Finite Group Databasebeta

← C2×#11754568 #14483670

Subgroups — C2×#11754568 #14483670

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×#91818C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×#91565C211yesmaximal, characteristic, complemented
5C2×#91558C211yesmaximal, characteristic, complemented
6C2×#91533C211yesmaximal, characteristic, complemented
7C2×#91531C211yesmaximal, characteristic, complemented
8#11754568C2116yesmaximal, direct product factor
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91440C211yesmaximal, characteristic, complemented
11C2×#91405C211yesmaximal, characteristic, complemented
12C2×#91403C211yesmaximal, characteristic, complemented
13C2×D3×#683C211yesmaximal, characteristic, complemented
14C2×#91378C211yesmaximal, characteristic, complemented
15C2×#91363C211yesmaximal, characteristic, complemented
16C2×#91348C211yesmaximal, characteristic, complemented
17C2×#65874—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1200C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31#91818C2218yescomplemented
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C4×C5×#67C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C4×C5×Dic3C2211yescharacteristic
41C2×C3×C22⋊Dic5C2211yescharacteristic
42C3×C4×C22⋊D5C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46#91565C2218yescomplemented
47#91558C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57#91533C2218yescomplemented
58#91531C2218yescomplemented
59C2×Dic3×Dic5C2211yescharacteristic
60#91454C2218yescomplemented
61#91440C2218yescomplemented
62#91405C2218yescomplemented
63#91403C2218yescomplemented
64D3×#683C2218yescomplemented
65#91378C2218yescomplemented
66#91363C2218yescomplemented
67#91348C2218yescomplemented
68C2×#5558—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4076—31no—
73C2×#4075—31no—
74C2×C4×C22⋊D5D311yescharacteristic, complemented
75C22×#683—31no—
76#65874—316no—
77C2×#4040—31no—
78C2×#4035—31no—
79C2×#4030—31no—
80C2×#4027—31no—
81C2×#4027—31no—
82C2×#4025—31no—
83C2×#4022—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5—42no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2314yes—
93C2×#1220—42no—
94C2×#1220C2314yes—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×C5×#67—24no—
99C2×C5×#67C2314yes—
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C2×C4×C5×D3—42no—
104C2×C4×C5×D3C2314yes—
105C2×C3×C22⋊D5—24no—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×C3×C4×D5—42no—
111C2×C3×C4×D5C2314yes—
112C2×#1203—24no—
113C2×#1203C2314yes—
114C2×#1202—42no—
115C2×#1202C2314yes—
116C2×#1201—24no—
117C2×#1201C2314yes—
118C2×#1200—24no—
119C2×#1200C2314yes—
120C2×D3×Dic5—24no—
121C2×D3×Dic5—42no—
122C2×D3×Dic5C2314yes—
123C2×D3×Dic5C2314yes—
124#6719C2314yes—
125#6714C2314yes—
126#6714C2314yes—
127#6712C2314yes—
128#6712C2314yes—
129C5×#217C2314yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×Dic3⋊C4C2314yes—
132C4×C5×Dic3C2314yes—
133C3×C22⋊Dic5C2314yes—
134C3×#685C2314yes—
135C3×#683C2314yes—
136C3×C4×Dic5C2314yes—
137Dic3⋊Dic5C2314yes—
138#6669C2314yes—
139#6669C2314yes—
140#6668C2314yes—
141#6668C2314yes—
142#6668C2314yes—
143#6667C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×C4×D4—51no—
148C2×#938—51no—
149C2×#938—51no—
150C2×#929—51no—
151C2×#929—51no—
152C2×C4×#67—51no—
153C2×C4×#67D511yescharacteristic, complemented
154#5558—516no—
155C2×#892—51no—
156C2×D3×C4⋊C4—51no—
157C2×#884—51no—
158C2×#884—51no—
159C2×#879—51no—
160C2×#879—51no—
161C2×C4×D12—51no—
162C2×#870—51no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C23×C4×C5C2×D311yescharacteristic
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5C2×D311yescharacteristic
170C23×Dic5—31no—
171C23×Dic5—31no—
172C22×D20—31no—
173C22×C4×D5—31no—
174C22×C4×D5C2×D311yescharacteristic
175C4×C5×D4—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C42×C5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5C2×D311yescharacteristic
182#4085—38no—
183#4085—38no—
184#4076—38no—
185#4075—38no—
186C4×C22⋊D5C2×D318yescomplemented
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685C2×D311yescharacteristic
193C2×C4⋊Dic5—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—38no—
202C2×#683C2×D311yescharacteristic
203C2×C4×Dic5—31no—
204C2×C4×Dic5C2×D311yescharacteristic
205#4040—38no—
206#4035—38no—
207#4030—38no—
208#4027—38no—
209#4027—38no—
210#4025—38no—
211#4022—38no—
212#4018—38no—
213C2×#553—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15C2412yes—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3#4114yes—
226C22×C5×D3C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—44no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236#1220—44no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C5×#67—28no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3C2412yes—
248C2×C5×Dic3C2412yes—
249C2×C5×Dic3C2412yes—
250C4×C5×D3—44no—
251C3×C22⋊D5—28no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5#4114yes—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C3×C4×D5—44no—
