Finite Group Databasebeta

← #14417448

Subgroups — #14417448

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
1C3×#65879C211yesmaximal, characteristic
2C2×D5×#214C211yesmaximal, characteristic
3#11752516C211yesmaximal, characteristic, complemented
4#11751119C211yesmaximal, characteristic, complemented
5C4×C5×#214C211yesmaximal, characteristic, complemented
6#11749004C211yesmaximal, characteristic, complemented
7Dic5×#214C211yesmaximal, characteristic, complemented
8#11748962C211yesmaximal, characteristic
9#11747487C211yesmaximal, characteristic, complemented
10#11747471C211yesmaximal, characteristic, complemented
11#11747433C211yesmaximal, characteristic, complemented
12#11747268C211yesmaximal, characteristic, complemented
13C4×#6657C211yesmaximal, characteristic, complemented
14#11747048C211yesmaximal, characteristic, complemented
15#11746974C211yesmaximal, characteristic, complemented
16#10611380—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×D5×Dic6C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C4×Dic30C2211yescharacteristic, complemented
22C2×C5×#214C2211yescharacteristic
23C4×C5×Dic6C2211yescharacteristic, complemented
24C3×D4×Dic5C2211yescharacteristic
25C3×C4×C22⋊D5—21no—
26C2×C3×#685—21no—
27C3×#4039C2211yescharacteristic
28C3×#4038C2211yescharacteristic
29C3×#4027—21no—
30C3×D5×C22⋊C4—21no—
31C3×C4×D20C2211yescharacteristic
32C3×#4018C2211yescharacteristic
33D5×#214C418yescomplemented
34#91394—21no—
35#91393—21no—
36#91358C2211yescharacteristic
37#91333C2211yescharacteristic, complemented
38Dic5×Dic6C2211yescharacteristic, complemented
39#91325—21no—
40#91324—21no—
41C2×#6657C2211yescharacteristic
42C2×#6655C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91116C2211yescharacteristic
46#91094C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48#91087C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic
50C5×#810C2211yescharacteristic, complemented
51C5×#808C2211yescharacteristic, complemented
52C4×C5×C3⋊C8C2211yescharacteristic, complemented
53#90989C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90974C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90952C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#82543—51nomaximal, Hall
62C2×D5×SD16—31no—
63#65906—31no—
64#65879D311yescharacteristic
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×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×Dic30C2311yescharacteristic
81C2×C5×Dic6C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C22×C3×Dic5—21no—
84C3×D4×D5—22no—
85C3×D4×D5C2×C414yes—
86C2×C3×D20C2311yescharacteristic
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×#1204—21no—
91C2×D5×Dic3—21no—
92D5×Dic6—22no—
93D5×Dic6C2×C414yescomplemented
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97#6716C2×C414yescomplemented
98C4⋊Dic15C2311yescharacteristic
99#6712—21no—
100C4×Dic15—21no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#214C2×C414yescomplemented
104C5×C4⋊Dic3C2311yescharacteristic
105C5×Dic3⋊C4—21no—
106C4×C5×Dic3—21no—
107C2×C5×C3⋊C8C2311yescharacteristic
108C2×C5×C3⋊C8C2311yescharacteristic
109C3×C22⋊Dic5—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×#685D411yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683D411yescharacteristic
117C3×#683D411yescharacteristic
118C3×C4×Dic5—21no—
119C3×C4×Dic5C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6665—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126#6657C2×C414yescomplemented
127#6655C2×C414yescomplemented
128#6649—22no—
129D5×C3⋊C8C2×C414yescomplemented
130C3×#518—51no—
131C22×#214—51no—
132#5516—51no—
133#5215—51no—
134#5018—51no—
135#5018—51no—
136#5018—51no—
137#5018—51no—
138C4×#214—51no—
139C4×#214—51no—
140C4×#214—51no—
141C4×#214D511yescharacteristic, complemented
