Finite Group Databasebeta

← #14415789

Subgroups — #14415789

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#208C211yesmaximal, characteristic, complemented
2C2×#91931C211yesmaximal, characteristic, complemented
3C2×#91444C211yesmaximal, characteristic
4C3×#65755C211yesmaximal, characteristic, complemented
5#11752012C211yesmaximal, characteristic, complemented
6#11752003C211yesmaximal, characteristic, complemented
7Dic3×#704C211yesmaximal, characteristic, complemented
8#11751925C212yesmaximal, complemented
9#11751903C212yesmaximal, complemented
10#11751882C212yesmaximal, complemented
11#11751779C212yesmaximal, complemented
12#10617084—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1202C411yescharacteristic
15C22×#1200C2211yescharacteristic
16C2×#6762C2211yescharacteristic
17C2×#6762C2211yescharacteristic
18D5⋊#208—24no—
19C2×#6758C2212yescomplemented
20C2×D5⋊(C3⋊C8)C2212yescomplemented
21C2×C3×#704C2211yescharacteristic
22C2×C3×#704C2211yescharacteristic
23C2×#6740C2212yescomplemented
24#91931—24no—
25C2×#6738C2212yescomplemented
26C2×#6714C411yescharacteristic
27C2×C5×Dic3⋊C4C411yescharacteristic
28C2×#6665C411yescharacteristic
29C2×Dic3×Dic5C2211yescharacteristic
30#91444C411yescharacteristic
31#91444C411yescharacteristic
32#91444C411yescharacteristic
33#91444C411yescharacteristic
34#91444C2211yescharacteristic
35#91444C2211yescharacteristic
36#91444C2211yescharacteristic
37#91444C2211yescharacteristic
38C3×#4003C2212yescomplemented
39C3×#4003C2212yescomplemented
40#91177C2212yescomplemented
41Dic3⋊#170C2212yescomplemented
42#91171C2212yescomplemented
43#91171C2212yescomplemented
44#91169C2212yescomplemented
45Dic3×#170C2212yescomplemented
46#78628—51nomaximal, Hall
47C2×D5⋊M16—31no—
48C2×D5⋊M16—31no—
49C2×#4039—31no—
50#65758—31no—
51#65755—31no—
52#65755D311yescharacteristic, complemented
53C4×#704—31no—
54#65705—32no—
55#65704—32no—
56#65704—32no—
57#65702—32no—
58C23×D15C2×C411yescharacteristic
59C23×C3×D5C2×C411yescharacteristic
60C22×C3×C4×C5C2×C411yescharacteristic
61C22×Dic15C2×C411yescharacteristic
62C22×C5×Dic3C2×C411yescharacteristic
63C22×C5×Dic3C2×C411yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C411yescharacteristic
68C2×C3×C4×D5C2×C411yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×#1202—24no—
72C2×#1202C2×C411yescharacteristic
73C2×#1202C2×C411yescharacteristic
74C2×#1202C2×C411yescharacteristic
75C2×#1202C2×C411yescharacteristic
76C2×#1200—22no—
77C2×#1200—22no—
78C2×#1200C2×C411yescharacteristic
79C2×#1200C2×C411yescharacteristic
80C2×#1200C2311yescharacteristic
81C2×#1200C2311yescharacteristic
82#6762—22no—
83#6762D414yescomplemented
84C2×C3⋊#170C2312yes—
85C2×C3⋊#170C2312yes—
86#6758—24no—
87D5⋊(C3⋊C8)—24no—
88C3×#704—22no—
89C3×#704—22no—
90C2×C3×#170C2312yes—
91C2×C3×#170C2312yes—
92#6740—24no—
93#6738—24no—
94#6714C2×C411yescharacteristic
95#6714C2×C411yescharacteristic
96#6714C2×C411yescharacteristic
97#6714C2×C411yescharacteristic
98C5×Dic3⋊C4C2×C411yescharacteristic
99C5×Dic3⋊C4C2×C411yescharacteristic
100C5×Dic3⋊C4C2×C411yescharacteristic
101C5×Dic3⋊C4C2×C411yescharacteristic
102#6665C2×C411yescharacteristic
103#6665C2×C411yescharacteristic
104#6665C2×C411yescharacteristic
105#6665C2×C411yescharacteristic
106Dic3×Dic5C2×C411yescharacteristic
