Finite Group Databasebeta

← C59×#10151 #28422260

Subgroups — C59×#10151 #28422260

Order 15104.

544 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3229C211yesmaximal, characteristic, complemented
2C59×#3138C211yesmaximal, characteristic
3C2×C59×#486C211yesmaximal, characteristic
4C59×#1966C211yesmaximal, characteristic, complemented
5C59×#1545C211yesmaximal, characteristic
6C59×#1493C211yesmaximal, characteristic, complemented
7C59×#1278C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C2×#127×C59C2211yescharacteristic
11C59×#498—21no—
12C59×#490—22no—
13C59×#487—21no—
14C59×#486—21no—
15C59×#486—21no—
16C59×#486—22no—
17C59×#486—22no—
18C59×#483—22no—
19C59×#475—22no—
20C59×#431C2211yescharacteristic
21C59×#423C2211yescharacteristic
22C59×#418—22no—
23C2×#102×C59—22no—
24C2×#101×C59—22no—
25C4×M16×C59C2211yescharacteristic
26C2×C4×C8×C59C2211yescharacteristic
27C59×#331—22no—
28C59×Q8⋊C8—22no—
29C22×Q8×C59—21no—
30C22×D4×C59—21no—
31C22×D4×C59—21no—
32C22×D4×C59—21no—
33C2×M16×C59—21no—
34C2×M16×C59D412yes—
35C22×C8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59—21no—
38C4⋊Q8×C59—21no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59D411yescharacteristic
41C4⋊Q8×C59D411yescharacteristic
42#127×C59—21no—
43#127×C59—21no—
44#127×C59—21no—
45#127×C59D412yes—
46#125×C59—21no—
47C22⋊Q8×C59—21no—
48C22⋊Q8×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51#117×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59D412yes—
54C2×C42×C59C2311yescharacteristic
55#106×C59—24no—
56C4⋊C8×C59—21no—
57C4⋊C8×C59—21no—
58C4⋊C8×C59D412yes—
59#103×C59—24no—
60#102×C59—28no—
61#102×C59—24no—
62#102×C59—24no—
63#101×C59—44no—
64C22⋊C8×C59—21no—
65#97×C59—21no—
66C4×C8×C59—21no—
67C4×C8×C59—21no—
68C4×C8×C59—21no—
69C4×C8×C59D412yes—
70C24×C59—41no—
71C2×Q8×C59—21no—
72C2×Q8×C59—21no—
73C2×Q8×C59—41no—
74C2×Q8×C59—41no—
75C2×Q8×C59—42no—
76C2×Q8×C59—42no—
77C2×D4×C59—22no—
78C2×D4×C59—22no—
79C2×D4×C59—22no—
80C2×D4×C59—44no—
81C2×D4×C59—41no—
82C2×D4×C59—41no—
83C2×D4×C59—41no—
84C2×D4×C59—42no—
85C2×D4×C59—42no—
86C2×D4×C59—82no—
87C22×C4×C59—22no—
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59#4111yescharacteristic
91M16×C59—22no—
92M16×C59—22no—
93M16×C59—42no—
94C2×C8×C59—22no—
95C2×C8×C59—22no—
96C2×C8×C59—22no—
97C2×C8×C59—42no—
98C2×C8×C59—41no—
99C4⋊C4×C59—22no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—22no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—41no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—41no—
109C22⋊C4×C59—41no—
110C42×C59—41no—
111C42×C59C2×D411yescharacteristic
112C42×C59C2×D411yescharacteristic
113C42×C59C2×D411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C23×C59—42no—
116C23×C59—82no—
117C23×C59—82no—
118C23×C59—82no—
119C23×C59#12111yescharacteristic
120Q8×C59—42no—
121Q8×C59—42no—
122Q8×C59—82no—
123Q8×C59—81no—
124Q8×C59—81no—
125D4×C59—44no—
126D4×C59—44no—
127D4×C59—82no—
128D4×C59—82no—
129D4×C59—82no—
130D4×C59—81no—
131D4×C59—81no—
132C2×C4×C59—22no—
133C2×C4×C59—22no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—42no—
137C2×C4×C59—44no—
138C2×C4×C59#12011yescharacteristic
139C2×C4×C59#12011yescharacteristic
140C2×C4×C59#12011yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#12111yescharacteristic
143C2×C4×C59#12711yescharacteristic
144C2×C4×C59#13512yes—
145C2×C4×C59AGL(1,ℤ/8)12yes—
146C8×C59—42no—
147C8×C59—42no—
148C8×C59—42no—
149C8×C59—81no—
150#10151C5911yesmaximal, characteristic, direct product factor, Sylow
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—82no—
154C22×C59—82no—
155C22×C59—82no—
156C22×C59—164no—
157C22×C59#39211yescharacteristic
158C22×C59#46312yes—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—81no—
