Finite Group Databasebeta

← C101×#13050 #38795201

Subgroups — C101×#13050 #38795201

Order 25856.

732 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#455×C101C211yesmaximal, characteristic
2C101×#2379C211yesmaximal, characteristic, complemented
3C2×#354×C101C211yesmaximal, characteristic, complemented
4C101×#1790C212yesmaximal
5C101×#1390C212yesmaximal, complemented
6C2×H(5,𝔽2)×C101C2211yescharacteristic
7C2×#137×C101—21no—
8C2×#124×C101C2211yescharacteristic
9#455×C101—22no—
10#455×C101C414yescomplemented
11C2×#104×C101—21no—
12C2×#100×C101C2211yescharacteristic
13C2×#99×C101—22no—
14C2×#99×C101C2212yes—
15#391×C101—21no—
16#388×C101—22no—
17#386×C101—22no—
18#386×C101C2212yes—
19#385×C101—22no—
20#382×C101—21no—
21#354×C101—22no—
22H(5,𝔽2)×C101—22no—
23H(5,𝔽2)×C101—21no—
24H(5,𝔽2)×C101—42no—
25H(5,𝔽2)×C101C2×C412yes—
26C2×#41×C101—21no—
27C2×#41×C101—41no—
28C22×Q8×C101D411yescharacteristic
29C22×D4×C101—22no—
30C22×D4×C101—41no—
31C22×D4×C101C2311yescharacteristic
32C23×C4×C101D412yes—
33#137×C101—24no—
34#137×C101—42no—
35C2×Q16×C101—41no—
36C2×SD16×C101—41no—
37C2×M16×C101—21no—
38#124×C101—22no—
39#124×C101C2×C412yes—
40#124×C101D412yes—
41C2×C4⋊C4×C101—21no—
42C2×C4⋊C4×C101—21no—
43C2×C4⋊C4×C101—21no—
44C2×C22⋊C4×C101—22no—
45C2×C22⋊C4×C101—22no—
46C2×C22⋊C4×C101—22no—
47C2×C22⋊C4×C101—42no—
48C2×C22⋊C4×C101D412yes—
49C2×C42×C101—21no—
50C2×C42×C101D411yescharacteristic
51#104×C101—24no—
52#100×C101—21no—
53#100×C101C2×C412yes—
54#99×C101—22no—
55#99×C101—22no—
56#99×C101—44no—
57#95×C101—22no—
58#95×C101—22no—
59#95×C101—22no—
60#95×C101—42no—
61C24×C101—22no—
62C24×C101C2×D412yes—
63#41×C101—22no—
64#41×C101—22no—
65#41×C101—42no—
66#41×C101—41no—
67#41×C101—44no—
68#41×C101—42no—
69#41×C101—41no—
70C2×Q8×C101—21no—
71C2×Q8×C101—21no—
72C2×Q8×C101—41no—
73C2×Q8×C101—41no—
74C2×Q8×C101C22⋊C412yescomplemented
75C2×D4×C101—21no—
76C2×D4×C101—24no—
77C2×D4×C101—24no—
78C2×D4×C101—41no—
79C2×D4×C101—41no—
80C2×D4×C101—42no—
81C2×D4×C101—42no—
82C2×D4×C101—42no—
83C2×D4×C101—42no—
84C2×D4×C101—44no—
85C2×D4×C101—41no—
86C2×D4×C101—42no—
87C2×D4×C101C22×C411yescharacteristic
88C2×D4×C101C2×D411yescharacteristic
89C2×D4×C101#4112yes—
90C22×C4×C101—22no—
91C22×C4×C101—21no—
92C22×C4×C101—21no—
93C22×C4×C101—22no—
94C22×C4×C101—22no—
95C22×C4×C101—41no—
96C22×C4×C101—42no—
97C22×C4×C101—42no—
98C22×C4×C101—82no—
99C22×C4×C101C2×D411yescharacteristic
100Q16×C101—44no—
101SD16×C101—44no—
102M16×C101—22no—
103M16×C101—41no—
104C2×C8×C101—41no—
105C4⋊C4×C101—81no—
106C4⋊C4×C101—81no—
107C4⋊C4×C101—81no—
108C22⋊C4×C101—24no—
109C22⋊C4×C101—24no—
110C22⋊C4×C101—42no—
111C22⋊C4×C101—42no—
112C22⋊C4×C101—42no—
113C22⋊C4×C101—82no—
114C22⋊C4×C101—84no—
115C42×C101—21no—
116C42×C101—81no—
