Finite Group Databasebeta

← #14326008

Subgroups — #14326008

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C2×#91770C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5#11751321C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7#11751057C211yesmaximal, characteristic, complemented
8#11751057C211yesmaximal, characteristic, complemented
9#11751044C211yesmaximal, characteristic, complemented
10#11751043C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
12#11750765C211yesmaximal, characteristic, complemented
13D15×#95C211yesmaximal, characteristic, complemented
14#11750747C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10606403—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C23×Dic15C2211yescharacteristic
23C23×Dic15C2211yescharacteristic
24C2×#6819—24no—
25C2×#6819—24no—
26C2×#6819C418yescomplemented
27C22×C4×D15C2211yescharacteristic
28C22×C4×D15C2211yescharacteristic
29C22×C4×D15C2211yescharacteristic
30C22×Dic30C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37C4×#1220—24no—
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44#91770—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#91115C2211yescharacteristic
56#91115C2211yescharacteristic
57#74672—51nomaximal, Hall
58C22×#711—31no—
59C2×C4×C22⋊D5—31no—
60C2×#4027—31no—
61C5×#386D311yescharacteristic, complemented
62#65509—31no—
63C2×#3963—31no—
64#65245—31no—
65#65245—31no—
66#65232—31no—
67#65231—31no—
68C22⋊C4×Dic5—31no—
69#64953—31no—
70D5×#95—31no—
71#64935—31no—
72#64935—31no—
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4C2×C414yescomplemented
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5—41no—
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C2×#1220—22no—
88C2×#1220—22no—
89C2×#1220C2×C414yes—
90C2×#1220C2×C414yescomplemented
91C2×#1220D414yes—
92C2×#1220D414yes—
93C22×Dic15—22no—
94C22×Dic15—22no—
95C22×Dic15—22no—
96C22×Dic15—22no—
97C22×Dic15—22no—
98C22×Dic15—22no—
99C22×Dic15—41no—
100C22×Dic15C2×C414yescomplemented
101C22×Dic15C2×C414yescomplemented
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109#6819—232no—
110C2×C4×D15—22no—
111C2×C4×D15—22no—
112C2×C4×D15—22no—
113C2×C4×D15—22no—
114C2×C4×D15—22no—
115C2×C4×D15—22no—
116C2×C4×D15—41no—
117C2×C4×D15—41no—
118C2×C4×D15C2×C414yescomplemented
119C2×Dic30—22no—
120C2×Dic30—22no—
121C2×Dic30C2×C414yescomplemented
122C3×C5×C22⋊C4—22no—
123C3×C5×C22⋊C4—22no—
124C3×C5×C22⋊C4—41no—
125#6719—22no—
126#6719—22no—
127#6719—41no—
128#6714—22no—
129#6714—22no—
130#6712—22no—
131#6712—22no—
132C4×Dic15—22no—
133C4×Dic15—22no—
134C22×#237—51no—
135C2×C4×#67—51no—
136C2×#67⋊C4—51no—
137C3×#386D511yescharacteristic, complemented
138#5220—51no—
139C2×C3⋊#95—51no—
140#4956—51no—
141#4956—51no—
142#4943—51no—
143#4942—51no—
144Dic3×C22⋊C4—51no—
145#4664—51no—
146D3×#95—51no—
147#4646—51no—
148#4646—51no—
149C22×C5×D4C2×D311yescharacteristic
150C23×C4×C5C2×D311yescharacteristic
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C23×Dic5—31no—
154C23×Dic5—31no—
155C23×Dic5—31no—
156C2×#711—38no—
157C2×#711—64no—
158C2×#711—64no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×Dic10—31no—
163C2×C5×C22⋊C4C2×D311yescharacteristic
164C2×C5×C22⋊C4C2×D311yescharacteristic
165C2×C5×C22⋊C4C2×D311yescharacteristic
