Finite Group Databasebeta

← #14330636

Subgroups — #14330636

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×#91771C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3#11751091C211yesmaximal, characteristic, complemented
4#11751089C211yesmaximal, characteristic, complemented
5#11751058C211yesmaximal, characteristic, complemented
6#11751057C211yesmaximal, characteristic, complemented
7#11751056C211yesmaximal, characteristic, complemented
8#11751056C211yesmaximal, characteristic, complemented
9#11751052C211yesmaximal, characteristic, complemented
10#11751041C211yesmaximal, characteristic, complemented
11#11751040C211yesmaximal, characteristic, complemented
12#11750771C211yesmaximal, characteristic, complemented
13#11750770C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750766C211yesmaximal, characteristic, complemented
16#10607571—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic, complemented
40C2×#6714C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46#91771C418yescomplemented
47C3×C5×#95C2211yescharacteristic, complemented
48C3×C5×#95C2211yescharacteristic, complemented
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#75840—51nomaximal, Hall
54C2×#4028—31no—
55C5×#388D311yescharacteristic, complemented
56#65279—31no—
57#65277—31no—
58#65246—31no—
59#65245—31no—
60#65244—31no—
61#65244—31no—
62#65240—31no—
63#65229—31no—
64#65228—31no—
65#64959—31no—
66#64958—31no—
67#64954—31no—
68#64954—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15—41no—
71C23×D15—41no—
72C23×D15—41no—
73C23×D15—41no—
74C23×D15—41no—
75C23×D15—41no—
76C23×D15C2×C414yescomplemented
77C23×D15C2311yescharacteristic
78C23×D15C2311yescharacteristic
79C23×D15C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—41no—
87C2×#1220—41no—
88C2×#1220C2×C414yes—
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×D60—41no—
95C2×D60—41no—
96C2×D60—41no—
97C2×D60—41no—
98C2×D60C2×C414yes—
99C2×D60C2×C414yes—
100C2×C4×D15—41no—
101C2×C4×D15—41no—
102C2×C4×D15—41no—
103C3×C5×C4⋊C4—41no—
104C3×C5×C22⋊C4—41no—
105C3×C5×C22⋊C4—41no—
106C3×C5×C22⋊C4C2×C414yescomplemented
107C3×C42×C5—41no—
108#6719—41no—
109#6719—41no—
110#6714—41no—
111#6714—41no—
112#6714—41no—
113#6714—41no—
114#6714—41no—
115#6714—41no—
116#6714—41no—
117#6714—41no—
118#6714—41no—
119#6714—41no—
120#6714—41no—
121#6714C2×C414yescomplemented
122#6714C2×C414yescomplemented
123C4⋊Dic15—41no—
124#6712—41no—
125C4×Dic15—41no—
126C4×Dic15—41no—
127C2×#882—51no—
128C3×#388D511yescharacteristic, complemented
129#4990—51no—
130#4988—51no—
131#4957—51no—
132#4956—51no—
133#4955—51no—
134#4955—51no—
135#4951—51no—
136#4940—51no—
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⋊C4C2×D311yescharacteristic, complemented
148C2×C5×C22⋊C4C2×D311yescharacteristic
149C2×C5×C22⋊C4C2×D311yescharacteristic
150C2×C5×C22⋊C4C2×D311yescharacteristic
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×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×C4⋊Dic5—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171#4028—38no—
172C5×#95C2×D311yescharacteristic, complemented
173C5×#95C2×D311yescharacteristic, complemented
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#2375—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C2411yescharacteristic
187C22×D15—21no—
188C22×D15—21no—
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×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—44no—
206C22×D15—44no—
207C22×D15—44no—
208C22×D15—44no—
209C22×D15—44no—
210C22×D15—44no—
211C22×D15—44no—
212C22×D15C22×C412yes—
213C22×D15C22×C412yes—
214C22×D15C22×C412yes—
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—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5C22×C412yes—
232C2×C3×C4×C5C22×C412yes—
233#1220—44no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
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×Dic15C22×C412yes—
249D60—44no—
250D60—44no—
251C4×D15—44no—
252C24×D3—51no—
253C22×#67—51no—
254C22×D12—51no—
255C22×D12—51no—
256C22×C4×D3—51no—
257C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C22⋊C4C2×D511yescharacteristic
260C2×C3×C22⋊C4C2×D511yescharacteristic
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)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×C4⋊Dic3—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281#882—58no—
282C3×#95C2×D511yescharacteristic, complemented
283C3×#95C2×D511yescharacteristic, complemented
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5C22×D311yescharacteristic
289C23×D5—31no—
290C23×D5—31no—
291C23×D5—31no—
292C23×D5—34no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5—121no—
299C22×C4×C5C22×D311yescharacteristic
300C22×C4×C5C22×D311yescharacteristic
301C22×C4×C5C22×D311yescharacteristic
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×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—31no—
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—41no—
323C5×C22⋊C4—41no—
324C5×C22⋊C4—41no—
325C5×C22⋊C4C4×D314yescomplemented
