Finite Group Databasebeta

← C59×#8430 #28420539

Subgroups — C59×#8430 #28420539

Order 15104.

760 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3506C211yesmaximal, characteristic
2C59×#1804C211yesmaximal, characteristic, complemented
3C59×#1540C211yesmaximal, characteristic, complemented
4C59×#1518C211yesmaximal, characteristic, complemented
5C59×#1517C211yesmaximal, characteristic, complemented
6C59×#1481C211yesmaximal, characteristic, complemented
7C59×#1478C211yesmaximal, characteristic, complemented
8C59×#559—22no—
9C59×#556—21no—
10C59×#555C412yescomplemented
11C59×#553—22no—
12C59×#550—21no—
13C59×#547C412yescomplemented
14C59×#538—22no—
15C59×#535—21no—
16C59×#533C2211yescharacteristic
17C59×#532C2211yescharacteristic
18C59×#525—22no—
19C59×#520—21no—
20C2×C4×D4×C59C2211yescharacteristic
21C59×#431C2211yescharacteristic
22C59×#431C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×#102×C59—21no—
25C59×#382C2211yescharacteristic
26C59×#340—21no—
27C59×#332—21no—
28C59×#331—21no—
29C59×#328—22no—
30C59×#327—22no—
31C59×Q8⋊C8—22no—
32C59×D4⋊C8—22no—
33C2×#41×C59—22no—
34C2×#41×C59—21no—
35C22×D4×C59D411yescharacteristic
36C23×C4×C59—21no—
37C22×C8×C59—21no—
38C4⋊Q8×C59C2×C411yescharacteristic
39C4⋊Q8×C59C2×C411yescharacteristic
40C4⋊Q8×C59D411yescharacteristic
41#127×C59—22no—
42#127×C59D411yescharacteristic
43#126×C59—24no—
44#125×C59—21no—
45#124×C59—22no—
46#124×C59—24no—
47#124×C59—21no—
48#123×C59—24no—
49#123×C59—24no—
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59—22no—
52C22⋊Q8×C59D412yes—
53#121×C59—24no—
54#121×C59—22no—
55#121×C59—22no—
56#121×C59—22no—
57#121×C59—21no—
58#121×C59D412yes—
59#120×C59—24no—
60C4×Q8×C59—22no—
61C4×Q8×C59—21no—
62C4×Q8×C59D412yes—
63C4×D4×C59—24no—
64C4×D4×C59—22no—
65C4×D4×C59—24no—
66C4×D4×C59—21no—
67C4×D4×C59—21no—
68C4×D4×C59—21no—
69C4×D4×C59C2×C412yes—
70C4×D4×C59C2×C412yes—
71C4×D4×C59D412yes—
72#117×C59—21no—
73#117×C59—22no—
74#117×C59—22no—
75C2×C4⋊C4×C59—22no—
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59D411yescharacteristic
78C2×C22⋊C4×C59—21no—
79C2×C42×C59C2311yescharacteristic
80C4⋊C8×C59—21no—
81C4⋊C8×C59—21no—
82C4⋊C8×C59—21no—
83C4⋊C8×C59—21no—
84#102×C59—42no—
85C22⋊C8×C59—21no—
86C22⋊C8×C59—21no—
87C4×C8×C59—21no—
88C4×C8×C59—21no—
89#95×C59—21no—
90#95×C59—21no—
91C24×C59—21no—
92#41×C59—41no—
93#41×C59—41no—
94#41×C59—41no—
95#41×C59—41no—
96#41×C59—84no—
97C2×Q8×C59—21no—
98C2×Q8×C59—21no—
99C2×Q8×C59C22⋊C412yes—
100C2×D4×C59—22no—
101C2×D4×C59—24no—
102C2×D4×C59—24no—
103C2×D4×C59—21no—
104C2×D4×C59—21no—
105C2×D4×C59—21no—
106C2×D4×C59—21no—
107C2×D4×C59—21no—
108C2×D4×C59—21no—
109C2×D4×C59—21no—
110C2×D4×C59C22⋊C412yes—
111C2×D4×C59C22⋊C412yes—
112C22×C4×C59—24no—
113C22×C4×C59—21no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—41no—
118C22×C4×C59—82no—
119C22×C4×C59C2×D411yescharacteristic
120C22×C4×C59C2×D411yescharacteristic
121C22×C4×C59C2×D411yescharacteristic
122C2×C8×C59—41no—
123C2×C8×C59—41no—
124C2×C8×C59—41no—
125C2×C8×C59—41no—
126C2×C8×C59—41no—
127C4⋊C4×C59—24no—
128C4⋊C4×C59—21no—
129C4⋊C4×C59—21no—
130C4⋊C4×C59—21no—
131C4⋊C4×C59—21no—
132C4⋊C4×C59—22no—
133C4⋊C4×C59—21no—
134C4⋊C4×C59—22no—
135C4⋊C4×C59—41no—
136C4⋊C4×C59—41no—
137C4⋊C4×C59C22⋊C412yes—
138C4⋊C4×C59C22⋊C412yes—
139C4⋊C4×C59C22⋊C412yes—
140C22⋊C4×C59—24no—
141C22⋊C4×C59—24no—
142C22⋊C4×C59—24no—
143C22⋊C4×C59—22no—
144C22⋊C4×C59—22no—
145C22⋊C4×C59—22no—
146C22⋊C4×C59—22no—
