Finite Group Databasebeta

← #14330804

Subgroups — #14330804

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91413C211yesmaximal, characteristic
2#11751090C211yesmaximal, characteristic, complemented
3C5×#4972C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic, complemented
5#11748917C211yesmaximal, characteristic
6#11748913C211yesmaximal, characteristic
7#11748885C211yesmaximal, characteristic, complemented
8#11748878C211yesmaximal, characteristic, complemented
9#11748854C211yesmaximal, characteristic, complemented
10#11748801C211yesmaximal, characteristic, complemented
11#11748770C211yesmaximal, characteristic, complemented
12#11748731C211yesmaximal, characteristic, complemented
13#11748726C211yesmaximal, characteristic, complemented
14#11748683C211yesmaximal, characteristic, complemented
15#11748648C211yesmaximal, characteristic, complemented
16#10607938—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×#1202C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91413C418yescomplemented
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75489—51nomaximal, Hall
54C2×#4040—31no—
55C5×#389—31no—
56#65279D311yescharacteristic, complemented
57#65278—31no—
58#65278—31no—
59#65277—31no—
60#65276—31no—
61#65270—31no—
62#65261—31no—
63#65229—31no—
64#65229—31no—
65#64959—31no—
66#64956—31no—
67#64954—31no—
68#64941—31no—
69C23×D15C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C2×C4×D15—41no—
78C2×C4×D15—41no—
79C2×C4×D15—41no—
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×#1202—41no—
88C2×#1202—41no—
89C2×#1202C2×C414yes—
90C2×D5×Dic3—41no—
91C2×D5×Dic3—41no—
92C2×D5×Dic3C2×C414yescomplemented
93C3×C5×C4⋊C4—41no—
94#6714—41no—
95#6714C2×C414yes—
96#6712—41no—
97C5×C4⋊Dic3C2×C414yescomplemented
98C5×Dic3⋊C4—41no—
99C5×Dic3⋊C4—41no—
100C4×C5×Dic3—41no—
101C3×#685—41no—
102C3×#685—41no—
103C3×#685C2×C414yescomplemented
104C3×C4×Dic5—41no—
105Dic3⋊Dic5—41no—
106#6669—41no—
107#6668—41no—
108#6668C2×C414yescomplemented
109#6667—41no—
110#6667—41no—
111#6667C2×C414yes—
112#6665—41no—
113#6665—41no—
114Dic3×Dic5—41no—
115C2×#886—51no—
116C3×#388—51no—
117#4989—51no—
118#4972D511yescharacteristic, complemented
119#4957—51no—
120#4956—51no—
121#4951—51no—
122#4942—51no—
123#4942—51no—
124#4940—51no—
125#4928—51no—
126#4669—51no—
127#4668—51no—
128#4654—51no—
129#4653—51no—
130C22×D20—31no—
131C22×C4×D5—31no—
132C22×C4×D5—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4C2×D311yescharacteristic
137C2×C42×C5—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685C2×D311yescharacteristic
146C2×#685C2×D311yescharacteristic
147C2×#685C2×D311yescharacteristic
148C2×C4⋊Dic5—31no—
149C2×#683—31no—
150C2×#683—31no—
151C2×#683—31no—
152C2×#683—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5C2×D311yescharacteristic
155#4040—38no—
156C5×#95—31no—
157C5×#95—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2376—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×D15—21no—
169C22×D15—21no—
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15C22×C412yes—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C22×C412yes—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15C22×C412yes—
200C4×D15—44no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C22×C412yes—
212C2×C5×Dic3C22×C412yes—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5C22×C412yes—
