Finite Group Databasebeta

← C2×#11753089 #14483750

Subgroups — C2×#11753089 #14483750

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91768C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic, complemented
4C2×Dic5×#67C211yesmaximal, characteristic, complemented
5C2×#91549C211yesmaximal, characteristic, complemented
6C2×#91549C211yesmaximal, characteristic, complemented
7C2×#91539C211yesmaximal, characteristic, complemented
8C2×#91449C211yesmaximal, characteristic, complemented
9C2×#91442C211yesmaximal, characteristic, complemented
10C2×#91441C211yesmaximal, characteristic, complemented
11C2×#91423C211yesmaximal, characteristic, complemented
12C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#91372C211yesmaximal, characteristic, complemented
14C2×#91371C211yesmaximal, characteristic, complemented
15C2×#91343C211yesmaximal, characteristic, complemented
16#11753089C2116yesmaximal, direct product factor
17C2×#65948—31nomaximal, Hall
18C22×C5×#67C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C22×D5×Dic3C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37#91768C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C5×#884C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4027C2218yescomplemented
45Dic5×#67C2218yescomplemented
46#91549C2218yescomplemented
47#91549C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×#6669C2211yescharacteristic
52C2×#6669C2211yescharacteristic
53#91539C2218yescomplemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91449C2218yescomplemented
61#91442C2218yescomplemented
62#91441C2218yescomplemented
63#91423C2218yescomplemented
64D5×Dic3⋊C4C2218yescomplemented
65#91372C2218yescomplemented
66#91371C2218yescomplemented
67#91343C2218yescomplemented
68C2×#5540—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4084—31no—
71C2×#4084—31no—
72C2×#4084—31no—
73C2×#4081—31no—
74C2×#4081—31no—
75C2×D4×Dic5—31no—
76C2×C4×C22⋊D5—31no—
77C2×#4072—31no—
78#65948—316no—
79C2×D5×C4⋊C4—31no—
80C2×#4036—31no—
81C2×#4027—31no—
82C2×#4027D311yescharacteristic, complemented
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C5×#67—24no—
96C2×C5×#67—42no—
97C2×C5×#67C2314yes—
98C2×C5×#67C2314yes—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C5×D12—42no—
102C2×C5×D12C2314yes—
103C2×C4×C5×D3—24no—
104C2×C4×C5×D3C2314yes—
105C2×C3×C22⋊D5—24no—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5—42no—
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2314yes—
112C2×C3×C4×D5—42no—
113C2×C3×C4×D5C2314yes—
114C2×#1201—24no—
115C2×#1201—24no—
116C2×#1201C2314yes—
117C2×#1201C2314yes—
118C2×D3×Dic5—42no—
119C2×D3×Dic5C2314yes—
120C2×D5×Dic3—24no—
121C2×D5×Dic3—42no—
122C2×D5×Dic3C2314yes—
123C2×D5×Dic3C2314yes—
124C3×C5×C22⋊C4C2314yes—
125#6719C2314yes—
126#6719C2314yes—
127C4⋊Dic15C2314yes—
128#6712C2314yes—
129#6712C2314yes—
130C4×Dic15C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×Dic3⋊C4C2314yes—
133C3×#685C2314yes—
134C3×#683C2314yes—
135C3×C4×Dic5C2314yes—
136Dic3⋊Dic5C2314yes—
137Dic3⋊Dic5C2314yes—
138Dic3⋊Dic5C2314yes—
139#6669C2314yes—
140#6669C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×C4×D4—51no—
148C2×#939—51no—
149C2×#939—51no—
150C2×#930—51no—
151C2×#929—51no—
152C2×C4×#67—51no—
153C22×Dic3⋊C4—51no—
154#5540—516no—
155C2×#894—51no—
156C2×#889—51no—
157C2×#884D511yescharacteristic, complemented
158C2×#67⋊C4—51no—
159C2×#67⋊C4—51no—
160C2×#879—51no—
161C2×#876—51no—
162C2×#872—51no—
163C22×C5×D4—31no—
164C22×C5×D4—31no—
165C22×C5×D4—31no—
166C23×C4×C5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5C2×D311yescharacteristic
170C23×Dic5—31no—
171C23×Dic5C2×D311yescharacteristic
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic
175C5×#121—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186#4084—38no—
187#4084—38no—
188#4084—38no—
189#4081—38no—
190#4081—38no—
191D4×Dic5—38no—
192C4×C22⋊D5—38no—
193C2×#685C2×D311yescharacteristic
194#4072—38no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198C2×C4⋊Dic5—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683C2×D311yescharacteristic
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5C2×D311yescharacteristic
207D5×C4⋊C4—38no—
208#4036—38no—
209#4027—38no—
210#4027C2×D318yescomplemented
211#4025—38no—
212#4025—38no—
213C2×#553—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3—22no—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3C2412yes—
226C22×C5×D3C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5#4114yes—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C2×Dic15—22no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15C2412yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C5×#67—28no—
244C5×#67—44no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3#4114yes—
247C2×C5×Dic3C2412yes—
248C2×C5×Dic3C2412yes—
249C5×D12—44no—
250C4×C5×D3—28no—
251C3×C22⋊D5—28no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—44no—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C3×C4×D5—44no—
260#1201—28no—
261#1201—28no—
262D3×Dic5—44no—
263D5×Dic3—28no—
264D5×Dic3—44no—
265C22×C3×D4—51no—
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C22×#67—51no—
269C22×#67—51no—
270C22×#67C2×D511yescharacteristic
271C22×#67C2×D511yescharacteristic
272C23×Dic3—51no—
273C23×Dic3—51no—
