Finite Group Databasebeta

← C5×#41×#67 #14483039

Subgroups — C5×#41×#67 #14483039

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C2×C5×D3×#41C211yesmaximal, characteristic, complemented
3C5×#5834C211yesmaximal, characteristic, complemented
4C5×#5832C213yesmaximal, complemented
5C5×#5831C211yesmaximal, characteristic, complemented
6C5×#5829C213yesmaximal, complemented
7C5×#5828C213yesmaximal, complemented
8C5×Dic3×#41C211yesmaximal, characteristic, complemented
9C5×#5824C213yesmaximal, complemented
10C5×#5817C211yesmaximal, characteristic, complemented
11C5×Q8×#67C211yesmaximal, characteristic, complemented
12C5×#5806C213yesmaximal, complemented
13C5×D4×#67C213yesmaximal, complemented
14C5×#5791C213yesmaximal, complemented
15C2×C4×C5×#67C213yesmaximal, complemented
16C5×D4×#41—31nomaximal, Hall
17C2×C3×C5×#41—28no—
18C2×C3×C5×#41C2211yescharacteristic
19C2×C3×C5×#41C2213yescomplemented
20C2×C3×C5×#41C2213yescomplemented
21C2×C3×C5×#41C2211yescharacteristic, complemented
22C22×C3×C5×Q8C2211yescharacteristic, complemented
23C22×C3×C5×D4C2213yescomplemented
24C23×C3×C4×C5C2213yescomplemented
25C22×C5×#67C2213yes—
26C5×D3×#41—28no—
27C2×C5×#239C2211yescharacteristic, complemented
28C2×C5×D3×Q8C2211yescharacteristic, complemented
29C2×C5×#237C2213yescomplemented
30C2×C5×D3×D4C2213yescomplemented
31C2×C5×#235C2213yescomplemented
32C22×C4×C5×D3C2213yescomplemented
33C5×#953C2216yescomplemented
34C2×C5×#217C2213yescomplemented
35C5×#947C2213yescomplemented
36C5×#946C2213yescomplemented
37C5×#946C2213yescomplemented
38C5×Q8×Dic3C2211yescharacteristic, complemented
39C5×Q8×Dic3C2211yescharacteristic, complemented
40C5×#944C2213yescomplemented
41C5×#940C2213yescomplemented
42C5×#939C2216yescomplemented
43C5×#939C2216yescomplemented
44C5×#938C2213yescomplemented
45C5×#938C2213yescomplemented
46C5×#937C2216yescomplemented
47C5×#936C2213yescomplemented
48C5×#935C2216yescomplemented
49C5×D4×Dic3C2213yescomplemented
50C5×D4×Dic3C2213yescomplemented
51C5×#930C2213yescomplemented
52C5×#930C2213yescomplemented
53C5×#929C2216yescomplemented
54C4×C5×#67C2211yescharacteristic
55C4×C5×#67C2213yes—
56C4×C5×#67C2213yescomplemented
57C4×C5×#67C2213yescomplemented
58C4×C5×#67C2213yescomplemented
59C4×C5×#67C2213yescomplemented
60C4×C5×#67C2213yescomplemented
61C4×C5×#67C2213yescomplemented
62C4×C5×#67C2216yescomplemented
63C2×C5×(C2×D3)⋊C4C2213yescomplemented
64C5×#926C2213yescomplemented
65C5×#924C2213yescomplemented
66C5×#924C2213yescomplemented
67C2×C5×Dic3⋊C4C2213yescomplemented
68C2×C4×C5×Dic3C2213yescomplemented
69#41×#67C511yesmaximal, characteristic, direct product factor, Hall
70C22×C5×#41—31no—
71C22×C5×#41D311yescharacteristic, complemented
72C5×#550—31no—
73C5×D4×Q8—31no—
74C5×#548—31no—
75C5×#548—31no—
76C5×#547—33no—
77C5×#546—33no—
78C5×#546—33no—
79C5×D42—33no—
80C5×#532—33no—
81C5×#525—33no—
82C5×#525—33no—
83C4×C5×#41—31no—
84C2×C4×C5×D4—33no—
85C24×C3×C5C2313yes—
86C23×C5×D3C2313yes—
87C3×C5×#41—24no—
88C3×C5×#41—212no—
89C3×C5×#41—212no—
90C3×C5×#41D418yescomplemented
91C2×C3×C5×Q8—24no—
92C2×C3×C5×Q8C2313yes—
93C2×C3×C5×Q8C2311yescharacteristic
