Finite Group Databasebeta

← #14323968

Subgroups — #14323968

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×#91459C211yesmaximal, characteristic
2C2×#91444C211yesmaximal, characteristic, complemented
3C2×#91403C211yesmaximal, characteristic, complemented
4#11751089C211yesmaximal, characteristic, complemented
5C5×#4976C211yesmaximal, characteristic, complemented
6C3×#65278C211yesmaximal, characteristic, complemented
7#11748913C211yesmaximal, characteristic, complemented
8#11748912C211yesmaximal, characteristic, complemented
9#11748907C211yesmaximal, characteristic, complemented
10#11748904C211yesmaximal, characteristic, complemented
11#11748894C211yesmaximal, characteristic, complemented
12#11748882C211yesmaximal, characteristic, complemented
13#11748791C211yesmaximal, characteristic, complemented
14#11748671C211yesmaximal, characteristic, complemented
15#11748651C211yesmaximal, characteristic, complemented
16#10607929—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91459C418yescomplemented
47#91444—24no—
48#91403—24no—
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74385—51nomaximal, Hall
56C2×#4041—31no—
57C2×#4039—31no—
58C2×#4018—31no—
59C5×#389—31no—
60#65278—31no—
61#65278D311yescharacteristic, complemented
62#65277—31no—
63#65277—31no—
64#65276—31no—
65C4⋊C4×Dic5—31no—
66#65228—31no—
67#64958—31no—
68#64958—31no—
69#64954—31no—
70#64954—31no—
71C23×D15C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×D60—41no—
80C2×D60—41no—
81C2×D60C2×C414yescomplemented
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—41no—
91C2×C3×C4×D5—41no—
92C2×#1202—22no—
93C2×#1202—22no—
94C2×#1202—41no—
95C2×#1202—41no—
96C2×#1202C2×C414yes—
97C2×#1202C2×C414yescomplemented
98C2×#1200—22no—
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—41no—
102C2×#1200—41no—
103C2×#1200C2×C414yescomplemented
104C3×C5×C4⋊C4—41no—
105#6714—22no—
106#6714—22no—
107#6714—41no—
108#6714—41no—
109C4×Dic15—41no—
110C5×Dic3⋊C4—22no—
111C5×Dic3⋊C4—41no—
112C5×Dic3⋊C4C2×C414yescomplemented
113C4×C5×Dic3—22no—
114C3×#685—41no—
115C3×#685C2×C414yescomplemented
116C3×#683—22no—
117Dic3⋊Dic5—22no—
118#6668—22no—
119#6667—22no—
120#6667—41no—
121#6667—41no—
122#6667C2×C414yescomplemented
123#6665—22no—
124#6665—41no—
125Dic3×Dic5—41no—
126Dic3×Dic5D414yescomplemented
127C2×C4×#67—51no—
128C2×#892—51no—
129C2×#884—51no—
130C3×#385—51no—
131#5213—51no—
132#4989—51no—
133#4988—51no—
134#4976D511yescharacteristic, complemented
135#4957—51no—
136#4957—51no—
137#4951—51no—
138#4670—51no—
139#4667—51no—
140#4665—51no—
141#4649—51no—
142C22×D20—31no—
143C22×D20—31no—
144C22×D20—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C22×C4×D5C2×D311yescharacteristic
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—31no—
151C2×C5×C4⋊C4C2×D311yescharacteristic
152C2×C42×C5—31no—
153C2×#685—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×#685—31no—
163C2×#685C2×D311yescharacteristic
164C2×#685C2×D311yescharacteristic
165C2×C4⋊Dic5—31no—
166C2×#683—31no—
167C2×#683C2×D311yescharacteristic
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4041—38no—
172#4039—64no—
173#4018—64no—
174C5×#95—31no—
175C5×#95—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic
179#3963C2×D311yescharacteristic
180#2324—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15C22×C412yes—
195C22×D15C22×C412yes—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5C22×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×C5C22×C412yes—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15C2×D412yes—
218D60—44no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3C22×C412yes—