222#1202—44no—
223D5×Dic3—44no—
224C22×#67—51no—
225C23×Dic3—51no—
226C22×C4×D3—51no—
227C2×C3×C4⋊C4C2×D511yescharacteristic
228C2×C3×C22⋊C4—51no—
229C2×C3×C22⋊C4—51no—
230C2×C3×C22⋊C4—51no—
231C2×C3×C42—51no—
232C2×#217—51no—
233C2×#217—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×C4⋊Dic3—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3C2×D511yescharacteristic
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4C2×D511yescharacteristic
246C2×Dic3⋊C4C2×D511yescharacteristic
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249#886—58no—
250C3×#95—51no—
251C3×#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C23×D5—31no—
261C23×D5C22×D311yescharacteristic
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C22×Dic5C22×D311yescharacteristic
275C2×D20—34no—
276C2×D20—121no—
277C2×D20—121no—
278C2×C4×D5—34no—
279C2×C4×D5—121no—
280C2×C4×D5—121no—
281C2×C4×D5—121no—
282C2×C4×D5—121no—
283C2×C4×D5—121no—
284C5×C4⋊C4—34no—
285C5×C4⋊C4—41no—
286C5×C4⋊C4—121no—
287C5×C4⋊C4—121no—
288C42×C5—121no—
289#685—34no—
290#685—34no—
291#685—41no—
292#685—41no—
293#685—121no—
294#685—121no—
295#685—121no—
296#685—121no—
297#685—121no—
298#685C4×D314yescomplemented
299C4⋊Dic5—121no—
300#683—34no—
301#683—121no—
302#683—121no—
303#683—121no—
304C4×Dic5—41no—
305C4×Dic5—121no—
306C2×#123—151no—
307#390—151no—
308#389—31no—
309#389—151no—
310#388—51no—
311#388—151no—
312#388—151no—
313#388—151no—
314#387—151no—
315#387—151no—
316#386—151no—
317#385—151no—
318#385—151no—
319#380—151no—
320#380—151no—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5H(5,𝔽2)11yescharacteristic
323C22×C3×C5H(5,𝔽2)11yescharacteristic
324C22×C3×C5H(5,𝔽2)11yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C52−1+411yescharacteristic
327C22×C3×C52−1+411yescharacteristic
328C2×D15—22no—
329C2×D15—22no—
330C2×D15—22no—
331C2×D15—41no—
332C2×D15—41no—
333C2×D15—41no—
334C2×D15—41no—
335C2×C3×D5—22no—
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C3×C4×C5—22no—
343C3×C4×C5—41no—
344C3×C4×C5—41no—
345Dic15—22no—
346Dic15—41no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—41no—
350C3×Dic5—41no—
351C5×Dic3—22no—
352C5×Dic3—22no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C24×C3—51no—
356C23×D3—51no—
357C22×C3×C4—51no—
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4C22×D511yescharacteristic
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C2×#67—54no—
364C2×#67—201no—
365C2×#67—201no—
366C22×Dic3—51no—
367C22×Dic3—54no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—201no—
371C22×Dic3—201no—
372C22×Dic3C22×D511yescharacteristic
373C22×Dic3C22×D511yescharacteristic
374C22×Dic3C22×D511yescharacteristic
375C22×Dic3C22×D511yescharacteristic
376C2×C4×D3—201no—
377C2×C4×D3—201no—
378C2×C4×D3—201no—
379C3×C4⋊C4—41no—
380C3×C22⋊C4—54no—
381C3×C22⋊C4—201no—
382C3×C22⋊C4—201no—
383C3×C42—201no—
384#217—201no—
385#217—201no—
386(C2×D3)⋊C4—54no—
387(C2×D3)⋊C4—54no—
388(C2×D3)⋊C4—201no—
389(C2×D3)⋊C4—201no—
390(C2×D3)⋊C4—201no—
391C4⋊Dic3—54no—
392C4⋊Dic3—201no—
393C4⋊Dic3C4×D514yescomplemented
394Dic3⋊C4—41no—
395Dic3⋊C4—41no—
396Dic3⋊C4—201no—
397Dic3⋊C4—201no—
398Dic3⋊C4—201no—
399C4×Dic3—41no—
400C4×Dic3—201no—
401C23×C5C23×D311yescharacteristic
402C22×D5—21no—
403C22×D5—21no—
404C22×D5—21no—
405C22×D5—21no—
406C22×D5—21no—
407C22×D5—21no—
408C22×D5—32no—
409C22×D5—61no—
