Finite Group Databasebeta

← #14322909

Subgroups — #14322909

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91404C211yesmaximal, characteristic
2C2×#91403C211yesmaximal, characteristic
3C2×#91402C211yesmaximal, characteristic
4#11751090C211yesmaximal, characteristic
5C5×#4976C211yesmaximal, characteristic, complemented
6C3×#65265C211yesmaximal, characteristic, complemented
7#11748898C211yesmaximal, characteristic
8#11748894C211yesmaximal, characteristic
9#11748820C211yesmaximal, characteristic, complemented
10#11748729C211yesmaximal, characteristic
11#11748677C211yesmaximal, characteristic, complemented
12#11748664C211yesmaximal, characteristic, complemented
13#11748642C211yesmaximal, characteristic, complemented
14#11748641C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10607699—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91404—24no—
45#91403—24no—
46#91402C418yescomplemented
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74359—51nomaximal, Hall
56C2×#4038—31no—
57C2×D5×C4⋊C4—31no—
58C2×#4018—31no—
59C5×#389—31no—
60#65278—31no—
61#65278—31no—
62#65274—31no—
63#65265—31no—
64#65265D311yescharacteristic, complemented
65#65262—31no—
66#65217—31no—
67#64957—31no—
68#64957—31no—
69#64939—31no—
70#64939—31no—
71C23×D15C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C2×C4×D15—22no—
79C2×C4×D15—41no—
80C2×C4×D15—41no—
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×#1200—22no—
90C2×#1200—41no—
91C2×#1200—41no—
92C2×#1200C2×C414yes—
93C2×#1200D414yes—
94C2×#1200Q814yes—
95C3×C5×C4⋊C4—41no—
96#6714—22no—
97#6714C2×C414yes—
98#6712—41no—
99C5×Dic3⋊C4—22no—
100C5×Dic3⋊C4—41no—
101C5×Dic3⋊C4C2×C414yescomplemented
102C4×C5×Dic3—22no—
103C3×C4⋊Dic5—41no—
104C3×#683—22no—
105C3×#683—22no—
106C3×#683—41no—
107C3×#683—41no—
108C3×C4×Dic5C2×C414yescomplemented
109Dic3⋊Dic5—22no—
110Dic3⋊Dic5—41no—
111Dic3⋊Dic5C2×C414yescomplemented
112#6669—41no—
113#6668—22no—
114#6668—22no—
115#6667—22no—
116#6667C2×C414yes—
117Dic3×Dic5—22no—
118Dic3×Dic5C2×C414yescomplemented
119C2×#892—51no—
120C2×D3×C4⋊C4—51no—
121C2×#872—51no—
122C3×#384—51no—
123#4989—51no—
124#4989—51no—
125#4989—51no—
126#4989—51no—
127#4977—51no—
128#4976—51no—
129#4976—51no—
130#4976—51no—
131#4976D511yescharacteristic, complemented
132#4975—51no—
133#4936—51no—
134C22×C4×D5—31no—
135C22×C4×D5—31no—
136C22×C4×D5—31no—
137C2×C5×C4⋊C4—31no—
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C4⋊C4C2×D311yescharacteristic
141C2×C42×C5—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—31no—
149C2×C4⋊Dic5C2×D311yescharacteristic
150C2×#683—31no—
151C2×#683—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683C2×D311yescharacteristic
155C2×#683C2×D311yescharacteristic
156C2×#683C2×D311yescharacteristic
157C2×#683C2×D311yescharacteristic
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5C2×D311yescharacteristic
161#4038—38no—
162D5×C4⋊C4—64no—
163#4018—64no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#2317—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×D15—21no—
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15C22×C412yes—
179C22×D15C2×D412yes—
180C22×D15C2×Q812yes—
181C2×C3×C4×C5—21no—
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×C5C22×C412yes—
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—
199C4×D15—44no—
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×Dic3C22×C412yes—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C2×D412yes—
