Finite Group Databasebeta

← D5×#5006 #14411935

Subgroups — D5×#5006 #14411935

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C3×D5×#117C211yesmaximal, characteristic, complemented
3D5×#926C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5C5×#5006C211yesmaximal, characteristic, complemented
6#11748626C211yesmaximal, characteristic, complemented
7#11748625C211yesmaximal, characteristic, complemented
8#11747129C214yesmaximal, complemented
9D5×#806C214yesmaximal, complemented
10D5×#410—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C2×D5×#67C2212yes—
15C2×#6782C2212yes—
16D5×#235—21no—
17D5×#235—21no—
18D5×#235—21no—
19D5×#235—21no—
20D5×#235—21no—
21D5×#235—21no—
22D5×#235—21no—
23D5×#235—21no—
24C2×D5×D12C411yescharacteristic, complemented
25C2×C4×D3×D5C412yescomplemented
26C2×#6773C411yescharacteristic, complemented
27C2×#6772C411yescharacteristic, complemented
28C2×#6771C412yescomplemented
29C2×D5×Dic6C411yescharacteristic, complemented
30C3×C5×#117C2211yescharacteristic, complemented
31#91815C2211yescharacteristic, complemented
32C5×#926C2211yescharacteristic, complemented
33C3×#4072C2211yescharacteristic, complemented
34C3×#4038—21no—
35C3×D5×C4⋊C4—21no—
36C3×D5×C22⋊C4C2212yes—
37C3×#4023C2212yescomplemented
38C3×#4018—21no—
39C3×C42×D5—21no—
40D5×#217C2212yes—
41#91528C2212yescomplemented
42D5×C4⋊Dic3—21no—
43C4×D5×Dic3—21no—
44#91358—21no—
45#91357—21no—
46#91090C2214yescomplemented
47C5×#806C2214yescomplemented
48#90997C2214yescomplemented
49#90996C2214yescomplemented
50C2×#5006—51nomaximal, Hall
51C2×D5×#41—31no—
52D5×#117—31no—
53D5×#117D311yescharacteristic, complemented
54C5×#410—31no—
55#65529—31no—
56#65295—31no—
57#65295—31no—
58D5×#99—34no—
59#65029—34no—
60C23×C3×D5C2311yescharacteristic
61C22×D3×D5C2×C412yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220C2312yes—
64#6817—21no—
65#6817—21no—
66#6817—21no—
67#6817—21no—
68C2×D60C2×C411yescharacteristic, complemented
69C2×C4×D15C2×C412yescomplemented
70C2×Dic30C2×C411yescharacteristic, complemented
71C2×C5×#67C2312yes—
72C5×#235—21no—
73C5×#235—21no—
74C5×#235—21no—
75C5×#235—21no—
76C2×C5×D12C2×C411yescharacteristic, complemented
77C2×C4×C5×D3C2×C412yescomplemented
78C2×C5×Dic6C2×C411yescharacteristic, complemented
79C22×C3×Dic5C2311yescharacteristic
80C2×C3×C4×D5—22no—
81C2×C3×C4×D5C2×C411yescharacteristic
82C2×C3×C4×D5C2×C411yescharacteristic
83C2×C3×C4×D5C2×C411yescharacteristic
84C2×C3×C4×D5C2×C411yescharacteristic
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5D411yescharacteristic
87C2×C3×C4×D5D411yescharacteristic
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D411yescharacteristic
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5D411yescharacteristic
92C2×C3×C4×D5D411yescharacteristic
93D5×#67—22no—
94D5×#67—22no—
95D5×#67—22no—
96D5×#67—22no—
97C2×#1204C2×C412yescomplemented
98C2×#1203C2×C412yescomplemented
99C2×#1202C2×C412yes—
100C2×#1201C2×C412yes—
