Finite Group Databasebeta

← C59×#13400 #28425509

Subgroups — C59×#13400 #28425509

Order 15104.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3060C211yesmaximal, characteristic
2C2×C59×#365C211yesmaximal, characteristic, complemented
3C59×#2148C211yesmaximal, characteristic, complemented
4C59×#2145C211yesmaximal, characteristic, complemented
5C59×#2117C211yesmaximal, characteristic, complemented
6C59×#1814C211yesmaximal, characteristic, complemented
7C59×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C59C2211yescharacteristic
9C2×#131×C59C2211yescharacteristic
10C59×#537—21no—
11C2×M32×C59C2211yescharacteristic
12C2×M32×C59C2211yescharacteristic
13C59×#470—21no—
14C59×#469—21no—
15C59×#465—22no—
16C2×#108×C59C2211yescharacteristic
17C59×#427C2211yescharacteristic
18C2×#106×C59C2211yescharacteristic
19C59×#421—21no—
20C59×#417—21no—
21C59×#365—22no—
22C59×#362—21no—
23C59×#361—21no—
24C59×#360—22no—
25C59×#350—22no—
26C59×#344—21no—
27C2×#41×C59—21no—
28C2×#41×C59D411yescharacteristic
29#135×C59—21no—
30#135×C59—21no—
31#135×C59—21no—
32#135×C59—21no—
33C2×Q16×C59D411yescharacteristic
34C2×SD16×C59—21no—
35C2×D8×C59D411yescharacteristic
36#131×C59—21no—
37#131×C59—21no—
38#131×C59—21no—
39#131×C59—21no—
40C2×M16×C59—21no—
41C2×M16×C59—21no—
42C2×M16×C59D411yescharacteristic
43C22×C8×C59—21no—
44C22×C8×C59C2311yescharacteristic
45C22⋊Q8×C59—22no—
46C22⋊Q8×C59—41no—
47#121×C59—22no—
48#121×C59—42no—
49#121×C59—41no—
50#117×C59—21no—
51C2×C4⋊C4×C59—21no—
52M32×C59—21no—
53M32×C59—21no—
54M32×C59—21no—
55M32×C59D412yescomplemented
56C2×C16×C59—21no—
57C2×C16×C59—21no—
58#108×C59—21no—
59#108×C59—21no—
60#107×C59—21no—
61#106×C59—21no—
62#106×C59—21no—
63#106×C59D412yes—
64#104×C59—42no—
65#103×C59—22no—
66#102×C59—22no—
67#41×C59—21no—
68#41×C59—21no—
69#41×C59—21no—
70#41×C59—21no—
71#41×C59—41no—
72#41×C59—41no—
73#41×C59—41no—
74#41×C59—41no—
75C2×Q8×C59—21no—
76C2×Q8×C59SD1611yescharacteristic
77C2×D4×C59—21no—
78C2×D4×C59—21no—
79C2×D4×C59—41no—
80C2×D4×C59—42no—
81C2×D4×C59SD1611yescharacteristic
82C22×C4×C59—21no—
83C22×C4×C59—41no—
84C22×C4×C59—41no—
85C22×C4×C59C2×D411yescharacteristic
86Q16×C59—21no—
87Q16×C59—21no—
88SD16×C59—41no—
89SD16×C59—41no—
90D8×C59—21no—
91D8×C59—21no—
92M16×C59—21no—
93M16×C59—21no—
94M16×C59—41no—
95M16×C59—41no—
96M16×C59—41no—
97M16×C59—41no—
98C2×C8×C59—21no—
99C2×C8×C59—41no—
100C2×C8×C59—41no—
101C2×C8×C59—41no—
102C2×C8×C59C2×D411yescharacteristic
103C2×C8×C59C2×D411yescharacteristic
104C2×C8×C59C2×D411yescharacteristic
105C2×C8×C59#4111yescharacteristic
106C2×C8×C59#4111yescharacteristic
107C2×C8×C59#4111yescharacteristic
108C4⋊C4×C59—22no—
109C4⋊C4×C59—42no—
110C4⋊C4×C59—41no—
111C4⋊C4×C59—41no—
112C22⋊C4×C59—42no—
113C22⋊C4×C59—42no—
114C22⋊C4×C59—41no—
115C42×C59—41no—
116C16×C59—22no—
117C16×C59—41no—
118C23×C59—21no—
119C23×C59—41no—
120C23×C59AGL(1,ℤ/8)11yescharacteristic
121Q8×C59—21no—
122Q8×C59—21no—
123Q8×C59—41no—
124Q8×C59—41no—
125D4×C59—21no—
126D4×C59—21no—
127D4×C59—41no—
128D4×C59—41no—
129D4×C59—41no—
130D4×C59—41no—
131D4×C59—81no—
132D4×C59—81no—
133D4×C59—162no—
134C2×C4×C59—21no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—42no—
138C2×C4×C59—41no—
139C2×C4×C59—81no—
140C2×C4×C59—81no—
141C2×C4×C59—81no—
142C2×C4×C59—161no—
143C2×C4×C59#12011yescharacteristic
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12311yescharacteristic
146C2×C4×C59C2×SD1611yescharacteristic
147C2×C4×C59#13511yescharacteristic
148C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
149C8×C59—41no—
150C8×C59—81no—
151C8×C59#12111yescharacteristic
152C8×C59#12111yescharacteristic
153C8×C59#12311yescharacteristic
154C8×C59#12411yescharacteristic
155#13400C5911yesmaximal, characteristic, direct product factor, Sylow
156C22×C59—41no—
157C22×C59—42no—
158C22×C59—41no—
159C22×C59—81no—
160C22×C59—81no—
161C22×C59—81no—
162C22×C59#45011yescharacteristic
163C22×C59#46911yescharacteristic
164C22×C59#48211yescharacteristic
