Subgroups — C₂×#953 #5840

Order 192.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#67	C₂	1	3	yes	maximal, complemented
3	#953	C₂	1	8	yes	maximal, direct product factor
4	C₂×#217	C₂	1	3	yes	maximal, complemented
5	C₂×#120	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	—	2	12	no	—
7	C₂⁴×C₃	C₂²	1	3	yes	—
8	C₂⁴×C₃	C₂²	1	4	yes	complemented
9	C₂³×D₃	C₂²	1	1	yes	characteristic, complemented
10	C₂×#67	—	2	12	no	—
11	C₂×#67	C₂²	1	12	yes	complemented
12	C₂²×Dic₃	C₂²	1	3	yes	complemented
13	#217	C₂²	1	12	yes	complemented
14	C₂⁵	D₃	1	1	yes	characteristic, complemented
15	C₂²×D₄	—	3	3	no	—
16	#120	—	3	8	no	—
17	C₂×C₂²⋊C₄	—	3	3	no	—
18	C₂³×C₃	—	2	32	no	—
19	C₂³×C₃	—	2	12	no	—
20	C₂³×C₃	—	2	24	no	—
21	C₂³×C₃	D₄	1	12	yes	complemented
22	C₂³×C₃	C₂³	1	6	yes	—
23	C₂³×C₃	C₂³	1	1	yes	characteristic
24	C₂²×D₃	—	2	6	no	—
25	C₂²×D₃	C₂³	1	2	yes	complemented
26	#67	—	2	24	no	—
27	C₂×Dic₃	—	2	6	no	—
28	C₂×Dic₃	C₂³	1	6	yes	complemented
29	C₂⁴	—	2	12	no	—
30	C₂⁴	—	3	1	no	—
31	C₂⁴	C₂×D₃	1	3	yes	—
32	C₂⁴	C₂×D₃	1	4	yes	complemented
33	C₂×D₄	—	3	12	no	—
34	C₂×D₄	—	6	12	no	—
35	C₂²×C₄	—	3	3	no	—
36	C₂²⋊C₄	—	3	12	no	—
37	C₂²×C₃	—	2	32	no	—
38	C₂²×C₃	—	2	24	no	—
39	C₂²×C₃	—	2	12	no	—
40	C₂²×C₃	C₂×D₄	1	6	yes	—
41	C₂²×C₃	C₂×D₄	1	12	yes	complemented
42	C₂²×C₃	C₂⁴	1	1	yes	characteristic
43	C₂×D₃	—	2	6	no	—
44	C₂×D₃	—	4	4	no	—
45	Dic₃	—	2	6	no	—
46	C₂³	—	2	32	no	—
47	C₂³	—	2	12	no	—
48	C₂³	—	2	24	no	—
49	C₂³	—	3	2	no	—
50	C₂³	—	6	6	no	—
51	C₂³	#67	1	12	yes	complemented
52	C₂³	C₂²×D₃	1	6	yes	—
53	C₂³	C₂²×D₃	1	1	yes	characteristic
54	D₄	—	6	24	no	—
55	C₂×C₄	—	3	6	no	—
56	C₂×C₄	—	6	6	no	—
57	C₂×C₃	—	2	12	no	—
58	C₂×C₃	#120	1	4	yes	complemented
59	C₂×C₃	C₂²×D₄	1	3	yes	—
60	D₃	—	4	2	no	—
61	C₂²	—	2	32	no	—
62	C₂²	—	2	24	no	—
63	C₂²	—	2	12	no	—
64	C₂²	—	6	6	no	—
65	C₂²	—	12	4	no	—
66	C₂²	C₂×#67	1	6	yes	—
67	C₂²	C₂×#67	1	12	yes	complemented
68	C₂²	C₂³×D₃	1	1	yes	characteristic
69	C₄	—	6	6	no	—
70	C₃	C₂×#120	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	2	12	no	—
72	C₂	—	12	2	no	—
73	C₂	#953	1	4	yes	direct product factor
74	C₂	C₂²×#67	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂⁵×C₃	C₂
socle	C₂³×C₃	C₂³
hypercenter	C₂⁵	D₃
hypocenter	C₃	C₂×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₃	C₂	semidirect
2. C₂²×#67	C₂	semidirect
3. #953	C₂	direct (N × H)
4. C₂×#217	C₂	semidirect
8. C₂⁴×C₃	C₂²	semidirect
9. C₂³×D₃	C₂²	semidirect
11. C₂×#67	C₂²	semidirect
12. C₂²×Dic₃	C₂²	semidirect
13. #217	C₂²	semidirect
14. C₂⁵	D₃	semidirect
21. C₂³×C₃	D₄	semidirect
25. C₂²×D₃	C₂³	semidirect
28. C₂×Dic₃	C₂³	semidirect
32. C₂⁴	C₂×D₃	semidirect
41. C₂²×C₃	C₂×D₄	semidirect
51. C₂³	#67	semidirect
58. C₂×C₃	#120	semidirect
67. C₂²	C₂×#67	semidirect
70. C₃	C₂×#120	semidirect
73. C₂	#953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃	2
C₂²×#67	2
#953	2
C₂×#217	2
C₂×#120	3

Subgroups — C2×#953 #5840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#953 #5840