107Dic3×Dic5C2×C411yescharacteristic
108Dic3×Dic5C2311yescharacteristic
109Dic3×Dic5C2311yescharacteristic
110C2×C4×#67—51no—
111C22×#208—51no—
112C2×D3×M16—51no—
113C3×#407—51no—
114#5126—51no—
115#5118—51no—
116Dic3×M16—51no—
117#4730—52no—
118#4729—52no—
119#4728—52no—
120#67⋊C8—52no—
121C22×D20—31no—
122C22×C4×D5—31no—
123C22×C4×D5C2×D311yescharacteristic
124C2×#704—31no—
125C2×#704—31no—
126C2×#704C2×D311yescharacteristic
127C2×#704C2×D311yescharacteristic
128D5⋊M16—64no—
129D5⋊M16—64no—
130C2×#700—32no—
131C2×#700—32no—
132C2×D5⋊C8—32no—
133C2×D5⋊C8—32no—
134C2×C5×C4⋊C4—31no—
135C2×#685—31no—
136C2×#685—31no—
137C2×C4×Dic5—31no—
138#4039—31no—
139#4039—31no—
140#4039—31no—
141#4039—31no—
142#4039—31no—
143#4039—31no—
144#4039—31no—
145#4039—31no—
146#4004—32no—
147#4003—32no—
148#4003—32no—
149#4003C2×D312yescomplemented
150#4003C2×D312yescomplemented
151#4002—32no—
152C4⋊#170—32no—
153C4×#170—32no—
154D4×M16—151noSylow
155C23×C3×C5C22×C411yescharacteristic
156C22×D15—22no—
157C22×D15—22no—
158C22×D15—41no—
159C22×D15C22×C411yescharacteristic
160C22×D15C22×C411yescharacteristic
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5—41no—
164C22×C3×D5C22×C411yescharacteristic
165C22×C3×D5C22×C411yescharacteristic
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×Dic15—41no—
170C2×Dic15C22×C411yescharacteristic
171C2×Dic15C22×C411yescharacteristic
172C2×C5×Dic3—22no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3C22×C411yescharacteristic
175C2×C5×Dic3C22×C411yescharacteristic
176C2×C5×Dic3C22×C411yescharacteristic
177C2×C5×Dic3C22×C411yescharacteristic
178C2×C3×Dic5C22×C411yescharacteristic
179C2×C3×Dic5C2×D412yes—
180C2×C3×Dic5#4112yes—
181C2×C3×Dic5C2411yescharacteristic
182C3×C4×D5—22no—
183C3×C4×D5—22no—
184C3×C4×D5—21no—
185C3×C4×D5—21no—
186C3×C4×D5—21no—
187C3×C4×D5—21no—
188#1202—22no—
189#1202—22no—
190#1202—22no—
191#1202M1614yescomplemented
192#1200—22no—
193#1200—22no—
194#1200—21no—
195#1200—21no—
196#1200—21no—
197#1200—21no—
198C3⋊#170—22no—
199C3⋊#170C2×D414yescomplemented
200C3×#170—22no—
201C3×#170—22no—
202C23×C3×C4—51no—
203C22×#67—51no—
204C22×C4×D3—51no—
205C2×C3×M16—51no—
206C2×C3×M16—51no—
207C2×#217—51no—
208C4×#67—51no—
209C4×#67—51no—
210C4×#67—51no—
211C4×#67—51no—
212C4×#67—51no—
213C4×#67—51no—
214C4×#67—51no—
215C4×#67—51no—
216C2×(C2×D3)⋊C4—51no—
217C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic
218C2×C4×Dic3—51no—
219C2×#208—51no—
220C2×#208—51no—
221C2×#208—52no—
222C2×#208—104no—
223C22×C3⋊C8—52no—
224D3×M16—104no—
225C2×ΓL(1,𝔽25)—52no—
226C2×D3×C8—52no—
227C3×C22⋊C8—52no—
228C3×C22⋊C8—52no—
229(C2×D3)⋊C8—52no—
230(C2×D3)⋊C8—52no—
231#815—52no—
232Dic3⋊C8—52no—
233Dic3⋊C8—52no—
234C8×Dic3—52no—
235C23×D5—31no—
236C23×D5C4×D311yescharacteristic
237C22×C4×C5—31no—
238C22×C4×C5—31no—
239C22×C4×C5C4×D311yescharacteristic
240C22×Dic5—31no—
241C22×Dic5C22×D311yescharacteristic
242C2×D20—31no—
243C2×D20—31no—
244C2×D20—31no—
245C2×D20—31no—
246C2×D20—64no—
247C2×C4×D5—22no—
248C2×C4×D5—22no—
249C2×C4×D5—31no—
250C2×C4×D5—31no—
251C2×C4×D5—31no—
252C2×C4×D5—31no—
253C2×C4×D5—62no—
254C2×C4×D5—62no—
255C2×C4×D5C4×D311yescharacteristic
256C2×C4×D5C4×D311yescharacteristic
257C2×C4×D5C22×D311yescharacteristic
