Subgroups — #100×C₇₃₉ #37556521

Order 23648.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₇₃₉	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₇₃₉	C₂	1	2	yes	maximal, complemented
3	C₂³×C₇₃₉	C₄	1	2	yes	—
4	D₄×C₇₃₉	—	2	2	no	—
5	C₂×C₄×C₇₃₉	C₂²	1	1	yes	characteristic
6	C₈×C₇₃₉	—	2	2	no	—
7	C₂²×C₇₃₉	—	2	2	no	—
8	C₂²×C₇₃₉	—	4	2	no	—
9	C₂²×C₇₃₉	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇₃₉	D₄	1	2	yes	—
11	C₂×C₇₃₉	—	2	1	no	—
12	C₂×C₇₃₉	—	4	2	no	—
13	C₂×C₇₃₉	C₂²⋊C₄	1	1	yes	characteristic
14	C₇₃₉	#100	1	1	yes	characteristic, direct product factor, Sylow
15	#100	C₇₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×D₄	C₂×C₇₃₉	1	1	yes	characteristic
17	M₁₆	C₂×C₇₃₉	1	2	yes	complemented
18	C₂³	C₄×C₇₃₉	1	2	yes	—
19	D₄	—	2	2	no	—
20	C₂×C₄	C₂²×C₇₃₉	1	1	yes	characteristic
21	C₈	—	2	2	no	—
22	C₂²	—	2	2	no	—
23	C₂²	—	4	2	no	—
24	C₂²	C₂×C₄×C₇₃₉	1	1	yes	characteristic
25	C₄	D₄×C₇₃₉	1	2	yes	—
26	C₂	—	2	1	no	—
27	C₂	—	4	2	no	—
28	C₂	C₂²⋊C₄×C₇₃₉	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.