Finite Group Databasebeta

← #14306102

Subgroups — #14306102

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#939C211yesmaximal, characteristic
2C2×#91118C211yesmaximal, characteristic, complemented
3C2×C3×#3966C211yesmaximal, characteristic, complemented
4#11749513C211yesmaximal, characteristic, complemented
5Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C2×#90996C211yesmaximal, characteristic, complemented
7C2×#90996C211yesmaximal, characteristic, complemented
8#10602479—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×#67C411yescharacteristic, complemented
11C22×C5×#67C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×C5×#217C411yescharacteristic, complemented
16C5×#939—21no—
17C5×#939—21no—
18C5×#939—21no—
19C5×#939—21no—
20C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
21C2×C5×Dic3⋊C4C411yescharacteristic, complemented
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×Dic3⋊Dic5—21no—
25C2×Dic3×Dic5—21no—
26#91118—22no—
27C3×#3966—22no—
28#90996—22no—
29#90996—22no—
30#90994—21no—
31#90994—21no—
32#70030—51nomaximal, Hall
33C2×C5×#121—31no—
34C2×#3966—31no—
35C2×#3966—31no—
36C2×#3966—31no—
37C2×#3966D311yescharacteristic, complemented
38#65501—31no—
39C4×C22⋊Dic5—31no—
40C24×C3×C5C2×C411yescharacteristic
41C24×C3×C5C2311yescharacteristic
42C23×C5×D3C2×C411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C22×C3×C4×C5C2×C411yescharacteristic
50C22×Dic15—21no—
51C22×Dic15—21no—
52C2×C5×#67—21no—
53C2×C5×#67—21no—
54C2×C5×#67—21no—
55C2×C5×#67—21no—
56C2×C5×#67—21no—
57C2×C5×#67—21no—
58C2×C5×#67—21no—
59C2×C5×#67—21no—
60C2×C5×#67—42no—
61C22×C5×Dic3—42no—
62C22×C5×Dic3C2×C411yescharacteristic
63C22×C5×Dic3C2×C411yescharacteristic
64C22×C5×Dic3C2×C411yescharacteristic
65C22×C5×Dic3D411yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C22×C5×Dic3D411yescharacteristic
68C22×C5×Dic3D411yescharacteristic
69C22×C3×Dic5—21no—
70C22×C3×Dic5—21no—
71#6719—21no—
72#6719—21no—
73#6719—21no—
74#6719D412yescomplemented
75C5×#217—21no—
76C5×#217—21no—
77C5×(C2×D3)⋊C4—21no—
78C5×(C2×D3)⋊C4—21no—
79C5×Dic3⋊C4—21no—
80C5×Dic3⋊C4—21no—
81C3×C22⋊Dic5—21no—
82C3×C22⋊Dic5—21no—
83C3×C22⋊Dic5—21no—
84C3×C22⋊Dic5D412yescomplemented
85Dic3⋊Dic5—42no—
86Dic3×Dic5—42no—
87C2×#939D511yescharacteristic
88C2×C3×#99—51no—
89C2×#834—51no—
90C2×#806—51no—
91C2×#806—51no—
92#4942—51no—
93Dic3×C22⋊C4—51no—
94C22×C5×D4—31no—
95C22×C5×D4—31no—
96C22×C5×D4C2×D311yescharacteristic
97C23×C4×C5—31no—
98C5×#121—61no—
99C5×#121—61no—
100C5×#121—61no—
101C5×#121—61no—
102C2×C5×C4⋊C4—31no—
103C2×C5×C22⋊C4—31no—
104C2×C5×C22⋊C4—31no—
105C2×C22⋊Dic5—31no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5C2×D311yescharacteristic
108C2×C22⋊Dic5C2×D311yescharacteristic
109C2×C4⋊Dic5—61no—
110C2×C4×Dic5—61no—
111#3966—22no—
112#3966—62no—
113#3966—62no—
114#3966—62no—
115#3963—61no—
116#3963—61no—
117#1964—151noSylow
118C23×C3×C5—21no—
