Finite Group Databasebeta

← D5×#4670 #14320461

Subgroups — D5×#4670 #14320461

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
6#11750771C211yesmaximal, characteristic, complemented
7C5×#4670C211yesmaximal, characteristic, complemented
8C3×D5×#95C211yesmaximal, characteristic, complemented
9D5×C3⋊#95C211yesmaximal, characteristic, complemented
10#11748730C211yesmaximal, characteristic, complemented
11#11748724C211yesmaximal, characteristic, complemented
12#11748723C211yesmaximal, characteristic, complemented
13#11748686C211yesmaximal, characteristic, complemented
14#11748685C211yesmaximal, characteristic, complemented
15#11748671C211yesmaximal, characteristic, complemented
16D5×#388—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic, complemented
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C2×#6668C2211yescharacteristic, complemented
35C2×#6668C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic, complemented
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44D5×(C2×D3)⋊C4—24no—
45D5×(C2×D3)⋊C4—24no—
46D5×(C2×D3)⋊C4C418yescomplemented
47D5×C4⋊Dic3—24no—
48C4×D5×Dic3—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C5×C3⋊#95C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57C2×#4670—51nomaximal, Hall
58C2×D5×C4⋊C4—31no—
59C2×D5×C22⋊C4—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4—31no—
62C2×C42×D5—31no—
63C5×#388—31no—
64#65279—31no—
65#65240—31no—
66#65234—31no—
67#65233—31no—
68#65229—31no—
69#64959—31no—
70#64958—31no—
71D5×#95—31no—
72D5×#95D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×D3×D5—22no—
77C22×D3×D5—22no—
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—22no—
82C22×D3×D5C2×C414yes—
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5C2×C414yes—
103C2×C3×C4×D5D414yes—
104C2×D5×Dic3—22no—
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3—22no—
108C2×D5×Dic3—22no—
109C2×D5×Dic3—22no—
110C2×D5×Dic3—22no—
111C2×D5×Dic3C2×C414yes—
112C2×D5×Dic3D414yes—
113#6714—22no—
114#6714—22no—
115#6714C2×C414yescomplemented
116C4⋊Dic15—22no—
117C4×Dic15—22no—
118C5×(C2×D3)⋊C4—22no—
119C5×(C2×D3)⋊C4—22no—
120C5×(C2×D3)⋊C4C2×C414yescomplemented
121C5×C4⋊Dic3—22no—
122C4×C5×Dic3—22no—
123#6668—22no—
124#6668—22no—
125#6667—22no—
126#6667—22no—
127#6667C2×C414yescomplemented
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5—22no—
130(C2×D3)⋊Dic5C2×C414yescomplemented
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C22×(C2×D3)⋊C4—51no—
134C22×(C2×D3)⋊C4—51no—
135C22×(C2×D3)⋊C4—51no—
136C22×C4⋊Dic3—51no—
137C22×C4×Dic3—51no—
138C2×C3×#95—51no—
139C2×C3⋊#95—51no—
140#4670—51no—
141#4670—51no—
142#4670—51no—
143#4670—51no—
144#4670—51no—
145#4670—51no—
146#4670—51no—
147#4670D511yescharacteristic, direct product factor
148C24×D5—31no—
149C22×C4×D5—31no—
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5C2×D311yescharacteristic
153C22×C4×D5C2×D311yescharacteristic
154C22×C4×D5C2×D311yescharacteristic
155C2×C5×C4⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×C4⋊Dic5—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—31no—
175D5×C4⋊C4—64no—
176D5×C22⋊C4—38no—
177D5×C22⋊C4—64no—
178D5×C22⋊C4—64no—
179C42×D5—64no—
180C5×#95—31no—
181C5×#95C2×D311yescharacteristic, complemented
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963C2×D311yescharacteristic, complemented
186#3963C2×D311yescharacteristic, complemented
187#3963C2×D311yescharacteristic, complemented
