Subgroups — #23765629

Order 10112.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098943	C₂	1	1	yes	maximal, characteristic
2	#19098366	C₂	1	4	yes	maximal
3	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#500×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₁₆	—	2	1	no	—
6	C₂×Dic₃₁₆	C₂²	1	2	yes	—
7	#14579161	—	2	1	no	—
8	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₇₉	—	2	1	no	—
10	#107×C₇₉	—	2	1	no	—
11	#107×C₇₉	C₂²	1	2	yes	—
12	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₅₈	—	2	2	no	—
14	Dic₃₁₆	—	2	4	no	—
15	Dic₃₁₆	—	4	2	no	—
16	C₄⋊Dic₇₉	—	4	1	no	—
17	C₄⋊Dic₇₉	—	4	1	no	—
18	C₇₉⋊C₁₆	—	2	2	no	—
19	C₂×Q₈×C₇₉	—	4	1	no	—
20	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₇₉	—	2	2	no	—
23	C₄⋊C₄×C₇₉	—	4	1	no	—
24	C₄²×C₇₉	D₄	1	1	yes	characteristic
25	Q₈×C₇₉	—	8	2	no	—
26	C₂×C₄×C₇₉	—	4	2	no	—
27	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₇₉	—	4	2	no	—
31	Dic₁₅₈	—	4	2	no	—
32	Dic₁₅₈	—	4	2	no	—
33	C₈×C₇₉	SD₁₆	1	2	yes	—
34	C₈×C₇₉	#41	1	2	yes	—
35	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₇₉	—	8	2	no	—
37	C₄×C₇₉	SD₃₂	1	2	yes	—
38	C₄×C₇₉	Q₃₂	1	2	yes	—
39	C₄×C₇₉	#124	1	1	yes	characteristic
40	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₇₉	—	8	2	no	—
42	C₂×C₇₉	#486	1	1	yes	characteristic
43	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
44	C₂×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
45	#2241	—	79	1	no	maximal, Sylow
46	C₇₉	#2241	1	1	yes	characteristic, complemented, Sylow
47	#500	D₇₉	1	1	yes	characteristic
48	#494	—	79	1	no	—
49	#358	—	79	4	no	—
50	C₄×C₁₆	—	79	1	no	—
51	C₂×Q₁₆	—	79	2	no	—
52	C₂×Q₁₆	—	158	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	158	1	no	—
55	C₂×C₁₆	—	79	2	no	—
56	#107	—	2	1	no	—
57	#107	C₂×D₇₉	1	2	yes	—
58	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	158	2	no	—
61	Q₁₆	—	316	2	no	—
62	Q₁₆	—	158	4	no	—
63	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	316	1	no	—
68	C₄⋊C₄	—	316	1	no	—
69	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
70	C₁₆	—	158	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	316	2	no	—
73	Q₈	—	316	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	316	2	no	—
76	C₂×C₄	#11929609	1	1	yes	characteristic
77	C₂×C₄	#11929609	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
79	C₈	#11929611	1	2	yes	—
80	C₈	#11929625	1	2	yes	—
81	C₂²	C₂×#11929609	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	632	2	no	—
84	C₄	#14579105	1	2	yes	—
85	C₄	#14579107	1	2	yes	—
86	C₄	#14579150	1	1	yes	characteristic
87	C₄	C₂×#11929611	1	1	yes	characteristic
88	C₂	#19098911	1	1	yes	characteristic
89	C₂	C₂×#14579105	1	1	yes	characteristic
90	C₂	C₂×#14579107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#500×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#500	D₇₉
hypocenter	C₇₉	#2241
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
46. C₇₉	#2241	semidirect