Finite Group Databasebeta

← #14325881

Subgroups — #14325881

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4093C211yesmaximal, characteristic
2#11751330C211yesmaximal, characteristic, complemented
3C5×#5229C211yesmaximal, characteristic, complemented
4#11748900C211yesmaximal, characteristic, complemented
5#11748899C211yesmaximal, characteristic, complemented
6#11748896C211yesmaximal, characteristic
7#11748896C211yesmaximal, characteristic
8#11748884C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10#11748791C211yesmaximal, characteristic, complemented
11#11748772C211yesmaximal, characteristic, complemented
12#11748771C211yesmaximal, characteristic, complemented
13#11748770C211yesmaximal, characteristic, complemented
14#11748638C211yesmaximal, characteristic, complemented
15#11748612C211yesmaximal, characteristic, complemented
16#10608219—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C3×#4093C418yescomplemented
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#82954—51nomaximal, Hall
54C2×#4093D311yescharacteristic
55C5×#391—31no—
56#65519—31no—
57#65279—31no—
58#65278—31no—
59#65229—31no—
60C4×#685—31no—
61#64959—31no—
62#64958—31no—
63#64957—31no—
64#64955—31no—
65#64954—31no—
66#64954—31no—
67#64940—31no—
68#64938—31no—
69C23×C3×D5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C2×C3×C5×Q8—41no—
72C2×C3×C5×Q8—41no—
73C2×C3×C5×Q8C2×C414yescomplemented
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×C3×D20—41no—
88C2×C3×D20—41no—
89C2×C3×D20C2×C414yes—
90C2×D5×Dic3—22no—
91C2×D5×Dic3—22no—
92C2×D5×Dic3—41no—
93C2×D5×Dic3—41no—
94C2×D5×Dic3—41no—
95C2×D5×Dic3—41no—
96C4⋊Dic15—41no—
97C4×Dic15—41no—
98C5×C4⋊Dic3—41no—
99C4×C5×Dic3—41no—
100C3×#685C2×C414yescomplemented
101C3×#685C2×C414yescomplemented
102C3×#685C2×C414yescomplemented
103C3×#685C2×C414yescomplemented
104C3×C4×Dic5C2×C414yescomplemented
105#6668—22no—
106#6668—22no—
107#6665—22no—
108#6665—22no—
109#6665—41no—
110#6665—41no—
111#6665—41no—
112#6665—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5—41no—
115C2×C3×#124—51no—
116#5229—51no—
117#5229D511yescharacteristic, complemented
118#5220—51no—
119#5220—51no—
120#4951—51no—
121#4951—51no—
122#4951—51no—
123#4951—51no—
124#4950—51no—
125#4950—51no—
126Dic3×C22⋊C4—51no—
127Dic3×C22⋊C4—51no—
128#4937—51no—
129C4×C4⋊Dic3—51no—
130C22×C5×Q8C2×D311yescharacteristic
131C22×D20C2×D311yescharacteristic
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C2×C5×C4⋊C4—31no—
135C2×C42×C5—31no—
136#4093Dic318yescomplemented
137C2×#685—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685C2×D311yescharacteristic
144C2×#685C2×D311yescharacteristic
145C2×#685C2×D311yescharacteristic
146C2×#685C2×D311yescharacteristic
147C2×C4⋊Dic5—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5C2×D311yescharacteristic
154C5×#95—31no—
155C5×#95—31no—
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#3963—31no—
165#3963—31no—
166#2337—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—21no—
173C22×C3×D5—21no—
174C22×C3×D5—21no—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5C22×C412yes—
181C22×C3×D5C22×C412yes—
182C3×C5×Q8—44no—
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×C5C22×C412yes—
190C2×C3×C4×C5C22×C412yes—
191C2×C3×C4×C5C22×C412yes—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15#4112yes—
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×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3#4112yes—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5C22×C412yes—