142#5004—51no—
143#4998—51no—
144#4997—51no—
145C2×Q8×D5—31no—
146C2×D4×D5C2×D311yescharacteristic
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4C2×D311yescharacteristic
150Q8×Dic5—31no—
151C2×#688—31no—
152D4×Dic5C2×D311yescharacteristic
153C2×#687—31no—
154C4×C22⋊D5—21no—
155C2×#685—21no—
156D5×SD16—38no—
157C2×#677—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4039C2×D311yescharacteristic
161#4038—31no—
162#4038—61no—
163#4038C2×D311yescharacteristic
164#4033—31no—
165#4033—61no—
166#4027—21no—
167D5×C22⋊C4—21no—
168C4×D20C2×D311yescharacteristic
169#4018—61no—
170#4018C2×D311yescharacteristic
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×D4—21no—
197C3×C5×D4C22×C412yes—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205Dic30—21no—
206Dic30C22×C412yes—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C5×Dic6—21no—
210C5×Dic6C22×C412yes—
211C3×C22⋊D5—24no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—81no—
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—21no—
218C3×D20C22×C412yes—
219C3×C4×D5—81no—
220C3×C4×D5—81no—
221C3×C4×D5C22×C412yes—
222C3×C4×D5#4112yes—
223#1204—24no—
224D5×Dic3—24no—
225C3⋊#168—21no—
226C3⋊#168C22×C412yes—
227C5×C3⋊C8—21no—
228C5×C3⋊C8C22×C412yes—
229C22×C3×D4—51no—
230C22×Dic6—51no—
231C3×C4×D4—51no—
232C3×C4×D4—51no—
233C3×C4×D4—51no—
234C3×C4×D4—101no—
235C3×C4×D4—101no—
236C3×C4×D4C2×D511yescharacteristic
237C3×#117—51no—
238C3×#117—51no—
239C2×C3×C22⋊C4—101no—
240C2×C3×C22⋊C4—101no—
241C2×#214—51no—
242C2×#214—51no—
243C2×#214—58no—
244C2×#214—51no—
245C2×#214C2×D511yescharacteristic
246#926—51no—
247C2×#208—51no—
248C22×C3⋊C8—51no—
249#887—101no—
250#887—101no—
251#877—101no—
252#877—101no—
253C4×Dic6—51no—
254C4×Dic6—51no—
255C4×Dic6—51no—
256C4×Dic6C2×D511yescharacteristic, complemented
257#832—51no—
258#832—51no—
259#832—51no—
260#832C2×D511yescharacteristic
261#810—51no—
262#810—51no—
263#810—51no—
264#810C2×D511yescharacteristic, complemented
265#808—51no—
266#808C2×D511yescharacteristic, complemented
267#807—51no—
268#807—51no—
269#803—51no—
270#803—51no—
271C4×C3⋊C8—51no—
272C4×C3⋊C8C2×D511yescharacteristic, complemented
273C23×D5—21no—
274C2×C5×Q8—31no—
275C2×C5×D4C22×D311yescharacteristic
276C22×C4×C5—21no—
277C2×C22⋊D5—21no—
278C22×Dic5—21no—
279Q8×D5—34no—
280Q8×D5—62no—
281D4×D5—22no—
282D4×D5C4×D314yes—
283C2×D20C22×D311yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5—61no—
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—31no—
289C2×Dic10—61no—
290C5×SD16—34no—
291C2×C5×C8—31no—
292C2×C5×C8—31no—
293C5×C4⋊C4—31no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4C22×D311yescharacteristic
296C5×C22⋊C4—21no—
297C42×C5—61no—
298C42×C5C22×D311yescharacteristic
299C22⋊Dic5—21no—
300#688—34no—
301#687—34no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685—61no—
306#685#6711yescharacteristic
307#685#6711yescharacteristic
308C4⋊Dic5—31no—
309C4⋊Dic5—61no—
310C4⋊Dic5C22×D311yescharacteristic
311#683—61no—
312#683—61no—
313#683#6711yescharacteristic
314#683#6711yescharacteristic
315C4×Dic5—21no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C4×Dic5C22×D311yescharacteristic
321C2×#168—31no—
322C2×#168—31no—
323#677—34no—
324#676—62no—
325C8×D5—34no—
326C22×SD16—151no—
327#519—151no—
328#518—51no—
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—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5C23×C411yescharacteristic
356C3×C4×C5C2×#4111yescharacteristic
357Dic15—22no—
358Dic15—41no—
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—41no—
362C3×Dic5C4×D412yes—
363C5×Dic3—22no—
364C5×Dic3—41no—
365C24×C3—101no—
366C2×C3×D4—54no—
367C2×C3×D4—51no—
368C2×C3×D4—102no—
369C2×C3×D4—101no—
370C2×C3×D4C22×D511yescharacteristic
371C22×C3×C4—21no—