274C22×D12C2×D511yescharacteristic
275C22×C4×D3—51no—
276C22×C4×D3C2×D511yescharacteristic
277C3×C4×D4—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×C3×C42—51no—
282C2×#217—51no—
283C2×#217—51no—
284#939—58no—
285#939—58no—
286#930—58no—
287#929—58no—
288C4×#67—58no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—58no—
304C2×Dic3⋊C4C2×D511yescharacteristic
305C2×C4×Dic3—51no—
306C2×C4×Dic3—51no—
307#894—58no—
308#889—58no—
309#884C2×D518yescomplemented
310#67⋊C4—58no—
311#67⋊C4—58no—
312#879—58no—
313#876—58no—
314#872—58no—
315C24×C5—31no—
316C24×C5—31no—
317C24×C5C22×D311yescharacteristic
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—34no—
321C2×C5×D4—34no—
322C2×C5×D4—64no—
323C2×C5×D4—122no—
324C2×C5×D4—122no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—34no—
328C22×C4×C5—64no—
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C2×C22⋊D5—24no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5C22×D314yes—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—42no—
343C22×Dic5—122no—
344C22×Dic5C22×D311yescharacteristic
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D314yes—
348C2×C4×D5—34no—
349C2×C4×D5—34no—
350C2×C4×D5—42no—
351C2×C4×D5—64no—
352C2×C4×D5—122no—
353C2×C4×D5C22×D314yes—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4C22×D314yes—
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364#685C22×D314yes—
365C4⋊Dic5—34no—
366C4⋊Dic5—34no—
367C4⋊Dic5—34no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683C22×D314yes—
374C4×Dic5—34no—
375C4×Dic5—34no—
376C4×Dic5C22×D314yes—
377#553—1516no—
378C2×#126—151no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#121—31no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—51no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×#117—151no—
392C22×C4⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—44no—
397C22×C3×C5C2×#4112yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5H(5,𝔽2)12yes—
400C22×C3×C5C2511yescharacteristic
401C2×C5×D3—22no—
402C2×C5×D3—22no—
403C2×C5×D3—22no—
404C2×C5×D3—22no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—44no—
408C2×C5×D3—44no—
409C2×C3×D5—28no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5C2×#4114yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3C2×#4114yes—
424C24×C3—51no—
425C24×C3C22×D511yescharacteristic
426C23×D3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—104no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—54no—
434C22×C3×C4—54no—
435C22×C3×C4—202no—
436C22×C3×C4—202no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C2×#67—24no—
440C2×#67—42no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—104no—
444C2×#67—104no—
445C2×#67C22×D514yes—
446C2×#67C22×D514yes—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—54no—
452C22×Dic3—54no—
453C22×Dic3—104no—
454C22×Dic3—202no—
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D511yescharacteristic
457C2×D12—42no—
458C2×D12C22×D514yes—
459C2×C4×D3—24no—
460C2×C4×D3—54no—
461C2×C4×D3—202no—
462C2×C4×D3C22×D514yes—
463C3×C4⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4C22×D514yes—
466C3×C42—54no—
467#217—54no—
468#217—54no—
469(C2×D3)⋊C4—54no—
470(C2×D3)⋊C4—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4C22×D514yes—
475C4⋊Dic3—54no—
476Dic3⋊C4—54no—
477Dic3⋊C4—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4C22×D514yes—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—32no—
490C23×C5—32no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5—62no—
494C23×C5—62no—
495C23×C5—62no—
496C23×C5—62no—
497C23×C5C23×D312yes—
498C23×C5C23×D311yescharacteristic
499C22×D5—22no—
500C22×D5—22no—
501C22×D5#23514yes—
502C22×D5C23×D312yes—
503C5×D4—68no—
504C5×D4—124no—
505C5×D4—124no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—34no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—68no—
512C2×C4×C5—62no—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—28no—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—44no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—124no—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534C4×D5—44no—
535C4×D5—68no—
536C4×D5—124no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—31no—
540C22×D4—51no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—51no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#126—158no—
550#126—158no—
551#125—158no—
552#123—158no—
553#123—158no—
554#121—38no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—58no—
559C4×D4—158no—
560C4×D4—158no—
561C4×D4—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—158no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C4⋊C4—151no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4D3×D511yescharacteristic
584C2×C42—51no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5—42no—
588C2×C3×C5#55314yescomplemented
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592C3×D5—24no—
593C5×D3—42no—
594C5×D3—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—54no—
599C23×C3—52no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3C23×D512yes—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3C23×D512yes—
611C22×D3C23×D512yes—
612C3×D4—108no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—102no—
619C2×C3×C4—102no—
620C2×C3×C4—102no—
621C2×C3×C4—204no—
