Finite Group Databasebeta

← C2×#11751644 #14478154

Subgroups — C2×#11751644 #14478154

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91266C211yesmaximal, characteristic
2C2×D5⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
3C2×C3×#3990C211yesmaximal, characteristic, complemented
4C2×#91166C211yesmaximal, characteristic, complemented
5C2×#91165C211yesmaximal, characteristic, complemented
6C2×#91164C211yesmaximal, characteristic, complemented
7C2×D3×#674C211yesmaximal, characteristic, complemented
8#11751644C218yesmaximal, direct product factor
9C2×#65725—31nomaximal, Hall
10C2×#6771C411yescharacteristic
11C2×#6705C411yescharacteristic
12C2×C5×ΓL(1,𝔽25)C411yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C2×#6649C411yescharacteristic
15C2×#6648C2211yescharacteristic
16C2×D3×#168C2211yescharacteristic
17#91266C414yes—
18#91266C2214yes—
19C2×C3⋊#674C2211yescharacteristic
20C2×C3⋊#674C2211yescharacteristic
21D5⋊(C3⋊C16)C2214yescomplemented
22C2×C3×#674C2211yescharacteristic
23C2×C3×#674C2211yescharacteristic
24C3×#3990C2214yescomplemented
25#91166C2214yescomplemented
26#91165C2214yescomplemented
27#91164C2214yescomplemented
28D3×#674C2214yescomplemented
29C2×#4907—51nomaximal, Hall
30C2×#4053—31no—
31C2×#3998—31no—
32C22×#674—31no—
33#65725—38no—
34C2×#3990—31no—
35C2×#3990D311yescharacteristic, complemented
36C2×D5⋊C16—31no—
37C2×D5⋊C16—31no—
38C2×C4×D15C2×C411yescharacteristic
39C2×C4×C5×D3C2×C411yescharacteristic
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×#1204C811yescharacteristic
42C2×#1203C811yescharacteristic
43C2×#1202C811yescharacteristic
44C2×#1201C811yescharacteristic
45#6771C814yes—
46#6771C2×C414yes—
47C2×C3×C5×C8C2×C411yescharacteristic
48C2×C3⋊#168C2×C411yescharacteristic
49#6705C2×C414yes—
50C2×C5×C3⋊C8C2×C411yescharacteristic
51C5×ΓL(1,𝔽25)C2×C414yes—
52C2×C3×#168C2311yescharacteristic
53C3×C8×D5C2×C412yes—
54C3×C8×D5C2312yes—
55#6649C2×C414yes—
56#6648C2×C412yes—
57#6648C2312yes—
58D3×#168C2×C412yes—
59D3×#168C2312yes—
60C3⋊#674C2312yes—
61C3⋊#674C2312yes—
62C3×#674C2312yes—
63C3×#674C2312yes—
64C2×#901—51no—
65C2×C3×M32—51no—
66C22×C3⋊C16—51no—
67#4907—58no—
68C2×#798—51no—
69C2×#798—51no—
70C2×D3×C16—51no—
71C2×D3×C16—51no—
72C2×#709—31no—
73C2×C5×M16—31no—
74C22×#168—31no—
75#4053—34no—
76#4053—34no—
77C2×#676—31no—
78C2×#676—31no—
79C2×C8×D5—31no—
80C2×C8×D5C2×D311yescharacteristic
81#3998—34no—
82C2×#674—31no—
83C2×#674—31no—
84C2×#674—34no—
85C2×#674C2×D311yescharacteristic
86C2×#674C2×D311yescharacteristic
87#3990—34no—
88#3990C2×D314yescomplemented
89D5⋊C16—34no—
90D5⋊C16—34no—
91C2×#504—151noSylow
92C22×D15C2×C811yescharacteristic
93C22×C5×D3C2×C811yescharacteristic
94C22×C3×D5C2×C811yescharacteristic
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×Dic15C2×C811yescharacteristic
97C4×D15C2×C812yes—
98C4×D15C22×C412yes—
99C2×C5×Dic3C2×C811yescharacteristic
100C4×C5×D3C2×C812yes—
101C4×C5×D3C22×C412yes—
102C2×C3×Dic5C2×C811yescharacteristic
103C3×C4×D5C2×C812yes—
104C3×C4×D5C22×C412yes—
105#1204C2×C814yes—
106#1203C2×C814yes—
107#1202C2×C814yes—
108#1201C2×C814yes—
109C3×C5×C8C22×C412yes—
110C3⋊#168C22×C412yes—
111C3×#168C22×C411yescharacteristic