119C23×C3×C5—21no—
120C23×C3×C5—21no—
121C23×C3×C5—41no—
122C23×C3×C5—41no—
123C23×C3×C5—41no—
124C23×C3×C5—41no—
125C23×C3×C5C22×C411yescharacteristic
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×D411yescharacteristic
130C23×C3×C5#4111yescharacteristic
131C23×C3×C5#4111yescharacteristic
132C22×C5×D3—21no—
133C22×C5×D3—21no—
134C22×C5×D3—21no—
135C22×C5×D3—41no—
136C22×C5×D3—41no—
137C3×C5×D4—41no—
138C3×C5×D4—41no—
139C3×C5×D4—41no—
140C3×C5×D4—41no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×Dic15—22no—
145C2×Dic15—41no—
146C2×Dic15—41no—
147C2×Dic15—41no—
148C2×Dic15—41no—
149C2×Dic15—41no—
150C5×#67—42no—
151C5×#67—41no—
152C5×#67—41no—
153C5×#67—41no—
154C5×#67—41no—
155C5×#67—42no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—21no—
161C2×C5×Dic3—21no—
162C2×C5×Dic3—41no—
163C2×C5×Dic3—41no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3C22⋊C411yescharacteristic
166C2×C5×Dic3C22⋊C411yescharacteristic
167C2×C5×Dic3C22⋊C411yescharacteristic
168C2×C5×Dic3C22⋊C411yescharacteristic
169C2×C3×Dic5—22no—
170C2×C3×Dic5—41no—
171C2×C3×Dic5—41no—
172C2×C3×Dic5—41no—
173C2×C3×Dic5—41no—
174C2×C3×Dic5—41no—
175C22×C3×D4C2×D511yescharacteristic
176C22×#67Dic511yescharacteristic, complemented
177C22×#67C2×D511yescharacteristic
178C23×Dic3C2×D511yescharacteristic
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4—51no—
181C2×#217—51no—
182C2×#217—51no—
183C2×#217Dic511yescharacteristic, complemented
184#939—21no—
185#939—21no—
186#939—21no—
187#939—21no—
188C2×(C2×D3)⋊C4Dic511yescharacteristic, complemented
189C2×Dic3⋊C4—101no—
190C2×Dic3⋊C4Dic511yescharacteristic, complemented
191C2×C4×Dic3—101no—
192C3×#99—102no—
193#834—102no—
194C3⋊#95—101no—
195C3⋊#95—101no—
196#806—102no—
197#806—102no—
198C24×C5—31no—
199C24×C5C4×D311yescharacteristic
200C24×C5C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—61no—
208C2×C5×D4—61no—
209C2×C5×D4—61no—
210C2×C5×D4—61no—
211C2×C5×D4—61no—
212C2×C5×D4—61no—
213C2×C5×D4—61no—
214C2×C5×D4—61no—
215C2×C5×D4—122no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—31no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—122no—
224C22×C4×C5C4×D311yescharacteristic
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—61no—
228C22×Dic5—61no—
229C5×C4⋊C4—61no—
230C5×C4⋊C4—61no—
231C5×C22⋊C4—61no—
232C5×C22⋊C4—61no—
233C5×C22⋊C4—61no—
234C5×C22⋊C4—61no—
235C22⋊Dic5—21no—
236C22⋊Dic5—21no—
237C22⋊Dic5—21no—
238C22⋊Dic5—32no—
239C22⋊Dic5—61no—
240C22⋊Dic5—61no—
241C22⋊Dic5—61no—
242C22⋊Dic5#6712yescomplemented
243C4⋊Dic5—122no—
244C4×Dic5—122no—
245C2×#121—31no—
246C2×#99—51no—
247C2×#99—151no—
248C2×#99—151no—
249C2×#99—151no—
250#380—151no—
251C4×C22⋊C4—151no—
252C22×C3×C5—21no—
253C22×C3×C5—21no—
254C22×C3×C5—21no—
255C22×C3×C5—21no—
256C22×C3×C5—21no—
257C22×C3×C5—21no—
258C22×C3×C5—41no—
259C22×C3×C5—41no—
260C22×C3×C5—41no—
261C22×C3×C5—41no—
262C22×C3×C5—41no—
263C22×C3×C5—41no—