188C2×#388—151noSylow
189C23×C3×C5C2411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15C22×C412yes—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C5×D3C22×C412yes—
204C22×C3×D5C22×C412yes—
205C22×C3×D5C2×D412yes—
206C22×C3×D5C2×D412yes—
207C22×C3×D5#4112yes—
208C22×C3×D5#4112yes—
209C22×C3×D5#4112yes—
210C22×C3×D5#4112yes—
211C2×D3×D5—28no—
212C2×D3×D5—28no—
213C2×D3×D5—28no—
214C2×D3×D5—44no—
215C2×D3×D5—44no—
216C2×D3×D5—44no—
217C2×D3×D5—44no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C22×C412yes—
226C2×C3×C4×C5C2×D412yes—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15C22×C412yes—
235C2×Dic15C2×D412yes—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3C22×C412yes—
244C2×C5×Dic3C2×D412yes—
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×Dic5C22×C412yes—
253C2×C3×Dic5C2×D412yes—
254C3×C4×D5—28no—
255C3×C4×D5—28no—
256C3×C4×D5—44no—
257D5×Dic3—28no—
258D5×Dic3—28no—
259D5×Dic3—44no—
260C24×D3—51no—
261C23×C3×C4—51no—
262C23×C3×C4—51no—
263C23×C3×C4—51no—
264C23×Dic3—51no—
265C23×Dic3—51no—
266C23×Dic3—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—58no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—104no—
278C2×(C2×D3)⋊C4—104no—
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—104no—
286C2×C4⋊Dic3C2×D511yescharacteristic, complemented
287C2×C4×Dic3—51no—
288C2×C4×Dic3—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3—104no—
291C2×C4×Dic3C2×D511yescharacteristic, complemented
292C3×#95—51no—
293C3×#95—51no—
294C3×#95—51no—
295C3×#95C2×D511yescharacteristic, complemented
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5—31no—
301C23×D5—31no—
302C23×D5—34no—
303C23×D5—62no—
304C23×D5—62no—
305C23×D5—62no—
306C23×D5—62no—
307C23×D5—62no—
308C23×D5—62no—
309C23×D5C22×D311yescharacteristic
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5C22×D311yescharacteristic
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×C4×D5—22no—
323C2×C4×D5—22no—
324C2×C4×D5—22no—
325C2×C4×D5—22no—
326C2×C4×D5—22no—
327C2×C4×D5—22no—
328C2×C4×D5—22no—
329C2×C4×D5—34no—
330C2×C4×D5—34no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—62no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5C4×D314yes—
339C2×C4×D5D1214yes—
340C5×C4⋊C4—62no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—62no—
344C42×C5—62no—
345C22⋊Dic5—34no—
346C22⋊Dic5—62no—
347C22⋊Dic5—62no—
348#685—34no—
349#685—34no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354C4⋊Dic5—62no—
355#683—62no—
356#683—62no—
357C4×Dic5—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×C4⋊C4—151no—
361C22×C22⋊C4—151no—
362C22×C22⋊C4—151no—
363C22×C22⋊C4—151no—
364C22×C42—151no—
365#388—31no—
366#388—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#388—151no—
372#388—151no—
373C2×#95—51no—
374C2×#95—151no—
375C22×C3×C5C23×C411yescharacteristic
376C22×C3×C5C22×D411yescharacteristic
377C22×C3×C5C22×D411yescharacteristic
378C22×C3×C5C2×#4111yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5C2×#4111yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—22no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C3×D5#11714yes—
397C2×C3×D5C4×D414yes—
398C2×C3×D5C4×D414yes—
399C2×C3×D5#12114yes—
400C2×C3×D5#12314yes—
401C2×C3×D5#12414yes—
402C2×C3×D5#12614yes—
403D3×D5—416no—
404C3×C4×C5—22no—
405C3×C4×C5—22no—
406C3×C4×C5—41no—
407Dic15—22no—
408Dic15—22no—
409Dic15—41no—
