Subgroups — C₂×#19098398 #23765697

Order 10112.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098398	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₇₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₆₃₂	—	2	1	no	—
6	D₁₂₆₄	—	2	1	no	—
7	D₁₂₆₄	C₂²	1	2	yes	complemented
8	C₇₉⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₇₉	—	2	1	no	—
10	D₁₆×C₇₉	—	2	1	no	—
11	D₁₆×C₇₉	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×D₃₁₆	—	4	1	no	—
14	D₆₃₂	—	2	2	no	—
15	D₆₃₂	—	4	1	no	—
16	C₂×D₄×C₇₉	—	4	1	no	—
17	D₈×C₇₉	—	2	2	no	—
18	D₈×C₇₉	—	4	1	no	—
19	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
20	C₁₆×C₇₉	D₄	1	1	yes	characteristic
21	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
22	C₂³×C₇₉	—	8	1	no	—
23	C₂²×D₇₉	—	8	1	no	—
24	D₄×C₇₉	—	4	2	no	—
25	D₄×C₇₉	—	8	1	no	—
26	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
27	D₃₁₆	—	4	2	no	—
28	D₃₁₆	—	8	1	no	—
29	C₈×C₇₉	D₈	1	1	yes	characteristic
30	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₇₉	—	8	2	no	—
32	C₂²×C₇₉	—	16	2	no	—
33	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
34	C₂×D₇₉	—	8	2	no	—
35	C₂×D₇₉	—	16	2	no	—
36	C₄×C₇₉	D₁₆	1	1	yes	characteristic
37	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
38	C₂×C₇₉	—	16	2	no	—
39	C₂×C₇₉	D₃₂	1	2	yes	complemented
40	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
41	D₇₉	—	16	2	no	—
42	C₂×D₃₂	—	79	1	no	maximal, Sylow
43	C₇₉	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₁₆	—	79	1	no	—
45	C₂×D₁₆	D₇₉	1	1	yes	characteristic, complemented
46	D₃₂	—	79	4	no	—
47	C₂×C₃₂	—	79	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	158	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	79	2	no	—
52	D₁₆	—	158	1	no	—
53	D₁₆	C₂×D₇₉	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
55	C₃₂	—	79	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	316	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	316	1	no	—
61	D₈	—	158	2	no	—
62	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
64	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	632	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	316	2	no	—
70	D₄	—	632	1	no	—
71	C₂×C₄	#11929609	1	1	yes	characteristic
72	C₈	#11929609	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	632	2	no	—
77	C₂²	—	1264	2	no	—
78	C₂²	#14579102	1	1	yes	characteristic
79	C₄	#14579102	1	1	yes	characteristic
80	C₄	C₂×#11929609	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	1264	2	no	—
83	C₂	#19098398	1	2	yes	direct product factor
84	C₂	C₂×#14579102	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579102
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	C₂×D₁₆×C₇₉	C₂
socle	C₂²×C₇₉	D₁₆
hypercenter	C₂×D₁₆	D₇₉
hypocenter	C₇₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₂₆₄	C₂	semidirect
2. #19098398	C₂	direct (N × H)
3. C₂×C₇₉⋊C₃₂	C₂	semidirect
4. C₂×D₁₆×C₇₉	C₂	semidirect
7. D₁₂₆₄	C₂²	semidirect
8. C₇₉⋊C₃₂	C₂²	semidirect
11. D₁₆×C₇₉	C₂²	semidirect
39. C₂×C₇₉	D₃₂	semidirect
43. C₇₉	C₂×D₃₂	semidirect
45. C₂×D₁₆	D₇₉	semidirect
53. D₁₆	C₂×D₇₉	semidirect
83. C₂	#19098398	direct (N × H)

Subgroups — C2×#19098398 #23765697

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098398 #23765697