228C2×C5×Dic3C22×C412yes—
229C2×C5×Dic3C2×D412yes—
230C2×C5×Dic3#4112yes—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5C22×C412yes—
239C2×C3×Dic5C2×D412yes—
240C3×C4×D5—44no—
241#1202—28no—
242#1202—44no—
243#1200—28no—
244#1200—44no—
245C23×C3×C4—51no—
246C22×#67—51no—
247C22×#67—51no—
248C22×D12—51no—
249C22×C4×D3—51no—
250C22×C4×D3—51no—
251C2×C3×C4⋊C4—51no—
252C2×C3×C4⋊C4C2×D511yescharacteristic
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4—51no—
255C2×#217—51no—
256C2×#217—51no—
257C4×#67—104no—
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×(C2×D3)⋊C4—51no—
266C2×C4⋊Dic3—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4C2×D511yescharacteristic
269C2×Dic3⋊C4C2×D511yescharacteristic
270C2×Dic3⋊C4C2×D511yescharacteristic
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3C2×D511yescharacteristic
275#892—104no—
276#884—58no—
277C3×#95—51no—
278C3×#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95C2×D511yescharacteristic
282C3⋊#95C2×D511yescharacteristic
283C23×D5—31no—
284C23×D5—31no—
285C23×D5C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5—31no—
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×D20—34no—
299C2×D20—34no—
300C2×D20—34no—
301C2×D20—62no—
302C2×D20—62no—
303C2×D20—121no—
304C2×D20—121no—
305C2×D20—121no—
306C2×D20—121no—
307C2×C4×D5—22no—
308C2×C4×D5—34no—
309C2×C4×D5—41no—
310C2×C4×D5—41no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—121no—
315C2×C4×D5—121no—
316C5×C4⋊C4—34no—
317C5×C4⋊C4—41no—
318C5×C4⋊C4—62no—
319C5×C4⋊C4—121no—
320C42×C5—62no—
321#685—34no—
322#685—41no—
323#685—62no—
324#685—62no—
325#685—62no—
326#685—62no—
327#685—121no—
328#685—121no—
329#685—121no—
330#685—121no—
331#685—121no—
332#685C4×D314yescomplemented
333C4⋊Dic5—62no—
334#683—22no—
335#683—62no—
336C4×Dic5—34no—
337C4×Dic5—121no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—151no—
343#390—151no—
344#390—151no—
345#389—31no—
346#388—151no—
347#388—151no—
348#386—151no—
349#386—151no—
350#385—51no—
351#385—151no—
352#380—151no—
353C4×C4⋊C4—151no—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C2×#4111yescharacteristic
357C22×C3×C5H(5,𝔽2)11yescharacteristic
358C22×C3×C5H(5,𝔽2)11yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C52−1+411yescharacteristic
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—22no—
365C2×D15—22no—
366C2×D15—22no—
367C2×D15—41no—
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—41no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C3×C4×C5—22no—
383C3×C4×C5—41no—
384C3×C4×C5—41no—
385Dic15—22no—
386Dic15—41no—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—41no—
390C5×Dic3—22no—
391C5×Dic3—41no—
392C5×Dic3—41no—
393C5×Dic3C4×D414yes—
394C24×C3—51no—
395C23×D3—51no—
396C23×D3—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—102no—
401C22×C3×C4—201no—
402C22×C3×C4—201no—
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—54no—
407C2×#67—54no—
408C2×#67—102no—
409C2×#67—102no—
410C2×#67—201no—
411C2×#67—201no—
412C22×Dic3—51no—
413C22×Dic3—51no—
414C22×Dic3C22×D511yescharacteristic
415C22×Dic3C22×D511yescharacteristic
416C22×Dic3C22×D511yescharacteristic
417C22×Dic3C22×D511yescharacteristic
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—41no—
428C3×C4⋊C4—102no—
429C3×C22⋊C4—54no—
430C3×C22⋊C4—201no—
431#217—102no—
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—
442Dic3⋊C4—22no—
443Dic3⋊C4—41no—
444Dic3⋊C4—102no—
445Dic3⋊C4C4×D514yescomplemented
446C4×Dic3—22no—
447C4×Dic3—54no—
448C4×Dic3—201no—
449C4×Dic3—201no—
450C23×C5C23×D311yescharacteristic
451C22×D5—21no—
452C22×D5—21no—
453C22×D5—21no—
