Subgroups — C₂×C₈×C₉×C₁₃×C₁₇ #72208586

Order 31824.

132 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₈×C₉×C₁₃×C₁₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₈×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₈×C₁₃×C₁₇	C₂×C₃	1	2	yes	—
6	C₂×C₈×C₁₃×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₈×C₉×C₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₉×C₁₃×C₁₇	C₄	1	1	yes	characteristic
9	C₄×C₉×C₁₃×C₁₇	C₄	1	1	yes	characteristic
10	C₄×C₉×C₁₃×C₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₉×C₁₃×C₁₇	C₈	1	2	yes	direct product factor
12	C₂×C₉×C₁₃×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₃×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic
15	C₃×C₄×C₁₃×C₁₇	C₂²×C₃	1	1	yes	characteristic
16	C₉×C₁₃×C₁₇	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₈×C₉×C₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₄×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic
19	C₈×C₁₃×C₁₇	C₂×C₉	1	2	yes	direct product factor
20	C₂×C₃×C₁₃×C₁₇	C₃×C₈	1	2	yes	—
21	C₂×C₃×C₁₃×C₁₇	C₂×C₃×C₄	1	1	yes	characteristic
22	C₂×C₄×C₉×C₁₇	C₂×C₁₃	1	1	yes	characteristic
23	C₈×C₉×C₁₇	C₂×C₁₃	1	2	yes	direct product factor
24	C₂×C₄×C₉×C₁₃	C₂×C₁₇	1	1	yes	characteristic
25	C₈×C₉×C₁₃	C₂×C₁₇	1	2	yes	direct product factor
26	C₂²×C₁₃×C₁₇	C₄×C₉	1	1	yes	characteristic
27	C₄×C₁₃×C₁₇	C₄×C₉	1	1	yes	characteristic
28	C₄×C₁₃×C₁₇	C₂²×C₉	1	1	yes	characteristic
29	C₂×C₃×C₈×C₁₇	C₃×C₁₃	1	1	yes	characteristic
30	C₃×C₁₃×C₁₇	C₂×C₃×C₈	1	1	yes	characteristic
31	C₂×C₃×C₈×C₁₃	C₃×C₁₇	1	1	yes	characteristic
32	C₂²×C₉×C₁₇	C₄×C₁₃	1	1	yes	characteristic
33	C₄×C₉×C₁₇	C₄×C₁₃	1	1	yes	characteristic
34	C₄×C₉×C₁₇	C₂²×C₁₃	1	1	yes	characteristic
35	C₂²×C₉×C₁₃	C₄×C₁₇	1	1	yes	characteristic
36	C₄×C₉×C₁₃	C₄×C₁₇	1	1	yes	characteristic
37	C₄×C₉×C₁₃	C₂²×C₁₇	1	1	yes	characteristic
38	C₂×C₁₃×C₁₇	C₈×C₉	1	2	yes	direct product factor
39	C₂×C₁₃×C₁₇	C₂×C₄×C₉	1	1	yes	characteristic
40	C₂×C₃×C₄×C₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic
41	C₃×C₈×C₁₇	C₂×C₃×C₁₃	1	2	yes	—
42	C₂×C₃×C₄×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
43	C₃×C₈×C₁₃	C₂×C₃×C₁₇	1	2	yes	—
44	C₂×C₉×C₁₇	C₈×C₁₃	1	2	yes	direct product factor
45	C₂×C₉×C₁₇	C₂×C₄×C₁₃	1	1	yes	characteristic
46	C₂×C₈×C₁₇	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
