Subgroups — #10597669

Order 624.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₅₆	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#6106	—	3	1	no	maximal, Hall
5	C₂×D₃₉	—	2	1	no	—
6	C₃×C₄×C₁₃	—	2	1	no	—
7	C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
9	D₅₂	—	3	1	no	—
10	#1055	—	3	1	no	—
11	C₂×C₃×C₁₃	D₄	1	1	yes	characteristic
12	D₃₉	—	4	1	no	—
13	C₂×D₁₃	—	6	1	no	—
14	C₄×C₁₃	—	2	1	no	—
15	C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
16	#215	—	13	1	no	maximal, Hall
17	C₃×C₁₃	SD₁₆	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃	#67	1	1	yes	characteristic
19	D₁₃	—	12	1	no	—
20	C₃×Q₈	D₁₃	1	1	yes	characteristic, complemented
21	D₁₂	—	13	1	no	—
22	C₃⋊C₈	—	13	1	no	—
23	SD₁₆	—	39	1	no	Sylow
24	C₁₃	#215	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₃	—	26	1	no	—
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
28	Q₈	D₃₉	1	1	yes	characteristic, complemented
29	D₄	—	39	1	no	—
30	C₈	—	39	1	no	—
31	C₂×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
32	D₃	—	52	1	no	—
33	C₂²	—	78	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×D₃₉	1	1	yes	characteristic
36	C₃	#6106	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	156	1	no	—
38	C₂	#64625	1	1	yes	characteristic

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

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