258C2×C4×D5C22×D311yescharacteristic
259#704—22no—
260#704—22no—
261#704—34no—
262#704—62no—
263C2×#170—32no—
264C2×#170—32no—
265C2×#170C22×D312yes—
266C2×#170C22×D312yes—
267#700—64no—
268#700—64no—
269D5⋊C8—64no—
270D5⋊C8—64no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275#685—31no—
276#685—31no—
277#685—31no—
278#685—31no—
279#685—31no—
280#685—31no—
281#685—31no—
282#685—31no—
283C4×Dic5—31no—
284C4×Dic5—31no—
285C4×Dic5—31no—
286C4×Dic5—31no—
287C22×M16—151no—
288C22×M16—151no—
289C2×C4×D4—151no—
290#436—152no—
291#435—152no—
292#435—152no—
293C8×D4—152no—
294#423—151no—
295#407—51no—
296#407—151no—
297C4×M16—151no—
298C22×C3×C5—21no—
299C22×C3×C5—21no—
300C22×C3×C5C4×D412yes—
301C22×C3×C5C23×C411yescharacteristic
302C2×D15—21no—
303C2×D15—21no—
304C2×D15—21no—
305C2×D15—21no—
306C2×D15—21no—
307C2×D15—44no—
308C2×D15C2×M1612yescomplemented
309C2×C3×D5—21no—
310C2×C3×D5—21no—
311C2×C3×D5—21no—
312C2×C3×D5—21no—
313C2×C3×D5—21no—
314C2×C3×D5—44no—
315C2×C3×D5C2×M1612yescomplemented
316C3×C4×C5—21no—
317C3×C4×C5—21no—
318Dic15—21no—
319Dic15—21no—
320C3×Dic5C4×D412yes—
321C3×Dic5C22×D411yescharacteristic
322C3×Dic5C2×#4111yescharacteristic
323C5×Dic3—21no—
324C5×Dic3—21no—
325C5×Dic3—21no—
326C5×Dic3C2×M1612yescomplemented
327C24×C3—51no—
328C23×D3—51no—
329C22×C3×C4—51no—
330C22×C3×C4—51no—
331C22×C3×C4—51no—
332C22×C3×C4—51no—
333C22×C3×C4—51no—
334C22×C3×C4—102no—
335C22×C3×C4—102no—
336C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
337C2×#67—51no—
338C2×#67—51no—
339C2×#67—51no—
340C2×#67—51no—
341C2×#67—104no—
342C22×Dic3—51no—
343C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
344C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
345C2×C4×D3—51no—
346C2×C4×D3—51no—
347C2×C4×D3—51no—
348C2×C4×D3—51no—
349C2×C4×D3—102no—
350C2×C4×D3—102no—
351C3×M16—102no—
352C3×M16—102no—
353C2×C3×C8—52no—
354C2×C3×C8—52no—
355#217—51no—
356#217—51no—
357#217—51no—
358#217—51no—
359(C2×D3)⋊C4—51no—
360(C2×D3)⋊C4—51no—
361(C2×D3)⋊C4—51no—
362(C2×D3)⋊C4—51no—
363Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
364Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
365Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
366Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
367C4×Dic3—51no—
368C4×Dic3—51no—
369C4×Dic3—51no—
370C4×Dic3—51no—
371#208—54no—
372#208—104no—
373#208—102no—
374C2×C3⋊C8—52no—
375C2×C3⋊C8—52no—
376C2×C3⋊C8—104no—
377ΓL(1,𝔽25)—104no—
378D3×C8—104no—
379C23×C5C2×C4×D311yescharacteristic
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—31no—
383C22×D5—31no—
384C22×D5—41no—
385C22×D5—62no—
386C22×D5—62no—
387C22×D5—121no—
388C22×D5C2×C4×D311yescharacteristic
389C22×D5C2×C4×D311yescharacteristic
390C2×C4×C5—22no—
391C2×C4×C5—31no—
392C2×C4×C5—31no—
393C2×C4×C5—31no—
394C2×C4×C5—31no—
395C2×C4×C5—62no—
396C2×C4×C5—62no—
397C2×C4×C5C2×C4×D311yescharacteristic
398C2×C4×C5C2×C4×D311yescharacteristic
399C2×Dic5—31no—
400C2×Dic5—31no—
401C2×Dic5—121no—
402C2×Dic5C2×C4×D311yescharacteristic
403C2×Dic5D3×D412yes—
404C2×Dic5#23712yes—
405C2×Dic5C23×D311yescharacteristic
406D20—34no—
407D20—62no—
408D20—62no—
409D20—62no—
410C4×D5—22no—
411C4×D5—22no—
412C4×D5—21no—
413C4×D5—21no—
414C4×D5—21no—
415C4×D5—21no—
416C4×D5—62no—
417C4×D5—62no—
418C4×D5—61no—
