Subgroups — D₁₃×D₂₇₅ #28384663

Order 14300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₂₇₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₂₅×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₅₅	—	5	1	no	maximal
6	D₇₁₅	—	5	1	no	—
7	C₁₃×D₅₅	—	5	1	no	—
8	C₅×C₁₁×D₁₃	D₅	1	1	yes	characteristic
9	D₁₃×D₂₅	—	11	1	no	maximal, Hall
10	C₂×D₂₇₅	—	13	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic
12	D₃₂₅	—	11	1	no	—
13	C₂₅×D₁₃	D₁₁	1	1	yes	characteristic, complemented
14	C₁₃×D₂₅	—	11	1	no	—
15	D₁₁×D₁₃	—	25	1	no	Hall
16	C₂×C₁₁×C₂₅	—	13	1	no	—
17	D₂₇₅	—	13	1	no	—
18	D₂₇₅	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₁₄₃	—	25	1	no	—
21	C₁₁×D₁₃	D₂₅	1	1	yes	characteristic, complemented
22	C₁₃×D₁₁	—	25	1	no	—
23	C₁₁×C₂₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
24	D₅×D₁₃	—	55	1	no	—
25	C₂×D₅₅	—	65	1	no	—
26	C₁₁×C₁₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
27	D₆₅	—	55	1	no	—
28	C₅×D₁₃	D₅₅	1	1	yes	characteristic
29	D₅×C₁₃	—	55	1	no	—
30	C₂×C₅×C₁₁	—	13	1	no	—
31	D₅₅	—	5	1	no	—
32	D₅₅	—	65	1	no	—
33	C₂×D₂₅	—	143	1	no	Hall
34	C₅×C₁₃	C₂×D₅₅	1	1	yes	characteristic
35	C₅×C₁₁	D₅×D₁₃	1	1	yes	characteristic
36	C₂×D₁₃	—	275	1	no	Hall
37	C₂×C₂₅	—	13	1	no	—
38	D₂₅	—	11	1	no	—
39	D₂₅	—	143	1	no	—
40	C₂×D₁₁	—	325	1	no	Hall
41	C₂×C₁₃	—	275	1	no	—
42	D₁₃	—	275	1	no	—
43	D₁₃	D₂₇₅	1	1	yes	characteristic, direct product factor
44	C₂₅	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	13	1	no	—
46	D₁₁	—	25	1	no	—
47	D₁₁	—	325	1	no	—
48	C₂×D₅	—	715	1	no	—
49	C₁₃	C₂×D₂₇₅	1	1	yes	characteristic, complemented, Sylow
50	C₁₁	D₁₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	13	1	no	—
52	D₅	—	55	1	no	—
53	D₅	—	715	1	no	—
54	C₅	D₁₃×D₅₅	1	1	yes	characteristic
55	C₂²	—	3575	1	no	Sylow
56	C₂	—	13	1	no	—
57	C₂	—	275	1	no	—
58	C₂	—	3575	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₁×C₁₃×C₂₅	C₂²
Frattini	C₅	D₁₃×D₅₅
socle	C₅×C₁₁×C₁₃	C₂×D₅
LCS	G ▷ C₁₁×C₁₃×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₅₇₅	C₂	semidirect
2. C₁₃×D₂₇₅	C₂	semidirect
3. C₁₁×C₂₅×D₁₃	C₂	semidirect
4. C₁₁×C₁₃×C₂₅	C₂²	semidirect
13. C₂₅×D₁₃	D₁₁	semidirect
18. D₂₇₅	D₁₃	direct (N × H)
19. C₁₃×C₂₅	C₂×D₁₁	semidirect
21. C₁₁×D₁₃	D₂₅	semidirect
23. C₁₁×C₂₅	C₂×D₁₃	semidirect
26. C₁₁×C₁₃	C₂×D₂₅	semidirect
43. D₁₃	D₂₇₅	direct (N × H)
44. C₂₅	D₁₁×D₁₃	semidirect
49. C₁₃	C₂×D₂₇₅	semidirect
50. C₁₁	D₁₃×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
D₃₅₇₅	2
C₁₃×D₂₇₅	2
C₁₁×C₂₅×D₁₃	2
D₁₃×D₅₅	5
D₁₃×D₂₅	11
C₂×D₂₇₅	13

Subgroups — D13×D275 #28384663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₂₇₅ #28384663