410C22×D5—61no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5C2×C4×D312yes—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—32no—
425C2×C4×C5—32no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5C2×C4×D312yes—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—32no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5C2×C4×D312yes—
455D20—124no—
456C4×D5—124no—
457C4×D5—124no—
458C22×D4—151no—
459C23×C4—151no—
460C23×C4—151no—
461#123—158no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4D3×D511yescharacteristic
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C22⋊C4—151no—
480C2×C22⋊C4—151no—
481C2×C42—31no—
482C2×C42—51no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—51no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494C2×C3×C5#51811yescharacteristic
495C2×C3×C5#52011yescharacteristic
496C2×C3×C5#52011yescharacteristic
497C2×C3×C5#56011yescharacteristic
498C2×C3×C5#56211yescharacteristic
499C2×C3×C5#56211yescharacteristic
500C2×C3×C5#56311yescharacteristic
501D15—42no—
502C3×D5—42no—
503C23×C3—52no—
504C23×C3—101no—
505C23×C3—101no—
506C23×C3—101no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—101no—
510C23×C3C23×D511yescharacteristic
511C22×D3—52no—
512C22×D3—101no—
513C22×D3—101no—
514C22×D3—101no—
515C22×D3—101no—
516C22×D3—101no—
517C22×D3—101no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—52no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4C2×C4×D512yes—
536#67—204no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—52no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—204no—
557C2×Dic3C2×C4×D512yes—
558C2×Dic3C2×C4×D512yes—
559C4×D3—204no—
560C22×C5C22×C4×D311yescharacteristic
561C22×C5#100411yescharacteristic
562C22×C5#100411yescharacteristic
563C22×C5#100911yescharacteristic
564C22×C5#100911yescharacteristic
565C22×C5#101011yescharacteristic
566C22×C5#101011yescharacteristic
567C2×D5—22no—
568C2×D5—22no—
569C2×D5—22no—
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—62no—
575C2×D5—62no—
576C2×D5—62no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—22no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5—62no—
585C4×C5—62no—
586C4×C5—121no—
587C4×C5—121no—
588Dic5—22no—
589Dic5—41no—
590Dic5—41no—
591Dic5—62no—
592Dic5—121no—
593Dic5—121no—
594C24—51no—
595C24—151no—
596C2×D4—154no—
597C2×D4—601no—
598C2×D4—601no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—154no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—601no—
611C22×C4—601no—
612C22×C4—601no—
613C22×C4—601no—
614C22×C4—601no—
615C22×C4C2×D3×D511yescharacteristic
616C22×C4C2×D3×D511yescharacteristic
617C22×C4C2×D3×D511yescharacteristic
618C4⋊C4—34no—
619C4⋊C4—41no—
620C4⋊C4—121no—
621C4⋊C4—121no—
622C4⋊C4—154no—
623C4⋊C4—601no—
624C4⋊C4—601no—
625C4⋊C4—601no—
626C4⋊C4—601no—
627C22⋊C4—54no—
628C22⋊C4—154no—
629C22⋊C4—154no—
630C22⋊C4—201no—
631C22⋊C4—201no—
632C22⋊C4—601no—
633C22⋊C4—601no—
634C22⋊C4—601no—
635C22⋊C4—601no—
636C22⋊C4—601no—
637C42—121no—
638C42—201no—
639C42—601no—
640C3×C5#237611yescharacteristic, complemented, Hall
641C22×C3—102no—
642C22×C3—102no—
643C22×C3—102no—
644C22×C3—201no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3—201no—
648C22×C3C22×C4×D511yescharacteristic
649C22×C3#414411yescharacteristic
650C22×C3#414411yescharacteristic
651C22×C3#414711yescharacteristic
652C22×C3#414711yescharacteristic
