Finite Group Databasebeta

← Dic5×#885 #14321958

Subgroups — Dic5×#885 #14321958

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#885C211yesmaximal, characteristic
2C2×Dic5×#67C211yesmaximal, characteristic
3C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
4#11751052C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#11749482C211yesmaximal, characteristic
7#11749478C211yesmaximal, characteristic, complemented
8Dic5×#217C211yesmaximal, characteristic, complemented
9Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11748794C211yesmaximal, characteristic, complemented
12#11748692C211yesmaximal, characteristic, complemented
13#11748686C211yesmaximal, characteristic, complemented
14C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
15#11748600C211yesmaximal, characteristic, complemented
16Dic5×#124—31nomaximal, Hall
17C22×C5×#67C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C5×#885C418yescomplemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34Dic5×#67—24no—
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46Dic5×Dic6—24no—
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55C4×#885—51nomaximal, Hall
56C2×C5×#124—31no—
57C2×Q8×Dic5—31no—
58C2×D4×Dic5—31no—
59#65519—31no—
60#65510—31no—
61#65240—31no—
62#65240—31no—
63#65240—31no—
64#65240—31no—
65C22⋊C4×Dic5—31no—
66C22⋊C4×Dic5—31no—
67C22⋊C4×Dic5—31no—
68C22⋊C4×Dic5D311yescharacteristic, complemented
69#65225—31no—
70C42×Dic5—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C5×#67—22no—
80C2×C5×#67—22no—
81C2×C5×#67C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C2×C5×Dic6—22no—
86C2×C5×Dic6—22no—
87C2×C5×Dic6C2×C414yescomplemented
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5—22no—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×D3×Dic5—22no—
96C2×D3×Dic5—22no—
97C2×D3×Dic5—22no—
98C3×C5×C22⋊C4C2×C414yescomplemented
99#6719—22no—
100#6719—22no—
101C4⋊Dic15—22no—
102C4×Dic15—22no—
103C5×#217C2×C414yescomplemented
104C5×(C2×D3)⋊C4C2×C414yescomplemented
105C5×(C2×D3)⋊C4C2×C414yescomplemented
106C4×C5×Dic3C2×C414yescomplemented
107C3×C22⋊Dic5—22no—
108C3×C4×Dic5—22no—
109C3×C4×Dic5—22no—
110Dic3⋊Dic5—22no—
111Dic3⋊Dic5—22no—
112Dic3⋊Dic5—22no—
113(C2×D3)⋊Dic5—22no—
114(C2×D3)⋊Dic5—22no—
115(C2×D3)⋊Dic5—22no—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5D414yes—
121C2×C4×#67—51no—
122C2×#885D511yescharacteristic
123C2×C4×Dic6—51no—
124C3×C4×C22⋊C4—51no—
125C4×#217—51no—
126#4957—51no—
127#4951—51no—
128#4944—51no—
129C4×(C2×D3)⋊C4—51no—
130C4×(C2×D3)⋊C4—51no—
131C42×Dic3—51no—
132#4670—51no—
133#4669—51no—
134#4650—51no—
135#4646—51no—
136C22×C5×Q8—31no—
137C22×C5×D4—31no—
138C23×Dic5—31no—
139C23×Dic5C2×D311yescharacteristic
140C5×#124—38no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4C2×D311yescharacteristic
145C2×C42×C5—31no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5C2×D311yescharacteristic
152Q8×Dic5—64no—
153D4×Dic5—64no—
154C2×C4⋊Dic5—31no—
155C2×C4⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5C2×D311yescharacteristic
165C2×C4×Dic5C2×D311yescharacteristic
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174C4×#124—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5C22×C412yes—
182C23×C3×C5C2411yescharacteristic
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×C3×C4×C5C22×C412yes—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15C2×D412yes—
207C2×Dic15#4112yes—
208C5×#67—28no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C22×C412yes—
214C2×C5×Dic3C22×C412yes—
215C2×C5×Dic3C22×C412yes—