454C22×D5—21no—
455C22×D5—21no—
456C22×D5—21no—
457C22×D5—32no—
458C22×D5—32no—
459C22×D5—61no—
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×D5C2×C4×D312yes—
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—32no—
481C2×C4×C5—32no—
482C2×C4×C5—32no—
483C2×C4×C5—32no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5—61no—
488C2×C4×C5—61no—
489C2×C4×C5—61no—
490C2×C4×C5—61no—
491C2×C4×C5—61no—
492C2×C4×C5C2×C4×D312yes—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—21no—
500C2×Dic5—32no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5C2×C4×D312yes—
507C2×Dic5D3×D412yes—
508D20—68no—
509D20—124no—
510D20—124no—
511C4×D5—44no—
512C4×D5—68no—
513C4×D5—124no—
514C22×D4—151no—
515C22×D4—151no—
516C22×D4—151no—
517C23×C4—51no—
518C23×C4—151no—
519C23×C4—151no—
520#121—158no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4D3×D511yescharacteristic
530C2×C22⋊C4—51no—
531C2×C22⋊C4—51no—
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⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C42—31no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546#95—31no—
547#95—31no—
548#95—51no—
549#95—51no—
550#95—151no—
551#95—151no—
552C2×C3×C5C2×C4×D411yescharacteristic
553C2×C3×C5#51811yescharacteristic
554C2×C3×C5#52011yescharacteristic
555C2×C3×C5#53511yescharacteristic
556C2×C3×C5#53711yescharacteristic
557C2×C3×C5#54011yescharacteristic
558C2×C3×C5#54211yescharacteristic
559D15—42no—
560D15—42no—
561C3×D5—42no—
562C23×C3—52no—
563C23×C3—101no—
564C23×C3—101no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—101no—
568C23×C3—101no—
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—52no—
593C2×C3×C4—52no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—204no—
602C2×C3×C4C2×C4×D512yes—
603#67—108no—
604#67—204no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—52no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3C2×C4×D512yes—
620C2×Dic3C2×C4×D512yes—
621C2×Dic3D4×D512yes—
622C2×Dic3#71312yes—
623D12—204no—
624C4×D3—108no—
625C4×D3—204no—
626C22×C5C22×C4×D311yescharacteristic
627C22×C5C2×D3×D411yescharacteristic
628C22×C5#100411yescharacteristic
629C22×C5#100411yescharacteristic
630C22×C5#100711yescharacteristic
631C22×C5D3×#4111yescharacteristic
632C22×C5#100911yescharacteristic
633C2×D5—22no—
634C2×D5—22no—
635C2×D5—22no—
636C2×D5—41no—
637C2×D5—41no—
638C2×D5—41no—
639C2×D5—41no—
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—34no—
656C4×C5—41no—
657C4×C5—41no—
658C4×C5—62no—
659C4×C5—121no—
660C4×C5—121no—
661Dic5—22no—
662Dic5—22no—
663Dic5—41no—
664Dic5—62no—
665Dic5—121no—
666C24—51no—
667C24—151no—
668C24—151no—
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—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—51no—
685C22×C4—102no—
686C22×C4—154no—
687C22×C4—151no—
688C22×C4—151no—
689C22×C4—201no—
690C22×C4—201no—
691C22×C4—302no—
692C22×C4—302no—
693C22×C4—302no—
694C22×C4—601no—
695C22×C4—601no—
696C22×C4C2×D3×D511yescharacteristic
697C22×C4C2×D3×D511yescharacteristic
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—41no—
701C4⋊C4—62no—
702C4⋊C4—102no—
703C4⋊C4—121no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C22⋊C4—54no—
707C22⋊C4—154no—
708C22⋊C4—201no—
709C22⋊C4—302no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—601no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C22⋊C4—601no—
717C22⋊C4—601no—
718C42—62no—
719C42—154no—
720C42—601no—
721C42—601no—
722C3×C5#232411yescharacteristic, complemented, Hall
723C22×C3—102no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—201no—
727C22×C3—201no—
728C22×C3—201no—
729C22×C3—201no—
