Finite Group Databasebeta

← C59×#10250 #28422359

Subgroups — C59×#10250 #28422359

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3208C211yesmaximal, characteristic
2C59×#3078C211yesmaximal, characteristic, complemented
3C59×#2548C211yesmaximal, characteristic
4C59×#1545C211yesmaximal, characteristic
5C59×#1503C211yesmaximal, characteristic, complemented
6C59×#1479C211yesmaximal, characteristic, complemented
7C59×#1303C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×#127×C59C2211yescharacteristic
10C2×#124×C59—21no—
11C2×C4×Q8×C59C2211yescharacteristic
12C59×#492—21no—
13C59×#486—21no—
14C59×#479—22no—
15C59×#477—21no—
16C59×#475—21no—
17C59×#460—22no—
18C59×#450—22no—
19C59×#431C2211yescharacteristic
20C59×#431C2211yescharacteristic
21C59×#428—21no—
22C59×#423C2211yescharacteristic
23C59×#419—21no—
24C59×#394—22no—
25C59×#390—22no—
26C59×#390—21no—
27C4×C4⋊C4×C59C2211yescharacteristic
28C59×#331—22no—
29C59×#328—22no—
30C59×Q8⋊C8—22no—
31C22×Q8×C59D411yescharacteristic
32C22×D4×C59—21no—
33C22×D4×C59—21no—
34C22×D4×C59D412yes—
35C2×SD16×C59—24no—
36C2×M16×C59—21no—
37C4⋊Q8×C59D411yescharacteristic
38C4⋊Q8×C59D411yescharacteristic
39#127×C59—21no—
40#127×C59—21no—
41#127×C59—21no—
42#127×C59—21no—
43#125×C59—21no—
44#124×C59—42no—
45#124×C59—42no—
46C22⋊Q8×C59—21no—
47C22⋊Q8×C59—21no—
48C4×Q8×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51C4×Q8×C59—21no—
52C4×Q8×C59—21no—
53C4×Q8×C59—21no—
54#117×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59D411yescharacteristic
58C2×C22⋊C4×C59—24no—
59C2×C22⋊C4×C59—24no—
60C2×C42×C59—21no—
61C2×C42×C59—21no—
62C2×C42×C59C2311yescharacteristic
63#107×C59—22no—
64#106×C59—22no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59D412yes—
68C4⋊C8×C59D412yes—
69#103×C59—22no—
70#103×C59—22no—
71#102×C59—24no—
72C22⋊C8×C59—21no—
73C22⋊C8×C59—21no—
74C4×C8×C59—21no—
75C4×C8×C59—21no—
76#95×C59D412yes—
77C24×C59—22no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—21no—
81C2×Q8×C59—21no—
82C2×Q8×C59—21no—
83C2×Q8×C59—21no—
84C2×Q8×C59—21no—
85C2×Q8×C59SD1612yescomplemented
86C2×D4×C59—22no—
87C2×D4×C59—22no—
88C2×D4×C59—44no—
89C2×D4×C59—41no—
90C2×D4×C59—41no—
91C2×D4×C59—41no—
92C2×D4×C59—41no—
93C2×D4×C59—41no—
94C2×D4×C59—41no—
95C2×D4×C59—41no—
96C2×D4×C59—41no—
97C2×D4×C59—82no—
98C22×C4×C59—21no—
99C22×C4×C59—22no—
100C22×C4×C59—21no—
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104SD16×C59—84no—
105M16×C59—41no—
106M16×C59—41no—
107C2×C8×C59—22no—
108C2×C8×C59—22no—
109C2×C8×C59—41no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—21no—
115C4⋊C4×C59—21no—
116C4⋊C4×C59—42no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59—41no—
120C4⋊C4×C59—41no—
121C22⋊C4×C59—48no—
122C22⋊C4×C59—41no—
123C22⋊C4×C59—84no—
124C42×C59—41no—
125C42×C59—41no—
126C42×C59—41no—
127C42×C59—41no—
128C42×C59—41no—
129C42×C59C2×D411yescharacteristic
130C42×C59C2×D411yescharacteristic
131C42×C59C2×D411yescharacteristic
132C42×C59#4111yescharacteristic
133C23×C59—44no—
134C23×C59—44no—
135C23×C59—42no—
136C23×C59—42no—
137C23×C59—42no—
138C23×C59#12011yescharacteristic
139Q8×C59—22no—
140Q8×C59—22no—
141Q8×C59—41no—
142Q8×C59—41no—
143Q8×C59—42no—
144Q8×C59—81no—
145D4×C59—44no—
146D4×C59—82no—
147D4×C59—82no—
148D4×C59—82no—
149D4×C59—81no—
150D4×C59—81no—
151D4×C59—81no—
152D4×C59—81no—
153C2×C4×C59—22no—
154C2×C4×C59—22no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—41no—
158C2×C4×C59—42no—
159C2×C4×C59—42no—
160C2×C4×C59—42no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—42no—
165C2×C4×C59#12011yescharacteristic
166C2×C4×C59#12011yescharacteristic
167C2×C4×C59#12111yescharacteristic
168C2×C4×C59#12111yescharacteristic
169C2×C4×C59#12111yescharacteristic
170C2×C4×C59#12711yescharacteristic
171C2×C4×C59C2×SD1611yescharacteristic
172C2×C4×C59#13511yescharacteristic
173C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C59#13711yescharacteristic
175C8×C59—42no—
176C8×C59—42no—
177C8×C59—81no—
178#10250C5911yesmaximal, characteristic, direct product factor, Sylow
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—84no—
182C22×C59—84no—
183C22×C59—82no—
184C22×C59—82no—
185C22×C59—82no—
186C22×C59#39211yescharacteristic
187C22×C59#45011yescharacteristic
188C22×C59#45211yescharacteristic
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—21no—
192C4×C59—42no—
193C4×C59—82no—
