Finite Group Databasebeta

← #14323004

Subgroups — #14323004

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91552C211yesmaximal, characteristic
2#11751314C211yesmaximal, characteristic
3C5×#5210C211yesmaximal, characteristic, complemented
4C2×C3×#3963C211yesmaximal, characteristic, complemented
5#11749509C211yesmaximal, characteristic, complemented
6#11749494C211yesmaximal, characteristic
7Dic5×#217C211yesmaximal, characteristic, complemented
8#11748889C211yesmaximal, characteristic, complemented
9#11748882C211yesmaximal, characteristic, complemented
10#11748669C211yesmaximal, characteristic, complemented
11#11748668C211yesmaximal, characteristic, complemented
12#11748662C211yesmaximal, characteristic, complemented
13#11748661C211yesmaximal, characteristic, complemented
14#11748652C211yesmaximal, characteristic, complemented
15#11748646C211yesmaximal, characteristic, complemented
16#10606114—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29#91552C418yescomplemented
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73367—51nomaximal, Hall
54C2×#4027—31no—
55C5×#385—31no—
56#65502—31no—
57C2×#3963D311yescharacteristic, complemented
58#65279—31no—
59#65276—31no—
60#65267—31no—
61#65266—31no—
62#65247—31no—
63#65239—31no—
64C22⋊C4×Dic5—31no—
65#64959—31no—
66#64953—31no—
67#64944—31no—
68#64940—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C22×C3×C4×C5—22no—
72C22×C3×C4×C5—41no—
73C22×C3×C4×C5—41no—
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C2×#1220—22no—
77C2×#1220—22no—
78C2×#1220C2×C414yes—
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
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×Dic5—41no—
90C22×C3×Dic5—41no—
91C22×C3×Dic5C2×C414yes—
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×#1200—41no—
97C2×#1200—41no—
98C2×#1200C2×C414yescomplemented
99#6719—22no—
100#6714—41no—
101#6714—41no—
102C5×#217—22no—
103C5×#217C2×C414yes—
104C5×Dic3⋊C4—41no—
105C5×Dic3⋊C4—41no—
106Dic3⋊Dic5—41no—
107Dic3⋊Dic5—41no—
108#6669C2×C414yescomplemented
109#6667—41no—
110#6667—41no—
111#6667C2×C414yescomplemented
112Dic3×Dic5—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×C4×#67—51no—
116C2×C3×#95—51no—
117#5213—51no—
118#5213—51no—
119#5210—51no—
120#5210D511yescharacteristic, complemented
121C4×#217—51no—
122#4669—51no—
123#4669—51no—
124#4667—51no—
125#4664—51no—
126#4652—51no—
127#4652—51no—
128#4651—51no—
129#4650—51no—
130C23×C4×C5C2×D311yescharacteristic
131C22×C22⋊D5—31no—
132C23×Dic5C2×D311yescharacteristic
133C23×Dic5C2×D311yescharacteristic
134C22×C4×D5—31no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4—31no—
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4—31no—
139C2×C22⋊Dic5—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×C4⋊Dic5—31no—
146C2×C4⋊Dic5—31no—
147C2×#683—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151#4027—38no—
152C5×#95—31no—
153C5×#95—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2318—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5C22×C412yes—
172C23×C3×C5#4112yes—
173C23×C3×C5#4112yes—
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—
188C2×C3×C4×C5—44no—
189#1220—28no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15C22×C412yes—
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—21no—
221C2×C3×Dic5—44no—
222C2×C3×Dic5—44no—
223C2×C3×Dic5C22×C412yes—
224C2×C3×Dic5C22×C412yes—
225#1200—44no—
