Finite Group Databasebeta

← #14326522

Subgroups — #14326522

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91338C211yesmaximal, characteristic
2#11750755C211yesmaximal, characteristic, complemented
3C5×D3×#95C211yesmaximal, characteristic
4C3×#64942C211yesmaximal, characteristic, complemented
5#11748777C211yesmaximal, characteristic
6#11748722C211yesmaximal, characteristic
7#11748719C211yesmaximal, characteristic
8#11748716C211yesmaximal, characteristic
9C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
10#11748697C211yesmaximal, characteristic, complemented
11#11748689C211yesmaximal, characteristic, complemented
12#11748646C211yesmaximal, characteristic, complemented
13#11748644C211yesmaximal, characteristic, complemented
14#11748637C211yesmaximal, characteristic, complemented
15#11748635C211yesmaximal, characteristic, complemented
16#10605066—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6669C2211yescharacteristic
27C2×#6668C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2211yescharacteristic
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×(C2×D3)⋊Dic5C2211yescharacteristic
31C2×(C2×D3)⋊Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2211yescharacteristic
34C2×Dic3×Dic5C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36#91338C418yescomplemented
37C3×C5×#95C2211yescharacteristic
38#91115C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75303—51nomaximal, Hall
54C2×#4072—31no—
55C2×C5×#95—31no—
56#65500—31no—
57#65499—31no—
58#65499—31no—
59C4×C22⋊Dic5—31no—
60C4×C22⋊Dic5—31no—
61#64943—31no—
62#64943—31no—
63#64942—31no—
64#64942D311yescharacteristic, complemented
65#64940—31no—
66#64939—31no—
67#64938—31no—
68#64937—31no—
69C23×C5×D3C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C2×C4×C5×D3—22no—
81C2×C4×C5×D3—22no—
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3—41no—
87C2×C4×C5×D3—41no—
88C2×C4×C5×D3C2×C414yes—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C4⋊Dic15C2×C414yescomplemented
94#6712—41no—
95C4×Dic15—41no—
96C3×C4⋊Dic5C2×C414yescomplemented
97C3×#683—22no—
98C3×C4×Dic5—22no—
99#6669—41no—
100#6668—22no—
101(C2×D3)⋊Dic5—22no—
102(C2×D3)⋊Dic5—22no—
103(C2×D3)⋊Dic5C2×C414yes—
104(C2×D3)⋊Dic5C2×C414yes—
105Dic3×Dic5—22no—
106Dic3×Dic5—41no—
107Dic3×Dic5C2×C414yescomplemented
108Dic3×Dic5C2×C414yescomplemented
109C2×#892—51no—
110C3×#387—51no—
111#4989—51no—
112#4980—51no—
113Dic3×C4⋊C4—51no—
114C4×(C2×D3)⋊C4—51no—
115#4932—51no—
116#4668—51no—
117#4666—51no—
118#4664—51no—
119D3×#95D511yescharacteristic
120#4654—51no—
121#4653—51no—
122#4651—51no—
123#4650—51no—
124C23×C4×C5—31no—
125C23×C4×C5—31no—
126C23×C4×C5—31no—
127C2×C22⋊Dic5—31no—
128C2×C22⋊Dic5—31no—
129C2×C22⋊Dic5—31no—
130C2×C22⋊Dic5—31no—
131#4072—38no—
132C2×C4⋊Dic5—31no—
133C2×C4⋊Dic5C2×D311yescharacteristic
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—31no—
137C2×#683C2×D311yescharacteristic
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5C2×D311yescharacteristic
144C5×#95—31no—
145C5×#95—31no—
146C5×#95—31no—
147C5×#95C2×D311yescharacteristic
148#3963—31no—
149#3963—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963C2×D311yescharacteristic
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2343—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C5×D3—21no—
163C22×C5×D3—21no—
164C22×C5×D3—21no—
165C22×C5×D3—21no—
166C22×C5×D3C22×C412yes—
167C22×C5×D3#4112yes—
168C22×C5×D3#4112yes—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5C22×C412yes—
177C2×C3×C4×C5#4112yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15C22×C412yes—
189C2×Dic15C22×C412yes—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3C22×C412yes—
198C2×C5×Dic3#4112yes—
199C4×C5×D3—28no—
200C4×C5×D3—44no—
201C4×C5×D3—44no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5C22×C412yes—
213C2×C3×Dic5C22×C412yes—
214C22×C4×D3C2×D511yescharacteristic
215C22×C4×D3C2×D511yescharacteristic
216C22×C4×D3C2×D511yescharacteristic
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4—51no—
219C2×C3×C42—51no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—51no—
223C2×(C2×D3)⋊C4—51no—
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×C4×Dic3—51no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233#892—58no—
