Finite Group Databasebeta

← C59×#18730 #28430839

Subgroups — C59×#18730 #28430839

Order 15104.

864 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3550C211yesmaximal, characteristic
2C59×#3230C211yesmaximal, characteristic, complemented
3C59×#3227C211yesmaximal, characteristic
4C59×#3139C211yesmaximal, characteristic, complemented
5C59×#1638C214yesmaximal, complemented
6C59×#1637C214yesmaximal, complemented
7C59×#1544C211yesmaximal, characteristic, complemented
8C59×#1485C211yesmaximal, characteristic, complemented
9C59×#1484C211yesmaximal, characteristic
10C59×#563—22no—
11C59×#559—21no—
12Q82×C59—21no—
13C59×#556—21no—
14C59×#556C2212yes—
15D4×Q8×C59—21no—
16D4×Q8×C59C2212yes—
17C59×#542—22no—
18C59×#542—22no—
19C59×#536—22no—
20C59×#533C2211yescharacteristic
21C59×#533C2211yescharacteristic
22C59×#532C2211yescharacteristic
23C2×C4⋊Q8×C59C2211yescharacteristic
24C59×#500—21no—
25C59×#498—21no—
26C59×#491—22no—
27C59×#487—21no—
28C59×#487C2212yes—
29C59×#487C2212yes—
30C59×#486—21no—
31C59×#484—22no—
32C59×#481—22no—
33C59×#477C2214yes—
34C59×#476C2214yes—
35C59×#431C2211yescharacteristic
36C59×#431C2211yescharacteristic
37C59×#419—22no—
38C4×M16×C59C2211yescharacteristic
39C59×#332C2212yes—
40C59×#332C2212yes—
41C59×Q8⋊C8C2214yes—
42C59×D4⋊C8C2214yes—
43C2×#41×C59—21no—
44C22×Q8×C59—22no—
45C22×Q8×C59—21no—
46C2×M16×C59—21no—
47C4⋊Q8×C59—24no—
48C4⋊Q8×C59—22no—
49C4⋊Q8×C59—22no—
50C4⋊Q8×C59—21no—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59D411yescharacteristic
54C4⋊Q8×C59D411yescharacteristic
55C4⋊Q8×C59D411yescharacteristic
56C4⋊Q8×C59C2312yes—
57C4⋊Q8×C59C2311yescharacteristic
58C4⋊Q8×C59C2311yescharacteristic
59#127×C59D411yescharacteristic
60#126×C59—24no—
61#126×C59—24no—
62#125×C59—21no—
63#125×C59D412yes—
64#124×C59—24no—
65#124×C59—22no—
66#124×C59—22no—
67#124×C59—21no—
68#123×C59—24no—
69#123×C59—24no—
70C22⋊Q8×C59—24no—
71C22⋊Q8×C59—22no—
72C22⋊Q8×C59—21no—
73C22⋊Q8×C59—21no—
74C22⋊Q8×C59—21no—
75C22⋊Q8×C59—22no—
76C22⋊Q8×C59—24no—
77C22⋊Q8×C59D412yes—
78#121×C59—21no—
79#121×C59D412yes—
80C4×Q8×C59—22no—
81C4×Q8×C59—22no—
82C4×Q8×C59—21no—
83C4×Q8×C59—21no—
84C4×Q8×C59—21no—
85C4×Q8×C59C2312yes—
86C4×D4×C59—22no—
87C4×D4×C59—22no—
88C4×D4×C59—21no—
89C4×D4×C59C2312yes—
90#117×C59—21no—
91#117×C59—22no—
92#117×C59D412yes—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—21no—
95C2×C42×C59C2311yescharacteristic
96#107×C59—24no—
97#106×C59—24no—
98C4⋊C8×C59C2312yes—
99C4⋊C8×C59C2312yes—
100#103×C59—24no—
101#103×C59—24no—
102#103×C59—24no—
103#102×C59—24no—
104C22⋊C8×C59—21no—
105C22⋊C8×C59—21no—
106#97×C59—21no—
107C4×C8×C59—21no—
108C4×C8×C59—21no—
109C4×C8×C59C2312yes—
110#41×C59—82no—
111C2×Q8×C59—24no—
112C2×Q8×C59—21no—
113C2×Q8×C59—21no—
114C2×Q8×C59—21no—
115C2×Q8×C59—21no—
116C2×Q8×C59—22no—
117C2×Q8×C59—44no—
118C2×Q8×C59—41no—
119C2×Q8×C59—84no—
120C2×Q8×C59C2×D412yes—
121C2×D4×C59—22no—
122C2×D4×C59—21no—
123C2×D4×C59—21no—
124C2×D4×C59C2×D412yes—
125C22×C4×C59—24no—
126C22×C4×C59—22no—
127C22×C4×C59—41no—
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131M16×C59—42no—
132C2×C8×C59—22no—
133C2×C8×C59—22no—
134C2×C8×C59—22no—
135C4⋊C4×C59—24no—
