Finite Group Databasebeta

← C5×#10197 #11932917

Subgroups — C5×#10197 #11932917

Order 1280.

524 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3246C211yesmaximal, characteristic
2C5×#3206C211yesmaximal, characteristic
3C5×#3165C211yesmaximal, characteristic, complemented
4C5×#1987C211yesmaximal, characteristic, complemented
5C5×#1980C211yesmaximal, characteristic
6C5×#1503C211yesmaximal, characteristic, complemented
7C5×#1283C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C2×C5×C4⋊Q8C2211yescharacteristic
11C5×#501—22no—
12C5×#500—21no—
13C5×#498—21no—
14C5×#492—21no—
15C5×#487—21no—
16C5×#476—21no—
17C5×#475—21no—
18C5×#465—22no—
19C5×#461—21no—
20C5×#461—22no—
21C5×#460—21no—
22C5×#448—22no—
23C5×#431C2211yescharacteristic
24C5×#428—22no—
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×#104—22no—
27C4×C5×M16C2211yescharacteristic
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#340—22no—
30C5×#328—22no—
31#10197C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×Q8—21no—
34C2×C5×SD16—24no—
35C2×C5×SD16—22no—
36C2×C5×M16D412yes—
37C22×C5×C8D412yes—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8D411yescharacteristic
42C5×C4⋊Q8D412yes—
43C5×C4⋊Q8D411yescharacteristic
44C5×C4⋊Q8D411yescharacteristic
45C5×#127D411yescharacteristic
46C5×#125—21no—
47C5×#124—21no—
48C5×C22⋊Q8—21no—
49C5×C22⋊Q8—21no—
50C5×#121—21no—
51C5×#121—21no—
52C4×C5×Q8—21no—
53C4×C5×Q8—21no—
54C4×C5×D4—21no—
55C4×C5×D4—21no—
56C5×#117—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C42×C5—21no—
61C2×C42×C5C2311yescharacteristic
62C5×#107—24no—
63C5×#106—24no—
64C5×#106—22no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8—21no—
67C5×C4⋊C8—21no—
68C5×#104—44no—
69C5×#103—24no—
70C5×#103—22no—
71C5×#102—22no—
72C5×C22⋊C8D412yes—
73C5×#97—21no—
74C4×C5×C8—21no—
75C4×C5×C8—21no—
76C5×#95—21no—
77#3246C2×C511yescharacteristic
78#3206C2×C511yescharacteristic
79#3165C2×C511yescharacteristic, complemented
80#1987C2×C511yescharacteristic, complemented
81#1980C2×C511yescharacteristic
82#1503C2×C511yescharacteristic, complemented
83#1283C2×C511yescharacteristic, complemented
84C5×#41—42no—
85C5×#41—42no—
86C2×C5×Q8—21no—
87C2×C5×Q8—22no—
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8—41no—
91C2×C5×Q8—82no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—21no—
95C2×C5×D4—41no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C5×SD16—84no—
103C5×SD16—82no—
104C5×M16—22no—
105C5×M16SD1614yescomplemented
106C2×C5×C8—22no—
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—42no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—41no—
127C42×C5—41no—
128C42×C5—42no—
129C42×C5C2×D411yescharacteristic
130C42×C5C2×D411yescharacteristic
131C42×C5C2×D411yescharacteristic
132C42×C5#4111yescharacteristic
133#533C22×C511yescharacteristic
134#532C22×C511yescharacteristic
135C2×C4⋊Q8C22×C511yescharacteristic
136#501—22no—
137#500—21no—
138#498—21no—
139#492—21no—
140#487—21no—
141#476—21no—
142#475—21no—
143#465—22no—
144#461—22no—
145#461—21no—
146#460—21no—
147#448—22no—
148#431C22×C511yescharacteristic
149#428—22no—
150C2×C4⋊C8C22×C511yescharacteristic
151C2×#104—22no—
152C4×M16C22×C511yescharacteristic
153C4×C4⋊C4C22×C511yescharacteristic
154#340—22no—
155#328—22no—
156C23×C5—41no—
157C23×C5#12711yescharacteristic
158C5×Q8—44no—
159C5×Q8—41no—
160C5×Q8—41no—
161C5×Q8—42no—
162C5×Q8—81no—
163C5×Q8—82no—
164C5×D4—42no—
165C5×D4—41no—
166C5×D4—41no—
167C5×D4—42no—
168C5×D4—81no—
169C5×D4—81no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—41no—