730C22×C3C22×C4×D511yescharacteristic
731C22×C3C2×D4×D511yescharacteristic
732C22×C3#414411yescharacteristic
733C22×C3C2×#71311yescharacteristic
734C22×C3#414711yescharacteristic
735C22×C3#414911yescharacteristic
736C22×C3#414911yescharacteristic
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—41no—
753C3×C4—41no—
754C3×C4—102no—
755C3×C4—102no—
756C3×C4—201no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—102no—
761Dic3—201no—
762Dic3#403914yes—
763C2×C5#550411yescharacteristic
764C2×C5C4×D3×D411yescharacteristic
765C2×C5#554511yescharacteristic
766C2×C5#559211yescharacteristic
767C2×C5#562911yescharacteristic
768C2×C5#564011yescharacteristic
769C2×C5#566311yescharacteristic
770D5—42no—
771D5—122no—
772D5—122no—
773C23—52no—
774C23—101no—
775C23—101no—
776C23—101no—
777C23—101no—
778C23—101no—
779C23—101no—
780C23—152no—
781C23—152no—
782C23—301no—
783C23—301no—
784C23—301no—
785C23—301no—
786C23—301no—
787C23—301no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23—301no—
794C23C22×D3×D511yescharacteristic
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—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—101no—
826C2×C4—101no—
827C2×C4—152no—
828C2×C4—204no—
829C2×C4—308no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—604no—
836C2×C4C4×D3×D512yes—
837C2×C3—202no—
838C2×C3C2×#403911yescharacteristic
839C2×C3#6587911yescharacteristic
840C2×C3#6590811yescharacteristic
841C2×C3#6594111yescharacteristic
842C2×C3#6596311yescharacteristic
843C2×C3#6603211yescharacteristic
844C2×C3#6606711yescharacteristic
845D3—202no—
846D3—202no—
847C5#7438511yescharacteristic, complemented, Sylow
848C22—102no—
849C22—102no—
850C22—102no—
851C22—201no—
852C22—201no—
853C22—201no—
854C22—201no—
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—
869C22C2×C4×D3×D511yescharacteristic
870C22#9201911yescharacteristic
871C22D3×D4×D511yescharacteristic
872C22#9202611yescharacteristic
873C22#9202911yescharacteristic
874C22D3×#71311yescharacteristic
875C22#9204911yescharacteristic
876C4—22no—
877C4—34no—
878C4—41no—
879C4—41no—
880C4—62no—
881C4—102no—
882C4—102no—
883C4—121no—
884C4—121no—
885C4—201no—
886C4—302no—
887C4—601no—
888C3#1060792911yescharacteristic, complemented, Sylow
889C2—202no—
890C2—602no—
891C2—602no—
892C2#1175333611yescharacteristic
893C2#1175368311yescharacteristic
894C2#1175378211yescharacteristic
895C2D3×#403911yescharacteristic
896C2#1175462911yescharacteristic
897C2#1175502911yescharacteristic
898C2#1175513011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91459C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91444C2semidirect
3. C2×#91403C2semidirect
4. #11751089C2semidirect
5. C5×#4976C2semidirect
6. C3×#65278C2semidirect
7. #11748913C2semidirect
8. #11748912C2semidirect
9. #11748907C2semidirect
10. #11748904C2semidirect
11. #11748894C2semidirect
12. #11748882C2semidirect
13. #11748791C2semidirect
14. #11748671C2semidirect
15. #11748651C2semidirect
46. #91459C4semidirect
61. #65278D3semidirect
81. C2×D60C2×C4semidirect
97. C2×#1202C2×C4semidirect
103. C2×#1200C2×C4semidirect
112. C5×Dic3⋊C4C2×C4semidirect
115. C3×#685C2×C4semidirect
122. #6667C2×C4semidirect
126. Dic3×Dic5D4semidirect
134. #4976D5semidirect
332. #685C4×D3semidirect
445. Dic3⋊C4C4×D5semidirect
722. C3×C5#2324semidirect
847. C5#74385semidirect
888. C3#10607929semidirect

Maximal subgroups

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

subgroupindex
C2×#914592
C2×#914442
C2×#914032
#117510892
C5×#49762
C3×#652782
#117489132
#117489122
#117489072
#117489042
#117488942
#117488822
#117487912
#117486712
#117486512
#106079293
#743855