C3×SD16C4×D514yescomplemented
386C2×C3×C8—51no—
387C2×C3×C8—54no—
388C2×C3×C8C22×D511yescharacteristic
389#217—21no—
390#217—51no—
391#217—51no—
392#217—101no—
393#217—101no—
394#217—101no—
395#217—101no—
396#217—101no—
397C4⋊Dic3—21no—
398C4⋊Dic3—51no—
399C4⋊Dic3—51no—
400C4⋊Dic3—51no—
401C4⋊Dic3—51no—
402C4⋊Dic3—101no—
403C4⋊Dic3—101no—
404C4⋊Dic3—101no—
405C4⋊Dic3C22×D511yescharacteristic
406C4⋊Dic3C22×D511yescharacteristic
407C4×Dic3—21no—
408C4×Dic3—51no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C4×Dic3—101no—
412C4×Dic3—101no—
413C4×Dic3—101no—
414C4×Dic3C22×D511yescharacteristic
415#208—102no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8C22×D511yescharacteristic
418C23×C5—21no—
419C22×D5—21no—
420C22×D5—24no—
421C22×D5—81no—
422C22×D5—81no—
423C22×D5D3×D411yescharacteristic
424C5×Q8—21no—
425C5×Q8C22×Dic312yes—
426C5×D4—21no—
427C5×D4C22×Dic312yes—
428C2×C4×C5—21no—
429C2×C4×C5—31no—
430C2×C4×C5—31no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—241no—
434C2×C4×C5C23×D311yescharacteristic
435C22⋊D5—24no—
436C2×Dic5—21no—
437C2×Dic5—31no—
438C2×Dic5—31no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441C2×Dic5—241no—
442C2×Dic5D3×D411yescharacteristic
443D20—21no—
444D20C22×Dic312yes—
445C4×D5—24no—
446C4×D5—241no—
447C4×D5—241no—
448C4×D5#23712yes—
449C4×D5C22×Dic312yes—
450Dic10—21no—
451Dic10—24no—
452Dic10C22×Dic312yes—
453C5×C8—61no—
454C5×C8C22×Dic312yes—
455#168—61no—
456#168C22×Dic312yes—
457C22×Q8—51no—
458C22×D4—51no—
459C2×SD16—51no—
460C2×SD16—51no—
461C2×SD16—58no—
462C2×SD16—51no—
463C2×SD16D3×D511yescharacteristic
464C2×M16—151no—
465C22×C8—51no—
466C4×Q8—31no—
467C4×Q8—151no—
468C4×Q8—151no—
469C4×Q8—151no—
470C4×Q8—301no—
471C4×Q8—301no—
472C4×D4—31no—
473C4×D4—151no—
474C4×D4—151no—
475C4×D4—151no—
476C4×D4—301no—
477C4×D4—301no—
478#117—151no—
479#117—151no—
480#117—151no—
481#117—301no—
482#117—301no—
483C2×C22⋊C4—301no—
484C2×C22⋊C4—301no—
485#107—151no—
486#107—151no—
487#106—31no—
488#106—151no—
489#103—31no—
490#103—151no—
491#103—151no—
492#103—151no—
493#102—31no—
494#102—151no—
495#102—151no—
496#102—151no—
497#97—151no—
498#97—151no—
499C4×C8—31no—
500C4×C8—151no—
501C2×C3×C5—42no—
502C2×C3×C5C2×C4×D411yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C3×D5—22no—
506C3×D5—42no—
507C23×C3—21no—
508C23×C3—51no—
509C23×C3—104no—
510C23×C3—101no—
511C23×C3—401no—
512C23×C3—401no—
513C3×Q8—21no—
514C3×Q8—52no—
515C3×Q8—104no—
516C3×Q8—101no—
517C3×Q8C2×C4×D512yes—
518C3×D4—21no—
519C3×D4—52no—
520C3×D4—104no—
521C3×D4—101no—
522C3×D4C2×C4×D512yes—
523C2×C3×C4—21no—
524C2×C3×C4—51no—
525C2×C3×C4—52no—
526C2×C3×C4—52no—
527C2×C3×C4—104no—
528C2×C3×C4—101no—
529C2×C3×C4C23×D511yescharacteristic