94C2×C3×C5×D4—212no—
95C2×C3×C5×D4C2316yes—
96C2×C3×C5×D4C2313yes—
97C2×C3×C5×D4C2313yes—
98C22×C3×C4×C5—212no—
99C22×C3×C4×C5C2313yes—
100C22×C3×C4×C5C2313yes—
101C22×C3×C4×C5C2313yes—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2313yes—
104C22×C3×C4×C5C2313yes—
105C2×C5×#67—212no—
106C2×C5×#67C2313yes—
107C2×C5×#67C2313yes—
108C2×C5×#67C2313yes—
109C2×C5×#67C2316yes—
110C2×C5×#67C2316yes—
111C2×C5×#67C2311yescharacteristic
112C22×C5×Dic3C2313yes—
113C22×C5×Dic3C2313yes—
114C22×C5×Dic3C2313yes—
115C5×#239—24no—
116C5×D3×Q8—24no—
117C5×#237—212no—
118C5×D3×D4—212no—
119C5×#235—212no—
120C2×C5×D12C2313yes—
121C2×C4×C5×D3—212no—
122C2×C4×C5×D3C2311yescharacteristic
123C2×C4×C5×D3C2313yes—
124C2×C4×C5×D3C2313yes—
125C2×C4×C5×D3C2313yes—
126C2×C5×Dic6C2313yes—
127C5×#217C2313yes—
128C5×#217C2316yes—
129C5×#217C2316yes—
130C5×#217C2311yescharacteristic
131C5×#217C2313yes—
132C5×#217C2313yes—
133C5×(C2×D3)⋊C4C2311yescharacteristic
134C5×(C2×D3)⋊C4C2313yes—
135C5×(C2×D3)⋊C4C2313yes—
136C5×(C2×D3)⋊C4C2313yes—
137C5×(C2×D3)⋊C4C2316yes—
138C5×C4⋊Dic3C2313yes—
139C5×C4⋊Dic3C2313yes—
140C5×Dic3⋊C4C2311yescharacteristic
141C5×Dic3⋊C4C2313yes—
142C5×Dic3⋊C4C2313yes—
143C5×Dic3⋊C4C2313yes—
144C5×Dic3⋊C4C2316yes—
145C4×C5×Dic3C2311yescharacteristic
146C4×C5×Dic3C2313yes—
147C4×C5×Dic3C2313yes—
148C4×C5×Dic3C2313yes—
149C22×C3×#41C2×C511yescharacteristic, complemented
150C2×D3×#41C2×C511yescharacteristic, complemented
151#5834C2×C511yescharacteristic, complemented
152#5832C2×C513yescomplemented
153#5831C2×C511yescharacteristic, complemented
154#5829C2×C513yescomplemented
155#5828C2×C513yescomplemented
156Dic3×#41C2×C511yescharacteristic, complemented
157#5824C2×C513yescomplemented
158#5817C2×C511yescharacteristic, complemented
159Q8×#67C2×C511yescharacteristic, complemented
160#5806C2×C513yescomplemented
161D4×#67C2×C513yescomplemented
162#5791C2×C513yescomplemented
163C2×C4×#67C2×C513yescomplemented
164C2×C5×#41—28no—
165C2×C5×#41—31no—
166C2×C5×#41—33no—
167C2×C5×#41—33no—
168C2×C5×#41—68no—
169C2×C5×#41C2×D311yescharacteristic
170C2×C5×#41C2×D313yescomplemented
171C2×C5×#41C2×D313yescomplemented
172C2×C5×#41C2×D311yescharacteristic, complemented
173C22×C5×Q8—31no—
174C22×C5×Q8C2×D311yescharacteristic, complemented
175C22×C5×D4—33no—
176C22×C5×D4—33no—
177C22×C5×D4C2×D313yescomplemented
178C23×C4×C5—33no—
179C23×C4×C5C2×D313yescomplemented
180C5×C4⋊Q8—33no—
181C5×#127—33no—
182C5×#124—33no—
183C5×#124—33no—
184C5×#123—36no—
185C5×#123—36no—
186C5×C22⋊Q8—33no—
187C5×C22⋊Q8—33no—
188C5×C22⋊Q8—33no—
189C5×C22⋊Q8—33no—
190C5×#121—33no—
191C5×#121—33no—
192C5×#121—36no—
193C5×#121—36no—
194C5×#121—33no—
195C5×#121—33no—
196C5×#120—36no—
197C5×#120—36no—
198C4×C5×Q8—31no—
199C4×C5×Q8—31no—
200C4×C5×D4—33no—
201C4×C5×D4—33no—
202C4×C5×D4—31no—
203C4×C5×D4—33no—
204C4×C5×D4—33no—
205C4×C5×D4—33no—
206C4×C5×D4—33no—
207C4×C5×D4—33no—
208C4×C5×D4—33no—
209C4×C5×D4—33no—
210C4×C5×D4—36no—
211C5×#117—33no—
212C2×C5×C4⋊C4—33no—
213C2×C5×C22⋊C4—33no—
214C2×C5×C22⋊C4—33no—
215C2×C42×C5—33no—
216D4×#41—31noSylow
217C23×C3×C5—26no—
218C23×C3×C5—26no—
219C23×C3×C5—43no—
