Finite Group Databasebeta

← C101×#13129 #38795280

Subgroups — C101×#13129 #38795280

Order 25856.

306 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2150C211yesmaximal, characteristic, complemented
2C101×#2117C211yesmaximal, characteristic
3C101×#2115C211yesmaximal, characteristic
4C101×#2110C211yesmaximal, characteristic, complemented
5C101×#1764C211yesmaximal, characteristic
6C101×#1378C211yesmaximal, characteristic, complemented
7C101×#1376C211yesmaximal, characteristic, complemented
8C2×#131×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12C2×M32×C101C2211yescharacteristic
13C2×#104×C101C411yescharacteristic
14#416×C101C411yescharacteristic
15#405×C101C2211yescharacteristic
16C2×C4×C8×C101C2211yescharacteristic
17C4⋊C16×C101—22no—
18#350×C101—22no—
19#349×C101—22no—
20#347×C101—22no—
21#341×C101C411yescharacteristic
22#339×C101C411yescharacteristic
23C2×#41×C101C2×C411yescharacteristic
24#131×C101—21no—
25#131×C101—21no—
26#131×C101—21no—
27#131×C101—21no—
28C2×M16×C101—21no—
29C2×M16×C101C2×C411yescharacteristic
30C2×M16×C101C2×C411yescharacteristic
31C22×C8×C101—21no—
32C22×C8×C101C2×C411yescharacteristic
33C22×C8×C101C2311yescharacteristic
34#117×C101C2×C411yescharacteristic
35C2×C42×C101C2×C411yescharacteristic
36M32×C101—21no—
37M32×C101—21no—
38M32×C101—21no—
39M32×C101—21no—
40M32×C101—21no—
41M32×C101—21no—
42M32×C101—21no—
43M32×C101D412yes—
44C2×C16×C101—21no—
45C2×C16×C101—21no—
46C2×C16×C101—21no—
47C2×C16×C101D412yes—
48#104×C101—21no—
49#104×C101—21no—
50#103×C101—21no—
51#102×C101—21no—
52#97×C101—21no—
53C4×C8×C101—21no—
54C4×C8×C101—21no—
55C4×C8×C101—21no—
56#41×C101—21no—
57#41×C101—21no—
58#41×C101—21no—
59#41×C101—21no—
60C2×Q8×C101M1611yescharacteristic
61C2×D4×C101—21no—
62C2×D4×C101M1611yescharacteristic
63C22×C4×C101—21no—
64C22×C4×C101—21no—
65C22×C4×C101C22×C411yescharacteristic
66M16×C101—21no—
67M16×C101—21no—
68M16×C101—21no—
69M16×C101—21no—
70M16×C101—41no—
71M16×C101—41no—
72C2×C8×C101—21no—
73C2×C8×C101—21no—
74C2×C8×C101—21no—
75C2×C8×C101—21no—
76C2×C8×C101—21no—
77C2×C8×C101—41no—
78C2×C8×C101—41no—
79C2×C8×C101C2×D411yescharacteristic
80C2×C8×C101C2×D411yescharacteristic
81C2×C8×C101#4111yescharacteristic
82C2×C8×C101#4111yescharacteristic
83C2×C8×C101#4111yescharacteristic
84C2×C8×C101#4111yescharacteristic
85C4⋊C4×C101—21no—
86C22⋊C4×C101—21no—
87C42×C101—21no—
88C42×C101—21no—
89C42×C101M1611yescharacteristic
90C42×C101M1611yescharacteristic
91C16×C101—22no—
92C16×C101—22no—
93C16×C101—41no—
94C16×C101—41no—
95C23×C101—21no—
96C23×C101#13111yescharacteristic
97Q8×C101—21no—
98Q8×C101—21no—
99D4×C101—21no—
100D4×C101—21no—
101D4×C101—41no—
102D4×C101—41no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—42no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—41no—
110C2×C4×C101#11711yescharacteristic
111C2×C4×C101C4×D411yescharacteristic
112C2×C4×C101C4×D411yescharacteristic
113C2×C4×C101C2×M1611yescharacteristic
114C2×C4×C101C2×M1611yescharacteristic
115C2×C4×C101#13111yescharacteristic
116C8×C101—41no—
117C8×C101—41no—
118C8×C101—41no—
119C8×C101#12111yescharacteristic
120C8×C101#12311yescharacteristic
121C8×C101#12411yescharacteristic
122C8×C101#12611yescharacteristic
123C22×C101—41no—
124C22×C101—41no—
125C22×C101—81no—
126C22×C101#43311yescharacteristic
127C22×C101#43511yescharacteristic
128C22×C101#43511yescharacteristic
129C4×C101—22no—
130C4×C101—41no—
131C4×C101—41no—
132C4×C101—81no—
133C4×C101#38811yescharacteristic
134C4×C101#43211yescharacteristic
135C4×C101#43511yescharacteristic
136C4×C101#43611yescharacteristic
137#13129C10111yesmaximal, characteristic, direct product factor, Sylow
138C2×C101—21no—
139C2×C101—21no—
140C2×C101—21no—
141C2×C101—81no—
142C2×C101#192411yescharacteristic
143#2150C2×C10111yescharacteristic, complemented