653C22×C3#414911yescharacteristic
654C22×C3#414911yescharacteristic
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—102no—
658C2×D3—201no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—22no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—102no—
666C3×C4—201no—
667C3×C4—201no—
668Dic3—22no—
669Dic3—22no—
670Dic3—41no—
671Dic3—41no—
672Dic3—102no—
673Dic3—201no—
674Dic3—201no—
675C2×C5#552111yescharacteristic
676C2×C5#554611yescharacteristic
677C2×C5#554611yescharacteristic
678C2×C5#562011yescharacteristic
679C2×C5#566711yescharacteristic
680C2×C5#568411yescharacteristic
681C2×C5#571211yescharacteristic
682D5—42no—
683D5—122no—
684C23—52no—
685C23—101no—
686C23—101no—
687C23—101no—
688C23—101no—
689C23—101no—
690C23—101no—
691C23—152no—
692C23—301no—
693C23—301no—
694C23—301no—
695C23—301no—
696C23—301no—
697C23—301no—
698C23C22×D3×D511yescharacteristic
699D4—604no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—52no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—152no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—604no—
739C2×C4—604no—
740C2×C4C4×D3×D512yes—
741C2×C3—202no—
742C2×C3#6583811yescharacteristic
743C2×C3#6587911yescharacteristic
744C2×C3#6590811yescharacteristic
745C2×C3#6595411yescharacteristic
746C2×C3#6598111yescharacteristic
747C2×C3#6603411yescharacteristic
748C2×C3#6606911yescharacteristic
749D3—202no—
750C5#7548911yescharacteristic, complemented, Sylow
751C22—102no—
752C22—102no—
753C22—102no—
754C22—201no—
755C22—201no—
756C22—201no—
757C22—201no—
758C22—302no—
759C22—302no—
760C22—302no—
761C22—601no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22#9200011yescharacteristic
766C22C2×C4×D3×D511yescharacteristic
767C22#9202611yescharacteristic
768C22#9202711yescharacteristic
769C22#9202811yescharacteristic
770C22#9203511yescharacteristic
771C22#9204911yescharacteristic
772C4—22no—
773C4—41no—
774C4—41no—
775C4—62no—
776C4—62no—
777C4—102no—
778C4—121no—
779C4—121no—
780C4—201no—
781C4—201no—
782C4—302no—
783C4—601no—
784C4—601no—
785C3#1060793811yescharacteristic, complemented, Sylow
786C2—202no—
787C2—602no—
788C2#1175340111yescharacteristic
789C2#1175364811yescharacteristic
790C2#1175365711yescharacteristic
791C2#1175383711yescharacteristic
792C2#1175428411yescharacteristic
793C2#1175499711yescharacteristic
794C2#1175526111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2376
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. #11751090C2semidirect
3. C5×#4972C2semidirect
4. C3×#65279C2semidirect
7. #11748885C2semidirect
8. #11748878C2semidirect
9. #11748854C2semidirect
10. #11748801C2semidirect
11. #11748770C2semidirect
12. #11748731C2semidirect
13. #11748726C2semidirect
14. #11748683C2semidirect
15. #11748648C2semidirect
42. #91413C4semidirect
56. #65279D3semidirect
92. C2×D5×Dic3C2×C4semidirect
97. C5×C4⋊Dic3C2×C4semidirect
103. C3×#685C2×C4semidirect
108. #6668C2×C4semidirect
118. #4972D5semidirect
298. #685C4×D3semidirect
393. C4⋊Dic3C4×D5semidirect
640. C3×C5#2376semidirect
750. C5#75489semidirect
785. C3#10607938semidirect

Maximal subgroups

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

subgroupindex
C2×#914132
#117510902
C5×#49722
C3×#652792
#117489172
#117489132
#117488852
#117488782
#117488542
#117488012
#117487702
#117487312
#117487262
#117486832
#117486482
#106079383
#754895