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C4×C22⋊D5—64no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176#4027—64no—
177C5×#95C2×D311yescharacteristic
178C5×#95C2×D311yescharacteristic
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188#3963—31no—
189#2339—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C22×C412yes—
202C23×C3×C5C2×D412yes—
203C23×C3×C5C2×D412yes—
204C23×C3×C5C2411yescharacteristic
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15C22×C412yes—
210C22×D15C2×D412yes—
211C22×D15C2×D412yes—
212C3×C5×D4—28no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—44no—
227C2×C3×C4×C5C22×C412yes—
228C2×C3×C4×C5#4112yescomplemented
229#1220—28no—
230#1220C22⋊C4116yescomplemented
231C2×Dic15—28no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—28no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15—44no—
249C2×Dic15C22×C412yes—
250C2×Dic15C22×C412yes—
251C2×Dic15C22×C412yes—
252C2×Dic15C2×D412yes—
253C2×Dic15C2×D412yes—
254C2×Dic15#4112yescomplemented
255C4×D15—28no—
256C4×D15—44no—
257C4×D15—44no—
258Dic30—28no—
259C22×C3×D4C2×D511yescharacteristic
260C23×C3×C4C2×D511yescharacteristic
261C22×#67—51no—
262C22×#67—51no—
263C23×Dic3—51no—
264C23×Dic3—51no—
265C23×Dic3—51no—
266C2×#237—58no—
267C2×#237—104no—
268C2×#237—104no—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C22×Dic6—51no—
273C2×C3×C22⋊C4C2×D511yescharacteristic
274C2×C3×C22⋊C4C2×D511yescharacteristic
275C2×C3×C22⋊C4C2×D511yescharacteristic
276C2×#217—51no—
277C2×#217—51no—
278C2×#217—51no—
279C4×#67—104no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286#67⋊C4—104no—
287C3×#95C2×D511yescharacteristic
288C3×#95C2×D511yescharacteristic
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C24×C5C22×D311yescharacteristic
300C24×C5C22×D311yescharacteristic
301C23×D5—31no—
302C2×C5×D4—22no—
303C2×C5×D4—22no—
304C2×C5×D4C4×D314yescomplemented
305C22×C4×C5—22no—
306C22×C4×C5—22no—
307C22×C4×C5—41no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C22×C4×C5C22×D311yescharacteristic
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—34no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C22×Dic5—31no—
320C22×Dic5—34no—
321C22×Dic5—34no—
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—62no—
329C22×Dic5—62no—
330C22×Dic5—62no—
331C22×Dic5—62no—
332C22×Dic5—62no—
333C22×Dic5—62no—
334C22×Dic5—121no—
335#711—632no—
336C2×C4×D5—34no—
337C2×C4×D5—62no—
338C2×C4×D5—62no—
339C2×C4×D5—62no—
340C2×C4×D5—62no—
341C2×C4×D5—62no—
342C2×C4×D5—62no—
343C2×C4×D5—121no—
344C2×C4×D5—121no—
345C2×Dic10—34no—
346C2×Dic10—62no—
347C2×Dic10—62no—
348C5×C22⋊C4—22no—
349C5×C22⋊C4—22no—
350C5×C22⋊C4—41no—
351C22⋊Dic5—62no—
352C22⋊Dic5—62no—
353C22⋊Dic5—121no—
354#685—62no—
355#685—62no—
356#683—62no—
357#683—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×#41—151no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—151no—
364#391—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386D1511yescharacteristic, complemented
369#381—151no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C2×C22⋊C414yes—
389C22×C3×C5C23×C411yescharacteristic
390C22×C3×C5C22×D411yescharacteristic
391C22×C3×C5C22×D411yescharacteristic
392C22×C3×C5C2×#4111yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C52−1+411yescharacteristic
