Finite Group Databasebeta

← C2×#11746810 #14478135

Subgroups — C2×#11746810 #14478135

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×#91265C211yesmaximal, characteristic
2C2×C16×D15C211yesmaximal, characteristic, complemented
3C2×C5×D3×C16C211yesmaximal, characteristic, complemented
4C2×C3×D5×C16C211yesmaximal, characteristic, complemented
5C2×#90936C211yesmaximal, characteristic, complemented
6C2×#90935C211yesmaximal, characteristic, complemented
7C2×#90934C211yesmaximal, characteristic, complemented
8#11746810C218yesmaximal, direct product factor
9C2×#65190—31nomaximal, Hall
10C2×#6771C411yescharacteristic
11C2×C8×D15C2211yescharacteristic
12C2×C5×D3×C8C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C2×#6651C411yescharacteristic
15C2×#6650C411yescharacteristic
16C2×#6649C411yescharacteristic
17#91265C414yes—
18#91265C2214yes—
19C2×C3×C5×C16C2211yescharacteristic
20C2×C3⋊#672C2211yescharacteristic
21C16×D15C2214yescomplemented
22C2×C5×C3⋊C16C2211yescharacteristic
23C5×D3×C16C2214yescomplemented
24C2×C3×#672C2211yescharacteristic
25C3×D5×C16C2214yescomplemented
26#90936C2214yescomplemented
27#90935C2214yescomplemented
28#90934C2214yescomplemented
29C2×#4901—51nomaximal, Hall
30C2×#4047—31no—
31C22×C5×C16—31no—
32C2×#3944—31no—
33#65190—38no—
34C2×#3930—31no—
35C2×#3930—31no—
36C2×D5×C16—31no—
37C2×D5×C16D311yescharacteristic, complemented
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×C8C2311yescharacteristic
48C2×C3⋊#168C2×C411yescharacteristic
49C8×D15C2×C412yes—
50C8×D15C2312yes—
51C2×C5×C3⋊C8C2×C411yescharacteristic
52C5×D3×C8C2×C412yes—
53C5×D3×C8C2312yes—
54C2×C3×#168C2×C411yescharacteristic
55C3×C8×D5C2×C412yes—
56C3×C8×D5C2312yes—
57#6651C2×C414yes—
58#6650C2×C414yes—
59#6649C2×C414yes—
60C3×C5×C16C2312yes—
61C3⋊#672C2312yes—
62C3×#672C2312yes—
63C5×C3⋊C16C2312yes—
64C2×#901—51no—
65C22×C3×C16—51no—
66C2×#812—51no—
67#4901—58no—
68C2×#798—51no—
69C2×#798—51no—
70C2×D3×C16—51no—
71C2×D3×C16D511yescharacteristic, complemented
72C2×#709—31no—
73C22×C5×C8—31no—
74C2×#681—31no—
75#4047—34no—
76#4047—34no—
77C2×#676—31no—
78C2×#676—31no—
79C2×C8×D5—31no—
80C2×C8×D5C2×D311yescharacteristic
81C2×C5×C16—31no—
82C2×C5×C16—34no—
83C2×C5×C16C2×D311yescharacteristic
84#3944—34no—
85C2×#672—31no—
86C2×#672C2×D311yescharacteristic
87#3930—34no—
88#3930—34no—
89D5×C16—34no—
90D5×C16C2×D314yescomplemented
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×C411yescharacteristic
110C3×C5×C8C2411yescharacteristic
111C3⋊#168C22×C412yes—
112C3×#168C22×C412yes—
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)—51no—
121C2×D3×C8—51no—
122C2×D3×C8C2×D511yescharacteristic
123C2×C3×C16—51no—
124C2×C3×C16—54no—
125C2×C3×C16C2×D511yescharacteristic
126#812—54no—
127C2×C3⋊C16—51no—
128C2×C3⋊C16C2×D511yescharacteristic
129#798—54no—
130#798—54no—
131D3×C16—54no—
132D3×C16C2×D514yescomplemented
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—
142C2×C5×C8—31no—
143C2×C5×C8—32no—
144C2×C5×C8—32no—
145C2×C5×C8C22×D311yescharacteristic
146#681—34no—
147C2×#168—31no—
148C2×#168C4×D311yescharacteristic
149#676—34no—
150#676—34no—
151C8×D5—32no—
152C8×D5—32no—
153C8×D5C4×D312yes—
154C8×D5C22×D312yes—
155C5×C16—32no—
156C5×C16C22×D312yes—
157#672—32no—
158#672C22×D312yes—
159C2×#131—151no—
160#504—158no—
161C2×M32—151no—
162C2×M32—151no—
163C2×M32—151no—
164C22×C16—31no—
165C22×C16—51no—
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×D3C4×D511yescharacteristic
187C2×Dic6—51no—
188C2×C3×C8—51no—
189C2×C3×C8—52no—
190C2×C3×C8—52no—
191C2×C3×C8C22×D511yescharacteristic
192#208—54no—
193C2×C3⋊C8—51no—
194C2×C3⋊C8C4×D511yescharacteristic
195ΓL(1,𝔽25)—54no—
196ΓL(1,𝔽25)—54no—