216C2×C5×Dic3C2×D412yes—
217C2×C5×Dic3#4112yes—
218C5×Dic6—28no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—44no—
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5#4112yes—
230C2×C3×Dic5#4112yes—
231C2×C3×Dic5#4112yes—
232D3×Dic5—44no—
233C23×C3×C4—51no—
234C22×#67C2×D511yescharacteristic
235C22×C4×D3—51no—
236C22×Dic6C2×D511yescharacteristic
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4C2×D511yescharacteristic
239C2×C3×C42—51no—
240C2×C3×C42—51no—
241C2×#217—51no—
242C2×#217—51no—
243C2×#217C2×D511yescharacteristic
244C4×#67—104no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4C2×D511yescharacteristic
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×C4⋊Dic3—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3C2×D511yescharacteristic
261#885Dic518yesdirect product factor
262C4×Dic6—104no—
263C3×#95—51no—
264C3×#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C24×C5—31no—
272C24×C5C22×D311yescharacteristic
273C2×C5×Q8—34no—
274C2×C5×Q8—62no—
275C2×C5×Q8—62no—
276C2×C5×D4—34no—
277C2×C5×D4—62no—
278C2×C5×D4—62no—
279C22×C4×C5—31no—
280C22×C4×C5—31no—
281C22×C4×C5—31no—
282C22×C4×C5C22×D311yescharacteristic
283C22×C4×C5C22×D311yescharacteristic
284C22×Dic5—22no—
285C22×Dic5—22no—
286C22×Dic5—22no—
287C22×Dic5—31no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—62no—
292C22×Dic5—62no—
293C22×Dic5—62no—
294C22×Dic5C22×D311yescharacteristic
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C5×C22⋊C4—34no—
299C5×C22⋊C4—34no—
300C5×C22⋊C4—34no—
301C5×C22⋊C4C4×D314yescomplemented
302C42×C5—34no—
303C22⋊Dic5—22no—
304C22⋊Dic5—62no—
305C22⋊Dic5—62no—
306C22⋊Dic5—62no—
307C22⋊Dic5—62no—
308C22⋊Dic5—62no—
309C4⋊Dic5—62no—
310C4⋊Dic5—62no—
311C4⋊Dic5—62no—
312C4⋊Dic5—62no—
313C4×Dic5—22no—
314C4×Dic5—22no—
315C4×Dic5—34no—
316C4×Dic5—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C2×#124—31no—
322C2×C4×Q8—151no—
323C2×C4×D4—151no—
324#391—151no—
325#390—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#388—151no—
330#382—151no—
331C4×C22⋊C4—51no—
332C4×C22⋊C4—151no—
333C4×C22⋊C4—151no—
334C4×C22⋊C4—151no—
335C43—151no—
336C22×C3×C5—22no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5C23×C411yescharacteristic
344C22×C3×C5C22×D411yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5C2×#4111yescharacteristic
349C22×C3×C5C2×#4111yescharacteristic
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3—22no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359Dic15—22no—
360Dic15—22no—
361Dic15—41no—
362Dic15—41no—
363C3×Dic5—22no—
364C3×Dic5—41no—
365C3×Dic5—41no—
366C3×Dic5#12414yescomplemented
367C5×Dic3—22no—
368C5×Dic3—22no—
369C5×Dic3C4×D414yes—
370C24×C3C22×D511yescharacteristic
371C23×D3C22×D511yescharacteristic
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—102no—
377C22×C3×C4—102no—
378C22×C3×C4—102no—
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C2×#67—22no—
382C2×#67—22no—
383C2×#67C2×Dic514yes—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—51no—
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×Dic6—22no—
395C2×Dic6—22no—
396C2×Dic6C2×Dic514yescomplemented
397C3×C22⋊C4—102no—
398C3×C22⋊C4C2×Dic514yescomplemented
399C3×C42—102no—
400C3×C42—102no—
401#217—102no—
402#217—102no—
403#217C2×Dic514yescomplemented
404(C2×D3)⋊C4—102no—
405(C2×D3)⋊C4—102no—
406(C2×D3)⋊C4—102no—
407(C2×D3)⋊C4C2×Dic514yescomplemented
408(C2×D3)⋊C4C2×Dic514yescomplemented
409C4⋊Dic3—102no—
410Dic3⋊C4—102no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413C4×Dic3—54no—
