Subgroups — D₇×D₈₀₅ #36376802

Order 22540.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₈₀₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(C₇⋊D₁₆₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₁₆₁	—	5	1	no	maximal, Hall
6	C₂×D₈₀₅	—	7	1	no	maximal
7	D₇×D₁₁₅	—	7	1	no	maximal
8	C₇⋊D₁₆₁	—	5	1	no	—
9	C₇×D₁₆₁	—	5	1	no	—
10	C₇×D₇×C₂₃	D₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₇×C₂₃	—	7	1	no	—
12	D₈₀₅	—	7	1	no	—
13	D₈₀₅	—	7	1	no	—
14	D₈₀₅	—	14	3	no	—
15	D₈₀₅	D₇	1	1	yes	characteristic, direct product factor
16	C₇×D₁₁₅	—	7	1	no	—
17	C₅×D₇×C₂₃	D₇	1	1	yes	characteristic, complemented
18	C₇²×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	D₇×D₃₅	—	23	1	no	maximal, Hall
20	C₅×C₇×C₂₃	—	2	3	no	—
21	C₅×C₇×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented
22	C₅×C₇×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented
23	C₂×D₁₆₁	—	35	1	no	—
24	D₇×D₂₃	—	35	1	no	—
25	C₅⋊(C₇⋊D₇)	—	23	1	no	—
26	C₇×D₃₅	—	23	1	no	—
27	C₅×C₇×D₇	D₂₃	1	1	yes	characteristic, complemented
28	C₂×D₁₁₅	—	49	1	no	Hall
29	C₂×C₇×C₂₃	—	7	1	no	—
30	D₁₆₁	—	5	1	no	—
31	D₁₆₁	—	35	1	no	—
32	D₁₆₁	—	35	1	no	—
33	D₁₆₁	—	70	3	no	—
34	C₇×D₂₃	—	35	1	no	—
35	D₇×C₂₃	D₃₅	1	1	yes	characteristic, complemented
36	C₅×C₇²	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₂₃	—	7	1	no	—
38	D₁₁₅	—	7	1	no	—
39	D₁₁₅	—	49	1	no	—
40	D₇²	—	115	1	no	Hall
41	C₇×C₂₃	—	2	3	no	—
42	C₇×C₂₃	D₅×D₇	1	1	yes	characteristic, complemented
43	C₇×C₂₃	C₂×D₃₅	1	1	yes	characteristic, complemented
44	C₂×D₃₅	—	161	1	no	—
45	D₅×D₇	—	161	1	no	—
46	C₅×C₂₃	D₇²	1	1	yes	characteristic, complemented, Hall
47	C₇⋊D₇	—	115	1	no	—
48	C₇×D₇	—	115	1	no	—
49	C₇×D₇	D₁₁₅	1	1	yes	characteristic, complemented
50	C₂×D₂₃	—	245	1	no	Hall
51	C₂×C₅×C₇	—	7	1	no	—
52	D₃₅	—	23	1	no	—
53	D₃₅	—	322	3	no	—
54	D₃₅	—	161	1	no	—
55	D₃₅	—	161	1	no	—
56	C₅×D₇	D₁₆₁	1	1	yes	characteristic, complemented
57	C₇×D₅	—	161	1	no	—
58	C₇²	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₂₃	—	7	1	no	—
60	D₂₃	—	35	1	no	—
61	D₂₃	—	245	1	no	—
62	C₅×C₇	—	2	3	no	—
63	C₅×C₇	D₇×D₂₃	1	1	yes	characteristic, complemented
64	C₅×C₇	C₂×D₁₆₁	1	1	yes	characteristic, complemented
65	C₂×D₇	—	805	1	no	—
66	C₂×D₇	—	805	1	no	—
67	C₂₃	D₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₅	—	1127	1	no	Hall
69	C₂×C₇	—	7	1	no	—
70	C₂×C₇	—	805	1	no	—
71	D₇	—	805	1	no	—
72	D₇	—	805	1	no	—
73	D₇	—	1610	3	no	—
74	D₇	—	115	1	no	—
75	D₇	D₈₀₅	1	1	yes	characteristic, direct product factor
76	C₂×C₅	—	7	1	no	—
77	D₅	—	1127	1	no	—
78	D₅	—	161	1	no	—
79	C₇	—	2	3	no	—
80	C₇	D₇×D₁₁₅	1	1	yes	characteristic, complemented
81	C₇	C₂×D₈₀₅	1	1	yes	characteristic, complemented
82	C₅	D₇×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	5635	1	no	Sylow
84	C₂	—	5635	1	no	—
85	C₂	—	7	1	no	—
86	C₂	—	805	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₂₃	C₂²
LCS	G ▷ C₅×C₇²×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₂₃	C₂	semidirect
2. C₇×D₈₀₅	C₂	semidirect
3. C₅⋊(C₇⋊D₁₆₁)	C₂	semidirect
4. C₅×C₇²×C₂₃	C₂²	semidirect
10. C₇×D₇×C₂₃	D₅	semidirect
15. D₈₀₅	D₇	direct (N × H)
17. C₅×D₇×C₂₃	D₇	semidirect
18. C₇²×C₂₃	C₂×D₅	semidirect
21. C₅×C₇×C₂₃	C₂×D₇	semidirect
22. C₅×C₇×C₂₃	C₂×D₇	semidirect
27. C₅×C₇×D₇	D₂₃	semidirect
35. D₇×C₂₃	D₃₅	semidirect
36. C₅×C₇²	C₂×D₂₃	semidirect
42. C₇×C₂₃	D₅×D₇	semidirect
43. C₇×C₂₃	C₂×D₃₅	semidirect
46. C₅×C₂₃	D₇²	semidirect
49. C₇×D₇	D₁₁₅	semidirect
56. C₅×D₇	D₁₆₁	semidirect
58. C₇²	C₂×D₁₁₅	semidirect
63. C₅×C₇	D₇×D₂₃	semidirect
64. C₅×C₇	C₂×D₁₆₁	semidirect
67. C₂₃	D₇×D₃₅	semidirect
75. D₇	D₈₀₅	direct (N × H)
80. C₇	D₇×D₁₁₅	semidirect
81. C₇	C₂×D₈₀₅	semidirect
82. C₅	D₇×D₁₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₇×C₂₃	2
C₇×D₈₀₅	2
C₅⋊(C₇⋊D₁₆₁)	2
D₇×D₁₆₁	5
C₂×D₈₀₅	7
D₇×D₁₁₅	7
D₇×D₃₅	23

Subgroups — D7×D805 #36376802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₈₀₅ #36376802