Finite Group Databasebeta

← #14304793

Subgroups — #14304793

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C3⋊#168C211yesmaximal, characteristic, complemented
2C2×C5×#805C211yesmaximal, characteristic
3#11748433C211yesmaximal, characteristic, complemented
4#11748382C211yesmaximal, characteristic
5#11748347C211yesmaximal, characteristic
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745982C211yesmaximal, characteristic, complemented
8#10601164—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C4×C3⋊#168—22no—
17C5×#805—22no—
18#90982—22no—
19#90972C412yescomplemented
20#90966C412yescomplemented
21(C2×D3)⋊#168—22no—
22#68745—51nomaximal, Hall
23C2×C5×#104—31no—
24#65523—31no—
25#65522—31no—
26#65408—31no—
27C2×C4×#168—31no—
28#64778—31no—
29#64743D311yescharacteristic, complemented
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C5×#67—21no—
33C5×#235—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6C2×C411yescharacteristic
40C3×C42×C5—21no—
41C3×C42×C5D412yes—
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C2×C3⋊#168C2×C412yes—
47C2×C3⋊#168D412yes—
48C5×#208—21no—
49C5×#208—21no—
50C2×C5×C3⋊C8—21no—
51C3×C22⋊Dic5—21no—
52C3×C4⋊Dic5C2×C412yes—
53C3×C4×Dic5—21no—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57#5129—51no—
58#5002—51no—
59#4999—51no—
60C2×#805D511yescharacteristic
61C2×C4×C3⋊C8—51no—
62C3×#339—51no—
63#4558—51no—
64C2×C5×#41—31no—
65C2×C5×M16—31no—
66C2×C42×C5C2×D311yescharacteristic
67#4072C2×D311yescharacteristic
68C2×#681C2×D311yescharacteristic
69C22×#168—31no—
70C22×#168—31no—
71C5×#104—62no—
72#3967—32no—
73#3964—32no—
74C22⋊#168—62no—
75#3946—62no—
76C4×#168—62no—
77#1937—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C5×D3—21no—
80C2×C3×C4×C5—24no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C5×#67—41no—
89C5×#67—41no—
90C2×C5×Dic3—21no—
91C5×D12—21no—
92C5×D12—21no—
93C4×C5×D3—41no—
94C4×C5×D3—41no—
95C5×Dic6—21no—
96C5×Dic6—21no—
97C2×C3×Dic5—22no—
98C3⋊#168—22no—
99C3⋊#168—22no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C2×#235C2×D511yescharacteristic
103C2×C3×M16—51no—
104C3×#117—51no—
105C2×C3×C42C2×D511yescharacteristic
106C2×#208C2×D511yescharacteristic
107C22×C3⋊C8—51no—
108C22×C3⋊C8—51no—
109(C2×D3)⋊C8—102no—
110#810—52no—
111#809—52no—
112#805—22no—
113C4⋊(C3⋊C8)—102no—
114C4×C3⋊C8—102no—
115C5×#41—61no—
116C5×#41—61no—
117C5×#41—61no—
118C5×#41—61no—
119C2×C5×Q8—31no—
120C2×C5×D4—31no—
121C2×C5×D4—61no—
122C22×C4×C5—21no—
123C22×C4×C5—61no—
124C22×C4×C5C22×D311yescharacteristic
125C5×M16—61no—
126C5×M16—61no—
127C2×C5×C8—61no—
128C42×C5—21no—
129C42×C5D1212yes—
130C22⋊Dic5—21no—
131C4⋊Dic5C4×D312yes—
132C4×Dic5—21no—
133#681—21no—
134#681—21no—
135C2×#168—21no—
136C2×#168—32no—
137C2×#168—32no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168—61no—
142#424—151no—
143C2×#104—31no—
144#416—151no—
145#408—151no—
146C2×C4×C8—151no—
147#341—151no—
148#339—51no—
149C22×C3×C5—22no—
150C22×C3×C5C4×D411yescharacteristic
151C22×C3×C5#12311yescharacteristic
152C22×C3×C5#12611yescharacteristic
153C2×C5×D3—41no—
154C2×C5×D3—42no—
155C3×C4×C5—24no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
160C3×Dic5—42no—
161C5×Dic3—41no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D511yescharacteristic
164C2×#67—21no—
165#235—21no—
166#235—21no—
167#235—21no—
168#235—21no—
169C2×D12C4×D511yescharacteristic
170C2×C4×D3—21no—
171C2×Dic6C4×D511yescharacteristic
172C3×M16—101no—
173C3×M16—101no—
174C2×C3×C8—101no—
175C3×C4⋊C4—52no—
176C3×C22⋊C4—101no—
177C3×C42—21no—
178C3×C42—101no—
179C3×C42C22⋊D512yes—
180#208—21no—
181#208—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—52no—
184C2×C3⋊C8—52no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—61no—
190C23×C5#23711yescharacteristic
191C5×Q8—61no—
192C5×Q8—61no—
193C5×D4—61no—
194C5×D4—61no—
195C5×D4—121no—
196C5×D4—121no—
197C2×C4×C5—24no—
