Finite Group Databasebeta

← #14326973

Subgroups — #14326973

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91394C211yesmaximal, characteristic
2C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
3C5×#4976C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic
5#11748878C211yesmaximal, characteristic
6Dic3×#685C211yesmaximal, characteristic
7C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
8#11748772C211yesmaximal, characteristic
9#11748710C211yesmaximal, characteristic
10#11748709C211yesmaximal, characteristic
11#11748693C211yesmaximal, characteristic, complemented
12#11748651C211yesmaximal, characteristic, complemented
13#11748646C211yesmaximal, characteristic, complemented
14Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11748621C211yesmaximal, characteristic, complemented
16#10607711—31nomaximal, Hall
17C22×D5×Dic3C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×Dic3⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91394C418yescomplemented
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75474—51nomaximal, Hall
54C2×#4038—31no—
55C5×#389—31no—
56#65279—31no—
57#65279D311yescharacteristic
58#65276—31no—
59#65274—31no—
60C4⋊C4×Dic5—31no—
61C4⋊C4×Dic5—31no—
62C4⋊C4×Dic5—31no—
63C4×#685—31no—
64C4×C4⋊Dic5—31no—
65#64959—31no—
66#64959—31no—
67#64940—31no—
68#64940—31no—
69C23×C3×D5C2311yescharacteristic
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
80C22×C5×Dic3C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×D5×Dic3—22no—
85C2×D5×Dic3—22no—
86C2×D5×Dic3C2×C414yes—
87C3×C5×C4⋊C4—22no—
88C4⋊Dic15—22no—
89C4×Dic15—41no—
90C4×Dic15—41no—
91C4×Dic15C2×C414yes—
92C5×Dic3⋊C4—22no—
93C5×Dic3⋊C4—22no—
94C5×Dic3⋊C4C2×C414yes—
95C4×C5×Dic3—22no—
96C3×#685—22no—
97C3×#685—41no—
98C3×#685C2×C414yes—
99C3×C4×Dic5—41no—
100Dic3⋊Dic5—22no—
101Dic3⋊Dic5—22no—
102Dic3⋊Dic5C2×C414yes—
103#6665—22no—
104#6665—41no—
105#6665C2×C414yes—
106Dic3×Dic5—22no—
107Dic3×Dic5—41no—
108Dic3×Dic5C2×C414yes—
109C2×#877—51no—
110C3×#388—51no—
111#4976D511yescharacteristic, complemented
112Dic3×C4⋊C4—51no—
113#4951—51no—
114#4945—51no—
115#4944—51no—
116#4942—51no—
117Dic3×C22⋊C4—51no—
118C4×Dic3⋊C4—51no—
119C4×Dic3⋊C4—51no—
120#4651—51no—
121#4651—51no—
122#4649—51no—
123#4647—51no—
124C22×C4×D5—31no—
125C2×C5×C4⋊C4—31no—
126C2×C5×C4⋊C4—31no—
127C2×C5×C4⋊C4—31no—
128C2×C5×C4⋊C4C2×D311yescharacteristic
129C2×C42×C5—31no—
130C2×#685—31no—
131C2×#685—31no—
132C2×#685—31no—
133C2×#685C2×D311yescharacteristic
134C2×#685C2×D311yescharacteristic
135C2×#685C2×D311yescharacteristic
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5—31no—
146C2×C4×Dic5C2×D311yescharacteristic
147#4038—38no—
148C5×#95—31no—
149C5×#95—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2347—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C3×D5—21no—
163C22×C3×D5—21no—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×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×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×Dic15C22×C412yes—
188C2×Dic15C22×C412yes—
189C2×Dic15#4112yes—
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×Dic3—21no—
198C2×C5×Dic3C22×C412yes—
199C2×C5×Dic3C22×C412yes—
200C2×C5×Dic3#4112yes—
201C2×C5×Dic3#4112yes—
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×Dic5C22×C412yes—
211D5×Dic3—28no—
212C23×Dic3—51no—
213C2×C3×C4⋊C4C2×D511yescharacteristic
214C2×C3×C22⋊C4—51no—
215C2×C3×C22⋊C4—51no—
216C2×C3×C22⋊C4—51no—
217C2×C3×C42—51no—
218C2×#217—51no—
219C2×#217—51no—
220C2×#217—51no—
221C2×C4⋊Dic3—51no—
222C2×Dic3⋊C4—51no—
223C2×Dic3⋊C4—51no—
224C2×Dic3⋊C4—51no—
225C2×Dic3⋊C4C2×D511yescharacteristic
226C2×Dic3⋊C4C2×D511yescharacteristic
227C2×Dic3⋊C4C2×D511yescharacteristic
228C2×C4×Dic3—51no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3C2×D511yescharacteristic
235#877—58no—
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⋊#95C2×D511yescharacteristic
247C3⋊#95C2×D511yescharacteristic
248C23×D5C22×D311yescharacteristic
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×Dic5—31no—
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5C22×D311yescharacteristic
