Finite Group Databasebeta

← C59×#10502 #28422611

Subgroups — C59×#10502 #28422611

Order 15104.

412 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3227C211yesmaximal, characteristic
2C59×#1997C211yesmaximal, characteristic, complemented
3C59×#1987C211yesmaximal, characteristic, complemented
4C59×#1980C211yesmaximal, characteristic
5C59×#1565C211yesmaximal, characteristic, complemented
6C59×#1547C211yesmaximal, characteristic
7C59×#1303C211yesmaximal, characteristic, complemented
8C59×#532C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C59×#498—21no—
11C59×#486—21no—
12C59×#481—22no—
13C59×#476—21no—
14C59×#476—21no—
15C59×#431C2211yescharacteristic
16C59×#423C2211yescharacteristic
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×#104×C59—21no—
19C2×#104×C59—21no—
20C4×M16×C59C2211yescharacteristic
21C4×C4⋊C4×C59C2211yescharacteristic
22C59×#343—21no—
23C59×#343—21no—
24C59×#340—22no—
25C59×#335—21no—
26C59×#334—21no—
27C59×#332—21no—
28C59×#331—21no—
29C2×#41×C59—21no—
30C22×Q8×C59—21no—
31C2×M16×C59—21no—
32C2×M16×C59D411yescharacteristic
33C2×M16×C59D411yescharacteristic
34C22×C8×C59—21no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59D411yescharacteristic
40#127×C59D411yescharacteristic
41#124×C59—21no—
42#121×C59—21no—
43#121×C59—21no—
44C4×D4×C59—21no—
45C4×D4×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59D412yes—
49C2×C42×C59—21no—
50C2×C42×C59C2311yescharacteristic
51#106×C59—22no—
52#106×C59—22no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56C4⋊C8×C59—21no—
57C4⋊C8×C59D411yescharacteristic
58C4⋊C8×C59D411yescharacteristic
59#104×C59—42no—
60#104×C59—42no—
61#102×C59—22no—
62#102×C59—22no—
63C22⋊C8×C59—21no—
64#97×C59—21no—
65C4×C8×C59—21no—
66C4×C8×C59—21no—
67#95×C59—21no—
68#41×C59—41no—
69#41×C59—41no—
70#41×C59—41no—
71#41×C59—41no—
72C2×Q8×C59—21no—
73C2×Q8×C59—41no—
74C2×Q8×C59—41no—
75C2×Q8×C59—82no—
76C2×D4×C59—21no—
77C2×D4×C59—21no—
78C2×D4×C59—21no—
79C2×D4×C59—41no—
80C22×C4×C59—22no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59#4111yescharacteristic
86M16×C59—21no—
87M16×C59—21no—
88M16×C59—21no—
89M16×C59—41no—
90M16×C59—41no—
91M16×C59SD1612yes—
92C2×C8×C59—21no—
93C2×C8×C59—21no—
94C2×C8×C59—21no—
95C2×C8×C59—21no—
96C2×C8×C59—42no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C4⋊C4×C59—22no—
100C4⋊C4×C59—22no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—22no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—41no—
107C22⋊C4×C59—41no—
108C22⋊C4×C59—41no—
109C42×C59—41no—
110C42×C59—41no—
111C42×C59C2×D411yescharacteristic
112C42×C59C2×D411yescharacteristic
113C42×C59#4111yescharacteristic
114C42×C59#4111yescharacteristic
115C23×C59—41no—
116C23×C59#12111yescharacteristic
117Q8×C59—41no—
118Q8×C59—41no—
119Q8×C59—82no—
120Q8×C59—82no—
121D4×C59—41no—
122D4×C59—41no—
123D4×C59—41no—
124D4×C59—41no—
125D4×C59—81no—
126D4×C59—81no—
127D4×C59—81no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—41no—
131C2×C4×C59—42no—
132C2×C4×C59—41no—
133C2×C4×C59—42no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59—81no—
137C2×C4×C59—81no—
138C2×C4×C59—82no—
139C2×C4×C59#12011yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#12311yescharacteristic
143C2×C4×C59#12311yescharacteristic
144C2×C4×C59#12411yescharacteristic
145C2×C4×C59C2×SD1611yescharacteristic
146C2×C4×C59#13511yescharacteristic
147C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C59#13711yescharacteristic
149C8×C59—22no—
150C8×C59—41no—
151C8×C59—41no—
152C8×C59—41no—
153C8×C59—81no—
154C8×C59—81no—
155#10502C5911yesmaximal, characteristic, direct product factor, Sylow
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—81no—
159C22×C59—81no—
160C22×C59—81no—
161C22×C59#39411yescharacteristic
162C22×C59#46011yescharacteristic
163C22×C59#46411yescharacteristic
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—82no—
168C4×C59—82no—
169C4×C59—81no—
170C4×C59#45411yescharacteristic
