Subgroups — D₅×D₁₁₇₃ #37553339

Order 23460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₈₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₃₉₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₁₇₃	—	5	1	no	maximal, Hall
7	D₁₉₅₅	—	3	1	no	—
8	D₅×C₁₇×C₂₃	D₃	1	1	yes	characteristic, complemented
9	C₅×D₃₉₁	—	3	1	no	—
10	D₁₁₇₃	—	5	1	no	—
11	D₁₁₇₃	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₁₇×C₂₃	—	5	1	no	—
13	C₅×C₁₇×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₃₉₁	—	15	1	no	Hall
15	D₅×D₆₉	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₅×D₅₁	—	23	1	no	maximal, Hall
18	C₂×C₁₇×C₂₃	—	5	1	no	—
19	D₃₉₁	—	3	1	no	—
20	D₃₉₁	—	15	1	no	—
21	D₃₄₅	—	17	1	no	—
22	C₅×D₆₉	—	17	1	no	—
23	C₃×D₅×C₂₃	D₁₇	1	1	yes	characteristic, complemented
24	D₂₅₅	—	23	1	no	—
25	C₅×D₅₁	—	23	1	no	—
26	C₃×D₅×C₁₇	D₂₃	1	1	yes	characteristic, complemented
27	D₅×D₂₃	—	51	1	no	Hall
28	C₁₇×C₂₃	D₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₅×D₁₇	—	69	1	no	Hall
31	C₂×D₆₉	—	85	1	no	Hall
32	C₃×C₅×C₁₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
33	D₁₁₅	—	51	1	no	—
34	C₅×D₂₃	—	51	1	no	—
35	D₅×C₂₃	D₅₁	1	1	yes	characteristic, complemented
36	C₂×D₅₁	—	115	1	no	Hall
37	D₈₅	—	69	1	no	—
38	C₅×D₁₇	—	69	1	no	—
39	D₅×C₁₇	D₆₉	1	1	yes	characteristic, complemented
40	C₂×C₃×C₂₃	—	5	1	no	—
41	D₆₉	—	17	1	no	—
42	D₆₉	—	85	1	no	—
43	C₅×C₂₃	C₂×D₅₁	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₇	—	5	1	no	—
45	D₅₁	—	23	1	no	—
46	D₅₁	—	115	1	no	—
47	C₂×D₂₃	—	255	1	no	Hall
48	C₅×C₁₇	C₂×D₆₉	1	1	yes	characteristic, complemented, Hall
49	C₃×C₂₃	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₇	—	345	1	no	Hall
51	D₃×D₅	—	391	1	no	Hall
52	C₃×C₁₇	D₅×D₂₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₂₃	—	5	1	no	—
54	D₂₃	—	51	1	no	—
55	D₂₃	—	255	1	no	—
56	C₂×C₁₇	—	5	1	no	—
57	D₁₇	—	69	1	no	—
58	D₁₇	—	345	1	no	—
59	D₁₅	—	391	1	no	—
60	C₃×D₅	D₃₉₁	1	1	yes	characteristic, complemented
61	C₅×D₃	—	391	1	no	—
62	C₂₃	D₅×D₅₁	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	1173	1	no	Hall
64	C₁₇	D₅×D₆₉	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	C₂×D₃₉₁	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	1955	1	no	Hall
67	C₂×C₅	—	1173	1	no	—
68	D₅	—	1173	1	no	—
69	D₅	D₁₁₇₃	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	D₃	—	391	1	no	—
72	D₃	—	1955	1	no	—
73	C₅	C₂×D₁₁₇₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	5865	1	no	Sylow
75	C₃	D₅×D₃₉₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	1173	1	no	—
78	C₂	—	5865	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₇×C₂₃	C₂²
LCS	G ▷ C₃×C₅×C₁₇×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₈₆₅	C₂	semidirect
2. C₅×D₁₁₇₃	C₂	semidirect
3. C₃×D₅×C₁₇×C₂₃	C₂	semidirect
5. C₃×C₅×C₁₇×C₂₃	C₂²	semidirect
8. D₅×C₁₇×C₂₃	D₃	semidirect
11. D₁₁₇₃	D₅	direct (N × H)
13. C₅×C₁₇×C₂₃	C₂×D₃	semidirect
16. C₃×C₁₇×C₂₃	C₂×D₅	semidirect
23. C₃×D₅×C₂₃	D₁₇	semidirect
26. C₃×D₅×C₁₇	D₂₃	semidirect
28. C₁₇×C₂₃	D₃×D₅	semidirect
29. C₃×C₅×C₂₃	C₂×D₁₇	semidirect
32. C₃×C₅×C₁₇	C₂×D₂₃	semidirect
35. D₅×C₂₃	D₅₁	semidirect
39. D₅×C₁₇	D₆₉	semidirect
43. C₅×C₂₃	C₂×D₅₁	semidirect
48. C₅×C₁₇	C₂×D₆₉	semidirect
49. C₃×C₂₃	D₅×D₁₇	semidirect
52. C₃×C₁₇	D₅×D₂₃	semidirect
60. C₃×D₅	D₃₉₁	semidirect
62. C₂₃	D₅×D₅₁	semidirect
64. C₁₇	D₅×D₆₉	semidirect
65. C₃×C₅	C₂×D₃₉₁	semidirect
69. D₅	D₁₁₇₃	direct (N × H)
73. C₅	C₂×D₁₁₇₃	semidirect
75. C₃	D₅×D₃₉₁	semidirect

Maximal subgroups

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

subgroup	index
D₅₈₆₅	2
C₅×D₁₁₇₃	2
C₃×D₅×C₁₇×C₂₃	2
D₅×D₃₉₁	3
C₂×D₁₁₇₃	5
D₅×D₆₉	17
D₅×D₅₁	23

Subgroups — D5×D1173 #37553339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₁₇₃ #37553339