136C4⋊C4×C59—24no—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—21no—
139C4⋊C4×C59—21no—
140C4⋊C4×C59—21no—
141C4⋊C4×C59—22no—
142C4⋊C4×C59—22no—
143C4⋊C4×C59—22no—
144C4⋊C4×C59—21no—
145C4⋊C4×C59—21no—
146C4⋊C4×C59—22no—
147C4⋊C4×C59—22no—
148C4⋊C4×C59—22no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59C2×D412yes—
152C4⋊C4×C59C2×D412yes—
153C4⋊C4×C59C2×D412yes—
154C4⋊C4×C59C2×D412yes—
155C22⋊C4×C59—24no—
156C22⋊C4×C59—24no—
157C22⋊C4×C59—24no—
158C22⋊C4×C59—22no—
159C22⋊C4×C59—22no—
160C22⋊C4×C59—22no—
161C22⋊C4×C59—22no—
162C42×C59—24no—
163C42×C59—22no—
164C42×C59—22no—
165C42×C59C2×D411yescharacteristic
166C42×C59C2×D411yescharacteristic
167C42×C59C2×D411yescharacteristic
168C42×C59C2411yescharacteristic
169C23×C59—22no—
170C23×C59#12011yescharacteristic
171Q8×C59—24no—
172Q8×C59—44no—
173Q8×C59—42no—
174Q8×C59—42no—
175Q8×C59—42no—
176Q8×C59—81no—
177Q8×C59—84no—
178Q8×C59—82no—
179D4×C59—24no—
180D4×C59—42no—
181D4×C59—81no—
182D4×C59—82no—
183C2×C4×C59—22no—
184C2×C4×C59—22no—
185C2×C4×C59—22no—
186C2×C4×C59—22no—
187C2×C4×C59—22no—
188C2×C4×C59—22no—
189C2×C4×C59—22no—
190C2×C4×C59—22no—
191C2×C4×C59—44no—
192C2×C4×C59—42no—
193C2×C4×C59—84no—
194C2×C4×C59—82no—
195C2×C4×C59#12011yescharacteristic
196C2×C4×C59#12011yescharacteristic
197C2×C4×C59#12011yescharacteristic
198C2×C4×C59C22×D411yescharacteristic
199C2×C4×C59C22×D411yescharacteristic
200C2×C4×C59C22×D411yescharacteristic
201C8×C59—42no—
202C8×C59—42no—
203C8×C59—42no—
204#18730C5911yesmaximal, characteristic, direct product factor, Sylow
205C22×C59—21no—
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—42no—
209C22×C59—42no—
210C22×C59—42no—
211C22×C59C2×#12011yescharacteristic
212C4×C59—21no—
213C4×C59—21no—
214C4×C59—21no—
215C4×C59—42no—
216C4×C59—42no—
217C4×C59—42no—
218C4×C59—42no—
219C4×C59—42no—
220C4×C59—82no—
221C4×C59#45412yes—
222C4×C59#57712yes—
223C4×C59#57812yes—
224#3550C2×C5911yescharacteristic
225#3230C2×C5911yescharacteristic, complemented
226#3227C2×C5911yescharacteristic
227#3139C2×C5911yescharacteristic, complemented
228#1638C2×C5914yescomplemented
229#1637C2×C5914yescomplemented
230#1544C2×C5911yescharacteristic, complemented
231#1485C2×C5911yescharacteristic, complemented
232#1484C2×C5911yescharacteristic
233C2×C59—41no—
234C2×C59—82no—
235C2×C59#300911yescharacteristic
236C2×C59#301111yescharacteristic
237C2×C59C2×#45411yescharacteristic
238#563—22no—
239#559—21no—
240Q82—21no—
241#556—21no—
242#556C22×C5912yes—
243D4×Q8—21no—
244D4×Q8C22×C5912yes—
245#542—22no—
246#542—22no—
247#536—22no—
248#533C22×C5911yescharacteristic
249#533C22×C5911yescharacteristic
250#532C22×C5911yescharacteristic
251C2×C4⋊Q8C22×C5911yescharacteristic
252#500—21no—
253#498—21no—
254#491—22no—
255#487—21no—
256#487C22×C5912yes—
257#487C22×C5912yes—
258#486—21no—
259#484—22no—
260#481—22no—
261#477C22×C5914yes—
262#476C22×C5914yes—
263#431C22×C5911yescharacteristic
264#431C22×C5911yescharacteristic
265#419—22no—
266C4×M16C22×C5911yescharacteristic
267#332C22×C5912yes—
268#332C22×C5912yes—
269Q8⋊C8C22×C5914yes—
270D4⋊C8C22×C5914yes—
271C59#1873011yescharacteristic, direct product factor, Sylow
