Finite Group Databasebeta

← #14325856

Subgroups — #14325856

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×#91526C211yesmaximal, characteristic
2#11751057C211yesmaximal, characteristic
3C5×#4944C211yesmaximal, characteristic, complemented
4C3×#65235C211yesmaximal, characteristic, complemented
5#11749494C211yesmaximal, characteristic
6#11749485C211yesmaximal, characteristic, complemented
7Dic5×#217C211yesmaximal, characteristic, complemented
8#11748731C211yesmaximal, characteristic, complemented
9#11748728C211yesmaximal, characteristic, complemented
10#11748670C211yesmaximal, characteristic, complemented
11#11748666C211yesmaximal, characteristic, complemented
12#11748646C211yesmaximal, characteristic, complemented
13Dic3×#683C211yesmaximal, characteristic, complemented
14#11748631C211yesmaximal, characteristic, complemented
15#11748628C211yesmaximal, characteristic, complemented
16#10607202—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×#6667C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91526C418yescomplemented
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74391—51nomaximal, Hall
54C2×#4031—31no—
55C5×#388—31no—
56#65278—31no—
57#65263—31no—
58#65247—31no—
59#65245—31no—
60#65235D311yescharacteristic, complemented
61#65233—31no—
62C22⋊C4×Dic5—31no—
63#65229—31no—
64C4×#683—31no—
65#64958—31no—
66#64955—31no—
67#64940—31no—
68#64935—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C2×#1220—41no—
74C2×#1220—41no—
75C2×#1220C2×C414yes—
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C4×D15—22no—
80C2×C4×D15—41no—
81C2×C4×D15—41no—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5—22no—
87C22×C3×Dic5—41no—
88C22×C3×Dic5—41no—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×#1204—41no—
94C2×#1204—41no—
95C2×#1204C2×C414yescomplemented
96C3×C5×C22⋊C4—41no—
97#6719—22no—
98#6714—41no—
99C5×#217—41no—
100C5×#217C2×C414yescomplemented
101C5×Dic3⋊C4—41no—
102C4×C5×Dic3—41no—
103C3×C22⋊Dic5C2×C414yescomplemented
104C3×#683—22no—
105C3×#683—41no—
106#6668—22no—
107#6667—22no—
108#6667—41no—
109#6667C2×C414yescomplemented
110#6667C2×C414yescomplemented
111Dic3×Dic5—41no—
112Dic3×Dic5—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×#885—51no—
116C3×#385—51no—
117#5213—51no—
118C4×#217—51no—
119#4990—51no—
120#4990—51no—
121Dic3×C4⋊C4—51no—
122#4973—51no—
123#4956—51no—
124#4951—51no—
125#4944D511yescharacteristic, complemented
126#4668—51no—
127#4666—51no—
128#4651—51no—
129#4646—51no—
130C22×C22⋊D5—31no—
131C23×Dic5C2×D311yescharacteristic
132C22×C4×D5—31no—
133C22×Dic10—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C22⋊C4—31no—
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4C2×D311yescharacteristic
138C2×C42×C5—31no—
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5C2×D311yescharacteristic
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#683—31no—
147C2×#683C2×D311yescharacteristic
148C2×#683C2×D311yescharacteristic
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153#4031—38no—
154C5×#95—31no—
155C5×#95—31no—
156#3963—31no—
157#3963—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#2337—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15C22×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—
188#1220—44no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C22×C412yes—
197C2×Dic15#4112yes—
198C4×D15—44no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
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×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
