Finite Group Databasebeta

← #14323106

Subgroups — #14323106

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#893C211yesmaximal, characteristic
2#11751081C211yesmaximal, characteristic, complemented
3C3×#65270C211yesmaximal, characteristic, complemented
4#11748903C211yesmaximal, characteristic, complemented
5#11748901C211yesmaximal, characteristic
6#11748901C211yesmaximal, characteristic
7#11748897C211yesmaximal, characteristic, complemented
8D3×#3963C211yesmaximal, characteristic, complemented
9#11748794C211yesmaximal, characteristic, complemented
10#11748786C211yesmaximal, characteristic, complemented
11#11748777C211yesmaximal, characteristic, complemented
12#11748747C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
14#11748618C211yesmaximal, characteristic, complemented
15#11748600C211yesmaximal, characteristic, complemented
16#10614055—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C5×#893C418yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊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#74945—51nomaximal, Hall
54C2×C4×C5×D4—31no—
55#65509—31no—
56#65509—31no—
57#65501—31no—
58#65500—31no—
59C4×C22⋊Dic5—31no—
60C2×#3963—31no—
61#65270—31no—
62#65270D311yescharacteristic, complemented
63#65240—31no—
64#65240—31no—
65#65239—31no—
66#65239—31no—
67#65226—31no—
68#65225—31no—
69C23×C5×D3C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
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
80C2×C5×D12—22no—
81C2×C5×D12—22no—
82C2×C5×D12C2×C414yes—
83C2×C4×C5×D3—41no—
84C2×C4×C5×D3—41no—
85C2×C4×C5×D3—41no—
86C2×C4×C5×D3—41no—
87C2×C4×C5×D3C2×C414yes—
88C2×C4×C5×D3C2×C414yescomplemented
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×D3×Dic5—22no—
94C2×D3×Dic5—22no—
95C2×D3×Dic5—41no—
96C2×D3×Dic5—41no—
97C2×D3×Dic5—41no—
98C2×D3×Dic5—41no—
99C3×C5×C4⋊C4C2×C414yescomplemented
100C4⋊Dic15—41no—
101C4×Dic15—41no—
102C5×(C2×D3)⋊C4C2×C414yes—
103C5×(C2×D3)⋊C4C2×C414yescomplemented
104C4×C5×Dic3C2×C414yescomplemented
105C3×C4⋊Dic5—41no—
106C3×C4×Dic5—41no—
107Dic3⋊Dic5—41no—
108Dic3⋊Dic5—41no—
109(C2×D3)⋊Dic5—22no—
110(C2×D3)⋊Dic5—22no—
111(C2×D3)⋊Dic5—41no—
112(C2×D3)⋊Dic5—41no—
113(C2×D3)⋊Dic5—41no—
114(C2×D3)⋊Dic5—41no—
115C2×#893D511yescharacteristic
116C3×#387—51no—
117#4989—51no—
118#4987—51no—
119#4980—51no—
120#4940—51no—
121C4×(C2×D3)⋊C4—51no—
122#4669—51no—
123#4668—51no—
124#4665—51no—
125#4665—51no—
126#4664—51no—
127D3×#95—51no—
128#4651—51no—
129#4650—51no—
130C22×C5×D4—31no—
131C23×C4×C5—31no—
132C23×C4×C5—31no—
133C23×Dic5—31no—
134C23×Dic5—31no—
135C4×C5×D4—38no—
136C2×C5×C4⋊C4C2×D311yescharacteristic
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4—31no—
139C2×C42×C5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5—31no—
142C2×C22⋊Dic5—31no—
143C2×C22⋊Dic5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—31no—
149C2×C4⋊Dic5C2×D311yescharacteristic
150C2×C4×Dic5—31no—
151C2×C4×Dic5C2×D311yescharacteristic
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2318—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×D3—21no—
175C22×C5×D3—21no—
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3C22×C412yes—
179C22×C5×D3C22×C412yes—
180C22×C5×D3#4112yes—
181C22×C5×D3#4112yes—
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×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
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×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3C22×C412yes—
