Finite Group Databasebeta

← D5×#4840 #14413877

Subgroups — D5×#4840 #14413877

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#872C211yesmaximal, characteristic
2#11750941C211yesmaximal, characteristic, complemented
3C5×#4840C211yesmaximal, characteristic, complemented
4C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
5D5×(C2×D3)⋊C8C211yesmaximal, characteristic
6D5×(C2×D3)⋊C8C211yesmaximal, characteristic
7#11747663C211yesmaximal, characteristic, complemented
8#11747662C211yesmaximal, characteristic, complemented
9#11747659C211yesmaximal, characteristic, complemented
10#11747656C211yesmaximal, characteristic, complemented
11D5×#815C211yesmaximal, characteristic, complemented
12C8×D5×Dic3C211yesmaximal, characteristic, complemented
13D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
14#11746860C211yesmaximal, characteristic, complemented
15#11746854C211yesmaximal, characteristic, complemented
16D5×#433—31nomaximal, Hall
17C2×C4×D3×D5C2211yescharacteristic
18#91761C2211yescharacteristic
19C5×#872C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21C2×C3×C8×D5C2211yescharacteristic
22C3×C42×D5C2211yescharacteristic
23D5×(C2×D3)⋊C4C411yescharacteristic
24D5×(C2×D3)⋊C4C411yescharacteristic
25#91402C411yescharacteristic
26#91402C411yescharacteristic
27#91398C411yescharacteristic
28#91398C411yescharacteristic
29D5×Dic3⋊C4C411yescharacteristic
30D5×Dic3⋊C4C411yescharacteristic
31C4×D5×Dic3C2211yescharacteristic
32#91386C2211yescharacteristic
33#91371C2211yescharacteristic
34C2×D5×C3⋊C8C2211yescharacteristic
35C2×D5×C3⋊C8C2211yescharacteristic
36C3×C5×C4⋊C8C2211yescharacteristic, complemented
37#91104C2211yescharacteristic
38#91104C2211yescharacteristic
39#91099C2211yescharacteristic, complemented
40C8×Dic15C2211yescharacteristic, complemented
41C4⋊(C3⋊#168)C2211yescharacteristic, complemented
42C5×(C2×D3)⋊C8C2211yescharacteristic
43C5×(C2×D3)⋊C8C2211yescharacteristic
44C5×#815C2211yescharacteristic, complemented
45C5×C8×Dic3C2211yescharacteristic, complemented
46C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#3946C2211yescharacteristic, complemented
48C3×#3946C2211yescharacteristic, complemented
49C3×C4⋊#168C2211yescharacteristic, complemented
50#90982C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90957C2211yescharacteristic
53#90957C2211yescharacteristic
54(C2×D3)⋊#168C2211yescharacteristic
55(C2×D3)⋊#168C2211yescharacteristic
56#90954C2211yescharacteristic, complemented
57#90953C2211yescharacteristic, complemented
58#90951C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60C2×#4840—51nomaximal, Hall
61D5×#117—31no—
62C5×#433—31no—
63#65289—31no—
64#65129—31no—
65#65129—31no—
66D5×C4⋊C8—31no—
67D5×C4⋊C8D311yescharacteristic, complemented
68D5×C22⋊C8—31no—
69D5×C22⋊C8—31no—
70#65009—31no—
71#65009—31no—
72#64998—31no—
73D5×#97—31no—
74#64979—31no—
75C4×C8×D5—31no—
76C22×D3×D5C2×C411yescharacteristic
77C2×C4×D15C2311yescharacteristic