372C22×C3×C4—51no—
373C22×C3×C4—101no—
374C22×C3×C4—101no—
375C22×C3×C4—101no—
376C22×Dic3—101no—
377C2×Dic6—51no—
378C2×Dic6—54no—
379C2×Dic6—102no—
380C2×Dic6—101no—
381C2×Dic6C22×D511yescharacteristic
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4C22×D511yescharacteristic
386C3×C22⋊C4—21no—
387C3×C22⋊C4—51no—
388C3×C22⋊C4—51no—
389C3×C22⋊C4—101no—
390C3×C22⋊C4—101no—
391C3×C22⋊C4—101no—
392C3×C22⋊C4—101no—
393C3×C42—51no—
394C3×C42—101no—
395C3×C42C22×D511yescharacteristic
396#217—101no—
397#214—54no—
398#214—54no—
399#214—54no—
400#214C4×D514yescomplemented
401C4⋊Dic3—51no—
402C4⋊Dic3C22×D511yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—101no—
405Dic3⋊C4—101no—
406Dic3⋊C4—101no—
407C4×Dic3—21no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C4×Dic3—101no—
412#208—102no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—54no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8C22×D511yescharacteristic
417C2×C3⋊C8C22×D511yescharacteristic
418C23×C5—21no—
419C22×D5—21no—
420C22×D5—24no—
421C22×D5—81no—
422C22×D5—81no—
423C22×D5C2×#6711yescharacteristic
424C5×Q8—32no—
425C5×Q8—61no—
426C5×D4—21no—
427C5×D4C2×C4×D312yes—
428C2×C4×C5—21no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—81no—
432C2×C4×C5C2×#6711yescharacteristic
433C2×C4×C5C2×#6711yescharacteristic
434C2×C4×C5C23×D311yescharacteristic
435C22⋊D5—24no—
436C2×Dic5—21no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C2×Dic5—81no—
440C2×Dic5C2×#6711yescharacteristic
441C2×Dic5C2×#6711yescharacteristic
442C2×Dic5C2×#6711yescharacteristic
443D20—21no—
444D20C2×C4×D312yes—
445C4×D5—64no—
446C4×D5—81no—
447C4×D5—81no—
448C4×D5C2×C4×D312yes—
449C4×D5#23512yes—
450Dic10—32no—
451Dic10—61no—
452Dic10—64no—
453C5×C8—32no—
454C5×C8—61no—
455#168—32no—
456#168—61no—
457C22×Q8—151no—
458C22×D4—51no—
459C2×SD16—31no—
460C2×SD16—151no—
461C2×SD16—158no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×M16—151no—
465C22×C8—151no—
466C4×Q8—31no—
467C4×Q8—151no—
468C4×Q8—151no—
469C4×Q8—151no—
470C4×Q8—301no—
471C4×Q8—301no—
472C4×D4—51no—
473C4×D4—51no—
474C4×D4—51no—
475C4×D4—101no—
476C4×D4—101no—
477C4×D4D3×D511yescharacteristic
478#117—51no—
479#117—51no—
480#117—151no—
481#117—301no—
482#117—301no—
483C2×C22⋊C4—101no—
484C2×C22⋊C4—101no—
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×D4—21no—
514C3×D4—52no—
515C3×D4—104no—
516C3×D4—101no—
517C3×D4C2×C4×D512yes—
518C2×C3×C4—21no—
519C2×C3×C4—51no—
520C2×C3×C4—52no—
521C2×C3×C4—52no—
522C2×C3×C4—51no—
523C2×C3×C4—51no—
524C2×C3×C4—81no—
525C2×C3×C4—101no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4—401no—
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—104no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537Dic6—21no—
538Dic6—52no—
539Dic6—104no—
540Dic6—101no—
541Dic6C2×C4×D512yes—
542C3⋊C8—21no—
543C3⋊C8—52no—
544C3⋊C8—101no—
545C3⋊C8C2×C4×D512yes—
546C22×C5—22no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5C22×#6711yescharacteristic
550C2×D5—21no—
551C2×D5—21no—
552C2×D5—22no—
553C2×D5—41no—
554C2×D5—41no—
555C2×D5—84no—
556C2×D5C4×#6712yes—
557C4×C5—21no—
558C4×C5—21no—
559C4×C5—41no—
560C4×C5—62no—
561C4×C5—121no—
562C4×C5C22×C4×D311yescharacteristic
563C4×C5C2×#23511yescharacteristic
564Dic5—21no—
565Dic5—21no—
566Dic5—41no—
567Dic5—62no—
568Dic5—121no—
569Dic5C4×#6712yes—
570C24—101no—
571C2×Q8—31no—
572C2×Q8—154no—
573C2×Q8—151no—
574C2×Q8—301no—
575C2×Q8—302no—
576C2×D4—54no—
577C2×D4—51no—
578C2×D4—102no—
579C2×D4—101no—
580C2×D4C2×D3×D511yescharacteristic
581C22×C4—21no—
582C22×C4—51no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—301no—
587SD16—34no—
588SD16—154no—
589SD16—154no—
590SD16—154no—
591M16—302no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—154no—
595C2×C8—151no—
596C2×C8—151no—
