Finite Group Databasebeta

← #14328014

Subgroups — #14328014

Order 1920.

1120 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×#91440C211yesmaximal, characteristic
2#11750750C211yesmaximal, characteristic, complemented
3C5×#4669C211yesmaximal, characteristic, complemented
4C3×#64953C211yesmaximal, characteristic, complemented
5#11748916C211yesmaximal, characteristic
6#11748915C211yesmaximal, characteristic
7#11748886C211yesmaximal, characteristic, complemented
8#11748880C211yesmaximal, characteristic, complemented
9#11748794C211yesmaximal, characteristic, complemented
10#11748711C211yesmaximal, characteristic, complemented
11#11748710C211yesmaximal, characteristic, complemented
12C4×#6665C211yesmaximal, characteristic, complemented
13#11748651C211yesmaximal, characteristic, complemented
14#11748645C211yesmaximal, characteristic, complemented
15#11748644C211yesmaximal, characteristic, complemented
16#10607207—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×#1201C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91440C418yescomplemented
43C3×C5×#95C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74061—51nomaximal, Hall
54C2×#4027—31no—
55C5×#388—31no—
56#65279—31no—
57C4⋊C4×Dic5—31no—
58#65246—31no—
59#65246—31no—
60#65240—31no—
61#65232—31no—
62C22⋊C4×Dic5—31no—
63C4×#685—31no—
64C4×#683—31no—
65#64959—31no—
66#64953D311yescharacteristic, complemented
67#64939—31no—
68#64938—31no—
69C23×C5×D3C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—41no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5C2×C414yes—
87C2×#1201—22no—
88C2×#1201—22no—
89C2×#1201C2×C414yes—
90C2×D3×Dic5—41no—
91C2×D3×Dic5—41no—
92C2×D3×Dic5C2×C414yes—
93#6712—22no—
94#6712C2×C414yes—
95C4×Dic15—22no—
96C4×Dic15—41no—
97C4×Dic15—41no—
98C5×(C2×D3)⋊C4—22no—
99C5×(C2×D3)⋊C4—41no—
100C5×(C2×D3)⋊C4C2×C414yes—
101C5×Dic3⋊C4—22no—
102C4×C5×Dic3—41no—
103C3×#685—41no—
104C3×#685—41no—
105Dic3⋊Dic5—22no—
106#6669—22no—
107(C2×D3)⋊Dic5—22no—
108(C2×D3)⋊Dic5—41no—
109#6665—22no—
110#6665—22no—
111#6665C2×C414yes—
112Dic3×Dic5—22no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yes—
115C2×C4×#67—51no—
116C3×#381—51no—
117C4×#217—51no—
118#4957—51no—
119#4957—51no—
120#4944—51no—
121#4944—51no—
122#4669—51no—
123#4669D511yescharacteristic, complemented
124#4666—51no—
125#4664—51no—
126#4650—51no—
127#4649—51no—
128#4649—51no—
129#4649—51no—
130C22×C22⋊D5—31no—
131C23×Dic5—31no—
132C22×C4×D5C2×D311yescharacteristic
133C2×C5×C4⋊C4—31no—
134C2×C5×C22⋊C4—31no—
135C2×C5×C22⋊C4—31no—
136C2×C5×C22⋊C4—31no—
137C2×C42×C5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685C2×D311yescharacteristic
144C2×#685C2×D311yescharacteristic
145C2×C4⋊Dic5—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155#4027—38no—
156C5×#95—31no—
157C5×#95C2×D311yescharacteristic
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963C2×D311yescharacteristic
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2357—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×C5×D3—21no—
169C22×C5×D3—21no—
170C22×C5×D3—21no—
171C22×C5×D3—21no—
172C22×C5×D3—21no—
173C22×C5×D3—21no—
174C22×C5×D3C22×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×Dic15C22×C412yes—
199C2×Dic15C22×C412yes—
200C2×Dic15#4112yes—
201C2×Dic15#4112yes—
202C2×Dic15#4112yes—
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×Dic3C22×C412yes—
211C2×C5×Dic3#4112yes—
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×Dic5C22×C412yes—
221C3×C4×D5—44no—
222#1201—28no—
223D3×Dic5—44no—
224C23×C3×C4—51no—
225C22×#67—51no—
226C22×C4×D3—51no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4—51no—
229C2×#217—51no—
230C2×#217—51no—
231C2×#217—51no—
232C4×#67—58no—
233C2×(C2×D3)⋊C4—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4C2×D511yescharacteristic
236C2×(C2×D3)⋊C4C2×D511yescharacteristic
237C2×(C2×D3)⋊C4C2×D511yescharacteristic
238C2×Dic3⋊C4—51no—
239C2×Dic3⋊C4—51no—
240C2×Dic3⋊C4—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4C2×D511yescharacteristic
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249C2×C4×Dic3C2×D511yescharacteristic
250C3×#95—51no—
251C3×#95—51no—
252C3×#95—51no—
253C3×#95C2×D511yescharacteristic
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95C2×D511yescharacteristic
260C24×C5—31no—
261C23×D5C22×D311yescharacteristic