173C2×C4×C5—42no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—81no—
179C2×C4×C5—82no—
180C2×C4×C5—81no—
181C2×C4×C5—82no—
182C2×C4×C5#12011yescharacteristic
183C2×C4×C5#12011yescharacteristic
184C2×C4×C5#12011yescharacteristic
185C2×C4×C5#12111yescharacteristic
186C2×C4×C5#12111yescharacteristic
187C2×C4×C5#12111yescharacteristic
188C2×C4×C5C2×SD1612yes—
189C2×C4×C5#13712yes—
190C5×C8—24no—
191C5×C8—42no—
192C5×C8—42no—
193C2×#41—21no—
194C22×Q8—21no—
195C2×SD16—24no—
196C2×SD16—22no—
197C2×M16C5×D412yes—
198C22×C8C5×D412yes—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C5×D412yes—
203C4⋊Q8C5×D411yescharacteristic
204C4⋊Q8C5×D411yescharacteristic
205C4⋊Q8C5×D411yescharacteristic
206#127C5×D411yescharacteristic
207#125—21no—
208#124—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C42—21no—
222C2×C42C23×C511yescharacteristic
223#107—24no—
224#106—24no—
225#106—22no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229#104—44no—
230#103—24no—
231#103—22no—
232#102—22no—
233C22⋊C8C5×D412yes—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237#95—21no—
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5—81no—
243C22×C5#39211yescharacteristic
244C22×C5#49211yescharacteristic
245C22×C5#49711yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—82no—
250C4×C5—81no—
251C4×C5—82no—
252C4×C5—81no—
253C4×C5—81no—
254C4×C5#44812yes—
255C4×C5#45511yescharacteristic
256C4×C5#45611yescharacteristic
257C4×C5#46112yes—
258#41—42no—
259#41—42no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—41no—
265C2×Q8—82no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C2×C5×D411yescharacteristic
274C22×C4C2×C5×D411yescharacteristic
275C22×C4C2×C5×D411yescharacteristic
276SD16—84no—
277SD16—82no—
278M16—22no—
279M16C5×SD1614yescomplemented
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—42no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C42—41no—
302C42—42no—
303C42C2×C5×D411yescharacteristic
304C42C2×C5×D411yescharacteristic
305C42C2×C5×D411yescharacteristic
306C42C5×#4111yescharacteristic
307C2×C5—21no—
308C2×C5—21no—
309C2×C5—161no—
310C2×C5#200711yescharacteristic
311C2×C5#200811yescharacteristic
312C2×C5#201311yescharacteristic
313C23—41no—
314C23C5×#12711yescharacteristic
315Q8—44no—
316Q8—41no—
317Q8—41no—
318Q8—42no—
319Q8—81no—
320Q8—82no—
321D4—42no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4C5×#12011yescharacteristic
340C2×C4C5×#12011yescharacteristic
341C2×C4C5×#12011yescharacteristic
342C2×C4C5×#12111yescharacteristic
343C2×C4C5×#12111yescharacteristic
344C2×C4C5×#12111yescharacteristic
345C2×C4C2×C5×SD1612yes—
346C2×C4C5×#13712yes—
347C8—24no—
348C8—42no—
349C8—42no—
350C5#1019711yescharacteristic, direct product factor, Sylow
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C5×#39211yescharacteristic
357C22C5×#49211yescharacteristic
358C22C5×#49711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4C5×#44812yes—
368C4C5×#45511yescharacteristic
369C4C5×#45611yescharacteristic
370C4C5×#46112yes—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C5×#200711yescharacteristic
375C2C5×#200811yescharacteristic
376C2C5×#201311yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#3165C2semidirect
4. C5×#1987C2semidirect
6. C5×#1503C2semidirect
7. C5×#1283C2semidirect
31. #10197C5direct (N × H)
79. #3165C2×C5semidirect
80. #1987C2×C5semidirect
82. #1503C2×C5semidirect
83. #1283C2×C5semidirect
105. C5×M16SD16semidirect
279. M16C5×SD16semidirect
350. C5#10197direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32462
C5×#32062
C5×#31652
C5×#19872
C5×#19802
C5×#15032
C5×#12832
#101975