Subgroups — #44500765

Order 30656.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29506382	C₂	1	1	yes	maximal, characteristic
2	#29506305	C₂	1	4	yes	maximal
3	#29506293	C₂	1	1	yes	maximal, characteristic
4	#125×C₄₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₉₅₈	C₂²	1	2	yes	—
6	C₂×C₄₇₉⋊C₈	C₂²	1	2	yes	—
7	C₄⋊Dic₄₇₉	—	2	2	no	—
8	C₄⋊C₄×C₄₇₉	—	2	2	no	—
9	C₄⋊C₄×C₄₇₉	C₂²	1	2	yes	—
10	C₄²×C₄₇₉	C₂²	1	1	yes	characteristic
11	Dic₉₅₈	—	2	4	no	—
12	C₂×Dic₄₇₉	—	2	2	no	—
13	C₄₇₉⋊C₈	—	2	2	no	—
14	C₂×C₄×C₄₇₉	—	2	2	no	—
15	C₂×C₄×C₄₇₉	D₄	1	2	yes	—
16	C₂×C₄×C₄₇₉	C₂³	1	1	yes	characteristic
17	C₂²×C₄₇₉	C₂×D₄	1	1	yes	characteristic
18	C₄×C₄₇₉	—	2	2	no	—
19	C₄×C₄₇₉	—	4	2	no	—
20	C₄×C₄₇₉	#41	1	2	yes	—
21	Dic₄₇₉	—	4	2	no	—
22	C₂×C₄₇₉	#124	1	1	yes	characteristic
23	C₂×C₄₇₉	#137	1	2	yes	—
24	C₄₇₉	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	479	1	no	maximal, Sylow
26	C₄⋊Q₈	—	479	1	no	—
27	#125	D₄₇₉	1	1	yes	characteristic
28	#103	—	479	4	no	—
29	#97	—	479	1	no	—
30	C₂×Q₈	—	479	2	no	—
31	C₂×C₈	—	479	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	958	2	no	—
34	C₄⋊C₄	C₂×D₄₇₉	1	2	yes	—
35	C₄²	C₂×D₄₇₉	1	1	yes	characteristic
36	Q₈	—	958	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	958	2	no	—
39	C₂×C₄	C₂²⋊D₄₇₉	1	2	yes	—
40	C₂×C₄	C₂²×D₄₇₉	1	1	yes	characteristic
41	C₈	—	958	2	no	—
42	C₂²	C₂×C₂²⋊D₄₇₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	1916	2	no	—
46	C₄	#21440163	1	2	yes	—
47	C₂	#29506371	1	1	yes	characteristic
48	C₂	#29506412	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇₉
commutator, cosocle	C₂×C₄×C₄₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₄₇₉
Fitting	#125×C₄₇₉	C₂
socle, prime radical	C₂²×C₄₇₉	C₂×D₄
hypercenter	#125	D₄₇₉
hypocenter	C₄₇₉	#491
LCS	G ▷ C₂×C₄×C₄₇₉ ▷ C₂×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
24. C₄₇₉	#491	semidirect

Maximal subgroups

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

subgroup	index
#29506382	2
#29506305	2
#29506293	2
#125×C₄₇₉	2
#491	479