Subgroups — #20300946

Order 7328.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₂₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16814643	C₂	1	2	yes	maximal
4	C₄×Dic₂₂₉	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₄×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₂₂₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₂₉	C₂²	1	2	yes	—
8	C₂×Dic₂₂₉	C₂²	1	1	yes	characteristic
9	C₄×D₂₂₉	C₄	1	4	yes	complemented
10	C₂×C₄×C₂₂₉	C₂²	1	2	yes	—
11	C₂×C₄×C₂₂₉	C₂²	1	1	yes	characteristic
12	C₂²×C₂₂₉	C₂³	1	1	yes	characteristic
13	C₂×D₂₂₉	—	2	1	no	—
14	C₂×D₂₂₉	—	2	1	no	—
15	C₂×D₂₂₉	C₂×C₄	1	2	yes	—
16	C₄×C₂₂₉	—	2	2	no	—
17	C₄×C₂₂₉	C₂×C₄	1	2	yes	—
18	Dic₂₂₉	—	2	2	no	—
19	Dic₂₂₉	C₂×C₄	1	2	yes	—
20	C₂×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₂₂₉	#41	1	1	yes	characteristic
22	C₂×C₂₂₉	#41	1	1	yes	characteristic
23	D₂₂₉	—	2	2	no	—
24	C₂₂₉	#117	1	1	yes	characteristic, complemented, Sylow
25	#117	—	229	1	no	maximal, Sylow
26	C₂²×C₄	—	229	1	no	—
27	C₄⋊C₄	—	229	1	no	—
28	C₄⋊C₄	D₂₂₉	1	1	yes	characteristic, complemented
29	C₂²⋊C₄	—	229	2	no	—
30	C₄²	—	229	2	no	—
31	C₂³	—	229	1	no	—
32	C₂×C₄	—	229	2	no	—
33	C₂×C₄	—	229	1	no	—
34	C₂×C₄	—	229	4	no	—
35	C₂×C₄	C₂×D₂₂₉	1	2	yes	—
36	C₂×C₄	C₂×D₂₂₉	1	1	yes	characteristic
37	C₂²	—	458	1	no	—
38	C₂²	—	458	1	no	—
39	C₂²	—	229	2	no	—
40	C₂²	C₂²×D₂₂₉	1	1	yes	characteristic
41	C₄	—	2	2	no	—
42	C₄	—	458	2	no	—
43	C₄	—	229	2	no	—
44	C₄	C₄×D₂₂₉	1	2	yes	—
45	C₂	—	458	2	no	—
46	C₂	C₂×C₄×D₂₂₉	1	1	yes	characteristic
47	C₂	#16814665	1	1	yes	characteristic
48	C₂	#16814667	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₂₂₉
commutator	C₂×C₂₂₉	C₂²×C₄
Fitting	C₄⋊C₄×C₂₂₉	C₂
socle	C₂²×C₂₂₉	C₂³
hypercenter	C₄⋊C₄	D₂₂₉
hypocenter	C₂₂₉	#117
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₂₂₉	C₂	semidirect
4. C₄×Dic₂₂₉	C₂	semidirect
5. C₄⋊C₄×C₂₂₉	C₂	semidirect
9. C₄×D₂₂₉	C₄	semidirect
24. C₂₂₉	#117	semidirect
28. C₄⋊C₄	D₂₂₉	semidirect