Finite Group Databasebeta

← #14331070

Subgroups — #14331070

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#897C211yesmaximal, characteristic
2#11751081C211yesmaximal, characteristic, complemented
3C3×#65270C211yesmaximal, characteristic, complemented
4#11748868C211yesmaximal, characteristic, complemented
5#11748842C211yesmaximal, characteristic, complemented
6#11748794C211yesmaximal, characteristic
7#11748782C211yesmaximal, characteristic
8#11748777C211yesmaximal, characteristic
9#11748747C211yesmaximal, characteristic
10#11748692C211yesmaximal, characteristic, complemented
11#11748692C211yesmaximal, characteristic, complemented
12#11748686C211yesmaximal, characteristic
13#11748683C211yesmaximal, characteristic, complemented
14#11748682C211yesmaximal, characteristic, complemented
15#11748675C211yesmaximal, characteristic
16#10614481—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C5×#897C418yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75314—51nomaximal, Hall
54C2×C5×C22⋊Q8—31no—
55#65519—31no—
56#65519—31no—
57#65501—31no—
58#65500—31no—
59#65274—31no—
60#65274—31no—
61#65270—31no—
62#65270—31no—
63#65270—31no—
64#65270D311yescharacteristic, complemented
65#65240—31no—
66#65240—31no—
67#65240—31no—
68#65240—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—41no—
81C2×C4×C5×D3—41no—
82C2×C4×C5×D3C2×C414yes—
83C2×C5×Dic6—41no—
84C2×C5×Dic6—41no—
85C2×C5×Dic6C2×C414yes—
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C3×C5×C4⋊C4C2×C414yes—
91C4⋊Dic15—41no—
92C4×Dic15—41no—
93C5×(C2×D3)⋊C4C2×C414yes—
94C5×(C2×D3)⋊C4C2×C414yes—
95C5×C4⋊Dic3C2×C414yes—
96C5×C4⋊Dic3C2×C414yes—
97C3×C4⋊Dic5—41no—
98C3×C4×Dic5—41no—
99Dic3⋊Dic5—41no—
100Dic3⋊Dic5—41no—
101Dic3⋊Dic5—41no—
102Dic3⋊Dic5—41no—
103(C2×D3)⋊Dic5—41no—
104(C2×D3)⋊Dic5—41no—
105(C2×D3)⋊Dic5—41no—
106(C2×D3)⋊Dic5—41no—
107Dic3×Dic5—41no—
108Dic3×Dic5—41no—
109C2×#897D511yescharacteristic
110C3×#387—51no—
111#4990—51no—
112#4980—51no—
113#4972—51no—
114#4940—51no—
115#4928—51no—
116#4670—51no—
117#4669—51no—
118#4667—51no—
119#4664—51no—
120#4654—51no—
121#4653—51no—
122#4646—51no—
123#4646—51no—
124C22×C5×Q8—31no—
125C23×C4×C5—31no—
126C5×C22⋊Q8—38no—
127C2×C5×C4⋊C4—31no—
128C2×C5×C4⋊C4—31no—
129C2×C5×C4⋊C4C2×D311yescharacteristic
130C2×C5×C22⋊C4—31no—
131C2×C5×C22⋊C4—31no—
132C2×C22⋊Dic5—31no—
133C2×C22⋊Dic5—31no—
134C2×C22⋊Dic5—31no—
135C2×C22⋊Dic5—31no—
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5C2×D311yescharacteristic
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5C2×D311yescharacteristic
146#3963—31no—
147#3963—31no—
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#3963C2×D311yescharacteristic
157#3963C2×D311yescharacteristic
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2378—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C5×D3—21no—
163C22×C5×D3—21no—
164C22×C5×D3—21no—
165C22×C5×D3—21no—
166C22×C5×D3—21no—
167C22×C5×D3—21no—
168C22×C5×D3C22×C412yes—
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×C5C22×C412yes—
176C2×C3×C4×C5C22×C412yes—
177C2×C3×C4×C5C22×C412yes—
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×Dic15—21no—
189C2×Dic15—21no—
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×Dic3C22×C412yes—
197C2×C5×Dic3C22×C412yes—
198C2×C5×Dic3C22×C412yes—
199C4×C5×D3—44no—
200C5×Dic6—44no—
201C2×C3×Dic5—21no—
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×Dic5—21no—
213C22×C4×D3C2×D511yescharacteristic
214C22×Dic6C2×D511yescharacteristic
215C2×C3×C4⋊C4—51no—
216C2×C3×C4⋊C4C2×D511yescharacteristic
217C2×C3×C42—51no—
218C2×(C2×D3)⋊C4—51no—
219C2×(C2×D3)⋊C4—51no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4C2×D511yescharacteristic
223C2×(C2×D3)⋊C4C2×D511yescharacteristic
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3C2×D511yescharacteristic
226C2×C4⋊Dic3C2×D511yescharacteristic
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234#897Dic518yescomplemented
235C3×#95—51no—
236C3×#95—51no—
237C3×#95—51no—
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⋊#95—51no—
248C3⋊#95—51no—
249C24×C5—31no—
250C2×C5×Q8—34no—
251C2×C5×Q8—121no—
252C2×C5×Q8—121no—
253C22×C4×C5—31no—
