Subgroups — #23765646

Order 10112.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098965	C₂	1	1	yes	maximal, characteristic
2	#19098943	C₂	1	1	yes	maximal, characteristic
3	#19098368	C₂	1	4	yes	maximal
4	#346×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	#14579153	—	2	1	no	—
9	#14579095	C₂²	1	2	yes	—
10	#14579093	—	2	1	no	—
11	C₂×C₁₆×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	—	2	2	no	—
17	C₄⋊Dic₇₉	—	4	2	no	—
18	Dic₇₉⋊C₄	—	4	2	no	—
19	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
21	C₄²×C₇₉	D₄	1	1	yes	characteristic
22	C₁₆×C₇₉	—	2	2	no	—
23	C₂×C₄×C₇₉	D₈	1	2	yes	—
24	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₇₉	—	4	2	no	—
26	C₂×Dic₇₉	—	4	2	no	—
27	Dic₁₅₈	—	4	2	no	—
28	Dic₁₅₈	—	4	2	no	—
29	C₈×C₇₉	SD₁₆	1	2	yes	—
30	C₈×C₇₉	#41	1	2	yes	—
31	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
32	C₄×C₇₉	—	2	2	no	—
33	C₄×C₇₉	#124	1	1	yes	characteristic
34	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
35	Dic₇₉	—	8	2	no	—
36	Dic₇₉	—	8	2	no	—
37	C₂×C₇₉	#486	1	1	yes	characteristic
38	C₂×C₇₉	#510	1	2	yes	—
39	#2245	—	79	1	no	maximal, Sylow
40	C₇₉	#2245	1	1	yes	characteristic, complemented, Sylow
41	#499	—	79	1	no	—
42	#494	—	79	1	no	—
43	#358	—	79	4	no	—
44	#346	D₇₉	1	1	yes	characteristic
45	C₂×Q₁₆	—	79	2	no	—
46	C₂×Q₁₆	—	158	1	no	—
47	C₄⋊Q₈	—	158	1	no	—
48	#125	—	158	1	no	—
49	C₂×C₁₆	C₂×D₇₉	1	2	yes	—
50	#107	—	79	2	no	—
51	#106	—	158	1	no	—
52	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
53	C₂×Q₈	—	158	2	no	—
54	Q₁₆	—	316	2	no	—
55	Q₁₆	—	158	4	no	—
56	C₂×C₈	D₃₁₆	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
58	C₄⋊C₄	—	316	2	no	—
59	C₄⋊C₄	—	316	2	no	—
60	C₄⋊C₄	—	158	2	no	—
61	C₄²	D₃₁₆	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	316	2	no	—
64	Q₈	—	316	2	no	—
65	C₂×C₄	—	316	2	no	—
66	C₂×C₄	—	316	2	no	—
67	C₂×C₄	D₆₃₂	1	2	yes	—
68	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
69	C₈	#11929613	1	2	yes	—
70	C₈	#11929624	1	2	yes	—
71	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	632	2	no	—
74	C₄	—	632	2	no	—
75	C₄	#14579149	1	1	yes	characteristic
76	C₄	C₂×#11929613	1	1	yes	characteristic
77	C₂	#19098910	1	1	yes	characteristic
78	C₂	#19099006	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#346×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#346	D₇₉
hypocenter	C₇₉	#2245
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
40. C₇₉	#2245	semidirect