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5C22×D311yescharacteristic
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C2×C22⋊D5—34no—
269C2×C22⋊D5—62no—
270C2×C22⋊D5—62no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—34no—
275C22×Dic5—31no—
276C22×Dic5—121no—
277C22×Dic5—121no—
278C22×Dic5C22×D311yescharacteristic
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C2×C4×D5—41no—
282C2×C4×D5—41no—
283C2×C4×D5C4×D314yes—
284C5×C4⋊C4—62no—
285C5×C22⋊C4—34no—
286C5×C22⋊C4—62no—
287C5×C22⋊C4—121no—
288C42×C5—121no—
289C22⋊Dic5—62no—
290C22⋊Dic5—121no—
291#685—34no—
292#685—41no—
293#685—41no—
294#685—62no—
295#685—62no—
296C4⋊Dic5—62no—
297#683—34no—
298#683—62no—
299#683—62no—
300C4×Dic5—34no—
301C4×Dic5—62no—
302C4×Dic5—62no—
303C4×Dic5—121no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C2×C4×D4—151no—
307#390—151no—
308#390—151no—
309#388—31no—
310#388—151no—
311#388—151no—
312#388—151no—
313#382—151no—
314#381—51no—
315#381—151no—
316C4×C4⋊C4—151no—
317C4×C4⋊C4—151no—
318C4×C4⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5C2×#4111yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C2×C5×D3—22no—
329C2×C5×D3—22no—
330C2×C5×D3—22no—
331C2×C5×D3—41no—
332C2×C5×D3—41no—
333C2×C5×D3—41no—
334C2×C5×D3—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—22no—
347Dic15—41no—
348Dic15#11714yes—
349C3×Dic5—22no—
350C3×Dic5—41no—
351C3×Dic5—41no—
352C5×Dic3—22no—
353C5×Dic3—22no—
354C5×Dic3—41no—
355C24×C3—51no—
356C23×D3C22×D511yescharacteristic
357C22×C3×C4—51no—
358C22×C3×C4—54no—
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—201no—
362C22×C3×C4—201no—
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C2×#67—54no—
367C2×#67—102no—
368C2×#67—102no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3C22×D511yescharacteristic
374C22×Dic3C22×D511yescharacteristic
375C22×Dic3C22×D511yescharacteristic
376C2×C4×D3—54no—
377C2×C4×D3—201no—
378C2×C4×D3—201no—
379C3×C22⋊C4—201no—
380C3×C22⋊C4—201no—
381#217—54no—
382#217—102no—
383#217—102no—
384(C2×D3)⋊C4—22no—
385(C2×D3)⋊C4—41no—
386(C2×D3)⋊C4—102no—
387(C2×D3)⋊C4—201no—
388(C2×D3)⋊C4C4×D514yes—
389Dic3⋊C4—22no—
390Dic3⋊C4—54no—
391Dic3⋊C4—102no—
392Dic3⋊C4—102no—
393Dic3⋊C4—102no—
394C4×Dic3—41no—
395C4×Dic3—54no—
396C4×Dic3—102no—
397C4×Dic3—102no—
398C4×Dic3—201no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C23×C5—32no—
402C23×C5—61no—
403C23×C5—61no—
404C23×C5—61no—
405C23×C5—61no—
406C23×C5—61no—
407C23×C5—61no—
408C23×C5C23×D311yescharacteristic
409C22×D5—21no—
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
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×C5C2×C4×D312yes—
434C22⋊D5—68no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—32no—
444C2×Dic5—32no—
445C2×Dic5—32no—
446C2×Dic5—32no—
447C2×Dic5—32no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—124no—
456C2×Dic5C2×C4×D312yes—
457C4×D5—44no—
458C22×D4—151no—
459C23×C4—51no—
460C23×C4—151no—
461C4×D4—158no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—151no—
464C2×C4⋊C4—151no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—51no—
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×C42—31no—
478C2×C42—151no—
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—51no—
486#95—51no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95D3×D511yescharacteristic
494C2×C3×C5C2×#11711yescharacteristic
495C2×C3×C5C4×#4111yescharacteristic
496C2×C3×C5#51811yescharacteristic
497C2×C3×C5#55311yescharacteristic
498C2×C3×C5#55311yescharacteristic
499C2×C3×C5#55911yescharacteristic
500C2×C3×C5#55911yescharacteristic
501C3×D5—42no—
502C5×D3—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—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3C2×C4×D512yes—
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×C4—204no—
536C2×C3×C4C2×C4×D512yes—
537#67—108no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—52no—
546C2×Dic3—52no—
547C2×Dic3—52no—
548C2×Dic3—52no—
549C2×Dic3—52no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3C2×C4×D512yes—
558C2×Dic3#71112yes—
559C4×D3—204no—
560C22×C5—62no—
561C22×C5—62no—
562C22×C5—62no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5C22×C4×D311yescharacteristic
568C22×C5#100411yescharacteristic
569C22×C5#100411yescharacteristic
570C22×C5D3×#4111yescharacteristic
571C22×C5D3×#4111yescharacteristic
572C22×C5D3×#4111yescharacteristic
