Finite Group Databasebeta

← C2×#11752922 #14483769

Subgroups — C2×#11752922 #14483769

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×#886C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91565C211yesmaximal, characteristic, complemented
5C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91440C211yesmaximal, characteristic, complemented
9C2×#91434C211yesmaximal, characteristic, complemented
10C2×#91414C211yesmaximal, characteristic, complemented
11C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C2×#91408C211yesmaximal, characteristic, complemented
13C2×#91400C211yesmaximal, characteristic, complemented
14C2×#91361C211yesmaximal, characteristic, complemented
15C2×#91335C211yesmaximal, characteristic, complemented
16#11752922C2116yesmaximal, direct product factor
17C2×#65995—31nomaximal, Hall
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×C4⋊Dic3C2211yescharacteristic
41C2×C5×C4⋊Dic3C2211yescharacteristic
42C5×#886C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C3×#4030C2218yescomplemented
46#91565C2218yescomplemented
47Dic3×C22⋊D5C2218yescomplemented
48Dic3×C22⋊D5C2218yescomplemented
49#91549C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91440C2218yescomplemented
61#91434C2218yescomplemented
62#91414C2218yescomplemented
63D5×C4⋊Dic3C2218yescomplemented
64#91408C2218yescomplemented
65#91400C2218yescomplemented
66#91361C2218yescomplemented
67#91335C2218yescomplemented
68C2×#5618—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4085—31no—
71C2×#4084—31no—
72C2×C4×C22⋊D5—31no—
73C2×C4×C22⋊D5—31no—
74#65995—316no—
75C2×#4044—31no—
76C2×#4039—31no—
77C2×D5×C4⋊C4—31no—
78C2×#4035—31no—
79C2×#4030—31no—
80C2×#4030D311yescharacteristic, complemented
81C2×#4029—31no—
82C2×#4027—31no—
83C2×#4025—31no—
84C2×#4023—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C5×#67—42no—
96C2×C5×#67C2314yes—
97C22×C5×Dic3—42no—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2314yes—
102C2×C3×C22⋊D5—24no—
103C2×C3×C22⋊D5—24no—
104C2×C3×C22⋊D5C2314yes—
105C2×C3×C22⋊D5C2314yes—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×D20—24no—
109C2×C3×D20C2314yes—
110C2×C3×C4×D5—24no—
111C2×C3×C4×D5C2314yes—
112C2×#1201—24no—
113C2×#1201—42no—
114C2×#1201C2314yes—
115C2×#1201C2314yes—
116C2×D3×Dic5—24no—
117C2×D3×Dic5C2314yes—
118C2×D5×Dic3—42no—
119C2×D5×Dic3—42no—
120C2×D5×Dic3—42no—
121C2×D5×Dic3C2314yes—
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×(C2×D3)⋊C4C2314yes—
133C5×C4⋊Dic3C2314yes—
134C5×C4⋊Dic3C2314yes—
135C3×#685C2314yes—
136C3×#683C2314yes—
137Dic3⋊Dic5C2314yes—
138#6668C2314yes—
139#6668C2314yes—
140#6668C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#121—51no—
148C2×#939—51no—
149C2×#939—51no—
150C2×#938—51no—
151C2×D4×Dic3—51no—
152C2×D4×Dic3—51no—
153C2×D4×Dic3—51no—
154C2×C4×#67—51no—
155C22×C4⋊Dic3—51no—
156#5618—516no—
157C2×#892—51no—
158C2×#890—51no—
159C2×#886—51no—
160C2×#886D511yescharacteristic, complemented
161C2×#879—51no—
162C2×#879—51no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5C2×D311yescharacteristic
168C22×C22⋊D5C2×D311yescharacteristic
169C23×Dic5—31no—
170C22×D20C2×D311yescharacteristic
171C22×C4×D5—31no—
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic
175C5×#123—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4C2×D311yescharacteristic
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184#4085—38no—
185#4084—38no—
186C4×C22⋊D5—38no—
187C4×C22⋊D5—38no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685C2×D311yescharacteristic
192C2×C4⋊Dic5—31no—
193C2×C4⋊Dic5—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683C2×D311yescharacteristic
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203#4044—38no—
204#4039—38no—
205D5×C4⋊C4—38no—
206#4035—38no—
207#4030—38no—
208#4030C2×D318yescomplemented
209#4029—38no—
210#4027—38no—
211#4025—38no—
212#4023—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×D3C2412yes—
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5#4114yes—
229C22×C3×D5C2412yes—
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—44no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—44no—
248C2×C5×Dic3C2412yes—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C3×C22⋊D5—28no—
252C3×C22⋊D5—28no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5#4114yes—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C3×D20—28no—
258C3×C4×D5—28no—
259#1201—28no—
260#1201—44no—
261D3×Dic5—28no—
262D5×Dic3—44no—
263D5×Dic3—44no—
264D5×Dic3—44no—
265C22×C3×D4—51no—
266C22×C3×D4—51no—
267C22×C3×D4—51no—
268C23×C3×C4—51no—
269C22×#67—51no—
270C22×#67—51no—
271C22×#67C2×D511yescharacteristic
272C23×Dic3—51no—
273C23×Dic3—51no—
274C23×Dic3—51no—
275C23×Dic3C2×D511yescharacteristic
276C22×C4×D3—51no—
277C3×#121—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286#939—58no—
287#939—58no—
288#938—58no—
289D4×Dic3—58no—
290D4×Dic3—58no—
291D4×Dic3—58no—