198C2×C4×C5—22no—
199C2×C4×C5—61no—
200C2×C4×C5—121no—
201C2×C4×C5—121no—
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5#23511yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5#23711yescharacteristic
207C2×C4×C5#23911yescharacteristic
208C2×Dic5—22no—
209C5×C8—121no—
210#168—41no—
211#168—62no—
212#168—62no—
213C2×#41—31no—
214C2×M16—31no—
215C2×M16—51no—
216C22×C8—151no—
217C22×C8—151no—
218#117—51no—
219C2×C42D3×D511yescharacteristic
220C4⋊C8—302no—
221#104—62no—
222#103—152no—
223#102—152no—
224C22⋊C8—302no—
225C4×C8—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44312yes—
230C5×D3—81no—
231C23×C3#71111yescharacteristic
232C22×D3—21no—
233C2×C3×C4—24no—
234C2×C3×C4—22no—
235C2×C3×C4—102no—
236C2×C3×C4C2×C4×D511yescharacteristic
237C2×C3×C4#70911yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4#71111yescharacteristic
240C2×C3×C4#71111yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242#67—41no—
243#67—41no—
244C2×Dic3—21no—
245D12—21no—
246D12—21no—
247C4×D3—41no—
248C4×D3—41no—
249Dic6—21no—
250Dic6—21no—
251C3×C8—201no—
252C3⋊C8—41no—
253C3⋊C8—102no—
254C3⋊C8—102no—
255C22×C5—22no—
256C22×C5—121no—
257C22×C5—122no—
258C22×C5#67⋊C411yescharacteristic
259C22×C5#88611yescharacteristic
260C22×C5#89811yescharacteristic
261C4×C5—24no—
262C4×C5—121no—
263C4×C5C4×D1211yescharacteristic
264C4×C5#88511yescharacteristic
265C4×C5#89211yescharacteristic
266C4×C5#89511yescharacteristic
267Dic5—42no—
268#41—61no—
269#41—61no—
270#41—61no—
271#41—61no—
272C2×Q8—31no—
273C2×D4—31no—
274C2×D4—61no—
275C22×C4—21no—
276C22×C4—61no—
277C22×C4C2×D3×D511yescharacteristic
278M16—61no—
279M16—61no—
280M16—101no—
281M16—101no—
282C2×C8—61no—
283C2×C8—101no—
284C2×C8—152no—
285C2×C8—152no—
286C2×C8—301no—
287C2×C8—301no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4—52no—
291C22⋊C4—101no—
292C42—21no—
293C42—101no—
294C42#120312yes—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3#402511yescharacteristic
298C22×C3#402711yescharacteristic
299C22×C3#408111yescharacteristic
300C2×D3—42no—
301C2×D3—41no—
302C3×C4—24no—
303C3×C4—202no—
304C3×C4#402311yescharacteristic
305C3×C4#403111yescharacteristic
306C3×C4C4×C22⋊D511yescharacteristic
307C3×C4#408411yescharacteristic
308Dic3—41no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—241no—
312C2×C5#467011yescharacteristic
313C2×C5#482412yes—
314C23—61no—
315C23#678011yescharacteristic
316Q8—61no—
317Q8—61no—
318D4—61no—
319D4—61no—
320D4—121no—
321D4—121no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—61no—
325C2×C4—102no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4#676811yescharacteristic
329C2×C4#677111yescharacteristic
330C2×C4C4×D3×D511yescharacteristic
331C2×C4#677711yescharacteristic
332C2×C4#678011yescharacteristic
333C2×C4C2×#120311yescharacteristic
334C8—121no—
335C8—201no—
336C8—302no—
337C8—302no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#6511312yes—
341C2×C3#6523311yescharacteristic
342D3—81no—
343C5#6874511yescharacteristic, complemented, Sylow
344C22—22no—
345C22—122no—
346C22—121no—
347C22#9136711yescharacteristic
348C22#9144211yescharacteristic
349C22#9154311yescharacteristic
350C4—24no—
351C4—121no—
352C4—202no—
353C4#9140011yescharacteristic
354C4C4×#120311yescharacteristic
355C4#9146411yescharacteristic
356C4#9146611yescharacteristic
357C3#1060116411yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—241no—
361C2#1174710612yes—
362C2#1174872411yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊#168C2semidirect
3. #11748433C2semidirect
6. C3×#64743C2semidirect
7. #11745982C2semidirect
19. #90972C4semidirect
20. #90966C4semidirect
29. #64743D3semidirect
295. C3×C5#1937semidirect
343. C5#68745semidirect
357. C3#10601164semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊#1682
C2×C5×#8052
#117484332
#117483822
#117483472
C3×#647432
#117459822
#106011643
#687455