144#2117C2×C10111yescharacteristic
145#2115C2×C10111yescharacteristic
146#2110C2×C10111yescharacteristic, complemented
147#1764C2×C10111yescharacteristic
148#1378C2×C10111yescharacteristic, complemented
149#1376C2×C10111yescharacteristic, complemented
150C101#1312911yescharacteristic, direct product factor, Sylow
151C2×#131C22×C10111yescharacteristic
152C2×M32C22×C10111yescharacteristic
153C2×M32C22×C10111yescharacteristic
154C2×M32C22×C10111yescharacteristic
155C2×M32C22×C10111yescharacteristic
156C2×#104C4×C10111yescharacteristic
157#416C4×C10111yescharacteristic
158#405C22×C10111yescharacteristic
159C2×C4×C8C22×C10111yescharacteristic
160C4⋊C16—22no—
161#350—22no—
162#349—22no—
163#347—22no—
164#341C4×C10111yescharacteristic
165#339C4×C10111yescharacteristic
166C2×#41C2×C4×C10111yescharacteristic
167#131—21no—
168#131—21no—
169#131—21no—
170#131—21no—
171C2×M16—21no—
172C2×M16C2×C4×C10111yescharacteristic
173C2×M16C2×C4×C10111yescharacteristic
174C22×C8—21no—
175C22×C8C2×C4×C10111yescharacteristic
176C22×C8C23×C10111yescharacteristic
177#117C2×C4×C10111yescharacteristic
178C2×C42C2×C4×C10111yescharacteristic
179M32—21no—
180M32—21no—
181M32—21no—
182M32—21no—
183M32—21no—
184M32—21no—
185M32—21no—
186M32D4×C10112yes—
187C2×C16—21no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16D4×C10112yes—
191#104—21no—
192#104—21no—
193#103—21no—
194#102—21no—
195#97—21no—
196C4×C8—21no—
197C4×C8—21no—
198C4×C8—21no—
199#41—21no—
200#41—21no—
201#41—21no—
202#41—21no—
203C2×Q8M16×C10111yescharacteristic
204C2×D4—21no—
205C2×D4M16×C10111yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4C22×C4×C10111yescharacteristic
209M16—21no—
210M16—21no—
211M16—21no—
212M16—21no—
213M16—41no—
214M16—41no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×D4×C10111yescharacteristic
223C2×C8C2×D4×C10111yescharacteristic
224C2×C8#41×C10111yescharacteristic
225C2×C8#41×C10111yescharacteristic
226C2×C8#41×C10111yescharacteristic
227C2×C8#41×C10111yescharacteristic
228C4⋊C4—21no—
229C22⋊C4—21no—
230C42—21no—
231C42—21no—
232C42M16×C10111yescharacteristic
233C42M16×C10111yescharacteristic
234C16—22no—
235C16—22no—
236C16—41no—
237C16—41no—
238C23—21no—
239C23#131×C10111yescharacteristic
240Q8—21no—
241Q8—21no—
242D4—21no—
243D4—21no—
244D4—41no—
245D4—41no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4#117×C10111yescharacteristic
254C2×C4C4×D4×C10111yescharacteristic
255C2×C4C4×D4×C10111yescharacteristic
256C2×C4C2×M16×C10111yescharacteristic
257C2×C4C2×M16×C10111yescharacteristic
258C2×C4#131×C10111yescharacteristic
259C8—41no—
260C8—41no—
261C8—41no—
262C8#121×C10111yescharacteristic
263C8#123×C10111yescharacteristic
264C8#124×C10111yescharacteristic
265C8#126×C10111yescharacteristic
266C22—41no—
267C22—41no—
268C22—81no—
269C22#433×C10111yescharacteristic
270C22#435×C10111yescharacteristic
271C22#435×C10111yescharacteristic
272C4—22no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4#388×C10111yescharacteristic
277C4#432×C10111yescharacteristic
278C4#435×C10111yescharacteristic
279C4#436×C10111yescharacteristic
280C2—21no—
281C2—21no—
282C2—21no—
283C2—81no—
284C2C101×#192411yescharacteristic
subgroupG/H
centerC8×C101#124
commutatorC22×C4C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC2×C101#1924
prime radicalC2×#41×C101C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C101 ◁ C22×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2150C2semidirect
4. C101×#2110C2semidirect
6. C101×#1378C2semidirect
7. C101×#1376C2semidirect
137. #13129C101direct (N × H)
143. #2150C2×C101semidirect
146. #2110C2×C101semidirect
148. #1378C2×C101semidirect
149. #1376C2×C101semidirect
150. C101#13129direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#21502
C101×#21172
C101×#21152
C101×#21102
C101×#17642
C101×#13782
C101×#13762
#13129101