Subgroups — C₃×C₇×#11760384 #36347952

Order 22050.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#11760384	C₃	1	3	yes	maximal, direct product factor
4	C₇²×C₅²⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#11760384	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₇×(C₅⋊D₅)⋊C₃	—	7	1	no	maximal
8	C₇×C₅⋊D₃₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₅²⋊C₃	—	2	3	no	—
10	C₃×C₇×C₅²⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₃×C₇×C₅²⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×C₇×D₃₅	—	15	2	no	—
13	C₅²×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅⋊D₃₅	C₃×C₇	1	1	yes	characteristic, complemented
15	C₃×C₇×C₅⋊D₅	—	7	1	no	—
16	#11760384	C₃×C₇	1	3	yes	direct product factor
17	C₇×(C₅⋊D₅)⋊C₃	—	7	3	no	—
18	C₃²×C₇×D₇	—	25	1	no	maximal, Hall
19	C₃×C₅×C₇²	—	3	2	no	—
20	C₃×C₅²×C₇	—	2	3	no	—
21	C₃×C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
22	C₃×C₅²×C₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₇×C₅²⋊C₃	—	2	9	no	—
24	C₇×C₅²⋊C₃	C₃×D₇	1	3	yes	complemented
25	C₇×C₅²⋊C₃	C₂×C₃×C₇	1	3	yes	complemented
26	C₇×D₃₅	—	15	2	no	—
27	C₃×(C₅⋊D₅)⋊C₃	—	7	1	no	Hall
28	C₃²×C₇²	—	25	1	no	Hall
29	C₅⋊D₃₅	C₃²×C₇	1	1	yes	characteristic, complemented
30	C₇×C₅⋊D₅	—	7	1	no	—
31	C₃×C₇×D₇	—	25	3	no	—
32	C₃×C₇×D₇	—	75	1	no	—
33	C₅×C₇²	—	3	2	no	—
34	C₃×C₅²⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
35	C₃×D₃₅	—	15	2	no	—
36	C₃×C₇×D₅	—	105	2	no	—
37	C₅²×C₇	—	2	3	no	—
38	C₅²×C₇	C₃²×D₇	1	1	yes	characteristic, complemented
39	C₅²×C₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
40	C₃×C₅⋊D₅	—	7	1	no	—
41	(C₅⋊D₅)⋊C₃	—	7	3	no	—
42	C₃×C₇²	—	25	3	no	—
43	C₃×C₇²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
44	C₂×C₃²×C₇	—	175	1	no	—
45	C₃²×D₇	—	25	1	no	—
46	C₃×C₅×C₇	—	3	2	no	—
47	C₃×C₅×C₇	—	3	2	no	—
48	C₃×C₅×C₇	—	6	6	no	—
49	C₇×D₇	—	75	1	no	Hall
50	C₃×C₅²	C₃×C₇×D₇	1	1	yes	characteristic, complemented
51	C₅²⋊C₃	C₃×C₇×D₇	1	3	yes	complemented
52	D₃₅	—	15	2	no	—
53	C₇×D₅	—	105	2	no	—
54	C₃²×C₇	—	25	1	no	—
55	C₃²×C₇	—	25	1	no	—
56	C₃²×C₇	—	50	3	no	—
57	C₅⋊D₅	—	7	1	no	Hall
58	C₇²	C₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	525	1	no	—
60	C₂×C₃×C₇	—	175	3	no	—
61	C₃×D₇	—	25	3	no	—
62	C₃×D₇	—	75	1	no	—
63	C₅×C₇	—	3	2	no	—
64	C₅×C₇	—	3	2	no	—
65	C₅×C₇	—	6	6	no	—
66	C₃×D₅	—	105	2	no	—
67	C₅²	C₃²×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
68	C₃×C₇	—	2	3	no	—
69	C₃×C₇	—	25	3	no	—
70	C₃×C₇	—	25	3	no	—
71	C₃×C₇	—	50	9	no	—
72	C₃×C₇	C₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
73	C₃×C₇	#11760384	1	1	yes	characteristic, direct product factor
74	C₂×C₃²	—	175	1	no	Hall
75	C₃×C₅	—	3	2	no	—
76	C₂×C₇	—	525	1	no	—
77	D₇	—	75	1	no	—
78	D₅	—	105	2	no	—
79	C₃²	—	25	1	no	Sylow
80	C₇	—	2	3	no	—
81	C₇	C₃×C₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
82	C₇	C₃×#11760384	1	1	yes	characteristic, direct product factor
83	C₂×C₃	—	525	1	no	—
84	C₂×C₃	—	175	3	no	—
85	C₅	—	3	2	no	—
86	C₃	—	25	3	no	—
87	C₃	C₇×#11760384	1	1	yes	characteristic, direct product factor
88	C₂	—	525	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	#11760384
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₅²⋊C₃	C₂	semidirect
2. C₃×C₇×C₅⋊D₃₅	C₃	semidirect
3. C₇×#11760384	C₃	direct (N × H)
4. C₇²×C₅²⋊C₃	C₂×C₃	semidirect
5. C₃×C₅²×C₇²	C₂×C₃	semidirect
6. C₃×#11760384	C₇	direct (N × H)
8. C₇×C₅⋊D₃₅	C₃²	semidirect
10. C₃×C₇×C₅²⋊C₃	D₇	semidirect
11. C₃×C₇×C₅²⋊C₃	C₂×C₇	semidirect
13. C₅²×C₇²	C₂×C₃²	semidirect
14. C₃×C₅⋊D₃₅	C₃×C₇	semidirect
16. #11760384	C₃×C₇	direct (N × H)
21. C₃×C₅²×C₇	C₃×D₇	semidirect
22. C₃×C₅²×C₇	C₂×C₃×C₇	semidirect
24. C₇×C₅²⋊C₃	C₃×D₇	semidirect
25. C₇×C₅²⋊C₃	C₂×C₃×C₇	semidirect
29. C₅⋊D₃₅	C₃²×C₇	semidirect
34. C₃×C₅²⋊C₃	C₇×D₇	semidirect
38. C₅²×C₇	C₃²×D₇	semidirect
39. C₅²×C₇	C₂×C₃²×C₇	semidirect
43. C₃×C₇²	(C₅⋊D₅)⋊C₃	semidirect
50. C₃×C₅²	C₃×C₇×D₇	semidirect
51. C₅²⋊C₃	C₃×C₇×D₇	semidirect
58. C₇²	C₃×(C₅⋊D₅)⋊C₃	semidirect
67. C₅²	C₃²×C₇×D₇	semidirect
72. C₃×C₇	C₇×(C₅⋊D₅)⋊C₃	semidirect
73. C₃×C₇	#11760384	direct (N × H)
81. C₇	C₃×C₇×(C₅⋊D₅)⋊C₃	semidirect
82. C₇	C₃×#11760384	direct (N × H)
87. C₃	C₇×#11760384	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇²×C₅²⋊C₃	2
C₃×C₇×C₅⋊D₃₅	3
C₇×#11760384	3
C₃×#11760384	7
C₃×C₇×(C₅⋊D₅)⋊C₃	7
C₃²×C₇×D₇	25

Subgroups — C3×C7×#11760384 #36347952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#11760384 #36347952