Finite Group Databasebeta

← #14330675

Subgroups — #14330675

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91476C211yesmaximal, characteristic
2#11751040C211yesmaximal, characteristic, complemented
3C5×#4940C211yesmaximal, characteristic, complemented
4C3×#65229C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748919C211yesmaximal, characteristic, complemented
8#11748913C211yesmaximal, characteristic, complemented
9#11748909C211yesmaximal, characteristic, complemented
10#11748904C211yesmaximal, characteristic, complemented
11#11748772C211yesmaximal, characteristic, complemented
12#11748700C211yesmaximal, characteristic, complemented
13#11748686C211yesmaximal, characteristic, complemented
14#11748669C211yesmaximal, characteristic, complemented
15#11748666C211yesmaximal, characteristic, complemented
16#10607571—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1200C2211yescharacteristic, complemented
22C2×C3×C42×C5C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic, complemented
26C2×#6714C2211yescharacteristic, complemented
27C2×C4⋊Dic15C2211yescharacteristic, complemented
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic, complemented
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91476C418yescomplemented
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75840—51nomaximal, Hall
54C2×#4028—31no—
55C5×#388—31no—
56#65279—31no—
57#65277—31no—
58#65246—31no—
59#65245—31no—
60#65244—31no—
61#65244—31no—
62#65240—31no—
63#65229D311yescharacteristic, complemented
64#65228—31no—
65#64959—31no—
66#64958—31no—
67#64954—31no—
68#64954—31no—
69C23×D15C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—41no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5C2×C414yescomplemented
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×D60—41no—
86C2×D60—41no—
87C2×D60C2×C414yes—
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1203—41no—
95C2×#1203—41no—
96C2×#1203C2×C414yes—
97C2×#1202—41no—
98C2×#1202—41no—
99C2×#1202C2×C414yes—
100C2×#1200—41no—
101C2×#1200—41no—
102C2×#1200—41no—
103C3×C42×C5—41no—
104#6714—41no—
105#6714—41no—
106#6714—41no—
107#6714—41no—
108C4⋊Dic15—41no—
109C5×(C2×D3)⋊C4—41no—
110C5×(C2×D3)⋊C4—41no—
111C5×(C2×D3)⋊C4C2×C414yescomplemented
112C5×Dic3⋊C4—41no—
113C3×#685—41no—
114C3×#685—41no—
115C3×#685C2×C414yescomplemented
116C3×#683—41no—
117#6667—41no—
118#6667—41no—
119#6667—41no—
120#6667C2×C414yescomplemented
121(C2×D3)⋊Dic5—41no—
122(C2×D3)⋊Dic5—41no—
123#6665—41no—
124#6665—41no—
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C2×#882—51no—
128C3×#388—51no—
129#4990—51no—
130#4988—51no—
131#4957—51no—
132#4956—51no—
133#4955—51no—
134#4955—51no—
135#4951—51no—
136#4940D511yescharacteristic, complemented
137#4939—51no—
138#4670—51no—
139#4669—51no—
140#4665—51no—
141#4665—51no—
142C24×D5—31no—
143C22×C22⋊D5—31no—
144C22×D20—31no—
145C22×D20—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C42×C5C2×D311yescharacteristic, complemented
152C2×C22⋊Dic5—31no—
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×#685—31no—
163C2×#685—31no—
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×C4⋊Dic5—31no—
168C2×#683C2×D311yescharacteristic, complemented
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4028—38no—
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963C2×D311yescharacteristic, complemented
177#3963C2×D311yescharacteristic, complemented
178#2375—151noSylow
179C23×C3×C5C2411yescharacteristic
180C22×D15—21no—
181C22×D15—21no—
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×D15C22×C412yes—
193C22×D15C22×C412yes—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3C22×C412yes—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
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×C5C22×C412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230D60—44no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3C22×C412yes—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5C22×C412yes—
249#1203—44no—
250#1202—44no—
251#1200—44no—
252C24×D3—51no—
253C22×#67—51no—
254C22×D12—51no—
255C22×D12—51no—
256C22×C4×D3—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C42C2×D511yescharacteristic, complemented
262C2×#217—51no—
263C2×#217—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4C2×D511yescharacteristic
276C2×(C2×D3)⋊C4C2×D511yescharacteristic
277C2×C4⋊Dic3—51no—
278C2×Dic3⋊C4C2×D511yescharacteristic, complemented
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281#882—58no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5—31no—
289C23×D5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—121no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5C22×D311yescharacteristic
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—34no—
306C2×C22⋊D5—121no—
307C2×C22⋊D5—121no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5C22×D311yescharacteristic
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C2×D20—34no—