147C22⋊C4×C59—22no—
148C42×C59—24no—
149C42×C59—22no—
150C42×C59C22×C411yescharacteristic
151C42×C59C2×D411yescharacteristic
152C42×C59C2×D411yescharacteristic
153C42×C59C2×D411yescharacteristic
154C23×C59—22no—
155C23×C59—22no—
156C23×C59—41no—
157C23×C59—41no—
158C23×C59—81no—
159C23×C59—81no—
160C23×C59#12011yescharacteristic
161Q8×C59—42no—
162Q8×C59—42no—
163Q8×C59—41no—
164Q8×C59—41no—
165D4×C59—22no—
166D4×C59—22no—
167D4×C59—42no—
168D4×C59—42no—
169D4×C59—42no—
170D4×C59—41no—
171D4×C59—41no—
172D4×C59—41no—
173D4×C59—41no—
174D4×C59—81no—
175D4×C59—84no—
176D4×C59—84no—
177C2×C4×C59—22no—
178C2×C4×C59—22no—
179C2×C4×C59—22no—
180C2×C4×C59—22no—
181C2×C4×C59—41no—
182C2×C4×C59—41no—
183C2×C4×C59—44no—
184C2×C4×C59—42no—
185C2×C4×C59—42no—
186C2×C4×C59—82no—
187C2×C4×C59—81no—
188C2×C4×C59—84no—
189C2×C4×C59—81no—
190C2×C4×C59—81no—
191C2×C4×C59—81no—
192C2×C4×C59C2×C22⋊C411yescharacteristic
193C2×C4×C59C2×C22⋊C411yescharacteristic
194C2×C4×C59C2×C22⋊C411yescharacteristic
195C2×C4×C59#12011yescharacteristic
196C2×C4×C59#12011yescharacteristic
197C2×C4×C59#12011yescharacteristic
198C2×C4×C59#13511yescharacteristic
199C2×C4×C59#13511yescharacteristic
200C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C59#13711yescharacteristic
202C8×C59—81no—
203C8×C59—81no—
204C8×C59—81no—
205#8430C5911yesmaximal, characteristic, direct product factor, Sylow
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—42no—
209C22×C59—42no—
210C22×C59—42no—
211C22×C59—42no—
212C22×C59—42no—
213C22×C59—42no—
214C22×C59—82no—
215C22×C59—82no—
216C22×C59#37911yescharacteristic
217C22×C59#44911yescharacteristic
218C22×C59#45211yescharacteristic
219C4×C59—21no—
220C4×C59—21no—
221C4×C59—21no—
222C4×C59—21no—
223C4×C59—42no—
224C4×C59—42no—
225C4×C59—42no—
226C4×C59—42no—
227C4×C59—161no—
228C4×C59#41611yescharacteristic
229C4×C59#41711yescharacteristic
230C4×C59#44911yescharacteristic
231C4×C59#45211yescharacteristic
232#3506C2×C5911yescharacteristic
233#1804C2×C5911yescharacteristic, complemented
234#1540C2×C5911yescharacteristic, complemented
235#1518C2×C5911yescharacteristic, complemented
236#1517C2×C5911yescharacteristic, complemented
237#1481C2×C5911yescharacteristic, complemented
238#1478C2×C5911yescharacteristic, complemented
239C2×C59—21no—
240C2×C59—21no—
241C2×C59—82no—
242C2×C59—82no—
243C2×C59#178811yescharacteristic
244C2×C59#179411yescharacteristic
245C2×C59#179511yescharacteristic
246#559—22no—
247#556—21no—
248#555C4×C5912yescomplemented
249#553—22no—
250#550—21no—
251#547C4×C5912yescomplemented
252#538—22no—
253#535—21no—
254#533C22×C5911yescharacteristic
255#532C22×C5911yescharacteristic
256#525—22no—
257#520—21no—
258C2×C4×D4C22×C5911yescharacteristic
259#431C22×C5911yescharacteristic
260#431C22×C5911yescharacteristic
261C2×C4⋊C8C22×C5911yescharacteristic
262C2×#102—21no—
263#382C22×C5911yescharacteristic
264#340—21no—
265#332—21no—
266#331—21no—
267#328—22no—
268#327—22no—
269Q8⋊C8—22no—
270D4⋊C8—22no—
271C59#843011yescharacteristic, direct product factor, Sylow
272C2×#41—22no—
273C2×#41—21no—
274C22×D4D4×C5911yescharacteristic
275C23×C4—21no—
276C22×C8—21no—
277C4⋊Q8C2×C4×C5911yescharacteristic
278C4⋊Q8C2×C4×C5911yescharacteristic
279C4⋊Q8D4×C5911yescharacteristic
280#127—22no—
281#127D4×C5911yescharacteristic
282#126—24no—
283#125—21no—
284#124—22no—
285#124—24no—
286#124—21no—
287#123—24no—
288#123—24no—
289C22⋊Q8—21no—
290C22⋊Q8—22no—
291C22⋊Q8D4×C5912yes—
292#121—24no—
