Subgroups — #20300916

Order 7328.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16814666	C₂	1	1	yes	maximal, characteristic
2	#16814650	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₅₈	C₄	1	1	yes	characteristic, complemented
5	D₉₁₆	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊D₂₂₉	—	2	1	no	—
7	C₄×D₂₂₉	—	2	1	no	—
8	#14270080	—	2	1	no	—
9	C₂×C₄×C₂₂₉	—	2	1	no	—
10	C₂×C₄×C₂₂₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂₂₉	D₄	1	1	yes	characteristic
12	C₂×D₂₂₉	—	2	1	no	—
13	C₄×C₂₂₉	—	2	2	no	—
14	C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₂₂₉	D₄	1	1	yes	characteristic
16	Dic₂₂₉	—	2	1	no	—
17	C₂×C₂₂₉	—	2	1	no	—
18	C₂×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	D₂₂₉	—	4	1	no	—
20	C₂₂₉	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	229	1	no	maximal, Sylow
22	#41	—	229	1	no	—
23	M₁₆	—	229	1	no	—
24	C₄²	D₂₂₉	1	1	yes	characteristic, complemented
25	Q₈	—	229	1	no	—
26	D₄	—	458	1	no	—
27	D₄	—	229	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	458	1	no	—
30	C₂×C₄	C₂×D₂₂₉	1	1	yes	characteristic
31	C₈	—	458	1	no	—
32	C₂²	—	458	1	no	—
33	C₂²	C₂²⋊D₂₂₉	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	458	1	no	—
36	C₄	C₄×D₂₂₉	1	1	yes	characteristic
37	C₄	D₉₁₆	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	916	1	no	—
40	C₂	#16814643	1	1	yes	characteristic

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