264C22×C3×C5—41no—
265C22×C3×C5—81no—
266C22×C3×C5—81no—
267C22×C3×C5C2×C22⋊C411yescharacteristic
268C22×C3×C5C4×D411yescharacteristic
269C22×C3×C5C4×D411yescharacteristic
270C22×C3×C5#12111yescharacteristic
271C22×C3×C5#12111yescharacteristic
272C22×C3×C5#12411yescharacteristic
273C22×C3×C5#12711yescharacteristic
274C2×C5×D3—41no—
275C2×C5×D3—41no—
276C2×C5×D3—41no—
277C2×C5×D3—81no—
278C2×C5×D3—81no—
279C3×C4×C5—41no—
280Dic15—42no—
281Dic15—81no—
282C3×Dic5—42no—
283C3×Dic5—81no—
284C5×Dic3—21no—
285C5×Dic3—21no—
286C5×Dic3—21no—
287C5×Dic3—41no—
288C5×Dic3#9912yescomplemented
289C24×C3C2×Dic511yescharacteristic
290C24×C3C22×D511yescharacteristic
291C23×D3C2×Dic511yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C22×C3×C4—101no—
299C22×C3×C4—101no—
300C22×C3×C4C2×Dic511yescharacteristic
301C2×#67—21no—
302C2×#67—21no—
303C2×#67—21no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—42no—
310C22×Dic3—42no—
311C22×Dic3—101no—
312C22×Dic3—101no—
313C22×Dic3C2×Dic511yescharacteristic
314C22×Dic3C2×Dic511yescharacteristic
315C22×Dic3C2×Dic511yescharacteristic
316C22×Dic3C22⋊D511yescharacteristic
317C22×Dic3C22⋊D511yescharacteristic
318C22×Dic3C22⋊D511yescharacteristic
319C22×Dic3C22⋊D511yescharacteristic
320C3×C22⋊C4—52no—
321C3×C22⋊C4—101no—
322C3×C22⋊C4—101no—
323C3×C22⋊C4—101no—
324#217—21no—
325#217—21no—
326#217—52no—
327#217—101no—
328#217—101no—
329#217—101no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332Dic3⋊C4—21no—
333Dic3⋊C4—21no—
334Dic3⋊C4—202no—
335C4×Dic3—202no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—61no—
344C23×C5—61no—
345C23×C5—61no—
346C23×C5—121no—
347C23×C5—121no—
348C23×C5C2×C4×D311yescharacteristic
349C23×C5#23511yescharacteristic
350C23×C5D3×D411yescharacteristic
351C23×C5D3×D411yescharacteristic
352C23×C5D3×D411yescharacteristic
353C23×C5#23711yescharacteristic
354C23×C5C2×#6711yescharacteristic
355C5×D4—41no—
356C5×D4—41no—
357C5×D4—41no—
358C5×D4—41no—
359C5×D4—122no—
360C5×D4—122no—
361C5×D4—121no—
362C5×D4—121no—
363C5×D4—121no—
364C5×D4—121no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—31no—
369C2×C4×C5—31no—
370C2×C4×C5—31no—
371C2×C4×C5—31no—
372C2×C4×C5—62no—
373C2×C4×C5—62no—
374C2×C4×C5—62no—
375C2×C4×C5—61no—
376C2×C4×C5—61no—
377C2×C4×C5—61no—
378C2×C4×C5—121no—
379C2×C4×C5—121no—
380C2×C4×C5—121no—
381C2×Dic5—22no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—41no—
387C2×Dic5—62no—
388C2×Dic5—121no—
389C2×Dic5—121no—
390C2×Dic5—121no—
391C2×Dic5—121no—
392C2×Dic5—121no—
393C22×D4—31no—
394C22×D4—31no—
395C22×D4D3×D511yescharacteristic
396C23×C4—31no—
397#121—61no—
398#121—61no—
399#121—61no—
400#121—61no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—301no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—51no—
406C2×C22⋊C4—51no—
407C2×C22⋊C4—151no—
408C2×C22⋊C4—151no—
409C2×C42—301no—
410#99—102no—
411#99—302no—
412#99—302no—
413#99—302no—
414#95—301no—
