Finite Group Databasebeta

← C5×#9307 #11932027

Subgroups — C5×#9307 #11932027

Order 1280.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3077C211yesmaximal, characteristic
2C5×#2975C211yesmaximal, characteristic
3C5×#1804C211yesmaximal, characteristic
4C5×#1518C211yesmaximal, characteristic, complemented
5C5×#1481C211yesmaximal, characteristic, complemented
6C5×#1301C211yesmaximal, characteristic, complemented
7C5×#1286C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C5×#478—22no—
11C5×#476C412yescomplemented
12C5×#474C412yescomplemented
13C5×#436—22no—
14C5×#436—22no—
15C5×#431C2211yescharacteristic
16C5×#431C2211yescharacteristic
17C5×#428—21no—
18C5×#423C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20C5×#418—21no—
21C2×C5×#102—21no—
22C5×#407—22no—
23C5×#382C2211yescharacteristic
24C5×#340—21no—
25C5×#328—22no—
26C5×Q8⋊C8—22no—
27#9307C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×D4D411yescharacteristic
29C23×C4×C5—21no—
30C2×C5×M16—21no—
31C2×C5×M16—24no—
32C22×C5×C8—21no—
33C5×C4⋊Q8C2×C411yescharacteristic
34C5×C4⋊Q8C2×C411yescharacteristic
35C5×#125—21no—
36C5×C22⋊Q8—21no—
37C5×C22⋊Q8—21no—
38C4×C5×Q8—21no—
39C4×C5×Q8—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4C2×C412yes—
43C4×C5×D4D412yes—
44C5×#117—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C22⋊C4—21no—
48C2×C42×C5C2311yescharacteristic
49C5×#107—22no—
50C5×#106—22no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8C2×C412yes—
57C5×#102—22no—
58C5×#102—22no—
59C5×#102—42no—
60C5×C22⋊C8—24no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8D412yes—
63C4×C5×C8—21no—
64C4×C5×C8D412yes—
65C5×#95—21no—
66C5×#95—21no—
67#3077C2×C511yescharacteristic
68#2975C2×C511yescharacteristic
69#1804C2×C511yescharacteristic
70#1518C2×C511yescharacteristic, complemented
71#1481C2×C511yescharacteristic, complemented
72#1301C2×C511yescharacteristic, complemented
73#1286C2×C511yescharacteristic, complemented
74C24×C5—21no—
75C2×C5×Q8—21no—
76C2×C5×Q8—21no—
77C2×C5×D4—21no—
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4C22⋊C412yes—
83C22×C4×C5—21no—
84C22×C4×C5—22no—
85C22×C4×C5—22no—
86C22×C4×C5—41no—
87C22×C4×C5—82no—
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5#4111yescharacteristic
91C5×M16—41no—
92C5×M16—41no—
93C5×M16—84no—
94C2×C5×C8—22no—
95C2×C5×C8—22no—
96C2×C5×C8—22no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—41no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4C22⋊C412yes—
110C5×C22⋊C4—22no—
111C5×C22⋊C4—22no—
112C5×C22⋊C4—41no—
113C42×C5—41no—
114C42×C5C22×C411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C42×C5C2×D411yescharacteristic
117C42×C5#4111yescharacteristic
118#533C22×C511yescharacteristic
119C2×C4×D4C22×C511yescharacteristic
120#478—22no—
121#476C4×C512yescomplemented
122#474C4×C512yescomplemented
123#436—22no—
124#436—22no—
125#431C22×C511yescharacteristic
126#431C22×C511yescharacteristic
127#428—21no—
128#423C22×C511yescharacteristic
129C2×C4⋊C8C22×C511yescharacteristic
130#418—21no—
131C2×#102—21no—
132#407—22no—
133#382C22×C511yescharacteristic
134#340—21no—
135#328—22no—
136Q8⋊C8—22no—
137C23×C5—22no—
138C23×C5—41no—
139C23×C5—41no—
140C23×C5—81no—
141C23×C5—81no—
142C23×C5#12111yescharacteristic
143C5×Q8—42no—
144C5×Q8—81no—
145C5×D4—22no—
146C5×D4—22no—
147C5×D4—41no—
148C5×D4—41no—
149C2×C4×C5—22no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—44no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—82no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5—81no—
160C2×C4×C5C2×C22⋊C411yescharacteristic
161C2×C4×C5C4×D411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5#12011yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12311yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5#13711yescharacteristic