78C2×C4×C5×D3C2311yescharacteristic
79C2×C3×C4×D5C2×C411yescharacteristic
80C2×C3×C4×D5C2×C411yescharacteristic
81C2×C3×C4×D5C2311yescharacteristic
82C2×#1200C2×C411yescharacteristic
83C2×D3×Dic5C2×C411yescharacteristic
84C2×D5×Dic3C2×C411yescharacteristic
85C2×D5×Dic3C2×C411yescharacteristic
86C2×D5×Dic3C2×C411yescharacteristic
87C4×D3×D5—22no—
88C4×D3×D5—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C42×C5C2311yescharacteristic
92#6714C2×C411yescharacteristic
93#6714C2×C411yescharacteristic
94#6712C2×C411yescharacteristic
95#6712C2×C411yescharacteristic
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C5×(C2×D3)⋊C4C2×C411yescharacteristic
100C5×(C2×D3)⋊C4C2×C411yescharacteristic
101C5×Dic3⋊C4C2×C411yescharacteristic
102C5×Dic3⋊C4C2×C411yescharacteristic
103C4×C5×Dic3C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C2×C5×C3⋊C8C2311yescharacteristic
106C3×C4×Dic5C2×C411yescharacteristic
107C3×C4×Dic5C2×C411yescharacteristic
108C3×C4×Dic5C2311yescharacteristic
109C2×C3×#168C2311yescharacteristic
110C2×C3×#168C2311yescharacteristic
111C3×C8×D5—22no—
112C3×C8×D5—22no—
113Dic3⋊Dic5C2×C411yescharacteristic
114Dic3⋊Dic5C2×C411yescharacteristic
115#6669C2×C411yescharacteristic
116#6669C2×C411yescharacteristic
117#6667C2×C411yescharacteristic
118#6667C2×C411yescharacteristic
119(C2×D3)⋊Dic5C2×C411yescharacteristic
120(C2×D3)⋊Dic5C2×C411yescharacteristic
121Dic3×Dic5C2×C411yescharacteristic
122Dic3×Dic5C2×C411yescharacteristic
123D5×C3⋊C8—22no—
124D5×C3⋊C8—22no—
125C2×#872—51no—
126C2×C3×C4⋊C8—51no—
127C2×(C2×D3)⋊C8—51no—
128C2×(C2×D3)⋊C8—51no—
129C2×#815—51no—
130C2×C8×Dic3—51no—
131C2×C4⋊(C3⋊C8)—51no—
132#4840—51no—
133#4840—51no—
134#4840—51no—
135#4840—51no—
136#4840—51no—
137#4840—51no—
138#4840—51no—
139#4840D511yescharacteristic, direct product factor
140C22×C4×D5—31no—
141C5×#117—31no—
142#4072—31no—
143C2×C8×D5—31no—
144C2×C8×D5—31no—
145C2×C8×D5C2×D311yescharacteristic
146C2×C8×D5C2×D311yescharacteristic
147#4038—31no—
148#4038—31no—
149D5×C4⋊C4—31no—
150D5×C4⋊C4—31no—
151D5×C22⋊C4—31no—
152D5×C22⋊C4—31no—
153#4023—31no—
154#4023—31no—
155#4018—31no—
156#4018—31no—
157C42×D5—31no—
158C42×D5C2×D311yescharacteristic
159C5×C4⋊C8—31no—
160C5×C4⋊C8C2×D311yescharacteristic, complemented
161C5×C22⋊C8—31no—
162C5×C22⋊C8—31no—
163C5×#97—31no—
164C4×C5×C8—31no—
165C22⋊#168—31no—
166C22⋊#168—31no—
167#3952—31no—
168#3952—31no—
169#3952—31no—
170#3952—31no—
171#3947—31no—
172#3947—31no—
173#3946—31no—
174#3946—31no—
175#3946C2×D311yescharacteristic, complemented
176#3946C2×D311yescharacteristic, complemented
177C8×Dic5—31no—
178C8×Dic5—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic, complemented
181#3935—31no—
182C4×#168—31no—
183C2×#433—151noSylow
184C22×D15C22×C411yescharacteristic
185C22×C5×D3C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C2×D3×D5—22no—
188C2×D3×D5—22no—
189C2×D3×D5—22no—
190C2×C3×C4×C5C22×C411yescharacteristic
