Subgroups — C₂×C₃²×C₄×C₁₇×C₂₅ #72207366

Order 30600.

288 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×C₃×C₄×C₁₇×C₂₅	C₃	1	4	yes	maximal, direct product factor
2	C₂×C₃²×C₄×C₅×C₁₇	C₅	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₇×C₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅×C₁₇	C₃×C₅	1	4	yes	—
5	C₂²×C₃²×C₁₇×C₂₅	C₂	1	1	yes	maximal, characteristic
6	C₃²×C₄×C₁₇×C₂₅	C₂	1	2	yes	maximal, direct product factor
7	C₂×C₃²×C₁₇×C₂₅	C₄	1	2	yes	direct product factor
8	C₂×C₃²×C₁₇×C₂₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₁₇×C₂₅	C₂×C₃	1	4	yes	—
10	C₃×C₄×C₁₇×C₂₅	C₂×C₃	1	8	yes	direct product factor
11	C₃²×C₁₇×C₂₅	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₃²×C₅×C₁₇	C₂×C₅	1	1	yes	characteristic
13	C₃²×C₄×C₅×C₁₇	C₂×C₅	1	2	yes	—
14	C₂×C₃×C₁₇×C₂₅	C₃×C₄	1	8	yes	direct product factor
15	C₂×C₃×C₁₇×C₂₅	C₂²×C₃	1	4	yes	—
16	C₂×C₃²×C₄×C₂₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₁₇×C₂₅	C₂×C₃²	1	1	yes	characteristic
18	C₄×C₁₇×C₂₅	C₂×C₃²	1	2	yes	direct product factor
19	C₂×C₃²×C₅×C₁₇	C₄×C₅	1	2	yes	—
20	C₂×C₃²×C₅×C₁₇	C₂²×C₅	1	1	yes	characteristic
21	C₃×C₁₇×C₂₅	C₂×C₃×C₄	1	4	yes	direct product factor
22	C₂×C₃²×C₄×C₁₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₃×C₅×C₁₇	C₂×C₃×C₅	1	4	yes	—
24	C₃×C₄×C₅×C₁₇	C₂×C₃×C₅	1	8	yes	—
25	C₂²×C₃²×C₂₅	C₂×C₁₇	1	1	yes	characteristic
26	C₃²×C₄×C₂₅	C₂×C₁₇	1	2	yes	direct product factor
27	C₂×C₁₇×C₂₅	C₃²×C₄	1	2	yes	direct product factor
28	C₂×C₁₇×C₂₅	C₂²×C₃²	1	1	yes	characteristic
29	C₃²×C₅×C₁₇	C₂×C₄×C₅	1	1	yes	characteristic
30	C₂×C₄×C₅×C₁₇	C₃²×C₅	1	1	yes	characteristic
31	C₂²×C₃²×C₁₇	C₂×C₂₅	1	1	yes	characteristic
32	C₃²×C₄×C₁₇	C₂×C₂₅	1	2	yes	direct product factor
33	C₂×C₃×C₄×C₂₅	C₃×C₁₇	1	4	yes	direct product factor
34	C₂×C₃×C₅×C₁₇	C₃×C₄×C₅	1	8	yes	—
35	C₂×C₃×C₅×C₁₇	C₂²×C₃×C₅	1	4	yes	—
36	C₂×C₃²×C₂₅	C₄×C₁₇	1	2	yes	direct product factor
37	C₂×C₃²×C₂₅	C₂²×C₁₇	1	1	yes	characteristic
38	C₁₇×C₂₅	C₂×C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃×C₄×C₁₇	C₃×C₂₅	1	4	yes	direct product factor
40	C₂×C₃²×C₄×C₅	C₅×C₁₇	1	1	yes	characteristic
41	C₂²×C₅×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic
42	C₄×C₅×C₁₇	C₂×C₃²×C₅	1	2	yes	—
43	C₂×C₃²×C₁₇	C₄×C₂₅	1	2	yes	direct product factor
44	C₂×C₃²×C₁₇	C₂²×C₂₅	1	1	yes	characteristic
45	C₂²×C₃×C₂₅	C₂×C₃×C₁₇	1	4	yes	—
46	C₃×C₄×C₂₅	C₂×C₃×C₁₇	1	8	yes	direct product factor
47	C₃×C₅×C₁₇	C₂×C₃×C₄×C₅	1	4	yes	—
48	C₃²×C₂₅	C₂×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