226C23×C3×C4—51no—
227C23×C3×C4—51no—
228C23×C3×C4C2×D511yescharacteristic
229C22×#67—51no—
230C22×C4×D3—51no—
231C2×#217—51no—
232C2×#217C2×D511yescharacteristic
233C2×#217C2×D511yescharacteristic
234C4×#67—58no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×Dic3⋊C4—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4C2×D511yescharacteristic
244C2×Dic3⋊C4C2×D511yescharacteristic
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C3×#95—51no—
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⋊#95—51no—
260C3⋊#95C2×D511yescharacteristic
261C3⋊#95C2×D511yescharacteristic
262C24×C5C22×D311yescharacteristic
263C23×D5—31no—
264C22×C4×C5—22no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—41no—
270C22×C4×C5—41no—
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C2×C22⋊D5—34no—
274C2×C22⋊D5—62no—
275C2×C22⋊D5—62no—
276C22×Dic5—22no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—41no—
281C22×Dic5—41no—
282C22×Dic5—41no—
283C22×Dic5—41no—
284C22×Dic5C4×D314yes—
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C2×C4×D5—34no—
290C2×C4×D5—121no—
291C2×C4×D5—121no—
292C5×C4⋊C4—121no—
293C5×C4⋊C4—121no—
294C5×C22⋊C4—34no—
295C5×C22⋊C4—62no—
296C22⋊Dic5—62no—
297#685—34no—
298#685—121no—
299#685—121no—
300#685—121no—
301#685—121no—
302C4⋊Dic5—121no—
303C4⋊Dic5—121no—
304#683—34no—
305C4×Dic5—34no—
306C4×Dic5—121no—
307C4×Dic5—121no—
308C2×C4×D4—151no—
309#388—151no—
310#388—151no—
311#387—151no—
312#387—151no—
313#386—151no—
314#386—151no—
315#385—31no—
316#385—151no—
317#383—151no—
318#382—151no—
319#381—151no—
320#380—151no—
321C4×C22⋊C4—151no—
322C2×#95—51no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—22no—
329C22×C3×C5#11714yes—
330C22×C3×C5C23×C411yescharacteristic
331C22×C3×C5C2×#4111yescharacteristic
332C22×C3×C5C2×#4111yescharacteristic
333C22×C3×C5H(5,𝔽2)11yescharacteristic
334C22×C3×C5H(5,𝔽2)11yescharacteristic
335C22×C3×C5H(5,𝔽2)11yescharacteristic
336C22×C3×C52−1+411yescharacteristic
337C2×D15—22no—
338C2×D15—22no—
339C2×D15—22no—
340C2×D15—41no—
341C2×D15—41no—
342C2×D15—41no—
343C2×D15—41no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346Dic15—22no—
347Dic15—41no—
348Dic15—41no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C5×Dic3—22no—
354C5×Dic3—22no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C24×C3C22×D511yescharacteristic
358C23×D3—51no—
359C22×C3×C4—22no—
360C22×C3×C4—41no—
361C22×C3×C4—41no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—54no—
365C22×C3×C4—51no—
366C22×C3×C4—51no—
367C22×C3×C4—102no—
368C22×C3×C4—201no—
369C22×C3×C4—201no—
370C22×C3×C4—201no—
371C22×C3×C4—201no—
372C22×C3×C4C22×D511yescharacteristic
373C22×C3×C4C22×D511yescharacteristic
374C2×#67—54no—
375C2×#67—102no—
376C2×#67—102no—
377C22×Dic3—51no—
378C22×Dic3—51no—
379C22×Dic3—51no—
380C22×Dic3C22×D511yescharacteristic
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C2×C4×D3—54no—
385C2×C4×D3—201no—
386C2×C4×D3—201no—
387#217—22no—
388#217—102no—
389#217C4×D514yes—
390(C2×D3)⋊C4—54no—
391(C2×D3)⋊C4—201no—
392(C2×D3)⋊C4—201no—
393(C2×D3)⋊C4—201no—
394(C2×D3)⋊C4—201no—
395Dic3⋊C4—41no—
396Dic3⋊C4—41no—
397Dic3⋊C4—54no—
398Dic3⋊C4—201no—
399Dic3⋊C4—201no—
400C4×Dic3—54no—
401C4×Dic3—201no—
402C4×Dic3—201no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C2×C4×D312yes—
408C23×C5#23512yes—
409C23×C5#23512yes—
410C23×C5C23×D311yescharacteristic