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C4×D15—21no—
197C4×D15—21no—
198C2×C5×Dic3C22×C411yescharacteristic
199C2×C5×Dic3C22×C411yescharacteristic
200C2×C5×Dic3C22×C411yescharacteristic
201C4×C5×D3—21no—
202C4×C5×D3—21no—
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C22×C411yescharacteristic
206C3×C4×D5—22no—
207C3×C4×D5—22no—
208C3×C4×D5#4112yes—
209C3×C4×D5#4112yes—
210#1200—22no—
211D3×Dic5—22no—
212D5×Dic3—22no—
213D5×Dic3—22no—
214D5×Dic3—22no—
215C3×C5×C8—21no—
216C3×C5×C8—21no—
217C3⋊#168—21no—
218C3⋊#168—21no—
219C3×#168—21no—
220C3×#168—21no—
221C5×C3⋊C8—21no—
222C5×C3⋊C8—21no—
223C22×C4×D3—51no—
224C22×C3×C8—51no—
225C22×C3×C8—51no—
226C2×C3×C42—51no—
227C2×(C2×D3)⋊C4—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—51no—
231C2×C4×Dic3—51no—
232C22×C3⋊C8—51no—
233C22×C3⋊C8—51no—
234#872—51no—
235#872—51no—
236#872—51no—
237#872—51no—
238#872—51no—
239#872—51no—
240#872—51no—
241#872C2×D511yescharacteristic
242C3×C4⋊C8—51no—
243C3×C4⋊C8—51no—
244C3×C4⋊C8—51no—
245C3×C4⋊C8C2×D511yescharacteristic, complemented
246(C2×D3)⋊C8—51no—
247(C2×D3)⋊C8—51no—
248(C2×D3)⋊C8—51no—
249(C2×D3)⋊C8—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8C2×D511yescharacteristic
253(C2×D3)⋊C8C2×D511yescharacteristic
254#815—51no—
255#815—51no—
256#815—51no—
257#815C2×D511yescharacteristic, complemented
258C8×Dic3—51no—
259C8×Dic3—51no—
260C8×Dic3—51no—
261C8×Dic3C2×D511yescharacteristic, complemented
262C4⋊(C3⋊C8)—51no—
263C4⋊(C3⋊C8)—51no—
264C4⋊(C3⋊C8)—51no—
265C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
266C23×D5—31no—
267C22×C4×C5—31no—
268C22×Dic5—31no—
269C2×C4×D5—31no—
270C2×C4×D5—31no—
271C2×C4×D5—31no—
272C2×C4×D5—31no—
273C2×C4×D5—31no—
274C2×C4×D5—62no—
275C2×C4×D5—62no—
276C2×C4×D5C4×D311yescharacteristic
277C2×C4×D5C4×D311yescharacteristic
278C2×C4×D5C22×D311yescharacteristic
279C2×C5×C8—31no—
280C2×C5×C8—31no—
281C2×C5×C8C22×D311yescharacteristic
282C2×C5×C8C22×D311yescharacteristic
283C5×C4⋊C4—31no—
284C5×C4⋊C4—31no—
285C5×C22⋊C4—31no—
286C5×C22⋊C4—31no—
287C42×C5—31no—
288C42×C5C22×D311yescharacteristic
289C22⋊Dic5—31no—
290C22⋊Dic5—31no—
291#685—31no—
292#685—31no—
293#685—31no—
294#685—31no—
295C4⋊Dic5—31no—
296C4⋊Dic5—31no—
297#683—31no—
298#683—31no—
299#683—31no—
300#683—31no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—31no—
304C4×Dic5C4×D311yescharacteristic
305C4×Dic5C4×D311yescharacteristic
306C4×Dic5C22×D311yescharacteristic
307C2×#168—31no—
308C2×#168—31no—
309C2×#168C22×D311yescharacteristic
310C2×#168C22×D311yescharacteristic
311C8×D5—22no—
312C8×D5—22no—
313C8×D5—62no—
314C8×D5—62no—
315C2×#117—151no—
316#433—31no—
317#433—151no—
318#433—151no—
319#433—151no—
320#433—151no—
321#433—151no—
322#433—151no—
323#433—151no—
324C2×C4⋊C8—51no—
325C2×C4⋊C8—151no—
326C2×C22⋊C8—151no—
327C2×C22⋊C8—151no—
328C2×#97—151no—
329C2×C4×C8—151no—
330C22×C3×C5C23×C411yescharacteristic
331C2×D15—21no—
332C2×D15—21no—
333C2×D15—21no—