220C23×C3×C5C2413yes—
221C23×C3×C5C2413yes—
222C23×C3×C5C2411yescharacteristic
223C22×C5×D3—26no—
224C22×C5×D3—26no—
225C22×C5×D3—43no—
226C22×C5×D3C2413yes—
227C22×C5×D3C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—212no—
231C3×C5×D4—26no—
232C3×C5×D4C2×D4112yescomplemented
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—26no—
236C2×C3×C4×C5—26no—
237C2×C3×C4×C5—26no—
238C2×C3×C4×C5C2×D4112yescomplemented
239C2×C3×C4×C5C2411yescharacteristic
240C2×C3×C4×C5C2413yes—
241C2×C3×C4×C5C2413yes—
242C2×C3×C4×C5C2411yescharacteristic
243C5×#67—212no—
244C5×#67—26no—
245C5×#67—26no—
246C5×#67—26no—
247C5×#67—46no—
248C5×#67#4114yesdirect product factor
249C2×C5×Dic3—26no—
250C2×C5×Dic3—26no—
251C2×C5×Dic3—43no—
252C2×C5×Dic3C2411yescharacteristic
253C2×C5×Dic3C2413yes—
254C2×C5×Dic3C2413yes—
255C2×C5×Dic3C2413yes—
256C2×C5×Dic3C2411yescharacteristic
257C2×C5×Dic3C2411yescharacteristic
258C5×D12—26no—
259C4×C5×D3—22no—
260C4×C5×D3—26no—
261C4×C5×D3—26no—
262C4×C5×D3—26no—
263C5×Dic6—26no—
264C2×C3×#41—28no—
265C2×C3×#41C22×C511yescharacteristic
266C2×C3×#41C22×C513yescomplemented
267C2×C3×#41C22×C513yescomplemented
268C2×C3×#41C22×C511yescharacteristic, complemented
269C22×C3×Q8C22×C511yescharacteristic, complemented
270C22×C3×D4C22×C513yescomplemented
271C23×C3×C4C22×C513yescomplemented
272C22×#67C22×C513yes—
273D3×#41—28no—
274C2×#239C22×C511yescharacteristic, complemented
275C2×D3×Q8C22×C511yescharacteristic, complemented
276C2×#237C22×C513yescomplemented
277C2×D3×D4C22×C513yescomplemented
278C2×#235C22×C513yescomplemented
279C22×C4×D3C22×C513yescomplemented
280#953C22×C516yescomplemented
281C2×#217C22×C513yescomplemented
282#947C22×C513yescomplemented
283#946C22×C513yescomplemented
284#946C22×C513yescomplemented
285Q8×Dic3C22×C511yescharacteristic, complemented
286Q8×Dic3C22×C511yescharacteristic, complemented
287#944C22×C513yescomplemented
288#940C22×C513yescomplemented
289#939C22×C516yescomplemented
290#939C22×C516yescomplemented
291#938C22×C513yescomplemented
292#938C22×C513yescomplemented
293#937C22×C516yescomplemented
294#936C22×C513yescomplemented
295#935C22×C516yescomplemented
296D4×Dic3C22×C513yescomplemented
297D4×Dic3C22×C513yescomplemented
298#930C22×C513yescomplemented
299#930C22×C513yescomplemented
300#929C22×C516yescomplemented
301C4×#67C22×C511yescharacteristic
302C4×#67C22×C513yes—
303C4×#67C22×C513yescomplemented
304C4×#67C22×C513yescomplemented
305C4×#67C22×C513yescomplemented
306C4×#67C22×C513yescomplemented
307C4×#67C22×C513yescomplemented
308C4×#67C22×C513yescomplemented
309C4×#67C22×C516yescomplemented
310C2×(C2×D3)⋊C4C22×C513yescomplemented
311#926C22×C513yescomplemented
312#924C22×C513yescomplemented
313#924C22×C513yescomplemented
314C2×Dic3⋊C4C22×C513yescomplemented
315C2×C4×Dic3C22×C513yescomplemented
316C24×C5—33no—
317C24×C5C22×D313yes—
318C5×#41—24no—
319C5×#41—212no—
320C5×#41—212no—
321C5×#41—64no—
322C5×#41—612no—
323C5×#41—612no—
324C5×#41#6718yesdirect product factor
325C2×C5×Q8—24no—
326C2×C5×Q8—33no—
327C2×C5×Q8—64no—
328C2×C5×Q8C22×D313yes—
329C2×C5×Q8C22×D311yescharacteristic
330C2×C5×D4—212no—
331C2×C5×D4—31no—