396C2×D15—22no—
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15C2×C22⋊C414yes—
403C3×C4×C5—22no—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406C3×C4×C5—41no—
407C3×C4×C5—41no—
408Dic15—22no—
409Dic15—22no—
410Dic15—22no—
411Dic15—41no—
412Dic15—41no—
413Dic15—41no—
414Dic15C2×C22⋊C414yes—
415C24×C3C22×D511yescharacteristic
416C24×C3C22×D511yescharacteristic
417C23×D3—51no—
418C2×C3×D4—22no—
419C2×C3×D4—22no—
420C2×C3×D4C4×D514yescomplemented
421C22×C3×C4—22no—
422C22×C3×C4—22no—
423C22×C3×C4—41no—
424C22×C3×C4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C22×C3×C4C22×D511yescharacteristic
429C2×#67—54no—
430C2×#67—54no—
431C2×#67—54no—
432C2×#67—54no—
433C2×#67—102no—
434C2×#67—102no—
435C22×Dic3—51no—
436C22×Dic3—54no—
437C22×Dic3—54no—
438C22×Dic3—51no—
439C22×Dic3—51no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—51no—
444C22×Dic3—102no—
445C22×Dic3—102no—
446C22×Dic3—102no—
447C22×Dic3—102no—
448C22×Dic3—102no—
449C22×Dic3—102no—
450C22×Dic3—201no—
451#237—1032no—
452C2×C4×D3—54no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—102no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×Dic6—54no—
462C2×Dic6—102no—
463C2×Dic6—102no—
464C3×C22⋊C4—22no—
465C3×C22⋊C4—22no—
466C3×C22⋊C4—41no—
467#217—102no—
468#217—102no—
469#217—201no—
470(C2×D3)⋊C4—102no—
471(C2×D3)⋊C4—102no—
472Dic3⋊C4—102no—
473Dic3⋊C4—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5C2×C4×D312yes—
487C23×C5C2×C4×D312yes—
488C23×C5D3×D412yes—
489C23×C5D3×D412yes—
490C23×C5C23×D311yescharacteristic
491C22×D5—32no—
492C22×D5—32no—
493C22×D5—32no—
494C22×D5—61no—
495C22×D5—61no—
496C22×D5—61no—
497C22×D5—61no—
498C5×D4—28no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—44no—
513C2×C4×C5C2×C4×D312yes—
514C2×C4×C5#23712yescomplemented
515C22⋊D5—316no—
516C22⋊D5—68no—
517C2×Dic5—32no—
518C2×Dic5—32no—
519C2×Dic5—32no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—68no—
524C2×Dic5—68no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5—124no—
541C4×D5—68no—
542C4×D5—124no—
543C4×D5—124no—
544Dic10—68no—
545C2×#41—158no—
546C2×#41—304no—
547C2×#41—304no—
548C22×Q8—151no—
549C22×D4—151no—
550C22×D4—151no—
551C22×D4C2×D1511yescharacteristic
552C23×C4—151no—
553C23×C4—151no—
554C23×C4—151no—
555C23×C4—151no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4C2×D1511yescharacteristic
559C4×D4—304no—
560C4×D4—304no—
561C2×C4⋊C4—151no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4C2×D1511yescharacteristic
569C2×C22⋊C4C2×D1511yescharacteristic
570C2×C22⋊C4C2×D1511yescharacteristic
571C2×C42—151no—
572C2×C42—151no—
573#95—151no—
574#95—151no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95—151no—
581#95—151no—
582#95—151no—
583#95C2×D1511yescharacteristic
584#95C2×D1511yescharacteristic
585C2×C3×C5—24no—
586C2×C3×C5—42no—
587C2×C3×C5C22×C22⋊C411yescharacteristic
588C2×C3×C5C4×#4111yescharacteristic
589C2×C3×C5#52011yescharacteristic
590C2×C3×C5#54611yescharacteristic
591C2×C3×C5#54611yescharacteristic
592C2×C3×C5#54711yescharacteristic
593C2×C3×C5#54711yescharacteristic
594D15—24no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3C2×C4×D512yes—
606C23×C3C2×C4×D512yes—
607C23×C3D4×D512yes—
608C23×C3D4×D512yes—
609C23×C3C23×D511yescharacteristic