293#121—22no—
294#121—22no—
295#121—22no—
296#121—21no—
297#121D4×C5912yes—
298#120—24no—
299C4×Q8—22no—
300C4×Q8—21no—
301C4×Q8D4×C5912yes—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4—24no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4C2×C4×C5912yes—
309C4×D4C2×C4×C5912yes—
310C4×D4D4×C5912yes—
311#117—21no—
312#117—22no—
313#117—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C5911yescharacteristic
317C2×C22⋊C4—21no—
318C2×C42C23×C5911yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323#102—42no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C4×C8—21no—
327C4×C8—21no—
328#95—21no—
329#95—21no—
330C24—21no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335#41—84no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8C22⋊C4×C5912yes—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4C22⋊C4×C5912yes—
350C2×D4C22⋊C4×C5912yes—
351C22×C4—24no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—82no—
358C22×C4C2×D4×C5911yescharacteristic
359C22×C4C2×D4×C5911yescharacteristic
360C22×C4C2×D4×C5911yescharacteristic
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C22⋊C4×C5912yes—
377C4⋊C4C22⋊C4×C5912yes—
378C4⋊C4C22⋊C4×C5912yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—24no—
388C42—22no—
389C42C22×C4×C5911yescharacteristic
390C42C2×D4×C5911yescharacteristic
391C42C2×D4×C5911yescharacteristic
392C42C2×D4×C5911yescharacteristic
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—81no—
398C23—81no—
399C23#120×C5911yescharacteristic
400Q8—42no—
401Q8—42no—
402Q8—41no—
403Q8—41no—
404D4—22no—
405D4—22no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—81no—
414D4—84no—
415D4—84no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—84no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4C2×C22⋊C4×C5911yescharacteristic
432C2×C4C2×C22⋊C4×C5911yescharacteristic
433C2×C4C2×C22⋊C4×C5911yescharacteristic
434C2×C4#120×C5911yescharacteristic
435C2×C4#120×C5911yescharacteristic
436C2×C4#120×C5911yescharacteristic
437C2×C4#135×C5911yescharacteristic
438C2×C4#135×C5911yescharacteristic
439C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
440C2×C4#137×C5911yescharacteristic
441C8—81no—
442C8—81no—
443C8—81no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—82no—
453C22—82no—
454C22C59×#37911yescharacteristic
455C22C59×#44911yescharacteristic
456C22C59×#45211yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—161no—
466C4C59×#41611yescharacteristic
467C4C59×#41711yescharacteristic
468C4C59×#44911yescharacteristic
469C4C59×#45211yescharacteristic
470C2—21no—
471C2—21no—
472C2—82no—
473C2—82no—
474C2C59×#178811yescharacteristic
475C2C59×#179411yescharacteristic
476C2C59×#179511yescharacteristic
subgroupG/H
center, socleC22×C59#379
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
prime radicalC59×#3506C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1804C2semidirect
3. C59×#1540C2semidirect
4. C59×#1518C2semidirect
5. C59×#1517C2semidirect
6. C59×#1481C2semidirect
7. C59×#1478C2semidirect
10. C59×#555C4semidirect
13. C59×#547C4semidirect
205. #8430C59direct (N × H)
233. #1804C2×C59semidirect
234. #1540C2×C59semidirect
235. #1518C2×C59semidirect
236. #1517C2×C59semidirect
237. #1481C2×C59semidirect
238. #1478C2×C59semidirect
248. #555C4×C59semidirect
251. #547C4×C59semidirect
271. C59#8430direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35062
C59×#18042
C59×#15402
C59×#15182
C59×#15172
C59×#14812
C59×#14782
#843059