Finite Group Databasebeta

← #14322601

Subgroups — #14322601

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
2#11750770C211yesmaximal, characteristic, complemented
3C5×#4669C211yesmaximal, characteristic, complemented
4C3×#64955C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic
6#11748940C211yesmaximal, characteristic
7#11748885C211yesmaximal, characteristic, complemented
8#11748878C211yesmaximal, characteristic, complemented
9#11748854C211yesmaximal, characteristic, complemented
10#11748794C211yesmaximal, characteristic, complemented
11#11748727C211yesmaximal, characteristic, complemented
12#11748726C211yesmaximal, characteristic, complemented
13#11748715C211yesmaximal, characteristic, complemented
14#11748714C211yesmaximal, characteristic, complemented
15C4×#6665C211yesmaximal, characteristic, complemented
16#10607556—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6712C2211yescharacteristic, complemented
24C2×C4×Dic15C2211yescharacteristic, complemented
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
29C2×C4×C5×Dic3C2211yescharacteristic, complemented
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic, complemented
33C2×C3×C4×Dic5C2211yescharacteristic, complemented
34C2×Dic3⋊Dic5C2211yescharacteristic, complemented
35C2×#6669C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44D5×(C2×D3)⋊C4C418yescomplemented
45C3×C5×#95C2211yescharacteristic, complemented
46#91115C2211yescharacteristic, complemented
47C5×C3⋊#95C2211yescharacteristic, complemented
48C3×#3963C2211yescharacteristic, complemented
49#90994C2211yescharacteristic, complemented
50#90994C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#73567—51nomaximal, Hall
54C2×D5×C22⋊C4—31no—
55C5×#388—31no—
56#65279—31no—
57#65276—31no—
58#65244—31no—
59#65244—31no—
60#65240—31no—
61#65234—31no—
62#65233—31no—
63#65229—31no—
64C4×#685—31no—
65#64959—31no—
66#64958—31no—
67#64956—31no—
68#64955D311yescharacteristic, complemented
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C22×D3×D5—22no—
73C22×D3×D5—22no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5C2×C414yes—
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×C3×C4×D5—41no—
92C2×C3×C4×D5—41no—
93C2×C3×C4×D5C2×C414yes—
94C2×D5×Dic3—41no—
95C2×D5×Dic3—41no—
96C2×D5×Dic3C2×C414yes—
97#6714—41no—
98#6714—41no—
99#6714C2×C414yes—
100#6712—41no—
101C4×Dic15—41no—
102C5×(C2×D3)⋊C4—41no—
103C5×(C2×D3)⋊C4—41no—
104C5×(C2×D3)⋊C4C2×C414yes—
105C5×Dic3⋊C4—41no—
106C4×C5×Dic3—41no—
107C3×#685—22no—
108C3×#685—22no—
109C3×C4×Dic5—41no—
110C3×C4×Dic5—41no—
111Dic3⋊Dic5—41no—
112#6669—41no—
113#6667—41no—
114#6667—41no—
115#6667C2×C414yes—
116(C2×D3)⋊Dic5—41no—
117(C2×D3)⋊Dic5—41no—
118(C2×D3)⋊Dic5C2×C414yes—
119#6665—22no—
120#6665—22no—
121C22×(C2×D3)⋊C4—51no—
122C3×C4×C22⋊C4—51no—
123C4×#217—51no—
124#4955—51no—
125#4955—51no—
126#4942—51no—
127#4942—51no—
128#4940—51no—
129#4940—51no—
130#4940—51no—
131#4940—51no—
132#4669—51no—
133#4669—51no—
134#4669—51no—
135#4669D511yescharacteristic, complemented
136C24×D5—31no—
137C22×C4×D5—31no—
138C22×C4×D5C2×D311yescharacteristic
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C42×C5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685C2×D311yescharacteristic
156C2×#685C2×D311yescharacteristic
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5C2×D311yescharacteristic, complemented