573C22×C5D3×#4111yescharacteristic
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5—41no—
581C4×C5—22no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5—62no—
585C4×C5—62no—
586C4×C5—121no—
587Dic5—22no—
588Dic5—34no—
589Dic5—41no—
590Dic5—41no—
591Dic5—62no—
592Dic5—62no—
593Dic5—121no—
594C24—31no—
595C24—51no—
596C2×D4—154no—
597C2×D4—302no—
598C2×D4—302no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—51no—
603C22×C4—54no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—154no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—151no—
611C22×C4—201no—
612C22×C4—201no—
613C22×C4—601no—
614C22×C4—601no—
615C22×C4C2×D3×D511yescharacteristic
616C22×C4C2×D3×D511yescharacteristic
617C22×C4C2×D3×D511yescharacteristic
618C4⋊C4—62no—
619C4⋊C4—154no—
620C4⋊C4—302no—
621C4⋊C4—302no—
622C4⋊C4—302no—
623C22⋊C4—34no—
624C22⋊C4—62no—
625C22⋊C4—121no—
626C22⋊C4—154no—
627C22⋊C4—201no—
628C22⋊C4—201no—
629C22⋊C4—302no—
630C22⋊C4—302no—
631C22⋊C4—302no—
632C22⋊C4—601no—
633C42—121no—
634C42—154no—
635C42—302no—
636C42—302no—
637C42—601no—
638C42—601no—
639C42—601no—
640C3×C5#235711yescharacteristic, 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×C3C2×#71111yescharacteristic
650C22×C3#414411yescharacteristic
651C22×C3D5×#4111yescharacteristic
652C22×C3D5×#4111yescharacteristic
653C22×C3D5×#4111yescharacteristic
654C22×C3#414911yescharacteristic
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
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—54no—
672Dic3—102no—
673Dic3—102no—
674Dic3—201no—
675C2×C5—122no—
676C2×C5#548611yescharacteristic
677C2×C5D3×#11711yescharacteristic
678C2×C5#552211yescharacteristic
679C2×C5#566111yescharacteristic
680C2×C5#566111yescharacteristic
681C2×C5#566411yescharacteristic
682C2×C5#566411yescharacteristic
683D5—42no—
684C23—32no—
685C23—52no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—101no—
693C23—101no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23—101no—
698C23C22×D3×D511yescharacteristic
699D4—308no—
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—101no—
719C2×C4—101no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—152no—
727C2×C4—152no—
728C2×C4—152no—
729C2×C4—152no—
730C2×C4—152no—
731C2×C4—204no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—604no—
740C2×C4C4×D3×D512yes—
741C2×C3—202no—
742C2×C3D5×#11711yescharacteristic
743C2×C3C4×#71111yescharacteristic
744C2×C3#6587911yescharacteristic
745C2×C3#6593511yescharacteristic
746C2×C3#6599811yescharacteristic
747C2×C3#6601511yescharacteristic
748C2×C3#6604311yescharacteristic
749D3—42no—
750C5#7406111yescharacteristic, complemented, Sylow
751C22—62no—
752C22—62no—
753C22—62no—
754C22—102no—
755C22—102no—
756C22—102no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22C2×C4×D3×D511yescharacteristic
766C22#9201611yescharacteristic
767C22#9201611yescharacteristic
768C22D3×#71111yescharacteristic
769C22#9202511yescharacteristic
770C22#9202611yescharacteristic
771C22#9203411yescharacteristic
772C4—22no—
773C4—41no—
774C4—41no—
775C4—62no—
776C4—62no—
777C4—102no—
778C4—121no—
779C4—154no—
780C4—201no—
781C4—201no—
782C4—302no—
783C4—302no—
784C4—601no—
785C3#1060720711yescharacteristic, complemented, Sylow
786C2—122no—
787C2—202no—
788C2#1175272311yescharacteristic
789C2#1175313311yescharacteristic
790C2#1175313911yescharacteristic
791C2#1175320011yescharacteristic
792C2#1175340211yescharacteristic
793C2#1175360411yescharacteristic
794C2#1175378811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenter#95D3×D5
hypocenterC3×C5#2357
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750750C2semidirect
3. C5×#4669C2semidirect
4. C3×#64953C2semidirect
7. #11748886C2semidirect
8. #11748880C2semidirect
9. #11748794C2semidirect
10. #11748711C2semidirect
11. #11748710C2semidirect
12. C4×#6665C2semidirect
13. #11748651C2semidirect
14. #11748645C2semidirect
15. #11748644C2semidirect
42. #91440C4semidirect
66. #64953D3semidirect
123. #4669D5semidirect
640. C3×C5#2357semidirect
750. C5#74061semidirect
785. C3#10607207semidirect

Maximal subgroups

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

subgroupindex
C2×#914402
#117507502
C5×#46692
C3×#649532
#117489162
#117489152
#117488862
#117488802
#117487942
#117487112
#117487102
C4×#66652
#117486512
#117486452
#117486442
#106072073
#740615