332C2×C5×D4—33no—
333C2×C5×D4—33no—
334C2×C5×D4—33no—
335C2×C5×D4—36no—
336C2×C5×D4—36no—
337C2×C5×D4—33no—
338C2×C5×D4—612no—
339C2×C5×D4—612no—
340C2×C5×D4C22×D316yes—
341C2×C5×D4C22×D313yes—
342C2×C5×D4C22×D313yes—
343C22×C4×C5—212no—
344C22×C4×C5—33no—
345C22×C4×C5—33no—
346C22×C4×C5—33no—
347C22×C4×C5—33no—
348C22×C4×C5—33no—
349C22×C4×C5—31no—
350C22×C4×C5—33no—
351C22×C4×C5—612no—
352C22×C4×C5C22×D313yes—
353C22×C4×C5C22×D313yes—
354C22×C4×C5C22×D313yes—
355C22×C4×C5C22×D311yescharacteristic
356C22×C4×C5C22×D313yes—
357C22×C4×C5C22×D313yes—
358C5×C4⋊C4—31no—
359C5×C4⋊C4—33no—
360C5×C4⋊C4—33no—
361C5×C4⋊C4—33no—
362C5×C4⋊C4—33no—
363C5×C4⋊C4—33no—
364C5×C4⋊C4—36no—
365C5×C22⋊C4—31no—
366C5×C22⋊C4—33no—
367C5×C22⋊C4—33no—
368C5×C22⋊C4—33no—
369C5×C22⋊C4—36no—
370C5×C22⋊C4—36no—
371C5×C22⋊C4—31no—
372C5×C22⋊C4—33no—
373C5×C22⋊C4—33no—
374C5×C22⋊C4—33no—
375C5×C22⋊C4—36no—
376C42×C5—33no—
377C42×C5—33no—
378C42×C5—31no—
379C42×C5—33no—
380C22×#41—31no—
381C22×#41C5×D311yescharacteristic, complemented
382#550—31no—
383D4×Q8—31no—
384#548—31no—
385#548—31no—
386#547—33no—
387#546—33no—
388#546—33no—
389D42—33no—
390#532—33no—
391#525—33no—
392#525—33no—
393C4×#41—31no—
394C2×C4×D4—33no—
395C22×C3×C5—21no—
396C22×C3×C5—23no—
397C22×C3×C5—23no—
398C22×C3×C5—21no—
399C22×C3×C5—23no—
400C22×C3×C5—23no—
401C22×C3×C5—23no—
402C22×C3×C5—412no—
403C22×C3×C5C22×D416yes—
404C22×C3×C5C2×#4112yescomplemented
405C22×C3×C5C2511yescharacteristic
406C2×C5×D3—21no—
407C2×C5×D3—21no—
408C2×C5×D3—23no—
409C2×C5×D3—23no—
410C2×C5×D3—23no—
411C2×C5×D3—412no—
412C2×C5×D3C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5C22×D416yes—
416C3×C4×C5C22×D412yes—
417C5×Dic3—23no—
418C5×Dic3—21no—
419C5×Dic3—23no—
420C5×Dic3—21no—
421C5×Dic3—23no—
422C5×Dic3C2×#4112yescomplemented
423C24×C3C23×C513yes—
424C23×D3C23×C513yes—
425C3×#41—24no—
426C3×#41—212no—
427C3×#41—212no—
428C3×#41C5×D418yescomplemented
429C2×C3×Q8—24no—
430C2×C3×Q8C23×C513yes—
431C2×C3×Q8C23×C511yescharacteristic
432C2×C3×D4—212no—
433C2×C3×D4C23×C516yes—
434C2×C3×D4C23×C513yes—
435C2×C3×D4C23×C513yes—
436C22×C3×C4—212no—
437C22×C3×C4C23×C513yes—
438C22×C3×C4C23×C513yes—
439C22×C3×C4C23×C513yes—
440C22×C3×C4C23×C511yescharacteristic
441C22×C3×C4C23×C513yes—
442C22×C3×C4C23×C513yes—
443C2×#67—212no—
444C2×#67C23×C513yes—
445C2×#67C23×C513yes—
446C2×#67C23×C513yes—
447C2×#67C23×C516yes—
448C2×#67C23×C516yes—
449C2×#67C23×C511yescharacteristic
450C22×Dic3C23×C513yes—
451C22×Dic3C23×C513yes—
452C22×Dic3C23×C513yes—
453#239—24no—
454D3×Q8—24no—
455#237—212no—
456D3×D4—212no—
457#235—212no—
458C2×D12C23×C513yes—
459C2×C4×D3—212no—
460C2×C4×D3C23×C511yescharacteristic
461C2×C4×D3C23×C513yes—
462C2×C4×D3C23×C513yes—
463C2×C4×D3C23×C513yes—
464C2×Dic6C23×C513yes—
465#217C23×C513yes—
466#217C23×C516yes—
467#217C23×C516yes—
468#217C23×C511yescharacteristic
469#217C23×C513yes—
470#217C23×C513yes—
471(C2×D3)⋊C4C23×C511yescharacteristic
472(C2×D3)⋊C4C23×C513yes—
473(C2×D3)⋊C4C23×C513yes—
474(C2×D3)⋊C4C23×C513yes—
475(C2×D3)⋊C4C23×C516yes—
476C4⋊Dic3C23×C513yes—
477C4⋊Dic3C23×C513yes—
478Dic3⋊C4C23×C511yescharacteristic