259#1203—28no—
260#1202—44no—
261#1201—28no—
262#1200—28no—
263D3×Dic5—28no—
264D3×Dic5—44no—
265C22×C3×D4—51no—
266C23×C3×C4—51no—
267C23×C3×C4C2×D511yescharacteristic
268C22×#67—51no—
269C22×#67—51no—
270C22×#67—51no—
271C22×#67C2×D511yescharacteristic
272C22×D12—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
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⋊C4—51no—
281C2×C3×C42—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217C2×D511yescharacteristic
286#938—58no—
287#938—58no—
288#929—58no—
289#929—58no—
290C4×#67—58no—
291C4×#67C2×D518yescomplemented
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4C2×D511yescharacteristic
305C2×C4×Dic3—51no—
306C2×C4×Dic3C2×D511yescharacteristic
307#892—58no—
308D3×C4⋊C4—58no—
309#884—58no—
310#884—58no—
311#879—58no—
312#879—58no—
313C4×D12—58no—
314#870—58no—
315C24×C5—31no—
316C24×C5C22×D311yescharacteristic
317C23×D5—31no—
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—64no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
325C22×C4×C5—42no—
326C22×C4×C5—122no—
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D314yes—
330C2×C22⋊D5—24no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5—122no—
337C2×C22⋊D5C22×D314yes—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—64no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C2×D20—34no—
349C2×D20—122no—
350C2×C4×D5—34no—
351C2×C4×D5—42no—
352C2×C4×D5—64no—
353C2×C4×D5C22×D314yes—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C42×C5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5C22×D314yes—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685C22×D314yes—
366C4⋊Dic5—34no—
367#683—34no—
368#683—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683C22×D314yes—
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—151no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—31no—
388C2×C4×D4—51no—
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×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—44no—
405C2×C5×D3—28no—
406C2×C5×D3—22no—
407C2×C5×D3—22no—
408C2×C5×D3C2×#4114yes—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5C2×#4114yes—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3C22×D511yescharacteristic
426C23×D3—51no—
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—104no—
430C22×C3×C4—42no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—54no—
435C22×C3×C4—202no—
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D514yes—
439C2×#67—24no—
440C2×#67—54no—
441C2×#67—54no—
442C2×#67—54no—
443C2×#67—104no—
444C2×#67—202no—
445C2×#67—202no—
446C2×#67C22×D514yes—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3C22×D511yescharacteristic
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C2×D12—54no—
454C2×D12—104no—
455C2×C4×D3—42no—
456C2×C4×D3—54no—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—104no—
461C2×C4×D3—202no—
462C2×C4×D3C22×D514yes—
463C3×C4⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C42—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217C22×D514yes—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4C22×D514yes—
475C4⋊Dic3—54no—
476C4⋊Dic3—54no—
477C4⋊Dic3—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4C22×D514yes—
484C4×Dic3—54no—
485C4×Dic3C22×D514yes—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—34no—
490C23×C5—32no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5C23×D312yes—
494C23×C5C23×D311yescharacteristic
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—32no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5C23×D312yes—
503C5×D4—68no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—44no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—124no—
514C2×C4×C5C23×D312yes—
515C2×C4×C5C23×D312yes—
516C22⋊D5—28no—
517C22⋊D5—68no—
518C22⋊D5—68no—
519C22⋊D5—124no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—68no—
529C2×Dic5—124no—
530C2×Dic5#23514yes—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534D20—124no—
535C4×D5—44no—
536C4×D5—68no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4D3×D511yescharacteristic
549#126—158no—
550#126—158no—
551#125—158no—
552#123—158no—
553#123—158no—
554#121—158no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—38no—
559C4×D4—58no—
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—31no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C42—31no—
585C2×C42—51no—
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
592D15—42no—
593C3×D5—42no—
594C5×D3—24no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—52no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3C23×D512yes—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—52no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3#70914yes—
611C22×D3C23×D512yes—
612C3×D4—108no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—44no—