419C4×D5—61no—
420C4×D5—61no—
421C4×D5—61no—
422#170—22no—
423#170—22no—
424#170—34no—
425#170—62no—
426C22×D4—151no—
427C23×C4—51no—
428C23×C4—151no—
429C2×M16—51no—
430C2×M16—51no—
431C2×M16—152no—
432C2×M16—151no—
433C2×M16—152no—
434C2×M16—151no—
435C2×M16—304no—
436C2×M16—304no—
437C22×C8—152no—
438C22×C8—152no—
439C4×D4—151no—
440C4×D4—151no—
441C4×D4—151no—
442C4×D4—151no—
443C4×D4—151no—
444C4×D4—151no—
445C4×D4—151no—
446C4×D4—151no—
447C2×C4⋊C4—31no—
448C2×C22⋊C4—151no—
449C2×C22⋊C4—151no—
450C2×C42—151no—
451C4⋊C8—152no—
452C4⋊C8—152no—
453C22⋊C8—52no—
454C22⋊C8—52no—
455C22⋊C8—152no—
456C22⋊C8—152no—
457#97—152no—
458C4×C8—152no—
459C2×C3×C5—22no—
460C2×C3×C5C2×C4×D411yescharacteristic
461C2×C3×C5C22×M1611yescharacteristic
462C2×C3×C5#56811yescharacteristic
463D15—22no—
464D15—41no—
465C3×D5—22no—
466C3×D5—41no—
467C23×C3—51no—
468C23×C3—51no—
469C23×C3—102no—
470C23×C3—102no—
471C23×C3—201no—
472C23×C3C22×AGL(1,𝔽5)11yescharacteristic
473C22×D3—51no—
474C22×D3—51no—
475C22×D3—102no—
476C22×D3—102no—
477C22×D3—201no—
478C2×C3×C4—22no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—51no—
482C2×C3×C4—51no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
490C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
491#67—54no—
492#67—102no—
493#67—102no—
494#67—102no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—51no—
498C2×Dic3—51no—
499C2×Dic3—201no—
500C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
501C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
502C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
503C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
504C4×D3—101no—
505C4×D3—101no—
506C4×D3—102no—
507C4×D3—102no—
508C4×D3—101no—
509C4×D3—101no—
510C3×C8—102no—
511C3×C8—102no—
512C3⋊C8—54no—
513C3⋊C8—102no—
514C22×C5—21no—
515C22×C5—21no—
516C22×C5#67⋊C412yes—
517C22×C5C22×C4×D311yescharacteristic
518C2×D5—21no—
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—21no—
522C2×D5—21no—
523C2×D5—32no—
524C2×D5—44no—
525C2×D5—61no—
526C2×D5—61no—
527C2×D5—61no—
528C2×D5—61no—
529C2×D5—61no—
530C2×D5—124no—
531C2×D5D3×M1612yescomplemented
532C4×C5—21no—
533C4×C5—21no—
534C4×C5—32no—
535C4×C5—61no—
536C4×C5—61no—
537C4×C5—61no—
538Dic5—61no—
539Dic5—61no—
540Dic5#67⋊C412yes—
541Dic5C2×D3×D411yescharacteristic
542Dic5C2×#23711yescharacteristic
543C24—51no—
544C24—151no—
545C2×D4—151no—
546C2×D4—151no—
547C2×D4—151no—
548C2×D4—151no—
549C2×D4—304no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—51no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4D3×AGL(1,𝔽5)11yescharacteristic
567M16—102no—
568M16—102no—
569M16—154no—
570M16—304no—
571M16—304no—
572M16—302no—
573C2×C8—52no—
574C2×C8—52no—
575C2×C8—152no—
576C2×C8—152no—
577C2×C8—304no—
578C2×C8—304no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C22⋊C4—151no—
584C22⋊C4—151no—
585C22⋊C4—151no—
586C22⋊C4—151no—
587C22⋊C4—151no—
588C22⋊C4—151no—
589C22⋊C4—151no—
590C22⋊C4—151no—
591C42—151no—
592C42—151no—
593C42—151no—
594C42—151no—
595C3×C5D4×M1611yescharacteristic, complemented, Hall
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—52no—
599C22×C3—101no—
600C22×C3—101no—
601C22×C3—101no—
602C22×C3—101no—
603C22×C3—101no—
604C22×C3—204no—
605C22×C3D4×AGL(1,𝔽5)12yes—