49	C₂²×C₃×C₁₇	C₂×C₃×C₂₅	1	4	yes	—
50	C₃×C₄×C₁₇	C₂×C₃×C₂₅	1	8	yes	direct product factor
51	C₂×C₄×C₂₅	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
52	C₂²×C₃²×C₅	C₂×C₅×C₁₇	1	1	yes	characteristic
53	C₃²×C₄×C₅	C₂×C₅×C₁₇	1	2	yes	—
54	C₂×C₅×C₁₇	C₃²×C₄×C₅	1	2	yes	—
55	C₂×C₅×C₁₇	C₂²×C₃²×C₅	1	1	yes	characteristic
56	C₃²×C₁₇	C₂×C₄×C₂₅	1	1	yes	characteristic, direct product factor, Hall
57	C₂×C₃×C₂₅	C₃×C₄×C₁₇	1	8	yes	direct product factor
58	C₂×C₃×C₂₅	C₂²×C₃×C₁₇	1	4	yes	—
59	C₂×C₄×C₁₇	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
60	C₂×C₃×C₄×C₅	C₃×C₅×C₁₇	1	4	yes	—
61	C₂×C₃×C₁₇	C₃×C₄×C₂₅	1	8	yes	direct product factor
62	C₂×C₃×C₁₇	C₂²×C₃×C₂₅	1	4	yes	—
63	C₂²×C₂₅	C₂×C₃²×C₁₇	1	1	yes	characteristic
64	C₄×C₂₅	C₂×C₃²×C₁₇	1	2	yes	direct product factor
65	C₂×C₃²×C₅	C₄×C₅×C₁₇	1	2	yes	—
66	C₂×C₃²×C₅	C₂²×C₅×C₁₇	1	1	yes	characteristic
67	C₅×C₁₇	C₂×C₃²×C₄×C₅	1	1	yes	characteristic
68	C₃×C₂₅	C₂×C₃×C₄×C₁₇	1	4	yes	direct product factor
69	C₂×C₃²×C₄	C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
70	C₂²×C₁₇	C₂×C₃²×C₂₅	1	1	yes	characteristic
71	C₄×C₁₇	C₂×C₃²×C₂₅	1	2	yes	direct product factor
72	C₂²×C₃×C₅	C₂×C₃×C₅×C₁₇	1	4	yes	—
73	C₃×C₄×C₅	C₂×C₃×C₅×C₁₇	1	8	yes	—
74	C₃×C₁₇	C₂×C₃×C₄×C₂₅	1	4	yes	direct product factor
75	C₂×C₂₅	C₃²×C₄×C₁₇	1	2	yes	direct product factor
76	C₂×C₂₅	C₂²×C₃²×C₁₇	1	1	yes	characteristic
77	C₃²×C₅	C₂×C₄×C₅×C₁₇	1	1	yes	characteristic
78	C₂×C₄×C₅	C₃²×C₅×C₁₇	1	1	yes	characteristic
79	C₂²×C₃²	C₂×C₁₇×C₂₅	1	1	yes	characteristic
80	C₃²×C₄	C₂×C₁₇×C₂₅	1	2	yes	direct product factor
81	C₂×C₁₇	C₃²×C₄×C₂₅	1	2	yes	direct product factor
82	C₂×C₁₇	C₂²×C₃²×C₂₅	1	1	yes	characteristic
83	C₂×C₃×C₅	C₃×C₄×C₅×C₁₇	1	8	yes	—
84	C₂×C₃×C₅	C₂²×C₃×C₅×C₁₇	1	4	yes	—
85	C₂₅	C₂×C₃²×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₃×C₄	C₃×C₁₇×C₂₅	1	4	yes	direct product factor
87	C₂²×C₅	C₂×C₃²×C₅×C₁₇	1	1	yes	characteristic
88	C₄×C₅	C₂×C₃²×C₅×C₁₇	1	2	yes	—
89	C₂×C₃²	C₄×C₁₇×C₂₅	1	2	yes	direct product factor
90	C₂×C₃²	C₂²×C₁₇×C₂₅	1	1	yes	characteristic
91	C₁₇	C₂×C₃²×C₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₃×C₅	C₂×C₃×C₄×C₅×C₁₇	1	4	yes	—
93	C₂²×C₃	C₂×C₃×C₁₇×C₂₅	1	4	yes	—
94	C₃×C₄	C₂×C₃×C₁₇×C₂₅	1	8	yes	direct product factor
95	C₂×C₅	C₃²×C₄×C₅×C₁₇	1	2	yes	—
96	C₂×C₅	C₂²×C₃²×C₅×C₁₇	1	1	yes	characteristic
97	C₃²	C₂×C₄×C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₄	C₃²×C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂×C₃	C₃×C₄×C₁₇×C₂₅	1	8	yes	direct product factor
