Subgroups — #23764979

Order 10112.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098591	C₂	1	1	yes	maximal, characteristic
2	#19098334	C₂	1	2	yes	maximal
3	#19098327	C₂	1	2	yes	maximal
4	C₇₉⋊#338	C₂	1	1	yes	maximal, characteristic
5	#430×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	2	yes	—
7	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	#14579120	C₂²	1	1	yes	characteristic
9	Dic₇₉⋊C₈	—	2	2	no	—
10	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
11	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	#108×C₇₉	—	2	2	no	—
13	#11929608	—	2	2	no	—
14	#11929608	—	2	2	no	—
15	C₂×C₇₉⋊C₈	—	2	1	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₄⋊Dic₇₉	—	2	1	no	—
19	C₂²⋊Dic₇₉	Q₈	1	2	yes	—
20	C₄×Dic₇₉	—	2	1	no	—
21	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₇₉	—	2	2	no	—
23	M₁₆×C₇₉	—	2	2	no	—
24	M₁₆×C₇₉	—	2	2	no	—
25	C₂×C₈×C₇₉	—	2	2	no	—
26	C₂×C₈×C₇₉	D₄	1	2	yes	—
27	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	#41	1	2	yes	—
30	C₂×C₄×C₇₉	#41	1	2	yes	—
31	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
32	C₂×Dic₇₉	—	2	2	no	—
33	C₈×C₇₉	—	2	2	no	—
34	C₈×C₇₉	—	4	2	no	—
35	C₇₉⋊C₈	—	4	1	no	—
36	C₇₉⋊C₈	—	4	2	no	—
37	C₂²×C₇₉	—	4	1	no	—
38	C₂²×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₇₉	#125	1	2	yes	—
40	C₄×C₇₉	#123	1	1	yes	characteristic
41	C₄×C₇₉	#124	1	1	yes	characteristic
42	C₄×C₇₉	#126	1	2	yes	—
43	Dic₇₉	—	4	2	no	—
44	C₂×C₇₉	—	2	1	no	—
45	C₂×C₇₉	—	2	2	no	—
46	C₂×C₇₉	#400	1	1	yes	characteristic
47	#2103	—	79	1	no	maximal, Sylow
48	C₇₉	#2103	1	1	yes	characteristic, complemented, Sylow
49	#430	D₇₉	1	1	yes	characteristic
50	#424	—	79	1	no	—
51	#344	—	79	2	no	—
52	#341	—	79	2	no	—
53	#338	—	79	1	no	—
54	C₂×M₁₆	—	79	2	no	—
55	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
56	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
57	C₂²×C₈	—	79	1	no	—
58	#117	—	79	1	no	—
59	#108	—	2	2	no	—
60	C₄⋊C₈	—	158	2	no	—
61	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	158	2	no	—
66	M₁₆	—	158	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	158	1	no	—
69	C₂×C₈	—	158	2	no	—
70	C₂×C₈	—	158	2	no	—
71	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
72	C₄⋊C₄	—	158	1	no	—
73	C₂²⋊C₄	—	79	2	no	—
74	C₄²	—	158	1	no	—
75	C₂³	Q₈×D₇₉	1	1	yes	characteristic
76	C₂×C₄	—	158	2	no	—
77	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
78	C₂×C₄	#11929623	1	2	yes	—
79	C₂×C₄	#11929624	1	2	yes	—
80	C₂×C₄	#11929625	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₈	—	316	1	no	—
84	C₈	—	316	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#14579137	1	1	yes	characteristic
87	C₂²	#14579151	1	2	yes	—
88	C₄	—	316	2	no	—
89	C₄	#14579144	1	1	yes	characteristic
90	C₄	#14579148	1	1	yes	characteristic
91	C₄	#14579156	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#19098501	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14579148
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#430×C₇₉	C₂
socle	C₂×C₇₉	#400
prime radical	C₂³×C₇₉	C₂×Q₈
hypercenter	#430	D₇₉
hypocenter	C₇₉	#2103
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

Complements

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

N	H ≅ G/N	type
48. C₇₉	#2103	semidirect