292C4×#67—58no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3—58no—
301C2×C4⋊Dic3C2×D511yescharacteristic
302C2×C4⋊Dic3C2×D511yescharacteristic
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308C2×C4×Dic3—51no—
309#892—58no—
310#890—58no—
311#886—58no—
312#886C2×D518yescomplemented
313#879—58no—
314#879—58no—
315C24×C5—31no—
316C24×C5C22×D311yescharacteristic
317C23×D5C22×D311yescharacteristic
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—122no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
325C22×C4×C5—122no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C2×C22⋊D5—24no—
329C2×C22⋊D5—24no—
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—64no—
333C2×C22⋊D5—122no—
334C2×C22⋊D5C22×D314yes—
335C2×C22⋊D5C22×D314yes—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—64no—
342C22×Dic5C22×D311yescharacteristic
343C22×Dic5C22×D311yescharacteristic
344C2×D20—24no—
345C2×D20C22×D314yes—
346C2×C4×D5—24no—
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—34no—
350C2×C4×D5—122no—
351C2×C4×D5—122no—
352C2×C4×D5—122no—
353C2×C4×D5C22×D314yes—
354C5×C4⋊C4—34no—
355C5×C4⋊C4—34no—
356C5×C22⋊C4—34no—
357C5×C22⋊C4—34no—
358C5×C22⋊C4C22×D314yes—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685C22×D314yes—
366C4⋊Dic5—34no—
367C4⋊Dic5—34no—
368#683—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683C22×D314yes—
374C4×Dic5—34no—
375C4×Dic5—34no—
376C4×Dic5—34no—
377#553—1516no—
378C2×#126—151no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—31no—
382C2×#123—151no—
383C2×#121—51no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—151no—
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—44no—
405C2×C3×D5—28no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—44no—
412C2×C3×D5C2×#4114yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419C3×Dic5—22no—
420C3×Dic5C2×#4114yes—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—54no—
430C2×C3×D4—54no—
431C2×C3×D4—104no—
432C2×C3×D4—104no—
433C2×C3×D4—104no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—54no—
437C22×C3×C4—104no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C2×#67—42no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—104no—
444C2×#67—202no—
445C2×#67C22×D514yes—
446C22×Dic3—42no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—54no—
452C22×Dic3—54no—
453C22×Dic3—54no—
454C22×Dic3—202no—
455C22×Dic3—202no—
456C22×Dic3—202no—
457C22×Dic3C22×D511yescharacteristic
458C22×Dic3C22×D511yescharacteristic
459C22×Dic3C22×D511yescharacteristic
460C22×Dic3C22×D514yes—
461C2×C4×D3—54no—
462C2×C4×D3—104no—
463C3×C4⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4C22×D514yes—
466#217—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4C22×D514yes—
473(C2×D3)⋊C4C22×D514yes—
474C4⋊Dic3—54no—
475C4⋊Dic3—54no—
476C4⋊Dic3—54no—
477C4⋊Dic3—54no—
478C4⋊Dic3C22×D514yes—
479C4⋊Dic3C22×D514yes—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483C4×Dic3—54no—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—32no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5C23×D312yes—
494C23×C5C23×D311yescharacteristic
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—22no—
499C22×D5—22no—
500C22×D5#23714yes—
501C22×D5C23×D312yes—
502C22×D5C23×D312yes—
503C5×D4—124no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—124no—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—28no—
516C22⋊D5—28no—
517C22⋊D5—68no—
518C22⋊D5—124no—
519C2×Dic5—22no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—62no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—68no—
529C2×Dic5#23714yes—
530C2×Dic5C23×D312yes—
531C2×Dic5C23×D312yes—
532D20—28no—
533C4×D5—28no—
534C4×D5—124no—
535C4×D5—124no—
536C4×D5—124no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—51no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#126—158no—
550#126—158no—
551#125—158no—
552#123—38no—
553#123—158no—
554#121—58no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—158no—
559C4×D4—158no—
560C4×D4—158no—
561C4×D4—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—158no—
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—31no—
576C2×C22⋊C4—51no—
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—151no—
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—
593C3×D5—42no—
594C5×D3—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—54no—
599C23×C3—52no—
600C23×C3—52no—
601C23×C3—102no—
602C23×C3—102no—
603C23×C3—102no—
604C23×C3—102no—
605C23×C3—102no—
606C23×C3C23×D512yes—
607C23×C3C23×D511yescharacteristic
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3C23×D512yes—
612C3×D4—108no—
613C3×D4—108no—
614C3×D4—108no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—54no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—108no—
621C2×C3×C4—102no—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—44no—
625#67—108no—