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—44no—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C22×C412yes—
223C2×C3×Dic5#4112yes—
224#1204—44no—
225C23×C3×C4—51no—
226C22×#67—51no—
227C22×C4×D3—51no—
228C22×Dic6—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C4⋊C4—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4C2×D511yescharacteristic
233C2×#217—51no—
234C2×#217C2×D511yescharacteristic
235C2×#217C2×D511yescharacteristic
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4—51no—
241C2×C4⋊Dic3—51no—
242C2×Dic3⋊C4C2×D511yescharacteristic
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3C2×D511yescharacteristic
248#885—58no—
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⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95C2×D511yescharacteristic
260C3⋊#95C2×D511yescharacteristic
261C24×C5C22×D311yescharacteristic
262C23×D5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5C22×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C2×C22⋊D5—34no—
270C2×C22⋊D5—121no—
271C2×C22⋊D5—121no—
272C22×Dic5—22no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5—41no—
277C22×Dic5—41no—
278C22×Dic5C22×D311yescharacteristic
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C22×Dic5C22×D311yescharacteristic
282C2×C4×D5—62no—
283C2×C4×D5—121no—
284C2×C4×D5—121no—
285C2×Dic10—34no—
286C2×Dic10—121no—
287C2×Dic10—121no—
288C5×C4⋊C4—121no—
289C5×C22⋊C4—34no—
290C5×C22⋊C4—41no—
291C5×C22⋊C4—121no—
292C42×C5—121no—
293C22⋊Dic5—62no—
294C22⋊Dic5C4×D314yescomplemented
295#685—34no—
296#685—34no—
297#685—62no—
298#685—121no—
299#685—121no—
300#683—22no—
301#683—41no—
302#683—62no—
303C4×Dic5—34no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C4×Dic5—121no—
307C2×#124—151no—
308#391—151no—
309#391—151no—
310#388—31no—
311#388—151no—
312#388—151no—
313#388—151no—
314#386—151no—
315#386—151no—
316#385—51no—
317#385—151no—
318#383—151no—
319C4×C4⋊C4—151no—
320C4×C22⋊C4—151no—
321C4×C22⋊C4—151no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5—41no—
329C22×C3×C5C23×C411yescharacteristic
330C22×C3×C5C2×#4111yescharacteristic
331C22×C3×C5C2×#4111yescharacteristic
332C22×C3×C5H(5,𝔽2)11yescharacteristic
333C22×C3×C5H(5,𝔽2)11yescharacteristic
334C22×C3×C5H(5,𝔽2)11yescharacteristic
335C22×C3×C52−1+411yescharacteristic
336C2×D15—22no—
337C2×D15—22no—
338C2×D15—22no—
339C2×D15—41no—
340C2×D15—41no—
341C2×D15—41no—
342C2×D15—41no—
343C3×C4×C5—41no—
344C3×C4×C5—41no—
345Dic15—22no—
346Dic15—22no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5—41no—
352C5×Dic3—22no—
353C5×Dic3—22no—
354C5×Dic3—41no—
355C5×Dic3—41no—
356C24×C3C22×D511yescharacteristic
357C23×D3—51no—
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—102no—
363C22×C3×C4—201no—
364C22×C3×C4—201no—
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C2×#67—54no—
368C2×#67—201no—
369C2×#67—201no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3C22×D511yescharacteristic
374C22×Dic3C22×D511yescharacteristic
375C22×Dic3C22×D511yescharacteristic
376C22×Dic3C22×D511yescharacteristic
377C2×C4×D3—102no—
378C2×C4×D3—201no—
379C2×C4×D3—201no—
380C2×Dic6—54no—
381C2×Dic6—201no—
382C2×Dic6—201no—
383C3×C4⋊C4—102no—
384C3×C4⋊C4—201no—
385C3×C22⋊C4—41no—
386C3×C22⋊C4—54no—
387#217—41no—
388#217—102no—
389#217C4×D514yescomplemented
390(C2×D3)⋊C4—54no—
391(C2×D3)⋊C4—54no—
392(C2×D3)⋊C4—102no—
393(C2×D3)⋊C4—201no—
394(C2×D3)⋊C4—201no—
395C4⋊Dic3—102no—
396Dic3⋊C4—41no—
397C4×Dic3—41no—