334C2×C5×D3—21no—
335C2×C5×D3—21no—
336C2×C5×D3—21no—
337C2×C3×D5#11712yes—
338C2×C3×D5#13112yes—
339C2×C3×D5#13112yes—
340D3×D5—44no—
341C3×C4×C5—21no—
342C3×C4×C5—21no—
343C3×C4×C5C2×#4111yescharacteristic
344C3×C4×C5C2×#4111yescharacteristic
345Dic15—21no—
346Dic15—21no—
347Dic15—21no—
348C3×Dic5—21no—
349C3×Dic5—21no—
350C3×Dic5#11712yes—
351C5×Dic3—21no—
352C5×Dic3—21no—
353C5×Dic3—21no—
354C23×D3—51no—
355C22×C3×C4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C22×Dic3—51no—
359C22×Dic3—51no—
360C22×Dic3—51no—
361C2×C4×D3—51no—
362C2×C4×D3—51no—
363C2×C4×D3—51no—
364C2×C4×D3—102no—
365C2×C4×D3—102no—
366C2×C4×D3C22×D511yescharacteristic
367C2×C3×C8—51no—
368C2×C3×C8—51no—
369C2×C3×C8—102no—
370C2×C3×C8—102no—
371C2×C3×C8C22×D511yescharacteristic
372C2×C3×C8C22×D511yescharacteristic
373C3×C42—51no—
374C3×C42—51no—
375C3×C42—51no—
376C3×C42C22×D511yescharacteristic
377(C2×D3)⋊C4—51no—
378(C2×D3)⋊C4—51no—
379(C2×D3)⋊C4—51no—
380(C2×D3)⋊C4—51no—
381(C2×D3)⋊C4—51no—
382(C2×D3)⋊C4—51no—
383(C2×D3)⋊C4C4×D511yescharacteristic
384(C2×D3)⋊C4C4×D511yescharacteristic
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4—51no—
388Dic3⋊C4—51no—
389Dic3⋊C4—51no—
390Dic3⋊C4—51no—
391Dic3⋊C4C4×D511yescharacteristic
392Dic3⋊C4C4×D511yescharacteristic
393C4×Dic3—51no—
394C4×Dic3—51no—
395C4×Dic3—51no—
396C4×Dic3C22×D511yescharacteristic
397C2×C3⋊C8—51no—
398C2×C3⋊C8—51no—
399C2×C3⋊C8—102no—
400C2×C3⋊C8—102no—
401C2×C3⋊C8C22×D511yescharacteristic
402C2×C3⋊C8C22×D511yescharacteristic
403C23×C5—31no—
404C22×D5—31no—
405C22×D5—62no—
406C22×D5—62no—
407C22×D5—62no—
408C22×D5C2×C4×D311yescharacteristic
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—31no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5C2×C4×D311yescharacteristic
415C2×C4×C5C2×C4×D311yescharacteristic
416C2×C4×C5C23×D311yescharacteristic
417C2×Dic5—31no—
418C2×Dic5—31no—
419C2×Dic5—31no—
420C2×Dic5—62no—
421C2×Dic5C2×C4×D311yescharacteristic
422C2×Dic5C2×C4×D311yescharacteristic
423C2×Dic5C2×C4×D311yescharacteristic
424C4×D5—22no—
425C4×D5—22no—
426C4×D5—62no—
427C4×D5—62no—
428C4×D5—62no—
429C4×D5—61no—
430C4×D5—61no—
431C4×D5—62no—
432C4×D5#23712yes—
433C4×D5#23912yes—
434C5×C8—21no—
435C5×C8—21no—
436C5×C8—61no—
437C5×C8—61no—
438#168—21no—
439#168—21no—
440#168—61no—
441#168—61no—
442C23×C4—151no—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8—151no—
446C22×C8—151no—
447#117—31no—
448#117—151no—
449#117—151no—
450#117—151no—
451#117—151no—
452#117—151no—
453#117—151no—
454#117—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C22⋊C4—151no—
458C2×C22⋊C4—151no—
459C2×C42—51no—
460C2×C42—151no—
461C4⋊C8—31no—
462C4⋊C8—51no—
463C4⋊C8—51no—
464C4⋊C8—51no—
465C4⋊C8—151no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8D3×D511yescharacteristic, complemented
469C22⋊C8—31no—
470C22⋊C8—31no—
471C22⋊C8—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474C22⋊C8—151no—
475C22⋊C8—151no—
476C22⋊C8—151no—