222C3×D20—44no—
223D5×Dic3—44no—
224D5×Dic3—44no—
225C22×C3×Q8C2×D511yescharacteristic
226C22×C3×D4—51no—
227C23×Dic3—51no—
228C23×Dic3—51no—
229C3×#124—58no—
230C2×C3×C22⋊C4—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4—51no—
233C2×C3×C22⋊C4—51no—
234C2×C3×C42—51no—
235C2×#217—51no—
236C2×#217—51no—
237C2×#217—51no—
238C2×#217—51no—
239C2×#217—51no—
240C2×#217—51no—
241C2×C4⋊Dic3—51no—
242C2×C4⋊Dic3—51no—
243C2×C4⋊Dic3—51no—
244C2×C4⋊Dic3C2×D511yescharacteristic
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95C2×D511yescharacteristic
258C3⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C3⋊#95C2×D511yescharacteristic
261C23×D5C22×D311yescharacteristic
262C23×D5C22×D311yescharacteristic
263C2×C5×Q8—41no—
264C2×C5×Q8—41no—
265C2×C5×Q8C2×Dic314yescomplemented
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C2×D20—41no—
280C2×D20—41no—
281C2×D20C2×Dic314yes—
282C2×C4×D5—62no—
283C2×C4×D5—62no—
284C2×C4×D5—121no—
285C2×C4×D5—121no—
286C2×C4×D5—121no—
287C2×C4×D5—121no—
288C5×C4⋊C4—121no—
289C42×C5—121no—
290#685—62no—
291#685—62no—
292#685—121no—
293#685—121no—
294#685—121no—
295#685—121no—
296#685C2×Dic314yescomplemented
297#685C2×Dic314yescomplemented
298#685C2×Dic314yescomplemented
299#685C2×Dic314yescomplemented
300C4⋊Dic5—121no—
301#683—62no—
302#683—62no—
303C4×Dic5—121no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C4×Dic5C2×Dic314yescomplemented
307C2×#124—51no—
308#391—31no—
309#391—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388—151no—
314#386—151no—
315#386—151no—
316#385—151no—
317#385—151no—
318#383—151no—
319C4×C4⋊C4—151no—
320C4×C22⋊C4—151no—
321C4×C22⋊C4—151no—
322C22×C3×C5C23×C411yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C22×C3×C52−1+411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—22no—
331C2×C3×D5—22no—
332C2×C3×D5—22no—
333C2×C3×D5—22no—
334C2×C3×D5—22no—
335C2×C3×D5—41no—
336C2×C3×D5—41no—
337C2×C3×D5—41no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C3×C4×C5—22no—
344C3×C4×C5—22no—
345C3×C4×C5—22no—
346Dic15—22no—
347Dic15—41no—
348Dic15—41no—
349Dic15—41no—
350C3×Dic5—22no—
351C3×Dic5—22no—
352C5×Dic3—22no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C5×Dic3—41no—
356C24×C3—51no—
357C24×C3—51no—
358C2×C3×Q8—41no—
359C2×C3×Q8—41no—
360C2×C3×Q8C4×D514yescomplemented
361C2×C3×D4—54no—
362C2×C3×D4—201no—
363C2×C3×D4—201no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C22×C3×C4C22×D511yescharacteristic
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—102no—
374C22×Dic3—102no—
375C22×Dic3—201no—
376C22×Dic3—201no—
377C22×Dic3—201no—
378C22×Dic3—201no—
379C22×Dic3C22×D511yescharacteristic
380C22×Dic3C22×D511yescharacteristic
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C3×C22⋊C4—54no—
384C3×C22⋊C4—54no—
385C3×C22⋊C4—54no—
386C3×C22⋊C4—54no—
387C3×C42—54no—
388#217—102no—
389#217—102no—
390#217—201no—
391#217—201no—
392#217—201no—
393#217—201no—
394C4⋊Dic3—41no—
395C4⋊Dic3—102no—
396C4⋊Dic3—102no—
397C4⋊Dic3—201no—
398C4×Dic3—41no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C4×Dic3—201no—
402C23×C5C23×D311yescharacteristic
403C22×D5—21no—
404C22×D5—21no—
405C22×D5—21no—
406C22×D5—21no—
407C22×D5—21no—
408C22×D5—21no—
409C22×D5—21no—
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5C22×Dic312yes—
416C22×D5C22×Dic312yes—
417C5×Q8—44no—
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—61no—