626#67—204no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—44no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—204no—
640C2×Dic3—204no—
641C2×Dic3—204no—
642C2×Dic3C23×D512yes—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645C4×D3—108no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—44no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—124no—
654C22×C5C2×#23712yes—
655C22×C5C2×#23712yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—28no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—44no—
665C2×D5C2×#23714yes—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—62no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5C2×#23714yes—
677C24—31no—
678C24—51no—
679C24—51no—
680C24C2×D3×D511yescharacteristic
681C2×D4—34no—
682C2×D4—54no—
683C2×D4—54no—
684C2×D4—54no—
685C2×D4—104no—
686C2×D4—104no—
687C2×D4—104no—
688C2×D4—122no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—304no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—34no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—54no—
700C22×C4—104no—
701C22×C4—122no—
702C22×C4—154no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—304no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4—602no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—54no—
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—34no—
728C22⋊C4—54no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4C2×D3×D514yes—
736C42—154no—
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×C3—102no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—204no—
752C22×C3#414412yes—
753C22×C3D5×#4112yes—
754C22×C3D5×#4112yes—
755C22×C3C24×D511yescharacteristic
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—44no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—54no—
763C3×C4—102no—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—42no—
772C2×C5—122no—
773C2×C5#561814yescomplemented
774C2×C5C22×#23711yescharacteristic
775C2×C5C22×#23711yescharacteristic
776C2×C5C2×#100911yescharacteristic
777D5—24no—
778D5—42no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—32no—
783C23—54no—
784C23—52no—
785C23—52no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—102no—
790C23—102no—
791C23—102no—
792C23—102no—
793C23—102no—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796D4—108no—
797D4—108no—
798D4—108no—
799D4—124no—
800D4—308no—
801D4—604no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—54no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—108no—
814C2×C4—102no—
815C2×C4—124no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—308no—
821C2×C4—302no—
822C2×C4—302no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—42no—
831C2×C3—104no—
832C2×C3—202no—
833C2×C3#6599514yescomplemented
834C2×C3C2×#414411yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836C2×C3C2×D5×#4111yescharacteristic
837D3—42no—
838C5C2×#561811yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—44no—
843C22—54no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—108no—
848C22—102no—
849C22—102no—
850C22—102no—
851C22—102no—
852C22—102no—
853C22—124no—
854C22—204no—
855C22#9201812yes—
856C22D5×#23712yes—
857C22D5×#23712yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—54no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—302no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6599511yescharacteristic, complemented, Sylow
871C2—42no—
872C2—104no—
873C2—122no—
874C2—202no—
875C2#1175292214yesdirect product factor
876C2C2×#9201811yescharacteristic
877C2C2×D5×#23711yescharacteristic
878C2C2×D5×#23711yescharacteristic
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×#886C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91565C2semidirect
5. C2×Dic3×C22⋊D5C2semidirect
6. C2×Dic3×C22⋊D5C2semidirect
7. C2×#91549C2semidirect
8. C2×#91440C2semidirect
9. C2×#91434C2semidirect
10. C2×#91414C2semidirect
11. C2×D5×C4⋊Dic3C2semidirect
12. C2×#91408C2semidirect
13. C2×#91400C2semidirect
14. C2×#91361C2semidirect
15. C2×#91335C2semidirect
16. #11752922C2direct (N × H)
37. #91768C22semidirect
42. C5×#886C22semidirect
45. C3×#4030C22semidirect
46. #91565C22semidirect
47. Dic3×C22⋊D5C22semidirect
48. Dic3×C22⋊D5C22semidirect
49. #91549C22semidirect
60. #91440C22semidirect
61. #91434C22semidirect
62. #91414C22semidirect
63. D5×C4⋊Dic3C22semidirect
64. #91408C22semidirect
65. #91400C22semidirect
66. #91361C22semidirect
67. #91335C22semidirect
80. C2×#4030D3semidirect
160. C2×#886D5semidirect
208. #4030C2×D3semidirect
312. #886C2×D5semidirect
588. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
773. C2×C5#5618semidirect
833. C2×C3#65995semidirect
838. C5C2×#5618semidirect
870. C3C2×#65995semidirect
875. C2#11752922direct (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×#8862
C2×C3×#40302
C2×#915652
C2×Dic3×C22⋊D52
C2×#915492
C2×#914402
C2×#914342
C2×#914142
C2×D5×C4⋊Dic32
C2×#914082
C2×#914002
C2×#913612
C2×#913352
#117529222
C2×#659953
C2×#56185