162C2×C4×Dic5C2×D311yescharacteristic, complemented
163D5×C22⋊C4—38no—
164C5×#95—31no—
165C5×#95C2×D311yescharacteristic, complemented
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963C2×D311yescharacteristic, complemented
172#2312—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×D15—21no—
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15C22×C412yes—
181C22×C5×D3—21no—
182C22×C5×D3—21no—
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3C22×C412yes—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5C22×C412yes—
193C22×C3×D5#4112yes—
194C22×C3×D5#4112yes—
195C2×D3×D5—28no—
196C2×D3×D5—44no—
197C2×D3×D5—44no—
198C2×D3×D5—44no—
199C2×D3×D5—44no—
200C2×D3×D5—44no—
201C2×D3×D5—44no—
202C2×C3×C4×C5—21no—
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×C5C22×C412yes—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C22×C412yes—
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×Dic3—21no—
228C2×C5×Dic3C22×C412yes—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
238C3×C4×D5—44no—
239D5×Dic3—44no—
240C24×D3—51no—
241C23×C3×C4—51no—
242C23×Dic3—51no—
243C2×C3×C22⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C42—51no—
246C2×C3×C42—51no—
247C2×#217—51no—
248C2×#217—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—58no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×(C2×D3)⋊C4—51no—
259C2×(C2×D3)⋊C4C2×D511yescharacteristic
260C2×(C2×D3)⋊C4C2×D511yescharacteristic
261C2×(C2×D3)⋊C4C2×D511yescharacteristic
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4—51no—
264C2×Dic3⋊C4—51no—
265C2×Dic3⋊C4C2×D511yescharacteristic, complemented
266C2×C4×Dic3—51no—
267C2×C4×Dic3C2×D511yescharacteristic, complemented
268C3×#95—51no—
269C3×#95C2×D511yescharacteristic, complemented
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95—51no—
275C3⋊#95C2×D511yescharacteristic, complemented
276C24×C5—31no—
277C23×D5—31no—
278C23×D5—34no—
279C23×D5—62no—
280C23×D5—62no—
281C23×D5—121no—
282C23×D5—121no—
283C23×D5—121no—
284C23×D5—121no—
285C23×D5C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×C4×D5—34no—
299C2×C4×D5—41no—
300C2×C4×D5—41no—
301C2×C4×D5—121no—
302C2×C4×D5—121no—
303C2×C4×D5C4×D314yes—
304C5×C4⋊C4—121no—
305C5×C22⋊C4—34no—
306C5×C22⋊C4—121no—
307C5×C22⋊C4—121no—
308C42×C5—121no—
309C22⋊Dic5—34no—
310C22⋊Dic5—121no—
311C22⋊Dic5—121no—
312#685—22no—
313#685—22no—
314#685—34no—
315#685—34no—
316#685—62no—
317#685—62no—
318#685—121no—
319#685—121no—
320#685—121no—
321#685—121no—
322C4⋊Dic5—121no—
323#683—121no—
324#683—121no—
325C4×Dic5—41no—
326C4×Dic5—41no—
327C4×Dic5—121no—
328C22×C22⋊C4—151no—
329#388—31no—
330#388—151no—
331#388—151no—
332#388—151no—
333#388—151no—
334#388—151no—
335#388—151no—
336#388—151no—
337#380—151no—
338#380—151no—
339#379—151no—
340#379—151no—
341C4×C22⋊C4—51no—
342C4×C22⋊C4—151no—
343C22×C3×C5C23×C411yescharacteristic
344C22×C3×C5C2×#4111yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5H(5,𝔽2)11yescharacteristic
347C22×C3×C5H(5,𝔽2)11yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C2×D15—22no—
351C2×D15—22no—
352C2×D15—22no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×C5×D3—22no—
358C2×C5×D3—22no—
359C2×C5×D3—22no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—41no—
363C2×C5×D3—41no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5—22no—
