Subgroups — #330×C₄₆₃ #44444255

Order 29632.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#125×C₄₆₃	C₂	1	1	yes	maximal, characteristic
2	#97×C₄₆₃	C₂	1	2	yes	maximal
3	C₂×C₈×C₄₆₃	—	2	2	no	—
4	C₄⋊C₄×C₄₆₃	—	2	2	no	—
5	C₄⋊C₄×C₄₆₃	C₄	1	2	yes	—
6	C₄²×C₄₆₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₄₆₃	—	2	2	no	—
8	C₂×C₄×C₄₆₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₄₆₃	D₄	1	2	yes	—
10	C₈×C₄₆₃	—	2	4	no	—
11	C₂²×C₄₆₃	C₂²⋊C₄	1	1	yes	characteristic
12	C₄×C₄₆₃	—	2	1	no	—
13	C₄×C₄₆₃	—	2	2	no	—
14	C₄×C₄₆₃	—	4	2	no	—
15	C₂×C₄₆₃	#101	1	1	yes	characteristic
16	C₂×C₄₆₃	#104	1	2	yes	—
17	C₄₆₃	#330	1	1	yes	characteristic, direct product factor, Sylow
18	#330	C₄₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	#125	C₂×C₄₆₃	1	1	yes	characteristic
20	#97	C₂×C₄₆₃	1	2	yes	—
21	C₂×C₈	—	2	2	no	—
22	C₄⋊C₄	—	2	2	no	—
23	C₄⋊C₄	C₄×C₄₆₃	1	2	yes	—
24	C₄²	C₂²×C₄₆₃	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	C₂×C₄×C₄₆₃	1	1	yes	characteristic
27	C₂×C₄	D₄×C₄₆₃	1	2	yes	—
28	C₈	—	2	4	no	—
29	C₂²	C₂²⋊C₄×C₄₆₃	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	4	2	no	—
33	C₂	#101×C₄₆₃	1	1	yes	characteristic
34	C₂	#104×C₄₆₃	1	2	yes	—

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

N	H ≅ G/N	type
17. C₄₆₃	#330	direct (N × H)
18. #330	C₄₆₃	direct (N × H)

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