Finite Group Databasebeta

← #14324399

Subgroups — #14324399

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#940C211yesmaximal, characteristic
2C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6#11749519C211yesmaximal, characteristic, complemented
7#11749519C211yesmaximal, characteristic, complemented
8#11749501C211yesmaximal, characteristic, complemented
9#11749492C211yesmaximal, characteristic, complemented
10#11749482C211yesmaximal, characteristic, complemented
11#11749482C211yesmaximal, characteristic, complemented
12#11748901C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748643C211yesmaximal, characteristic, complemented
15#11748600C211yesmaximal, characteristic, complemented
16#10614903—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C5×#940C418yescomplemented
31C2×C4×C5×Dic3C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35#67⋊Dic5—24no—
36Dic5×#67—24no—
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74667—51nomaximal, Hall
56C2×C5×#127—31no—
57C2×D4×Dic5—31no—
58C2×D4×Dic5—31no—
59#65510—31no—
60#65510—31no—
61#65509—31no—
62#65509—31no—
63#65509—31no—
64#65509—31no—
65#65509—31no—
66#65509—31no—
67#65509—31no—
68#65509D311yescharacteristic, complemented
69#65225—31no—
70#65221—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4—41no—
77C2×C3×C5×D4C2×C414yescomplemented
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—22no—
80C22×Dic15—41no—
81C22×Dic15—41no—
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C5×#67—22no—
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C2×C5×#67—22no—
90C2×C5×#67—41no—
91C2×C5×#67—41no—
92C2×C5×#67—41no—
93C2×C5×#67—41no—
94C2×C5×#67C2×C414yescomplemented
95C2×C5×#67C2×C414yescomplemented
96C2×C5×#67C2×C414yescomplemented
97C2×C5×#67C2×C414yescomplemented
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C5×D12—41no—
101C2×C5×D12—41no—
102C2×C5×D12C2×C414yescomplemented
103C22×C3×Dic5—22no—
104C22×C3×Dic5—41no—
105C22×C3×Dic5—41no—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×D3×Dic5—22no—
111C2×D3×Dic5—22no—
112C2×D3×Dic5—41no—
113C2×D3×Dic5—41no—
114C2×D3×Dic5—41no—
115C2×D3×Dic5—41no—
116#6719—22no—
117#6719—41no—
118#6719—41no—
119C4×C5×Dic3C2×C414yescomplemented
120C3×C22⋊Dic5—22no—
121C3×C22⋊Dic5—41no—
122C3×C22⋊Dic5—41no—
123Dic3⋊Dic5—22no—
124Dic3⋊Dic5—22no—
125(C2×D3)⋊Dic5—22no—
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5—41no—
128(C2×D3)⋊Dic5—41no—
129(C2×D3)⋊Dic5—41no—
130(C2×D3)⋊Dic5—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5D414yescomplemented
133C2×#940D511yescharacteristic
134C2×C4×#67—51no—
135C2×#67⋊C4—51no—
136C3×#386—51no—
137#5220—51no—
138#5213—51no—
139#4958—51no—
140#4957—51no—
141#4957—51no—
142#4956—51no—
143#4956—51no—
144#4665—51no—
145#4665—51no—
146#4650—51no—
147#4648—51no—
148C22×C5×D4—31no—
149C22×C5×D4—31no—
150C22×C5×D4—31no—
151C22×C5×D4—31no—
152C22×C5×D4—31no—
153C22×C5×D4C2×D311yescharacteristic
154C23×Dic5—31no—
155C23×Dic5—31no—
156C23×Dic5—31no—
157C23×Dic5C2×D311yescharacteristic
158C5×#127—38no—
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5C2×D311yescharacteristic
170C2×C22⋊Dic5C2×D311yescharacteristic
171C2×C22⋊Dic5C2×D311yescharacteristic
