Subgroups — C₂×C₂²⋊Dic₇₉ #14579113

Order 2528.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₉	C₂	1	2	yes	maximal, complemented
2	C₂²⋊Dic₇₉	C₂	1	4	yes	maximal, direct product factor
3	C₂⁴×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₇₉	—	2	4	no	—
5	C₂³×C₇₉	C₄	1	4	yes	complemented
6	C₂³×C₇₉	C₂²	1	2	yes	—
7	C₂³×C₇₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₇₉	—	2	4	no	—
9	C₂×Dic₇₉	C₂²	1	4	yes	complemented
10	C₂²×C₇₉	—	2	8	no	—
11	C₂²×C₇₉	—	2	4	no	—
12	C₂²×C₇₉	C₂×C₄	1	2	yes	—
13	C₂²×C₇₉	C₂×C₄	1	4	yes	complemented
14	C₂²×C₇₉	D₄	1	4	yes	—
15	C₂²×C₇₉	C₂³	1	1	yes	characteristic
16	Dic₇₉	—	2	4	no	—
17	C₂×C₇₉	—	2	4	no	—
18	C₂×C₇₉	C₂²⋊C₄	1	4	yes	complemented
19	C₂×C₇₉	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₇₉	C₂×D₄	1	2	yes	—
21	C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂²⋊C₄	—	79	1	no	maximal, Sylow
23	C₂⁴	D₇₉	1	1	yes	characteristic
24	C₂²×C₄	—	79	2	no	—
25	C₂²⋊C₄	—	79	4	no	—
26	C₂³	—	2	4	no	—
27	C₂³	Dic₇₉	1	4	yes	complemented
28	C₂³	C₂×D₇₉	1	2	yes	—
29	C₂³	C₂×D₇₉	1	1	yes	characteristic
30	C₂×C₄	—	79	4	no	—
31	C₂×C₄	—	158	4	no	—
32	C₂²	—	2	8	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂×Dic₇₉	1	2	yes	—
35	C₂²	C₂×Dic₇₉	1	4	yes	complemented
36	C₂²	C₂²⋊D₇₉	1	4	yes	—
37	C₂²	C₂²×D₇₉	1	1	yes	characteristic
38	C₄	—	158	4	no	—
39	C₂	—	2	4	no	—
40	C₂	C₂²⋊Dic₇₉	1	4	yes	direct product factor
41	C₂	C₂²×Dic₇₉	1	1	yes	characteristic
42	C₂	C₂×C₂²⋊D₇₉	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.