410C3×Dic5—22no—
411C3×Dic5—22no—
412C3×Dic5—41no—
413C5×Dic3—22no—
414C5×Dic3—22no—
415C5×Dic3—41no—
416C24×C3—51no—
417C23×D3—51no—
418C23×D3—54no—
419C23×D3—102no—
420C23×D3—102no—
421C23×D3—102no—
422C23×D3—102no—
423C23×D3—102no—
424C23×D3—102no—
425C23×D3C22×D511yescharacteristic
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—54no—
429C22×C3×C4—54no—
430C22×C3×C4—51no—
431C22×C3×C4—102no—
432C22×C3×C4—102no—
433C22×C3×C4—102no—
434C22×C3×C4—102no—
435C22×C3×C4—102no—
436C22×C3×C4—102no—
437C22×C3×C4—102no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—54no—
444C22×Dic3—54no—
445C22×Dic3—51no—
446C22×Dic3—102no—
447C22×Dic3—102no—
448C22×Dic3—102no—
449C22×Dic3—102no—
450C22×Dic3—102no—
451C22×Dic3—102no—
452C22×Dic3—102no—
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—54no—
459(C2×D3)⋊C4—54no—
460(C2×D3)⋊C4—54no—
461(C2×D3)⋊C4—102no—
462(C2×D3)⋊C4—102no—
463(C2×D3)⋊C4—102no—
464(C2×D3)⋊C4—102no—
465(C2×D3)⋊C4—102no—
466(C2×D3)⋊C4—102no—
467(C2×D3)⋊C4C4×D514yescomplemented
468C4⋊Dic3—22no—
469C4⋊Dic3—102no—
470C4⋊Dic3—102no—
471C4⋊Dic3—102no—
472C4×Dic3—22no—
473C4×Dic3—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—32no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5C23×D311yescharacteristic
484C22×D5—32no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—68no—
492C22×D5—68no—
493C22×D5—68no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5C2×C4×D312yes—
499C22×D5C2×D1212yes—
500C22×D5#23512yes—
501C22×D5D3×D412yes—
502C22×D5#23712yes—
503C22×D5#23712yes—
504C22×D5#23912yes—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5C2×C4×D312yes—
522C2×C4×C5C2×D1212yes—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—32no—
531C2×Dic5—32no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5C2×C4×D312yes—
540C2×Dic5C2×D1212yes—
541C4×D5—28no—
542C4×D5—28no—
543C4×D5—44no—
544C4×D5—68no—
545C4×D5—68no—
546C4×D5—124no—
547C25—151no—
548C23×C4—51no—
549C23×C4—51no—
550C23×C4—51no—
551C23×C4—151no—
552C23×C4—151no—
553C23×C4—151no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—151no—
556C2×C4⋊C4—151no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—304no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—158no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C22⋊C4—151no—
572C2×C22⋊C4—304no—
573C2×C22⋊C4—304no—
574C2×C42—31no—
575C2×C42—151no—
576C2×C42—151no—
577C2×C42—151no—
578C2×C42—304no—
579#95—31no—
580#95—51no—
581#95—51no—
582#95—51no—
583#95—151no—
584#95—151no—
585#95—151no—
586#95D3×D511yescharacteristic, complemented
587C2×C3×C5C2×#11711yescharacteristic
588C2×C3×C5C2×C4×D411yescharacteristic
589C2×C3×C5C2×C4×D411yescharacteristic
590C2×C3×C5C2×#12111yescharacteristic
591C2×C3×C5C2×#12311yescharacteristic
592C2×C3×C5C2×#12411yescharacteristic
593C2×C3×C5C2×#12611yescharacteristic
594D15—42no—
595C3×D5#38818yescomplemented
596C5×D3—42no—
597C23×C3—52no—
598C23×C3—52no—
599C23×C3—52no—
600C23×C3—52no—
601C23×C3—52no—
602C23×C3—52no—
603C23×C3—52no—
604C23×C3C23×D511yescharacteristic
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—52no—
612C22×D3—108no—
613C22×D3—108no—
614C22×D3—108no—
615C22×D3—101no—
616C22×D3—101no—
617C22×D3—101no—
618C22×D3—101no—
619C22×D3—101no—
620C22×D3—101no—
621C22×D3—204no—
622C22×D3—204no—
623C22×D3—204no—
624C22×D3—204no—
625C22×D3C2×C4×D512yes—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—52no—
634C2×C3×C4—52no—
