Finite Group Databasebeta

← C59×#13391 #28425500

Subgroups — C59×#13391 #28425500

Order 15104.

390 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3067C211yesmaximal, characteristic
2C59×#2161C211yesmaximal, characteristic, complemented
3C59×#2148C211yesmaximal, characteristic, complemented
4C2×C59×#360C211yesmaximal, characteristic, complemented
5C59×#2115C211yesmaximal, characteristic, complemented
6C59×#1815C211yesmaximal, characteristic, complemented
7C59×#1383C211yesmaximal, characteristic, complemented
8C59×#575—21no—
9C2×#135×C59C2211yescharacteristic
10C2×#131×C59C2211yescharacteristic
11C2×M32×C59C2211yescharacteristic
12C2×M32×C59C2211yescharacteristic
13C59×#473—21no—
14C59×#472—21no—
15C59×#471—22no—
16C2×#108×C59C2211yescharacteristic
17C2×#108×C59C2211yescharacteristic
18C2×#106×C59C2211yescharacteristic
19C59×#417—21no—
20C59×#413—21no—
21C59×#368—22no—
22C59×#362—21no—
23C59×#361—21no—
24C59×#360—22no—
25C59×#349—22no—
26C59×#343—21no—
27C2×#41×C59—21no—
28C2×#41×C59D411yescharacteristic
29#137×C59—22no—
30#137×C59—41no—
31AGL(1,ℤ/8)×C59—22no—
32AGL(1,ℤ/8)×C59—41no—
33#135×C59—21no—
34#135×C59—21no—
35#135×C59—21no—
36#135×C59—21no—
37#135×C59—42no—
38C2×Q16×C59D411yescharacteristic
39C2×SD16×C59—21no—
40C2×D8×C59D411yescharacteristic
41#131×C59—21no—
42#131×C59—21no—
43#131×C59—21no—
44#131×C59—21no—
45C2×M16×C59—21no—
46C2×M16×C59—21no—
47C2×M16×C59—21no—
48C2×M16×C59D411yescharacteristic
49C22×C8×C59—21no—
50C22×C8×C59C2311yescharacteristic
51C2×C4⋊C4×C59—21no—
52M32×C59—21no—
53M32×C59—21no—
54M32×C59—21no—
55M32×C59D412yes—
56C2×C16×C59—21no—
57C2×C16×C59—21no—
58#108×C59—21no—
59#108×C59—21no—
60#108×C59—21no—
61#108×C59D412yes—
62#106×C59—21no—
63#106×C59—21no—
64#103×C59—41no—
65#102×C59—41no—
66#101×C59—22no—
67#100×C59—22no—
68#41×C59—21no—
69#41×C59—21no—
70#41×C59—21no—
71#41×C59—21no—
72#41×C59—41no—
73#41×C59—41no—
74#41×C59—41no—
75#41×C59—41no—
76C2×Q8×C59—21no—
77C2×Q8×C59D811yescharacteristic
78C2×D4×C59—21no—
79C2×D4×C59—21no—
80C2×D4×C59—41no—
81C2×D4×C59D811yescharacteristic
82C22×C4×C59—21no—
83C22×C4×C59—41no—
84C22×C4×C59—41no—
85C22×C4×C59C2×D411yescharacteristic
86Q16×C59—21no—
87Q16×C59—21no—
88Q16×C59—42no—
89SD16×C59—42no—
90SD16×C59—42no—
91SD16×C59—41no—
92SD16×C59—41no—
93D8×C59—21no—
94D8×C59—21no—
95D8×C59—42no—
96M16×C59—21no—
97M16×C59—22no—
98M16×C59—21no—
99M16×C59—41no—
100M16×C59—41no—
101M16×C59—41no—
102M16×C59—41no—
103M16×C59—41no—
104C2×C8×C59—21no—
105C2×C8×C59—41no—
106C2×C8×C59—41no—
107C2×C8×C59—41no—
108C2×C8×C59—41no—
109C2×C8×C59C2×D411yescharacteristic
110C2×C8×C59C2×D411yescharacteristic
111C2×C8×C59C2×D411yescharacteristic
112C2×C8×C59#4111yescharacteristic
113C2×C8×C59#4111yescharacteristic
114C2×C8×C59#4111yescharacteristic
115C4⋊C4×C59—41no—
116C4⋊C4×C59—41no—
117C16×C59—22no—
118C16×C59—41no—
119C23×C59—21no—
120C23×C59—41no—
121C23×C59#13511yescharacteristic
122Q8×C59—21no—
123Q8×C59—21no—
124Q8×C59—41no—
125Q8×C59—41no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—41no—
129D4×C59—41no—
130D4×C59—41no—
131D4×C59—41no—
132D4×C59—81no—
133D4×C59—81no—
134C2×C4×C59—21no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—81no—
139C2×C4×C59—81no—
140C2×C4×C59—81no—
141C2×C4×C59—161no—
142C2×C4×C59#12011yescharacteristic
143C2×C4×C59#12111yescharacteristic
144C2×C4×C59#12311yescharacteristic
145C2×C4×C59C2×D811yescharacteristic
146C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C59#13711yescharacteristic
148C8×C59—41no—
149C8×C59—42no—
150C8×C59—81no—
151C8×C59#12111yescharacteristic
152C8×C59#12111yescharacteristic
153C8×C59#12311yescharacteristic
154C8×C59#12411yescharacteristic
155#13391C5911yesmaximal, characteristic, direct product factor, Sylow
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—81no—
159C22×C59—81no—
160C22×C59—161no—
161C22×C59#45211yescharacteristic
162C22×C59#46611yescharacteristic
163C22×C59#48211yescharacteristic
164C4×C59—41no—
165C4×C59—81no—
166C4×C59—161no—
167C4×C59#39411yescharacteristic
168C4×C59#44711yescharacteristic