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—51no—
533C2×Dic3—51no—
534C2×Dic3—81no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—401no—
538C2×Dic3—401no—
539C2×Dic3—401no—
540C2×Dic3D4×D511yescharacteristic
541C2×Dic3D4×D511yescharacteristic
542C3×C8—52no—
543C3×C8C2×C4×D512yes—
544C3⋊C8—21no—
545C3⋊C8—101no—
546C22×C5—22no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5C2×D3×D411yescharacteristic
550C2×D5—21no—
551C2×D5—21no—
552C2×D5—22no—
553C2×D5—41no—
554C2×D5—41no—
555C2×D5—84no—
556C2×D5D4×Dic312yes—
557C4×C5—22no—
558C4×C5—61no—
559C4×C5—61no—
560C4×C5—121no—
561C4×C5—121no—
562C4×C5C2×#23711yescharacteristic
563C4×C5C23×Dic311yescharacteristic
564Dic5—22no—
565Dic5—61no—
566Dic5—61no—
567Dic5—121no—
568Dic5—121no—
569Dic5D4×Dic312yes—
570C24—101no—
571C2×Q8—54no—
572C2×Q8—51no—
573C2×Q8—101no—
574C2×Q8—102no—
575C2×Q8C2×D3×D511yescharacteristic
576C2×D4—54no—
577C2×D4—51no—
578C2×D4—102no—
579C2×D4—101no—
580C2×D4C2×D3×D511yescharacteristic
581C22×C4—51no—
582C22×C4—61no—
583C22×C4—101no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587SD16—54no—
588SD16—54no—
589SD16—54no—
590SD16D5×Dic314yescomplemented
591M16—302no—
592C2×C8—31no—
593C2×C8—51no—
594C2×C8—54no—
595C2×C8—151no—
596C2×C8C2×D3×D511yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—151no—
601C4⋊C4—151no—
602C4⋊C4—151no—
603C4⋊C4—151no—
604C4⋊C4—301no—
605C4⋊C4—301no—
606C4⋊C4—301no—
607C22⋊C4—61no—
608C22⋊C4—151no—
609C22⋊C4—151no—
610C22⋊C4—301no—
611C22⋊C4—301no—
612C22⋊C4—301no—
613C22⋊C4—301no—
614C22⋊C4—301no—
615C42—31no—
616C42—61no—
617C42—151no—
618C42—301no—
619C42—301no—
620C42—301no—
621C42—301no—
622C42—301no—
623C3×C5#294911yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—52no—
628C22×C3—101no—
629C22×C3—101no—
630C22×C3—102no—
631C22×C3—201no—
632C22×C3—201no—
633C22×C3—404no—
634C22×C3C2×D4×D511yescharacteristic
635C3×C4—22no—
636C3×C4—52no—
637C3×C4—102no—
638C3×C4C22×C4×D511yescharacteristic
639C3×C4D5×#4111yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—41no—
643Dic3—41no—
644Dic3—101no—
645Dic3—101no—
646Dic3—201no—
647Dic3—201no—
648C2×C5—42no—
649C2×C5#576211yescharacteristic
650C2×C5#576211yescharacteristic
651C2×C5C2×D4×Dic311yescharacteristic
652D5—22no—
653D5—42no—
654C23—21no—
655C23—51no—
656C23—104no—
657C23—101no—
658C23—401no—
659C23—401no—
660Q8—21no—
661Q8—52no—
662Q8—104no—
663Q8—101no—
664Q8C2×D5×Dic312yes—
665D4—21no—
666D4—52no—
667D4—104no—
668D4—101no—
669D4C2×D5×Dic312yes—
670C2×C4—21no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—51no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—104no—
679C2×C4—101no—
680C2×C4—151no—
681C2×C4—151no—
682C2×C4—241no—
