Subgroups — C₇₉×#7531 #34119220

Order 20224.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#1709	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#1411	C₂	1	2	yes	maximal, complemented
3	#494×C₇₉	C₂²	1	1	yes	characteristic
4	#493×C₇₉	C₄	1	1	yes	characteristic
5	#486×C₇₉	—	2	2	no	—
6	#356×C₇₉	—	2	2	no	—
7	C₈²×C₇₉	C₄	1	1	yes	characteristic
8	C₂×Q₁₆×C₇₉	—	4	1	no	—
9	C₂×D₈×C₇₉	—	4	1	no	—
10	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
11	#127×C₇₉	—	2	1	no	—
12	#102×C₇₉	—	4	4	no	—
13	#101×C₇₉	—	4	2	no	—
14	C₄×C₈×C₇₉	—	2	1	no	—
15	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₂×Q₈×C₇₉	—	2	2	no	—
17	C₂×D₄×C₇₉	—	4	2	no	—
18	C₂×D₄×C₇₉	—	4	1	no	—
19	Q₁₆×C₇₉	—	8	2	no	—
20	D₈×C₇₉	—	8	2	no	—
21	M₁₆×C₇₉	—	8	2	no	—
22	C₂×C₈×C₇₉	—	2	2	no	—
23	C₂×C₈×C₇₉	—	2	1	no	—
24	C₄⋊C₄×C₇₉	—	4	2	no	—
25	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂³×C₇₉	—	8	1	no	—
27	Q₈×C₇₉	—	8	2	no	—
28	D₄×C₇₉	—	8	2	no	—
29	D₄×C₇₉	—	8	4	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	#99	1	1	yes	characteristic
33	C₈×C₇₉	—	2	2	no	—
34	C₈×C₇₉	—	4	2	no	—
35	C₈×C₇₉	—	16	2	no	—
36	C₂²×C₇₉	—	16	2	no	—
37	C₂²×C₇₉	—	16	1	no	—
38	C₂²×C₇₉	#353	1	1	yes	characteristic
39	C₄×C₇₉	—	2	2	no	—
40	C₄×C₇₉	—	2	1	no	—
41	C₄×C₇₉	—	8	2	no	—
42	#7531	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₇₉	—	2	1	no	—
44	C₂×C₇₉	—	32	1	no	—
45	C₂×C₇₉	#1408	1	1	yes	characteristic
46	#1709	C₂×C₇₉	1	1	yes	characteristic
47	#1411	C₂×C₇₉	1	2	yes	complemented
48	C₇₉	#7531	1	1	yes	characteristic, direct product factor, Sylow
49	#494	C₂²×C₇₉	1	1	yes	characteristic
50	#493	C₄×C₇₉	1	1	yes	characteristic
51	#486	—	2	2	no	—
52	#356	—	2	2	no	—
53	C₈²	C₄×C₇₉	1	1	yes	characteristic
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×D₈	—	4	1	no	—
56	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
57	#127	—	2	1	no	—
58	#102	—	4	4	no	—
59	#101	—	4	2	no	—
60	C₄×C₈	—	2	1	no	—
61	C₄×C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	4	2	no	—
64	C₂×D₄	—	4	1	no	—
65	Q₁₆	—	8	2	no	—
66	D₈	—	8	2	no	—
67	M₁₆	—	8	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	8	2	no	—
74	D₄	—	8	2	no	—
75	D₄	—	8	4	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	2	no	—
78	C₂×C₄	#99×C₇₉	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	4	2	no	—
81	C₈	—	16	2	no	—
82	C₂²	—	16	2	no	—
83	C₂²	—	16	1	no	—
84	C₂²	#353×C₇₉	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	8	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	32	1	no	—
90	C₂	C₇₉×#1408	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₉	#1408
commutator	C₄×C₈	C₂×C₄×C₇₉
Frattini, cosocle	#494	C₂²×C₇₉
prime radical	#493×C₇₉	C₄
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂²×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄²×C₇₉ ◁ #494×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#1411	C₂	semidirect
42. #7531	C₇₉	direct (N × H)
47. #1411	C₂×C₇₉	semidirect
48. C₇₉	#7531	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×#1709	2
C₇₉×#1411	2
#7531	79

Subgroups — C79×#7531 #34119220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#7531 #34119220