117C42×C101C22⋊C412yescomplemented
118C23×C101—22no—
119C23×C101—22no—
120C23×C101—24no—
121C23×C101—42no—
122C23×C101—42no—
123C23×C101—42no—
124C23×C101—41no—
125C23×C101—82no—
126C23×C101—82no—
127C23×C101C4×D412yes—
128C23×C101#12011yescharacteristic
129C23×C101#12112yes—
130Q8×C101—22no—
131Q8×C101—42no—
132Q8×C101—41no—
133Q8×C101—81no—
134D4×C101—22no—
135D4×C101—41no—
136D4×C101—41no—
137D4×C101—42no—
138D4×C101—41no—
139D4×C101—44no—
140D4×C101—44no—
141D4×C101—42no—
142D4×C101—42no—
143C2×C4×C101—21no—
144C2×C4×C101—21no—
145C2×C4×C101—24no—
146C2×C4×C101—22no—
147C2×C4×C101—22no—
148C2×C4×C101—42no—
149C2×C4×C101—42no—
150C2×C4×C101—41no—
151C2×C4×C101—41no—
152C2×C4×C101—42no—
153C2×C4×C101—41no—
154C2×C4×C101—41no—
155C2×C4×C101—41no—
156C2×C4×C101—42no—
157C2×C4×C101—42no—
158C2×C4×C101—42no—
159C2×C4×C101—42no—
160C2×C4×C101—44no—
161C2×C4×C101—42no—
162C2×C4×C101—42no—
163C2×C4×C101—82no—
164C2×C4×C101—82no—
165C2×C4×C101—82no—
166C2×C4×C101—82no—
167C2×C4×C101C2×C22⋊C411yescharacteristic
168C2×C4×C101#12311yescharacteristic
169C8×C101—42no—
170C22×C101—21no—
171C22×C101—21no—
172C22×C101—22no—
173C22×C101—22no—
174C22×C101—42no—
175C22×C101—42no—
176C22×C101—42no—
177C22×C101—42no—
178C22×C101—42no—
179C22×C101—82no—
180C22×C101—84no—
181C22×C101—81no—
182C22×C101—81no—
183C22×C101—162no—
184C22×C101#38611yescharacteristic
185C22×C101B(4,𝔽2)11yescharacteristic
186C22×C101B(4,𝔽2)11yescharacteristic
187C4×C101—21no—
188C4×C101—21no—
189C4×C101—42no—
190C4×C101—42no—
191C4×C101—42no—
192C4×C101—82no—
193C4×C101—82no—
194C4×C101—162no—
195#13050C10111yesmaximal, characteristic, direct product factor, Sylow
196C2×C101—21no—
197C2×C101—21no—
198C2×C101—42no—
199C2×C101—42no—
200C2×C101—82no—
201C2×C101#188911yescharacteristic
202C2×C101#219911yescharacteristic
203C2×C101#220111yescharacteristic
204C2×#455C2×C10111yescharacteristic
205#2379C2×C10111yescharacteristic, complemented
206C2×#354C2×C10111yescharacteristic, complemented
207#1790C2×C10112yes—
208#1390C2×C10112yescomplemented
209C101#1305011yescharacteristic, direct product factor, Sylow
210C2×H(5,𝔽2)C22×C10111yescharacteristic
211C2×#137—21no—
212C2×#124C22×C10111yescharacteristic
213#455—22no—
214#455C4×C10114yescomplemented
215C2×#104—21no—
216C2×#100C22×C10111yescharacteristic
217C2×#99—22no—
218C2×#99C22×C10112yes—
219#391—21no—
220#388—22no—
221#386—22no—
222#386C22×C10112yes—
223#385—22no—
224#382—21no—
225#354—22no—
226H(5,𝔽2)—22no—
227H(5,𝔽2)—21no—
228H(5,𝔽2)—42no—
229H(5,𝔽2)C2×C4×C10112yes—
230C2×#41—21no—
231C2×#41—41no—
232C22×Q8D4×C10111yescharacteristic
233C22×D4—22no—
234C22×D4—41no—
235C22×D4C23×C10111yescharacteristic
236C23×C4D4×C10112yes—
237#137—24no—
238#137—42no—
239C2×Q16—41no—
240C2×SD16—41no—
241C2×M16—21no—
242#124—22no—