194C4×C59—81no—
195C4×C59—81no—
196C4×C59—81no—
197C4×C59#44811yescharacteristic
198C4×C59#44911yescharacteristic
199C4×C59#45512yes—
200C4×C59#46511yescharacteristic
201C4×C59#46811yescharacteristic
202#3208C2×C5911yescharacteristic
203#3078C2×C5911yescharacteristic, complemented
204#2548C2×C5911yescharacteristic
205#1545C2×C5911yescharacteristic
206#1503C2×C5911yescharacteristic, complemented
207#1479C2×C5911yescharacteristic, complemented
208#1303C2×C5911yescharacteristic, complemented
209C2×C59—21no—
210C2×C59—21no—
211C2×C59—162no—
212C2×C59#200011yescharacteristic
213C2×C59#200411yescharacteristic
214C2×C59#200811yescharacteristic
215#533C22×C5911yescharacteristic
216C2×#127C22×C5911yescharacteristic
217C2×#124—21no—
218C2×C4×Q8C22×C5911yescharacteristic
219#492—21no—
220#486—21no—
221#479—22no—
222#477—21no—
223#475—21no—
224#460—22no—
225#450—22no—
226#431C22×C5911yescharacteristic
227#431C22×C5911yescharacteristic
228#428—21no—
229#423C22×C5911yescharacteristic
230#419—21no—
231#394—22no—
232#390—22no—
233#390—21no—
234C4×C4⋊C4C22×C5911yescharacteristic
235#331—22no—
236#328—22no—
237Q8⋊C8—22no—
238C59#1025011yescharacteristic, direct product factor, Sylow
239C22×Q8D4×C5911yescharacteristic
240C22×D4—21no—
241C22×D4—21no—
242C22×D4D4×C5912yes—
243C2×SD16—24no—
244C2×M16—21no—
245C4⋊Q8D4×C5911yescharacteristic
246C4⋊Q8D4×C5911yescharacteristic
247#127—21no—
248#127—21no—
249#127—21no—
250#127—21no—
251#125—21no—
252#124—42no—
253#124—42no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262#117—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C5911yescharacteristic
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42C23×C5911yescharacteristic
271#107—22no—
272#106—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C5912yes—
276C4⋊C8D4×C5912yes—
277#103—22no—
278#103—22no—
279#102—24no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#95D4×C5912yes—
285C24—22no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8SD16×C5912yescomplemented
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—44no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—82no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4C2×D4×C5911yescharacteristic
310C22×C4C2×D4×C5911yescharacteristic
311C22×C4C2×D4×C5911yescharacteristic
312SD16—84no—
313M16—41no—
314M16—41no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—41no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—48no—
330C22⋊C4—41no—
331C22⋊C4—84no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42C2×D4×C5911yescharacteristic
338C42C2×D4×C5911yescharacteristic
339C42C2×D4×C5911yescharacteristic
340C42#41×C5911yescharacteristic
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23#120×C5911yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—81no—
353D4—44no—
354D4—82no—
355D4—82no—
356D4—82no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4#120×C5911yescharacteristic
374C2×C4#120×C5911yescharacteristic
375C2×C4#121×C5911yescharacteristic
376C2×C4#121×C5911yescharacteristic
377C2×C4#121×C5911yescharacteristic
378C2×C4#127×C5911yescharacteristic
379C2×C4C2×SD16×C5911yescharacteristic
380C2×C4#135×C5911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
382C2×C4#137×C5911yescharacteristic
383C8—42no—
384C8—42no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—84no—
389C22—84no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22C59×#39211yescharacteristic
394C22C59×#45011yescharacteristic
395C22C59×#45211yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4C59×#44811yescharacteristic
405C4C59×#44911yescharacteristic
406C4C59×#45512yes—
407C4C59×#46511yescharacteristic
408C4C59×#46811yescharacteristic
409C2—21no—
410C2—21no—
411C2—162no—
412C2C59×#200011yescharacteristic
413C2C59×#200411yescharacteristic
414C2C59×#200811yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC2×#127×C59C22
LCSG ▷ C2×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×#3078C2semidirect
5. C59×#1503C2semidirect
6. C59×#1479C2semidirect
7. C59×#1303C2semidirect
85. C2×Q8×C59SD16semidirect
178. #10250C59direct (N × H)
203. #3078C2×C59semidirect
206. #1503C2×C59semidirect
207. #1479C2×C59semidirect
208. #1303C2×C59semidirect
238. C59#10250direct (N × H)
293. C2×Q8SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#32082
C59×#30782
C59×#25482
C59×#15452
C59×#15032
C59×#14792
C59×#13032
#1025059