47	C₂×C₉×C₁₃	C₈×C₁₇	1	2	yes	direct product factor
48	C₂×C₉×C₁₃	C₂×C₄×C₁₇	1	1	yes	characteristic
49	C₁₃×C₁₇	C₂×C₈×C₉	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₈×C₁₃	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
51	C₂²×C₃×C₁₇	C₃×C₄×C₁₃	1	1	yes	characteristic
52	C₃×C₄×C₁₇	C₃×C₄×C₁₃	1	1	yes	characteristic
53	C₃×C₄×C₁₇	C₂²×C₃×C₁₃	1	1	yes	characteristic
54	C₂²×C₃×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic
55	C₃×C₄×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic
56	C₃×C₄×C₁₃	C₂²×C₃×C₁₇	1	1	yes	characteristic
57	C₉×C₁₇	C₂×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
58	C₂×C₈×C₉	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
59	C₂×C₄×C₁₇	C₂×C₉×C₁₃	1	1	yes	characteristic
60	C₈×C₁₇	C₂×C₉×C₁₃	1	2	yes	direct product factor
61	C₉×C₁₃	C₂×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
62	C₂×C₄×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic
63	C₈×C₁₃	C₂×C₉×C₁₇	1	2	yes	direct product factor
64	C₂×C₃×C₁₇	C₃×C₈×C₁₃	1	2	yes	—
65	C₂×C₃×C₁₇	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
66	C₂×C₃×C₁₃	C₃×C₈×C₁₇	1	2	yes	—
67	C₂×C₃×C₁₃	C₂×C₃×C₄×C₁₇	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂×C₁₃×C₁₇	1	1	yes	characteristic
69	C₈×C₉	C₂×C₁₃×C₁₇	1	2	yes	direct product factor
70	C₂²×C₁₇	C₄×C₉×C₁₃	1	1	yes	characteristic
71	C₄×C₁₇	C₄×C₉×C₁₃	1	1	yes	characteristic
72	C₄×C₁₇	C₂²×C₉×C₁₃	1	1	yes	characteristic
73	C₂²×C₁₃	C₄×C₉×C₁₇	1	1	yes	characteristic
74	C₄×C₁₃	C₄×C₉×C₁₇	1	1	yes	characteristic
75	C₄×C₁₃	C₂²×C₉×C₁₇	1	1	yes	characteristic
76	C₃×C₁₇	C₂×C₃×C₈×C₁₃	1	1	yes	characteristic
77	C₂×C₃×C₈	C₃×C₁₃×C₁₇	1	1	yes	characteristic
78	C₃×C₁₃	C₂×C₃×C₈×C₁₇	1	1	yes	characteristic
79	C₂²×C₉	C₄×C₁₃×C₁₇	1	1	yes	characteristic
80	C₄×C₉	C₄×C₁₃×C₁₇	1	1	yes	characteristic
81	C₄×C₉	C₂²×C₁₃×C₁₇	1	1	yes	characteristic
82	C₂×C₁₇	C₈×C₉×C₁₃	1	2	yes	direct product factor
83	C₂×C₁₇	C₂×C₄×C₉×C₁₃	1	1	yes	characteristic
84	C₂×C₁₃	C₈×C₉×C₁₇	1	2	yes	direct product factor
85	C₂×C₁₃	C₂×C₄×C₉×C₁₇	1	1	yes	characteristic
86	C₂×C₃×C₄	C₂×C₃×C₁₃×C₁₇	1	1	yes	characteristic
87	C₃×C₈	C₂×C₃×C₁₃×C₁₇	1	2	yes	—
88	C₂×C₉	C₈×C₁₃×C₁₇	1	2	yes	direct product factor
89	C₂×C₉	C₂×C₄×C₁₃×C₁₇	1	1	yes	characteristic