254C22×C4×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—34no—
257C22×C4×C5—121no—
258C22×C4×C5—121no—
259C22×C4×C5C22×D311yescharacteristic
260C22×C4×C5C22×D311yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C22×Dic5—31no—
266C22×Dic5C22×D311yescharacteristic
267C22×Dic5C22×D311yescharacteristic
268C22×Dic5C22×D311yescharacteristic
269C22×Dic5C22×D311yescharacteristic
270C5×C4⋊C4—34no—
271C5×C4⋊C4—34no—
272C5×C4⋊C4C4×D314yes—
273C5×C22⋊C4—34no—
274C5×C22⋊C4—34no—
275C22⋊Dic5—121no—
276C22⋊Dic5—121no—
277C22⋊Dic5—121no—
278C22⋊Dic5—121no—
279C4⋊Dic5—41no—
280C4⋊Dic5—121no—
281C4⋊Dic5—121no—
282C4⋊Dic5—121no—
283C4⋊Dic5—121no—
284C4⋊Dic5—121no—
285C4×Dic5—41no—
286C4×Dic5—121no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C2×C22⋊Q8—31no—
290#391—151no—
291#391—151no—
292#389—151no—
293#389—151no—
294#388—151no—
295#388—151no—
296#388—151no—
297#388—151no—
298#387—51no—
299#387—151no—
300#387—151no—
301#387—151no—
302#381—151no—
303#380—151no—
304C22×C3×C5C23×C411yescharacteristic
305C22×C3×C5H(5,𝔽2)11yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C22×C3×C52−1+411yescharacteristic
311C2×C5×D3—22no—
312C2×C5×D3—22no—
313C2×C5×D3—22no—
314C2×C5×D3—41no—
315C2×C5×D3—41no—
316C2×C5×D3—41no—
317C2×C5×D3—41no—
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321Dic15—41no—
322Dic15—41no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—41no—
326C3×Dic5—41no—
327C3×Dic5—41no—
328C3×Dic5—41no—
329C5×Dic3—22no—
330C5×Dic3—22no—
331C5×Dic3—22no—
332C23×D3C22×D511yescharacteristic
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4C22×D511yescharacteristic
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D511yescharacteristic
340C22×Dic3—51no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3C22×D511yescharacteristic
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C2×C4×D3—41no—
348C2×C4×D3—41no—
349C2×C4×D3C2×Dic514yes—
350C2×Dic6—41no—
351C2×Dic6—41no—
352C2×Dic6C2×Dic514yes—
353C3×C4⋊C4—201no—
354C3×C4⋊C4C2×Dic514yes—
355C3×C42—201no—
356(C2×D3)⋊C4—201no—
357(C2×D3)⋊C4—201no—
358(C2×D3)⋊C4—201no—
359(C2×D3)⋊C4—201no—
360(C2×D3)⋊C4C2×Dic514yes—
361(C2×D3)⋊C4C2×Dic514yes—
362C4⋊Dic3—201no—
363C4⋊Dic3C2×Dic514yes—
364C4⋊Dic3C2×Dic514yes—
365Dic3⋊C4—201no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368Dic3⋊C4—201no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C23×C5—32no—
373C23×C5—61no—
374C23×C5—61no—
375C23×C5—61no—
376C23×C5—61no—
377C23×C5—61no—
378C23×C5—61no—
379C23×C5C23×D311yescharacteristic
380C5×Q8—124no—
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—32no—
388C2×C4×C5—32no—
389C2×C4×C5—32no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5—124no—
397C2×C4×C5C2×C4×D312yes—
398C2×C4×C5C2×C4×D312yes—
399C2×C4×C5C2×C4×D312yes—
400C2×Dic5—21no—
401C2×Dic5—21no—
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—61no—
413C2×Dic5—61no—
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—
424C22×Q8—31no—
425C23×C4—31no—
426C22⋊Q8—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4D3×D511yescharacteristic
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
442C2×C42—51no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—51no—
447#95—51no—
448#95—51no—
449#95—51no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460C2×C3×C5#51811yescharacteristic
461C2×C3×C5#51911yescharacteristic
462C2×C3×C5#52011yescharacteristic
463C2×C3×C5#56211yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56311yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C5×D3—42no—
468C23×C3C23×D511yescharacteristic
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C22×Dic512yes—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—101no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
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×C4C22×Dic512yes—
495C2×C3×C4C22×Dic512yes—
496C2×C3×C4C22×Dic512yes—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—101no—
504C2×Dic3—101no—
505C2×Dic3—101no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3C22×Dic512yes—
516C2×Dic3C22×Dic512yes—
517C2×Dic3C22×Dic512yes—
518C4×D3—44no—
519Dic6—44no—
520C22×C5—62no—
521C22×C5—62no—