197D3×C8—52no—
198D3×C8—52no—
199D3×C8C4×D512yes—
200D3×C8C22×D512yes—
201C3×C16—52no—
202C3×C16C22×D512yes—
203C3⋊C16—52no—
204C3⋊C16C22×D512yes—
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×D311yescharacteristic
224C5×C8C23×D311yescharacteristic
225#168—32no—
226#168C2×C4×D312yes—
227C2×#41—151no—
228#131—154no—
229#131—154no—
230C2×M16—151no—
231C2×M16—151no—
232C2×M16—151no—
233C22×C8—31no—
234C22×C8—51no—
235C22×C8—151no—
236M32—154no—
237M32—154no—
238M32—154no—
239C2×C16—31no—
240C2×C16—34no—
241C2×C16—51no—
242C2×C16—54no—
243C2×C16—151no—
244C2×C16—154no—
245C2×C16D3×D511yescharacteristic
246C2×C3×C5#50412yescomplemented
247C2×C3×C5C23×C811yescharacteristic
248D15—22no—
249C3×D5—22no—
250C5×D3—22no—
251C23×C3—51no—
252C22×D3—51no—
253C22×D3C8×D511yescharacteristic
254C2×C3×C4—51no—
255C2×C3×C4—52no—
256C2×C3×C4—52no—
257C2×C3×C4C2×C4×D511yescharacteristic
258#67—54no—
259#67—54no—
260C2×Dic3—51no—
261C2×Dic3C8×D511yescharacteristic
262D12—54no—
263C4×D3—52no—
264C4×D3—52no—
265C4×D3C8×D512yes—
266C4×D3C2×C4×D512yes—
267Dic6—54no—
268C3×C8—52no—
269C3×C8C2×C4×D511yescharacteristic
270C3×C8C23×D511yescharacteristic
271C3⋊C8—52no—
272C3⋊C8C2×C4×D512yes—
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—154no—
295M16—154no—
296M16—154no—
297C2×C8—31no—
298C2×C8—32no—
299C2×C8—32no—
300C2×C8—51no—
301C2×C8—52no—
302C2×C8—52no—
303C2×C8—151no—
304C2×C8—152no—
305C2×C8—152no—
306C2×C8C2×D3×D511yescharacteristic
307C16—32no—
308C16—52no—
309C16—152no—
310C16C2×D3×D512yes—
311C3×C5C2×#50411yescharacteristic, complemented, Hall
312C22×C3—52no—
313C22×C3—102no—
314C22×C3C2×C8×D511yescharacteristic
315C2×D3—22no—
316C2×D3—52no—
317C2×D3—102no—
318C2×D3C2×C8×D512yes—
319C3×C4—52no—
320C3×C4C2×C8×D511yescharacteristic
321C3×C4C22×C4×D511yescharacteristic
322Dic3—52no—
323Dic3C2×C8×D512yes—
324C2×C5—62no—
325C2×C5#490112yescomplemented
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×C4C4×D3×D511yescharacteristic
346C8—32no—
347C8—52no—
348C8—152no—
349C8C4×D3×D511yescharacteristic
350C8C22×D3×D511yescharacteristic
351C2×C3—102no—
352C2×C3#6519012yescomplemented
353C2×C3C22×C8×D511yescharacteristic
354D3—22no—
355D3—102no—
356C5C2×#490111yescharacteristic, complemented, Sylow
357C22—32no—
358C22—52no—
359C22—62no—
360C22—102no—
361C22—152no—
362C22—302no—
363C22D3×C8×D511yescharacteristic
364C4—32no—
365C4—52no—
366C4—152no—
367C4D3×C8×D511yescharacteristic
368C4C2×C4×D3×D511yescharacteristic
369C3C2×#6519011yescharacteristic, complemented, Sylow
370C2—62no—
371C2—102no—
372C2—302no—
373C2#1174681012yesdirect product factor
374C2C2×D3×C8×D511yescharacteristic
subgroupG/H
center, hypercenterC2×C16D3×D5
commutatorC2×C3×C5C23×C8
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C22×C8
prime radicalC2×#6771C4
cosocleC3×C5×C8C24
hypocenterC3×C5C2×#504
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. C2×C16×D15C2semidirect
3. C2×C5×D3×C16C2semidirect
4. C2×C3×D5×C16C2semidirect
5. C2×#90936C2semidirect
6. C2×#90935C2semidirect
7. C2×#90934C2semidirect
8. #11746810C2direct (N × H)
21. C16×D15C22semidirect
23. C5×D3×C16C22semidirect
25. C3×D5×C16C22semidirect
26. #90936C22semidirect
27. #90935C22semidirect
28. #90934C22semidirect
37. C2×D5×C16D3semidirect
71. C2×D3×C16D5semidirect
90. D5×C16C2×D3semidirect
132. D3×C16C2×D5semidirect
246. C2×C3×C5#504semidirect
311. C3×C5C2×#504semidirect
325. C2×C5#4901semidirect
352. C2×C3#65190semidirect
356. C5C2×#4901semidirect
369. C3C2×#65190semidirect
373. C2#11746810direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#912652
C2×C16×D152
C2×C5×D3×C162
C2×C3×D5×C162
C2×#909362
C2×#909352
C2×#909342
#117468102
C2×#651903
C2×#49015