622C2×C3×C4—204no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625#67—28no—
626#67—44no—
627#67—108no—
628#67—108no—
629C2×Dic3—22no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—102no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—108no—
639C2×Dic3—204no—
640C2×Dic3#71114yes—
641C2×Dic3C23×D512yes—
642C2×Dic3C23×D512yes—
643D12—44no—
644C4×D3—28no—
645C4×D3—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—44no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—62no—
656C22×C5—124no—
657C22×C5—124no—
658C22×C5C2×#23512yes—
659C22×C5#100412yes—
660C22×C5D3×#4112yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—28no—
665C2×D5C2×#23514yes—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—34no—
669C4×C5—62no—
670Dic5—22no—
671Dic5—22no—
672Dic5—22no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—31no—
679C24—51no—
680C24C2×D3×D511yescharacteristic
681C2×D4—34no—
682C2×D4—34no—
683C2×D4—34no—
684C2×D4—54no—
685C2×D4—64no—
686C2×D4—104no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—304no—
692C2×D4—304no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—51no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—54no—
700C22×C4—54no—
701C22×C4—64no—
702C22×C4—154no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—202no—
710C22×C4—202no—
711C22×C4—304no—
712C22×C4—602no—
713C22×C4—602no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—54no—
718C4⋊C4—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C22⋊C4—34no—
727C22⋊C4—54no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4C2×D3×D514yes—
736C42—54no—
737C42—154no—
738C42—154no—
739C3×C5C2×#55311yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—44no—
744C22×C3—54no—
745C22×C3—108no—
746C22×C3—102no—
747C22×C3—102no—
748C22×C3C2×#71112yes—
749C22×C3#414412yes—
750C22×C3D5×#4112yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—44no—
759C2×D3—44no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—102no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—102no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3C2×#71114yes—
771C2×C5—42no—
772C2×C5—122no—
773C2×C5—122no—
774C2×C5#554014yescomplemented
775C2×C5C22×#23511yescharacteristic
776C2×C5C2×#100411yescharacteristic
777C2×C5C2×D3×#4111yescharacteristic
778D5—24no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—32no—
783C23—32no—
784C23—54no—
785C23—52no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—102no—
793C23—102no—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796D4—68no—
797D4—108no—
798D4—124no—
799D4—124no—
800D4—308no—
801D4—308no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—34no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—52no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—68no—
811C2×C4—62no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—152no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—204no—
820C2×C4—204no—
821C2×C4—308no—
822C2×C4—302no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—42no—
831C2×C3—104no—
832C2×C3#6594814yescomplemented
833C2×C3C22×#71111yescharacteristic
834C2×C3C2×#414411yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836D3—42no—
837D3—42no—
838C5C2×#554011yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—44no—
843C22—54no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—108no—
851C22—102no—
852C22—102no—
853C22—124no—
854C22—124no—
855C22D5×#23512yes—
856C22D3×#71112yes—
857C22#9202512yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—34no—
862C4—62no—
863C4—102no—
864C4—102no—
865C4—102no—
866C4—302no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6594811yescharacteristic, complemented, Sylow
871C2—42no—
872C2—104no—
873C2—122no—
874C2—122no—
875C2#1175308914yesdirect product factor
876C2C2×D5×#23511yescharacteristic
877C2C2×D3×#71111yescharacteristic
878C2C2×#9202511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#553
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
1. C2×#91768C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4027C2semidirect
4. C2×Dic5×#67C2semidirect
5. C2×#91549C2semidirect
6. C2×#91549C2semidirect
7. C2×#91539C2semidirect
8. C2×#91449C2semidirect
9. C2×#91442C2semidirect
10. C2×#91441C2semidirect
11. C2×#91423C2semidirect
12. C2×D5×Dic3⋊C4C2semidirect
13. C2×#91372C2semidirect
14. C2×#91371C2semidirect
15. C2×#91343C2semidirect
16. #11753089C2direct (N × H)
37. #91768C22semidirect
40. C5×#884C22semidirect
44. C3×#4027C22semidirect
45. Dic5×#67C22semidirect
46. #91549C22semidirect
47. #91549C22semidirect
53. #91539C22semidirect
60. #91449C22semidirect
61. #91442C22semidirect
62. #91441C22semidirect
63. #91423C22semidirect
64. D5×Dic3⋊C4C22semidirect
65. #91372C22semidirect
66. #91371C22semidirect
67. #91343C22semidirect
82. C2×#4027D3semidirect
157. C2×#884D5semidirect
210. #4027C2×D3semidirect
309. #884C2×D5semidirect
588. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
774. C2×C5#5540semidirect
832. C2×C3#65948semidirect
838. C5C2×#5540semidirect
870. C3C2×#65948semidirect
875. C2#11753089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917682
C2×C5×#8842
C2×C3×#40272
C2×Dic5×#672
C2×#915492
C2×#915392
C2×#914492
C2×#914422
C2×#914412
C2×#914232
C2×D5×Dic3⋊C42
C2×#913722
C2×#913712
C2×#913432
#117530892
C2×#659483
C2×#55405