Subgroups — #10597668

Order 624.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	Dic₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#6105	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₁₃	—	2	1	no	—
6	C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	Dic₃₉	—	2	1	no	—
8	D₄×C₁₃	D₃	1	1	yes	characteristic
9	Dic₂₆	—	3	1	no	—
10	#1055	—	3	1	no	—
11	C₂×C₃×C₁₃	—	4	1	no	—
12	C₂×C₃×C₁₃	D₄	1	1	yes	characteristic
13	C₂²×C₁₃	—	2	1	no	—
14	C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
15	Dic₁₃	—	6	1	no	—
16	#214	—	13	1	no	maximal, Hall
17	C₃×C₁₃	SD₁₆	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃	—	4	1	no	—
19	C₂×C₁₃	#67	1	1	yes	characteristic
20	C₃×D₄	D₁₃	1	1	yes	characteristic
21	Dic₆	—	13	1	no	—
22	C₃⋊C₈	—	13	1	no	—
23	SD₁₆	—	39	1	no	Sylow
24	C₁₃	#214	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₃	—	2	1	no	—
26	C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
27	Dic₃	—	26	1	no	—
28	Q₈	—	39	1	no	—
29	D₄	D₃₉	1	1	yes	characteristic
30	C₈	—	39	1	no	—
31	C₂×C₃	—	4	1	no	—
32	C₂×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
33	C₂²	—	2	1	no	—
34	C₄	—	78	1	no	—
35	C₄	C₂×D₃₉	1	1	yes	characteristic
36	C₃	#6105	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	4	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.