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263C2×C4×D5—34no—
264C2×C4×D5—62no—
265C2×C4×D5—62no—
266C5×C4⋊C4—22no—
267C5×C4⋊C4—34no—
268C5×C4⋊C4—62no—
269C5×C4⋊C4—62no—
270C42×C5—62no—
271#685—22no—
272#685—34no—
273#685—41no—
274#685—62no—
275#685—121no—
276#685C4×D314yes—
277C4⋊Dic5—34no—
278C4⋊Dic5—62no—
279C4⋊Dic5—62no—
280C4⋊Dic5—62no—
281C4×Dic5—34no—
282C4×Dic5—34no—
283C4×Dic5—41no—
284C4×Dic5—62no—
285C4×Dic5—121no—
286C4×Dic5—121no—
287C4×Dic5—121no—
288C2×#117—151no—
289#389—31no—
290#389—151no—
291#388—51no—
292#388—151no—
293#388—151no—
294#388—151no—
295#383—151no—
296#383—151no—
297#380—151no—
298C4×C4⋊C4—151no—
299C4×C4⋊C4—151no—
300C4×C4⋊C4—151no—
301C4×C4⋊C4—151no—
302C4×C22⋊C4—151no—
303C22×C3×C5C23×C411yescharacteristic
304C22×C3×C5C2×#4111yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5H(5,𝔽2)11yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—41no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C3×C4×C5—22no—
318C3×C4×C5—22no—
319C3×C4×C5—41no—
320Dic15—22no—
321Dic15—22no—
322Dic15—22no—
323Dic15—41no—
324C3×Dic5—22no—
325C3×Dic5—41no—
326C3×Dic5—41no—
327C5×Dic3—22no—
328C5×Dic3—41no—
329C5×Dic3—41no—
330C5×Dic3#11714yes—
331C24×C3—51no—
332C22×C3×C4—51no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4C22×D511yescharacteristic
336C22×C3×C4C22×D511yescharacteristic
337C22×C3×C4C22×D511yescharacteristic
338C22×Dic3—51no—
339C22×Dic3—51no—
340C22×Dic3—51no—
341C22×Dic3—54no—
342C22×Dic3—51no—
343C22×Dic3—102no—
344C22×Dic3—102no—
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C22×Dic3C22×D511yescharacteristic
349C3×C4⋊C4—22no—
350C3×C22⋊C4—54no—
351C3×C22⋊C4—102no—
352C3×C22⋊C4—201no—
353C3×C42—201no—
354#217—54no—
355#217—102no—
356#217—201no—
357C4⋊Dic3—102no—
358Dic3⋊C4—22no—
359Dic3⋊C4—22no—
360Dic3⋊C4—54no—
361Dic3⋊C4—102no—
362Dic3⋊C4—102no—
363Dic3⋊C4C4×D514yes—
364C4×Dic3—22no—
365C4×Dic3—54no—
366C4×Dic3—54no—
367C4×Dic3—102no—
368C4×Dic3—201no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C23×C5C23×D311yescharacteristic
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5C2×C4×D312yes—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—32no—
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—61no—
397C2×C4×C5—61no—
398C2×C4×C5C2×C4×D312yes—
399C2×C4×C5#23712yes—
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—32no—
409C2×Dic5—32no—
410C2×Dic5—32no—
411C2×Dic5—61no—
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×Dic5C2×C4×D312yes—
421C4×D5—68no—
422C23×C4—151no—
423#117—158no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—151no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4D3×D511yescharacteristic
432C2×C22⋊C4—51no—
433C2×C22⋊C4—51no—
434C2×C22⋊C4—51no—
435C2×C22⋊C4—151no—
436C2×C22⋊C4—151no—
437C2×C22⋊C4—151no—
438C2×C42—31no—
439C2×C42—51no—
440C2×C42—151no—
441C2×C42—151no—
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
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—
458C2×C3×C5C2×#11711yescharacteristic
459C2×C3×C5C4×#4111yescharacteristic
460C2×C3×C5#52011yescharacteristic
461C2×C3×C5#55311yescharacteristic
462C2×C3×C5#55311yescharacteristic
463C2×C3×C5#55611yescharacteristic
464C2×C3×C5#55611yescharacteristic
465C3×D5—42no—
466C23×C3—52no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3C23×D511yescharacteristic
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—52no—
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×C4C2×C4×D512yes—
491C2×C3×C4#71112yes—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—52no—
501C2×Dic3—52no—
502C2×Dic3—52no—
503C2×Dic3—101no—
504C2×Dic3—101no—
505C2×Dic3—101no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—108no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3C2×C4×D512yes—
514C2×Dic3C2×C4×D512yes—
515C2×Dic3#71112yes—
516C2×Dic3#71312yes—
517C22×C5C22×C4×D311yescharacteristic
518C22×C5C2×#23711yescharacteristic
519C22×C5#100411yescharacteristic
520C22×C5D3×#4111yescharacteristic
521C22×C5D3×#4111yescharacteristic
522C22×C5D3×#4111yescharacteristic
523C22×C5#101011yescharacteristic
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—41no—