398C4×Dic3—54no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C4×Dic3—201no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5C2×C4×D312yes—
409C23×C5C23×D311yescharacteristic
410C22×D5—32no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—61no—
416C22×D5—61no—
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—32no—
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—
435C22⋊D5—124no—
436C2×Dic5—21no—
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—32no—
447C2×Dic5—44no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5C2×C4×D312yes—
456C2×Dic5C2×C4×D312yes—
457C2×Dic5#23712yes—
458C4×D5—124no—
459Dic10—124no—
460C22×Q8—151no—
461C22×D4—151no—
462C23×C4—51no—
463C23×C4—151no—
464#124—158no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—151no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4D3×D511yescharacteristic
479C2×C42—31no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
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—
494#95—151no—
495#95—151no—
496C2×C3×C5—42no—
497C2×C3×C5C4×#4111yescharacteristic
498C2×C3×C5#51811yescharacteristic
499C2×C3×C5#52011yescharacteristic
500C2×C3×C5#53811yescharacteristic
501C2×C3×C5#53811yescharacteristic
502C2×C3×C5#54211yescharacteristic
503C2×C3×C5#54211yescharacteristic
504D15—42no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3C2×C4×D512yes—
512C23×C3C23×D511yescharacteristic
513C22×D3—52no—
514C22×D3—101no—
515C22×D3—101no—
516C22×D3—101no—
517C22×D3—101no—
518C22×D3—101no—
519C22×D3—101no—
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—52no—
528C2×C3×C4—52no—
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×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—204no—
539#67—204no—
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—21no—
549C2×Dic3—21no—
550C2×Dic3—52no—
551C2×Dic3—52no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3C2×C4×D512yes—
560C2×Dic3C2×C4×D512yes—
561C4×D3—204no—
562Dic6—204no—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—22no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5C22×C4×D311yescharacteristic
571C22×C5C2×#23711yescharacteristic
572C22×C5#100411yescharacteristic
573C22×C5#100411yescharacteristic
574C22×C5#100711yescharacteristic
575C22×C5D3×#4111yescharacteristic
576C22×C5#100911yescharacteristic
577C2×D5—62no—
578C2×D5—62no—
579C2×D5—62no—
580C2×D5—121no—
581C2×D5—121no—
582C2×D5—121no—
583C2×D5—121no—
584C4×C5—41no—
585C4×C5—41no—
586C4×C5—62no—
587C4×C5—62no—
588C4×C5—121no—
589C4×C5—121no—
590Dic5—22no—
591Dic5—22no—
592Dic5—22no—
593Dic5—41no—
594Dic5—62no—
595Dic5—62no—
596Dic5—121no—
597C24—151no—
598C24C2×D3×D511yescharacteristic
599C2×Q8—154no—
600C2×Q8—601no—
601C2×Q8—601no—
602C2×D4—154no—
603C2×D4—601no—
604C2×D4—601no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—102no—
614C22×C4—151no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—201no—
618C22×C4—201no—
619C22×C4—302no—
620C22×C4—601no—
621C22×C4—601no—
622C22×C4C2×D3×D511yescharacteristic
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—102no—
625C4⋊C4—121no—
626C4⋊C4—201no—
627C4⋊C4—302no—
628C22⋊C4—34no—
629C22⋊C4—41no—
630C22⋊C4—54no—
631C22⋊C4—121no—
632C22⋊C4—154no—
633C22⋊C4—154no—
634C22⋊C4—302no—
635C22⋊C4—302no—
636C22⋊C4—601no—
637C22⋊C4—601no—
638C42—121no—
639C42—154no—
640C42—601no—
641C42—601no—
642C42—601no—
643C3×C5#233711yescharacteristic, complemented, Hall
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3C22×C4×D511yescharacteristic
652C22×C3#414411yescharacteristic