112C3×#168C2411yescharacteristic
113C5×C3⋊C8C22×C412yes—
114C2×#235—51no—
115C22×C3×C8—51no—
116C2×#208—51no—
117#901—54no—
118#901—54no—
119C2×ΓL(1,𝔽25)—51no—
120C2×ΓL(1,𝔽25)AGL(1,𝔽5)11yescharacteristic
121C2×D3×C8—51no—
122C2×D3×C8—51no—
123C3×M32—54no—
124C2×C3×C16—51no—
125C2×C3×C16—51no—
126C2×C3⋊C16—51no—
127C2×C3⋊C16—51no—
128C2×C3⋊C16—54no—
129#798—54no—
130#798—54no—
131D3×C16—54no—
132D3×C16—54no—
133C22×C4×C5—31no—
134C2×C22⋊D5—31no—
135C2×C22⋊D5—31no—
136#709—34no—
137#709—34no—
138C2×D20—31no—
139C2×C4×D5—31no—
140C2×C4×D5C4×D311yescharacteristic
141C2×Dic10—31no—
142C5×M16—34no—
143C2×C5×C8—31no—
144C2×C5×C8C4×D311yescharacteristic
145C2×#168—31no—
146C2×#168—32no—
147C2×#168—32no—
148C2×#168C22×D311yescharacteristic
149#676—34no—
150#676—34no—
151C8×D5—32no—
152C8×D5—32no—
153C8×D5C4×D312yes—
154C8×D5C22×D312yes—
155#674—32no—
156#674—32no—
157#674C22×D312yes—
158#674C22×D312yes—
159C2×#131—151no—
160#504—158no—
161C2×M32—51no—
162C2×M32—151no—
163C2×M32—151no—
164C22×C16—151no—
165C22×C16—151no—
166C22×C16—151no—
167C22×C3×C5C22×C811yescharacteristic
168C2×D15—22no—
169C2×D15C22×C812yes—
170C2×C5×D3—22no—
171C2×C5×D3C22×C812yes—
172C2×C3×D5—22no—
173C2×C3×D5C22×C812yes—
174C3×C4×C5C22×C811yescharacteristic
175C3×C4×C5C23×C411yescharacteristic
176Dic15C22×C812yes—
177C3×Dic5C22×C812yes—
178C5×Dic3C22×C812yes—
179C22×C3×C4—51no—
180C2×#67—51no—
181C2×#67—51no—
182#235—54no—
183#235—54no—
184C2×D12—51no—
185C2×C4×D3—51no—
186C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
187C2×Dic6—51no—
188C2×C3×C8—51no—
189C2×C3×C8—52no—
190C2×C3×C8—52no—
191C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
192#208—54no—
193C2×C3⋊C8—51no—
194C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
195ΓL(1,𝔽25)—54no—
196ΓL(1,𝔽25)C2×AGL(1,𝔽5)14yes—
197D3×C8—52no—
198D3×C8—52no—
199D3×C8—52no—
200D3×C8—52no—
201C3×C16—52no—
202C3×C16—52no—
203C3⋊C16—52no—
204C3⋊C16—52no—
205C23×C5—31no—
206C22×D5—31no—
207C22×D5D3×C811yescharacteristic
208C2×C4×C5—31no—
209C2×C4×C5—32no—
210C2×C4×C5—32no—
211C2×C4×C5C2×C4×D311yescharacteristic
212C22⋊D5—34no—
213C22⋊D5—34no—
214C2×Dic5—31no—
215C2×Dic5D3×C811yescharacteristic
216D20—34no—
217C4×D5—32no—
218C4×D5—32no—
219C4×D5D3×C812yes—
220C4×D5C2×C4×D312yes—
221Dic10—34no—
222C5×C8—32no—
223C5×C8C2×C4×D312yes—
224#168—32no—
225#168C2×C4×D311yescharacteristic
226#168C23×D311yescharacteristic
227C2×#41—151no—
228#131—154no—
229#131—154no—
230C2×M16—31no—
231C2×M16—151no—
232C2×M16—151no—
233C22×C8—51no—
234C22×C8—151no—
235C22×C8—151no—
236M32—54no—
237M32—154no—
238M32—154no—
239C2×C16—51no—
240C2×C16—51no—
241C2×C16—154no—
242C2×C16—154no—
243C2×C16—154no—
244C2×C16—151no—
245C2×C16—151no—
246C2×C3×C5#50412yescomplemented
247C2×C3×C5C23×C811yescharacteristic
248D15—22no—
249C3×D5—22no—
250C5×D3—22no—
251C23×C3—51no—
252C22×D3—51no—
253C22×D3D5⋊C811yescharacteristic
254C2×C3×C4—51no—
255C2×C3×C4—52no—
256C2×C3×C4—52no—
257C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
258#67—54no—
259#67—54no—
260C2×Dic3—51no—
261C2×Dic3D5⋊C811yescharacteristic
262D12—54no—
263C4×D3—52no—
264C4×D3—52no—
265C4×D3D5⋊C812yes—
266C4×D3C22×AGL(1,𝔽5)12yes—