172D4×Dic5—64no—
173D4×Dic5—64no—
174C2×C4⋊Dic5—31no—
175C2×C4⋊Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178#3963—31no—
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186#2328—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3C22×C412yes—
215C22×C5×D3C22×C412yes—
216C3×C5×D4—44no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C22×C412yes—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—44no—
232C2×Dic15C2×D412yes—
233C5×#67—28no—
234C5×#67—28no—
235C5×#67—44no—
236C5×#67—44no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3C22×C412yes—
240C2×C5×Dic3C22×C412yes—
241C2×C5×Dic3C2×D412yes—
242C2×C5×Dic3#4112yes—
243C5×D12—44no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—44no—
256C2×C3×Dic5C2×D412yes—
257D3×Dic5—44no—
258D3×Dic5—44no—
259C22×C3×D4C2×D511yescharacteristic
260C23×C3×C4—51no—
261C22×#67C2×D511yescharacteristic
262C22×#67C2×D511yescharacteristic
263C22×#67C2×D511yescharacteristic
264C22×#67C2×D511yescharacteristic
265C23×Dic3—51no—
266C22×D12C2×D511yescharacteristic
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275#940Dic518yescomplemented
276C4×#67—104no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3C2×D511yescharacteristic
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C24×C5—31no—
298C24×C5—31no—
299C24×C5C22×D311yescharacteristic
300C24×C5C22×D311yescharacteristic
301C2×C5×D4—34no—
302C2×C5×D4—34no—
303C2×C5×D4—34no—
304C2×C5×D4—34no—
305C2×C5×D4—34no—
306C2×C5×D4—41no—
307C2×C5×D4—41no—
308C2×C5×D4—62no—
309C2×C5×D4—62no—
310C2×C5×D4—62no—
311C2×C5×D4—62no—
312C2×C5×D4—121no—
313C2×C5×D4—121no—
314C2×C5×D4—121no—
315C2×C5×D4—121no—
316C2×C5×D4—121no—
317C2×C5×D4—121no—
318C2×C5×D4C4×D314yescomplemented
319C22×C4×C5—31no—
320C22×C4×C5—31no—
321C22×C4×C5C22×D311yescharacteristic
322C22×Dic5—22no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—41no—
328C22×Dic5—41no—
329C22×Dic5—62no—
330C22×Dic5—62no—
331C22×Dic5—62no—
332C22×Dic5—121no—
333C22×Dic5—121no—
334C22×Dic5—121no—
335C22×Dic5—121no—
336C22×Dic5—121no—
337C22×Dic5—121no—
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C42×C5—34no—
343C22⋊Dic5—22no—
344C22⋊Dic5—41no—
345C22⋊Dic5—41no—
346C22⋊Dic5—62no—
347C22⋊Dic5—62no—
348C22⋊Dic5—62no—
349C22⋊Dic5—121no—
350C22⋊Dic5—121no—
351C22⋊Dic5—121no—
352C22⋊Dic5—121no—
353C22⋊Dic5—121no—
354C22⋊Dic5—121no—
355C4⋊Dic5—62no—
356C4⋊Dic5—62no—
357C4×Dic5—34no—
358C4×Dic5—62no—
359C2×#127—31no—
360C2×C4×D4—151no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—51no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#386—151no—
370#386—151no—
371#386—151no—
372#382—151no—
373#376—151no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C23×C411yescharacteristic
389C22×C3×C5C22×D411yescharacteristic
390C22×C3×C5C2×#4111yescharacteristic
391C22×C3×C5H(5,𝔽2)11yescharacteristic
392C22×C3×C5H(5,𝔽2)11yescharacteristic
393C22×C3×C5H(5,𝔽2)11yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—41no—
402C2×C5×D3—41no—
403C2×C5×D3—41no—
404C2×C5×D3—41no—
405C2×C5×D3—41no—
406C2×C5×D3—41no—
407C2×C5×D3—41no—
408C2×C5×D3—41no—
409C3×C4×C5—22no—
410Dic15—22no—
411Dic15—41no—
412Dic15—41no—
413Dic15—41no—
414C3×Dic5—22no—
415C3×Dic5—41no—