528C2×D5—41no—
529C2×D5—41no—
530C2×D5—41no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—34no—
534C4×C5—41no—
535C4×C5—62no—
536C4×C5—121no—
537C4×C5—121no—
538Dic5—22no—
539Dic5—41no—
540Dic5—41no—
541Dic5—62no—
542Dic5—62no—
543Dic5—62no—
544Dic5—121no—
545C24—51no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—154no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—151no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D511yescharacteristic
561C22×C4C2×D3×D511yescharacteristic
562C22×C4C2×D3×D511yescharacteristic
563C4⋊C4—22no—
564C4⋊C4—34no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—154no—
568C4⋊C4—302no—
569C4⋊C4—302no—
570C4⋊C4—302no—
571C22⋊C4—54no—
572C22⋊C4—102no—
573C22⋊C4—154no—
574C22⋊C4—201no—
575C22⋊C4—302no—
576C22⋊C4—601no—
577C42—62no—
578C42—154no—
579C42—154no—
580C42—201no—
581C42—302no—
582C42—601no—
583C42—601no—
584C42—601no—
585C3×C5#234711yescharacteristic, complemented, Hall
586C22×C3—102no—
587C22×C3—102no—
588C22×C3—102no—
589C22×C3—201no—
590C22×C3—201no—
591C22×C3—201no—
592C22×C3—201no—
593C22×C3C22×C4×D511yescharacteristic
594C22×C3C2×#71111yescharacteristic
595C22×C3C2×#71111yescharacteristic
596C22×C3C2×#71311yescharacteristic
597C22×C3#414711yescharacteristic
598C22×C3D5×#4111yescharacteristic
599C22×C3#414911yescharacteristic
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—41no—
603C3×C4—102no—
604C3×C4—201no—
605C3×C4—201no—
606Dic3—22no—
607Dic3—41no—
608Dic3—41no—
609Dic3—102no—
610Dic3—102no—
611Dic3—102no—
612Dic3—201no—
613Dic3#403814yes—
614C2×C5D3×#11711yescharacteristic
615C2×C5C4×#23711yescharacteristic
616C2×C5#554611yescharacteristic
617C2×C5#560111yescharacteristic
618C2×C5#566111yescharacteristic
619C2×C5#567111yescharacteristic
620C2×C5#570211yescharacteristic
621D5—42no—
622C23—52no—
623C23—101no—
624C23—101no—
625C23—101no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23C22×D3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—32no—
641C2×C4—52no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
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—152no—
659C2×C4—152no—
660C2×C4—152no—
661C2×C4—308no—
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×C4C4×D3×D512yes—
672C2×C4#678012yes—
673C2×C3—202no—
674C2×C3C2×#403811yescharacteristic
675C2×C3C4×#71111yescharacteristic
676C2×C3#6590811yescharacteristic
677C2×C3#6595211yescharacteristic
678C2×C3#6597511yescharacteristic
679C2×C3#6602911yescharacteristic
680C2×C3#6606611yescharacteristic
681C5#7547411yescharacteristic, complemented, Sylow
682C22—102no—
683C22—102no—
684C22—102no—
685C22—201no—
686C22—201no—
687C22—201no—
688C22—201no—
689C22C2×C4×D3×D511yescharacteristic
690C22#9201611yescharacteristic
691C22D3×#71111yescharacteristic
692C22#9202611yescharacteristic
693C22#9202811yescharacteristic
694C22D3×#71311yescharacteristic
695C22C2×#678011yescharacteristic
696C4—22no—
697C4—22no—
698C4—34no—
699C4—41no—
700C4—62no—
701C4—102no—
702C4—121no—
703C4—121no—
704C4—201no—
705C4—201no—
706C4—302no—
707C4—302no—
708C4—302no—
709C4—601no—
710C3#1060771111yescharacteristic, complemented, Sylow
711C2—202no—
712C2#1175340111yescharacteristic
713C2#1175359111yescharacteristic
714C2#1175376111yescharacteristic
715C2D3×#403811yescharacteristic
716C2C4×#678011yescharacteristic
717C2#1175487011yescharacteristic
718C2#1175520611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2347
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. C4⋊C4×Dic15C2semidirect
3. C5×#4976C2semidirect
7. C4×Dic3⋊Dic5C2semidirect
11. #11748693C2semidirect
12. #11748651C2semidirect
13. #11748646C2semidirect
14. Dic5×Dic3⋊C4C2semidirect
15. #11748621C2semidirect
40. #91394C4semidirect
111. #4976D5semidirect
585. C3×C5#2347semidirect
681. C5#75474semidirect
710. C3#10607711semidirect

Maximal subgroups

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

subgroupindex
C2×#913942
C4⋊C4×Dic152
C5×#49762
C3×#652792
#117488782
Dic3×#6852
C4×Dic3⋊Dic52
#117487722
#117487102
#117487092
#117486932
#117486512
#117486462
Dic5×Dic3⋊C42
#117486212
#106077113
#754745