162C4×C59—82no—
163C4×C59—81no—
164C4×C59#44912yes—
165C4×C59#45412yes—
166C4×C59#47112yes—
167C4×C59#49511yescharacteristic
168C4×C59#49611yescharacteristic
169#3229C2×C5911yescharacteristic, complemented
170#3138C2×C5911yescharacteristic
171C2×#486C2×C5911yescharacteristic
172#1966C2×C5911yescharacteristic, complemented
173#1545C2×C5911yescharacteristic
174#1493C2×C5911yescharacteristic, complemented
175#1278C2×C5911yescharacteristic, complemented
176C2×C59—22no—
177C2×C59—162no—
178C2×C59#200311yescharacteristic
179C2×C59#201211yescharacteristic
180C2×C59#201911yescharacteristic
181#533C22×C5911yescharacteristic
182C2×C4⋊Q8C22×C5911yescharacteristic
183C2×#127C22×C5911yescharacteristic
184#498—21no—
185#490—22no—
186#487—21no—
187#486—21no—
188#486—21no—
189#486—22no—
190#486—22no—
191#483—22no—
192#475—22no—
193#431C22×C5911yescharacteristic
194#423C22×C5911yescharacteristic
195#418—22no—
196C2×#102—22no—
197C2×#101—22no—
198C4×M16C22×C5911yescharacteristic
199C2×C4×C8C22×C5911yescharacteristic
200#331—22no—
201Q8⋊C8—22no—
202C59#1015111yescharacteristic, direct product factor, Sylow
203C22×Q8—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C2×M16—21no—
208C2×M16D4×C5912yes—
209C22×C8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C5911yescharacteristic
215C4⋊Q8D4×C5911yescharacteristic
216#127—21no—
217#127—21no—
218#127—21no—
219#127D4×C5912yes—
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225#117—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C5912yes—
228C2×C42C23×C5911yescharacteristic
229#106—24no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8D4×C5912yes—
233#103—24no—
234#102—28no—
235#102—24no—
236#102—24no—
237#101—44no—
238C22⋊C8—21no—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8D4×C5912yes—
244C24—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—82no—
261C22×C4—22no—
262C22×C4C2×D4×C5911yescharacteristic
263C22×C4C2×D4×C5911yescharacteristic
264C22×C4#41×C5911yescharacteristic
265M16—22no—
266M16—22no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—41no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42C2×D4×C5911yescharacteristic
286C42C2×D4×C5911yescharacteristic
287C42C2×D4×C5911yescharacteristic
288C42C2×D4×C5911yescharacteristic
289C23—42no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23#121×C5911yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—82no—
297Q8—81no—
298Q8—81no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—82no—
303D4—82no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4#120×C5911yescharacteristic
313C2×C4#120×C5911yescharacteristic
314C2×C4#120×C5911yescharacteristic
315C2×C4#121×C5911yescharacteristic
316C2×C4#121×C5911yescharacteristic
317C2×C4#127×C5911yescharacteristic
318C2×C4#135×C5912yes—
319C2×C4AGL(1,ℤ/8)×C5912yes—
320C8—42no—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22C59×#39211yescharacteristic
331C22C59×#46312yes—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—82no—
336C4—81no—
337C4C59×#44912yes—
338C4C59×#45412yes—
339C4C59×#47112yes—
340C4C59×#49511yescharacteristic
341C4C59×#49611yescharacteristic
342C2—22no—
343C2—162no—
344C2C59×#200311yescharacteristic
345C2C59×#201211yescharacteristic
346C2C59×#201911yescharacteristic
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
1. C59×#3229C2semidirect
4. C59×#1966C2semidirect
6. C59×#1493C2semidirect
7. C59×#1278C2semidirect
150. #10151C59direct (N × H)
169. #3229C2×C59semidirect
172. #1966C2×C59semidirect
174. #1493C2×C59semidirect
175. #1278C2×C59semidirect
202. C59#10151direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32292
C59×#31382
C2×C59×#4862
C59×#19662
C59×#15452
C59×#14932
C59×#12782
#1015159