479Dic3⋊C4C23×C513yes—
480Dic3⋊C4C23×C513yes—
481Dic3⋊C4C23×C513yes—
482Dic3⋊C4C23×C516yes—
483C4×Dic3C23×C511yescharacteristic
484C4×Dic3C23×C513yes—
485C4×Dic3C23×C513yes—
486C4×Dic3C23×C513yes—
487C23×C5—26no—
488C23×C5—26no—
489C23×C5—31no—
490C23×C5—33no—
491C23×C5—43no—
492C23×C5—66no—
493C23×C5—66no—
494C23×C5—123no—
495C23×C5C23×D313yes—
496C23×C5C23×D311yescharacteristic
497C23×C5C23×D313yes—
498C5×Q8—26no—
499C5×Q8—66no—
500C5×Q8C2×#6714yescomplemented
501C5×D4—212no—
502C5×D4—26no—
503C5×D4—34no—
504C5×D4—66no—
505C5×D4—66no—
506C5×D4—66no—
507C5×D4—612no—
508C5×D4—66no—
509C5×D4—126no—
510C5×D4C2×#67112yescomplemented
511C2×C4×C5—26no—
512C2×C4×C5—22no—
513C2×C4×C5—26no—
514C2×C4×C5—26no—
515C2×C4×C5—26no—
516C2×C4×C5—31no—
517C2×C4×C5—31no—
518C2×C4×C5—33no—
519C2×C4×C5—33no—
520C2×C4×C5—31no—
521C2×C4×C5—33no—
522C2×C4×C5—66no—
523C2×C4×C5—66no—
524C2×C4×C5—62no—
525C2×C4×C5—66no—
526C2×C4×C5—66no—
527C2×C4×C5—66no—
528C2×C4×C5—123no—
529C2×C4×C5C2×#67112yescomplemented
530C2×C4×C5C23×D311yescharacteristic
531C2×C4×C5C23×D313yes—
532C2×C4×C5C23×D313yes—
533C2×C4×C5C23×D311yescharacteristic
534C2×#41—28no—
535C2×#41—31no—
536C2×#41—33no—
537C2×#41—33no—
538C2×#41—68no—
539C2×#41C2×C5×D311yescharacteristic
540C2×#41C2×C5×D313yescomplemented
541C2×#41C2×C5×D313yescomplemented
542C2×#41C2×C5×D311yescharacteristic, complemented
543C22×Q8—31no—
544C22×Q8C2×C5×D311yescharacteristic, complemented
545C22×D4—33no—
546C22×D4—33no—
547C22×D4C2×C5×D313yescomplemented
548C23×C4—33no—
549C23×C4C2×C5×D313yescomplemented
550C4⋊Q8—33no—
551#127—33no—
552#124—33no—
553#124—33no—
554#123—36no—
555#123—36no—
556C22⋊Q8—33no—
557C22⋊Q8—33no—
558C22⋊Q8—33no—
559C22⋊Q8—33no—
560#121—33no—
561#121—33no—
562#121—36no—
563#121—36no—
564#121—33no—
565#121—33no—
566#120—36no—
567#120—36no—
568C4×Q8—31no—
569C4×Q8—31no—
570C4×D4—33no—
571C4×D4—33no—
572C4×D4—31no—
573C4×D4—33no—
574C4×D4—33no—
575C4×D4—33no—
576C4×D4—33no—
577C4×D4—33no—
578C4×D4—33no—
579C4×D4—33no—
580C4×D4—36no—
581#117—33no—
582C2×C4⋊C4—33no—
583C2×C22⋊C4—33no—
584C2×C22⋊C4—33no—
585C2×C42—33no—
586C2×C3×C5—26no—
587C2×C3×C5—22no—
588C2×C3×C5—43no—
589C2×C3×C5C23×D411yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5#58511yescharacteristic
592C5×D3—22no—
593C5×D3—43no—
594C23×C3—26no—
595C23×C3—26no—
596C23×C3—43no—
597C23×C3C24×C513yes—
598C23×C3C24×C513yes—
599C23×C3C24×C511yescharacteristic
600C22×D3—26no—
601C22×D3—26no—
602C22×D3—43no—
603C22×D3C24×C513yes—
604C22×D3C24×C511yescharacteristic
605C3×Q8—26no—
606C3×Q8C2×C5×D414yescomplemented
607C3×D4—212no—
608C3×D4—26no—
609C3×D4C2×C5×D4112yescomplemented
610C2×C3×C4—26no—
611C2×C3×C4—22no—
612C2×C3×C4—26no—
613C2×C3×C4—26no—
614C2×C3×C4—26no—
615C2×C3×C4C2×C5×D4112yescomplemented
616C2×C3×C4C24×C511yescharacteristic
617C2×C3×C4C24×C513yes—
618C2×C3×C4C24×C511yescharacteristic
619C2×C3×C4C24×C513yes—
620#67—212no—
621#67—26no—
622#67—26no—
623#67—26no—
624#67—46no—
625#67C5×#4114yesdirect product factor
626C2×Dic3—26no—
627C2×Dic3—26no—
628C2×Dic3—43no—
629C2×Dic3C24×C511yescharacteristic
630C2×Dic3C24×C513yes—
631C2×Dic3C24×C513yes—
