Finite Group Databasebeta

← C59×#9300 #28421409

Subgroups — C59×#9300 #28421409

Order 15104.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3226C211yesmaximal, characteristic
2C59×#2327C211yesmaximal, characteristic, complemented
3C59×#1963C211yesmaximal, characteristic
4C59×#1546C211yesmaximal, characteristic, complemented
5C59×#1517C211yesmaximal, characteristic
6C59×#1286C211yesmaximal, characteristic, complemented
7C59×#1274C211yesmaximal, characteristic, complemented
8C59×#532C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×C4×Q8×C59—21no—
11C59×#500C412yescomplemented
12C59×#486C412yescomplemented
13C59×#480—22no—
14C59×#474—22no—
15C59×#431C2211yescharacteristic
16C59×#431C2211yescharacteristic
17C59×#423C2211yescharacteristic
18C2×#104×C59—21no—
19C2×#104×C59—21no—
20C59×#391—21no—
21C59×#387—22no—
22C59×#387—22no—
23C59×#382C2211yescharacteristic
24C59×#376C2211yescharacteristic
25C59×#332—22no—
26C59×#327—22no—
27C2×#41×C59—21no—
28C22×Q8×C59—21no—
29C2×M16×C59—21no—
30C4⋊Q8×C59—21no—
31C4⋊Q8×C59—21no—
32C4⋊Q8×C59C2×C411yescharacteristic
33C4⋊Q8×C59C2×C412yes—
34C4⋊Q8×C59D412yes—
35#127×C59C2×C411yescharacteristic
36#124×C59—21no—
37#121×C59—21no—
38#121×C59—21no—
39C4×Q8×C59—42no—
40C4×Q8×C59—42no—
41C4×D4×C59—21no—
42C4×D4×C59—21no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59—22no—
45C2×C4⋊C4×C59—21no—
46C2×C4⋊C4×C59D412yes—
47C2×C42×C59—22no—
48C2×C42×C59D411yescharacteristic
49C2×C42×C59D411yescharacteristic
50C2×C42×C59C2311yescharacteristic
51#107×C59—24no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56#104×C59—42no—
57#104×C59—42no—
58#102×C59—24no—
59C22⋊C8×C59—21no—
60C22⋊C8×C59—21no—
61C4×C8×C59—21no—
62C4×C8×C59C2×C412yes—
63#95×C59—24no—
64#95×C59—21no—
65#95×C59—21no—
66#95×C59—21no—
67#95×C59D412yes—
68#41×C59—41no—
69#41×C59—41no—
70#41×C59—41no—
71#41×C59—41no—
72C2×Q8×C59—22no—
73C2×Q8×C59—22no—
74C2×Q8×C59—21no—
75C2×Q8×C59—41no—
76C2×Q8×C59—41no—
77C2×Q8×C59—41no—
78C2×Q8×C59—41no—
79C2×D4×C59—21no—
80C2×D4×C59—21no—
81C2×D4×C59—21no—
82C2×D4×C59—41no—
83C22×C4×C59—21no—
84C22×C4×C59—22no—
85C22×C4×C59—21no—
86C22×C4×C59—22no—
87C22×C4×C59—41no—
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91M16×C59—41no—
92M16×C59—41no—
93C2×C8×C59—22no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C4⋊C4×C59—22no—
97C4⋊C4×C59—22no—
98C4⋊C4×C59—22no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—44no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59C22⋊C414yes—
105C22⋊C4×C59—41no—
106C22⋊C4×C59—41no—
107C42×C59—21no—
108C42×C59—21no—
109C42×C59—21no—
110C42×C59—44no—
111C42×C59D812yes—
112C42×C59C22×C411yescharacteristic
113C42×C59C2×D411yescharacteristic
114C42×C59#4111yescharacteristic
115C42×C59#4111yescharacteristic
116C23×C59—41no—
117C23×C59#12011yescharacteristic
118Q8×C59—42no—
119Q8×C59—42no—
120Q8×C59—42no—
121Q8×C59—42no—
122Q8×C59—41no—
123Q8×C59—41no—
124D4×C59—42no—
125D4×C59—41no—
126D4×C59—41no—
127D4×C59—81no—
128D4×C59—81no—
129D4×C59—81no—
130C2×C4×C59—24no—
131C2×C4×C59—22no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—42no—
137C2×C4×C59—42no—
138C2×C4×C59—41no—
139C2×C4×C59—42no—
140C2×C4×C59—41no—
141C2×C4×C59—42no—
142C2×C4×C59—41no—
143C2×C4×C59—42no—
144C2×C4×C59—41no—
145C2×C4×C59—81no—
146C2×C4×C59—81no—
147C2×C4×C59C2×C22⋊C411yescharacteristic
148C2×C4×C59C4×D411yescharacteristic
149C2×C4×C59C4×D411yescharacteristic
150C2×C4×C59#12111yescharacteristic
151C2×C4×C59#12111yescharacteristic
152C2×C4×C59#12311yescharacteristic
153C2×C4×C59C2×D811yescharacteristic
154C2×C4×C59#13511yescharacteristic
155C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
157C8×C59—42no—
158C8×C59—81no—
159C8×C59—81no—
160#9300C5911yesmaximal, characteristic, direct product factor, Sylow
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—81no—
164C22×C59—81no—
165C22×C59—81no—
166C22×C59#38611yescharacteristic
167C22×C59#44711yescharacteristic
168C22×C59#44911yescharacteristic
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—42no—
