Subgroups — C₃⋊#20301299 #36348019

Order 22050.

260 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⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	C₃	1	1	yes	maximal, characteristic, complemented
3	#20301299	—	3	1	no	maximal
4	C₇²×C₅²⋊C₃	—	2	1	no	—
5	C₇²×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊#11760384	—	7	1	no	maximal
8	C₃⋊#11760384	—	7	7	no	maximal
9	C₅⋊(C₅⋊(C₇⋊D₇))	—	3	1	no	Hall
10	C₃×C₇×C₅²⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₃×C₇×C₅²⋊C₃	D₇	1	7	yes	complemented
12	C₃⋊(C₅⋊(C₇⋊D₇))	—	15	2	no	—
13	C₅²×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
15	C₃⋊(C₅⋊D₃₅)	—	7	7	no	—
16	#11760384	—	21	1	no	—
17	#11760384	—	21	7	no	—
18	C₃×C₃⋊(C₇⋊D₇)	—	25	1	no	maximal, Hall
19	C₃×C₅×C₇²	—	3	2	no	—
20	C₃×C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×C₅²×C₇	C₃×D₇	1	7	yes	complemented
22	C₇×C₅²⋊C₃	—	2	1	no	—
23	C₇×C₅²⋊C₃	—	2	7	no	—
24	C₇×C₅²⋊C₃	D₂₁	1	1	yes	characteristic, complemented
25	C₇×C₅²⋊C₃	D₂₁	1	7	yes	complemented
26	C₅⋊(C₇⋊D₇)	—	45	2	no	—
27	C₃⋊((C₅⋊D₅)⋊C₃)	—	49	1	no	Hall
28	C₃²×C₇²	—	50	1	no	Hall
29	C₅⋊D₃₅	—	21	1	no	—
30	C₅⋊D₃₅	—	21	7	no	—
31	C₃⋊(C₇⋊D₇)	—	25	1	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	D₁₀₅	—	105	2	no	—
36	D₁₀₅	—	105	14	no	—
37	C₅²×C₇	C₃×D₂₁	1	1	yes	characteristic, complemented
38	C₅²×C₇	C₃×D₂₁	1	7	yes	complemented
39	C₃⋊(C₅⋊D₅)	—	49	1	no	—
40	(C₅⋊D₅)⋊C₃	—	147	1	no	—
41	C₃×C₇²	—	50	1	no	—
42	C₃×C₇²	—	50	1	no	—
43	C₃×C₇²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
44	C₃×D₂₁	—	175	1	no	—
45	C₃×D₂₁	—	175	7	no	—
46	C₃×C₅×C₇	—	3	2	no	—
47	C₃×C₅×C₇	—	3	14	no	—
48	C₇⋊D₇	—	75	1	no	Hall
49	C₃×C₅²	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
50	C₅²⋊C₃	—	2	1	no	—
51	C₅²⋊C₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
52	D₃₅	—	315	2	no	—
53	D₃₅	—	315	14	no	—
54	C₃²×C₇	—	50	1	no	—
55	C₃²×C₇	—	50	7	no	—
56	C₅⋊D₅	—	147	1	no	Hall
57	C₇²	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented, Sylow
58	D₂₁	—	175	1	no	—
59	D₂₁	—	175	7	no	—
60	C₃×D₇	—	525	1	no	—
61	C₃×D₇	—	525	7	no	—
62	C₅×C₇	—	3	2	no	—
63	C₅×C₇	—	3	14	no	—
64	D₁₅	—	735	2	no	—
65	C₅²	C₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
66	C₃×C₇	—	25	1	no	—
67	C₃×C₇	—	50	7	no	—
68	C₃×C₇	—	50	1	no	—
69	C₃×C₇	—	50	7	no	—
70	C₃×C₇	#11760384	1	1	yes	characteristic, complemented
71	C₃×C₇	#11760384	1	7	yes	complemented
72	C₃×D₃	—	1225	1	no	Hall
73	C₃×C₅	—	3	2	no	—
74	D₇	—	525	1	no	—
75	D₇	—	525	7	no	—
76	D₅	—	2205	2	no	—
77	C₃²	—	50	1	no	Sylow
78	C₇	C₃⋊#11760384	1	1	yes	characteristic, complemented
79	C₇	C₃⋊#11760384	1	7	yes	complemented
80	C₂×C₃	—	3675	1	no	—
81	D₃	—	1225	1	no	—
82	C₅	—	3	2	no	—
83	C₃	—	50	1	no	—
84	C₃	—	50	1	no	—
85	C₃	#20301299	1	1	yes	characteristic, complemented
86	C₂	—	3675	1	no	Sylow

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

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⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	C₃	semidirect
5. C₇²×C₅²⋊C₃	D₃	semidirect
6. C₃×C₅²×C₇²	C₂×C₃	semidirect
10. C₃×C₇×C₅²⋊C₃	D₇	semidirect
11. C₃×C₇×C₅²⋊C₃	D₇	semidirect
13. C₅²×C₇²	C₃×D₃	semidirect
20. C₃×C₅²×C₇	C₃×D₇	semidirect
21. C₃×C₅²×C₇	C₃×D₇	semidirect
24. C₇×C₅²⋊C₃	D₂₁	semidirect
25. C₇×C₅²⋊C₃	D₂₁	semidirect
34. C₃×C₅²⋊C₃	C₇⋊D₇	semidirect
37. C₅²×C₇	C₃×D₂₁	semidirect
38. C₅²×C₇	C₃×D₂₁	semidirect
43. C₃×C₇²	(C₅⋊D₅)⋊C₃	semidirect
49. C₃×C₅²	C₃×C₇⋊D₇	semidirect
51. C₅²⋊C₃	C₃⋊(C₇⋊D₇)	semidirect
57. C₇²	C₃⋊((C₅⋊D₅)⋊C₃)	semidirect
65. C₅²	C₃×C₃⋊(C₇⋊D₇)	semidirect
70. C₃×C₇	#11760384	semidirect
71. C₃×C₇	#11760384	semidirect
78. C₇	C₃⋊#11760384	semidirect
79. C₇	C₃⋊#11760384	semidirect
85. C₃	#20301299	semidirect

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⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	3
#20301299	3
C₃⋊#11760384	7
C₃×C₃⋊(C₇⋊D₇)	25

Subgroups — C3⋊#20301299 #36348019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#20301299 #36348019