211C2×C5×Dic3C2×Q812yes—
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—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C2×D412yes—
223C2×C3×Dic5C2×Q812yes—
224#1200—44no—
225#1200C4⋊C4116yescomplemented
226C22×C4×D3—51no—
227C22×C4×D3—51no—
228C22×C4×D3—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C4⋊C4—51no—
231C2×C3×C4⋊C4—51no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C4⋊C4—51no—
234C2×C3×C4⋊C4C2×D511yescharacteristic
235C2×C3×C42—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—51no—
247C2×Dic3⋊C4C2×D511yescharacteristic
248C2×Dic3⋊C4C2×D511yescharacteristic
249C2×Dic3⋊C4C2×D511yescharacteristic
250C2×C4×Dic3—51no—
251C2×C4×Dic3—51no—
252C2×C4×Dic3C2×D511yescharacteristic
253#892—104no—
254D3×C4⋊C4—104no—
255#872—58no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95C2×D511yescharacteristic
263C3⋊#95C2×D511yescharacteristic
264C23×D5—31no—
265C22×C4×C5—31no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5C22×D311yescharacteristic
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C2×C4×D5—34no—
280C2×C4×D5—34no—
281C2×C4×D5—34no—
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—34no—
289C5×C4⋊C4—41no—
290C5×C4⋊C4—62no—
291C5×C4⋊C4—121no—
292C42×C5—62no—
293#685—34no—
294#685—34no—
295#685—62no—
296#685—62no—
297C4⋊Dic5—34no—
298C4⋊Dic5—41no—
299C4⋊Dic5—62no—
300C4⋊Dic5—121no—
301#683—22no—
302#683—22no—
303#683—41no—
304#683—41no—
305#683—62no—
306#683—62no—
307#683—121no—
308#683—121no—
309C4×Dic5—34no—
310C4×Dic5—62no—
311C4×Dic5C4×D314yescomplemented
312C2×#117—151no—
313C2×#117—151no—
314C22×C4⋊C4—151no—
315#389—31no—
316#389—151no—
317#389—151no—
318#389—151no—
319#385—151no—
320#385—151no—
321#385—151no—
322#385—151no—
323#384—51no—
324#384—151no—
325#382—151no—
326#382—151no—
327C22×C3×C5C23×C411yescharacteristic
328C22×C3×C5C22×D411yescharacteristic
329C22×C3×C5C22×Q811yescharacteristic
330C22×C3×C5H(5,𝔽2)11yescharacteristic
331C22×C3×C5H(5,𝔽2)11yescharacteristic
332C22×C3×C52−1+411yescharacteristic
333C22×C3×C52−1+411yescharacteristic
334C2×D15—22no—
335C2×D15—22no—
336C2×D15—22no—
337C2×D15—22no—
338C2×D15—22no—
339C2×D15—22no—
340C2×D15C2×C4⋊C414yes—
341C3×C4×C5—22no—
342C3×C4×C5—41no—
343C3×C4×C5—41no—
344Dic15—22no—
345Dic15—41no—
346Dic15—41no—
347C3×Dic5—22no—
348C3×Dic5—41no—
349C3×Dic5—41no—
350C3×Dic5C2×C4⋊C414yes—
351C5×Dic3—22no—
352C5×Dic3—41no—
353C5×Dic3—41no—
354C5×Dic3C2×C4⋊C414yes—
355C23×D3—51no—
356C22×C3×C4—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
363C22×Dic3—51no—
364C22×Dic3—51no—
365C22×Dic3—51no—
366C22×Dic3C22×D511yescharacteristic
367C22×Dic3C22×D511yescharacteristic
368C22×Dic3C22×D511yescharacteristic
369C22×Dic3C22×D511yescharacteristic
370C2×C4×D3—54no—
371C2×C4×D3—54no—
372C2×C4×D3—54no—
373C2×C4×D3—102no—
374C2×C4×D3—102no—
375C2×C4×D3—201no—
376C2×C4×D3—201no—
377C2×C4×D3—201no—
378C2×C4×D3—201no—
379C3×C4⋊C4—41no—
380C3×C4⋊C4—102no—
381C3×C4⋊C4—102no—
382C3×C4⋊C4—201no—
383C3×C4⋊C4—201no—
384C3×C4⋊C4—201no—
385C3×C42—54no—
386(C2×D3)⋊C4—54no—
387(C2×D3)⋊C4—54no—
388(C2×D3)⋊C4—102no—
389(C2×D3)⋊C4—102no—
390C4⋊Dic3—102no—
391C4⋊Dic3—102no—
392Dic3⋊C4—22no—
393Dic3⋊C4—41no—
394Dic3⋊C4—54no—
395Dic3⋊C4—102no—
396Dic3⋊C4—201no—
397Dic3⋊C4—201no—
398Dic3⋊C4—201no—
399Dic3⋊C4C4×D514yescomplemented
400C4×Dic3—22no—
401C4×Dic3—54no—
402C4×Dic3—102no—
403C23×C5C23×D311yescharacteristic