272C2×#41—21no—
273C22×Q8—22no—
274C22×Q8—21no—
275C2×M16—21no—
276C4⋊Q8—24no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8D4×C5911yescharacteristic
283C4⋊Q8D4×C5911yescharacteristic
284C4⋊Q8D4×C5911yescharacteristic
285C4⋊Q8C23×C5912yes—
286C4⋊Q8C23×C5911yescharacteristic
287C4⋊Q8C23×C5911yescharacteristic
288#127D4×C5911yescharacteristic
289#126—24no—
290#126—24no—
291#125—21no—
292#125D4×C5912yes—
293#124—24no—
294#124—22no—
295#124—22no—
296#124—21no—
297#123—24no—
298#123—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8D4×C5912yes—
307#121—21no—
308#121D4×C5912yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C23×C5912yes—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4C23×C5912yes—
319#117—21no—
320#117—22no—
321#117D4×C5912yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C42C23×C5911yescharacteristic
325#107—24no—
326#106—24no—
327C4⋊C8C23×C5912yes—
328C4⋊C8C23×C5912yes—
329#103—24no—
330#103—24no—
331#103—24no—
332#102—24no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335#97—21no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8C23×C5912yes—
339#41—82no—
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—41no—
348C2×Q8—84no—
349C2×Q8C2×D4×C5912yes—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4C2×D4×C5912yes—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4C2×D4×C5911yescharacteristic
358C22×C4C2×D4×C5911yescharacteristic
359C22×C4C2×D4×C5911yescharacteristic
360M16—42no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C5912yes—
381C4⋊C4C2×D4×C5912yes—
382C4⋊C4C2×D4×C5912yes—
383C4⋊C4C2×D4×C5912yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42C2×D4×C5911yescharacteristic
395C42C2×D4×C5911yescharacteristic
396C42C2×D4×C5911yescharacteristic
397C42C24×C5911yescharacteristic
398C23—22no—
399C23#120×C5911yescharacteristic
400Q8—24no—
401Q8—44no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—81no—
406Q8—84no—
407Q8—82no—
408D4—24no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4#120×C5911yescharacteristic
425C2×C4#120×C5911yescharacteristic
426C2×C4#120×C5911yescharacteristic
427C2×C4C22×D4×C5911yescharacteristic
428C2×C4C22×D4×C5911yescharacteristic
429C2×C4C22×D4×C5911yescharacteristic
430C8—42no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×#120×C5911yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4C59×#45412yes—
450C4C59×#57712yes—
451C4C59×#57812yes—
452C2—41no—
453C2—82no—
454C2C59×#300911yescharacteristic
455C2C59×#301111yescharacteristic
456C2C2×C59×#45411yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC42C24×C59
prime radicalC59×#532C22
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×#3230C2semidirect
4. C59×#3139C2semidirect
5. C59×#1638C2semidirect
6. C59×#1637C2semidirect
7. C59×#1544C2semidirect
8. C59×#1485C2semidirect
204. #18730C59direct (N × H)
225. #3230C2×C59semidirect
227. #3139C2×C59semidirect
228. #1638C2×C59semidirect
229. #1637C2×C59semidirect
230. #1544C2×C59semidirect
231. #1485C2×C59semidirect
271. C59#18730direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35502
C59×#32302
C59×#32272
C59×#31392
C59×#16382
C59×#16372
C59×#15442
C59×#14852
C59×#14842
#1873059