243#124C2×C4×C10112yes—
244#124D4×C10112yes—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—42no—
252C2×C22⋊C4D4×C10112yes—
253C2×C42—21no—
254C2×C42D4×C10111yescharacteristic
255#104—24no—
256#100—21no—
257#100C2×C4×C10112yes—
258#99—22no—
259#99—22no—
260#99—44no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—42no—
265C24—22no—
266C24C2×D4×C10112yes—
267#41—22no—
268#41—22no—
269#41—42no—
270#41—41no—
271#41—44no—
272#41—42no—
273#41—41no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8C22⋊C4×C10112yescomplemented
279C2×D4—21no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—44no—
289C2×D4—41no—
290C2×D4—42no—
291C2×D4C22×C4×C10111yescharacteristic
292C2×D4C2×D4×C10111yescharacteristic
293C2×D4#41×C10112yes—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—82no—
303C22×C4C2×D4×C10111yescharacteristic
304Q16—44no—
305SD16—44no—
306M16—22no—
307M16—41no—
308C2×C8—41no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—82no—
318C22⋊C4—84no—
319C42—21no—
320C42—81no—
321C42C22⋊C4×C10112yescomplemented
322C23—22no—
323C23—22no—
324C23—24no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—82no—
330C23—82no—
331C23C4×D4×C10112yes—
332C23#120×C10111yescharacteristic
333C23#121×C10112yes—
334Q8—22no—
335Q8—42no—
336Q8—41no—
337Q8—81no—
338D4—22no—
339D4—41no—
340D4—41no—
341D4—42no—
342D4—41no—
343D4—44no—
344D4—44no—
345D4—42no—
346D4—42no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4C2×C22⋊C4×C10111yescharacteristic
372C2×C4#123×C10111yescharacteristic
373C8—42no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—82no—
384C22—84no—
385C22—81no—
386C22—81no—
387C22—162no—
388C22#386×C10111yescharacteristic
389C22B(4,𝔽2)×C10111yescharacteristic
390C22B(4,𝔽2)×C10111yescharacteristic
391C4—21no—
392C4—21no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4—82no—
398C4—162no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—82no—
404C2C101×#188911yescharacteristic
405C2C101×#219911yescharacteristic
406C2C101×#220111yescharacteristic
subgroupG/H
center, socleC22×C101B(4,𝔽2)
commutatorC2×D4C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC2×H(5,𝔽2)×C101C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C101 ◁ C22×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2379C2semidirect
3. C2×#354×C101C2semidirect
5. C101×#1390C2semidirect
10. #455×C101C4semidirect
74. C2×Q8×C101C22⋊C4semidirect
117. C42×C101C22⋊C4semidirect
195. #13050C101direct (N × H)
205. #2379C2×C101semidirect
206. C2×#354C2×C101semidirect
208. #1390C2×C101semidirect
209. C101#13050direct (N × H)
214. #455C4×C101semidirect
278. C2×Q8C22⋊C4×C101semidirect
321. C42C22⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#455×C1012
C101×#23792
C2×#354×C1012
C101×#17902
C101×#13902
#13050101