411C22×D5—32no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—61no—
416C22×D5—61no—
417C22×D5—61no—
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—44no—
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×C5—61no—
437C22⋊D5—68no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—32no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—61no—
459C2×Dic5C2×C4×D312yes—
460C2×Dic5C2×C4×D312yes—
461C4×D5—124no—
462C22×D4—151no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—151no—
466C23×C4D3×D511yescharacteristic
467C4×D4—158no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
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—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—51no—
487#95—51no—
488#95—51no—
489#95—51no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498C2×C3×C5—24no—
499C2×C3×C5C2×#11711yescharacteristic
500C2×C3×C5#51811yescharacteristic
501C2×C3×C5#52011yescharacteristic
502C2×C3×C5#53811yescharacteristic
503C2×C3×C5#53811yescharacteristic
504C2×C3×C5#53911yescharacteristic
505C2×C3×C5#53911yescharacteristic
506D15—42no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3C2×C4×D512yes—
512C23×C3#71112yes—
513C23×C3#71312yes—
514C23×C3C23×D511yescharacteristic
515C22×D3—52no—
516C22×D3—101no—
517C22×D3—101no—
518C22×D3—101no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—101no—
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—44no—
529C2×C3×C4—52no—
530C2×C3×C4—52no—
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—101no—
539C2×C3×C4—101no—
540C2×C3×C4—101no—
541C2×C3×C4—204no—
542C2×C3×C4—204no—
543#67—108no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—52no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3—101no—
562C2×Dic3—101no—
563C2×Dic3C2×C4×D512yes—
564C2×Dic3C2×C4×D512yes—
565C4×D3—204no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5#87214yes—
573C22×C5C22×C4×D311yescharacteristic
574C22×C5C2×#23511yescharacteristic
575C22×C5C2×#23511yescharacteristic
576C22×C5#100411yescharacteristic
577C22×C5#100411yescharacteristic
578C22×C5#100411yescharacteristic
579C22×C5#100711yescharacteristic
580C2×D5—62no—
581C2×D5—62no—
582C2×D5—62no—
583C2×D5—121no—
584C2×D5—121no—
585C2×D5—121no—
586C2×D5—121no—
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—62no—
590C4×C5—62no—
591C4×C5—121no—
592C4×C5—121no—
593Dic5—22no—
594Dic5—22no—
595Dic5—41no—
596Dic5—41no—
597Dic5—62no—
598Dic5—121no—
599Dic5—121no—
600C24—151no—
601C24C2×D3×D511yescharacteristic
602C2×D4—154no—
603C2×D4—302no—
604C2×D4—302no—
605C22×C4—22no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—51no—
613C22×C4—51no—
614C22×C4—54no—
615C22×C4—51no—
616C22×C4—51no—
617C22×C4—102no—
618C22×C4—154no—
619C22×C4—151no—
620C22×C4—151no—
621C22×C4—151no—
622C22×C4—201no—
623C22×C4—201no—
624C22×C4—201no—
625C22×C4—201no—
626C22×C4—601no—
627C22×C4—601no—
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—121no—
631C4⋊C4—121no—
632C4⋊C4—154no—
633C4⋊C4—601no—
634C4⋊C4—601no—
635C22⋊C4—34no—
636C22⋊C4—62no—
637C22⋊C4—154no—
638C22⋊C4—302no—
639C22⋊C4—601no—
640C22⋊C4—601no—
641C22⋊C4—601no—
642C22⋊C4—601no—
643C42—154no—
644C42—601no—
645C42—601no—
646C3×C5#231811yescharacteristic, complemented, Hall
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3#403814yes—
654C22×C3C22×C4×D511yescharacteristic
655C22×C3C2×#71111yescharacteristic
656C22×C3#414411yescharacteristic
657C22×C3#414411yescharacteristic
