Subgroups — #37556570

Order 23648.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₇₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₃₉	C₄	1	2	yes	—
5	C₇₃₉⋊C₈	C₄	1	2	yes	complemented
6	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
7	C₈×C₇₃₉	C₄	1	2	yes	complemented
8	C₂²×C₇₃₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇₃₉	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇₃₉	C₂×C₄	1	1	yes	characteristic
11	Dic₇₃₉	—	2	2	no	—
12	C₂×C₇₃₉	C₄²	1	1	yes	characteristic
13	C₂×C₇₃₉	M₁₆	1	2	yes	—
14	C₇₃₉	#97	1	1	yes	characteristic, complemented, Sylow
15	#97	—	739	1	no	maximal, Sylow
16	C₂×C₈	—	739	1	no	—
17	C₂×C₈	D₇₃₉	1	1	yes	characteristic
18	C₄²	—	739	1	no	—
19	C₂×C₄	—	739	2	no	—
20	C₂×C₄	C₂×D₇₃₉	1	1	yes	characteristic
21	C₈	—	739	2	no	—
22	C₈	Dic₇₃₉	1	2	yes	complemented
23	C₂²	C₄×D₇₃₉	1	1	yes	characteristic
24	C₄	—	1478	2	no	—
25	C₄	C₄×D₇₃₉	1	1	yes	characteristic
26	C₄	C₂×Dic₇₃₉	1	1	yes	characteristic
27	C₂	C₄×Dic₇₃₉	1	1	yes	characteristic
28	C₂	#26044764	1	2	yes	—

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.