Finite Group Databasebeta

← C5×#10182 #11932902

Subgroups — C5×#10182 #11932902

Order 1280.

508 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3209C211yesmaximal, characteristic, complemented
2C5×#3077C211yesmaximal, characteristic
3C2×C5×#476C211yesmaximal, characteristic
4C5×#1549C211yesmaximal, characteristic, complemented
5C5×#1481C211yesmaximal, characteristic, complemented
6C5×#1460C211yesmaximal, characteristic
7C5×#1301C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#494—21no—
12C5×#487—21no—
13C5×#478—22no—
14C5×#476—22no—
15C5×#476—22no—
16C5×#476—21no—
17C5×#474—21no—
18C5×#462—22no—
19C5×#451—22no—
20C5×#431C2211yescharacteristic
21C5×#431C2211yescharacteristic
22C5×#428—21no—
23C2×C5×#106—21no—
24C5×#423C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#418—21no—
27C2×C5×#102—21no—
28C5×#332—22no—
29C5×Q8⋊C8—22no—
30C5×#323—22no—
31#10182C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8—21no—
33C22×C5×D4D411yescharacteristic
34C23×C4×C5—21no—
35C2×C5×Q16—24no—
36C2×C5×M16—21no—
37C22×C5×C8—21no—
38C5×C4⋊Q8—21no—
39C5×C4⋊Q8—21no—
40C5×C4⋊Q8—21no—
41C5×C4⋊Q8D412yes—
42C5×C4⋊Q8D411yescharacteristic
43C5×C4⋊Q8D411yescharacteristic
44C5×#125—21no—
45C5×C22⋊Q8—21no—
46C5×C22⋊Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×Q8—21no—
49C4×C5×D4—21no—
50C4×C5×D4—21no—
51C4×C5×D4—21no—
52C4×C5×D4—21no—
53C5×#117—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C42×C5C2311yescharacteristic
59C5×#107—22no—
60C5×#106—24no—
61C5×#106—22no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8D412yes—
67C5×C4⋊C8D412yes—
68C5×#103—24no—
69C5×#102—24no—
70C5×#102—22no—
71C5×#102—22no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8D412yes—
74C4×C5×C8—21no—
75C4×C5×C8—21no—
76#3209C2×C511yescharacteristic, complemented
77#3077C2×C511yescharacteristic
78C2×#476C2×C511yescharacteristic
79#1549C2×C511yescharacteristic, complemented
80#1481C2×C511yescharacteristic, complemented
81#1460C2×C511yescharacteristic
82#1301C2×C511yescharacteristic, complemented
83C24×C5—21no—
84C2×C5×Q8—21no—
85C2×C5×Q8—22no—
86C2×C5×Q8—21no—
87C2×C5×Q8—41no—
88C2×C5×Q8—82no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4Q1612yescomplemented
95C22×C4×C5—21no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—82no—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5#4111yescharacteristic
103C5×Q16—84no—
104C5×M16—41no—
105C5×M16—41no—
106C2×C5×C8—22no—
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—21no—
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×C5C2×D411yescharacteristic
129C42×C5C2×D411yescharacteristic
130C42×C5C2×D411yescharacteristic
131C42×C5C2×D411yescharacteristic
132#533C22×C511yescharacteristic
133C2×C4⋊Q8C22×C511yescharacteristic
134C2×C4×D4C22×C511yescharacteristic
135#494—21no—
136#487—21no—
137#478—22no—
138#476—21no—
139#476—22no—
140#476—22no—
141#474—21no—
142#462—22no—
143#451—22no—
144#431C22×C511yescharacteristic
145#431C22×C511yescharacteristic
146#428—21no—
147C2×#106—21no—
148#423C22×C511yescharacteristic
149C2×C4⋊C8C22×C511yescharacteristic
150#418—21no—
151C2×#102—21no—
152#332—22no—
153Q8⋊C8—22no—
154#323—22no—
155C23×C5—22no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—81no—
159C23×C5—81no—
160C23×C5#12111yescharacteristic
161C5×Q8—42no—
162C5×Q8—44no—
163C5×Q8—42no—
164C5×Q8—82no—
165C5×D4—22no—
166C5×D4—22no—
167C5×D4—41no—
168C5×D4—41no—
169C2×C4×C5—22no—
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×C5—82no—
177C2×C4×C5—82no—
178C2×C4×C5—81no—
179C2×C4×C5#12011yescharacteristic
180C2×C4×C5#12011yescharacteristic
181C2×C4×C5#12011yescharacteristic
182C2×C4×C5#12111yescharacteristic
183C2×C4×C5#12111yescharacteristic
184C2×C4×C5#12711yescharacteristic
