Subgroups — C₃×#455 #5329

Order 192.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₃×#137	C₂	1	2	yes	maximal, complemented
3	C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	C₂	1	2	yes	maximal, complemented
5	C₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
6	#455	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	2	no	—
8	C₃×#41	C₂²	1	2	yes	—
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
10	C₂×C₃×D₄	—	2	2	no	—
11	C₂×C₃×D₄	—	2	2	no	—
12	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₃×Q₁₆	—	2	2	no	—
14	C₃×SD₁₆	—	2	2	no	—
15	C₃×M₁₆	C₂²	1	2	yes	complemented
16	C₃×C₂²⋊C₄	—	2	2	no	—
17	C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
18	H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
19	#137	C₂×C₃	1	2	yes	complemented
20	#124	C₂×C₃	1	1	yes	characteristic, complemented
21	#104	C₂×C₃	1	2	yes	complemented
22	#100	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	2	no	—
24	C₂³×C₃	D₄	1	2	yes	—
25	C₃×Q₈	—	2	2	no	—
26	C₃×Q₈	D₄	1	2	yes	—
27	C₃×D₄	—	2	4	no	—
28	C₃×D₄	—	2	2	no	—
29	C₃×D₄	—	2	2	no	—
30	C₃×D₄	D₄	1	2	yes	—
31	C₂×C₃×C₄	—	2	2	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	2	1	no	—
35	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
36	C₃×C₈	—	2	2	no	—
37	#41	—	2	2	no	—
38	#41	C₂²×C₃	1	2	yes	—
39	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
40	C₂×D₄	—	2	2	no	—
41	C₂×D₄	—	2	2	no	—
42	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
43	Q₁₆	—	2	2	no	—
44	SD₁₆	—	2	2	no	—
45	M₁₆	C₂²×C₃	1	2	yes	complemented
46	C₂²⋊C₄	—	2	2	no	—
47	C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	2	2	no	—
49	C₂²×C₃	—	2	2	no	—
50	C₂²×C₃	—	4	2	no	—
51	C₂²×C₃	—	8	2	no	—
52	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	C₂×D₄	1	2	yes	—
57	C₂³	—	2	2	no	—
58	C₂³	C₃×D₄	1	2	yes	—
59	Q₈	—	2	2	no	—
60	Q₈	C₃×D₄	1	2	yes	—
61	D₄	—	2	4	no	—
62	D₄	—	2	2	no	—
63	D₄	—	2	2	no	—
64	D₄	C₃×D₄	1	2	yes	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	—	4	2	no	—
73	C₂×C₃	—	4	2	no	—
74	C₂×C₃	#120	1	1	yes	characteristic
75	C₂²	—	2	2	no	—
76	C₂²	—	2	2	no	—
77	C₂²	—	4	2	no	—
78	C₂²	—	8	2	no	—
79	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	4	1	no	—
83	C₄	C₂×C₃×D₄	1	2	yes	—
84	C₃	#455	1	1	yes	characteristic, direct product factor, Sylow
85	C₂	—	2	1	no	—
86	C₂	—	4	2	no	—
87	C₂	—	4	2	no	—
88	C₂	C₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#120
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₃×H(5,𝔽₂)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#137	C₂	semidirect
3. C₃×#124	C₂	semidirect
4. C₃×#104	C₂	semidirect
5. C₃×#100	C₂	semidirect
6. #455	C₃	direct (N × H)
9. C₂×C₃×Q₈	C₂²	semidirect
15. C₃×M₁₆	C₂²	semidirect
17. C₃×C₄²	C₂²	semidirect
19. #137	C₂×C₃	semidirect
20. #124	C₂×C₃	semidirect
21. #104	C₂×C₃	semidirect
22. #100	C₂×C₃	semidirect
39. C₂×Q₈	C₂²×C₃	semidirect
45. M₁₆	C₂²×C₃	semidirect
47. C₄²	C₂²×C₃	semidirect
84. C₃	#455	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×H(5,𝔽₂)	2
C₃×#137	2
C₃×#124	2
C₃×#104	2
C₃×#100	2
#455	3

Subgroups — C3×#455 #5329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#455 #5329