234C3×#95—51no—
235C3×#95—51no—
236C3×#95—51no—
237C3×#95C2×D511yescharacteristic
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95—51no—
247C3⋊#95C2×D511yescharacteristic
248C3⋊#95C2×D511yescharacteristic
249C3⋊#95C2×D511yescharacteristic
250C24×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5—34no—
254C22×C4×C5—31no—
255C22×C4×C5—62no—
256C22×C4×C5—62no—
257C22×C4×C5—62no—
258C22×C4×C5—62no—
259C22×C4×C5—62no—
260C22×C4×C5—62no—
261C22×C4×C5—121no—
262C22×C4×C5—121no—
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×Dic5—31no—
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5C22×D311yescharacteristic
271C22×Dic5C22×D311yescharacteristic
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C22⋊Dic5—34no—
275C22⋊Dic5—34no—
276C22⋊Dic5—62no—
277C22⋊Dic5—62no—
278C4⋊Dic5—34no—
279C4⋊Dic5C4×D314yescomplemented
280#683—22no—
281#683—62no—
282#683—121no—
283#683—121no—
284C4×Dic5—22no—
285C4×Dic5—34no—
286C4×Dic5—34no—
287C4×Dic5—62no—
288C4×Dic5—121no—
289C4×Dic5—121no—
290C2×#117—151no—
291#387—51no—
292#387—151no—
293#387—151no—
294#387—151no—
295#385—151no—
296#385—151no—
297#383—151no—
298#382—151no—
299#381—151no—
300C4×C4⋊C4—151no—
301C4×C22⋊C4—151no—
302C4×C22⋊C4—151no—
303#376—151no—
304C2×#95—31no—
305C22×C3×C5C23×C411yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5C2×#4111yescharacteristic
309C22×C3×C5C2×#4111yescharacteristic
310C22×C3×C5H(5,𝔽2)11yescharacteristic
311C22×C3×C52−1+411yescharacteristic
312C2×C5×D3—22no—
313C2×C5×D3—22no—
314C2×C5×D3—22no—
315C2×C5×D3—22no—
316C2×C5×D3—22no—
317C2×C5×D3—22no—
318C2×C5×D3#11714yes—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321C3×C4×C5—41no—
322Dic15—22no—
323Dic15—22no—
324Dic15—41no—
325Dic15—41no—
326C3×Dic5—22no—
327C3×Dic5—22no—
328C3×Dic5—41no—
329C3×Dic5—41no—
330C5×Dic3—22no—
331C5×Dic3—22no—
332C5×Dic3—41no—
333C23×D3C22×D511yescharacteristic
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D511yescharacteristic
340C22×C3×C4C22×D511yescharacteristic
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—51no—
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—41no—
355C2×C4×D3—41no—
356C2×C4×D3C4×D514yes—
357C3×C4⋊C4—54no—
358C3×C4⋊C4—102no—
359C3×C42—102no—
360(C2×D3)⋊C4—54no—
361(C2×D3)⋊C4—54no—
362(C2×D3)⋊C4—102no—
363(C2×D3)⋊C4—102no—
364C4⋊Dic3—54no—
365C4⋊Dic3—102no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368C4×Dic3—54no—
369C4×Dic3—54no—
370C4×Dic3—102no—
371C4×Dic3—201no—
372C4×Dic3—201no—
373C23×C5—32no—
374C23×C5—32no—
375C23×C5—32no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5—61no—
379C23×C5—61no—
380C23×C5C23×D311yescharacteristic
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—32no—
389C2×C4×C5—32no—
390C2×C4×C5—68no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5—124no—
399C2×C4×C5—124no—
400C2×C4×C5C2×C4×D312yes—
401C2×C4×C5#23712yes—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—32no—
413C2×Dic5—32no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423C2×Dic5—61no—
424C2×Dic5C2×C4×D312yes—
425C2×Dic5C2×C4×D312yes—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429#117—158no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—151no—
436C2×C22⋊C4—151no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C42—51no—
441C2×C42—151no—
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—31no—
449#95—51no—
450#95—51no—
451#95—51no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460#95—151no—
461#95D3×D511yescharacteristic
462C2×C3×C5C2×#11711yescharacteristic
463C2×C3×C5C4×#4111yescharacteristic
464C2×C3×C5#52011yescharacteristic
465C2×C3×C5#55111yescharacteristic
466C2×C3×C5#55111yescharacteristic
467C2×C3×C5#55211yescharacteristic
468C2×C3×C5#55211yescharacteristic
469C5×D3—24no—
470C23×C3C23×D511yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C4×D512yes—
476C22×D3#71112yes—
477C22×D3#71112yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4C2×C4×D512yes—
498C2×C3×C4#70912yes—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—52no—
507C2×Dic3—52no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3C2×C4×D512yes—
519C2×Dic3#70912yes—
520C4×D3—28no—
521C4×D3—44no—
522C4×D3—44no—
523C22×C5—34no—
524C22×C5—62no—
525C22×C5—62no—
526C22×C5—62no—
527C22×C5—62no—
528C22×C5—62no—