208C2×C5×Dic3C22×C412yes—
209C5×D12—28no—
210C4×C5×D3—44no—
211C4×C5×D3—44no—
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×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224D3×Dic5—44no—
225D3×Dic5—44no—
226C22×D12C2×D511yescharacteristic
227C22×C4×D3—51no—
228C22×C4×D3—51no—
229C22×C4×D3C2×D511yescharacteristic
230C22×C4×D3C2×D511yescharacteristic
231C2×C3×C4⋊C4—51no—
232C2×C3×C4⋊C4C2×D511yescharacteristic
233C2×C3×C42—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4C2×D511yescharacteristic
241C2×(C2×D3)⋊C4C2×D511yescharacteristic
242C2×C4⋊Dic3—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3C2×D511yescharacteristic
247#893Dic518yescomplemented
248C3×#95—51no—
249C3×#95—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C24×C5—31no—
263C24×C5—31no—
264C2×C5×D4—34no—
265C2×C5×D4—62no—
266C2×C5×D4—62no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—34no—
270C22×C4×C5—34no—
271C22×C4×C5—121no—
272C22×C4×C5—121no—
273C22×C4×C5—121no—
274C22×C4×C5—121no—
275C22×C4×C5C22×D311yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—31no—
281C22×Dic5—31no—
282C22×Dic5—62no—
283C22×Dic5—62no—
284C22×Dic5—121no—
285C22×Dic5—121no—
286C22×Dic5—121no—
287C22×Dic5—121no—
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C5×C4⋊C4C4×D314yescomplemented
293C5×C22⋊C4—34no—
294C5×C22⋊C4—34no—
295C42×C5—34no—
296C22⋊Dic5—62no—
297C22⋊Dic5—62no—
298C22⋊Dic5—121no—
299C22⋊Dic5—121no—
300C22⋊Dic5—121no—
301C22⋊Dic5—121no—
302C4⋊Dic5—41no—
303C4⋊Dic5—121no—
304C4⋊Dic5—121no—
305C4⋊Dic5—121no—
306C4×Dic5—41no—
307C4×Dic5—121no—
308C2×C4×D4—31no—
309#388—151no—
310#388—151no—
311#387—51no—
312#387—151no—
313#386—151no—
314#386—151no—
315#385—151no—
316#385—151no—
317#383—151no—
318#382—151no—
319#381—151no—
320#380—151no—
321C4×C22⋊C4—151no—
322C2×#95—151no—
323C22×C3×C5C23×C411yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C22×C3×C5H(5,𝔽2)11yescharacteristic
329C22×C3×C52−1+411yescharacteristic
330C2×C5×D3—22no—
331C2×C5×D3—22no—
332C2×C5×D3—22no—
333C2×C5×D3—22no—
334C2×C5×D3—22no—
335C2×C5×D3—22no—
336C2×C5×D3—22no—
337C2×C5×D3—22no—
338C2×C5×D3—22no—
339C2×C5×D3—41no—
340C2×C5×D3—41no—
341C2×C5×D3—41no—
342C2×C5×D3—41no—
343C2×C5×D3#11714yes—
344C3×C4×C5—22no—
345C3×C4×C5—22no—
346C3×C4×C5—22no—
347Dic15—41no—
348Dic15—41no—
349Dic15—41no—
350Dic15—41no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C5×Dic3—22no—
356C5×Dic3—22no—
357C23×D3C22×D511yescharacteristic
358C23×D3C22×D511yescharacteristic
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×Dic3—51no—
367C22×Dic3—51no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3C22×D511yescharacteristic
371C22×Dic3C22×D511yescharacteristic
372C2×D12—22no—
373C2×D12—22no—
374C2×D12C2×Dic514yes—
375C2×C4×D3—41no—
376C2×C4×D3—41no—
377C2×C4×D3—41no—
378C2×C4×D3—41no—
379C2×C4×D3—102no—
380C2×C4×D3—102no—
381C2×C4×D3—201no—
382C2×C4×D3—201no—
383C2×C4×D3—201no—
384C2×C4×D3—201no—
385C2×C4×D3C2×Dic514yes—
386C2×C4×D3C2×Dic514yescomplemented
387C3×C4⋊C4—201no—
388C3×C4⋊C4C2×Dic514yescomplemented
389C3×C42—201no—
390(C2×D3)⋊C4—102no—
391(C2×D3)⋊C4—102no—
392(C2×D3)⋊C4—201no—
393(C2×D3)⋊C4—201no—
394(C2×D3)⋊C4—201no—
395(C2×D3)⋊C4—201no—
396(C2×D3)⋊C4C2×Dic514yes—
397(C2×D3)⋊C4C2×Dic514yescomplemented
398C4⋊Dic3—201no—
399Dic3⋊C4—201no—
400Dic3⋊C4—201no—
401C4×Dic3—201no—
402C4×Dic3C2×Dic514yescomplemented
403C23×C5—32no—