416C3×Dic5—41no—
417C3×Dic5—41no—
418C5×Dic3—22no—
419C5×Dic3C4×D414yes—
420C24×C3C22×D511yescharacteristic
421C24×C3C22×D511yescharacteristic
422C23×D3C22×D511yescharacteristic
423C23×D3C22×D511yescharacteristic
424C2×C3×D4—41no—
425C2×C3×D4—41no—
426C2×C3×D4C2×Dic514yescomplemented
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—102no—
432C22×C3×C4—201no—
433C22×C3×C4—201no—
434C22×C3×C4C22×D511yescharacteristic
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—41no—
440C2×#67—41no—
441C2×#67—41no—
442C2×#67—41no—
443C2×#67C2×Dic514yescomplemented
444C2×#67C2×Dic514yescomplemented
445C2×#67C2×Dic514yescomplemented
446C2×#67C2×Dic514yescomplemented
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—102no—
452C22×Dic3—201no—
453C22×Dic3—201no—
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C2×D12—41no—
457C2×D12—41no—
458C2×D12C2×Dic514yescomplemented
459C2×C4×D3—102no—
460C2×C4×D3—102no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—201no—
467C3×C22⋊C4—201no—
468#217—102no—
469#217—201no—
470#217—201no—
471(C2×D3)⋊C4—102no—
472(C2×D3)⋊C4—102no—
473(C2×D3)⋊C4—201no—
474(C2×D3)⋊C4—201no—
475(C2×D3)⋊C4—201no—
476(C2×D3)⋊C4—201no—
477Dic3⋊C4—102no—
478Dic3⋊C4—102no—
479C4×Dic3—54no—
480C4×Dic3—102no—
481C4×Dic3C2×Dic514yescomplemented
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5—32no—
495C23×C5—32no—
496C23×C5—61no—
497C23×C5—61no—
498C23×C5—61no—
499C23×C5—61no—
500C23×C5—61no—
501C23×C5—61no—
502C23×C5—61no—
503C23×C5—61no—
504C23×C5—61no—
505C23×C5—61no—
506C23×C5—61no—
507C23×C5—61no—
508C23×C5C2×C4×D312yes—
509C23×C5C2×C4×D312yes—
510C23×C5C23×D311yescharacteristic
511C5×D4—44no—
512C5×D4—68no—
513C5×D4—68no—
514C5×D4—124no—
515C5×D4—124no—
516C5×D4—124no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—32no—
520C2×C4×C5—32no—
521C2×C4×C5—32no—
522C2×C4×C5—32no—
523C2×C4×C5—61no—
524C2×C4×C5—61no—
525C2×C4×C5C2×C4×D312yes—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—21no—
531C2×Dic5—21no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—32no—
538C2×Dic5—44no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—124no—
551C2×Dic5—124no—
552C2×Dic5—124no—
553C2×Dic5D3×D412yes—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—31no—
557C22×D4—31no—
558C22×D4—31no—
559C22×D4D3×D511yescharacteristic
560C23×C4—51no—
561C23×C4—151no—
562C23×C4—151no—
563C23×C4—151no—
564#127—38no—
565C4×D4—304no—
566C4×D4—304no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C22⋊C4—51no—
570C2×C22⋊C4—51no—
571C2×C22⋊C4—51no—
572C2×C22⋊C4—151no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C42—31no—
582C2×C42—151no—
583C2×C42—151no—
584#95—51no—
585#95—51no—
586#95—151no—
587#95—151no—
588#95—151no—
589#95—151no—
590#95—151no—
591#95—151no—
592C2×C3×C5—42no—
593C2×C3×C5—42no—
594C2×C3×C5C2×C4×D411yescharacteristic
595C2×C3×C5#51811yescharacteristic
596C2×C3×C5#51811yescharacteristic
597C2×C3×C5#53511yescharacteristic
598C2×C3×C5#53511yescharacteristic
599C2×C3×C5#54011yescharacteristic
600C2×C3×C5#54011yescharacteristic
601C5×D3—42no—
602C5×D3—42no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3C22×Dic512yes—
616C23×C3C22×Dic512yes—
617C23×C3C23×D511yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3C22×Dic512yes—