368C2×C3×D5—22no—
369C2×C3×D5—22no—
370C2×C3×D5#11714yes—
371D3×D5—416no—
372C3×C4×C5—22no—
373C3×C4×C5—41no—
374C3×C4×C5—41no—
375Dic15—22no—
376Dic15—41no—
377Dic15—41no—
378C3×Dic5—22no—
379C3×Dic5—41no—
380C3×Dic5—41no—
381C5×Dic3—22no—
382C5×Dic3—41no—
383C5×Dic3—41no—
384C24×C3—51no—
385C23×D3—51no—
386C23×D3—54no—
387C23×D3—102no—
388C23×D3—102no—
389C23×D3—201no—
390C23×D3—201no—
391C23×D3—201no—
392C23×D3—201no—
393C23×D3C22×D511yescharacteristic
394C22×C3×C4—51no—
395C22×C3×C4—54no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—201no—
399C22×C3×C4—201no—
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×Dic3—51no—
404C22×Dic3—54no—
405C22×Dic3—51no—
406C22×Dic3—51no—
407C22×Dic3—201no—
408C22×Dic3—201no—
409C22×Dic3C22×D511yescharacteristic
410C22×Dic3C22×D511yescharacteristic
411C22×Dic3C22×D511yescharacteristic
412C3×C22⋊C4—102no—
413C3×C22⋊C4—102no—
414C3×C42—201no—
415C3×C42—201no—
416#217—102no—
417#217—102no—
418(C2×D3)⋊C4—41no—
419(C2×D3)⋊C4—41no—
420(C2×D3)⋊C4—54no—
421(C2×D3)⋊C4—54no—
422(C2×D3)⋊C4—54no—
423(C2×D3)⋊C4—201no—
424(C2×D3)⋊C4—201no—
425(C2×D3)⋊C4—201no—
426(C2×D3)⋊C4—201no—
427(C2×D3)⋊C4—201no—
428(C2×D3)⋊C4—201no—
429(C2×D3)⋊C4C4×D514yes—
430Dic3⋊C4—41no—
431Dic3⋊C4—201no—
432Dic3⋊C4—201no—
433Dic3⋊C4—201no—
434C4×Dic3—41no—
435C4×Dic3—201no—
436C23×C5—32no—
437C23×C5—61no—
438C23×C5—61no—
439C23×C5—61no—
440C23×C5—61no—
441C23×C5—61no—
442C23×C5—61no—
443C23×C5C23×D311yescharacteristic
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5—21no—
448C22×D5—32no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5—61no—
454C22×D5—61no—
455C22×D5—68no—
456C22×D5—124no—
457C22×D5—124no—
458C22×D5—124no—
459C22×D5—124no—
460C22×D5—124no—
461C22×D5—124no—
462C22×D5C2×C4×D312yes—
463C22×D5#23512yes—
464C22×D5#23512yes—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—32no—
474C2×C4×C5—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5C2×C4×D312yes—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—32no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—61no—
495C2×Dic5—61no—
496C2×Dic5—61no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5C2×C4×D312yes—
501C4×D5—44no—
502C4×D5—124no—
503C25—151no—
504C23×C4—51no—
505C23×C4—151no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—151no—
508C2×C4⋊C4—151no—
509C2×C4⋊C4—151no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—51no—
515C2×C22⋊C4—158no—
516C2×C22⋊C4—151no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4—151no—
527C2×C42—31no—
528C2×C42—51no—
529C2×C42—51no—
530C2×C42—151no—
531#95—31no—
532#95—51no—
533#95—151no—
534#95—151no—
535#95—151no—
536#95—151no—
537#95—151no—
538#95D3×D511yescharacteristic, complemented
539C2×C3×C5C2×#11711yescharacteristic
540C2×C3×C5#51811yescharacteristic
541C2×C3×C5#51811yescharacteristic
542C2×C3×C5#53811yescharacteristic
543C2×C3×C5#53811yescharacteristic
544C2×C3×C5#53811yescharacteristic
545C2×C3×C5#53811yescharacteristic
546D15—42no—
547C3×D5—24no—
548C5×D3—42no—
549C23×C3—52no—
550C23×C3—52no—
551C23×C3—52no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3—101no—
555C23×C3—101no—
556C23×C3C23×D511yescharacteristic
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—52no—
564C22×D3—108no—
565C22×D3—101no—
566C22×D3—101no—
567C22×D3—101no—
568C22×D3—101no—