314C2×D20—34no—
315C2×D20—121no—
316C2×D20—121no—
317C2×D20—121no—
318C2×D20—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—121no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4—121no—
326C42×C5—41no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329#685—34no—
330#685—41no—
331#685—41no—
332#685—121no—
333#685—121no—
334#685—121no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340#685—121no—
341#685C4×D314yescomplemented
342C4⋊Dic5—121no—
343#683—41no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—31no—
351#388—51no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—151no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5H(5,𝔽2)11yescharacteristic
363C22×C3×C5H(5,𝔽2)11yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
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—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—41no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396D3×D5—416no—
397C3×C4×C5—22no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—41no—
401Dic15—41no—
402C3×Dic5—22no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C5×Dic3—22no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C23×D3—51no—
410C23×D3—51no—
411C23×D3—54no—
412C23×D3—201no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3—201no—
418C23×D3C22×D511yescharacteristic
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—54no—
426C2×#67—201no—
427C2×#67—201no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C2×D12—54no—
434C2×D12—54no—
435C2×D12—201no—
436C2×D12—201no—
437C2×D12—201no—
438C2×D12—201no—
439C2×C4×D3—201no—
440C2×C4×D3—201no—
441C2×C4×D3—201no—
442C3×C4⋊C4—201no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C42—41no—
447#217—201no—
448#217—201no—
449(C2×D3)⋊C4—41no—
450(C2×D3)⋊C4—41no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—201no—
453(C2×D3)⋊C4—201no—
454(C2×D3)⋊C4—201no—
455(C2×D3)⋊C4—201no—
456(C2×D3)⋊C4—201no—
457(C2×D3)⋊C4—201no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4C4×D514yescomplemented
462C4⋊Dic3—201no—
463Dic3⋊C4—41no—
464C4×Dic3—201no—
465C4×Dic3—201no—
466C23×C5—32no—
467C23×C5—61no—
468C23×C5—61no—
469C23×C5—61no—
470C23×C5—61no—
471C23×C5—61no—
472C23×C5—61no—
473C23×C5C23×D311yescharacteristic
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—32no—
481C22×D5—32no—
482C22×D5—61no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5C2×C4×D312yes—
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—32no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5C2×C4×D312yes—
520C22⋊D5—124no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5C2×C4×D312yes—
536D20—124no—
537D20—124no—
538C4×D5—124no—
539C25—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—151no—
544#120—158no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—51no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42D3×D511yescharacteristic, complemented
569#95—31no—
570#95—31no—
571#95—51no—
572#95—51no—
573#95—151no—
574#95—151no—
575C2×C3×C5#51811yescharacteristic
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#56011yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5H(3,𝔽4)11yescharacteristic
582D15—42no—
583D15—42no—
584C3×D5—42no—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—52no—
601C22×D3—52no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3—204no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3—204no—
621C22×D3C2×C4×D512yes—
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—52no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4C2×C4×D512yes—
640#67—204no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3C2×C4×D512yes—
656D12—204no—
657D12—204no—
658C4×D3—204no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5—121no—
666C22×C5C22×C4×D311yescharacteristic
667C22×C5#100411yescharacteristic
668C22×C5#100411yescharacteristic
669C22×C5#100911yescharacteristic
670C22×C5#100911yescharacteristic
671C22×C5#100911yescharacteristic
672C22×C5#100911yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5—41no—
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C2×D5—1216no—
687C2×D5—121no—
688C2×D5—121no—
689C2×D5—121no—
690C2×D5—121no—
691C2×D5—121no—
692C2×D5—121no—
693C2×D5—121no—
694C2×D5—121no—
695C4×C5—22no—
696C4×C5—41no—
697C4×C5—41no—
698C4×C5—62no—
699C4×C5—121no—
700C4×C5—121no—
701Dic5—22no—
702Dic5—41no—
703Dic5—41no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—51no—
708C24—154no—
709C24—151no—
710C24—151no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24—601no—
717C2×D4—154no—
718C2×D4—154no—
719C2×D4—154no—
720C2×D4—601no—
721C2×D4—601no—
722C2×D4—601no—
723C2×D4—601no—
724C2×D4—601no—
725C2×D4—601no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—51no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—601no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4C2×D3×D511yescharacteristic