610C22×D3—52no—
611C22×D3—52no—
612C22×D3—52no—
613C22×D3—101no—
614C22×D3—101no—
615C22×D3—101no—
616C22×D3—101no—
617C3×D4—28no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—44no—
632C2×C3×C4C2×C4×D512yes—
633C2×C3×C4#71112yescomplemented
634#67—516no—
635#67—108no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—52no—
641C2×Dic3—52no—
642C2×Dic3—108no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—108no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—204no—
660C4×D3—108no—
661C4×D3—204no—
662C4×D3—204no—
663Dic6—108no—
664C22×C5—22no—
665C22×C5—22no—
666C22×C5—22no—
667C22×C5—22no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—22no—
672C22×C5—22no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5—41no—
676C22×C5—41no—
677C22×C5D3×C22⋊C414yes—
678C22×C5C22×C4×D311yescharacteristic
679C22×C5C2×D3×D411yescharacteristic
680C22×C5C2×D3×D411yescharacteristic
681C22×C5C2×#23711yescharacteristic
682C22×C5#100411yescharacteristic
683C22×C5D3×#4111yescharacteristic
684C22×C5#101011yescharacteristic
685C2×D5—34no—
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—62no—
691C2×D5—62no—
692C4×C5—22no—
693C4×C5—22no—
694C4×C5—41no—
695C4×C5—41no—
696C4×C5—41no—
697Dic5—34no—
698Dic5—62no—
699Dic5—62no—
700Dic5—62no—
701Dic5—121no—
702Dic5—121no—
703Dic5—121no—
704C24—151no—
705C24C22×D1511yescharacteristic
706C24C22×D1511yescharacteristic
707#41—3032no—
708C2×Q8—154no—
709C2×Q8—302no—
710C2×Q8—302no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—154no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—154no—
717C2×D4—302no—
718C2×D4—302no—
719C2×D4C4×D1514yescomplemented
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—41no—
723C22×C4—151no—
724C22×C4—154no—
725C22×C4—154no—
726C22×C4—151no—
727C22×C4—151no—
728C22×C4—151no—
729C22×C4—154no—
730C22×C4—151no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—302no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—302no—
737C22×C4—302no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—601no—
746C22×C4—601no—
747C22×C4—601no—
748C22×C4C22×D1511yescharacteristic
749C22×C4C22×D1511yescharacteristic
750C22×C4C22×D1511yescharacteristic
751C22×C4C22×D1511yescharacteristic
752C22×C4C22×D1511yescharacteristic
753C4⋊C4—302no—
754C4⋊C4—302no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—41no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—302no—
762C22⋊C4—601no—
763C42—302no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3D5×C22⋊C414yes—
780C22×C3C22×C4×D511yescharacteristic
781C22×C3C2×D4×D511yescharacteristic
782C22×C3C2×D4×D511yescharacteristic
783C22×C3C2×#71111yescharacteristic
784C22×C3#414411yescharacteristic
785C22×C3D5×#4111yescharacteristic
786C22×C3#415011yescharacteristic
787C2×D3—54no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799Dic3—54no—
800Dic3—102no—
801Dic3—102no—
802Dic3—102no—
803Dic3—201no—
804Dic3—201no—
805Dic3—201no—
806C2×C5—24no—
807C2×C5—42no—
808C2×C5C2×D3×C22⋊C411yescharacteristic
809C2×C5C4×#23711yescharacteristic
810C2×C5#554611yescharacteristic
811C2×C5#559111yescharacteristic
812C2×C5#561011yescharacteristic
813C2×C5#561111yescharacteristic
814C2×C5#565511yescharacteristic
815D5—64no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—152no—