100	C₂×C₃	C₂²×C₃×C₁₇×C₂₅	1	4	yes	—
101	C₅	C₂×C₃²×C₄×C₅×C₁₇	1	1	yes	characteristic
102	C₂²	C₂×C₃²×C₁₇×C₂₅	1	1	yes	characteristic
103	C₄	C₂×C₃²×C₁₇×C₂₅	1	2	yes	direct product factor
104	C₃	C₂×C₃×C₄×C₁₇×C₂₅	1	4	yes	direct product factor
105	C₂	C₃²×C₄×C₁₇×C₂₅	1	2	yes	direct product factor
106	C₂	C₂²×C₃²×C₁₇×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂²×C₃²×C₅×C₁₇
socle, prime radical	C₂²×C₃²×C₅×C₁₇	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₁₇×C₂₅	C₃	direct (N × H)
3. C₂×C₄×C₁₇×C₂₅	C₃²	direct (N × H)
6. C₃²×C₄×C₁₇×C₂₅	C₂	direct (N × H)
7. C₂×C₃²×C₁₇×C₂₅	C₄	direct (N × H)
10. C₃×C₄×C₁₇×C₂₅	C₂×C₃	direct (N × H)
11. C₃²×C₁₇×C₂₅	C₂×C₄	direct (N × H)
14. C₂×C₃×C₁₇×C₂₅	C₃×C₄	direct (N × H)
16. C₂×C₃²×C₄×C₂₅	C₁₇	direct (N × H)
18. C₄×C₁₇×C₂₅	C₂×C₃²	direct (N × H)
21. C₃×C₁₇×C₂₅	C₂×C₃×C₄	direct (N × H)
22. C₂×C₃²×C₄×C₁₇	C₂₅	direct (N × H)
26. C₃²×C₄×C₂₅	C₂×C₁₇	direct (N × H)
27. C₂×C₁₇×C₂₅	C₃²×C₄	direct (N × H)
32. C₃²×C₄×C₁₇	C₂×C₂₅	direct (N × H)
33. C₂×C₃×C₄×C₂₅	C₃×C₁₇	direct (N × H)
36. C₂×C₃²×C₂₅	C₄×C₁₇	direct (N × H)
38. C₁₇×C₂₅	C₂×C₃²×C₄	direct (N × H)
39. C₂×C₃×C₄×C₁₇	C₃×C₂₅	direct (N × H)
43. C₂×C₃²×C₁₇	C₄×C₂₅	direct (N × H)
46. C₃×C₄×C₂₅	C₂×C₃×C₁₇	direct (N × H)
48. C₃²×C₂₅	C₂×C₄×C₁₇	direct (N × H)
50. C₃×C₄×C₁₇	C₂×C₃×C₂₅	direct (N × H)
51. C₂×C₄×C₂₅	C₃²×C₁₇	direct (N × H)
56. C₃²×C₁₇	C₂×C₄×C₂₅	direct (N × H)
57. C₂×C₃×C₂₅	C₃×C₄×C₁₇	direct (N × H)
59. C₂×C₄×C₁₇	C₃²×C₂₅	direct (N × H)
61. C₂×C₃×C₁₇	C₃×C₄×C₂₅	direct (N × H)
64. C₄×C₂₅	C₂×C₃²×C₁₇	direct (N × H)
68. C₃×C₂₅	C₂×C₃×C₄×C₁₇	direct (N × H)
69. C₂×C₃²×C₄	C₁₇×C₂₅	direct (N × H)
71. C₄×C₁₇	C₂×C₃²×C₂₅	direct (N × H)
74. C₃×C₁₇	C₂×C₃×C₄×C₂₅	direct (N × H)
75. C₂×C₂₅	C₃²×C₄×C₁₇	direct (N × H)
80. C₃²×C₄	C₂×C₁₇×C₂₅	direct (N × H)
81. C₂×C₁₇	C₃²×C₄×C₂₅	direct (N × H)
85. C₂₅	C₂×C₃²×C₄×C₁₇	direct (N × H)
86. C₂×C₃×C₄	C₃×C₁₇×C₂₅	direct (N × H)
89. C₂×C₃²	C₄×C₁₇×C₂₅	direct (N × H)
91. C₁₇	C₂×C₃²×C₄×C₂₅	direct (N × H)
94. C₃×C₄	C₂×C₃×C₁₇×C₂₅	direct (N × H)
97. C₃²	C₂×C₄×C₁₇×C₂₅	direct (N × H)
98. C₂×C₄	C₃²×C₁₇×C₂₅	direct (N × H)
99. C₂×C₃	C₃×C₄×C₁₇×C₂₅	direct (N × H)
103. C₄	C₂×C₃²×C₁₇×C₂₅	direct (N × H)
104. C₃	C₂×C₃×C₄×C₁₇×C₂₅	direct (N × H)
105. C₂	C₃²×C₄×C₁₇×C₂₅	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×C₃×C₄×C₁₇×C₂₅	3
C₂×C₃²×C₄×C₅×C₁₇	5
C₂²×C₃²×C₁₇×C₂₅	2
C₃²×C₄×C₁₇×C₂₅	2
C₂×C₃²×C₄×C₂₅	17

Subgroups — C2×C32×C4×C17×C25 #72207366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₄×C₁₇×C₂₅ #72207366