597C4⋊C4—31no—
598C4⋊C4—51no—
599C4⋊C4—51no—
600C4⋊C4—51no—
601C4⋊C4—61no—
602C4⋊C4—151no—
603C4⋊C4—301no—
604C4⋊C4—301no—
605C4⋊C4—301no—
606C4⋊C4C2×D3×D511yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—51no—
609C22⋊C4—51no—
610C22⋊C4—101no—
611C22⋊C4—101no—
612C22⋊C4—101no—
613C22⋊C4—101no—
614C22⋊C4—301no—
615C42—51no—
616C42—61no—
617C42—101no—
618C42—301no—
619C42—301no—
620C42—301no—
621C42—301no—
622C42C2×D3×D511yescharacteristic
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—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—52no—
639C3×C4—101no—
640C3×C4—101no—
641C3×C4—201no—
642C3×C4C22×C4×D511yescharacteristic
643C3×C4D5×#4111yescharacteristic
644Dic3—22no—
645Dic3—41no—
646Dic3—102no—
647Dic3—201no—
648C2×C5—42no—
649C2×C5C2×C4×#6711yescharacteristic
650C2×C5#583611yescharacteristic
651C2×C5#583611yescharacteristic
652D5—22no—
653D5—42no—
654C23—21no—
655C23—51no—
656C23—104no—
657C23—101no—
658C23—401no—
659C23—401no—
660Q8—32no—
661Q8—61no—
662Q8—152no—
663Q8—304no—
664Q8—301no—
665D4—21no—
666D4—52no—
667D4—104no—
668D4—101no—
669D4C4×D3×D512yes—
670C2×C4—21no—
671C2×C4—51no—
672C2×C4—52no—
673C2×C4—52no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—81no—
679C2×C4—101no—
680C2×C4—304no—
681C2×C4—301no—
682C2×C4—301no—
683C2×C4—401no—
684C2×C4—401no—
685C2×C4—401no—
686C2×C4D5×#6711yescharacteristic
687C2×C4D5×#6711yescharacteristic
688C2×C4C22×D3×D511yescharacteristic
689C8—32no—
690C8—61no—
691C8—152no—
692C8—301no—
693C2×C3—42no—
694C2×C3—102no—
695C2×C3—202no—
696C2×C3C4×D4×D511yescharacteristic
697C2×C3#6609611yescharacteristic
698C2×C3#6610411yescharacteristic
699C5#8254311yescharacteristic, complemented, Sylow
700C22—22no—
701C22—41no—
702C22—41no—
703C22—52no—
704C22—101no—
705C22—101no—
706C22—102no—
707C22—201no—
708C22—201no—
709C22—404no—
710C22C2×D5×#6711yescharacteristic
711C4—21no—
712C4—21no—
713C4—41no—
714C4—52no—
715C4—62no—
716C4—101no—
717C4—101no—
718C4—121no—
719C4—201no—
720C4—302no—
721C4—601no—
722C4C2×C4×D3×D511yescharacteristic
723C4D5×#23511yescharacteristic
724C3#1061138011yescharacteristic, complemented, Sylow
725C2—42no—
726C2—102no—
727C2—202no—
728C2C4×D5×#6711yescharacteristic
729C2#1175470711yescharacteristic
730C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2949
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11752516C2semidirect
4. #11751119C2semidirect
5. C4×C5×#214C2semidirect
6. #11749004C2semidirect
7. Dic5×#214C2semidirect
9. #11747487C2semidirect
10. #11747471C2semidirect
11. #11747433C2semidirect
12. #11747268C2semidirect
13. C4×#6657C2semidirect
14. #11747048C2semidirect
15. #11746974C2semidirect
21. C4×Dic30C22semidirect
23. C4×C5×Dic6C22semidirect
33. D5×#214C4semidirect
37. #91333C22semidirect
38. Dic5×Dic6C22semidirect
46. #91094C22semidirect
47. #91091C22semidirect
48. #91087C22semidirect
50. C5×#810C22semidirect
51. C5×#808C22semidirect
52. C4×C5×C3⋊C8C22semidirect
53. #90989C22semidirect
54. #90987C22semidirect
55. #90974C22semidirect
56. #90972C22semidirect
59. #90952C22semidirect
60. Dic5×C3⋊C8C22semidirect
93. D5×Dic6C2×C4semidirect
97. #6716C2×C4semidirect
103. C5×#214C2×C4semidirect
126. #6657C2×C4semidirect
127. #6655C2×C4semidirect
129. D5×C3⋊C8C2×C4semidirect
141. C4×#214D5semidirect
256. C4×Dic6C2×D5semidirect
264. #810C2×D5semidirect
266. #808C2×D5semidirect
272. C4×C3⋊C8C2×D5semidirect
400. #214C4×D5semidirect
623. C3×C5#2949semidirect
699. C5#82543semidirect
724. C3#10611380semidirect

Maximal subgroups

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

subgroupindex
C3×#658792
C2×D5×#2142
#117525162
#117511192
C4×C5×#2142
#117490042
Dic5×#2142
#117489622
#117474872
#117474712
#117474332
#117472682
C4×#66572
#117470482
#117469742
#106113803
#825435