404C23×C5—32no—
405C23×C5—32no—
406C23×C5—32no—
407C23×C5—61no—
408C23×C5—61no—
409C23×C5—61no—
410C23×C5—61no—
411C23×C5—61no—
412C23×C5—61no—
413C23×C5—61no—
414C23×C5—61no—
415C23×C5—61no—
416C23×C5—61no—
417C23×C5C23×D311yescharacteristic
418C5×D4—68no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—32no—
426C2×C4×C5—32no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—124no—
432C2×C4×C5—124no—
433C2×C4×C5C2×C4×D312yes—
434C2×C4×C5C2×C4×D312yes—
435C2×C4×C5C2×C4×D312yes—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—61no—
459C2×Dic5—61no—
460C2×Dic5—124no—
461C2×Dic5—124no—
462C22×D4—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—151no—
466C23×C4—151no—
467C4×D4—38no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4D3×D511yescharacteristic
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C22⋊C4—151no—
480C2×C22⋊C4—151no—
481C2×C42—31no—
482C2×C42—51no—
483C2×C42—151no—
484#95—51no—
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#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498C2×C3×C5C2×#11711yescharacteristic
499C2×C3×C5#51811yescharacteristic
500C2×C3×C5#52011yescharacteristic
501C2×C3×C5#53811yescharacteristic
502C2×C3×C5#53811yescharacteristic
503C2×C3×C5#53911yescharacteristic
504C2×C3×C5#53911yescharacteristic
505C5×D3—24no—
506C5×D3—42no—
507C23×C3C23×D511yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3#70912yes—
519C22×D3#70912yes—
520C22×D3C22×Dic512yes—
521C22×D3C22×Dic512yes—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
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—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4C22×Dic512yes—
541C2×C3×C4C22×Dic512yes—
542C2×C3×C4C22×Dic512yes—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3C22×Dic512yes—
560C2×Dic3C22×Dic512yes—
561D12—28no—
562C4×D3—44no—
563C4×D3—44no—
564C4×D3—204no—
565C4×D3—204no—
566C22×C5—34no—
567C22×C5—62no—
568C22×C5—62no—
569C22×C5—62no—
570C22×C5—62no—
571C22×C5—62no—
572C22×C5—62no—
573C22×C5—62no—
574C22×C5—62no—
575C22×C5—62no—
576C22×C5—121no—
577C22×C5—121no—
578C22×C5—121no—
579C22×C5—121no—
580C22×C5C22×C4×D311yescharacteristic
581C22×C5#100411yescharacteristic
582C22×C5#100711yescharacteristic
583C22×C5D3×#4111yescharacteristic
584C22×C5D3×#4111yescharacteristic
585C22×C5#100911yescharacteristic
586C22×C5#100911yescharacteristic
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—22no—
590C4×C5—62no—
591C4×C5—62no—
592Dic5—41no—
593Dic5—41no—
594Dic5—41no—
595Dic5—41no—
596Dic5—121no—
597Dic5—121no—
598Dic5—121no—
599Dic5—121no—
600C24—31no—
601C24—31no—
602C2×D4—34no—
603C2×D4—62no—
604C2×D4—62no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—34no—
608C22×C4—34no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—121no—
614C22×C4—121no—
615C22×C4—121no—
616C22×C4—121no—
617C22×C4—151no—
618C22×C4—151no—
619C22×C4—151no—
620C22×C4—151no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—601no—
624C22×C4—601no—
625C22×C4—601no—
626C22×C4—601no—
627C22×C4C2×D3×D511yescharacteristic
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—201no—
631C4⋊C4—601no—
632C4⋊C4—601no—
633C4⋊C4—601no—
634C4⋊C4D3×Dic514yescomplemented
635C22⋊C4—34no—
636C22⋊C4—34no—
637C22⋊C4—302no—
638C22⋊C4—302no—
639C22⋊C4—601no—
640C22⋊C4—601no—
641C22⋊C4—601no—
642C22⋊C4—601no—
643C42—34no—
644C42—201no—
645C42—601no—
646C3×C5#231811yescharacteristic, complemented, Hall