683C2×C4—301no—
684C2×C4—301no—
685C2×C4—1201no—
686C2×C4—1201no—
687C2×C4—1201no—
688C2×C4C22×D3×D511yescharacteristic
689C8—52no—
690C8—61no—
691C8—301no—
692C8C2×D5×Dic312yes—
693C2×C3—42no—
694C2×C3—102no—
695C2×C3—202no—
696C2×C3C4×D4×D511yescharacteristic
697C2×C3#6609611yescharacteristic
698C2×C3#6610411yescharacteristic
699C5#8384311yescharacteristic, complemented, Sylow
700C22—22no—
701C22—41no—
702C22—41no—
703C22—52no—
704C22—101no—
705C22—101no—
706C22—102no—
707C22—201no—
708C22—201no—
709C22—404no—
710C22D3×D4×D511yescharacteristic
711C4—22no—
712C4—52no—
713C4—61no—
714C4—61no—
715C4—102no—
716C4—121no—
717C4—121no—
718C4—301no—
719C4—301no—
720C4—601no—
721C4—601no—
722C4D5×#23711yescharacteristic
723C4C22×D5×Dic311yescharacteristic
724C3#1061138011yescharacteristic, complemented, Sylow
725C2—42no—
726C2—102no—
727C2—202no—
728C2#1175408011yescharacteristic
729C2#1175408711yescharacteristic
730C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C3×C4×C5C24
hypercenterC2×SD16D3×D5
hypocenterC3×C5#2949
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #11755140C2semidirect
4. SD16×Dic15C2semidirect
5. C5×Dic3×SD16C2semidirect
6. #11749241C2semidirect
7. #11749234C2semidirect
8. #11749208C2semidirect
9. #11749018C2semidirect
10. #11749010C2semidirect
12. #11747806C2semidirect
13. Dic3×#677C2semidirect
14. #11747671C2semidirect
15. #11747645C2semidirect
20. Q8×Dic15C22semidirect
22. C5×Q8×Dic3C22semidirect
26. C3×D5×SD16C4semidirect
41. #91331C22semidirect
43. Dic3×Dic10C22semidirect
45. #91119C22semidirect
47. #91101C22semidirect
48. C8×Dic15C22semidirect
49. C5×#835C22semidirect
51. C5×#817C22semidirect
52. C5×C8×Dic3C22semidirect
53. #90988C22semidirect
54. #90988C22semidirect
55. #90971C22semidirect
56. #90970C22semidirect
59. #90954C22semidirect
60. #90953C22semidirect
84. C3×Q8×D5C2×C4semidirect
94. C3×C5×SD16C2×C4semidirect
110. C3×#688C2×C4semidirect
111. C3×#687C2×C4semidirect
113. C3×#677C2×C4semidirect
114. C3×C8×D5C2×C4semidirect
142. Dic3×SD16D5semidirect
156. D5×SD16Dic3semidirect
244. Q8×Dic3C2×D5semidirect
260. #835C2×D5semidirect
268. #817C2×D5semidirect
272. C8×Dic3C2×D5semidirect
280. Q8×D5C2×Dic3semidirect
290. C5×SD16C2×Dic3semidirect
300. #688C2×Dic3semidirect
301. #687C2×Dic3semidirect
323. #677C2×Dic3semidirect
325. C8×D5C2×Dic3semidirect
385. C3×SD16C4×D5semidirect
590. SD16D5×Dic3semidirect
623. C3×C5#2949semidirect
699. C5#83843semidirect
724. C3#10611380semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×SD162
#117551402
#117549102
SD16×Dic152
C5×Dic3×SD162
#117492412
#117492342
#117492082
#117490182
#117490102
#117489622
#117478062
Dic3×#6772
#117476712
#117476452
#106113803
#838435