631C22×D3C22×Dic512yes—
632C3×D4—44no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—52no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—204no—
648C2×C3×C4C22×Dic512yes—
649#67—28no—
650#67—28no—
651#67—44no—
652#67—44no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—52no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—204no—
668C2×Dic3D4×D512yes—
669C2×Dic3#71112yes—
670C2×Dic3C22×Dic512yes—
671C2×Dic3C22×Dic512yes—
672D12—44no—
673C4×D3—204no—
674C4×D3—204no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—41no—
682C22×C5—41no—
683C22×C5—41no—
684C22×C5—41no—
685C22×C5—41no—
686C22×C5—41no—
687C22×C5—41no—
688C22×C5—41no—
689C22×C5—62no—
690C22×C5—62no—
691C22×C5—62no—
692C22×C5—62no—
693C22×C5—62no—
694C22×C5—62no—
695C22×C5—121no—
696C22×C5—121no—
697C22×C5—121no—
698C22×C5—121no—
699C22×C5—121no—
700C22×C5—121no—
701C22×C5—121no—
702C22×C5—121no—
703C22×C5C22×C4×D311yescharacteristic
704C22×C5C2×D3×D411yescharacteristic
705C22×C5#100411yescharacteristic
706C22×C5#100411yescharacteristic
707C22×C5#100411yescharacteristic
708C22×C5D3×#4111yescharacteristic
709C22×C5#100911yescharacteristic
710C4×C5—22no—
711C4×C5—34no—
712C4×C5—62no—
713Dic5—22no—
714Dic5—41no—
715Dic5—41no—
716Dic5—41no—
717Dic5—62no—
718Dic5—121no—
719Dic5—121no—
720Dic5—121no—
721C24—31no—
722C24—31no—
723C24C2×D3×D511yescharacteristic
724C24C2×D3×D511yescharacteristic
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—34no—
730C2×D4—41no—
731C2×D4—41no—
732C2×D4—62no—
733C2×D4—62no—
734C2×D4—62no—
735C2×D4—62no—
736C2×D4—121no—
737C2×D4—121no—
738C2×D4—121no—
739C2×D4—121no—
740C2×D4—121no—
741C2×D4—121no—
742C2×D4D3×Dic514yescomplemented
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—102no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—201no—
755C22×C4—201no—
756C22×C4—302no—
757C22×C4—302no—
758C22×C4—302no—
759C22×C4—601no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4—601no—
764C22×C4—601no—
765C22×C4C2×D3×D511yescharacteristic
766C4⋊C4—302no—
767C4⋊C4—302no—
768C22⋊C4—102no—
769C22⋊C4—201no—
770C22⋊C4—201no—
771C22⋊C4—302no—
772C22⋊C4—302no—
773C22⋊C4—302no—
774C22⋊C4—601no—
775C22⋊C4—601no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—34no—
781C42—154no—
782C42—302no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3C2×D4×D511yescharacteristic
799C22×C3C2×#71111yescharacteristic
800C22×C3#414411yescharacteristic
801C22×C3#414411yescharacteristic
802C22×C3#414411yescharacteristic
803C22×C3#414411yescharacteristic
804C22×C3C23×Dic511yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C3×C4—22no—
820C3×C4—102no—
821C3×C4—201no—
822C3×C4—201no—
823C3×C4—201no—
824Dic3—22no—
825Dic3—102no—
826Dic3—201no—
827Dic3—201no—
828Dic3—201no—
829Dic3D4×Dic514yes—
830C2×C5—42no—
831C2×C5—42no—
832C2×C5—122no—
833C2×C5—122no—
834C2×C5#548611yescharacteristic
835C2×C5C4×D3×D411yescharacteristic
836C2×C5#554511yescharacteristic
837C2×C5#559211yescharacteristic
838C2×C5#560711yescharacteristic
839C2×C5#561511yescharacteristic
840C2×C5#566311yescharacteristic
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—32no—
