Subgroups — D₅₁×D₁₅₅ #44539384

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃₁×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₅₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₁×D₅₁	—	5	1	no	maximal, Hall
7	D₂₆₃₅	—	3	1	no	—
8	C₁₇×D₁₅₅	D₃	1	1	yes	characteristic, complemented
9	C₅×C₃₁×D₁₇	—	3	1	no	—
10	D₁₅₈₁	—	5	1	no	—
11	C₃₁×D₅₁	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₇×D₃₁	—	5	1	no	—
13	C₅×C₁₇×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₃₁	—	15	1	no	Hall
15	D₃×D₁₅₅	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₅₂₇	—	15	1	no	—
18	C₁₇×D₃₁	—	5	1	no	—
19	C₃₁×D₁₇	—	3	1	no	—
20	D₅×D₅₁	—	31	1	no	maximal, Hall
21	D₄₆₅	—	17	1	no	—
22	C₅×D₃×C₃₁	—	17	1	no	—
23	C₃×D₁₅₅	D₁₇	1	1	yes	characteristic, complemented
24	C₂×D₁₅₅	—	51	1	no	Hall
25	C₁₇×C₃₁	D₃×D₅	1	1	yes	characteristic, complemented, Hall
26	D₂₅₅	—	31	1	no	—
27	C₅×D₅₁	D₃₁	1	1	yes	characteristic, complemented
28	C₃×D₅×C₁₇	—	31	1	no	—
29	C₃×C₅×C₃₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₃×D₃₁	—	85	1	no	Hall
31	D₅×D₁₇	—	93	1	no	Hall
32	C₂×C₅×C₃₁	—	51	1	no	—
33	D₁₅₅	—	51	1	no	—
34	D₁₅₅	D₅₁	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×D₅₁	—	155	1	no	Hall
37	D₉₃	—	85	1	no	—
38	C₃×D₃₁	—	5	1	no	—
39	D₃×C₃₁	—	17	1	no	—
40	D₈₅	—	93	1	no	—
41	C₅×D₁₇	—	3	1	no	—
42	D₅×C₁₇	—	31	1	no	—
43	C₅×C₃₁	C₂×D₅₁	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	255	1	no	Hall
45	C₂×C₃×C₁₇	—	155	1	no	—
46	D₅₁	—	155	1	no	—
47	D₅₁	D₁₅₅	1	1	yes	characteristic, direct product factor
48	C₃×C₃₁	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	D₃×D₃₁	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₇	—	465	1	no	Hall
51	C₂×C₃₁	—	51	1	no	—
52	D₃₁	—	5	1	no	—
53	D₃₁	—	255	1	no	—
54	D₃×D₅	—	527	1	no	Hall
55	C₃×C₁₇	C₂×D₁₅₅	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₇	—	155	1	no	—
57	D₁₇	—	3	1	no	—
58	D₁₇	—	465	1	no	—
59	C₃₁	D₅×D₅₁	1	1	yes	characteristic, complemented, Sylow
60	D₁₅	—	527	1	no	—
61	C₃×D₅	—	31	1	no	—
62	C₅×D₃	—	17	1	no	—
63	C₂×D₅	—	1581	1	no	Hall
64	C₁₇	D₃×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	D₁₇×D₃₁	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	2635	1	no	Hall
67	C₂×C₅	—	51	1	no	—
68	D₅	—	31	1	no	—
69	D₅	—	1581	1	no	—
70	C₂×C₃	—	155	1	no	—
71	D₃	—	17	1	no	—
72	D₃	—	2635	1	no	—
73	C₅	D₃₁×D₅₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	7905	1	no	Sylow
75	C₃	D₁₇×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	51	1	no	—
77	C₂	—	155	1	no	—
78	C₂	—	7905	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₇×C₃₁	C₂²
LCS	G ▷ C₃×C₅×C₁₇×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₉₀₅	C₂	semidirect
2. C₅×C₃₁×D₅₁	C₂	semidirect
3. C₃×C₁₇×D₁₅₅	C₂	semidirect
5. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
8. C₁₇×D₁₅₅	D₃	semidirect
11. C₃₁×D₅₁	D₅	semidirect
13. C₅×C₁₇×C₃₁	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₁	C₂×D₅	semidirect
23. C₃×D₁₅₅	D₁₇	semidirect
25. C₁₇×C₃₁	D₃×D₅	semidirect
27. C₅×D₅₁	D₃₁	semidirect
29. C₃×C₅×C₃₁	C₂×D₁₇	semidirect
34. D₁₅₅	D₅₁	direct (N × H)
35. C₃×C₅×C₁₇	C₂×D₃₁	semidirect
43. C₅×C₃₁	C₂×D₅₁	semidirect
47. D₅₁	D₁₅₅	direct (N × H)
48. C₃×C₃₁	D₅×D₁₇	semidirect
49. C₅×C₁₇	D₃×D₃₁	semidirect
55. C₃×C₁₇	C₂×D₁₅₅	semidirect
59. C₃₁	D₅×D₅₁	semidirect
64. C₁₇	D₃×D₁₅₅	semidirect
65. C₃×C₅	D₁₇×D₃₁	semidirect
73. C₅	D₃₁×D₅₁	semidirect
75. C₃	D₁₇×D₁₅₅	semidirect

Maximal subgroups

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

subgroup	index
D₇₉₀₅	2
C₅×C₃₁×D₅₁	2
C₃×C₁₇×D₁₅₅	2
D₁₇×D₁₅₅	3
D₃₁×D₅₁	5
D₃×D₁₅₅	17
D₅×D₅₁	31

Subgroups — D51×D155 #44539384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₁×D₁₅₅ #44539384