404C22×D5—32no—
405C22×D5—32no—
406C22×D5—32no—
407C22×D5—61no—
408C22×D5—61no—
409C22×D5—61no—
410C22×D5—61no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—32no—
420C2×C4×C5—32no—
421C2×C4×C5—32no—
422C2×C4×C5—32no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
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×C5C2×C4×D312yes—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—32no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5C2×C4×D312yes—
450C2×Dic5C2×C4×D312yes—
451C2×Dic5D3×D412yes—
452C2×Dic5D3×Q812yes—
453C4×D5—316no—
454C4×D5—124no—
455C4×D5—124no—
456C23×C4—151no—
457C23×C4—151no—
458C23×C4—151no—
459#117—158no—
460#117—304no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C4⋊C4—151no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—151no—
476C2×C4⋊C4—304no—
477C2×C4⋊C4D3×D511yescharacteristic
478C2×C22⋊C4—151no—
479C2×C22⋊C4—151no—
480C2×C22⋊C4—151no—
481C2×C22⋊C4—151no—
482C2×C42—31no—
483C2×C42—51no—
484C2×C42—151no—
485C2×C42—151no—
486#95—31no—
487#95—31no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494C2×C3×C5C22×C4⋊C411yescharacteristic
495C2×C3×C5#52011yescharacteristic
496C2×C3×C5#52011yescharacteristic
497C2×C3×C5#53511yescharacteristic
498C2×C3×C5#53611yescharacteristic
499C2×C3×C5#54411yescharacteristic
500C2×C3×C5#54411yescharacteristic
501D15—24no—
502C23×C3C23×D511yescharacteristic
503C22×D3—52no—
504C22×D3—52no—
505C22×D3—52no—
506C22×D3—101no—
507C22×D3—101no—
508C22×D3—101no—
509C22×D3—101no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—52no—
521C2×C3×C4—52no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4C2×C4×D512yes—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—52no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3C2×C4×D512yes—
549C2×Dic3C2×C4×D512yes—
550C2×Dic3D4×D512yes—
551C2×Dic3Q8×D512yes—
552C4×D3—516no—
553C4×D3—204no—
554C4×D3—204no—
555C22×C5C22×C4×D311yescharacteristic
556C22×C5C2×D3×D411yescharacteristic
557C22×C5#100411yescharacteristic
558C22×C5#100411yescharacteristic
559C22×C5C2×D3×Q811yescharacteristic
560C22×C5#100711yescharacteristic
561C22×C5#100711yescharacteristic
562C2×D5—34no—
563C2×D5—62no—
564C2×D5—62no—
565C2×D5—62no—
566C2×D5—62no—
567C2×D5—62no—
568C2×D5—62no—
569C4×C5—22no—
570C4×C5—34no—
571C4×C5—41no—
572C4×C5—41no—
573C4×C5—62no—
574C4×C5—121no—
575C4×C5—121no—
576Dic5—22no—
577Dic5—41no—
578Dic5—41no—
579Dic5—62no—
580Dic5—121no—
581Dic5—121no—
582Dic5D3×C4⋊C414yes—
583C24—151no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—51no—
589C22×C4—51no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—154no—
593C22×C4—154no—
594C22×C4—154no—
595C22×C4—151no—
596C22×C4—151no—
597C22×C4—151no—
598C22×C4—302no—
599C22×C4—302no—
600C22×C4—601no—
601C22×C4—601no—
602C22×C4—601no—
603C22×C4—601no—
604C22×C4C2×D3×D511yescharacteristic
605C22×C4C2×D3×D511yescharacteristic
606C22×C4C2×D3×D511yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—41no—
609C4⋊C4—62no—
610C4⋊C4—102no—
611C4⋊C4—102no—
612C4⋊C4—121no—
613C4⋊C4—154no—
614C4⋊C4—201no—
615C4⋊C4—201no—
616C4⋊C4—201no—
617C4⋊C4—302no—
618C4⋊C4—302no—
619C4⋊C4—302no—
620C4⋊C4—601no—
621C4⋊C4—601no—
622C4⋊C4—601no—
623C22⋊C4—154no—
624C22⋊C4—154no—
625C22⋊C4—302no—
626C22⋊C4—302no—
627C42—54no—
628C42—62no—
629C42—154no—
630C42—302no—
631C3×C5#231711yescharacteristic, complemented, Hall
632C22×C3C22×C4×D511yescharacteristic
633C22×C3C2×D4×D511yescharacteristic