326C42×C5—41no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329#685—34no—
330#685—34no—
331#685—121no—
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#685—121no—
342C4⋊Dic5—121no—
343#683—121no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—151no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388D1511yescharacteristic, complemented
356#386—151no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5H(5,𝔽2)11yescharacteristic
370C22×C3×C5H(5,𝔽2)11yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—416no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C3×C4×C5—22no—
398C3×C4×C5—22no—
399C3×C4×C5—41no—
400C3×C4×C5—41no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403Dic15—22no—
404Dic15—41no—
405Dic15—41no—
406Dic15—41no—
407Dic15—41no—
408C24×C3C22×D511yescharacteristic
409C23×D3—51no—
410C23×D3—51no—
411C23×D3—51no—
412C23×D3—54no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3—201no—
418C23×D3—201no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
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×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3—51no—
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—41no—
443C3×C22⋊C4—41no—
444C3×C22⋊C4—41no—
445C3×C22⋊C4C4×D514yescomplemented
446C3×C42—41no—
447#217—201no—
448#217—201no—
449(C2×D3)⋊C4—54no—
450(C2×D3)⋊C4—54no—
451(C2×D3)⋊C4—201no—
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)⋊C4—201no—
462C4⋊Dic3—201no—
463Dic3⋊C4—201no—
464C4×Dic3—201no—
465C4×Dic3—201no—
466C23×C5—21no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5C2×C4×D312yes—
473C23×C5C23×D311yescharacteristic
474C22×D5—32no—
475C22×D5—32no—
476C22×D5—32no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—61no—
480C22×D5—61no—
481C22×D5—61no—
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—61no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5—124no—
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—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5C2×C4×D312yes—
519C2×C4×C5C2×C4×D312yes—
520C22⋊D5—124no—
521C2×Dic5—32no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
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—
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—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4C2×D1511yescharacteristic, complemented
548C2×C22⋊C4—151no—
549C2×C22⋊C4—151no—
550C2×C22⋊C4—151no—
551C2×C22⋊C4—151no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
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⋊C4C2×D1511yescharacteristic
564C2×C22⋊C4C2×D1511yescharacteristic
565C2×C22⋊C4C2×D1511yescharacteristic
566C2×C42—151no—
567C2×C42—151no—
568C2×C42C2×D1511yescharacteristic, complemented
569#95—151no—
570#95—151no—
571#95—151no—
572#95—151no—
573#95C2×D1511yescharacteristic, complemented
574#95C2×D1511yescharacteristic, complemented
575C2×C3×C5—42no—
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#51811yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5#56011yescharacteristic
582C2×C3×C5H(3,𝔽4)11yescharacteristic
583D15—42no—
584D15—42no—
585D15—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3C2×C4×D512yes—
593C23×C3C23×D511yescharacteristic
594C22×D3—52no—
595C22×D3—52no—
596C22×D3—52no—
597C22×D3—101no—
598C22×D3—101no—
599C22×D3—101no—
600C22×D3—101no—
601C22×D3—101no—
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—101no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3—204no—
621C22×D3—204no—
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—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4C2×C4×D512yes—
639C2×C3×C4C2×C4×D512yes—
640#67—204no—
641C2×Dic3—52no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656D12—204no—
657D12—204no—
658C4×D3—204no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—22no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5C22×C4×D311yescharacteristic
667C22×C5#100411yescharacteristic
668C22×C5#100411yescharacteristic
669C22×C5#100911yescharacteristic
670C22×C5#100911yescharacteristic
671C22×C5#100911yescharacteristic
672C22×C5#100911yescharacteristic
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—62no—
676C2×D5—62no—
677C2×D5—62no—
678C2×D5—62no—
679C2×D5—62no—
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—1216no—
683C2×D5—121no—
684C2×D5—121no—
685C2×D5—121no—
686C2×D5—121no—
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—22no—
697C4×C5—41no—
698C4×C5—41no—
699C4×C5—41no—
700C4×C5—41no—
701Dic5—62no—
702Dic5—121no—
703Dic5—121no—
704Dic5—121no—
705Dic5—121no—
706C24—151no—
707C24—151no—
708C24—151no—
709C24—154no—
710C24—601no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24C22×D1511yescharacteristic
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—151no—
727C22×C4—151no—
728C22×C4—151no—
729C22×C4—151no—
730C22×C4—151no—
731C22×C4—601no—
732C22×C4—601no—
733C22×C4—601no—
734C22×C4C22×D1511yescharacteristic
735C22×C4C22×D1511yescharacteristic
736C22×C4C22×D1511yescharacteristic
737C22×C4C22×D1511yescharacteristic