477#97—31no—
478#97—151no—
479#97—151no—
480#97—151no—
481C4×C8—31no—
482C4×C8—151no—
483C4×C8—151no—
484C4×C8—151no—
485C2×C3×C5C2×#11711yescharacteristic
486C2×C3×C5C2×#13111yescharacteristic
487C2×C3×C5C2×#13111yescharacteristic
488D15—41no—
489C3×D5#43314yescomplemented
490C5×D3—41no—
491C23×C3—51no—
492C22×D3—51no—
493C22×D3—102no—
494C22×D3—102no—
495C22×D3—102no—
496C22×D3C2×C4×D511yescharacteristic
497C2×C3×C4—51no—
498C2×C3×C4—52no—
499C2×C3×C4—52no—
500C2×C3×C4—51no—
501C2×C3×C4—51no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4C2×C4×D511yescharacteristic
505C2×C3×C4C2×C4×D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C2×Dic3—51no—
508C2×Dic3—51no—
509C2×Dic3—51no—
510C2×Dic3—102no—
511C2×Dic3—102no—
512C2×Dic3—102no—
513C2×Dic3C2×C4×D511yescharacteristic
514C2×Dic3C2×C4×D511yescharacteristic
515C2×Dic3C2×C4×D511yescharacteristic
516C4×D3—21no—
517C4×D3—21no—
518C4×D3—102no—
519C4×D3—102no—
520C4×D3—101no—
521C4×D3—101no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—101no—
525C3×C8—101no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—101no—
529C3⋊C8—101no—
530C22×C5—61no—
531C22×C5—61no—
532C22×C5—61no—
533C22×C5C22×C4×D311yescharacteristic
534C2×D5—61no—
535C2×D5—61no—
536C2×D5—61no—
537C2×D5—124no—
538C2×D5#89212yes—
539C2×D5#90112yes—
540C2×D5#90712yes—
541C4×C5—21no—
542C4×C5—21no—
543C4×C5—61no—
544C4×C5—61no—
545C4×C5—61no—
546C4×C5C2×#23711yescharacteristic
547C4×C5C2×#23911yescharacteristic
548Dic5—21no—
549Dic5—21no—
550Dic5—61no—
551Dic5—61no—
552Dic5—61no—
553Dic5#89212yes—
554C24—151no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—302no—
566C22×C4—302no—
567C2×C8—31no—
568C2×C8—31no—
569C2×C8—51no—
570C2×C8—51no—
571C2×C8—102no—
572C2×C8—102no—
573C2×C8—151no—
574C2×C8—151no—
575C2×C8—302no—
576C2×C8—302no—
577C2×C8C2×D3×D511yescharacteristic
578C2×C8C2×D3×D511yescharacteristic
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—151no—
582C4⋊C4—151no—
583C4⋊C4—151no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—151no—
590C22⋊C4—151no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4—151no—
594C22⋊C4—151no—
595C42—31no—
596C42—51no—
597C42—51no—
598C42—51no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42C2×D3×D511yescharacteristic
603C3×C5C2×#43311yescharacteristic, complemented, Hall
604C22×C3—52no—
605C22×C3—52no—
606C22×C3—52no—
607C22×C3C22×C4×D511yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—101no—
612C2×D3—101no—
613C2×D3—101no—
614C2×D3—204no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—52no—
618C3×C4—101no—
619C3×C4—101no—
620C3×C4D5×#4111yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—101no—
626Dic3—101no—
627Dic3—101no—
628C2×C5—121no—
629C2×C5C2×#89211yescharacteristic
630C2×C5C2×#90111yescharacteristic
631C2×C5C2×#90711yescharacteristic
632D5—121no—
633D5#484014yesdirect product factor
634C23—31no—
635C23—51no—
636C23—151no—
637C23—302no—
638C23—302no—
