Finite Group Databasebeta

← #14323866

Subgroups — #14323866

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic, complemented
2C2×#91773C211yesmaximal, characteristic
3C2×#91770C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic, complemented
5#11751091C211yesmaximal, characteristic, complemented
6#11751059C211yesmaximal, characteristic, complemented
7#11751058C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9#11751051C211yesmaximal, characteristic, complemented
10#11751040C211yesmaximal, characteristic, complemented
11C4×#6712C211yesmaximal, characteristic, complemented
12#11750769C211yesmaximal, characteristic, complemented
13#11750768C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750748C211yesmaximal, characteristic, complemented
16#10607192—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44C2×C4×Dic15C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46#91781—24no—
47#91773C418yescomplemented
48#91770—24no—
49C3×C5×#95C2211yescharacteristic
50C3×C5×#95C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#75461—51nomaximal, Hall
56C2×#4038—31no—
57C2×#4030—31no—
58C2×#4027—31no—
59C5×#388D311yescharacteristic, complemented
60#65279—31no—
61#65247—31no—
62#65246—31no—
63#65246—31no—
64#65239—31no—
65#65228—31no—
66C4×#683—31no—
67#64957—31no—
68#64956—31no—
69#64954—31no—
70#64936—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×D15C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—22no—
81C2×#1220—22no—
82C2×#1220—41no—
83C2×#1220—41no—
84C2×#1220C2×C414yes—
85C2×#1220C2×C414yescomplemented
86C22×Dic15—22no—
87C22×Dic15—41no—
88C22×Dic15—41no—
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×D60—41no—
96C2×D60—41no—
97C2×D60C2×C414yescomplemented
98C2×C4×D15—22no—
99C2×C4×D15—22no—
100C2×C4×D15—22no—
101C2×C4×D15—41no—
102C2×C4×D15—41no—
103C2×C4×D15C2×C414yescomplemented
104C3×C5×C4⋊C4—22no—
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4—41no—
107C3×C5×C22⋊C4C2×C414yescomplemented
108C3×C42×C5—41no—
109#6719—41no—
110#6714—22no—
111#6714—22no—
112#6714—22no—
113#6714—41no—
114#6714—41no—
115#6714—41no—
116#6714—41no—
117#6714C2×C414yescomplemented
118C4⋊Dic15—22no—
119C4⋊Dic15—41no—
120#6712—22no—
121#6712—22no—
122#6712—41no—
123#6712C2×C414yescomplemented
124C4×Dic15—22no—
125C4×Dic15—41no—
126C4×Dic15D414yescomplemented
127C2×#892—51no—
128C2×#884—51no—
129C2×#67⋊C4—51no—
130C3×#388D511yescharacteristic, complemented
131#4990—51no—
132#4958—51no—
133#4957—51no—
134#4957—51no—
135#4950—51no—
136#4939—51no—
137C4×Dic3⋊C4—51no—
138#4668—51no—
139#4667—51no—
140#4665—51no—
141#4647—51no—
142C22×C22⋊D5—31no—
143C22×C22⋊D5—31no—
144C23×Dic5—31no—
145C22×D20—31no—
146C22×C4×D5—31no—
147C22×C4×D5—31no—
148C2×C5×C4⋊C4C2×D311yescharacteristic
149C2×C5×C22⋊C4C2×D311yescharacteristic
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C5×C22⋊C4C2×D311yescharacteristic
152C2×C42×C5C2×D311yescharacteristic
153C2×C22⋊Dic5—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×C4⋊Dic5—31no—
163C2×C4⋊Dic5—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4038—64no—
172#4030—38no—
173#4027—64no—
174C5×#95C2×D311yescharacteristic
175C5×#95C2×D311yescharacteristic
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2324—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15C22×C412yes—
202C22×D15C22×C412yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
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×C5C22×C412yes—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5C2×D412yes—
221#1220—28no—
222#1220—44no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—44no—
237C2×Dic15C22×C412yes—
238C2×Dic15C22×C412yes—