632C2×Dic3C24×C513yes—
633C2×Dic3C24×C511yescharacteristic
634C2×Dic3C24×C511yescharacteristic
635D12—26no—
636C4×D3—22no—
637C4×D3—26no—
638C4×D3—26no—
639C4×D3—26no—
640Dic6—26no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5—21no—
644C22×C5—21no—
645C22×C5—23no—
646C22×C5—23no—
647C22×C5—23no—
648C22×C5—32no—
649C22×C5—412no—
650C22×C5—61no—
651C22×C5—61no—
652C22×C5—63no—
653C22×C5—63no—
654C22×C5—63no—
655C22×C5—1212no—
656C22×C5D3×#4112yescomplemented
657C22×C5C22×#6716yes—
658C22×C5C24×D311yescharacteristic
659C4×C5—21no—
660C4×C5—23no—
661C4×C5—32no—
662C4×C5—63no—
663C4×C5—61no—
664C4×C5—63no—
665C4×C5—61no—
666C4×C5—63no—
667C4×C5C22×#6712yes—
668C4×C5C22×#6716yes—
669C24—33no—
670C24C22×C5×D313yes—
671#41—24no—
672#41—212no—
673#41—212no—
674#41—64no—
675#41—612no—
676#41—612no—
677#41C5×#6718yesdirect product factor
678C2×Q8—24no—
679C2×Q8—33no—
680C2×Q8—64no—
681C2×Q8C22×C5×D313yes—
682C2×Q8C22×C5×D311yescharacteristic
683C2×D4—212no—
684C2×D4—31no—
685C2×D4—33no—
686C2×D4—33no—
687C2×D4—33no—
688C2×D4—36no—
689C2×D4—36no—
690C2×D4—33no—
691C2×D4—612no—
692C2×D4—612no—
693C2×D4C22×C5×D316yes—
694C2×D4C22×C5×D313yes—
695C2×D4C22×C5×D313yes—
696C22×C4—212no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—33no—
700C22×C4—31no—
701C22×C4—33no—
702C22×C4—33no—
703C22×C4—33no—
704C22×C4—612no—
705C22×C4C22×C5×D313yes—
706C22×C4C22×C5×D311yescharacteristic
707C22×C4C22×C5×D313yes—
708C22×C4C22×C5×D313yes—
709C22×C4C22×C5×D313yes—
710C22×C4C22×C5×D313yes—
711C4⋊C4—31no—
712C4⋊C4—33no—
713C4⋊C4—33no—
714C4⋊C4—33no—
715C4⋊C4—33no—
716C4⋊C4—33no—
717C4⋊C4—36no—
718C22⋊C4—31no—
719C22⋊C4—33no—
720C22⋊C4—33no—
721C22⋊C4—33no—
722C22⋊C4—36no—
723C22⋊C4—36no—
724C22⋊C4—31no—
725C22⋊C4—33no—
726C22⋊C4—33no—
727C22⋊C4—33no—
728C22⋊C4—36no—
729C42—31no—
730C42—33no—
731C42—33no—
732C42—33no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—23no—
736C22×C3—23no—
737C22×C3—21no—
738C22×C3—23no—
739C22×C3—23no—
740C22×C3—23no—
741C22×C3—412no—
742C22×C3C22×C5×D416yes—
743C22×C3C2×C5×#4112yescomplemented
744C22×C3C25×C511yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—23no—
748C2×D3—23no—
749C2×D3—23no—
750C2×D3—412no—
751C2×D3C2×C5×#4112yescomplemented
752C3×C4—21no—
753C3×C4—23no—
754C3×C4C22×C5×D416yes—
755C3×C4C22×C5×D412yes—
756Dic3—23no—
757Dic3—21no—
758Dic3—23no—
759Dic3—21no—
760Dic3—23no—
761Dic3C2×C5×#4112yescomplemented
762C2×C5—22no—
763C2×C5—26no—
764C2×C5—43no—
765C2×C5—62no—
766C2×C5—123no—
767C2×C5C2×D3×#4111yescharacteristic
768C2×C5#596411yescharacteristic
769C2×C5C23×#6711yescharacteristic
770C23—26no—
771C23—26no—
772C23—31no—
773C23—33no—
774C23—43no—
775C23—66no—
776C23—66no—
777C23—123no—
778C23C23×C5×D313yes—
779C23C23×C5×D311yescharacteristic
780C23C23×C5×D313yes—
781Q8—26no—
782Q8—66no—
783Q8C2×C5×#6714yescomplemented
784D4—212no—
785D4—26no—
786D4—34no—
787D4—66no—
788D4—66no—
789D4—66no—
790D4—612no—
791D4—66no—
792D4—126no—
793D4C2×C5×#67112yescomplemented
794C2×C4—26no—
795C2×C4—22no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—26no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—33no—
802C2×C4—33no—
