Subgroups — C₇×#10624454 #19099863

Order 5103.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₇×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
5	#10624454	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃×C₇×3₋¹⁺²	C₉	1	1	yes	characteristic
7	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
8	C₇×C₂₇⋊C₃	—	3	3	no	—
9	C₃×C₇×C₂₇	—	3	1	no	—
10	C₃×C₇×C₂₇	—	3	1	no	—
11	C₃×C₇×C₂₇	—	3	1	no	—
12	C₇×C₉⋊C₉	—	3	2	no	—
13	C₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
14	C₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
15	C₇×C₉²	—	3	1	no	—
16	C₃×C₂₇⋊C₃	C₃×C₇	1	1	yes	characteristic
17	C₉×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
18	C₃²⋊C₂₇	C₃×C₇	1	1	yes	characteristic
19	C₃²⋊C₂₇	C₃×C₇	1	1	yes	characteristic
20	C₃³×C₇	C₃×C₉	1	1	yes	characteristic
21	C₇×3₋¹⁺²	—	3	3	no	—
22	C₃×C₇×C₉	—	3	1	no	—
23	C₃×C₇×C₉	—	3	1	no	—
24	C₃×C₇×C₉	—	3	1	no	—
25	C₃×C₇×C₉	—	3	1	no	—
26	C₃×C₇×C₉	—	3	1	no	—
27	C₃×C₇×C₉	—	3	1	no	—
28	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×C₇×C₉	3₋¹⁺²	1	2	yes	—
30	C₇×C₂₇	—	3	3	no	—
31	C₇×C₂₇	—	9	1	no	—
32	C₇×C₂₇	—	9	1	no	—
33	C₃×3₋¹⁺²	C₇×C₉	1	1	yes	characteristic
34	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
35	C₂₇⋊C₃	—	3	3	no	—
36	C₃×C₂₇	—	3	1	no	—
37	C₃×C₂₇	—	3	1	no	—
38	C₃×C₂₇	—	3	1	no	—
39	C₉⋊C₉	—	3	2	no	—
40	C₃²⋊C₉	C₇×C₉	1	1	yes	characteristic
41	C₃²⋊C₉	C₇×C₉	1	1	yes	characteristic
42	C₉²	—	3	1	no	—
43	C₃²×C₇	—	3	1	no	—
44	C₃²×C₇	—	3	1	no	—
45	C₃²×C₇	—	3	1	no	—
46	C₃²×C₇	—	3	1	no	—
47	C₃²×C₇	C₃²⋊C₉	1	1	yes	characteristic
48	C₇×C₉	—	3	3	no	—
49	C₇×C₉	—	3	2	no	—
50	C₇×C₉	—	9	1	no	—
51	C₇×C₉	—	9	1	no	—
52	C₇×C₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
53	C₇×C₉	#731	1	1	yes	characteristic
54	C₇×C₉	#733	1	1	yes	characteristic
55	C₃³	C₃×C₇×C₉	1	1	yes	characteristic
56	3₋¹⁺²	—	3	3	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
64	C₃×C₉	C₇×3₋¹⁺²	1	2	yes	—
65	C₂₇	—	3	3	no	—
66	C₂₇	—	9	1	no	—
67	C₂₇	—	9	1	no	—
68	C₃×C₇	—	9	1	no	—
69	C₃×C₇	#6869	1	1	yes	characteristic
70	C₃×C₇	3₋¹⁺²⋊C₉	1	1	yes	characteristic
71	C₃×C₇	#6872	1	1	yes	characteristic
72	C₃×C₇	#6873	1	1	yes	characteristic
73	C₃²	—	3	1	no	—
74	C₃²	—	3	1	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	C₇×C₃²⋊C₉	1	1	yes	characteristic
78	C₉	—	3	3	no	—
79	C₉	—	3	2	no	—
80	C₉	—	9	1	no	—
81	C₉	—	9	1	no	—
82	C₉	C₇×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
83	C₉	C₇×#731	1	1	yes	characteristic
84	C₉	C₇×#733	1	1	yes	characteristic
85	C₇	#10624454	1	1	yes	characteristic, direct product factor, Sylow
86	C₃	—	9	1	no	—
87	C₃	C₇×#6869	1	1	yes	characteristic
88	C₃	C₇×3₋¹⁺²⋊C₉	1	1	yes	characteristic
89	C₃	C₇×#6872	1	1	yes	characteristic
90	C₃	C₇×#6873	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₇×C₉	H(3,𝔽₃)
commutator	C₃³	C₃×C₇×C₉
Frattini	C₃²×C₉	C₃²×C₇
socle	C₃²×C₇	C₃²⋊C₉
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₇×C₉ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. #10624454	C₇	direct (N × H)
85. C₇	#10624454	direct (N × H)

Subgroups — C7×#10624454 #19099863

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624454 #19099863