606C22×C3C23×AGL(1,𝔽5)11yescharacteristic
607C2×D3—52no—
608C2×D3—101no—
609C2×D3—101no—
610C2×D3—101no—
611C2×D3—101no—
612C2×D3—101no—
613C2×D3—204no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—52no—
617C3×C4—51no—
618C3×C4—51no—
619Dic3—21no—
620Dic3—21no—
621Dic3—21no—
622Dic3—101no—
623Dic3—101no—
624Dic3D5⋊M1612yescomplemented
625C2×C5—22no—
626C2×C5C2×#67⋊C411yescharacteristic
627C2×C5C2×D3×M1611yescharacteristic
628C2×C5#574511yescharacteristic
629D5—22no—
630D5—41no—
631D5—62no—
632D5—121no—
633C23—51no—
634C23—51no—
635C23—102no—
636C23—102no—
637C23—151no—
638C23—151no—
639C23—201no—
640C23—302no—
641C23—302no—
642C23—601no—
643C23C2×D3×AGL(1,𝔽5)11yescharacteristic
644D4—154no—
645D4—302no—
646D4—302no—
647D4—302no—
648C2×C4—22no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—52no—
654C2×C4—52no—
655C2×C4—51no—
656C2×C4—51no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—151no—
666C2×C4—151no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—601no—
674C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
675C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
676C8—102no—
677C8—102no—
678C8—154no—
679C8—302no—
680C2×C3—22no—
681C2×C3—102no—
682C2×C3—201no—
683C2×C3C2×D5⋊M1611yescharacteristic
684C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
685C2×C3#6626011yescharacteristic
686D3—102no—
687D3—201no—
688C5#7862811yescharacteristic, complemented, Sylow
689C22—21no—
690C22—21no—
691C22—52no—
692C22—101no—
693C22—101no—
694C22—101no—
695C22—101no—
696C22—101no—
697C22—152no—
698C22—204no—
699C22—301no—
700C22—301no—
701C22—301no—
702C22—301no—
703C22—301no—
704C22—604no—
705C22#67⋊AGL(1,𝔽5)12yes—
706C22C22×D3×AGL(1,𝔽5)11yescharacteristic
707C4—21no—
708C4—21no—
709C4—32no—
710C4—51no—
711C4—51no—
712C4—52no—
713C4—61no—
714C4—61no—
715C4—61no—
716C4—301no—
717C4—301no—
718C3#1061708411yescharacteristic, complemented, Sylow
719C2—22no—
720C2—102no—
721C2—201no—
722C2—302no—
723C2—601no—
724C2D3×D5⋊M1611yescharacteristic
725C2#1175682711yescharacteristic
726C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC22×#1202C4
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×D5⋊#208C2semidirect
2. C2×#91931C2semidirect
4. C3×#65755C2semidirect
5. #11752012C2semidirect
6. #11752003C2semidirect
7. Dic3×#704C2semidirect
8. #11751925C2semidirect
9. #11751903C2semidirect
10. #11751882C2semidirect
11. #11751779C2semidirect
19. C2×#6758C22semidirect
20. C2×D5⋊(C3⋊C8)C22semidirect
23. C2×#6740C22semidirect
25. C2×#6738C22semidirect
38. C3×#4003C22semidirect
39. C3×#4003C22semidirect
40. #91177C22semidirect
41. Dic3⋊#170C22semidirect
42. #91171C22semidirect
43. #91171C22semidirect
44. #91169C22semidirect
45. Dic3×#170C22semidirect
52. #65755D3semidirect
83. #6762D4semidirect
149. #4003C2×D3semidirect
150. #4003C2×D3semidirect
191. #1202M16semidirect
199. C3⋊#170C2×D4semidirect
308. C2×D15C2×M16semidirect
315. C2×C3×D5C2×M16semidirect
326. C5×Dic3C2×M16semidirect
531. C2×D5D3×M16semidirect
595. C3×C5D4×M16semidirect
624. Dic3D5⋊M16semidirect
688. C5#78628semidirect
718. C3#10617084semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#2082
C2×#919312
C2×#914442
C3×#657552
#117520122
#117520032
Dic3×#7042
#117519252
#117519032
#117518822
#117517792
#106170843
#786285