171C4×C59#45611yescharacteristic
172C4×C59#46111yescharacteristic
173C4×C59#46311yescharacteristic
174C4×C59#46511yescharacteristic
175C4×C59#46811yescharacteristic
176#3227C2×C5911yescharacteristic
177#1997C2×C5911yescharacteristic, complemented
178#1987C2×C5911yescharacteristic, complemented
179#1980C2×C5911yescharacteristic
180#1565C2×C5911yescharacteristic, complemented
181#1547C2×C5911yescharacteristic
182#1303C2×C5911yescharacteristic, complemented
183C2×C59—21no—
184C2×C59—21no—
185C2×C59—161no—
186C2×C59#203811yescharacteristic
187C2×C59#204811yescharacteristic
188C2×C59#205511yescharacteristic
189#532C22×C5911yescharacteristic
190C2×C4⋊Q8C22×C5911yescharacteristic
191#498—21no—
192#486—21no—
193#481—22no—
194#476—21no—
195#476—21no—
196#431C22×C5911yescharacteristic
197#423C22×C5911yescharacteristic
198C2×C4⋊C8C22×C5911yescharacteristic
199C2×#104—21no—
200C2×#104—21no—
201C4×M16C22×C5911yescharacteristic
202C4×C4⋊C4C22×C5911yescharacteristic
203#343—21no—
204#343—21no—
205#340—22no—
206#335—21no—
207#334—21no—
208#332—21no—
209#331—21no—
210C59#1050211yescharacteristic, direct product factor, Sylow
211C2×#41—21no—
212C22×Q8—21no—
213C2×M16—21no—
214C2×M16D4×C5911yescharacteristic
215C2×M16D4×C5911yescharacteristic
216C22×C8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C5911yescharacteristic
222#127D4×C5911yescharacteristic
223#124—21no—
224#121—21no—
225#121—21no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C5912yes—
231C2×C42—21no—
232C2×C42C23×C5911yescharacteristic
233#106—22no—
234#106—22no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8D4×C5911yescharacteristic
240C4⋊C8D4×C5911yescharacteristic
241#104—42no—
242#104—42no—
243#102—22no—
244#102—22no—
245C22⋊C8—21no—
246#97—21no—
247C4×C8—21no—
248C4×C8—21no—
249#95—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—82no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C5911yescharacteristic
266C22×C4C2×D4×C5911yescharacteristic
267C22×C4#41×C5911yescharacteristic
268M16—21no—
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16SD16×C5912yes—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42—41no—
293C42C2×D4×C5911yescharacteristic
294C42C2×D4×C5911yescharacteristic
295C42#41×C5911yescharacteristic
296C42#41×C5911yescharacteristic
297C23—41no—
298C23#121×C5911yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—82no—
302Q8—82no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4#120×C5911yescharacteristic
322C2×C4#121×C5911yescharacteristic
323C2×C4#121×C5911yescharacteristic
324C2×C4#123×C5911yescharacteristic
325C2×C4#123×C5911yescharacteristic
326C2×C4#124×C5911yescharacteristic
327C2×C4C2×SD16×C5911yescharacteristic
328C2×C4#135×C5911yescharacteristic
329C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
330C2×C4#137×C5911yescharacteristic
331C8—22no—
332C8—41no—
333C8—41no—
334C8—41no—
335C8—81no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C59×#39411yescharacteristic
343C22C59×#46011yescharacteristic
344C22C59×#46411yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4—81no—
351C4C59×#45411yescharacteristic
352C4C59×#45611yescharacteristic
353C4C59×#46111yescharacteristic
354C4C59×#46311yescharacteristic
355C4C59×#46511yescharacteristic
356C4C59×#46811yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C59×#203811yescharacteristic
361C2C59×#204811yescharacteristic
362C2C59×#205511yescharacteristic
subgroupG/H
center, socleC22×C59#394
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC59×#532C22
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×#1997C2semidirect
3. C59×#1987C2semidirect
5. C59×#1565C2semidirect
7. C59×#1303C2semidirect
155. #10502C59direct (N × H)
177. #1997C2×C59semidirect
178. #1987C2×C59semidirect
180. #1565C2×C59semidirect
182. #1303C2×C59semidirect
210. C59#10502direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32272
C59×#19972
C59×#19872
C59×#19802
C59×#15652
C59×#15472
C59×#13032
#1050259