Subgroups — C₂⁵×C₇×C₉₇ #72199231

Order 21728.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇×C₉₇	C₂	1	31	yes	maximal, direct product factor
2	C₂³×C₇×C₉₇	C₂²	1	155	yes	direct product factor
3	C₂⁵×C₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₇×C₉₇	C₂³	1	155	yes	direct product factor
5	C₂⁴×C₉₇	C₂×C₇	1	31	yes	direct product factor
6	C₂×C₇×C₉₇	C₂⁴	1	31	yes	direct product factor
7	C₂³×C₉₇	C₂²×C₇	1	155	yes	direct product factor
8	C₇×C₉₇	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₉₇	C₂³×C₇	1	155	yes	direct product factor
10	C₂⁵×C₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₉₇	C₂⁴×C₇	1	31	yes	direct product factor
12	C₂⁴×C₇	C₂×C₉₇	1	31	yes	direct product factor
13	C₉₇	C₂⁵×C₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂³×C₇	C₂²×C₉₇	1	155	yes	direct product factor
15	C₂⁵	C₇×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₇	C₂³×C₉₇	1	155	yes	direct product factor
17	C₂⁴	C₂×C₇×C₉₇	1	31	yes	direct product factor
18	C₂×C₇	C₂⁴×C₉₇	1	31	yes	direct product factor
19	C₂³	C₂²×C₇×C₉₇	1	155	yes	direct product factor
20	C₇	C₂⁵×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₂³×C₇×C₉₇	1	155	yes	direct product factor
22	C₂	C₂⁴×C₇×C₉₇	1	31	yes	direct product factor

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.