658C22×C3C2×#71311yescharacteristic
659C22×C3#414911yescharacteristic
660C22×C3#415011yescharacteristic
661C2×D3—102no—
662C2×D3—102no—
663C2×D3—102no—
664C2×D3—201no—
665C2×D3—201no—
666C2×D3—201no—
667C2×D3—201no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—102no—
671C3×C4—102no—
672C3×C4—201no—
673C3×C4—201no—
674Dic3—22no—
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3—102no—
679Dic3—201no—
680Dic3—201no—
681C2×C5—24no—
682C2×C5C2×#87211yescharacteristic
683C2×C5#548611yescharacteristic
684C2×C5#549411yescharacteristic
685C2×C5#549411yescharacteristic
686C2×C5#550411yescharacteristic
687C2×C5#551511yescharacteristic
688C2×C5#551511yescharacteristic
689D5—122no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—152no—
695C23—301no—
696C23—301no—
697C23—301no—
698C23—301no—
699C23—301no—
700C23—301no—
701C23#677312yes—
702C23C4×D3×D512yes—
703C23#678212yes—
704C23C22×D3×D511yescharacteristic
705D4—308no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—44no—
715C2×C4—52no—
716C2×C4—52no—
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—61no—
726C2×C4—61no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—152no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—301no—
746C2×C4—301no—
747C2×C4—301no—
748C2×C4—604no—
749C2×C3—24no—
750C2×C3C2×#403811yescharacteristic
751C2×C3#6587911yescharacteristic
752C2×C3#6588011yescharacteristic
753C2×C3#6592711yescharacteristic
754C2×C3#6597811yescharacteristic
755C2×C3#6597911yescharacteristic
756C2×C3#6599911yescharacteristic
757D3—202no—
758C5#7336711yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—302no—
766C22—302no—
767C22—302no—
768C22—601no—
769C22—601no—
770C22—601no—
771C22—601no—
772C22#9140214yes—
773C22#9200411yescharacteristic
774C22C2×#677311yescharacteristic
775C22C2×C4×D3×D511yescharacteristic
776C22#9201711yescharacteristic
777C22C2×#678211yescharacteristic
778C22#9204911yescharacteristic
779C22#9204911yescharacteristic
780C4—41no—
781C4—41no—
782C4—62no—
783C4—62no—
784C4—102no—
785C4—102no—
786C4—121no—
787C4—121no—
788C4—201no—
789C4—201no—
790C4—302no—
791C4—601no—
792C4—601no—
793C3#1060611411yescharacteristic, complemented, Sylow
794C2—24no—
795C2—602no—
796C2#1175429411yescharacteristic
797C2C2×#9140211yescharacteristic
798C2#1175448211yescharacteristic
799C2#1175449311yescharacteristic
800C2#1175459811yescharacteristic
801C2#1175462511yescharacteristic
802C2#1175541111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2318
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C5×#5210C2semidirect
4. C2×C3×#3963C2semidirect
5. #11749509C2semidirect
7. Dic5×#217C2semidirect
8. #11748889C2semidirect
9. #11748882C2semidirect
10. #11748669C2semidirect
11. #11748668C2semidirect
12. #11748662C2semidirect
13. #11748661C2semidirect
14. #11748652C2semidirect
15. #11748646C2semidirect
29. #91552C4semidirect
57. C2×#3963D3semidirect
98. C2×#1200C2×C4semidirect
108. #6669C2×C4semidirect
111. #6667C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
120. #5210D5semidirect
646. C3×C5#2318semidirect
758. C5#73367semidirect
793. C3#10606114semidirect

Maximal subgroups

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

subgroupindex
C2×#915522
#117513142
C5×#52102
C2×C3×#39632
#117495092
#117494942
Dic5×#2172
#117488892
#117488822
#117486692
#117486682
#117486622
#117486612
#117486522
#117486462
#106061143
#733675