634C22×C3#414411yescharacteristic
635C22×C3C2×Q8×D511yescharacteristic
636C22×C3#414711yescharacteristic
637C22×C3#414911yescharacteristic
638C22×C3#415011yescharacteristic
639C2×D3—54no—
640C2×D3—102no—
641C2×D3—102no—
642C2×D3—102no—
643C2×D3—102no—
644C2×D3—102no—
645C2×D3—102no—
646C3×C4—22no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—54no—
650C3×C4—102no—
651C3×C4—201no—
652C3×C4—201no—
653Dic3—22no—
654Dic3—41no—
655Dic3—41no—
656Dic3—102no—
657Dic3—201no—
658Dic3—201no—
659Dic3D5×C4⋊C414yes—
660C2×C5C2×D3×C4⋊C411yescharacteristic
661C2×C5#550411yescharacteristic
662C2×C5#550411yescharacteristic
663C2×C5#571511yescharacteristic
664C2×C5#572411yescharacteristic
665C2×C5#572911yescharacteristic
666C2×C5#572911yescharacteristic
667D5—64no—
668C23—152no—
669C23—152no—
670C23—152no—
671C23—301no—
672C23—301no—
673C23—301no—
674C23—301no—
675C23C22×D3×D511yescharacteristic
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—52no—
689C2×C4—52no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—101no—
701C2×C4—101no—
702C2×C4—101no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—1516no—
709C2×C4—152no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—301no—
714C2×C4—301no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—301no—
718C2×C4—604no—
719C2×C4—604no—
720C2×C4C4×D3×D512yes—
721C2×C3C2×D5×C4⋊C411yescharacteristic
722C2×C3#6588011yescharacteristic
723C2×C3#6590811yescharacteristic
724C2×C3#6594111yescharacteristic
725C2×C3#6596211yescharacteristic
726C2×C3#6602311yescharacteristic
727C2×C3#6606311yescharacteristic
728D3—104no—
729C5#7435911yescharacteristic, complemented, Sylow
730C22—154no—
731C22—302no—
732C22—302no—
733C22—302no—
734C22—302no—
735C22—302no—
736C22—302no—
737C22#9200411yescharacteristic
738C22C2×C4×D3×D511yescharacteristic
739C22D3×D4×D511yescharacteristic
740C22#9202611yescharacteristic
741C22#9202911yescharacteristic
742C22D3×Q8×D511yescharacteristic
743C22#9204911yescharacteristic
744C4—22no—
745C4—34no—
746C4—41no—
747C4—41no—
748C4—54no—
749C4—62no—
750C4—102no—
751C4—121no—
752C4—121no—
753C4—201no—
754C4—201no—
755C4—302no—
756C4—601no—
757C4—601no—
758C3#1060769911yescharacteristic, complemented, Sylow
759C2—304no—
760C2#1175333611yescharacteristic
761C2#1175333911yescharacteristic
762C2#1175346911yescharacteristic
763C2D3×D5×C4⋊C411yescharacteristic
764C2#1175429411yescharacteristic
765C2#1175505111yescharacteristic
766C2#1175518611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2317
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
5. C5×#4976C2semidirect
6. C3×#65265C2semidirect
9. #11748820C2semidirect
11. #11748677C2semidirect
12. #11748664C2semidirect
13. #11748642C2semidirect
14. #11748641C2semidirect
15. #11748580C2semidirect
46. #91402C4semidirect
64. #65265D3semidirect
101. C5×Dic3⋊C4C2×C4semidirect
108. C3×C4×Dic5C2×C4semidirect
111. Dic3⋊Dic5C2×C4semidirect
118. Dic3×Dic5C2×C4semidirect
131. #4976D5semidirect
225. #1200C4⋊C4semidirect
311. C4×Dic5C4×D3semidirect
399. Dic3⋊C4C4×D5semidirect
631. C3×C5#2317semidirect
729. C5#74359semidirect
758. C3#10607699semidirect

Maximal subgroups

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

subgroupindex
C2×#914042
C2×#914032
C2×#914022
#117510902
C5×#49762
C3×#652652
#117488982
#117488942
#117488202
#117487292
#117486772
#117486642
#117486422
#117486412
#117485802
#106076993
#743595