Subgroups — C₂⁵×D₉₇ #20261573

Order 6208.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₉₇	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₉₇	C₂²	1	620	yes	direct product factor
4	C₂⁴×C₉₇	C₂²	1	31	yes	complemented
5	C₂³×C₉₇	C₂³	1	155	yes	complemented
6	C₂²×D₉₇	C₂³	1	1240	yes	direct product factor
7	C₂²×C₉₇	C₂⁴	1	155	yes	complemented
8	C₂×D₉₇	C₂⁴	1	496	yes	direct product factor
9	C₂×C₉₇	C₂⁵	1	31	yes	complemented
10	D₉₇	C₂⁵	1	32	yes	direct product factor
11	C₉₇	C₂⁶	1	1	yes	characteristic, complemented, Sylow
12	C₂⁶	—	97	1	no	maximal, Sylow
13	C₂⁵	—	97	62	no	—
14	C₂⁵	D₉₇	1	1	yes	characteristic, direct product factor
15	C₂⁴	—	97	620	no	—
16	C₂⁴	C₂×D₉₇	1	31	yes	direct product factor
17	C₂³	—	97	1240	no	—
18	C₂³	C₂²×D₉₇	1	155	yes	direct product factor
19	C₂²	—	97	496	no	—
20	C₂²	C₂³×D₉₇	1	155	yes	direct product factor
21	C₂	—	97	32	no	—
22	C₂	C₂⁴×D₉₇	1	31	yes	direct product factor

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