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—121no—
741C4⋊C4—201no—
742C4⋊C4—601no—
743C22⋊C4—34no—
744C22⋊C4—54no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—154no—
748C22⋊C4—201no—
749C22⋊C4—201no—
750C22⋊C4—601no—
751C22⋊C4—601no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4—601no—
761C42—41no—
762C42—601no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—201no—
769C22×C3—201no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3C22×C4×D511yescharacteristic
773C22×C3#414411yescharacteristic
774C22×C3#414411yescharacteristic
775C22×C3#414911yescharacteristic
776C22×C3#414911yescharacteristic
777C22×C3#414911yescharacteristic
778C22×C3#414911yescharacteristic
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—2016no—
793C2×D3—201no—
794C2×D3—201no—
795C2×D3—201no—
796C2×D3—201no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—22no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—102no—
805C3×C4—201no—
806C3×C4—201no—
807Dic3—22no—
808Dic3—41no—
809Dic3—41no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—122no—
813C2×C5#552111yescharacteristic
814C2×C5#554511yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#562011yescharacteristic
817C2×C5#566611yescharacteristic
818C2×C5#568311yescharacteristic
819C2×C5#571111yescharacteristic
820D5—42no—
821D5—122no—
822D5—122no—
823C23—32no—
824C23—52no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—101no—
832C23—101no—
833C23—101no—
834C23—101no—
835C23—101no—
836C23—101no—
837C23—152no—
838C23—152no—
839C23—301no—
840C23—301no—
841C23—301no—
842C23—301no—
843C23—301no—
844C23—301no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—301no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23—604no—
858C23C22×D3×D511yescharacteristic
859D4—604no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—32no—
871C2×C4—52no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—604no—
895C2×C4C4×D3×D512yes—
896C2×C3—202no—
897C2×C3#6585511yescharacteristic
898C2×C3#6587911yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6595411yescharacteristic
901C2×C3#6600011yescharacteristic
902C2×C3#6601711yescharacteristic
903C2×C3#6604511yescharacteristic
904D3—42no—
905D3—202no—
906D3—202no—
907C5#7584011yescharacteristic, complemented, Sylow
908C22—62no—
909C22—62no—
910C22—62no—
911C22—102no—
912C22—102no—
913C22—102no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—201no—
919C22—201no—
920C22—201no—
921C22—201no—
922C22—302no—
923C22—302no—
924C22—302no—
925C22—302no—
926C22—302no—
927C22—302no—
928C22—6016no—
929C22—601no—
930C22—601no—
931C22—601no—
932C22—601no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201711yescharacteristic
939C22#9201811yescharacteristic
940C22#9201911yescharacteristic
941C22#9201911yescharacteristic
942C22#9201911yescharacteristic
943C22#9204911yescharacteristic
944C4—22no—
945C4—41no—
946C4—41no—
947C4—62no—
948C4—102no—
949C4—121no—
950C4—121no—
951C4—201no—
952C4—201no—
953C4—601no—
954C4—601no—
955C3#1060757111yescharacteristic, complemented, Sylow
956C2—122no—
957C2—202no—
958C2—602no—
959C2—602no—
960C2#1175272511yescharacteristic
961C2#1175272711yescharacteristic
962C2#1175277211yescharacteristic
963C2#1175277511yescharacteristic
964C2#1175462911yescharacteristic
965C2#1175468411yescharacteristic
966C2#1175468511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91476C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751040C2semidirect
3. C5×#4940C2semidirect
4. C3×#65229C2semidirect
5. #11748940C2semidirect
6. #11748940C2semidirect
7. #11748919C2semidirect
8. #11748913C2semidirect
9. #11748909C2semidirect
10. #11748904C2semidirect
11. #11748772C2semidirect
12. #11748700C2semidirect
13. #11748686C2semidirect
14. #11748669C2semidirect
15. #11748666C2semidirect
21. C22×#1200C22semidirect
22. C2×C3×C42×C5C22semidirect
25. C2×#6714C22semidirect
26. C2×#6714C22semidirect
27. C2×C4⋊Dic15C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
35. C2×C3×#683C22semidirect
39. C2×#6667C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91476C4semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
63. #65229D3semidirect
79. C22×D3×D5C2×C4semidirect
111. C5×(C2×D3)⋊C4C2×C4semidirect
115. C3×#685C2×C4semidirect
120. #6667C2×C4semidirect
136. #4940D5semidirect
151. C2×C42×C5C2×D3semidirect
168. C2×#683C2×D3semidirect
176. #3963C2×D3semidirect
177. #3963C2×D3semidirect
261. C2×C3×C42C2×D5semidirect
278. C2×Dic3⋊C4C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
341. #685C4×D3semidirect
461. (C2×D3)⋊C4C4×D5semidirect
568. C2×C42D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#75840semidirect
955. C3#10607571semidirect

Maximal subgroups

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

subgroupindex
C2×#914762
#117510402
C5×#49402
C3×#652292
#117489402
#117489192
#117489132
#117489092
#117489042
#117487722
#117487002
#117486862
#117486692
#117486662
#106075713
#758405