Subgroups — #34219475

Order 20224.

2286 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098433	C₂	1	14	yes	maximal
2	C₂×C₄³×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊Dic₇₉	C₂²	1	28	yes	—
4	#19098433	—	2	56	no	—
5	C₂²×C₄²×C₇₉	C₂²	1	7	yes	—
6	C₄³×C₇₉	C₄	1	8	yes	complemented
7	C₂³×Dic₇₉	C₂³	1	8	yes	—
8	C₂×C₄⋊Dic₇₉	—	2	168	no	—
9	C₂³×C₄×C₇₉	C₂³	1	7	yes	—
10	C₂×C₄²×C₇₉	C₂×C₄	1	28	yes	—
11	C₂×C₄²×C₇₉	D₄	1	28	yes	—
12	C₂×C₄²×C₇₉	Q₈	1	28	yes	—
13	C₂²×Dic₇₉	—	2	56	no	—
14	C₄⋊Dic₇₉	—	4	112	no	—
15	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
16	C₂²×C₄×C₇₉	C₂²×C₄	1	14	yes	—
17	C₂²×C₄×C₇₉	C₂×D₄	1	42	yes	—
18	C₂²×C₄×C₇₉	C₂×Q₈	1	42	yes	—
19	C₄²×C₇₉	C₄⋊C₄	1	112	yes	complemented
20	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
21	C₂³×C₇₉	C₂²×D₄	1	7	yes	—
22	C₂³×C₇₉	C₂²×Q₈	1	7	yes	—
23	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	84	yes	—
24	C₂×C₄×C₇₉	#127	1	28	yes	—
25	C₂×C₄×C₇₉	C₄⋊Q₈	1	84	yes	—
26	C₂×Dic₇₉	—	4	56	no	—
27	C₂²×C₇₉	C₂²×C₄⋊C₄	1	7	yes	—
28	C₂²×C₇₉	C₂×#127	1	7	yes	—
29	C₂²×C₇₉	C₂×C₄⋊Q₈	1	21	yes	—
30	C₄×C₇₉	#384	1	56	yes	complemented
31	Dic₇₉	—	8	8	no	—
32	#14692	—	79	1	no	maximal, Sylow
33	C₂×C₇₉	C₂×#384	1	7	yes	—
34	C₂×C₇₉	#2867	1	1	yes	characteristic
35	C₂×C₇₉	#2868	1	7	yes	—
36	C₂×#384	—	79	14	no	—
37	C₂×C₄³	D₇₉	1	1	yes	characteristic
38	C₇₉	#14692	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄⋊C₄	—	79	28	no	—
40	C₂²×C₄²	C₂×D₇₉	1	7	yes	—
41	#384	—	158	56	no	—
42	C₄³	Dic₇₉	1	8	yes	complemented
43	C₂³×C₄	—	79	8	no	—
44	C₂³×C₄	C₂²×D₇₉	1	7	yes	—
45	C₂×C₄⋊C₄	—	158	168	no	—
46	C₂×C₄²	Dic₁₅₈	1	28	yes	—
47	C₂×C₄²	D₃₁₆	1	28	yes	—
48	C₂×C₄²	C₂×Dic₇₉	1	28	yes	—
49	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
50	C₂²×C₄	—	158	56	no	—
51	C₂²×C₄	C₂²×Dic₇₉	1	14	yes	—
52	C₂²×C₄	C₂×D₃₁₆	1	42	yes	—
53	C₂²×C₄	C₂×Dic₁₅₈	1	42	yes	—
54	C₄⋊C₄	—	316	112	no	—
55	C₄²	C₄⋊Dic₇₉	1	112	yes	complemented
56	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
57	C₂³	C₂²×D₃₁₆	1	7	yes	—
58	C₂³	C₂²×Dic₁₅₈	1	7	yes	—
59	C₂×C₄	—	316	56	no	—
60	C₂×C₄	C₂×C₄⋊Dic₇₉	1	84	yes	—
61	C₂×C₄	#14579158	1	28	yes	—
62	C₂×C₄	#14579161	1	84	yes	—
63	C₂²	C₂²×C₄⋊Dic₇₉	1	7	yes	—
64	C₂²	C₂×#14579158	1	7	yes	—
65	C₂²	C₂×#14579161	1	21	yes	—
66	C₄	—	632	8	no	—
67	C₄	#19098433	1	56	yes	complemented
68	C₂	C₂×#19098433	1	7	yes	—
69	C₂	#23771795	1	1	yes	characteristic
70	C₂	#23771798	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₇₉
commutator	C₂³×C₇₉	C₂³×C₄
Fitting	C₂×C₄³×C₇₉	C₂
socle, prime radical, cosocle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂×C₄³	D₇₉
hypocenter	C₇₉	#14692
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
6. C₄³×C₇₉	C₄	semidirect
19. C₄²×C₇₉	C₄⋊C₄	semidirect
30. C₄×C₇₉	#384	semidirect
38. C₇₉	#14692	semidirect
42. C₄³	Dic₇₉	semidirect
55. C₄²	C₄⋊Dic₇₉	semidirect
67. C₄	#19098433	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098433	2
C₂×C₄³×C₇₉	2
#14692	79