185C2×C4×C5C2×Q1611yescharacteristic
186C2×C4×C5#13511yescharacteristic
187C2×C4×C5#13711yescharacteristic
188C2×C4×C5#13711yescharacteristic
189C5×C8—42no—
190C5×C8—42no—
191C5×C8—42no—
192C5×C8—81no—
193C22×Q8—21no—
194C22×D4C5×D411yescharacteristic
195C23×C4—21no—
196C2×Q16—24no—
197C2×M16—21no—
198C22×C8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C5×D412yes—
203C4⋊Q8C5×D411yescharacteristic
204C4⋊Q8C5×D411yescharacteristic
205#125—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—21no—
214#117—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C5×D411yescharacteristic
218C2×C22⋊C4—21no—
219C2×C42C23×C511yescharacteristic
220#107—22no—
221#106—24no—
222#106—22no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8C5×D412yes—
228C4⋊C8C5×D412yes—
229#103—24no—
230#102—24no—
231#102—22no—
232#102—22no—
233C22⋊C8—21no—
234C22⋊C8C5×D412yes—
235C4×C8—21no—
236C4×C8—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—42no—
240C22×C5—82no—
241C22×C5—82no—
242C22×C5—81no—
243C22×C5—81no—
244C22×C5#39211yescharacteristic
245C22×C5#46711yescharacteristic
246C22×C5#47011yescharacteristic
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—82no—
251C4×C5—81no—
252C4×C5—81no—
253C4×C5—81no—
254C4×C5#45111yescharacteristic
255C4×C5#45111yescharacteristic
256C4×C5#45211yescharacteristic
257C4×C5#45211yescharacteristic
258C4×C5#47112yes—
259C24—21no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—82no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4C5×Q1612yescomplemented
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—82no—
276C22×C4C2×C5×D411yescharacteristic
277C22×C4C2×C5×D411yescharacteristic
278C22×C4C5×#4111yescharacteristic
279Q16—84no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42C2×C5×D411yescharacteristic
305C42C2×C5×D411yescharacteristic
306C42C2×C5×D411yescharacteristic
307C42C2×C5×D411yescharacteristic
308C2×C5—21no—
309C2×C5—21no—
310C2×C5—82no—
311C2×C5#200111yescharacteristic
312C2×C5#200811yescharacteristic
313C2×C5#201911yescharacteristic
314C23—22no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23C5×#12111yescharacteristic
320Q8—42no—
321Q8—44no—
322Q8—42no—
323Q8—82no—
324D4—22no—
325D4—22no—
326D4—41no—
327D4—41no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4C5×#12011yescharacteristic
339C2×C4C5×#12011yescharacteristic
340C2×C4C5×#12011yescharacteristic
341C2×C4C5×#12111yescharacteristic
342C2×C4C5×#12111yescharacteristic
343C2×C4C5×#12711yescharacteristic
344C2×C4C2×C5×Q1611yescharacteristic
345C2×C4C5×#13511yescharacteristic
346C2×C4C5×#13711yescharacteristic
347C2×C4C5×#13711yescharacteristic
348C8—42no—
349C8—42no—
350C8—42no—
351C8—81no—
352C5#1018211yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22C5×#39211yescharacteristic
361C22C5×#46711yescharacteristic
362C22C5×#47011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—81no—
368C4—82no—
369C4—81no—
370C4C5×#45111yescharacteristic
371C4C5×#45111yescharacteristic
372C4C5×#45211yescharacteristic
373C4C5×#45211yescharacteristic
374C4C5×#47112yes—
375C2—21no—
376C2—21no—
377C2—82no—
378C2C5×#200111yescharacteristic
379C2C5×#200811yescharacteristic
380C2C5×#201911yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
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
1. C5×#3209C2semidirect
4. C5×#1549C2semidirect
5. C5×#1481C2semidirect
7. C5×#1301C2semidirect
31. #10182C5direct (N × H)
76. #3209C2×C5semidirect
79. #1549C2×C5semidirect
80. #1481C2×C5semidirect
82. #1301C2×C5semidirect
94. C2×C5×D4Q16semidirect
270. C2×D4C5×Q16semidirect
352. C5#10182direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32092
C5×#30772
C2×C5×#4762
C5×#15492
C5×#14812
C5×#14602
C5×#13012
#101825