Finite Group Databasebeta

← C59×#10551 #28422660

Subgroups — C59×#10551 #28422660

Order 15104.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3141C211yesmaximal, characteristic
2C59×#1950C211yesmaximal, characteristic, complemented
3C59×#1549C211yesmaximal, characteristic, complemented
4C59×#1547C211yesmaximal, characteristic
5C2×C59×#333C211yesmaximal, characteristic, complemented
6C59×#1480C211yesmaximal, characteristic
7C59×#1283C211yesmaximal, characteristic, complemented
8C59×#532C2211yescharacteristic
9C2×C4⋊Q8×C59C2211yescharacteristic
10C59×#489—22no—
11C59×#487—21no—
12C59×#486—21no—
13C59×#431C2211yescharacteristic
14C2×#108×C59—21no—
15C59×#423C2211yescharacteristic
16C2×C4⋊C8×C59C2211yescharacteristic
17C2×C4⋊C8×C59C2211yescharacteristic
18C59×#417—21no—
19C59×#417—21no—
20C4×M16×C59C2211yescharacteristic
21C59×#341—21no—
22C59×#333—22no—
23C59×#332—21no—
24C59×#332—22no—
25C59×#331—21no—
26C59×D4⋊C8—22no—
27C2×#41×C59—21no—
28C22×Q8×C59—21no—
29C2×M16×C59—21no—
30C2×M16×C59D411yescharacteristic
31C2×M16×C59D411yescharacteristic
32C22×C8×C59—21no—
33C22×C8×C59—21no—
34C4⋊Q8×C59—21no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59—21no—
37C4⋊Q8×C59D411yescharacteristic
38C4⋊Q8×C59D412yes—
39#127×C59D411yescharacteristic
40#124×C59—21no—
41#121×C59—21no—
42#121×C59—21no—
43C4×D4×C59—21no—
44C4×D4×C59—21no—
45C2×C4⋊C4×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C42×C59C2311yescharacteristic
48#108×C59—42no—
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59D412yes—
56#103×C59—22no—
57#103×C59—22no—
58#102×C59—22no—
59#102×C59—22no—
60C22⋊C8×C59—21no—
61#97×C59—21no—
62C4×C8×C59—21no—
63C4×C8×C59—21no—
64#41×C59—41no—
65#41×C59—41no—
66#41×C59—41no—
67#41×C59—41no—
68C2×Q8×C59—21no—
69C2×Q8×C59—22no—
70C2×Q8×C59—41no—
71C2×Q8×C59—82no—
72C2×D4×C59—21no—
73C2×D4×C59—21no—
74C2×D4×C59—21no—
75C2×D4×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59#4111yescharacteristic
80C22×C4×C59#4111yescharacteristic
81M16×C59—21no—
82M16×C59—21no—
83M16×C59—21no—
84M16×C59—21no—
85M16×C59—41no—
86M16×C59—41no—
87C2×C8×C59—21no—
88C2×C8×C59—21no—
89C2×C8×C59—22no—
90C2×C8×C59—41no—
91C2×C8×C59—41no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—81no—
96C4⋊C4×C59—22no—
97C4⋊C4×C59—21no—
98C4⋊C4×C59—22no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C22⋊C4×C59—41no—
103C22⋊C4×C59—41no—
104C42×C59C2×D411yescharacteristic
105C42×C59C2×D411yescharacteristic
106C42×C59C2×D411yescharacteristic
107C42×C59#4111yescharacteristic
108C23×C59—41no—
109C23×C59#12411yescharacteristic
110Q8×C59—41no—
111Q8×C59—41no—
112Q8×C59—82no—
113Q8×C59—82no—
114D4×C59—41no—
115D4×C59—41no—
116D4×C59—41no—
117D4×C59—41no—
118D4×C59—81no—
119D4×C59—81no—
120D4×C59—81no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—42no—
126C2×C4×C59—82no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59#12011yescharacteristic
130C2×C4×C59#12111yescharacteristic
131C2×C4×C59#12111yescharacteristic
132C2×C4×C59#12111yescharacteristic
133C2×C4×C59#12311yescharacteristic
134C2×C4×C59#12311yescharacteristic
135C2×C4×C59#13511yescharacteristic
136C2×C4×C59#13511yescharacteristic
137C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C59#13711yescharacteristic
139C8×C59—41no—
140C8×C59—41no—
141C8×C59—42no—
142C8×C59—81no—
143C8×C59—81no—
144C8×C59—81no—
145#10551C5911yesmaximal, characteristic, direct product factor, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—81no—
149C22×C59—81no—
150C22×C59—81no—
151C22×C59#39411yescharacteristic
152C22×C59#48811yescharacteristic
153C22×C59#48911yescharacteristic
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—82no—
158C4×C59—81no—
159C4×C59#44911yescharacteristic