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×C5C22×Dic312yes—
437C2×C4×C5C22×Dic312yes—
438C2×C4×C5C22×Dic312yes—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—32no—
444C2×Dic5—61no—
445C2×Dic5—61no—
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×Dic5—61no—
455C2×Dic5C22×Dic312yes—
456C2×Dic5C22×Dic312yes—
457D20—44no—
458C4×D5—124no—
459C4×D5—124no—
460C22×Q8D3×D511yescharacteristic
461C22×D4—51no—
462C23×C4—151no—
463C23×C4—151no—
464#124—58no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4—51no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—31no—
480C2×C42—51no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5C4×#4111yescharacteristic
497C2×C3×C5#51811yescharacteristic
498C2×C3×C5#52011yescharacteristic
499C2×C3×C5#53811yescharacteristic
500C2×C3×C5#53811yescharacteristic
501C2×C3×C5#54211yescharacteristic
502C2×C3×C5#54211yescharacteristic
503C3×D5—42no—
504C3×D5—42no—
505C23×C3—52no—
506C23×C3—52no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—101no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3—101no—
515C23×C3—101no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—101no—
519C23×C3C23×D511yescharacteristic
520C3×Q8—44no—
521C3×D4—204no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—52no—
529C2×C3×C4—52no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4C2×C4×D512yes—
535C2×C3×C4C2×C4×D512yes—
536C2×C3×C4C2×C4×D512yes—
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—21no—
548C2×Dic3—52no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—204no—
561C2×Dic3—204no—
562C2×Dic3#71312yes—
563C22×C5#100411yescharacteristic
564C22×C5#100411yescharacteristic
565C22×C5D3×#4111yescharacteristic
566C22×C5D3×#4111yescharacteristic
567C22×C5#100911yescharacteristic
568C22×C5#101011yescharacteristic
569C22×C5C23×Dic311yescharacteristic
570C2×D5—22no—
571C2×D5—22no—
572C2×D5—22no—
573C2×D5—22no—
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—41no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—41no—
583C2×D5—41no—
584C4×C5—22no—
585C4×C5—22no—
586C4×C5—22no—
587C4×C5—62no—
588C4×C5—121no—
589C4×C5—121no—
590C4×C5—121no—
591Dic5—22no—
592Dic5—22no—
593Dic5—62no—
594Dic5—121no—
595Dic5—121no—
596Dic5—121no—
597C24—51no—
598C24—51no—
599C2×Q8—41no—
600C2×Q8—41no—
601C2×Q8D5×Dic314yescomplemented
602C2×D4—54no—
603C2×D4—201no—
604C2×D4—201no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—151no—
612C22×C4—151no—
613C22×C4—151no—
614C22×C4—151no—
615C22×C4—302no—
616C22×C4—302no—
617C22×C4—601no—
618C22×C4—601no—
619C22×C4—601no—
620C22×C4—601no—
621C22×C4C2×D3×D511yescharacteristic
622C22×C4C2×D3×D511yescharacteristic
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—121no—
625C4⋊C4—302no—
626C4⋊C4—302no—
627C4⋊C4—601no—
628C22⋊C4—54no—
629C22⋊C4—54no—
630C22⋊C4—54no—
631C22⋊C4—54no—
632C22⋊C4—302no—
633C22⋊C4—302no—
634C22⋊C4—601no—
635C22⋊C4—601no—
636C22⋊C4—601no—
637C22⋊C4—601no—
638C42—54no—
639C42—121no—
640C42—601no—
641C42—601no—
642C42—601no—
643C3×C5#233711yescharacteristic, complemented, Hall
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—102no—
647C22×C3—102no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3—201no—
657C22×C3—201no—
658C22×C3C22×C4×D511yescharacteristic
659C22×C3#414411yescharacteristic
660C22×C3#414411yescharacteristic
661C22×C3C2×#71311yescharacteristic
662C22×C3#414711yescharacteristic
663C22×C3D5×#4111yescharacteristic