239C2×Dic15C2×D412yes—
240C2×Dic15C2×D412yes—
241C2×Dic15#4112yes—
242D60—44no—
243C4×D15—28no—
244C4×D15—44no—
245C22×#67—51no—
246C22×#67—51no—
247C23×Dic3—51no—
248C22×D12—51no—
249C22×C4×D3—51no—
250C22×C4×D3—51no—
251C2×C3×C4⋊C4C2×D511yescharacteristic
252C2×C3×C22⋊C4C2×D511yescharacteristic
253C2×C3×C22⋊C4C2×D511yescharacteristic
254C2×C3×C22⋊C4C2×D511yescharacteristic
255C2×C3×C42C2×D511yescharacteristic
256C2×#217—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×(C2×D3)⋊C4—51no—
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×C4⋊Dic3—51no—
266C2×C4⋊Dic3—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274#892—104no—
275#884—58no—
276#67⋊C4—104no—
277C3×#95C2×D511yescharacteristic
278C3×#95C2×D511yescharacteristic
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C24×C5C22×D311yescharacteristic
284C23×D5—31no—
285C23×D5—31no—
286C22×C4×C5C22×D311yescharacteristic
287C22×C4×C5C22×D311yescharacteristic
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C2×C22⋊D5—34no—
293C2×C22⋊D5—34no—
294C2×C22⋊D5—62no—
295C2×C22⋊D5—62no—
296C2×C22⋊D5—121no—
297C2×C22⋊D5—121no—
298C22×Dic5—31no—
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—62no—
305C22×Dic5—121no—
306C22×Dic5—121no—
307C2×D20—34no—
308C2×D20—121no—
309C2×D20—121no—
310C2×C4×D5—34no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—121no—
315C2×C4×D5—121no—
316C5×C4⋊C4—22no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—41no—
319C5×C22⋊C4C4×D314yescomplemented
320C42×C5—41no—
321C22⋊Dic5—121no—
322#685—34no—
323#685—62no—
324#685—62no—
325#685—62no—
326#685—121no—
327#685—121no—
328#685—121no—
329#685—121no—
330C4⋊Dic5—62no—
331C4⋊Dic5—121no—
332#683—34no—
333#683—62no—
334#683—62no—
335#683—121no—
336C4×Dic5—34no—
337C4×Dic5—62no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—151no—
343#390—151no—
344#390—151no—
345#389—151no—
346#388—151no—
347#388D1511yescharacteristic, complemented
348#386—151no—
349#386—151no—
350#385—151no—
351#385—151no—
352#380—151no—
353C4×C4⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5C22×D411yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C52−1+411yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15—22no—
373C2×D15—22no—
374C2×D15—41no—
375C2×D15—41no—
376C2×D15—41no—
377C2×D15—41no—
378C2×D15—41no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—41no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388Dic15—22no—
389Dic15—22no—
390Dic15—41no—
391Dic15—41no—
392Dic15—41no—
393Dic15C4×D414yes—
394C24×C3C22×D511yescharacteristic
395C23×D3—51no—
396C23×D3—51no—
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C2×#67—54no—
404C2×#67—54no—
405C2×#67—102no—
406C2×#67—102no—
407C2×#67—201no—
408C2×#67—201no—
409C22×Dic3—51no—
410C22×Dic3—51no—
411C22×Dic3—51no—
412C22×Dic3—51no—
413C22×Dic3—51no—
414C22×Dic3—51no—
415C22×Dic3—102no—
416C22×Dic3—201no—
417C22×Dic3—201no—
418C2×D12—54no—
419C2×D12—201no—
420C2×D12—201no—
421C2×C4×D3—54no—
422C2×C4×D3—102no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—201no—
426C2×C4×D3—201no—
427C3×C4⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—41no—
430C3×C22⋊C4C4×D514yescomplemented
431C3×C42—41no—
432#217—201no—
433(C2×D3)⋊C4—54no—
434(C2×D3)⋊C4—102no—
435(C2×D3)⋊C4—102no—
436(C2×D3)⋊C4—102no—
437(C2×D3)⋊C4—201no—
438(C2×D3)⋊C4—201no—
439(C2×D3)⋊C4—201no—
440(C2×D3)⋊C4—201no—
441C4⋊Dic3—102no—
442C4⋊Dic3—201no—
443Dic3⋊C4—54no—
444Dic3⋊C4—102no—
445Dic3⋊C4—102no—
446Dic3⋊C4—201no—
447C4×Dic3—54no—
448C4×Dic3—102no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5C2×C4×D312yes—
457C23×C5C23×D311yescharacteristic
458C22×D5—32no—
459C22×D5—32no—
460C22×D5—61no—
