Subgroups — #23761593

Order 10112.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098397	C₂	1	1	yes	maximal, characteristic
2	#19098393	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579097	—	2	1	no	—
5	C₇₉⋊C₃₂	—	2	1	no	—
6	C₂×Q₁₆×C₇₉	—	2	1	no	—
7	Q₃₂×C₇₉	—	2	1	no	—
8	Q₃₂×C₇₉	C₄	1	2	yes	—
9	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	#11929608	—	4	1	no	—
11	C₂×Q₈×C₇₉	—	4	1	no	—
12	Q₁₆×C₇₉	—	2	2	no	—
13	Q₁₆×C₇₉	—	4	1	no	—
14	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
15	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₉	D₄	1	1	yes	characteristic
17	Q₈×C₇₉	—	4	2	no	—
18	Q₈×C₇₉	—	8	1	no	—
19	C₂×C₄×C₇₉	—	8	1	no	—
20	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
21	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
23	C₇₉⋊C₈	—	8	1	no	—
24	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
25	C₄×C₇₉	—	8	2	no	—
26	C₄×C₇₉	#102	1	1	yes	characteristic
27	C₄×C₇₉	D₁₆	1	1	yes	characteristic
28	C₂×C₇₉	—	2	1	no	—
29	C₂×C₇₉	#357	1	1	yes	characteristic
30	#1420	—	79	1	no	maximal, Sylow
31	C₇₉	#1420	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₃₂	D₇₉	1	1	yes	characteristic
33	M₆₄	—	79	1	no	—
34	#368	—	79	1	no	—
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	Dic₇₉	1	2	yes	—
38	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
39	#108	—	158	1	no	—
40	C₃₂	—	158	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	316	1	no	—
45	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
46	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#11929609	1	1	yes	characteristic
52	C₈	—	632	1	no	—
53	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
54	C₈	#11929612	1	1	yes	characteristic
55	C₂²	#14579105	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#14579082	1	1	yes	characteristic
58	C₄	#14579102	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#19098364	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098364
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	C₂×Q₃₂×C₇₉	C₂
socle	C₂×C₇₉	#357
prime radical	C₂²×C₇₉	SD₃₂
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	C₂×Q₃₂	D₇₉
hypocenter	C₇₉	#1420
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
31. C₇₉	#1420	semidirect