569C22×D3—101no—
570C22×D3—101no—
571C22×D3—204no—
572C22×D3—204no—
573C22×D3—204no—
574C22×D3—204no—
575C22×D3—204no—
576C22×D3—204no—
577C22×D3C2×C4×D512yes—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—52no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—204no—
596C2×C3×C4C2×C4×D512yes—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—52no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—204no—
615C2×Dic3C2×C4×D512yes—
616C22×C5—62no—
617C22×C5—62no—
618C22×C5—62no—
619C22×C5—121no—
620C22×C5—121no—
621C22×C5—121no—
622C22×C5—121no—
623C22×C5C22×C4×D311yescharacteristic
624C22×C5C2×#23511yescharacteristic
625C22×C5C2×#23511yescharacteristic
626C22×C5#100411yescharacteristic
627C22×C5#100411yescharacteristic
628C22×C5#100911yescharacteristic
629C22×C5#100911yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—22no—
634C2×D5—22no—
635C2×D5—22no—
636C2×D5—62no—
637C2×D5—62no—
638C2×D5—62no—
639C2×D5—1216no—
640C2×D5—121no—
641C2×D5—121no—
642C2×D5—121no—
643C2×D5—121no—
644C2×D5#87214yes—
645C4×C5—22no—
646C4×C5—41no—
647C4×C5—41no—
648C4×C5—62no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—41no—
653Dic5—41no—
654Dic5—62no—
655Dic5—121no—
656Dic5—121no—
657C24—31no—
658C24—51no—
659C24—154no—
660C24—151no—
661C24—302no—
662C24—302no—
663C24—601no—
664C24—601no—
665C24—601no—
666C24—601no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—51no—
671C22×C4—54no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—154no—
675C22×C4—151no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—201no—
679C22×C4—201no—
680C22×C4—601no—
681C22×C4—601no—
682C22×C4C2×D3×D511yescharacteristic
683C22×C4C2×D3×D511yescharacteristic
684C22×C4C2×D3×D511yescharacteristic
685C4⋊C4—121no—
686C4⋊C4—601no—
687C4⋊C4—601no—
688C4⋊C4—601no—
689C22⋊C4—34no—
690C22⋊C4—102no—
691C22⋊C4—102no—
692C22⋊C4—121no—
693C22⋊C4—121no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—302no—
698C22⋊C4—302no—
699C22⋊C4—601no—
700C22⋊C4—601no—
701C22⋊C4—601no—
702C22⋊C4—601no—
703C22⋊C4—601no—
704C22⋊C4—601no—
705C42—121no—
706C42—201no—
707C42—201no—
708C42—601no—
709C3×C5#231211yescharacteristic, complemented, Hall
710C22×C3—54no—
711C22×C3—102no—
712C22×C3—102no—
713C22×C3—102no—
714C22×C3—102no—
715C22×C3—102no—
716C22×C3—102no—
717C22×C3C22×C4×D511yescharacteristic
718C22×C3#414411yescharacteristic
719C22×C3#414411yescharacteristic
720C22×C3D5×#4111yescharacteristic
721C22×C3D5×#4111yescharacteristic
722C22×C3#414911yescharacteristic
723C22×C3#414911yescharacteristic
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—102no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—2016no—
735C2×D3—201no—
736C2×D3—201no—
737C2×D3—201no—
738C2×D3—201no—
739C3×C4—22no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—102no—
743C3×C4—201no—
744C3×C4—201no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—102no—
749Dic3—201no—
750Dic3—201no—
751C2×C5—122no—
752C2×C5C2×#87211yescharacteristic
753C2×C5#548611yescharacteristic
754C2×C5#552111yescharacteristic
755C2×C5#556011yescharacteristic
756C2×C5#556011yescharacteristic
757C2×C5#556011yescharacteristic
758C2×C5#556011yescharacteristic
759D5—24no—
760D5—122no—
761C23—32no—
762C23—52no—
763C23—52no—
764C23—52no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—101no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—152no—