101C2×#1200C2×C412yescomplemented
102#6782—22no—
103#6782—22no—
104#6782—22no—
105#6782—22no—
106C2×D3×Dic5C2×C412yescomplemented
107C2×D5×Dic3—22no—
108C2×D5×Dic3C2×C412yes—
109D5×D12—21no—
110D5×D12—21no—
111D5×D12—21no—
112D5×D12—21no—
113C4×D3×D5—22no—
114C4×D3×D5—22no—
115C4×D3×D5—22no—
116C4×D3×D5—22no—
117#6773—21no—
118#6773—21no—
119#6773—21no—
120#6773—21no—
121#6772—21no—
122#6772—21no—
123#6772—21no—
124#6772—21no—
125#6771—22no—
126#6771—22no—
127#6771—22no—
128#6771—22no—
129D5×Dic6—21no—
130D5×Dic6—21no—
131D5×Dic6—21no—
132D5×Dic6—21no—
133C3×C5×C4⋊C4—21no—
134C3×C5×C22⋊C4C2312yes—
135C3×C42×C5—21no—
136#6719C2312yes—
137C4⋊Dic15—21no—
138C4×Dic15—21no—
139C5×#217C2312yes—
140C5×C4⋊Dic3—21no—
141C4×C5×Dic3—21no—
142C3×C22⋊Dic5C2312yes—
143C3×#685—22no—
144C3×C4⋊Dic5—21no—
145C3×#683—22no—
146C3×C4×Dic5—21no—
147C3×C4×Dic5—22no—
148#6668—22no—
149#6665—22no—
150Dic3×Dic5—22no—
151C22×#235—51no—
152C2×C3×#117—51no—
153C2×#926—51no—
154#5006—51no—
155#5006—51no—
156#5006—51no—
157#5006—54no—
158#5006D511yescharacteristic, direct product factor
159C2×#806—54no—
160C2×C5×#41—31no—
161D5×#41—61no—
162D5×#41—61no—
163D5×#41—61no—
164D5×#41—61no—
165D5×#41—61no—
166D5×#41—61no—
167D5×#41—61no—
168D5×#41—61no—
169C2×#713—31no—
170C2×Q8×D5—31no—
171C2×#711—32no—
172C2×#711—31no—
173C2×D4×D5—32no—
174C2×D4×D5—31no—
175C2×#709—31no—
176C2×#709—32no—
177C22×C4×D5—32no—
178C22×C4×D5C2×D311yescharacteristic
179C5×#117—31no—
180C5×#117C2×D311yescharacteristic, complemented
181#4072—31no—
182#4072C2×D311yescharacteristic, complemented
183#4038—21no—
184#4038—61no—
185D5×C4⋊C4—21no—
186D5×C4⋊C4—61no—
187D5×C22⋊C4—32no—
188D5×C22⋊C4C2×D312yes—
189#4023—32no—
190#4023C2×D312yescomplemented
191#4018—21no—
192#4018—61no—
193C42×D5—21no—
194C42×D5—61no—
195C5×#99—34no—
196#3966—34no—
197#3938—34no—
198#3938—34no—
199C2×#410—151noSylow
200C23×C3×C5C2411yescharacteristic
201C22×D15C22×C412yes—
202C22×C5×D3C22×C412yes—
203C22×C3×D5—42no—
204C22×C3×D5C22×C411yescharacteristic
205C22×C3×D5C22×C411yescharacteristic
206C22×C3×D5C2×D411yescharacteristic
207C22×C3×D5C2×D411yescharacteristic
208C22×C3×D5C2×D411yescharacteristic
209C22×C3×D5C2×D411yescharacteristic
210C2×D3×D5—22no—
211C2×D3×D5—22no—
212C2×D3×D5—44no—
213C2×C3×C4×C5—22no—
214C2×C3×C4×C5C22×C411yescharacteristic
215C2×C3×C4×C5C22×C411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2×D411yescharacteristic
220#1220—22no—
221#1220—22no—
222C2×Dic15—22no—
223C2×Dic15C22×C412yes—
224D60—21no—
225D60—21no—
226C4×D15—22no—
227C4×D15—22no—
228Dic30—21no—
229Dic30—21no—
230C5×#67—22no—
231C5×#67—22no—
232C2×C5×Dic3—22no—
233C2×C5×Dic3C22×C412yes—
234C5×D12—21no—
235C5×D12—21no—
236C4×C5×D3—22no—
237C4×C5×D3—22no—
238C5×Dic6—21no—
239C5×Dic6—21no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5C22×C411yescharacteristic
242C2×C3×Dic5C22×C411yescharacteristic
243C2×C3×Dic5C2×D411yescharacteristic
244C2×C3×Dic5C2×D411yescharacteristic