854C23—32no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23C2×D3×Dic512yes—
868C23C2×D3×Dic512yes—
869C23C22×D3×D511yescharacteristic
870D4—44no—
871D4—68no—
872D4—68no—
873D4—124no—
874D4—124no—
875D4—124no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—52no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—101no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—101no—
889C2×C4—101no—
890C2×C4—101no—
891C2×C4—101no—
892C2×C4—101no—
893C2×C4—101no—
894C2×C4—101no—
895C2×C4—101no—
896C2×C4—152no—
897C2×C4—204no—
898C2×C4—301no—
899C2×C4—301no—
900C2×C4—301no—
901C2×C4—301no—
902C2×C4—301no—
903C2×C4—301no—
904C2×C4—301no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—301no—
909C2×C4—604no—
910C2×C4—604no—
911C2×C4—604no—
912C2×C4C2×D3×Dic512yes—
913C2×C3—42no—
914C2×C3—42no—
915C2×C3#6604911yescharacteristic
916C2×C3#6604911yescharacteristic
917C2×C3#6605311yescharacteristic
918C2×C3#6605311yescharacteristic
919C2×C3C2×D4×Dic511yescharacteristic
920C2×C3#6613211yescharacteristic
921C2×C3#6613211yescharacteristic
922D3—42no—
923D3—42no—
924C5#7466711yescharacteristic, complemented, Sylow
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—121no—
952C22—121no—
953C22D3×D4×D511yescharacteristic
954C22D3×#71111yescharacteristic
955C22#9202511yescharacteristic
956C22#9202711yescharacteristic
957C22C22×D3×Dic511yescharacteristic
958C22#9204911yescharacteristic
959C22#9204911yescharacteristic
960C4—22no—
961C4—34no—
962C4—62no—
963C4—102no—
964C4—201no—
965C4—201no—
966C4—201no—
967C4—302no—
968C4—601no—
969C4—601no—
970C4—601no—
971C3#1061490311yescharacteristic, complemented, Sylow
972C2—42no—
973C2—42no—
974C2—122no—
975C2—122no—
976C2D3×D4×Dic511yescharacteristic
977C2#1175486911yescharacteristic
978C2#1175488111yescharacteristic
979C2#1175491411yescharacteristic
980C2#1175503011yescharacteristic
981C2#1175505011yescharacteristic
982C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#940C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#67⋊Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. #11751321C2semidirect
5. C3×#65509C2semidirect
6. #11749519C2semidirect
7. #11749519C2semidirect
8. #11749501C2semidirect
9. #11749492C2semidirect
10. #11749482C2semidirect
11. #11749482C2semidirect
12. #11748901C2semidirect
13. #11748901C2semidirect
14. #11748643C2semidirect
15. #11748600C2semidirect
30. C5×#940C4semidirect
68. #65509D3semidirect
77. C2×C3×C5×D4C2×C4semidirect
94. C2×C5×#67C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
96. C2×C5×#67C2×C4semidirect
97. C2×C5×#67C2×C4semidirect
102. C2×C5×D12C2×C4semidirect
119. C4×C5×Dic3C2×C4semidirect
132. Dic3×Dic5D4semidirect
275. #940Dic5semidirect
318. C2×C5×D4C4×D3semidirect
426. C2×C3×D4C2×Dic5semidirect
443. C2×#67C2×Dic5semidirect
444. C2×#67C2×Dic5semidirect
445. C2×#67C2×Dic5semidirect
446. C2×#67C2×Dic5semidirect
458. C2×D12C2×Dic5semidirect
481. C4×Dic3C2×Dic5semidirect
742. C2×D4D3×Dic5semidirect
783. C3×C5#2328semidirect
924. C5#74667semidirect
971. C3#10614903semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9402
C2×#67⋊Dic52
C2×Dic5×#672
#117513212
C3×#655092
#117495192
#117495012
#117494922
#117494822
#117489012
#117486432
#117486002
#106149033
#746675