169C4×C59#46811yescharacteristic
170C4×C59#48011yescharacteristic
171#3067C2×C5911yescharacteristic
172#2161C2×C5911yescharacteristic, complemented
173#2148C2×C5911yescharacteristic, complemented
174C2×#360C2×C5911yescharacteristic, complemented
175#2115C2×C5911yescharacteristic, complemented
176#1815C2×C5911yescharacteristic, complemented
177#1383C2×C5911yescharacteristic, complemented
178C2×C59—21no—
179C2×C59—21no—
180C2×C59—21no—
181C2×C59—81no—
182C2×C59—161no—
183C2×C59#203311yescharacteristic
184#575—21no—
185C2×#135C22×C5911yescharacteristic
186C2×#131C22×C5911yescharacteristic
187C2×M32C22×C5911yescharacteristic
188C2×M32C22×C5911yescharacteristic
189#473—21no—
190#472—21no—
191#471—22no—
192C2×#108C22×C5911yescharacteristic
193C2×#108C22×C5911yescharacteristic
194C2×#106C22×C5911yescharacteristic
195#417—21no—
196#413—21no—
197#368—22no—
198#362—21no—
199#361—21no—
200#360—22no—
201#349—22no—
202#343—21no—
203C59#1339111yescharacteristic, direct product factor, Sylow
204C2×#41—21no—
205C2×#41D4×C5911yescharacteristic
206#137—22no—
207#137—41no—
208AGL(1,ℤ/8)—22no—
209AGL(1,ℤ/8)—41no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—42no—
215C2×Q16D4×C5911yescharacteristic
216C2×SD16—21no—
217C2×D8D4×C5911yescharacteristic
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16D4×C5911yescharacteristic
226C22×C8—21no—
227C22×C8C23×C5911yescharacteristic
228C2×C4⋊C4—21no—
229M32—21no—
230M32—21no—
231M32—21no—
232M32D4×C5912yes—
233C2×C16—21no—
234C2×C16—21no—
235#108—21no—
236#108—21no—
237#108—21no—
238#108D4×C5912yes—
239#106—21no—
240#106—21no—
241#103—41no—
242#102—41no—
243#101—22no—
244#100—22no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8D8×C5911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4D8×C5911yescharacteristic
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C2×D4×C5911yescharacteristic
263Q16—21no—
264Q16—21no—
265Q16—42no—
266SD16—42no—
267SD16—42no—
268SD16—41no—
269SD16—41no—
270D8—21no—
271D8—21no—
272D8—42no—
273M16—21no—
274M16—22no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C5911yescharacteristic
287C2×C8C2×D4×C5911yescharacteristic
288C2×C8C2×D4×C5911yescharacteristic
289C2×C8#41×C5911yescharacteristic
290C2×C8#41×C5911yescharacteristic
291C2×C8#41×C5911yescharacteristic
292C4⋊C4—41no—
293C4⋊C4—41no—
294C16—22no—
295C16—41no—
296C23—21no—
297C23—41no—
298C23#135×C5911yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—41no—
303D4—21no—
304D4—21no—
305D4—41no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—161no—
319C2×C4#120×C5911yescharacteristic
320C2×C4#121×C5911yescharacteristic
321C2×C4#123×C5911yescharacteristic
322C2×C4C2×D8×C5911yescharacteristic
323C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
324C2×C4#137×C5911yescharacteristic
325C8—41no—
326C8—42no—
327C8—81no—
328C8#121×C5911yescharacteristic
329C8#121×C5911yescharacteristic
330C8#123×C5911yescharacteristic
331C8#124×C5911yescharacteristic
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22—161no—
337C22C59×#45211yescharacteristic
338C22C59×#46611yescharacteristic
339C22C59×#48211yescharacteristic
340C4—41no—
341C4—81no—
342C4—161no—
343C4C59×#39411yescharacteristic
344C4C59×#44711yescharacteristic
345C4C59×#46811yescharacteristic
346C4C59×#48011yescharacteristic
347C2—21no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2C59×#203311yescharacteristic
subgroupG/H
center, socleC2×C59#2033
commutator, Frattini, cosocleC22×C8C23×C59
prime radicalC59×#3067C2
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. C59×#2161C2semidirect
3. C59×#2148C2semidirect
4. C2×C59×#360C2semidirect
5. C59×#2115C2semidirect
6. C59×#1815C2semidirect
7. C59×#1383C2semidirect
155. #13391C59direct (N × H)
172. #2161C2×C59semidirect
173. #2148C2×C59semidirect
174. C2×#360C2×C59semidirect
175. #2115C2×C59semidirect
176. #1815C2×C59semidirect
177. #1383C2×C59semidirect
203. C59#13391direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#30672
C59×#21612
C59×#21482
C2×C59×#3602
C59×#21152
C59×#18152
C59×#13832
#1339159