174C4×C59—44no—
175C4×C59—82no—
176C4×C59—81no—
177C4×C59—81no—
178C4×C59C4×D811yescharacteristic
179C4×C59#44211yescharacteristic
180C4×C59#45911yescharacteristic
181C4×C59#46311yescharacteristic
182#3226C2×C5911yescharacteristic
183#2327C2×C5911yescharacteristic, complemented
184#1963C2×C5911yescharacteristic
185#1546C2×C5911yescharacteristic, complemented
186#1517C2×C5911yescharacteristic
187#1286C2×C5911yescharacteristic, complemented
188#1274C2×C5911yescharacteristic, complemented
189C2×C59—21no—
190C2×C59—21no—
191C2×C59—161no—
192C2×C59#187911yescharacteristic
193C2×C59#190511yescharacteristic
194C2×C59#191211yescharacteristic
195#532C22×C5911yescharacteristic
196C2×C4⋊Q8C22×C5911yescharacteristic
197C2×C4×Q8—21no—
198#500C4×C5912yescomplemented
199#486C4×C5912yescomplemented
200#480—22no—
201#474—22no—
202#431C22×C5911yescharacteristic
203#431C22×C5911yescharacteristic
204#423C22×C5911yescharacteristic
205C2×#104—21no—
206C2×#104—21no—
207#391—21no—
208#387—22no—
209#387—22no—
210#382C22×C5911yescharacteristic
211#376C22×C5911yescharacteristic
212#332—22no—
213#327—22no—
214C59#930011yescharacteristic, direct product factor, Sylow
215C2×#41—21no—
216C22×Q8—21no—
217C2×M16—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8C2×C4×C5911yescharacteristic
221C4⋊Q8C2×C4×C5912yes—
222C4⋊Q8D4×C5912yes—
223#127C2×C4×C5911yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×Q8—42no—
228C4×Q8—42no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C5912yes—
235C2×C42—22no—
236C2×C42D4×C5911yescharacteristic
237C2×C42D4×C5911yescharacteristic
238C2×C42C23×C5911yescharacteristic
239#107—24no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244#104—42no—
245#104—42no—
246#102—24no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C5912yes—
251#95—24no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95D4×C5912yes—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4C2×D4×C5911yescharacteristic
277C22×C4C2×D4×C5911yescharacteristic
278C22×C4C2×D4×C5911yescharacteristic
279M16—41no—
280M16—41no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—44no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4C22⋊C4×C5914yes—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—44no—
299C42D8×C5912yes—
300C42C22×C4×C5911yescharacteristic
301C42C2×D4×C5911yescharacteristic
302C42#41×C5911yescharacteristic
303C42#41×C5911yescharacteristic
304C23—41no—
305C23#120×C5911yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—41no—
311Q8—41no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4C2×C22⋊C4×C5911yescharacteristic
336C2×C4C4×D4×C5911yescharacteristic
337C2×C4C4×D4×C5911yescharacteristic
338C2×C4#121×C5911yescharacteristic
339C2×C4#121×C5911yescharacteristic
340C2×C4#123×C5911yescharacteristic
341C2×C4C2×D8×C5911yescharacteristic
342C2×C4#135×C5911yescharacteristic
343C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
344C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22C59×#38611yescharacteristic
354C22C59×#44711yescharacteristic
355C22C59×#44911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4C4×D8×C5911yescharacteristic
366C4C59×#44211yescharacteristic
367C4C59×#45911yescharacteristic
368C4C59×#46311yescharacteristic
369C2—21no—
370C2—21no—
371C2—161no—
372C2C59×#187911yescharacteristic
373C2C59×#190511yescharacteristic
374C2C59×#191211yescharacteristic
subgroupG/H
center, socleC22×C59#386
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×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×#2327C2semidirect
4. C59×#1546C2semidirect
6. C59×#1286C2semidirect
7. C59×#1274C2semidirect
11. C59×#500C4semidirect
12. C59×#486C4semidirect
160. #9300C59direct (N × H)
183. #2327C2×C59semidirect
185. #1546C2×C59semidirect
187. #1286C2×C59semidirect
188. #1274C2×C59semidirect
198. #500C4×C59semidirect
199. #486C4×C59semidirect
214. C59#9300direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32262
C59×#23272
C59×#19632
C59×#15462
C59×#15172
C59×#12862
C59×#12742
#930059