165C4×C59—41no—
166C4×C59—82no—
167C4×C59—81no—
168C4×C59—161no—
169C4×C59#39411yescharacteristic
170C4×C59#44911yescharacteristic
171C4×C59#46511yescharacteristic
172C4×C59#48111yescharacteristic
173#3060C2×C5911yescharacteristic
174C2×#365C2×C5911yescharacteristic, complemented
175#2148C2×C5911yescharacteristic, complemented
176#2145C2×C5911yescharacteristic, complemented
177#2117C2×C5911yescharacteristic, complemented
178#1814C2×C5911yescharacteristic, complemented
179#1386C2×C5911yescharacteristic, complemented
180C2×C59—21no—
181C2×C59—21no—
182C2×C59—21no—
183C2×C59—81no—
184C2×C59—161no—
185C2×C59#203411yescharacteristic
186C2×#135C22×C5911yescharacteristic
187C2×#131C22×C5911yescharacteristic
188#537—21no—
189C2×M32C22×C5911yescharacteristic
190C2×M32C22×C5911yescharacteristic
191#470—21no—
192#469—21no—
193#465—22no—
194C2×#108C22×C5911yescharacteristic
195#427C22×C5911yescharacteristic
196C2×#106C22×C5911yescharacteristic
197#421—21no—
198#417—21no—
199#365—22no—
200#362—21no—
201#361—21no—
202#360—22no—
203#350—22no—
204#344—21no—
205C59#1340011yescharacteristic, direct product factor, Sylow
206C2×#41—21no—
207C2×#41D4×C5911yescharacteristic
208#135—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212C2×Q16D4×C5911yescharacteristic
213C2×SD16—21no—
214C2×D8D4×C5911yescharacteristic
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16D4×C5911yescharacteristic
222C22×C8—21no—
223C22×C8C23×C5911yescharacteristic
224C22⋊Q8—22no—
225C22⋊Q8—41no—
226#121—22no—
227#121—42no—
228#121—41no—
229#117—21no—
230C2×C4⋊C4—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32D4×C5912yescomplemented
235C2×C16—21no—
236C2×C16—21no—
237#108—21no—
238#108—21no—
239#107—21no—
240#106—21no—
241#106—21no—
242#106D4×C5912yes—
243#104—42no—
244#103—22no—
245#102—22no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8SD16×C5911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4SD16×C5911yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C5911yescharacteristic
265Q16—21no—
266Q16—21no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C2×D4×C5911yescharacteristic
282C2×C8C2×D4×C5911yescharacteristic
283C2×C8C2×D4×C5911yescharacteristic
284C2×C8#41×C5911yescharacteristic
285C2×C8#41×C5911yescharacteristic
286C2×C8#41×C5911yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—41no—
295C16—22no—
296C16—41no—
297C23—21no—
298C23—41no—
299C23AGL(1,ℤ/8)×C5911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4#120×C5911yescharacteristic
323C2×C4#121×C5911yescharacteristic
324C2×C4#123×C5911yescharacteristic
325C2×C4C2×SD16×C5911yescharacteristic
326C2×C4#135×C5911yescharacteristic
327C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
328C8—41no—
329C8—81no—
330C8#121×C5911yescharacteristic
331C8#121×C5911yescharacteristic
332C8#123×C5911yescharacteristic
333C8#124×C5911yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C59×#45011yescharacteristic
341C22C59×#46911yescharacteristic
342C22C59×#48211yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4C59×#39411yescharacteristic
348C4C59×#44911yescharacteristic
349C4C59×#46511yescharacteristic
350C4C59×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C59×#203411yescharacteristic
subgroupG/H
center, socleC2×C59#2034
commutator, Frattini, cosocleC22×C8C23×C59
prime radicalC59×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C22×C4×C59 ◁ C2×#131×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#365C2semidirect
3. C59×#2148C2semidirect
4. C59×#2145C2semidirect
5. C59×#2117C2semidirect
6. C59×#1814C2semidirect
7. C59×#1386C2semidirect
55. M32×C59D4semidirect
155. #13400C59direct (N × H)
174. C2×#365C2×C59semidirect
175. #2148C2×C59semidirect
176. #2145C2×C59semidirect
177. #2117C2×C59semidirect
178. #1814C2×C59semidirect
179. #1386C2×C59semidirect
205. C59#13400direct (N × H)
234. M32D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#30602
C2×C59×#3652
C59×#21482
C59×#21452
C59×#21172
C59×#18142
C59×#13862
#1340059