414C4×Dic3—102no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3C2×Dic514yescomplemented
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5—32no—
427C23×C5—61no—
428C23×C5—61no—
429C23×C5—61no—
430C23×C5—61no—
431C23×C5—61no—
432C23×C5—61no—
433C23×C5C2×C4×D312yes—
434C23×C5C23×D311yescharacteristic
435C5×Q8—68no—
436C5×D4—68no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—32no—
442C2×C4×C5—32no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5C2×C4×D312yes—
451C2×C4×C5C2×C4×D312yes—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—44no—
463C2×Dic5—61no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—124no—
474C2×Dic5#23512yes—
475C2×Dic5#23512yes—
476C2×Dic5D3×D412yes—
477C2×Dic5#23712yes—
478C22×Q8—31no—
479C22×D4—31no—
480C23×C4—51no—
481C23×C4—151no—
482#124—38no—
483C4×Q8—304no—
484C4×D4—304no—
485C2×C4⋊C4—151no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—151no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4D3×D511yescharacteristic
499C2×C42—31no—
500C2×C42—51no—
501C2×C42—51no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—51no—
509#95—51no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516C2×C3×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5C4×#4111yescharacteristic
520C2×C3×C5C2×#12411yescharacteristic
521C2×C3×C5#52911yescharacteristic
522C2×C3×C5#52911yescharacteristic
523C2×C3×C5#53211yescharacteristic
524C5×D3—42no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3C22×Dic512yes—
532C23×C3C23×D511yescharacteristic
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3C22×Dic512yes—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—204no—
557C2×C3×C4C22×Dic512yes—
558C2×C3×C4C22×Dic512yes—
559#67—28no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—101no—
567C2×Dic3—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3D4×D512yes—
577C2×Dic3#71112yes—
578C2×Dic3C22×Dic512yes—
579C2×Dic3C22×Dic512yes—
580C2×Dic3C22×Dic512yes—
581C4×D3—204no—
582Dic6—28no—
583C22×C5—22no—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—41no—
590C22×C5—62no—
591C22×C5—62no—
592C22×C5—62no—
593C22×C5—121no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5—121no—
597C22×C5C22×C4×D311yescharacteristic
598C22×C5C2×#23511yescharacteristic
599C22×C5C2×#23511yescharacteristic
600C22×C5C2×D3×D411yescharacteristic
601C22×C5C2×#23711yescharacteristic
602C22×C5D3×#4111yescharacteristic
603C22×C5D3×#4111yescharacteristic
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—34no—
607C4×C5—62no—
608C4×C5—62no—
609Dic5—22no—
610Dic5—41no—
611Dic5—41no—
612Dic5—62no—
613Dic5—62no—
614Dic5—121no—
615Dic5—121no—
616Dic5#88514yesdirect product factor
617C24—31no—
618C24C2×D3×D511yescharacteristic
619C2×Q8—34no—
620C2×Q8—62no—
621C2×Q8—62no—
622C2×D4—34no—
623C2×D4—62no—
624C2×D4—62no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—151no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4—302no—
642C22×C4C2×D3×D511yescharacteristic
643C22×C4C2×D3×D511yescharacteristic
644C4⋊C4—302no—
645C4⋊C4—302no—
646C4⋊C4—302no—
647C4⋊C4—302no—
648C22⋊C4—34no—
649C22⋊C4—34no—
650C22⋊C4—34no—
651C22⋊C4—102no—
652C22⋊C4—302no—
653C22⋊C4—302no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4D3×Dic514yescomplemented
658C42—34no—
659C42—102no—
660C42—102no—
661C42—154no—
662C42—302no—
663C42—302no—
664C42—302no—
665C42—302no—
666C42—302no—
667C3×C5C4×#12411yescharacteristic, complemented, Hall
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3C2×D4×D511yescharacteristic
676C22×C3C2×#71111yescharacteristic
677C22×C3D5×#4111yescharacteristic