415#95—301no—
416C2×C3×C5—21no—
417C2×C3×C5—21no—
418C2×C3×C5—21no—
419C2×C3×C5—21no—
420C2×C3×C5—21no—
421C2×C3×C5—21no—
422C2×C3×C5—81no—
423C2×C3×C5#39011yescharacteristic
424C2×C3×C5C2×#9911yescharacteristic
425C2×C3×C5#41011yescharacteristic
426C5×D3—81no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3D4×D511yescharacteristic
435C23×C3D4×D511yescharacteristic
436C23×C3#71111yescharacteristic
437C23×C3#71111yescharacteristic
438C23×C3C22×Dic511yescharacteristic
439C23×C3C2×C22⋊D511yescharacteristic
440C23×C3C2×C22⋊D511yescharacteristic
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—41no—
445C22×D3—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—102no—
454C2×C3×C4—201no—
455C2×C3×C4—201no—
456C2×C3×C4—201no—
457C2×C3×C4—201no—
458C2×C3×C4—201no—
459#67—42no—
460#67—41no—
461#67—41no—
462#67—41no—
463#67—41no—
464#67—42no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—102no—
475C2×Dic3—201no—
476C2×Dic3—201no—
477C2×Dic3—201no—
478C2×Dic3—201no—
479C2×Dic3—201no—
480C2×Dic3C22⋊Dic511yescharacteristic
481C2×Dic3C22⋊Dic511yescharacteristic
482C2×Dic3C22⋊Dic511yescharacteristic
483C2×Dic3C22⋊Dic511yescharacteristic
484C22×C5—21no—
485C22×C5—21no—
486C22×C5—21no—
487C22×C5—21no—
488C22×C5—21no—
489C22×C5—21no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—41no—
497C22×C5—81no—
498C22×C5—81no—
499C22×C5—121no—
500C22×C5—121no—
501C22×C5—121no—
502C22×C5—241no—
503C22×C5—241no—
504C22×C5D3×C22⋊C411yescharacteristic
505C22×C5#67⋊C411yescharacteristic
506C22×C5#88411yescharacteristic
507C22×C5#88511yescharacteristic
508C22×C5C4×#6711yescharacteristic
509C22×C5#93911yescharacteristic
510C22×C5#94011yescharacteristic
511C4×C5—32no—
512C4×C5—41no—
513C4×C5—61no—
514C4×C5—61no—
515C4×C5—61no—
516C4×C5—121no—
517Dic5—42no—
518Dic5—81no—
519Dic5—122no—
520Dic5—241no—
521C24—31no—
522C24D3×Dic511yescharacteristic
523C24C2×D3×D511yescharacteristic
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—122no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—122no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4D3×Dic511yescharacteristic
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—602no—
555C22⋊C4—52no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—61no—
560C22⋊C4—101no—
561C22⋊C4—101no—
562C22⋊C4—101no—
563C22⋊C4—152no—
564C22⋊C4—301no—
565C22⋊C4—301no—
566C22⋊C4—301no—
567C42—602no—
568C3×C5#196411yescharacteristic, complemented, Hall
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3D4×Dic511yescharacteristic
585C22×C3D4×Dic511yescharacteristic
586C22×C3#408211yescharacteristic
587C22×C3#408411yescharacteristic
588C22×C3#408411yescharacteristic
589C22×C3#408611yescharacteristic
590C22×C3C2×C22⋊Dic511yescharacteristic
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—81no—
595C2×D3—81no—
596C3×C4—41no—
597C3×C4—202no—
598C3×C4—401no—
599Dic3—21no—
600Dic3—21no—
601Dic3—21no—
602Dic3—41no—