522C22×C5—62no—
523C22×C5—121no—
524C22×C5—121no—
525C22×C5—121no—
526C22×C5—121no—
527C22×C5C22×C4×D311yescharacteristic
528C22×C5#100411yescharacteristic
529C22×C5#100711yescharacteristic
530C22×C5#100911yescharacteristic
531C22×C5#100911yescharacteristic
532C22×C5#101011yescharacteristic
533C22×C5#101011yescharacteristic
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—62no—
538C4×C5—62no—
539C4×C5—62no—
540Dic5—41no—
541Dic5—41no—
542Dic5—41no—
543Dic5—41no—
544Dic5—121no—
545Dic5—121no—
546Dic5—121no—
547Dic5—121no—
548C24—31no—
549C2×Q8—34no—
550C2×Q8—121no—
551C2×Q8—121no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—34no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—121no—
561C22×C4—121no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4C2×D3×D511yescharacteristic
567C22×C4C2×D3×D511yescharacteristic
568C22×C4C2×D3×D511yescharacteristic
569C4⋊C4—34no—
570C4⋊C4—34no—
571C4⋊C4—201no—
572C4⋊C4—601no—
573C4⋊C4—601no—
574C4⋊C4—601no—
575C4⋊C4—601no—
576C4⋊C4—601no—
577C4⋊C4D3×Dic514yes—
578C22⋊C4—34no—
579C22⋊C4—34no—
580C22⋊C4—601no—
581C22⋊C4—601no—
582C22⋊C4—601no—
583C22⋊C4—601no—
584C42—201no—
585C42—601no—
586C42—601no—
587C42—601no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3#414411yescharacteristic
590C22×C3#414411yescharacteristic
591C22×C3#414711yescharacteristic
592C22×C3#414711yescharacteristic
593C22×C3#414911yescharacteristic
594C22×C3#415011yescharacteristic
595C22×C3C23×Dic511yescharacteristic
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—201no—
607C3×C4—201no—
608C3×C4—201no—
609C3×C4—201no—
610Dic3—22no—
611Dic3—22no—
612Dic3—22no—
613Dic3—201no—
614Dic3—201no—
615Dic3—201no—
616Dic3—201no—
617C2×C5—122no—
618C2×C5#552111yescharacteristic
619C2×C5#554611yescharacteristic
620C2×C5#557211yescharacteristic
621C2×C5#564711yescharacteristic
622C2×C5#566711yescharacteristic
623C2×C5#569911yescharacteristic
624C2×C5#571211yescharacteristic
625C23—32no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23C22×D3×D511yescharacteristic
633Q8—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—101no—
650C2×C4—101no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—124no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—301no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4C2×D3×Dic512yes—
675C2×C4C2×D3×Dic512yes—
676C2×C4C2×D3×Dic512yes—
677C2×C3#6598011yescharacteristic
678C2×C3#6598011yescharacteristic
679C2×C3#6598111yescharacteristic
680C2×C3#6598111yescharacteristic
681C2×C3#6613211yescharacteristic
682C2×C3#6614611yescharacteristic
683C2×C3#6616111yescharacteristic
684D3—42no—
685C5#7531411yescharacteristic, complemented, Sylow
686C22—62no—
687C22—62no—
688C22—62no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22—121no—
693C22#9201811yescharacteristic
694C22#9201811yescharacteristic
695C22#9202011yescharacteristic
696C22#9202611yescharacteristic
697C22#9202811yescharacteristic
698C22#9202911yescharacteristic
699C22C22×D3×Dic511yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—62no—
704C4—62no—
705C4—62no—
706C4—201no—
707C4—201no—
708C4—201no—
709C4—201no—
710C4—601no—
711C4—601no—
712C4—601no—
713C4—601no—
714C3#1061448111yescharacteristic, complemented, Sylow
715C2—122no—
716C2#1175337311yescharacteristic
717C2#1175365211yescharacteristic
718C2#1175381711yescharacteristic
719C2#1175381811yescharacteristic
720C2#1175450311yescharacteristic
721C2#1175492011yescharacteristic
722C2#1175514411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2378
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
2. #11751081C2semidirect
3. C3×#65270C2semidirect
4. #11748868C2semidirect
5. #11748842C2semidirect
10. #11748692C2semidirect
11. #11748692C2semidirect
13. #11748683C2semidirect
14. #11748682C2semidirect
26. C5×#897C4semidirect
64. #65270D3semidirect
234. #897Dic5semidirect
588. C3×C5#2378semidirect
685. C5#75314semidirect
714. C3#10614481semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8972
#117510812
C3×#652702
#117488682
#117488422
#117487942
#117487822
#117487772
#117487472
#117486922
#117486862
#117486832
#117486822
#117486752
#106144813
#753145