245C2×C3×Dic5C2×D411yescharacteristic
246C2×C3×Dic5C2×D411yescharacteristic
247C3×C4×D5—44no—
248C3×C4×D5C22⋊C411yescharacteristic
249C3×C4×D5C22⋊C411yescharacteristic
250C3×C4×D5C22⋊C411yescharacteristic
251C3×C4×D5C22⋊C411yescharacteristic
252C3×C4×D5C22⋊C411yescharacteristic
253C3×C4×D5C22⋊C411yescharacteristic
254C3×C4×D5C22⋊C411yescharacteristic
255C3×C4×D5C22⋊C411yescharacteristic
256C3×C4×D5C22⋊C411yescharacteristic
257C3×C4×D5C22⋊C411yescharacteristic
258C3×C4×D5C22⋊C411yescharacteristic
259C3×C4×D5C22⋊C411yescharacteristic
260C3×C4×D5C22⋊C411yescharacteristic
261C3×C4×D5C22⋊C411yescharacteristic
262C3×C4×D5C22⋊C411yescharacteristic
263C3×C4×D5C22⋊C411yescharacteristic
264#1204—22no—
265#1204—22no—
266#1203—22no—
267#1203—22no—
268#1202—22no—
269#1202—22no—
270#1201—22no—
271#1201—22no—
272#1200—22no—
273#1200—22no—
274D3×Dic5—22no—
275D3×Dic5—22no—
276D5×Dic3—22no—
277D5×Dic3—22no—
278D5×Dic3—44no—
279C23×C3×C4—51no—
280C22×#67—52no—
281C2×#235—51no—
282C2×#235—52no—
283C2×#235—51no—
284C2×#235—52no—
285C2×#235—51no—
286C2×#235—101no—
287C2×#235—101no—
288C2×#235—101no—
289C2×#235—101no—
290C2×#235—101no—
291C2×#235—101no—
292C2×#235—101no—
293C2×#235—101no—
294C2×#235C2×D511yescharacteristic
295C22×D12—51no—
296C22×C4×D3—52no—
297C22×Dic6—51no—
298C3×#117—51no—
299C3×#117—52no—
300C3×#117—101no—
301C3×#117—101no—
302C3×#117C2×D511yescharacteristic, complemented
303C2×C3×C4⋊C4—101no—
304C2×C3×C22⋊C4—52no—
305C2×C3×C42—101no—
306C2×#217—52no—
307#926—51no—
308#926—52no—
309#926—101no—
310#926—101no—
311#926C2×D511yescharacteristic, complemented
312C2×C4⋊Dic3—101no—
313C2×C4×Dic3—101no—
314#806—54no—
315#806—54no—
316#806—54no—
317#806C2×D514yescomplemented
318C23×D5—32no—
319C23×D5C22×D311yescharacteristic
320C5×#41—61no—
321C5×#41—61no—
322C5×#41—61no—
323C5×#41—61no—
324C2×C5×Q8—31no—
325C2×C5×D4—32no—
326C2×C5×D4—31no—
327C22×C4×C5—32no—
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—32no—
330C2×C22⋊D5—32no—
331C2×C22⋊D5—32no—
332C22×Dic5—32no—
333C22×Dic5C22×D311yescharacteristic
334#713—61no—
335#713—61no—
336#713—61no—
337#713—61no—
338Q8×D5—61no—
339Q8×D5—61no—
340Q8×D5—61no—
341Q8×D5—61no—
342#711—62no—
343#711—62no—
344#711—62no—
345#711—62no—
346#711—61no—
347#711—61no—
348#711—61no—
349#711—61no—
350D4×D5—62no—
351D4×D5—62no—
352D4×D5—62no—
353D4×D5—62no—
354D4×D5—61no—
355D4×D5—61no—
356D4×D5—61no—
357D4×D5—61no—
358#709—61no—
359#709—61no—
360#709—61no—
361#709—61no—
362#709—62no—
363#709—62no—
364#709—62no—
365#709—62no—
366C2×D20—32no—
367C2×D20—31no—
368C2×C4×D5—22no—
369C2×C4×D5—32no—
370C2×C4×D5—32no—
371C2×C4×D5—32no—
372C2×C4×D5—62no—
373C2×C4×D5—62no—
374C2×C4×D5—62no—
375C2×C4×D5—62no—
376C2×C4×D5—62no—
377C2×C4×D5C4×D311yescharacteristic
378C2×C4×D5C4×D311yescharacteristic
379C2×C4×D5C4×D311yescharacteristic
380C2×C4×D5C4×D311yescharacteristic
381C2×C4×D5D1211yescharacteristic
382C2×C4×D5D1211yescharacteristic
383C2×C4×D5D1211yescharacteristic