635C2×C3×C4—108no—
636C2×C3×C4—108no—
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—204no—
645C2×C3×C4C2×C4×D512yes—
646C2×C3×C4D4×D512yes—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—52no—
655C2×Dic3—52no—
656C2×Dic3—108no—
657C2×Dic3—108no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—204no—
666C2×Dic3C2×C4×D512yes—
667C2×Dic3D4×D512yes—
668C22×C5—62no—
669C22×C5—62no—
670C22×C5—62no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5—121no—
674C22×C5—121no—
675C22×C5C22×C4×D311yescharacteristic
676C22×C5C22×D1211yescharacteristic
677C22×C5C2×#23511yescharacteristic
678C22×C5C2×D3×D411yescharacteristic
679C22×C5C2×#23711yescharacteristic
680C22×C5C2×#23711yescharacteristic
681C22×C5C2×#23911yescharacteristic
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—121no—
686C2×D5—121no—
687C2×D5—121no—
688C2×D5—121no—
689C2×D5—1216no—
690C2×D5C4×D1214yes—
691C2×D5#67⋊C414yes—
692C2×D5#88514yes—
693C2×D5#88614yes—
694C2×D5#89214yes—
695C2×D5#89514yes—
696C2×D5#89814yes—
697C4×C5—22no—
698C4×C5—22no—
699C4×C5—41no—
700C4×C5—62no—
701C4×C5—62no—
702C4×C5—121no—
703Dic5—22no—
704Dic5—22no—
705Dic5—41no—
706Dic5—62no—
707Dic5—62no—
708Dic5—121no—
709C24—31no—
710C24—51no—
711C24—154no—
712C24—151no—
713C24—302no—
714C24—302no—
715C24—302no—
716C24—302no—
717C24—302no—
718C24—302no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—51no—
723C22×C4—51no—
724C22×C4—54no—
725C22×C4—54no—
726C22×C4—51no—
727C22×C4—102no—
728C22×C4—102no—
729C22×C4—102no—
730C22×C4—102no—
731C22×C4—102no—
732C22×C4—102no—
733C22×C4—102no—
734C22×C4—154no—
735C22×C4—154no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4C2×D3×D511yescharacteristic
747C22×C4C2×D3×D511yescharacteristic
748C22×C4C2×D3×D511yescharacteristic
749C4⋊C4—62no—
750C4⋊C4—302no—
751C4⋊C4—302no—
752C4⋊C4—302no—
753C22⋊C4—34no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—154no—
757C22⋊C4—154no—
758C22⋊C4—154no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—302no—
762C22⋊C4—302no—
763C22⋊C4—302no—
764C22⋊C4—302no—
765C42—62no—
766C42—302no—
767C42—302no—
768C42—302no—
769C3×C5C2×#38811yescharacteristic, complemented, Hall
770C22×C3—54no—
771C22×C3—54no—
772C22×C3—54no—
773C22×C3—54no—
774C22×C3—54no—
775C22×C3—54no—
776C22×C3—54no—
777C22×C3C22×C4×D511yescharacteristic
778C22×C3C2×D4×D511yescharacteristic
779C22×C3C2×D4×D511yescharacteristic
780C22×C3D5×#4111yescharacteristic
781C22×C3D5×#4111yescharacteristic
782C22×C3D5×#4111yescharacteristic
783C22×C3D5×#4111yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—2016no—
795C2×D3—201no—
796C2×D3—201no—
797C2×D3—201no—
798C2×D3—201no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—41no—
802C3×C4—102no—
803C3×C4—102no—
804C3×C4—201no—
805Dic3—22no—
806Dic3—22no—
807Dic3—41no—
808Dic3—102no—
809Dic3—102no—
810Dic3—201no—
811C2×C5—122no—
812C2×C5C2×C4×D1211yescharacteristic
813C2×C5C2×#67⋊C411yescharacteristic
814C2×C5C2×#88511yescharacteristic
815C2×C5C2×#88611yescharacteristic
816C2×C5C2×#89211yescharacteristic
817C2×C5C2×#89511yescharacteristic
818C2×C5C2×#89811yescharacteristic
819D5—122no—
820D5#467018yesdirect product factor
821C23—32no—
822C23—52no—
823C23—52no—
824C23—52no—
825C23—52no—
826C23—52no—
827C23—52no—
828C23—52no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—152no—
836C23—308no—
837C23—308no—
838C23—308no—
839C23—301no—
840C23—301no—
841C23—301no—