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—61no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5C2×C4×D312yes—
488C2×C4×C5C2×C4×D312yes—
489C2×C4×C5D3×D412yes—
490C22⋊D5—68no—
491C22⋊D5—124no—
492C2×Dic5—32no—
493C2×Dic5—32no—
494C2×Dic5—32no—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—124no—
511D20—124no—
512C4×D5—68no—
513C4×D5—124no—
514C22×D4—151no—
515C22×D4—151no—
516C22×D4—151no—
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520#121—158no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4C2×D1511yescharacteristic
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4C2×D1511yescharacteristic
540C2×C22⋊C4C2×D1511yescharacteristic
541C2×C22⋊C4C2×D1511yescharacteristic
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42C2×D1511yescharacteristic
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95C2×D1511yescharacteristic
551#95C2×D1511yescharacteristic
552C2×C3×C5—42no—
553C2×C3×C5C2×C4×D411yescharacteristic
554C2×C3×C5#51811yescharacteristic
555C2×C3×C5#52011yescharacteristic
556C2×C3×C5#53511yescharacteristic
557C2×C3×C5#53711yescharacteristic
558C2×C3×C5#54011yescharacteristic
559C2×C3×C5#54211yescharacteristic
560D15—42no—
561D15—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3C2×C4×D512yes—
569C23×C3C23×D511yescharacteristic
570C22×D3—52no—
571C22×D3—52no—
572C22×D3—101no—
573C22×D3—101no—
574C22×D3—101no—
575C22×D3—101no—
576C22×D3—101no—
577C22×D3—101no—
578C22×D3—101no—
579C22×D3—101no—
580C22×D3—101no—
581C22×D3—101no—
582C22×D3—101no—
583C22×D3—101no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4C2×C4×D512yes—
600C2×C3×C4C2×C4×D512yes—
601C2×C3×C4D4×D512yes—
602#67—108no—
603#67—204no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—52no—
608C2×Dic3—52no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—204no—
623D12—204no—
624C4×D3—108no—
625C4×D3—204no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5C22×C4×D311yescharacteristic
634C22×C5C2×D3×D411yescharacteristic
635C22×C5#100411yescharacteristic
636C22×C5D3×#4111yescharacteristic
637C22×C5#100911yescharacteristic
638C22×C5#100911yescharacteristic
639C22×C5#101011yescharacteristic
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—62no—
645C2×D5—62no—
646C2×D5—121no—
647C2×D5—121no—
648C2×D5—121no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C4×C5—22no—
655C4×C5—22no—
656C4×C5—22no—
657C4×C5—41no—
658C4×C5—41no—
659C4×C5—41no—
660Dic5—34no—
661Dic5—62no—
662Dic5—62no—
663Dic5—121no—
664Dic5—121no—
665Dic5—121no—
666C24—151no—
667C24—151no—
668C24C22×D1511yescharacteristic
669C2×D4—154no—
670C2×D4—154no—
671C2×D4—154no—
672C2×D4—302no—
673C2×D4—302no—
674C2×D4—601no—
675C2×D4—601no—
676C2×D4—601no—
677C2×D4—601no—
678C22×C4—151no—
679C22×C4—151no—
680C22×C4—151no—
681C22×C4—154no—
682C22×C4—151no—
683C22×C4—151no—
684C22×C4—151no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—302no—
689C22×C4—601no—
690C22×C4—601no—
691C22×C4—601no—
692C22×C4—601no—
693C22×C4C22×D1511yescharacteristic
694C22×C4C22×D1511yescharacteristic
695C22×C4C22×D1511yescharacteristic
696C22×C4C22×D1511yescharacteristic
697C22×C4C22×D1511yescharacteristic
698C22×C4C22×D1511yescharacteristic
699C4⋊C4—22no—
700C4⋊C4—154no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—601no—
705C4⋊C4—601no—
706C22⋊C4—22no—
707C22⋊C4—41no—
708C22⋊C4—154no—
709C22⋊C4—302no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4—601no—
713C22⋊C4—601no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C22⋊C4—601no—
717C22⋊C4C4×D1514yescomplemented
718C42—41no—
719C42—154no—
720C42—302no—
721C42—601no—
722C3×C5#232411yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3C22×C4×D511yescharacteristic
