Subgroups — C₇×#10624830 #19100239

Order 5103.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6887	C₃	1	1	yes	maximal, characteristic
2	C₇×#6875	C₃	1	9	yes	maximal, complemented
3	C₇×#6869	C₃	1	3	yes	maximal
4	#10624830	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
6	C₇×C₂₇⋊C₃	C₃²	1	9	yes	—
7	C₇×C₉⋊C₉	—	3	1	no	—
8	C₇×C₉⋊C₉	C₃²	1	3	yes	—
9	C₇×C₃²⋊C₉	—	3	1	no	—
10	C₇×C₉²	—	3	1	no	—
11	#6887	C₃×C₇	1	1	yes	characteristic
12	#6875	C₃×C₇	1	9	yes	complemented
13	#6869	C₃×C₇	1	3	yes	—
14	C₃³×C₇	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₇×C₉	—	3	3	no	—
16	C₃×C₇×C₉	—	3	3	no	—
17	C₃×C₇×C₉	3₋¹⁺²	1	1	yes	characteristic
18	C₃×C₇×C₉	3₋¹⁺²	1	1	yes	characteristic
19	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
20	C₇×C₂₇	—	3	9	no	—
21	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
22	C₂₇⋊C₃	C₃²×C₇	1	9	yes	—
23	C₉⋊C₉	—	3	1	no	—
24	C₉⋊C₉	C₃²×C₇	1	3	yes	—
25	C₃²⋊C₉	—	3	1	no	—
26	C₉²	—	3	1	no	—
27	C₃²×C₇	—	3	1	no	—
28	C₃²×C₇	—	9	1	no	—
29	C₃²×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₇×C₉	—	3	1	no	—
31	C₇×C₉	—	3	1	no	—
32	C₇×C₉	—	9	3	no	—
33	C₇×C₉	#737	1	3	yes	—
34	C₃³	C₇×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	C₇×3₋¹⁺²	1	1	yes	characteristic
38	C₃×C₉	C₇×3₋¹⁺²	1	1	yes	characteristic
39	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
40	C₂₇	—	3	9	no	—
41	C₃×C₇	—	3	1	no	—
42	C₃×C₇	—	9	1	no	—
43	C₃×C₇	#6895	1	1	yes	characteristic
44	C₃²	—	3	1	no	—
45	C₃²	—	9	1	no	—
46	C₃²	C₃×C₇×3₋¹⁺²	1	1	yes	characteristic
47	C₉	—	3	1	no	—
48	C₉	—	3	1	no	—
49	C₉	—	9	3	no	—
50	C₉	C₇×#737	1	3	yes	—
51	C₇	#10624830	1	1	yes	characteristic, direct product factor, Sylow
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	C₇×#6895	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	#6895
commutator, Frattini	C₃×C₉	C₃³×C₇
LCS	G ▷ C₃×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#6875	C₃	semidirect
4. #10624830	C₇	direct (N × H)
12. #6875	C₃×C₇	semidirect
51. C₇	#10624830	direct (N × H)

Subgroups — C7×#10624830 #19100239

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624830 #19100239