Finite Group Databasebeta

← C5×#9355 #11932075

Subgroups — C5×#9355 #11932075

Order 1280.

440 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3079C211yesmaximal, characteristic
2C5×#2990C211yesmaximal, characteristic
3C5×#1997C211yesmaximal, characteristic, complemented
4C5×#1546C211yesmaximal, characteristic, complemented
5C5×#1489C211yesmaximal, characteristic
6C5×#1309C211yesmaximal, characteristic, complemented
7C5×#1299C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C4×C5×#41C2211yescharacteristic
10C5×#477—21no—
11C5×#476—21no—
12C5×#475—21no—
13C5×#474—21no—
14C5×#446—21no—
15C5×#435—22no—
16C5×C8×D4—21no—
17C5×#432—21no—
18C5×#431C2211yescharacteristic
19C5×#428C412yes—
20C5×#423C2211yescharacteristic
21C5×#423C2211yescharacteristic
22C5×#423C2211yescharacteristic
23C2×C5×C4⋊C8—21no—
24C5×#417C412yes—
25C4×C5×M16C2211yescharacteristic
26C5×#343—22no—
27C5×#332—21no—
28C5×#332—21no—
29C5×Q8⋊C8—21no—
30C5×D4⋊C8—21no—
31#9355C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41C2×C411yescharacteristic
33C22×C5×Q8—21no—
34C2×C5×M16—21no—
35C2×C5×M16—21no—
36C2×C5×M16C2×C412yes—
37C2×C5×M16D412yes—
38C22×C5×C8—22no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8—21no—
42C5×C4⋊Q8—21no—
43C4×C5×Q8D411yescharacteristic
44C4×C5×Q8D411yescharacteristic
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4D411yescharacteristic
48C4×C5×D4D411yescharacteristic
49C5×#117—21no—
50C5×#117C2×C411yescharacteristic
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4C2×C412yes—
53C2×C42×C5—21no—
54C2×C42×C5C2311yescharacteristic
55C5×#107—22no—
56C5×#106—22no—
57C5×C4⋊C8—22no—
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8D411yescharacteristic
65C5×C4⋊C8D411yescharacteristic
66C5×#103—22no—
67C5×#102—22no—
68C5×C22⋊C8—22no—
69C5×C22⋊C8—21no—
70C5×#97—22no—
71C5×#97—21no—
72C4×C5×C8—21no—
73C4×C5×C8—21no—
74#3079C2×C511yescharacteristic
75#2990C2×C511yescharacteristic
76#1997C2×C511yescharacteristic, complemented
77#1546C2×C511yescharacteristic, complemented
78#1489C2×C511yescharacteristic
79#1309C2×C511yescharacteristic, complemented
80#1299C2×C511yescharacteristic, complemented
81C5×#41—22no—
82C5×#41—41no—
83C2×C5×Q8—41no—
84C2×C5×Q8—41no—
85C2×C5×Q8—81no—
86C2×C5×Q8—81no—
87C2×C5×Q8C22⋊C411yescharacteristic
88C2×C5×D4—21no—
89C2×C5×D4C22⋊C411yescharacteristic
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—22no—
94C22×C4×C5C22×C411yescharacteristic
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5#4111yescharacteristic
97C5×M16—22no—
98C5×M16—41no—
99C5×M16—42no—
100C5×M16—42no—
101C5×M16—81no—
102C2×C5×C8—22no—
103C2×C5×C8—21no—
104C2×C5×C8—22no—
105C2×C5×C8—21no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—82no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4C22⋊C411yescharacteristic
116C5×C4⋊C4C22⋊C411yescharacteristic
117C5×C22⋊C4—21no—
118C5×C22⋊C4—21no—
119C5×C22⋊C4—21no—
120C42×C5—21no—
121C42×C5—21no—
122C42×C5—21no—
123C42×C5C2×D411yescharacteristic
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C42×C5#4111yescharacteristic
127C2×C4⋊Q8C22×C511yescharacteristic
128C4×#41C22×C511yescharacteristic
129#477—21no—
130#476—21no—
131#475—21no—
132#474—21no—
133#446—21no—
134#435—22no—
135C8×D4—21no—
136#432—21no—
137#431C22×C511yescharacteristic
138#428C4×C512yes—
139#423C22×C511yescharacteristic
140#423C22×C511yescharacteristic
141#423C22×C511yescharacteristic
142C2×C4⋊C8—21no—
143#417C4×C512yes—
144C4×M16C22×C511yescharacteristic
145#343—22no—
146#332—21no—
147#332—21no—
148Q8⋊C8—21no—
149D4⋊C8—21no—
150C23×C5—21no—
151C23×C5C4×D411yescharacteristic
152C5×Q8—21no—
153C5×Q8—21no—
154C5×Q8—82no—
155C5×Q8—81no—
156C5×Q8—81no—
157C5×D4—21no—
158C5×D4—42no—
159C5×D4#10112yes—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—42no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—42no—
175C2×C4×C5—82no—