664C22×C3#414911yescharacteristic
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—102no—
669C3×C4—102no—
670Dic3—22no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—102no—
675Dic3—201no—
676Dic3—201no—
677Dic3—201no—
678C2×C5#566911yescharacteristic
679C2×C5#566911yescharacteristic
680C2×C5#567811yescharacteristic
681C2×C5#567811yescharacteristic
682C2×C5#579811yescharacteristic
683C2×C5Dic3×#4111yescharacteristic
684C2×C5#582711yescharacteristic
685D5—42no—
686D5—42no—
687C23—52no—
688C23—52no—
689C23—101no—
690C23—101no—
691C23—101no—
692C23—101no—
693C23—101no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23—101no—
698C23—101no—
699C23—101no—
700C23—101no—
701C23C22×D3×D511yescharacteristic
702Q8—44no—
703D4—204no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—52no—
712C2×C4—52no—
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—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—152no—
729C2×C4—301no—
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—301no—
739C2×C4—301no—
740C2×C4—604no—
741C2×C4—604no—
742C2×C4C2×D5×Dic312yes—
743C2×C4C2×D5×Dic312yes—
744C2×C4C2×D5×Dic312yes—
745C2×C3—202no—
746C2×C3—202no—
747C2×C3#6582011yescharacteristic
748C2×C3C4×#71311yescharacteristic
749C2×C3#6590811yescharacteristic
750C2×C3#6597411yescharacteristic
751C2×C3#6597811yescharacteristic
752C2×C3#6601211yescharacteristic
753C2×C3#6606711yescharacteristic
754C5#8295411yescharacteristic, complemented, Sylow
755C22—102no—
756C22—102no—
757C22—102no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—201no—
767C22—201no—
768C22—201no—
769C22#9202811yescharacteristic
770C22D3×#71311yescharacteristic
771C22#9203411yescharacteristic
772C22#9203511yescharacteristic
773C22C22×D5×Dic311yescharacteristic
774C22#9204911yescharacteristic
775C22#9204911yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—62no—
780C4—102no—
781C4—102no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—302no—
786C4—601no—
787C4—601no—
788C4—601no—
789C3#1060821911yescharacteristic, complemented, Sylow
790C2—202no—
791C2—202no—
792C2Dic3×#71311yescharacteristic
793C2#1175520511yescharacteristic
794C2#1175521211yescharacteristic
795C2#1175521711yescharacteristic
796C2#1175529111yescharacteristic
797C2#1175529311yescharacteristic
798C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2337
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11751330C2semidirect
3. C5×#5229C2semidirect
4. #11748900C2semidirect
5. #11748899C2semidirect
8. #11748884C2semidirect
9. Dic3×#685C2semidirect
10. #11748791C2semidirect
11. #11748772C2semidirect
12. #11748771C2semidirect
13. #11748770C2semidirect
14. #11748638C2semidirect
15. #11748612C2semidirect
25. C3×#4093C4semidirect
73. C2×C3×C5×Q8C2×C4semidirect
100. C3×#685C2×C4semidirect
101. C3×#685C2×C4semidirect
102. C3×#685C2×C4semidirect
103. C3×#685C2×C4semidirect
104. C3×C4×Dic5C2×C4semidirect
117. #5229D5semidirect
136. #4093Dic3semidirect
265. C2×C5×Q8C2×Dic3semidirect
296. #685C2×Dic3semidirect
297. #685C2×Dic3semidirect
298. #685C2×Dic3semidirect
299. #685C2×Dic3semidirect
306. C4×Dic5C2×Dic3semidirect
360. C2×C3×Q8C4×D5semidirect
601. C2×Q8D5×Dic3semidirect
643. C3×C5#2337semidirect
754. C5#82954semidirect
789. C3#10608219semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40932
#117513302
C5×#52292
#117489002
#117488992
#117488962
#117488842
Dic3×#6852
#117487912
#117487722
#117487712
#117487702
#117486382
#117486122
#106082193
#829545