678C22×C3D5×#4111yescharacteristic
679C22×C3D5×#4111yescharacteristic
680C22×C3D5×#4111yescharacteristic
681C22×C3C23×Dic511yescharacteristic
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—54no—
692C3×C4—102no—
693C3×C4—201no—
694C3×C4—201no—
695Dic3—22no—
696Dic3—22no—
697Dic3—102no—
698Dic3—102no—
699Dic3—201no—
700Dic3—201no—
701Dic3D4×Dic514yes—
702C2×C5—42no—
703C2×C5—122no—
704C2×C5C4×#23511yescharacteristic
705C2×C5C2×#88511yescharacteristic
706C2×C5#552811yescharacteristic
707C2×C5C4×#23711yescharacteristic
708C2×C5#553811yescharacteristic
709C2×C5C4×D3×D411yescharacteristic
710C2×C5#554811yescharacteristic
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—32no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23C2×D3×Dic512yes—
725C23C22×D3×D511yescharacteristic
726Q8—68no—
727D4—68no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—52no—
738C2×C4—52no—
739C2×C4—52no—
740C2×C4—52no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—152no—
754C2×C4—152no—
755C2×C4—204no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—604no—
767C2×C4C2×D3×Dic512yes—
768C2×C4C2×D3×Dic512yes—
769C2×C3—42no—
770C2×C3#6600211yescharacteristic
771C2×C3D5×#12411yescharacteristic
772C2×C3#6601411yescharacteristic
773C2×C3#6601411yescharacteristic
774C2×C3C2×D4×Dic511yescharacteristic
775C2×C3#41×Dic511yescharacteristic
776C2×C3#41×Dic511yescharacteristic
777D3—42no—
778C5C4×#88511yescharacteristic, complemented, Sylow
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22D5×#23511yescharacteristic
794C22D5×#23511yescharacteristic
795C22D3×D4×D511yescharacteristic
796C22D5×#23711yescharacteristic
797C22D3×#71111yescharacteristic
798C22#9202411yescharacteristic
799C22C22×D3×Dic511yescharacteristic
800C4—22no—
801C4—22no—
802C4—34no—
803C4—54no—
804C4—62no—
805C4—62no—
806C4—102no—
807C4—201no—
808C4—201no—
809C4—302no—
810C4—302no—
811C4—601no—
812C4—601no—
813C3Dic5×#12411yescharacteristic, complemented, Sylow
814C2—42no—
815C2—122no—
816C2#1175285111yescharacteristic
817C2#1175288511yescharacteristic
818C2#1175289711yescharacteristic
819C2D5×#88511yescharacteristic
820C2Dic5×#23511yescharacteristic
821C2D3×D4×Dic511yescharacteristic
822C2Dic5×#23711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×#124
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×Dic5×Dic6C2semidirect
4. #11751052C2semidirect
5. C3×C22⋊C4×Dic5C2semidirect
7. #11749478C2semidirect
8. Dic5×#217C2semidirect
9. Dic5×(C2×D3)⋊C4C2semidirect
10. Dic5×(C2×D3)⋊C4C2semidirect
11. #11748794C2semidirect
12. #11748692C2semidirect
13. #11748686C2semidirect
14. C4×Dic3×Dic5C2semidirect
15. #11748600C2semidirect
30. C5×#885C4semidirect
68. C22⋊C4×Dic5D3semidirect
87. C2×C5×Dic6C2×C4semidirect
98. C3×C5×C22⋊C4C2×C4semidirect
103. C5×#217C2×C4semidirect
104. C5×(C2×D3)⋊C4C2×C4semidirect
105. C5×(C2×D3)⋊C4C2×C4semidirect
106. C4×C5×Dic3C2×C4semidirect
261. #885Dic5direct (N × H)
301. C5×C22⋊C4C4×D3semidirect
366. C3×Dic5#124semidirect
396. C2×Dic6C2×Dic5semidirect
398. C3×C22⋊C4C2×Dic5semidirect
403. #217C2×Dic5semidirect
407. (C2×D3)⋊C4C2×Dic5semidirect
408. (C2×D3)⋊C4C2×Dic5semidirect
419. C4×Dic3C2×Dic5semidirect
616. Dic5#885direct (N × H)
657. C22⋊C4D3×Dic5semidirect
667. C3×C5C4×#124semidirect
778. C5C4×#885semidirect
813. C3Dic5×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8852
C2×Dic5×#672
C2×Dic5×Dic62
#117510522
C3×C22⋊C4×Dic52
#117494822
#117494782
Dic5×#2172
Dic5×(C2×D3)⋊C42
#117487942
#117486922
#117486862
C4×Dic3×Dic52
#117486002
Dic5×#1243
C4×#8855