384C2×C4×D5D1211yescharacteristic
385C2×C4×D5#6711yescharacteristic
386C2×C4×D5#6711yescharacteristic
387C2×C4×D5#6711yescharacteristic
388C2×C4×D5#6711yescharacteristic
389C2×Dic10—31no—
390C2×Dic10—32no—
391C5×C4⋊C4—21no—
392C5×C4⋊C4—61no—
393C5×C22⋊C4—32no—
394C5×C22⋊C4C22×D312yes—
395C42×C5—21no—
396C42×C5—61no—
397C22⋊Dic5—32no—
398C22⋊Dic5C22×D312yes—
399#685—22no—
400#685—62no—
401C4⋊Dic5—21no—
402C4⋊Dic5—61no—
403#683—22no—
404#683—62no—
405C4×Dic5—21no—
406C4×Dic5—22no—
407C4×Dic5—61no—
408C4×Dic5—62no—
409C22×#41—151no—
410C2×#117—51no—
411C2×#117—151no—
412#410—31no—
413#410—154no—
414#410—151no—
415#410—151no—
416#410—151no—
417C2×#99—154no—
418C22×C3×C5—41no—
419C22×C3×C5C23×C411yescharacteristic
420C22×C3×C5C22×D411yescharacteristic
421C22×C3×C5C22×D411yescharacteristic
422C2×D15—22no—
423C2×D15—42no—
424C2×C5×D3—22no—
425C2×C5×D3—42no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—22no—
429C2×C3×D5—41no—
430C2×C3×D5—41no—
431C2×C3×D5—41no—
432C2×C3×D5C2×C22⋊C411yescharacteristic
433C2×C3×D5C2×C22⋊C411yescharacteristic
434C2×C3×D5C2×C22⋊C411yescharacteristic
435C2×C3×D5C2×C22⋊C411yescharacteristic
436D3×D5—44no—
437D3×D5—44no—
438C3×C4×C5—42no—
439C3×C4×C5C2×C22⋊C411yescharacteristic
440C3×C4×C5C2×C22⋊C411yescharacteristic
441C3×C4×C5C2×C22⋊C411yescharacteristic
442C3×C4×C5C2×C22⋊C411yescharacteristic
443Dic15—22no—
444Dic15—42no—
445C3×Dic5—42no—
446C3×Dic5C2×C22⋊C411yescharacteristic
447C3×Dic5C2×C22⋊C411yescharacteristic
448C3×Dic5C2×C22⋊C411yescharacteristic
449C3×Dic5C2×C22⋊C411yescharacteristic
450C5×Dic3—22no—
451C5×Dic3—42no—
452C24×C3—51no—
453C23×D3—52no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—51no—
460C22×C3×C4—51no—
461C22×C3×C4—51no—
462C22×C3×C4—51no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—102no—
468C22×C3×C4C22×D511yescharacteristic
469C2×#67—52no—
470C2×#67—52no—
471C2×#67—52no—
472C2×#67—102no—
473C2×#67—102no—
474C2×#67—102no—
475C2×#67—102no—
476C2×#67C22×D512yes—
477C22×Dic3—52no—
478C22×Dic3—102no—
479#235—21no—
480#235—21no—
481#235—21no—
482#235—21no—
483#235—101no—
484#235—101no—
485#235—101no—
486#235—101no—
487#235—102no—
488#235—102no—
489#235—102no—
490#235—102no—
491#235—101no—
492#235—101no—
493#235—101no—
494#235—101no—
495#235—102no—
496#235—102no—
497#235—102no—
498#235—102no—
499#235—101no—
500#235—101no—
501#235—101no—
502#235—101no—
503C2×D12—52no—
504C2×D12—51no—
505C2×D12—101no—
506C2×D12—101no—
507C2×D12—101no—
508C2×D12—101no—
509C2×D12C4×D511yescharacteristic, complemented
510C2×C4×D3—52no—
511C2×C4×D3—52no—
512C2×C4×D3—52no—
513C2×C4×D3—102no—
514C2×C4×D3—102no—
515C2×C4×D3—102no—
516C2×C4×D3—102no—
517C2×C4×D3C4×D512yescomplemented
518C2×Dic6—51no—
519C2×Dic6—52no—
520C2×Dic6—101no—
521C2×Dic6—101no—
522C2×Dic6—101no—
523C2×Dic6—101no—
524C2×Dic6C4×D511yescharacteristic, complemented
525C3×C4⋊C4—21no—
526C3×C4⋊C4—102no—
527C3×C4⋊C4—101no—
528C3×C22⋊C4—52no—
529C3×C22⋊C4—102no—
