Subgroups — #23761471

Order 10112.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19098316	C₂	1	1	yes	maximal, characteristic
3	#335×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₄⋊C₈×C₇₉	—	2	1	no	—
8	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₈	—	4	1	no	—
10	C₇₉⋊C₁₆	—	2	1	no	—
11	C₇₉⋊C₁₆	C₈	1	2	yes	complemented
12	C₂×C₈×C₇₉	—	4	1	no	—
13	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
15	C₄²×C₇₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
18	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
19	C₈×C₇₉	—	2	1	no	—
20	C₈×C₇₉	—	8	1	no	—
21	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
22	C₈×C₇₉	M₁₆	1	1	yes	characteristic
23	C₇₉⋊C₈	—	8	1	no	—
24	C₂²×C₇₉	#107	1	1	yes	characteristic
25	C₄×C₇₉	—	2	1	no	—
26	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₇₉	#108	1	1	yes	characteristic
28	C₄×C₇₉	D₁₆	1	1	yes	characteristic
29	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
30	C₂×C₇₉	#335	1	1	yes	characteristic
31	C₂×C₇₉	#366	1	1	yes	characteristic
32	C₂×C₇₉	#368	1	1	yes	characteristic
33	#1371	—	79	1	no	maximal, Sylow
34	C₇₉	#1371	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₁₆	—	79	1	no	—
36	#335	—	79	1	no	—
37	#335	D₇₉	1	1	yes	characteristic
38	C₂×C₁₆	—	79	1	no	—
39	C₂×C₁₆	—	79	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	158	1	no	—
42	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	316	1	no	—
45	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
46	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
47	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
48	C₁₆	—	79	2	no	—
49	C₁₆	—	158	1	no	—
50	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
51	C₂×C₄	#11929609	1	1	yes	characteristic
52	C₂×C₄	#11929614	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	632	1	no	—
56	C₈	C₈×D₇₉	1	1	yes	characteristic
57	C₈	#11929607	1	1	yes	characteristic
58	C₂²	#14579094	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	Dic₇₉⋊C₈	1	1	yes	characteristic
61	C₄	#14579096	1	1	yes	characteristic
62	C₄	#14579102	1	1	yes	characteristic
63	C₄	#14579107	1	1	yes	characteristic
64	C₂	#19098315	1	1	yes	characteristic
65	C₂	#19098388	1	1	yes	characteristic
66	C₂	#19098392	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11929609
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#335×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#107
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#335	D₇₉
hypocenter	C₇₉	#1371
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. C₇₉⋊C₁₆	C₈	semidirect
34. C₇₉	#1371	semidirect