267Dic6—54no—
268C3×C8—51no—
269C3×C8—51no—
270C3×C8C22×AGL(1,𝔽5)12yes—
271C3⋊C8—52no—
272C3⋊C8C22×AGL(1,𝔽5)12yes—
273C22×C5—32no—
274C22×C5—62no—
275C22×C5C2×D3×C811yescharacteristic
276C2×D5—22no—
277C2×D5—32no—
278C2×D5—62no—
279C2×D5C2×D3×C812yes—
280C4×C5—32no—
281C4×C5C2×D3×C811yescharacteristic
282C4×C5C22×C4×D311yescharacteristic
283Dic5—32no—
284Dic5C2×D3×C812yes—
285#41—154no—
286#41—154no—
287C2×Q8—151no—
288C2×D4—151no—
289C2×D4—151no—
290C2×D4—151no—
291C22×C4—31no—
292C22×C4—51no—
293C22×C4—151no—
294M16—34no—
295M16—154no—
296M16—154no—
297C2×C8—31no—
298C2×C8—51no—
299C2×C8—52no—
300C2×C8—52no—
301C2×C8—152no—
302C2×C8—152no—
303C2×C8—152no—
304C2×C8—152no—
305C2×C8—151no—
306C2×C8D3×AGL(1,𝔽5)11yescharacteristic
307C16—52no—
308C16—52no—
309C16—152no—
310C16—152no—
311C3×C5C2×#50411yescharacteristic, complemented, Hall
312C22×C3—52no—
313C22×C3—102no—
314C22×C3C2×D5⋊C811yescharacteristic
315C2×D3—22no—
316C2×D3—52no—
317C2×D3—102no—
318C2×D3C2×D5⋊C812yes—
319C3×C4—52no—
320C3×C4C2×D5⋊C811yescharacteristic
321C3×C4C23×AGL(1,𝔽5)11yescharacteristic
322Dic3—52no—
323Dic3C2×D5⋊C812yes—
324C2×C5—62no—
325C2×C5#490712yescomplemented
326C2×C5C22×D3×C811yescharacteristic
327D5—22no—
328D5—62no—
329C23—31no—
330C23—51no—
331C23—151no—
332Q8—154no—
333D4—154no—
334D4—154no—
335D4—154no—
336C2×C4—31no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—51no—
340C2×C4—52no—
341C2×C4—52no—
342C2×C4—151no—
343C2×C4—152no—
344C2×C4—152no—
345C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
346C8—32no—
347C8—51no—
348C8—51no—
349C8—152no—
350C8C2×D3×AGL(1,𝔽5)12yes—
351C2×C3—102no—
352C2×C3#6572512yescomplemented
353C2×C3C22×D5⋊C811yescharacteristic
354D3—22no—
355D3—102no—
356C5C2×#490711yescharacteristic, complemented, Sylow
357C22—32no—
358C22—52no—
359C22—62no—
360C22—102no—
361C22—152no—
362C22—302no—
363C22D3×D5⋊C811yescharacteristic
364C4—32no—
365C4—52no—
366C4—152no—
367C4D3×D5⋊C811yescharacteristic
368C4C22×D3×AGL(1,𝔽5)11yescharacteristic
369C3C2×#6572511yescharacteristic, complemented, Sylow
370C2—62no—
371C2—102no—
372C2—302no—
373C2#1175164412yesdirect product factor
374C2C2×D3×D5⋊C811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C8
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C22×C8
prime radicalC2×#6771C4
cosocleC3×#168C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#504
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×D5⋊(C3⋊C16)C2semidirect
3. C2×C3×#3990C2semidirect
4. C2×#91166C2semidirect
5. C2×#91165C2semidirect
6. C2×#91164C2semidirect
7. C2×D3×#674C2semidirect
8. #11751644C2direct (N × H)
21. D5⋊(C3⋊C16)C22semidirect
24. C3×#3990C22semidirect
25. #91166C22semidirect
26. #91165C22semidirect
27. #91164C22semidirect
28. D3×#674C22semidirect
35. C2×#3990D3semidirect
88. #3990C2×D3semidirect
246. C2×C3×C5#504semidirect
311. C3×C5C2×#504semidirect
325. C2×C5#4907semidirect
352. C2×C3#65725semidirect
356. C5C2×#4907semidirect
369. C3C2×#65725semidirect
373. C2#11751644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#912662
C2×D5⋊(C3⋊C16)2
C2×C3×#39902
C2×#911662
C2×#911652
C2×#911642
C2×D3×#6742
#117516442
C2×#657253
C2×#49075