616C2×C3×C4—54no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4—204no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625#67—28no—
626#67—108no—
627#67—204no—
628#67—204no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3C23×D512yes—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641D12—108no—
642C4×D3—44no—
643C4×D3—108no—
644C4×D3—108no—
645C4×D3—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—34no—
650C22×C5—44no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—68no—
654C22×C5C2×#23512yes—
655C22×C5#100412yes—
656C22×C5D3×#4112yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—44no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—62no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5C2×#23514yes—
677C24—31no—
678C24—51no—
679C24—151no—
680C24C2×D3×D511yescharacteristic
681C2×D4—34no—
682C2×D4—54no—
683C2×D4—64no—
684C2×D4—104no—
685C2×D4—154no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—304no—
690C2×D4—304no—
691C2×D4—602no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—34no—
697C22×C4—42no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—54no—
702C22×C4—122no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—202no—
710C22×C4—304no—
711C22×C4—304no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D514yes—
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—34no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C42—34no—
737C42—54no—
738C42—154no—
739C3×C5C2×#55311yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—44no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—204no—
748C22×C3C2×#70912yes—
749C22×C3#414412yes—
750C22×C3D5×#4112yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—28no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—204no—
759C2×D3C2×#70914yes—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—54no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—42no—
772C2×C5—64no—
773C2×C5#555814yescomplemented
774C2×C5C22×#23511yescharacteristic
775C2×C5C2×#100411yescharacteristic
776C2×C5C2×D3×#4111yescharacteristic
777D5—42no—
778D5—122no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—34no—
783C23—32no—
784C23—52no—
785C23—62no—
786C23—62no—
787C23—102no—
788C23—102no—
789C23—102no—
790C23—152no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796D4—68no—
797D4—108no—
798D4—308no—
799D4—308no—
800D4—604no—
801D4—604no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—44no—
808C2×C4—54no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—124no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—204no—
822C2×C4—308no—
823C2×C4—308no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—302no—
827C2×C4—604no—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—42no—
831C2×C3—202no—
832C2×C3#6587414yescomplemented
833C2×C3C22×#70911yescharacteristic
834C2×C3C2×#414411yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836D3—24no—
837D3—202no—
838C5C2×#555811yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—34no—
843C22—44no—
844C22—62no—
845C22—68no—
846C22—62no—
847C22—102no—
848C22—102no—
849C22—102no—
850C22—204no—
851C22—302no—
852C22—302no—
853C22—302no—
854C22—604no—
855C22D5×#23512yes—
856C22D3×#70912yes—
857C22#9204912yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—54no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—102no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6587411yescharacteristic, complemented, Sylow
871C2—42no—
872C2—64no—
873C2—202no—
874C2—602no—
875C2#1175456814yesdirect product factor
876C2C2×D5×#23511yescharacteristic
877C2C2×D3×#70911yescharacteristic
878C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91818C2semidirect
2. C2×C4×C5×#67C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C2×#91565C2semidirect
5. C2×#91558C2semidirect
6. C2×#91533C2semidirect
7. C2×#91531C2semidirect
8. #11754568C2direct (N × H)
9. C2×#91454C2semidirect
10. C2×#91440C2semidirect
11. C2×#91405C2semidirect
12. C2×#91403C2semidirect
13. C2×D3×#683C2semidirect
14. C2×#91378C2semidirect
15. C2×#91363C2semidirect
16. C2×#91348C2semidirect
31. #91818C22semidirect
37. C4×C5×#67C22semidirect
42. C3×C4×C22⋊D5C22semidirect
46. #91565C22semidirect
47. #91558C22semidirect
57. #91533C22semidirect
58. #91531C22semidirect
60. #91454C22semidirect
61. #91440C22semidirect
62. #91405C22semidirect
63. #91403C22semidirect
64. D3×#683C22semidirect
65. #91378C22semidirect
66. #91363C22semidirect
67. #91348C22semidirect
74. C2×C4×C22⋊D5D3semidirect
153. C2×C4×#67D5semidirect
186. C4×C22⋊D5C2×D3semidirect
291. C4×#67C2×D5semidirect
588. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
773. C2×C5#5558semidirect
832. C2×C3#65874semidirect
838. C5C2×#5558semidirect
870. C3C2×#65874semidirect
875. C2#11754568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918182
C2×C4×C5×#672
C2×C3×C4×C22⋊D52
C2×#915652
C2×#915582
C2×#915332
C2×#915312
#117545682
C2×#914542
C2×#914402
C2×#914052
C2×#914032
C2×D3×#6832
C2×#913782
C2×#913632
C2×#913482
C2×#658743
C2×#55585