Subgroups — #34219471

Order 20224.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761627	C₂	1	14	yes	maximal
2	C₂×C₄³×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇₉⋊#95	C₂²	1	28	yes	—
4	C₂²×C₄²×C₇₉	C₂²	1	7	yes	—
5	C₄³×C₇₉	C₄	1	8	yes	complemented
6	C₂³×Dic₇₉	C₂³	1	8	yes	—
7	C₇₉⋊#95	—	2	56	no	—
8	C₂³×C₄×C₇₉	C₂³	1	7	yes	—
9	C₂×C₄²×C₇₉	—	2	28	no	—
10	C₂×C₄²×C₇₉	C₂×C₄	1	28	yes	—
11	C₂²×Dic₇₉	—	2	56	no	—
12	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₇₉	—	2	28	no	—
14	C₂²×C₄×C₇₉	C₂²×C₄	1	14	yes	—
15	C₂²×C₄×C₇₉	#41	1	28	yes	—
16	C₄²×C₇₉	—	2	56	no	—
17	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
18	C₂³×C₇₉	C₂×#41	1	14	yes	—
19	C₂×C₄×C₇₉	—	2	28	no	—
20	C₂×C₄×C₇₉	—	2	56	no	—
21	C₂×C₄×C₇₉	#117	1	28	yes	—
22	C₂×Dic₇₉	—	4	56	no	—
23	C₂²×C₇₉	C₂×#117	1	7	yes	—
24	C₂²×C₇₉	#529	1	28	yes	—
25	C₄×C₇₉	—	2	28	no	—
26	Dic₇₉	—	8	8	no	—
27	#14690	—	79	1	no	maximal, Sylow
28	C₂×C₇₉	#2283	1	7	yes	—
29	C₂×C₇₉	#2865	1	8	yes	—
30	C₂×C₄³	D₇₉	1	1	yes	characteristic
31	#1434	—	79	14	no	—
32	C₇₉	#14690	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄²	C₂×D₇₉	1	7	yes	—
34	C₂×#95	—	79	28	no	—
35	C₄³	Dic₇₉	1	8	yes	complemented
36	C₂³×C₄	—	79	8	no	—
37	C₂³×C₄	C₂²×D₇₉	1	7	yes	—
38	C₂×C₄²	—	2	28	no	—
39	C₂×C₄²	C₂×Dic₇₉	1	28	yes	—
40	#95	—	158	56	no	—
41	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
42	C₂²×C₄	—	2	28	no	—
43	C₂²×C₄	—	158	56	no	—
44	C₂²×C₄	C₂²×Dic₇₉	1	14	yes	—
45	C₂²×C₄	#11929624	1	28	yes	—
46	C₄²	—	2	56	no	—
47	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
48	C₂³	C₂×#11929624	1	14	yes	—
49	C₂×C₄	—	2	28	no	—
50	C₂×C₄	—	2	56	no	—
51	C₂×C₄	—	316	56	no	—
52	C₂×C₄	#14579120	1	28	yes	—
53	C₂²	C₂×#14579120	1	7	yes	—
54	C₂²	#19099097	1	28	yes	—
55	C₄	—	2	28	no	—
56	C₄	—	632	8	no	—
57	C₂	#23765798	1	7	yes	—
58	C₂	#23771789	1	8	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	#14690
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
5. C₄³×C₇₉	C₄	semidirect
32. C₇₉	#14690	semidirect
35. C₄³	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23761627	2
C₂×C₄³×C₇₉	2
#14690	79