Subgroups — #34176076

Order 20224.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761611	C₂	1	2	yes	maximal
2	C₇₉×#1397	C₂	1	1	yes	maximal, characteristic
3	C₇₉⋊C₆₄	C₄	1	4	yes	complemented
4	C₂×C₃₂×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₇₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₇₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₇₉	C₈	1	1	yes	characteristic
10	C₃₂×C₇₉	C₈	1	2	yes	—
11	C₃₂×C₇₉	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₇₉	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₇₉	C₁₆	1	1	yes	characteristic
15	C₁₆×C₇₉	C₁₆	1	2	yes	—
16	C₁₆×C₇₉	C₄²	1	1	yes	characteristic
17	C₁₆×C₇₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₇₉	—	2	1	no	—
19	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₇₉	—	2	1	no	—
21	C₈×C₇₉	C₄×C₈	1	1	yes	characteristic
22	C₈×C₇₉	C₂×C₁₆	1	1	yes	characteristic
23	C₂²×C₇₉	M₆₄	1	1	yes	characteristic
24	C₄×C₇₉	—	4	1	no	—
25	C₄×C₇₉	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₇₉	M₆₄	1	1	yes	characteristic
27	#7511	—	79	1	no	maximal, Sylow
28	C₂×C₇₉	—	2	1	no	—
29	C₂×C₇₉	#1397	1	1	yes	characteristic
30	M₁₂₈	—	79	2	no	—
31	#1397	D₇₉	1	1	yes	characteristic
32	C₇₉	#7511	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	Dic₇₉	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
35	C₄×C₁₆	Dic₇₉	1	1	yes	characteristic
36	C₆₄	—	79	4	no	—
37	C₂×C₁₆	C₇₉⋊C₈	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
39	C₄×C₈	C₇₉⋊C₈	1	1	yes	characteristic
40	C₃₂	C₇₉⋊C₈	1	2	yes	—
41	C₃₂	C₄×D₇₉	1	2	yes	—
42	C₂×C₈	C₇₉⋊C₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
44	C₄²	C₇₉⋊C₁₆	1	1	yes	characteristic
45	C₁₆	C₇₉⋊C₁₆	1	2	yes	—
46	C₁₆	C₄×Dic₇₉	1	1	yes	characteristic
47	C₁₆	C₂×C₇₉⋊C₈	1	1	yes	characteristic
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	C₂×C₇₉⋊C₁₆	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	C₄×C₇₉⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₇₉⋊C₁₆	1	1	yes	characteristic
53	C₂²	#19098397	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×C₇₉⋊C₁₆	1	1	yes	characteristic
56	C₄	#19098397	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#23761534	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₇₉
commutator	C₄×C₇₉	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₇₉×#1397	C₂
socle	C₂×C₇₉	#1397
prime radical	C₂²×C₇₉	M₆₄
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	#1397	D₇₉
hypocenter	C₇₉	#7511
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
3. C₇₉⋊C₆₄	C₄	semidirect
32. C₇₉	#7511	semidirect

Maximal subgroups

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

subgroup	index
#23761611	2
C₇₉×#1397	2
#7511	79