530C3×C22⋊C4C22×D512yes—
531C3×C42—21no—
532C3×C42—102no—
533C3×C42—101no—
534#217—52no—
535#217—102no—
536#217C22×D512yes—
537C4⋊Dic3—21no—
538C4⋊Dic3—102no—
539C4⋊Dic3—101no—
540C4×Dic3—21no—
541C4×Dic3—102no—
542C4×Dic3—101no—
543C23×C5—32no—
544C23×C5C23×D311yescharacteristic
545C22×D5—32no—
546C22×D5—42no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5—124no—
550C22×D5C2×C4×D311yescharacteristic
551C22×D5C2×C4×D311yescharacteristic
552C22×D5C2×D1211yescharacteristic
553C22×D5C2×D1211yescharacteristic
554C22×D5C2×#6711yescharacteristic
555C22×D5C2×#6711yescharacteristic
556C5×Q8—61no—
557C5×Q8—61no—
558C5×D4—62no—
559C5×D4—62no—
560C5×D4—61no—
561C5×D4—61no—
562C2×C4×C5—22no—
563C2×C4×C5—32no—
564C2×C4×C5—62no—
565C2×C4×C5—62no—
566C2×C4×C5—62no—
567C2×C4×C5C2×C4×D311yescharacteristic
568C2×C4×C5C2×C4×D311yescharacteristic
569C2×C4×C5C2×D1211yescharacteristic
570C2×C4×C5C2×D1211yescharacteristic
571C2×C4×C5C2×#6711yescharacteristic
572C2×C4×C5C2×#6711yescharacteristic
573C22⋊D5—62no—
574C22⋊D5—62no—
575C22⋊D5—62no—
576C22⋊D5—62no—
577C22⋊D5—62no—
578C22⋊D5—62no—
579C2×Dic5—22no—
580C2×Dic5—32no—
581C2×Dic5—62no—
582C2×Dic5—62no—
583C2×Dic5—62no—
584C2×Dic5C2×C4×D311yescharacteristic
585C2×Dic5C2×C4×D311yescharacteristic
586C2×Dic5C2×D1211yescharacteristic
587C2×Dic5C2×D1211yescharacteristic
588C2×Dic5C2×#6711yescharacteristic
589C2×Dic5C2×#6711yescharacteristic
590D20—62no—
591D20—62no—
592D20—61no—
593D20—61no—
594C4×D5—44no—
595C4×D5—62no—
596C4×D5—62no—
597C4×D5—62no—
598C4×D5—62no—
599C4×D5—62no—
600C4×D5—62no—
601C4×D5—124no—
602C4×D5(C2×D3)⋊C411yescharacteristic
603C4×D5(C2×D3)⋊C411yescharacteristic
604C4×D5(C2×D3)⋊C411yescharacteristic
605C4×D5(C2×D3)⋊C411yescharacteristic
606C4×D5(C2×D3)⋊C411yescharacteristic
607C4×D5(C2×D3)⋊C411yescharacteristic
608C4×D5(C2×D3)⋊C411yescharacteristic
609C4×D5(C2×D3)⋊C411yescharacteristic
610C4×D5(C2×D3)⋊C411yescharacteristic
611C4×D5(C2×D3)⋊C411yescharacteristic
612C4×D5(C2×D3)⋊C411yescharacteristic
613C4×D5(C2×D3)⋊C411yescharacteristic
614C4×D5(C2×D3)⋊C411yescharacteristic
615C4×D5(C2×D3)⋊C411yescharacteristic
616C4×D5(C2×D3)⋊C411yescharacteristic
617C4×D5(C2×D3)⋊C411yescharacteristic
618Dic10—61no—
619Dic10—61no—
620Dic10—62no—
621Dic10—62no—
622C2×#41—31no—
623C2×#41—152no—
624C2×#41—152no—
625C2×#41—151no—
626C2×#41—151no—
627C2×#41—151no—
628C2×#41—301no—
629C2×#41—301no—
630C2×#41—301no—
631C2×#41—301no—
632C2×#41—301no—
633C2×#41—301no—
634C2×#41—301no—
635C2×#41—301no—
636C22×Q8—151no—
637C22×D4—151no—
638C22×D4—152no—
639C23×C4—51no—
640C23×C4—152no—
641#117—31no—
642#117—51no—
643#117—52no—
644#117—101no—
645#117—101no—
646#117—152no—
647#117—151no—
648#117—301no—
649#117—301no—
650#117D3×D511yescharacteristic, complemented
651C2×C4⋊C4—101no—
652C2×C4⋊C4—301no—
653C2×C22⋊C4—52no—
654C2×C22⋊C4—152no—
655C2×C42—101no—
656C2×C42—301no—
657#99—34no—
658#99—154no—
659#99—154no—
660#99—154no—
661C2×C3×C5—21no—
662C2×C3×C5—21no—