639C23—302no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—51no—
644C2×C4—52no—
645C2×C4—52no—
646C2×C4—51no—
647C2×C4—51no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—151no—
653C2×C4—151no—
654C2×C4—151no—
655C2×C4—302no—
656C2×C4—302no—
657C2×C4—302no—
658C2×C4—302no—
659C2×C4—302no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4C4×D3×D511yescharacteristic
663C2×C4C4×D3×D511yescharacteristic
664C2×C4C22×D3×D511yescharacteristic
665C8—21no—
666C8—21no—
667C8—61no—
668C8—61no—
669C8—101no—
670C8—101no—
671C8—301no—
672C8—301no—
673C2×C3—54no—
674C2×C3D5×#11711yescharacteristic
675C2×C3D5×#13111yescharacteristic
676C2×C3D5×#13111yescharacteristic
677D3—41no—
678D3—201no—
679C5C2×#484011yescharacteristic, complemented, Sylow
680C22—52no—
681C22—52no—
682C22—52no—
683C22—61no—
684C22—61no—
685C22—61no—
686C22—301no—
687C22—301no—
688C22—301no—
689C22—604no—
690C22C2×C4×D3×D511yescharacteristic
691C4—21no—
692C4—21no—
693C4—52no—
694C4—61no—
695C4—61no—
696C4—61no—
697C4—101no—
698C4—101no—
699C4—301no—
700C4—301no—
701C4—301no—
702C4D5×#23711yescharacteristic
703C4D5×#23911yescharacteristic
704C3D5×#43311yescharacteristic, complemented, Sylow
705C2—54no—
706C2—121no—
707C2—601no—
708C2D5×#89211yescharacteristic
709C2D5×#90111yescharacteristic
710C2D5×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C8C22
prime radicalC22×D3×D5C2×C4
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5C2×#433
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750941C2semidirect
3. C5×#4840C2semidirect
4. C3×D5×C4⋊C8C2semidirect
7. #11747663C2semidirect
8. #11747662C2semidirect
9. #11747659C2semidirect
10. #11747656C2semidirect
11. D5×#815C2semidirect
12. C8×D5×Dic3C2semidirect
13. D5×C4⋊(C3⋊C8)C2semidirect
14. #11746860C2semidirect
15. #11746854C2semidirect
36. C3×C5×C4⋊C8C22semidirect
39. #91099C22semidirect
40. C8×Dic15C22semidirect
41. C4⋊(C3⋊#168)C22semidirect
44. C5×#815C22semidirect
45. C5×C8×Dic3C22semidirect
46. C5×C4⋊(C3⋊C8)C22semidirect
47. C3×#3946C22semidirect
48. C3×#3946C22semidirect
49. C3×C4⋊#168C22semidirect
50. #90982C22semidirect
51. #90982C22semidirect
56. #90954C22semidirect
57. #90953C22semidirect
58. #90951C22semidirect
59. Dic3×#168C22semidirect
67. D5×C4⋊C8D3semidirect
139. #4840D5direct (N × H)
160. C5×C4⋊C8C2×D3semidirect
175. #3946C2×D3semidirect
176. #3946C2×D3semidirect
180. C4⋊#168C2×D3semidirect
245. C3×C4⋊C8C2×D5semidirect
257. #815C2×D5semidirect
261. C8×Dic3C2×D5semidirect
265. C4⋊(C3⋊C8)C2×D5semidirect
468. C4⋊C8D3×D5semidirect
489. C3×D5#433semidirect
603. C3×C5C2×#433semidirect
633. D5#4840direct (N × H)
679. C5C2×#4840semidirect
704. C3D5×#433semidirect

Maximal subgroups

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

subgroupindex
D5×#8722
#117509412
C5×#48402
C3×D5×C4⋊C82
D5×(C2×D3)⋊C82
#117476632
#117476622
#117476592
#117476562
D5×#8152
C8×D5×Dic32
D5×C4⋊(C3⋊C8)2
#117468602
#117468542
D5×#4333
C2×#48405