827C23—152no—
828C23—152no—
829C23—301no—
830C23—301no—
831C23—301no—
832C23—301no—
833C23C2×C4×D1512yes—
834C23C2×C4×D1512yes—
835C23D4×D1512yes—
836C23D4×D1512yes—
837C23C23×D1511yescharacteristic
838Q8—308no—
839D4—28no—
840D4—1516no—
841D4—308no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—44no—
856C2×C4—152no—
857C2×C4—152no—
858C2×C4—152no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—308no—
863C2×C4—308no—
864C2×C4—308no—
865C2×C4—301no—
866C2×C4—301no—
867C2×C4—301no—
868C2×C4—301no—
869C2×C4—301no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—604no—
881C2×C4—604no—
882C2×C4—604no—
883C2×C4C2×C4×D1512yes—
884C2×C4#681912yescomplemented
885C2×C3—24no—
886C2×C3—42no—
887C2×C3C2×D5×C22⋊C411yescharacteristic
888C2×C3C4×#71111yescharacteristic
889C2×C3#6588011yescharacteristic
890C2×C3#6592511yescharacteristic
891C2×C3#6594411yescharacteristic
892C2×C3#6594511yescharacteristic
893C2×C3#6598911yescharacteristic
894D3—104no—
895C5#7467211yescharacteristic, complemented, Sylow
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—154no—
910C22—302no—
911C22—302no—
912C22—302no—
913C22—302no—
914C22—302no—
915C22—302no—
916C22C22⋊C4×D1514yes—
917C22C22×C4×D1511yescharacteristic
918C22C2×D4×D1511yescharacteristic
919C22C2×D4×D1511yescharacteristic
920C22C2×#681911yescharacteristic
921C22#9209511yescharacteristic
922C22#41×D1511yescharacteristic
923C22#9210111yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—154no—
930C4—302no—
931C4—302no—
932C4—302no—
933C4—601no—
934C4—601no—
935C4—601no—
936C3#1060640311yescharacteristic, complemented, Sylow
937C2—24no—
938C2—42no—
939C2—304no—
940C2C2×C22⋊C4×D1511yescharacteristic
941C2C4×#681911yescharacteristic
942C2#1175630511yescharacteristic
943C2#1175635011yescharacteristic
944C2#1175636911yescharacteristic
945C2#1175637011yescharacteristic
946C2#1175641411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#386C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#6819C2
hypercenter#386D15
hypocenterC3×C5#2339
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C2×#91770C2semidirect
4. C3×C5×#386C2semidirect
5. #11751321C2semidirect
6. C2×#91115C2semidirect
7. #11751057C2semidirect
8. #11751057C2semidirect
9. #11751044C2semidirect
10. #11751043C2semidirect
11. C22⋊C4×Dic15C2semidirect
12. #11750765C2semidirect
13. D15×#95C2semidirect
14. #11750747C2semidirect
15. #11750747C2semidirect
26. C2×#6819C4semidirect
61. C5×#386D3semidirect
78. C2×C3×C5×D4C2×C4semidirect
90. C2×#1220C2×C4semidirect
100. C22×Dic15C2×C4semidirect
101. C22×Dic15C2×C4semidirect
118. C2×C4×D15C2×C4semidirect
121. C2×Dic30C2×C4semidirect
137. C3×#386D5semidirect
228. C2×C3×C4×C5#41semidirect
230. #1220C22⋊C4semidirect
254. C2×Dic15#41semidirect
304. C2×C5×D4C4×D3semidirect
368. #386D15semidirect
420. C2×C3×D4C4×D5semidirect
514. C2×C4×C5#237semidirect
633. C2×C3×C4#711semidirect
719. C2×D4C4×D15semidirect
765. C3×C5#2339semidirect
884. C2×C4#6819semidirect
895. C5#74672semidirect
936. C3#10606403semidirect

Maximal subgroups

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

subgroupindex
C22×#68192
C2×C4×#12202
C2×#917702
C3×C5×#3862
#117513212
C2×#911152
#117510572
#117510442
#117510432
C22⋊C4×Dic152
#117507652
D15×#952
#117507472
#106064033
#746725