603Dic3—202no—
604Dic3—401no—
605Dic3#396612yescomplemented
606C2×C5—21no—
607C2×C5—21no—
608C2×C5—21no—
609C2×C5—21no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—81no—
613C2×C5—241no—
614C2×C5#474011yescharacteristic
615C2×C5D3×#9911yescharacteristic
616C2×C5#495711yescharacteristic
617C23—21no—
618C23—21no—
619C23—21no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—121no—
628C23—121no—
629C23#678011yescharacteristic
630C23C2×D3×Dic511yescharacteristic
631C23#678211yescharacteristic
632C23D5×#6711yescharacteristic
633C23D3×C22⋊D511yescharacteristic
634C23D3×C22⋊D511yescharacteristic
635C23#679011yescharacteristic
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—122no—
641D4—122no—
642D4—121no—
643D4—121no—
644D4—121no—
645D4—121no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—102no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—201no—
664C2×C4—201no—
665C2×C4—201no—
666C2×C4—201no—
667C2×C4—201no—
668C2×C4—302no—
669C2×C4—601no—
670C2×C4—601no—
671C2×C4—601no—
672C2×C4—601no—
673C2×C4—601no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—81no—
681C2×C3C2×#396611yescharacteristic
682C2×C3#6551011yescharacteristic
683C2×C3#6552911yescharacteristic
684D3—81no—
685C5#7003011yescharacteristic, complemented, Sylow
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—81no—
700C22—81no—
701C22—121no—
702C22—121no—
703C22—121no—
704C22—241no—
705C22—241no—
706C22#9152511yescharacteristic
707C22#9154911yescharacteristic
708C22Dic5×#6711yescharacteristic
709C22D3×C22⋊Dic511yescharacteristic
710C22#9155711yescharacteristic
711C22#67⋊Dic511yescharacteristic
712C22#9156711yescharacteristic
713C4—32no—
714C4—41no—
715C4—61no—
716C4—61no—
717C4—61no—
718C4—121no—
719C4—202no—
720C4—401no—
721C4—602no—
722C4—1201no—
723C3#1060247911yescharacteristic, complemented, Sylow
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—81no—
731C2—241no—
732C2D3×#396611yescharacteristic
733C2#1174917311yescharacteristic
734C2#1174948211yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#939C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1964
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91118C2semidirect
3. C2×C3×#3966C2semidirect
4. #11749513C2semidirect
5. Dic3×C22⋊Dic5C2semidirect
6. C2×#90996C2semidirect
7. C2×#90996C2semidirect
10. C22×C5×#67C4semidirect
15. C2×C5×#217C4semidirect
20. C2×C5×(C2×D3)⋊C4C4semidirect
21. C2×C5×Dic3⋊C4C4semidirect
37. C2×#3966D3semidirect
74. #6719D4semidirect
84. C3×C22⋊Dic5D4semidirect
176. C22×#67Dic5semidirect
183. C2×#217Dic5semidirect
188. C2×(C2×D3)⋊C4Dic5semidirect
190. C2×Dic3⋊C4Dic5semidirect
242. C22⋊Dic5#67semidirect
288. C5×Dic3#99semidirect
568. C3×C5#1964semidirect
605. Dic3#3966semidirect
685. C5#70030semidirect
723. C3#10602479semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9392
C2×#911182
C2×C3×#39662
#117495132
Dic3×C22⋊Dic52
C2×#909962
#106024793
#700305