Subgroups — C₂×#19098403 #23765704

Order 10112.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic
2	#19098403	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₇₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₁₆	—	2	1	no	—
6	Dic₆₃₂	—	2	1	no	—
7	Dic₆₃₂	C₂²	1	2	yes	—
8	C₇₉⋊C₃₂	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₇₉	—	2	1	no	—
10	Q₃₂×C₇₉	—	2	1	no	—
11	Q₃₂×C₇₉	C₂²	1	2	yes	—
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₅₈	—	4	1	no	—
14	Dic₃₁₆	—	2	2	no	—
15	Dic₃₁₆	—	4	1	no	—
16	C₂×Q₈×C₇₉	—	4	1	no	—
17	Q₁₆×C₇₉	—	2	2	no	—
18	Q₁₆×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	Q₈×C₇₉	—	4	2	no	—
23	Q₈×C₇₉	—	8	1	no	—
24	C₂×C₄×C₇₉	—	8	1	no	—
25	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
26	C₂×Dic₇₉	—	8	1	no	—
27	Dic₁₅₈	—	4	2	no	—
28	Dic₁₅₈	—	8	1	no	—
29	C₈×C₇₉	D₈	1	1	yes	characteristic
30	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
32	C₄×C₇₉	—	8	2	no	—
33	C₄×C₇₉	D₁₆	1	1	yes	characteristic
34	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
35	Dic₇₉	—	8	2	no	—
36	C₂×C₇₉	Q₆₄	1	2	yes	complemented
37	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
38	C₂×Q₆₄	—	79	1	no	maximal, Sylow
39	C₇₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₃₂	—	79	1	no	—
41	C₂×Q₃₂	D₇₉	1	1	yes	characteristic
42	Q₆₄	—	79	4	no	—
43	C₂×C₃₂	—	79	1	no	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	—	158	1	no	—
46	Q₃₂	—	2	1	no	—
47	Q₃₂	—	79	2	no	—
48	Q₃₂	—	158	1	no	—
49	Q₃₂	C₂×D₇₉	1	2	yes	—
50	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
51	C₃₂	—	79	2	no	—
52	C₂×Q₈	—	4	1	no	—
53	C₂×Q₈	—	316	1	no	—
54	Q₁₆	—	2	2	no	—
55	Q₁₆	—	4	1	no	—
56	Q₁₆	—	316	1	no	—
57	Q₁₆	—	158	2	no	—
58	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
59	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
60	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	316	2	no	—
64	Q₈	—	632	1	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	632	1	no	—
67	C₂×C₄	#11929609	1	1	yes	characteristic
68	C₈	#11929609	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
70	C₂²	#14579102	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	632	2	no	—
73	C₄	#14579102	1	1	yes	characteristic
74	C₄	C₂×#11929609	1	1	yes	characteristic
75	C₂	#19098403	1	2	yes	direct product factor
76	C₂	C₂×#14579102	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579102
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	C₂×Q₃₂×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	D₁₆
hypercenter	C₂×Q₃₂	D₇₉
hypocenter	C₇₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #19098403	C₂	direct (N × H)
36. C₂×C₇₉	Q₆₄	semidirect
39. C₇₉	C₂×Q₆₄	semidirect
75. C₂	#19098403	direct (N × H)

Subgroups — C2×#19098403 #23765704

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098403 #23765704