803C2×C4—31no—
804C2×C4—33no—
805C2×C4—66no—
806C2×C4—66no—
807C2×C4—62no—
808C2×C4—66no—
809C2×C4—66no—
810C2×C4—66no—
811C2×C4—123no—
812C2×C4C2×C5×#67112yescomplemented
813C2×C4C23×C5×D311yescharacteristic
814C2×C4C23×C5×D313yes—
815C2×C4C23×C5×D311yescharacteristic
816C2×C4C23×C5×D313yes—
817C2×C3—26no—
818C2×C3—22no—
819C2×C3—43no—
820C2×C3C23×C5×D411yescharacteristic
821C2×C3C22×C5×#4111yescharacteristic
822C2×C3C5×#58511yescharacteristic
823D3—22no—
824D3—43no—
825C5#41×#6711yescharacteristic, direct product factor, Sylow
826C22—23no—
827C22—23no—
828C22—21no—
829C22—21no—
830C22—23no—
831C22—23no—
832C22—23no—
833C22—32no—
834C22—412no—
835C22—61no—
836C22—61no—
837C22—63no—
838C22—63no—
839C22—63no—
840C22—1212no—
841C22C5×D3×#4112yescomplemented
842C22C22×C5×#6716yes—
843C22C24×C5×D311yescharacteristic
844C4—21no—
845C4—23no—
846C4—32no—
847C4—63no—
848C4—61no—
849C4—63no—
850C4—61no—
851C4—63no—
852C4C22×C5×#6712yes—
853C4C22×C5×#6716yes—
854C3C5×D4×#4111yescharacteristic, complemented, Sylow
855C2—22no—
856C2—26no—
857C2—43no—
858C2—62no—
859C2—123no—
860C2C2×C5×D3×#4111yescharacteristic
861C2C5×#596411yescharacteristic
862C2C23×C5×#6711yescharacteristic
subgroupG/H
centerC2×C4×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC22×C3×C5×#41C2
socleC22×C3×C5C25
hypercenterC22×C5×#41D3
hypocenterC3C5×D4×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C2×C5×D3×#41C2semidirect
3. C5×#5834C2semidirect
4. C5×#5832C2semidirect
5. C5×#5831C2semidirect
6. C5×#5829C2semidirect
7. C5×#5828C2semidirect
8. C5×Dic3×#41C2semidirect
9. C5×#5824C2semidirect
10. C5×#5817C2semidirect
11. C5×Q8×#67C2semidirect
12. C5×#5806C2semidirect
13. C5×D4×#67C2semidirect
14. C5×#5791C2semidirect
15. C2×C4×C5×#67C2semidirect
19. C2×C3×C5×#41C22semidirect
20. C2×C3×C5×#41C22semidirect
21. C2×C3×C5×#41C22semidirect
22. C22×C3×C5×Q8C22semidirect
23. C22×C3×C5×D4C22semidirect
24. C23×C3×C4×C5C22semidirect
27. C2×C5×#239C22semidirect
28. C2×C5×D3×Q8C22semidirect
29. C2×C5×#237C22semidirect
30. C2×C5×D3×D4C22semidirect
31. C2×C5×#235C22semidirect
32. C22×C4×C5×D3C22semidirect
33. C5×#953C22semidirect
34. C2×C5×#217C22semidirect
35. C5×#947C22semidirect
36. C5×#946C22semidirect
37. C5×#946C22semidirect
38. C5×Q8×Dic3C22semidirect
39. C5×Q8×Dic3C22semidirect
40. C5×#944C22semidirect
41. C5×#940C22semidirect
42. C5×#939C22semidirect
43. C5×#939C22semidirect
44. C5×#938C22semidirect
45. C5×#938C22semidirect
46. C5×#937C22semidirect
47. C5×#936C22semidirect
48. C5×#935C22semidirect
49. C5×D4×Dic3C22semidirect
50. C5×D4×Dic3C22semidirect
51. C5×#930C22semidirect
52. C5×#930C22semidirect
53. C5×#929C22semidirect
56. C4×C5×#67C22semidirect
57. C4×C5×#67C22semidirect
58. C4×C5×#67C22semidirect
59. C4×C5×#67C22semidirect
60. C4×C5×#67C22semidirect
61. C4×C5×#67C22semidirect
62. C4×C5×#67C22semidirect
63. C2×C5×(C2×D3)⋊C4C22semidirect
64. C5×#926C22semidirect
65. C5×#924C22semidirect
66. C5×#924C22semidirect
67. C2×C5×Dic3⋊C4C22semidirect
68. C2×C4×C5×Dic3C22semidirect
69. #41×#67C5direct (N × H)
71. C22×C5×#41D3semidirect
90. C3×C5×#41D4semidirect
149. C22×C3×#41C2×C5semidirect