90	C₁₇	C₂×C₈×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×C₈	C₉×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
92	C₁₃	C₂×C₈×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
93	C₂²×C₃	C₃×C₄×C₁₃×C₁₇	1	1	yes	characteristic
94	C₃×C₄	C₃×C₄×C₁₃×C₁₇	1	1	yes	characteristic
95	C₃×C₄	C₂²×C₃×C₁₃×C₁₇	1	1	yes	characteristic
96	C₉	C₂×C₈×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
97	C₂×C₄	C₂×C₉×C₁₃×C₁₇	1	1	yes	characteristic
98	C₈	C₂×C₉×C₁₃×C₁₇	1	2	yes	direct product factor
99	C₂×C₃	C₃×C₈×C₁₃×C₁₇	1	2	yes	—
100	C₂×C₃	C₂×C₃×C₄×C₁₃×C₁₇	1	1	yes	characteristic
101	C₂²	C₄×C₉×C₁₃×C₁₇	1	1	yes	characteristic
102	C₄	C₄×C₉×C₁₃×C₁₇	1	1	yes	characteristic
103	C₄	C₂²×C₉×C₁₃×C₁₇	1	1	yes	characteristic
104	C₃	C₂×C₃×C₈×C₁₃×C₁₇	1	1	yes	characteristic
105	C₂	C₈×C₉×C₁₃×C₁₇	1	2	yes	direct product factor
106	C₂	C₂×C₄×C₉×C₁₃×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₁₃×C₁₇
socle, prime radical	C₂²×C₃×C₁₃×C₁₇	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₉×C₁₃×C₁₇	C₂	direct (N × H)
6. C₂×C₈×C₁₃×C₁₇	C₉	direct (N × H)
7. C₂×C₈×C₉×C₁₇	C₁₃	direct (N × H)
11. C₂×C₉×C₁₃×C₁₇	C₈	direct (N × H)
16. C₉×C₁₃×C₁₇	C₂×C₈	direct (N × H)
17. C₂×C₈×C₉×C₁₃	C₁₇	direct (N × H)
19. C₈×C₁₃×C₁₇	C₂×C₉	direct (N × H)
23. C₈×C₉×C₁₇	C₂×C₁₃	direct (N × H)
25. C₈×C₉×C₁₃	C₂×C₁₇	direct (N × H)
38. C₂×C₁₃×C₁₇	C₈×C₉	direct (N × H)
44. C₂×C₉×C₁₇	C₈×C₁₃	direct (N × H)
46. C₂×C₈×C₁₇	C₉×C₁₃	direct (N × H)
47. C₂×C₉×C₁₃	C₈×C₁₇	direct (N × H)
49. C₁₃×C₁₇	C₂×C₈×C₉	direct (N × H)
50. C₂×C₈×C₁₃	C₉×C₁₇	direct (N × H)
57. C₉×C₁₇	C₂×C₈×C₁₃	direct (N × H)
58. C₂×C₈×C₉	C₁₃×C₁₇	direct (N × H)
60. C₈×C₁₇	C₂×C₉×C₁₃	direct (N × H)
61. C₉×C₁₃	C₂×C₈×C₁₇	direct (N × H)
63. C₈×C₁₃	C₂×C₉×C₁₇	direct (N × H)
69. C₈×C₉	C₂×C₁₃×C₁₇	direct (N × H)
82. C₂×C₁₇	C₈×C₉×C₁₃	direct (N × H)
84. C₂×C₁₃	C₈×C₉×C₁₇	direct (N × H)
88. C₂×C₉	C₈×C₁₃×C₁₇	direct (N × H)
90. C₁₇	C₂×C₈×C₉×C₁₃	direct (N × H)
91. C₂×C₈	C₉×C₁₃×C₁₇	direct (N × H)
92. C₁₃	C₂×C₈×C₉×C₁₇	direct (N × H)
96. C₉	C₂×C₈×C₁₃×C₁₇	direct (N × H)
98. C₈	C₂×C₉×C₁₃×C₁₇	direct (N × H)
105. C₂	C₈×C₉×C₁₃×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₉×C₁₃×C₁₇	2
C₈×C₉×C₁₃×C₁₇	2
C₂×C₃×C₈×C₁₃×C₁₇	3
C₂×C₈×C₉×C₁₇	13
C₂×C₈×C₉×C₁₃	17

Subgroups — C2×C8×C9×C13×C17 #72208586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₉×C₁₃×C₁₇ #72208586