Subgroups — C₂⁷×D₇₉ #35202173

Order 20224.

834398 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₇₉	C₂	1	254	yes	maximal, direct product factor
2	C₂⁷×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁵×D₇₉	C₂²	1	10668	yes	direct product factor
4	C₂⁶×C₇₉	C₂²	1	127	yes	complemented
5	C₂⁴×D₇₉	C₂³	1	94488	yes	direct product factor
6	C₂⁵×C₇₉	C₂³	1	2667	yes	complemented
7	C₂³×D₇₉	C₂⁴	1	188976	yes	direct product factor
8	C₂⁴×C₇₉	C₂⁴	1	11811	yes	complemented
9	C₂³×C₇₉	C₂⁵	1	11811	yes	complemented
10	C₂²×D₇₉	C₂⁵	1	85344	yes	direct product factor
11	C₂²×C₇₉	C₂⁶	1	2667	yes	complemented
12	C₂×D₇₉	C₂⁶	1	8128	yes	direct product factor
13	C₂⁸	—	79	1	no	maximal, Sylow
14	C₂×C₇₉	C₂⁷	1	127	yes	complemented
15	D₇₉	C₂⁷	1	128	yes	direct product factor
16	C₂⁷	—	79	254	no	—
17	C₂⁷	D₇₉	1	1	yes	characteristic, direct product factor
18	C₇₉	C₂⁸	1	1	yes	characteristic, complemented, Sylow
19	C₂⁶	—	79	10668	no	—
20	C₂⁶	C₂×D₇₉	1	127	yes	direct product factor
21	C₂⁵	—	79	94488	no	—
22	C₂⁵	C₂²×D₇₉	1	2667	yes	direct product factor
23	C₂⁴	—	79	188976	no	—
24	C₂⁴	C₂³×D₇₉	1	11811	yes	direct product factor
25	C₂³	—	79	85344	no	—
26	C₂³	C₂⁴×D₇₉	1	11811	yes	direct product factor
27	C₂²	—	79	8128	no	—
28	C₂²	C₂⁵×D₇₉	1	2667	yes	direct product factor
29	C₂	—	79	128	no	—
30	C₂	C₂⁶×D₇₉	1	127	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁷	D₇₉
commutator, cosocle, hypocenter	C₇₉	C₂⁸
Frattini	C₁	G
Fitting, socle	C₂⁷×C₇₉	C₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂⁷

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.