150. C2×D3×#41C2×C5semidirect
151. #5834C2×C5semidirect
152. #5832C2×C5semidirect
153. #5831C2×C5semidirect
154. #5829C2×C5semidirect
155. #5828C2×C5semidirect
156. Dic3×#41C2×C5semidirect
157. #5824C2×C5semidirect
158. #5817C2×C5semidirect
159. Q8×#67C2×C5semidirect
160. #5806C2×C5semidirect
161. D4×#67C2×C5semidirect
162. #5791C2×C5semidirect
163. C2×C4×#67C2×C5semidirect
170. C2×C5×#41C2×D3semidirect
171. C2×C5×#41C2×D3semidirect
172. C2×C5×#41C2×D3semidirect
174. C22×C5×Q8C2×D3semidirect
177. C22×C5×D4C2×D3semidirect
179. C23×C4×C5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
232. C3×C5×D4C2×D4semidirect
238. C2×C3×C4×C5C2×D4semidirect
248. C5×#67#41direct (N × H)
266. C2×C3×#41C22×C5semidirect
267. C2×C3×#41C22×C5semidirect
268. C2×C3×#41C22×C5semidirect
269. C22×C3×Q8C22×C5semidirect
270. C22×C3×D4C22×C5semidirect
271. C23×C3×C4C22×C5semidirect
274. C2×#239C22×C5semidirect
275. C2×D3×Q8C22×C5semidirect
276. C2×#237C22×C5semidirect
277. C2×D3×D4C22×C5semidirect
278. C2×#235C22×C5semidirect
279. C22×C4×D3C22×C5semidirect
280. #953C22×C5semidirect
281. C2×#217C22×C5semidirect
282. #947C22×C5semidirect
283. #946C22×C5semidirect
284. #946C22×C5semidirect
285. Q8×Dic3C22×C5semidirect
286. Q8×Dic3C22×C5semidirect
287. #944C22×C5semidirect
288. #940C22×C5semidirect
289. #939C22×C5semidirect
290. #939C22×C5semidirect
291. #938C22×C5semidirect
292. #938C22×C5semidirect
293. #937C22×C5semidirect
294. #936C22×C5semidirect
295. #935C22×C5semidirect
296. D4×Dic3C22×C5semidirect
297. D4×Dic3C22×C5semidirect
298. #930C22×C5semidirect
299. #930C22×C5semidirect
300. #929C22×C5semidirect
303. C4×#67C22×C5semidirect
304. C4×#67C22×C5semidirect
305. C4×#67C22×C5semidirect
306. C4×#67C22×C5semidirect
307. C4×#67C22×C5semidirect
308. C4×#67C22×C5semidirect
309. C4×#67C22×C5semidirect
310. C2×(C2×D3)⋊C4C22×C5semidirect
311. #926C22×C5semidirect
312. #924C22×C5semidirect
313. #924C22×C5semidirect
314. C2×Dic3⋊C4C22×C5semidirect
315. C2×C4×Dic3C22×C5semidirect
324. C5×#41#67direct (N × H)
381. C22×#41C5×D3semidirect
404. C22×C3×C5C2×#41semidirect
412. C2×C5×D3C2×#41semidirect
422. C5×Dic3C2×#41semidirect
428. C3×#41C5×D4semidirect
500. C5×Q8C2×#67semidirect
510. C5×D4C2×#67semidirect
529. C2×C4×C5C2×#67semidirect
540. C2×#41C2×C5×D3semidirect
541. C2×#41C2×C5×D3semidirect
542. C2×#41C2×C5×D3semidirect
544. C22×Q8C2×C5×D3semidirect
547. C22×D4C2×C5×D3semidirect
549. C23×C4C2×C5×D3semidirect
606. C3×Q8C2×C5×D4semidirect
609. C3×D4C2×C5×D4semidirect
615. C2×C3×C4C2×C5×D4semidirect
625. #67C5×#41direct (N × H)
656. C22×C5D3×#41semidirect
677. #41C5×#67direct (N × H)
733. C3×C5D4×#41semidirect
743. C22×C3C2×C5×#41semidirect
751. C2×D3C2×C5×#41semidirect
761. Dic3C2×C5×#41semidirect
783. Q8C2×C5×#67semidirect
793. D4C2×C5×#67semidirect
812. C2×C4C2×C5×#67semidirect
825. C5#41×#67direct (N × H)
841. C22C5×D3×#41semidirect
854. C3C5×D4×#41semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C2×C5×D3×#412
C5×#58342
C5×#58322
C5×#58312
C5×#58292
C5×#58282
C5×Dic3×#412
C5×#58242
C5×#58172
C5×Q8×#672
C5×#58062
C5×D4×#672
C5×#57912
C2×C4×C5×#672
C5×D4×#413
#41×#675