176C2×C4×C5C2×C22⋊C411yescharacteristic
177C2×C4×C5C4×D411yescharacteristic
178C2×C4×C5#12011yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12111yescharacteristic
181C2×C4×C5#12311yescharacteristic
182C5×C8—42no—
183C5×C8—42no—
184C5×C8—41no—
185C5×C8—42no—
186C5×C8—41no—
187C5×C8—81no—
188C2×#41C2×C4×C511yescharacteristic
189C22×Q8—21no—
190C2×M16—21no—
191C2×M16—21no—
192C2×M16C2×C4×C512yes—
193C2×M16C5×D412yes—
194C22×C8—22no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4×Q8C5×D411yescharacteristic
200C4×Q8C5×D411yescharacteristic
201C4×D4—21no—
202C4×D4—21no—
203C4×D4C5×D411yescharacteristic
204C4×D4C5×D411yescharacteristic
205#117—21no—
206#117C2×C4×C511yescharacteristic
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×C4×C512yes—
209C2×C42—21no—
210C2×C42C23×C511yescharacteristic
211#107—22no—
212#106—22no—
213C4⋊C8—22no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8C5×D411yescharacteristic
221C4⋊C8C5×D411yescharacteristic
222#103—22no—
223#102—22no—
224C22⋊C8—22no—
225C22⋊C8—21no—
226#97—22no—
227#97—21no—
228C4×C8—21no—
229C4×C8—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—22no—
233C22×C5—21no—
234C22×C5—41no—
235C22×C5—41no—
236C22×C5#38611yescharacteristic
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5—41no—
243C4×C5—82no—
244C4×C5C2×#10111yescharacteristic
245C4×C5#41311yescharacteristic
246C4×C5#45511yescharacteristic
247C4×C5#45611yescharacteristic
248C4×C5#47111yescharacteristic
249C4×C5#47211yescharacteristic
250#41—22no—
251#41—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—81no—
255C2×Q8—81no—
256C2×Q8C5×C22⋊C411yescharacteristic
257C2×D4—21no—
258C2×D4C5×C22⋊C411yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4C22×C4×C511yescharacteristic
264C22×C4C2×C5×D411yescharacteristic
265C22×C4C5×#4111yescharacteristic
266M16—22no—
267M16—41no—
268M16—42no—
269M16—42no—
270M16—81no—
271C2×C8—22no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—82no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4C5×C22⋊C411yescharacteristic
285C4⋊C4C5×C22⋊C411yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42C2×C5×D411yescharacteristic
293C42C2×C5×D411yescharacteristic
294C42C2×C5×D411yescharacteristic
295C42C5×#4111yescharacteristic
296C2×C5—41no—
297C2×C5—42no—
298C2×C5#188211yescharacteristic
299C2×C5#190111yescharacteristic
300C2×C5#190711yescharacteristic
301C23—21no—
302C23C4×C5×D411yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—82no—
306Q8—81no—
307Q8—81no—
308D4—21no—
309D4—42no—
310D4C5×#10112yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4C2×C5×C22⋊C411yescharacteristic
328C2×C4C4×C5×D411yescharacteristic
329C2×C4C5×#12011yescharacteristic
330C2×C4C5×#12111yescharacteristic
331C2×C4C5×#12111yescharacteristic
332C2×C4C5×#12311yescharacteristic
333C8—42no—
334C8—42no—
335C8—41no—
336C8—42no—
337C8—41no—
338C8—81no—
339C5#935511yescharacteristic, direct product factor, Sylow
340C22—21no—
341C22—21no—
342C22—22no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22C5×#38611yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—82no—
354C4C2×C5×#10111yescharacteristic
355C4C5×#41311yescharacteristic
356C4C5×#45511yescharacteristic
357C4C5×#45611yescharacteristic
358C4C5×#47111yescharacteristic
359C4C5×#47211yescharacteristic
360C2—41no—
361C2—42no—
362C2C5×#188211yescharacteristic
363C2C5×#190111yescharacteristic
364C2C5×#190711yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#41C2×C4
LCSG ▷ C22×C4 ▷ 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×#1997C2semidirect
4. C5×#1546C2semidirect
6. C5×#1309C2semidirect
7. C5×#1299C2semidirect
31. #9355C5direct (N × H)
76. #1997C2×C5semidirect
77. #1546C2×C5semidirect
79. #1309C2×C5semidirect
80. #1299C2×C5semidirect
339. C5#9355direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30792
C5×#29902
C5×#19972
C5×#15462
C5×#14892
C5×#13092
C5×#12992
#93555