776C23—308no—
777C23—301no—
778C23—301no—
779C23—301no—
780C23—301no—
781C23—301no—
782C23—301no—
783C23—604no—
784C23—604no—
785C23—604no—
786C23—604no—
787C23—604no—
788C23—604no—
789C23C22×D3×D511yescharacteristic
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—32no—
799C2×C4—52no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—152no—
817C2×C4—204no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—604no—
827C2×C4C4×D3×D512yes—
828C2×C3—104no—
829C2×C3D5×#11711yescharacteristic
830C2×C3#6587911yescharacteristic
831C2×C3#6587911yescharacteristic
832C2×C3#6594711yescharacteristic
833C2×C3#6599111yescharacteristic
834C2×C3#6601211yescharacteristic
835C2×C3#6603811yescharacteristic
836D3—42no—
837D3—202no—
838C5#7356711yescharacteristic, complemented, Sylow
839C22—54no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—102no—
844C22—102no—
845C22—102no—
846C22—102no—
847C22—102no—
848C22—102no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—302no—
854C22—302no—
855C22—302no—
856C22—6016no—
857C22—601no—
858C22—601no—
859C22—601no—
860C22—601no—
861C22C2×C4×D3×D511yescharacteristic
862C22D5×#23511yescharacteristic
863C22D5×#23511yescharacteristic
864C22#9202511yescharacteristic
865C22#9202611yescharacteristic
866C22#9202711yescharacteristic
867C22#9203511yescharacteristic
868C4—22no—
869C4—41no—
870C4—41no—
871C4—62no—
872C4—102no—
873C4—121no—
874C4—121no—
875C4—201no—
876C4—201no—
877C4—302no—
878C4—601no—
879C4—601no—
880C3#1060755611yescharacteristic, complemented, Sylow
881C2—104no—
882C2—122no—
883C2—602no—
884C2D5×#87211yescharacteristic
885C2#1175320011yescharacteristic
886C2#1175327711yescharacteristic
887C2#1175327811yescharacteristic
888C2#1175383711yescharacteristic
889C2#1175389411yescharacteristic
890C2#1175389511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5#2312
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750770C2semidirect
3. C5×#4669C2semidirect
4. C3×#64955C2semidirect
7. #11748885C2semidirect
8. #11748878C2semidirect
9. #11748854C2semidirect
10. #11748794C2semidirect
11. #11748727C2semidirect
12. #11748726C2semidirect
13. #11748715C2semidirect
14. #11748714C2semidirect
15. C4×#6665C2semidirect
23. C2×#6712C22semidirect
24. C2×C4×Dic15C22semidirect
28. C2×C5×Dic3⋊C4C22semidirect
29. C2×C4×C5×Dic3C22semidirect
32. C2×C3×C4×Dic5C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. C2×Dic3⋊Dic5C22semidirect
35. C2×#6669C22semidirect
44. D5×(C2×D3)⋊C4C4semidirect
45. C3×C5×#95C22semidirect
46. #91115C22semidirect
47. C5×C3⋊#95C22semidirect
48. C3×#3963C22semidirect
49. #90994C22semidirect
50. #90994C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
68. #64955D3semidirect
135. #4669D5semidirect
161. C2×C4×Dic5C2×D3semidirect
162. C2×C4×Dic5C2×D3semidirect
165. C5×#95C2×D3semidirect
171. #3963C2×D3semidirect
265. C2×Dic3⋊C4C2×D5semidirect
267. C2×C4×Dic3C2×D5semidirect
269. C3×#95C2×D5semidirect
275. C3⋊#95C2×D5semidirect
538. #95D3×D5semidirect
709. C3×C5#2312semidirect
838. C5#73567semidirect
880. C3#10607556semidirect

Maximal subgroups

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

subgroupindex
C2×D5×(C2×D3)⋊C42
#117507702
C5×#46692
C3×#649552
#117489402
#117488852
#117488782
#117488542
#117487942
#117487272
#117487262
#117487152
#117487142
C4×#66652
#106075563
#735675