842C23—301no—
843C23—301no—
844C23—301no—
845C23—604no—
846C23—604no—
847C23—604no—
848C23—604no—
849C23C22×D3×D511yescharacteristic
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—52no—
860C2×C4—52no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—108no—
869C2×C4—108no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—152no—
878C2×C4—152no—
879C2×C4—204no—
880C2×C4—308no—
881C2×C4—308no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—604no—
890C2×C4C4×D3×D512yes—
891C2×C4D5×D1212yes—
892C2×C3—58no—
893C2×C3D5×#11711yescharacteristic
894C2×C3C4×D4×D511yescharacteristic
895C2×C3C4×D4×D511yescharacteristic
896C2×C3D5×#12111yescharacteristic
897C2×C3D5×#12311yescharacteristic
898C2×C3D5×#12411yescharacteristic
899C2×C3D5×#12611yescharacteristic
900D3—42no—
901D3—202no—
902C5C2×#467011yescharacteristic, complemented, Sylow
903C22—54no—
904C22—54no—
905C22—54no—
906C22—54no—
907C22—54no—
908C22—54no—
909C22—54no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—302no—
918C22—302no—
919C22—302no—
920C22—6016no—
921C22—601no—
922C22—601no—
923C22—601no—
924C22—601no—
925C22C2×C4×D3×D511yescharacteristic
926C22C2×D5×D1211yescharacteristic
927C22D5×#23511yescharacteristic
928C22D3×D4×D511yescharacteristic
929C22D5×#23711yescharacteristic
930C22D5×#23711yescharacteristic
931C22D5×#23911yescharacteristic
932C4—22no—
933C4—22no—
934C4—41no—
935C4—62no—
936C4—62no—
937C4—102no—
938C4—102no—
939C4—121no—
940C4—201no—
941C4—302no—
942C4—302no—
943C4—601no—
944C3D5×#38811yescharacteristic, complemented, Sylow
945C2—58no—
946C2—122no—
947C2—602no—
948C2C4×D5×D1211yescharacteristic
949C2D5×#67⋊C411yescharacteristic
950C2D5×#88511yescharacteristic
951C2D5×#88611yescharacteristic
952C2D5×#89211yescharacteristic
953C2D5×#89511yescharacteristic
954C2D5×#89811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D5×C4⋊Dic3C2semidirect
5. C2×C4×D5×Dic3C2semidirect
6. #11750771C2semidirect
7. C5×#4670C2semidirect
8. C3×D5×#95C2semidirect
9. D5×C3⋊#95C2semidirect
10. #11748730C2semidirect
11. #11748724C2semidirect
12. #11748723C2semidirect
13. #11748686C2semidirect
14. #11748685C2semidirect
15. #11748671C2semidirect
27. C2×C4⋊Dic15C22semidirect
28. C2×C4×Dic15C22semidirect
32. C2×C5×C4⋊Dic3C22semidirect
33. C2×C4×C5×Dic3C22semidirect
34. C2×#6668C22semidirect
35. C2×#6668C22semidirect
42. C2×Dic3×Dic5C22semidirect
43. C2×Dic3×Dic5C22semidirect
46. D5×(C2×D3)⋊C4C4semidirect
49. C3×C5×#95C22semidirect
50. #91115C22semidirect
51. C5×C3⋊#95C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. D5×#95D3semidirect
115. #6714C2×C4semidirect
120. C5×(C2×D3)⋊C4C2×C4semidirect
127. #6667C2×C4semidirect
130. (C2×D3)⋊Dic5C2×C4semidirect
147. #4670D5direct (N × H)
181. C5×#95C2×D3semidirect
185. #3963C2×D3semidirect
186. #3963C2×D3semidirect
187. #3963C2×D3semidirect
286. C2×C4⋊Dic3C2×D5semidirect
291. C2×C4×Dic3C2×D5semidirect
295. C3×#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
467. (C2×D3)⋊C4C4×D5semidirect
586. #95D3×D5semidirect
595. C3×D5#388semidirect
769. C3×C5C2×#388semidirect
820. D5#4670direct (N × H)
902. C5C2×#4670semidirect
944. C3D5×#388semidirect

Maximal subgroups

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

subgroupindex
C2×D5×(C2×D3)⋊C42
C2×D5×C4⋊Dic32
C2×C4×D5×Dic32
#117507712
C5×#46702
C3×D5×#952
D5×C3⋊#952
#117487302
#117487242
#117487232
#117486862
#117486852
#117486712
D5×#3883
C2×#46705