160C4×C59#45211yescharacteristic
161C4×C59#46311yescharacteristic
162C4×C59#46411yescharacteristic
163C4×C59#47111yescharacteristic
164C4×C59#47311yescharacteristic
165#3141C2×C5911yescharacteristic
166#1950C2×C5911yescharacteristic, complemented
167#1549C2×C5911yescharacteristic, complemented
168#1547C2×C5911yescharacteristic
169C2×#333C2×C5911yescharacteristic, complemented
170#1480C2×C5911yescharacteristic
171#1283C2×C5911yescharacteristic, complemented
172C2×C59—21no—
173C2×C59—21no—
174C2×C59—161no—
175C2×C59#204211yescharacteristic
176C2×C59#204811yescharacteristic
177C2×C59#205211yescharacteristic
178#532C22×C5911yescharacteristic
179C2×C4⋊Q8C22×C5911yescharacteristic
180#489—22no—
181#487—21no—
182#486—21no—
183#431C22×C5911yescharacteristic
184C2×#108—21no—
185#423C22×C5911yescharacteristic
186C2×C4⋊C8C22×C5911yescharacteristic
187C2×C4⋊C8C22×C5911yescharacteristic
188#417—21no—
189#417—21no—
190C4×M16C22×C5911yescharacteristic
191#341—21no—
192#333—22no—
193#332—21no—
194#332—22no—
195#331—21no—
196D4⋊C8—22no—
197C59#1055111yescharacteristic, direct product factor, Sylow
198C2×#41—21no—
199C22×Q8—21no—
200C2×M16—21no—
201C2×M16D4×C5911yescharacteristic
202C2×M16D4×C5911yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8D4×C5912yes—
209C4⋊Q8D4×C5911yescharacteristic
210#127D4×C5911yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C42C23×C5911yescharacteristic
219#108—42no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8D4×C5912yes—
227#103—22no—
228#103—22no—
229#102—22no—
230#102—22no—
231C22⋊C8—21no—
232#97—21no—
233C4×C8—21no—
234C4×C8—21no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—82no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C2×D4×C5911yescharacteristic
250C22×C4#41×C5911yescharacteristic
251C22×C4#41×C5911yescharacteristic
252M16—21no—
253M16—21no—
254M16—21no—
255M16—21no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—81no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42C2×D4×C5911yescharacteristic
276C42C2×D4×C5911yescharacteristic
277C42C2×D4×C5911yescharacteristic
278C42#41×C5911yescharacteristic
279C23—41no—
280C23#124×C5911yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—82no—
284Q8—82no—
285D4—41no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—81no—
291D4—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#120×C5911yescharacteristic
301C2×C4#121×C5911yescharacteristic
302C2×C4#121×C5911yescharacteristic
303C2×C4#121×C5911yescharacteristic
304C2×C4#123×C5911yescharacteristic
305C2×C4#123×C5911yescharacteristic
306C2×C4#135×C5911yescharacteristic
307C2×C4#135×C5911yescharacteristic
308C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
309C2×C4#137×C5911yescharacteristic
310C8—41no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C59×#39411yescharacteristic
322C22C59×#48811yescharacteristic
323C22C59×#48911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—82no—
329C4C59×#44911yescharacteristic
330C4C59×#45211yescharacteristic
331C4C59×#46311yescharacteristic
332C4C59×#46411yescharacteristic
333C4C59×#47111yescharacteristic
334C4C59×#47311yescharacteristic
335C2—21no—
336C2—21no—
337C2—161no—
338C2C59×#204211yescharacteristic
339C2C59×#204811yescharacteristic
340C2C59×#205211yescharacteristic
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×#1950C2semidirect
3. C59×#1549C2semidirect
5. C2×C59×#333C2semidirect
7. C59×#1283C2semidirect
145. #10551C59direct (N × H)
166. #1950C2×C59semidirect
167. #1549C2×C59semidirect
169. C2×#333C2×C59semidirect
171. #1283C2×C59semidirect
197. C59#10551direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31412
C59×#19502
C59×#15492
C59×#15472
C2×C59×#3332
C59×#14802
C59×#12832
#1055159