653C22×C3#414411yescharacteristic
654C22×C3D5×#4111yescharacteristic
655C22×C3D5×#4111yescharacteristic
656C22×C3#414911yescharacteristic
657C22×C3#415011yescharacteristic
658C2×D3—102no—
659C2×D3—102no—
660C2×D3—102no—
661C2×D3—201no—
662C2×D3—201no—
663C2×D3—201no—
664C2×D3—201no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—102no—
668C3×C4—102no—
669C3×C4—102no—
670C3×C4—201no—
671Dic3—22no—
672Dic3—22no—
673Dic3—41no—
674Dic3—41no—
675Dic3—102no—
676Dic3—102no—
677Dic3—201no—
678C2×C5—42no—
679C2×C5#550411yescharacteristic
680C2×C5C4×#23711yescharacteristic
681C2×C5#554511yescharacteristic
682C2×C5#559311yescharacteristic
683C2×C5#564011yescharacteristic
684C2×C5#564311yescharacteristic
685C2×C5#565711yescharacteristic
686D5—122no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—152no—
694C23—301no—
695C23—301no—
696C23—301no—
697C23—301no—
698C23—301no—
699C23—301no—
700C23C4×D3×D512yes—
701C23C22×D3×D511yescharacteristic
702Q8—604no—
703D4—604no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—52no—
713C2×C4—52no—
714C2×C4—52no—
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—61no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—204no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—604no—
745C2×C3—42no—
746C2×C3#6585611yescharacteristic
747C2×C3#6587911yescharacteristic
748C2×C3#6588011yescharacteristic
749C2×C3#6594711yescharacteristic
750C2×C3#6599111yescharacteristic
751C2×C3#6600311yescharacteristic
752C2×C3#6604411yescharacteristic
753D3—202no—
754C5#7439111yescharacteristic, complemented, Sylow
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—302no—
763C22—302no—
764C22—302no—
765C22—601no—
766C22—601no—
767C22—601no—
768C22—601no—
769C22#9200411yescharacteristic
770C22C2×C4×D3×D511yescharacteristic
771C22D5×#23711yescharacteristic
772C22#9202411yescharacteristic
773C22#9202611yescharacteristic
774C22#9202711yescharacteristic
775C22#9204911yescharacteristic
776C4—41no—
777C4—41no—
778C4—62no—
779C4—62no—
780C4—102no—
781C4—102no—
782C4—102no—
783C4—121no—
784C4—121no—
785C4—201no—
786C4—302no—
787C4—302no—
788C4—601no—
789C3#1060720211yescharacteristic, complemented, Sylow
790C2—42no—
791C2—602no—
792C2#1175279411yescharacteristic
793C2#1175281811yescharacteristic
794C2#1175295711yescharacteristic
795C2#1175320411yescharacteristic
796C2#1175429411yescharacteristic
797C2#1175484611yescharacteristic
798C2#1175490111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2337
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4944C2semidirect
4. C3×#65235C2semidirect
6. #11749485C2semidirect
7. Dic5×#217C2semidirect
8. #11748731C2semidirect
9. #11748728C2semidirect
10. #11748670C2semidirect
11. #11748666C2semidirect
12. #11748646C2semidirect
13. Dic3×#683C2semidirect
14. #11748631C2semidirect
15. #11748628C2semidirect
40. #91526C4semidirect
60. #65235D3semidirect
95. C2×#1204C2×C4semidirect
100. C5×#217C2×C4semidirect
103. C3×C22⋊Dic5C2×C4semidirect
109. #6667C2×C4semidirect
110. #6667C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
125. #4944D5semidirect
294. C22⋊Dic5C4×D3semidirect
389. #217C4×D5semidirect
643. C3×C5#2337semidirect
754. C5#74391semidirect
789. C3#10607202semidirect

Maximal subgroups

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

subgroupindex
C2×#915262
#117510572
C5×#49442
C3×#652352
#117494942
#117494852
Dic5×#2172
#117487312
#117487282
#117486702
#117486662
#117486462
Dic3×#6832
#117486312
#117486282
#106072023
#743915