663C2×C3×C5—21no—
664C2×C3×C5C22×C22⋊C411yescharacteristic
665D15—42no—
666C3×D5—21no—
667C3×D5—21no—
668C3×D5—21no—
669C3×D5#41012yescomplemented
670C5×D3—42no—
671C23×C3—51no—
672C23×C3—51no—
673C23×C3—51no—
674C23×C3—51no—
675C23×C3—51no—
676C23×C3—51no—
677C23×C3—202no—
678C23×C3C23×D511yescharacteristic
679C22×D3—52no—
680C22×D3—102no—
681C22×D3—102no—
682C22×D3—204no—
683C22×D3C2×C4×D512yes—
684C2×C3×C4—22no—
685C2×C3×C4—51no—
686C2×C3×C4—51no—
687C2×C3×C4—51no—
688C2×C3×C4—51no—
689C2×C3×C4—51no—
690C2×C3×C4—51no—
691C2×C3×C4—51no—
692C2×C3×C4—51no—
693C2×C3×C4—51no—
694C2×C3×C4—51no—
695C2×C3×C4—51no—
696C2×C3×C4—51no—
697C2×C3×C4—51no—
698C2×C3×C4—51no—
699C2×C3×C4—51no—
700C2×C3×C4—51no—
701C2×C3×C4—51no—
702C2×C3×C4—51no—
703C2×C3×C4—51no—
704C2×C3×C4—51no—
705C2×C3×C4—51no—
706C2×C3×C4—51no—
707C2×C3×C4—102no—
708C2×C3×C4—204no—
709C2×C3×C4C2×C4×D511yescharacteristic
710C2×C3×C4C2×C4×D511yescharacteristic
711C2×C3×C4D4×D511yescharacteristic
712C2×C3×C4D4×D511yescharacteristic
713C2×C3×C4D4×D511yescharacteristic
714C2×C3×C4D4×D511yescharacteristic
715#67—22no—
716#67—22no—
717#67—102no—
718#67—102no—
719#67—102no—
720#67—102no—
721#67—102no—
722#67—102no—
723C2×Dic3—22no—
724C2×Dic3—52no—
725C2×Dic3—102no—
726C2×Dic3—102no—
727C2×Dic3—102no—
728C2×Dic3—204no—
729C2×Dic3C2×C4×D512yes—
730D12—21no—
731D12—21no—
732D12—102no—
733D12—102no—
734D12—101no—
735D12—101no—
736C4×D3—22no—
737C4×D3—22no—
738C4×D3—102no—
739C4×D3—102no—
740C4×D3—102no—
741C4×D3—102no—
742C4×D3—102no—
743C4×D3—102no—
744Dic6—21no—
745Dic6—21no—
746Dic6—102no—
747Dic6—102no—
748Dic6—101no—
749Dic6—101no—
750C22×C5—41no—
751C22×C5—62no—
752C22×C5—122no—
753C22×C5C22×C4×D311yescharacteristic
754C22×C5C22×D1211yescharacteristic
755C22×C5C22×#6711yescharacteristic
756C2×D5—22no—
757C2×D5—22no—
758C2×D5—22no—
759C2×D5—41no—
760C2×D5—41no—
761C2×D5—41no—
762C2×D5—62no—
763C2×D5—124no—
764C2×D5—124no—
765C2×D5—122no—
766C2×D5C2×(C2×D3)⋊C411yescharacteristic
767C2×D5C2×(C2×D3)⋊C411yescharacteristic
768C2×D5C2×(C2×D3)⋊C411yescharacteristic
769C2×D5C2×(C2×D3)⋊C411yescharacteristic
770C4×C5—42no—
771C4×C5—62no—
772C4×C5—122no—
773C4×C5C2×(C2×D3)⋊C411yescharacteristic
774C4×C5C2×(C2×D3)⋊C411yescharacteristic
775C4×C5C2×(C2×D3)⋊C411yescharacteristic
776C4×C5C2×(C2×D3)⋊C411yescharacteristic
777Dic5—42no—
778Dic5—62no—
779Dic5—122no—
780Dic5C2×(C2×D3)⋊C411yescharacteristic
781Dic5C2×(C2×D3)⋊C411yescharacteristic
782Dic5C2×(C2×D3)⋊C411yescharacteristic
783Dic5C2×(C2×D3)⋊C411yescharacteristic
784C24—51no—
785C24—152no—
786#41—61no—
787#41—61no—
788#41—61no—
789#41—61no—
790#41—302no—
791#41—302no—
792#41—302no—
793#41—302no—
794#41—302no—
795#41—302no—
796#41—302no—
797#41—302no—
798#41—301no—
799#41—301no—
800#41—301no—
801#41—301no—
802#41—301no—
803#41—301no—
804#41—301no—
805#41—301no—
806#41—301no—
807#41—301no—
808#41—301no—
809#41—301no—
810C2×Q8—31no—
811C2×Q8—152no—
812C2×Q8—151no—
813C2×Q8—301no—