731C22×C3C2×D4×D511yescharacteristic
732C22×C3#414411yescharacteristic
733C22×C3D5×#4111yescharacteristic
734C22×C3#414911yescharacteristic
735C22×C3#414911yescharacteristic
736C22×C3#415011yescharacteristic
737C2×D3—102no—
738C2×D3—102no—
739C2×D3—102no—
740C2×D3—102no—
741C2×D3—102no—
742C2×D3—102no—
743C2×D3—201no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757Dic3—54no—
758Dic3—102no—
759Dic3—102no—
760Dic3—201no—
761Dic3—201no—
762Dic3—201no—
763C2×C5—42no—
764C2×C5#552311yescharacteristic
765C2×C5C4×D3×D411yescharacteristic
766C2×C5#554511yescharacteristic
767C2×C5#559711yescharacteristic
768C2×C5#566311yescharacteristic
769C2×C5#567411yescharacteristic
770C2×C5#571011yescharacteristic
771D5—122no—
772D5—122no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—152no—
780C23—152no—
781C23—301no—
782C23—301no—
783C23—301no—
784C23—301no—
785C23—301no—
786C23—301no—
787C23—301no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23C2×C4×D1512yes—
794C23C23×D1511yescharacteristic
795D4—308no—
796D4—604no—
797D4—604no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—308no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—604no—
833C2×C4—604no—
834C2×C4C2×C4×D1512yes—
835C2×C4C2×C4×D1512yes—
836C2×C4D4×D1512yes—
837C2×C3—42no—
838C2×C3#6585711yescharacteristic
839C2×C3C4×D4×D511yescharacteristic
840C2×C3#6587911yescharacteristic
841C2×C3#6593111yescharacteristic
842C2×C3#6599711yescharacteristic
843C2×C3#6600811yescharacteristic
844C2×C3#6604411yescharacteristic
845D3—202no—
846D3—202no—
847C5#7546111yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—302no—
856C22—302no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—302no—
861C22—601no—
862C22—601no—
863C22—601no—
864C22—601no—
865C22—601no—
866C22—601no—
867C22—601no—
868C22—601no—
869C22C22×C4×D1511yescharacteristic
870C22C2×D4×D1511yescharacteristic
871C22#9209511yescharacteristic
872C22#41×D1511yescharacteristic
873C22#9210011yescharacteristic
874C22#9210011yescharacteristic
875C22#9210111yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—154no—
883C4—302no—
884C4—302no—
885C4—601no—
886C4—601no—
887C4—601no—
888C3#1060719211yescharacteristic, complemented, Sylow
889C2—42no—
890C2—602no—
891C2—602no—
892C2#1175628211yescharacteristic
893C2C4×D4×D1511yescharacteristic
894C2#1175630411yescharacteristic
895C2#1175635611yescharacteristic
896C2#1175642211yescharacteristic
897C2#1175643311yescharacteristic
898C2#1175646911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91773C2
hypercenter#388D15
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91781C2semidirect
3. C2×#91770C2semidirect
4. C3×C5×#388C2semidirect
5. #11751091C2semidirect
6. #11751059C2semidirect
7. #11751058C2semidirect
8. #11751058C2semidirect
9. #11751051C2semidirect
10. #11751040C2semidirect
11. C4×#6712C2semidirect
12. #11750769C2semidirect
13. #11750768C2semidirect
14. #11750766C2semidirect
15. #11750748C2semidirect
47. #91773C4semidirect
59. C5×#388D3semidirect
85. C2×#1220C2×C4semidirect
97. C2×D60C2×C4semidirect
103. C2×C4×D15C2×C4semidirect
107. C3×C5×C22⋊C4C2×C4semidirect
117. #6714C2×C4semidirect
123. #6712C2×C4semidirect
126. C4×Dic15D4semidirect
130. C3×#388D5semidirect
319. C5×C22⋊C4C4×D3semidirect
347. #388D15semidirect
430. C3×C22⋊C4C4×D5semidirect
717. C22⋊C4C4×D15semidirect
722. C3×C5#2324semidirect
847. C5#75461semidirect
888. C3#10607192semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×#917732
C2×#917702
C3×C5×#3882
#117510912
#117510592
#117510582
#117510512
#117510402
C4×#67122
#117507692
#117507682
#117507662
#117507482
#106071923
#754615