168C2×C4×C5#13711yescharacteristic
169C2×C4×C5#13711yescharacteristic
170C5×C8—42no—
171C5×C8—42no—
172C5×C8—42no—
173C5×C8—81no—
174C22×D4C5×D411yescharacteristic
175C23×C4—21no—
176C2×M16—21no—
177C2×M16—24no—
178C22×C8—21no—
179C4⋊Q8C2×C4×C511yescharacteristic
180C4⋊Q8C2×C4×C511yescharacteristic
181#125—21no—
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184C4×Q8—21no—
185C4×Q8—21no—
186C4×D4—21no—
187C4×D4—21no—
188C4×D4C2×C4×C512yes—
189C4×D4C5×D412yes—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C5×D411yescharacteristic
193C2×C22⋊C4—21no—
194C2×C42C23×C511yescharacteristic
195#107—22no—
196#106—22no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8C2×C4×C512yes—
203#102—22no—
204#102—22no—
205#102—42no—
206C22⋊C8—24no—
207C22⋊C8—21no—
208C22⋊C8C5×D412yes—
209C4×C8—21no—
210C4×C8C5×D412yes—
211#95—21no—
212#95—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—82no—
219C22×C5—82no—
220C22×C5#38611yescharacteristic
221C22×C5#46811yescharacteristic
222C22×C5#47011yescharacteristic
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5—81no—
229C4×C5—81no—
230C4×C5—161no—
231C4×C5#41711yescharacteristic
232C4×C5#41911yescharacteristic
233C4×C5#46811yescharacteristic
234C4×C5#47011yescharacteristic
235C24—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C5×C22⋊C412yes—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—82no—
249C22×C4C2×C5×D411yescharacteristic
250C22×C4C2×C5×D411yescharacteristic
251C22×C4C5×#4111yescharacteristic
252M16—41no—
253M16—41no—
254M16—84no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4C5×C22⋊C412yes—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—41no—
274C42—41no—
275C42C22×C4×C511yescharacteristic
276C42C2×C5×D411yescharacteristic
277C42C2×C5×D411yescharacteristic
278C42C5×#4111yescharacteristic
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—82no—
282C2×C5#188111yescharacteristic
283C2×C5#189411yescharacteristic
284C2×C5#190411yescharacteristic
285C23—22no—
286C23—41no—
287C23—41no—
288C23—81no—
289C23—81no—
290C23C5×#12111yescharacteristic
291Q8—42no—
292Q8—81no—
293D4—22no—
294D4—22no—
295D4—41no—
296D4—41no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—82no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4C2×C5×C22⋊C411yescharacteristic
309C2×C4C4×C5×D411yescharacteristic
310C2×C4C4×C5×D411yescharacteristic
311C2×C4C5×#12011yescharacteristic
312C2×C4C5×#12111yescharacteristic
313C2×C4C5×#12311yescharacteristic
314C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
315C2×C4C5×#13711yescharacteristic
316C2×C4C5×#13711yescharacteristic
317C2×C4C5×#13711yescharacteristic
318C8—42no—
319C8—42no—
320C8—42no—
321C8—81no—
322C5#930711yescharacteristic, direct product factor, Sylow
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22C5×#38611yescharacteristic
331C22C5×#46811yescharacteristic
332C22C5×#47011yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4C5×#41711yescharacteristic
342C4C5×#41911yescharacteristic
343C4C5×#46811yescharacteristic
344C4C5×#47011yescharacteristic
345C2—21no—
346C2—21no—
347C2—82no—
348C2C5×#188111yescharacteristic
349C2C5×#189411yescharacteristic
350C2C5×#190411yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1518C2semidirect
5. C5×#1481C2semidirect
6. C5×#1301C2semidirect
7. C5×#1286C2semidirect
11. C5×#476C4semidirect
12. C5×#474C4semidirect
27. #9307C5direct (N × H)
70. #1518C2×C5semidirect
71. #1481C2×C5semidirect
72. #1301C2×C5semidirect
73. #1286C2×C5semidirect
121. #476C4×C5semidirect
122. #474C4×C5semidirect
322. C5#9307direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30772
C5×#29752
C5×#18042
C5×#15182
C5×#14812
C5×#13012
C5×#12862
#93075