529C22×C5—62no—
530C22×C5C22×C4×D311yescharacteristic
531C22×C5C2×#23711yescharacteristic
532C22×C5#100711yescharacteristic
533C22×C5D3×#4111yescharacteristic
534C22×C5D3×#4111yescharacteristic
535C22×C5D3×#4111yescharacteristic
536C22×C5#100911yescharacteristic
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—41no—
540C4×C5—62no—
541C4×C5—62no—
542C4×C5—121no—
543Dic5—22no—
544Dic5—22no—
545Dic5—41no—
546Dic5—41no—
547Dic5—62no—
548Dic5—62no—
549Dic5—121no—
550Dic5—121no—
551C24—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—34no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—121no—
567C22×C4—121no—
568C22×C4—151no—
569C22×C4—151no—
570C22×C4—151no—
571C22×C4—151no—
572C22×C4C2×D3×D511yescharacteristic
573C22×C4C2×D3×D511yescharacteristic
574C22×C4C2×D3×D511yescharacteristic
575C4⋊C4—54no—
576C4⋊C4—102no—
577C4⋊C4—154no—
578C4⋊C4—302no—
579C4⋊C4—601no—
580C4⋊C4—601no—
581C22⋊C4—154no—
582C22⋊C4—154no—
583C22⋊C4—302no—
584C22⋊C4—302no—
585C42—102no—
586C42—154no—
587C42—154no—
588C42—302no—
589C42—601no—
590C42—601no—
591C3×C5#234311yescharacteristic, complemented, Hall
592C22×C3C22×C4×D511yescharacteristic
593C22×C3C2×#70911yescharacteristic
594C22×C3C2×#70911yescharacteristic
595C22×C3C2×#71111yescharacteristic
596C22×C3C2×#71111yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414711yescharacteristic
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—22no—
605C2×D3#402314yes—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—41no—
609C3×C4—102no—
610C3×C4—102no—
611C3×C4—201no—
612C3×C4—201no—
613Dic3—22no—
614Dic3—22no—
615Dic3—41no—
616Dic3—102no—
617Dic3—102no—
618Dic3—201no—
619Dic3—201no—
620C2×C5—64no—
621C2×C5D3×#11711yescharacteristic
622C2×C5C4×#23711yescharacteristic
623C2×C5#557411yescharacteristic
624C2×C5#563911yescharacteristic
625C2×C5#565811yescharacteristic
626C2×C5#569311yescharacteristic
627C2×C5#570511yescharacteristic
628C23—32no—
629C23—32no—
630C23—32no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23C22×D3×D511yescharacteristic
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—52no—
646C2×C4—52no—
647C2×C4—68no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—124no—
666C2×C4—124no—
667C2×C4—152no—
668C2×C4—152no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—301no—
678C2×C4—301no—
679C2×C4#676512yes—
680C2×C4C4×D3×D512yes—
681C2×C3C4×#70911yescharacteristic
682C2×C3C2×#402311yescharacteristic
683C2×C3#6582911yescharacteristic
684C2×C3#6582911yescharacteristic
685C2×C3#6583811yescharacteristic
686C2×C3#6584711yescharacteristic
687C2×C3#6584711yescharacteristic
688D3—24no—
689C5#7530311yescharacteristic, complemented, Sylow
690C22—34no—
691C22—62no—
692C22—62no—
693C22—62no—
694C22—62no—
695C22—62no—
696C22—62no—
697C22C2×#676511yescharacteristic
698C22C2×C4×D3×D511yescharacteristic
699C22D3×#70911yescharacteristic
700C22D3×#71111yescharacteristic
701C22D3×#71111yescharacteristic
702C22#9202711yescharacteristic
703C22#9202911yescharacteristic
704C4—22no—
705C4—22no—
706C4—41no—
707C4—62no—
708C4—62no—
709C4—102no—
710C4—102no—
711C4—121no—
712C4—201no—
713C4—201no—
714C4—302no—
715C4—302no—
716C4—601no—
717C4—601no—
718C3#1060506611yescharacteristic, complemented, Sylow
719C2—64no—
720C2C4×#676511yescharacteristic
721C2D3×#402311yescharacteristic
722C2#1175297211yescharacteristic
723C2#1175313711yescharacteristic
724C2#1175333711yescharacteristic
725C2#1175335411yescharacteristic
726C2#1175376411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750755C2semidirect
4. C3×#64942C2semidirect
10. #11748697C2semidirect
11. #11748689C2semidirect
12. #11748646C2semidirect
13. #11748644C2semidirect
14. #11748637C2semidirect
15. #11748635C2semidirect
36. #91338C4semidirect
64. #64942D3semidirect
93. C4⋊Dic15C2×C4semidirect
96. C3×C4⋊Dic5C2×C4semidirect
107. Dic3×Dic5C2×C4semidirect
108. Dic3×Dic5C2×C4semidirect
279. C4⋊Dic5C4×D3semidirect
591. C3×C5#2343semidirect
689. C5#75303semidirect
718. C3#10605066semidirect

Maximal subgroups

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

subgroupindex
C2×#913382
#117507552
C5×D3×#952
C3×#649422
#117487772
#117487222
#117487192
#117487162
C4×(C2×D3)⋊Dic52
#117486972
#117486892
#117486462
#117486442
#117486372
#117486352
#106050663
#753035