738C22×C4C22×D1511yescharacteristic
739C22×C4C22×D1511yescharacteristic
740C4⋊C4—41no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—41no—
744C22⋊C4—41no—
745C22⋊C4—154no—
746C22⋊C4—154no—
747C22⋊C4—601no—
748C22⋊C4—601no—
749C22⋊C4—601no—
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⋊C4C4×D1514yescomplemented
761C42—41no—
762C42—601no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3C22×C4×D511yescharacteristic
773C22×C3#414411yescharacteristic
774C22×C3#414411yescharacteristic
775C22×C3#414911yescharacteristic
776C22×C3#414911yescharacteristic
777C22×C3#414911yescharacteristic
778C22×C3#414911yescharacteristic
779C2×D3—102no—
780C2×D3—102no—
781C2×D3—102no—
782C2×D3—102no—
783C2×D3—102no—
784C2×D3—102no—
785C2×D3—102no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—2016no—
789C2×D3—201no—
790C2×D3—201no—
791C2×D3—201no—
792C2×D3—201no—
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—22no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—41no—
807Dic3—102no—
808Dic3—201no—
809Dic3—201no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—42no—
813C2×C5#552111yescharacteristic
814C2×C5#554511yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#562011yescharacteristic
817C2×C5#566611yescharacteristic
818C2×C5#568311yescharacteristic
819C2×C5#571111yescharacteristic
820D5—122no—
821D5—122no—
822D5—122no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—152no—
830C23—152no—
831C23—152no—
832C23—301no—
833C23—301no—
834C23—301no—
835C23—301no—
836C23—301no—
837C23—301no—
838C23—301no—
839C23—301no—
840C23—301no—
841C23—301no—
842C23—301no—
843C23—301no—
844C23—301no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—604no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23C2×C4×D1512yes—
858C23C23×D1511yescharacteristic
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—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—152no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—604no—
894C2×C4C2×C4×D1512yes—
895C2×C4C2×C4×D1512yes—
896C2×C3—42no—
897C2×C3#6585511yescharacteristic
898C2×C3#6587911yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6595411yescharacteristic
901C2×C3#6600011yescharacteristic
902C2×C3#6601711yescharacteristic
903C2×C3#6604511yescharacteristic
904D3—202no—
905D3—202no—
906D3—202no—
907C5#7584011yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—302no—
916C22—302no—
917C22—302no—
918C22—302no—
919C22—302no—
920C22—302no—
921C22—302no—
922C22—302no—
923C22—302no—
924C22—6016no—
925C22—601no—
926C22—601no—
927C22—601no—
928C22—601no—
929C22—601no—
930C22—601no—
931C22—601no—
932C22—601no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C22×C4×D1511yescharacteristic
938C22#9209511yescharacteristic
939C22#9209511yescharacteristic
940C22#9210011yescharacteristic
941C22#9210011yescharacteristic
942C22#9210011yescharacteristic
943C22#9210011yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—302no—
951C4—601no—
952C4—601no—
953C4—601no—
954C4—601no—
955C3#1060757111yescharacteristic, complemented, Sylow
956C2—42no—
957C2—602no—
958C2—602no—
959C2—602no—
960C2#1175628011yescharacteristic
961C2#1175630411yescharacteristic
962C2#1175630411yescharacteristic
963C2#1175637911yescharacteristic
964C2#1175642511yescharacteristic
965C2#1175644211yescharacteristic
966C2#1175647011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91771C2
hypercenter#388D15
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. #11751091C2semidirect
4. #11751089C2semidirect
5. #11751058C2semidirect
6. #11751057C2semidirect
7. #11751056C2semidirect
8. #11751056C2semidirect
9. #11751052C2semidirect
10. #11751041C2semidirect
11. #11751040C2semidirect
12. #11750771C2semidirect
13. #11750770C2semidirect
14. #11750766C2semidirect
15. #11750766C2semidirect
21. C22×C4×D15C22semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C3×C42×C5C22semidirect
39. C2×#6714C22semidirect
40. C2×#6714C22semidirect
41. C2×#6714C22semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. C2×C4×Dic15C22semidirect
45. C2×C4×Dic15C22semidirect
46. #91771C4semidirect
47. C3×C5×#95C22semidirect
48. C3×C5×#95C22semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
55. C5×#388D3semidirect
76. C23×D15C2×C4semidirect
106. C3×C5×C22⋊C4C2×C4semidirect
121. #6714C2×C4semidirect
122. #6714C2×C4semidirect
128. C3×#388D5semidirect
147. C2×C5×C4⋊C4C2×D3semidirect
151. C2×C42×C5C2×D3semidirect
172. C5×#95C2×D3semidirect
173. C5×#95C2×D3semidirect
257. C2×C3×C4⋊C4C2×D5semidirect
261. C2×C3×C42C2×D5semidirect
282. C3×#95C2×D5semidirect
283. C3×#95C2×D5semidirect
325. C5×C22⋊C4C4×D3semidirect
355. #388D15semidirect
445. C3×C22⋊C4C4×D5semidirect
547. C2×C4⋊C4C2×D15semidirect
568. C2×C42C2×D15semidirect
573. #95C2×D15semidirect
574. #95C2×D15semidirect
760. C22⋊C4C4×D15semidirect
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×#917712
C3×C5×#3882
#117510912
#117510892
#117510582
#117510572
#117510562
#117510522
#117510412
#117510402
#117507712
#117507702
#117507662
#106075713
#758405