647C22×C3C2×#70911yescharacteristic
648C22×C3C2×#70911yescharacteristic
649C22×C3#414411yescharacteristic
650C22×C3#414411yescharacteristic
651C22×C3#414911yescharacteristic
652C22×C3#415011yescharacteristic
653C22×C3C23×Dic511yescharacteristic
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3#407214yes—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—201no—
672C3×C4—201no—
673C3×C4—201no—
674C3×C4—201no—
675Dic3—22no—
676Dic3—22no—
677Dic3—201no—
678Dic3—201no—
679Dic3—201no—
680Dic3—201no—
681C2×C5—64no—
682C2×C5—122no—
683C2×C5D3×#11711yescharacteristic
684C2×C5#554511yescharacteristic
685C2×C5#557411yescharacteristic
686C2×C5#563811yescharacteristic
687C2×C5#565711yescharacteristic
688C2×C5#569211yescharacteristic
689C2×C5#570411yescharacteristic
690C23—32no—
691C23—32no—
692C23—32no—
693C23—32no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23C22×D3×D511yescharacteristic
705D4—68no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—32no—
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—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—124no—
731C2×C4—124no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—604no—
745C2×C4—604no—
746C2×C4C2×D3×Dic512yes—
747C2×C4C2×D3×Dic512yes—
748C2×C4C2×D3×Dic512yes—
749C2×C3#6589411yescharacteristic
750C2×C3#6589411yescharacteristic
751C2×C3#6589811yescharacteristic
752C2×C3#6589811yescharacteristic
753C2×C3C2×#407211yescharacteristic
754C2×C3#6613211yescharacteristic
755C2×C3#6616111yescharacteristic
756D3—24no—
757D3—42no—
758C5#7494511yescharacteristic, complemented, Sylow
759C22—34no—
760C22—62no—
761C22—62no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22D3×#70911yescharacteristic
774C22D3×#70911yescharacteristic
775C22#9202511yescharacteristic
776C22#9202711yescharacteristic
777C22#9203011yescharacteristic
778C22#9203511yescharacteristic
779C22C22×D3×Dic511yescharacteristic
780C4—22no—
781C4—22no—
782C4—22no—
783C4—62no—
784C4—62no—
785C4—201no—
786C4—201no—
787C4—201no—
788C4—201no—
789C4—601no—
790C4—601no—
791C4—601no—
792C4—601no—
793C3#1061405511yescharacteristic, complemented, Sylow
794C2—64no—
795C2—122no—
796C2#1175356711yescharacteristic
797C2#1175375011yescharacteristic
798C2#1175391711yescharacteristic
799C2#1175391811yescharacteristic
800C2D3×#407211yescharacteristic
801C2#1175491411yescharacteristic
802C2#1175522011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2318
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. #11748903C2semidirect
7. #11748897C2semidirect
8. D3×#3963C2semidirect
9. #11748794C2semidirect
10. #11748786C2semidirect
11. #11748777C2semidirect
12. #11748747C2semidirect
13. C4×(C2×D3)⋊Dic5C2semidirect
14. #11748618C2semidirect
15. #11748600C2semidirect
28. C5×#893C4semidirect
62. #65270D3semidirect
88. C2×C4×C5×D3C2×C4semidirect
99. C3×C5×C4⋊C4C2×C4semidirect
103. C5×(C2×D3)⋊C4C2×C4semidirect
104. C4×C5×Dic3C2×C4semidirect
247. #893Dic5semidirect
292. C5×C4⋊C4C4×D3semidirect
386. C2×C4×D3C2×Dic5semidirect
388. C3×C4⋊C4C2×Dic5semidirect
397. (C2×D3)⋊C4C2×Dic5semidirect
402. C4×Dic3C2×Dic5semidirect
634. C4⋊C4D3×Dic5semidirect
646. C3×C5#2318semidirect
758. C5#74945semidirect
793. C3#10614055semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
#117510812
C3×#652702
#117489032
#117489012
#117488972
D3×#39632
#117487942
#117487862
#117487772
#117487472
C4×(C2×D3)⋊Dic52
#117486182
#117486002
#106140553
#749455