Subgroups — #23761482

Order 10112.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579101	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579101	—	2	2	no	—
4	#14579101	C₄	1	4	yes	complemented
5	C₂×C₇₉⋊C₁₆	—	2	2	no	—
6	C₂²×C₈×C₇₉	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₇₉	C₄	1	1	yes	characteristic
9	C₄×C₈×C₇₉	—	2	2	no	—
10	C₇₉⋊C₁₆	—	2	4	no	—
11	C₂²×C₄×C₇₉	—	2	1	no	—
12	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₇₉	—	2	1	no	—
14	C₂×C₈×C₇₉	—	2	1	no	—
15	C₂×C₈×C₇₉	C₈	1	2	yes	—
16	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₇₉	D₄	1	2	yes	—
18	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
20	C₄²×C₇₉	—	2	1	no	—
21	C₄²×C₇₉	C₈	1	2	yes	—
22	C₂³×C₇₉	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₇₉	—	2	4	no	—
24	C₂×C₄×C₇₉	—	2	2	no	—
25	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
31	C₈×C₇₉	—	2	2	no	—
32	C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
33	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
34	C₂²×C₇₉	—	2	2	no	—
35	C₂²×C₇₉	#97	1	1	yes	characteristic
36	C₂²×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₇₉	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₇₉	—	2	4	no	—
39	C₄×C₇₉	#95	1	1	yes	characteristic
40	C₄×C₇₉	C₄×C₈	1	1	yes	characteristic
41	C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₇₉	—	2	1	no	—
44	C₂×C₇₉	—	2	1	no	—
45	C₂×C₇₉	#336	1	1	yes	characteristic
46	C₂×C₇₉	#364	1	2	yes	—
47	#1376	—	79	1	no	maximal, Sylow
48	C₇₉	#1376	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₃₂	—	79	2	no	—
50	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic
51	C₂²×C₈	Dic₇₉	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
53	C₂×C₄²	Dic₇₉	1	1	yes	characteristic
54	M₃₂	—	79	4	no	—
55	M₃₂	—	158	2	no	—
56	C₂×C₁₆	—	158	2	no	—
57	C₄×C₈	—	2	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₇₉⋊C₈	1	2	yes	—
63	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
64	C₂×C₈	C₄×D₇₉	1	2	yes	—
65	C₂×C₈	D₃₁₆	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
67	C₄²	—	2	1	no	—
68	C₄²	C₇₉⋊C₈	1	2	yes	—
69	C₁₆	—	158	4	no	—
70	C₂³	#11929608	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
75	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
76	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
77	C₂×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#11929608	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
81	C₈	Dic₇₉⋊C₄	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#14579072	1	1	yes	characteristic
84	C₂²	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
85	C₂²	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₇₉⋊#95	1	1	yes	characteristic
88	C₄	C₄×C₇₉⋊C₈	1	1	yes	characteristic
89	C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
90	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#19098318	1	1	yes	characteristic
94	C₂	#19098384	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₃₁₆
commutator	C₄×C₇₉	C₄×C₈
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle	C₂²×C₇₉	C₄⋊C₈
prime radical	C₂³×C₇₉	M₁₆
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	#1376
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #14579101	C₄	semidirect
48. C₇₉	#1376	semidirect