814C2×Q8—301no—
815C2×Q8—301no—
816C2×Q8—301no—
817C2×D4—32no—
818C2×D4—31no—
819C2×D4—152no—
820C2×D4—152no—
821C2×D4—152no—
822C2×D4—152no—
823C2×D4—151no—
824C2×D4—301no—
825C2×D4—301no—
826C2×D4—301no—
827C2×D4—301no—
828C2×D4—302no—
829C2×D4—302no—
830C2×D4—302no—
831C2×D4—302no—
832C22×C4—32no—
833C22×C4—51no—
834C22×C4—51no—
835C22×C4—51no—
836C22×C4—51no—
837C22×C4—51no—
838C22×C4—51no—
839C22×C4—51no—
840C22×C4—51no—
841C22×C4—51no—
842C22×C4—51no—
843C22×C4—51no—
844C22×C4—51no—
845C22×C4—51no—
846C22×C4—102no—
847C22×C4—152no—
848C22×C4—152no—
849C22×C4—152no—
850C22×C4—152no—
851C22×C4—302no—
852C22×C4—302no—
853C22×C4—302no—
854C22×C4—302no—
855C22×C4—302no—
856C22×C4C2×D3×D511yescharacteristic
857C4⋊C4—21no—
858C4⋊C4—61no—
859C4⋊C4—102no—
860C4⋊C4—101no—
861C4⋊C4—302no—
862C4⋊C4—301no—
863C22⋊C4—32no—
864C22⋊C4—52no—
865C22⋊C4—102no—
866C22⋊C4—152no—
867C22⋊C4—302no—
868C22⋊C4C2×D3×D512yes—
869C42—21no—
870C42—61no—
871C42—102no—
872C42—101no—
873C42—302no—
874C42—301no—
875C3×C5C2×#41011yescharacteristic, complemented, Hall
876C22×C3—41no—
877C22×C3—51no—
878C22×C3—51no—
879C22×C3—51no—
880C22×C3—51no—
881C22×C3—102no—
882C22×C3—102no—
883C22×C3—102no—
884C22×C3—201no—
885C22×C3—201no—
886C22×C3—201no—
887C22×C3C22×C4×D511yescharacteristic
888C22×C3C2×D4×D511yescharacteristic
889C22×C3C2×D4×D511yescharacteristic
890C2×D3—22no—
891C2×D3—42no—
892C2×D3—102no—
893C2×D3—204no—
894C2×D3—204no—
895C2×D3—202no—
896C3×C4—42no—
897C3×C4—51no—
898C3×C4—51no—
899C3×C4—51no—
900C3×C4—51no—
901C3×C4—202no—
902C3×C4D5×C22⋊C411yescharacteristic
903C3×C4D5×C22⋊C411yescharacteristic
904C3×C4D5×C22⋊C411yescharacteristic
905C3×C4D5×C22⋊C411yescharacteristic
906Dic3—22no—
907Dic3—42no—
908Dic3—102no—
909Dic3—202no—
910C2×C5—21no—
911C2×C5—21no—
912C2×C5—21no—
913C2×C5—122no—
914C2×C5C22×(C2×D3)⋊C411yescharacteristic
915D5—21no—
916D5—21no—
917D5—21no—
918D5—122no—
919D5#500612yesdirect product factor
920C23—32no—
921C23—51no—
922C23—51no—
923C23—51no—
924C23—51no—
925C23—51no—
926C23—51no—
927C23—152no—
928C23—202no—
929C23—302no—
930C23—302no—
931C23—604no—
932C23C22×D3×D511yescharacteristic
933Q8—61no—
934Q8—61no—
935Q8—302no—
936Q8—302no—
937Q8—301no—
938Q8—301no—
939D4—62no—
940D4—62no—
941D4—61no—
942D4—61no—
943D4—302no—
944D4—302no—
945D4—302no—
946D4—302no—
947D4—302no—
948D4—302no—
949D4—302no—
950D4—302no—
951D4—301no—
952D4—301no—
953C2×C4—22no—
954C2×C4—32no—
955C2×C4—51no—
956C2×C4—51no—
957C2×C4—51no—
958C2×C4—51no—
959C2×C4—51no—
960C2×C4—51no—
961C2×C4—51no—
962C2×C4—51no—
963C2×C4—51no—
964C2×C4—51no—
965C2×C4—51no—
966C2×C4—51no—
967C2×C4—51no—
968C2×C4—51no—
969C2×C4—51no—
970C2×C4—51no—
971C2×C4—51no—
972C2×C4—51no—
973C2×C4—51no—
974C2×C4—51no—
975C2×C4—51no—
976C2×C4—51no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—102no—
981C2×C4—152no—
982C2×C4—204no—
983C2×C4—302no—
984C2×C4—302no—
985C2×C4—302no—
986C2×C4—302no—
987C2×C4—302no—
988C2×C4—302no—
989C2×C4—302no—
990C2×C4—302no—
991C2×C4—302no—
992C2×C4—604no—
993C2×C4C4×D3×D511yescharacteristic
994C2×C4C4×D3×D511yescharacteristic
995C2×C4D5×D1211yescharacteristic
996C2×C4D5×D1211yescharacteristic
997C2×C4D5×#6711yescharacteristic
998C2×C4D5×#6711yescharacteristic
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—52no—
1003C2×C3—101no—
1004C2×C3—101no—
1005C2×C3—101no—
1006C2×C3C2×D5×C22⋊C411yescharacteristic
1007D3—42no—
1008D3—202no—
1009C5C2×#500611yescharacteristic, complemented, Sylow
1010C22—41no—
1011C22—51no—
1012C22—51no—
1013C22—51no—
1014C22—51no—
1015C22—62no—
1016C22—102no—
1017C22—102no—
1018C22—102no—
1019C22—122no—
1020C22—201no—
1021C22—201no—
1022C22—201no—
1023C22—302no—
1024C22—602no—
1025C22—604no—
1026C22—604no—
1027C22C2×C4×D3×D511yescharacteristic
1028C22C2×D5×D1211yescharacteristic
1029C22C2×D5×#6711yescharacteristic
1030C4—42no—
1031C4—51no—
1032C4—51no—
1033C4—51no—
1034C4—51no—
1035C4—62no—
1036C4—122no—
1037C4—202no—
1038C4—302no—
1039C4—602no—
1040C4D5×(C2×D3)⋊C411yescharacteristic
1041C4D5×(C2×D3)⋊C411yescharacteristic
1042C4D5×(C2×D3)⋊C411yescharacteristic
1043C4D5×(C2×D3)⋊C411yescharacteristic
1044C3D5×#41011yescharacteristic, complemented, Sylow
1045C2—21no—
1046C2—21no—
1047C2—21no—
1048C2—52no—
1049C2—101no—
1050C2—101no—
1051C2—101no—
1052C2—122no—
1053C2—602no—
1054C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×D5×#235C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×D5×#117C2semidirect
3. D5×#926C2semidirect
4. #11751107C2semidirect
5. C5×#5006C2semidirect
6. #11748626C2semidirect
7. #11748625C2semidirect
8. #11747129C2semidirect
9. D5×#806C2semidirect
24. C2×D5×D12C4semidirect
25. C2×C4×D3×D5C4semidirect
26. C2×#6773C4semidirect
27. C2×#6772C4semidirect
28. C2×#6771C4semidirect
29. C2×D5×Dic6C4semidirect
30. C3×C5×#117C22semidirect
31. #91815C22semidirect
32. C5×#926C22semidirect
33. C3×#4072C22semidirect
37. C3×#4023C22semidirect
41. #91528C22semidirect
46. #91090C22semidirect
47. C5×#806C22semidirect
48. #90997C22semidirect
49. #90996C22semidirect
53. D5×#117D3semidirect
68. C2×D60C2×C4semidirect
69. C2×C4×D15C2×C4semidirect
70. C2×Dic30C2×C4semidirect
76. C2×C5×D12C2×C4semidirect
77. C2×C4×C5×D3C2×C4semidirect
78. C2×C5×Dic6C2×C4semidirect
97. C2×#1204C2×C4semidirect
98. C2×#1203C2×C4semidirect
101. C2×#1200C2×C4semidirect
106. C2×D3×Dic5C2×C4semidirect
158. #5006D5direct (N × H)
180. C5×#117C2×D3semidirect
182. #4072C2×D3semidirect
190. #4023C2×D3semidirect
302. C3×#117C2×D5semidirect
311. #926C2×D5semidirect
317. #806C2×D5semidirect
509. C2×D12C4×D5semidirect
517. C2×C4×D3C4×D5semidirect
524. C2×Dic6C4×D5semidirect
650. #117D3×D5semidirect
669. C3×D5#410semidirect
875. C3×C5C2×#410semidirect
919. D5#5006direct (N × H)
1009. C5C2×#5006semidirect
1044. C3D5×#410semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C3×D5×#1172
D5×#9262
#117511072
C5×#50062
#117486262
#117486252
#117471292
D5×#8062
D5×#4103
C2×#50065