Subgroups — C₂²×C₈×C₁₇₉ #19153003

Order 5728.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₇₉	C₂	1	6	yes	maximal, direct product factor
3	C₂³×C₁₇₉	C₄	1	1	yes	characteristic
4	C₂×C₄×C₁₇₉	C₄	1	3	yes	—
5	C₂×C₄×C₁₇₉	C₂²	1	3	yes	—
6	C₈×C₁₇₉	C₂²	1	4	yes	direct product factor
7	C₂²×C₁₇₉	C₈	1	4	yes	direct product factor
8	C₂²×C₁₇₉	C₂×C₄	1	3	yes	—
9	C₄×C₁₇₉	C₂×C₄	1	3	yes	—
10	C₄×C₁₇₉	C₂³	1	1	yes	characteristic
11	C₂×C₁₇₉	C₂×C₈	1	6	yes	direct product factor
12	C₂×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
13	C₁₇₉	C₂²×C₈	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₈	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₄	C₂×C₁₇₉	1	1	yes	characteristic
16	C₂×C₈	C₂×C₁₇₉	1	6	yes	direct product factor
17	C₂³	C₄×C₁₇₉	1	1	yes	characteristic
18	C₂×C₄	C₄×C₁₇₉	1	3	yes	—
19	C₂×C₄	C₂²×C₁₇₉	1	3	yes	—
20	C₈	C₂²×C₁₇₉	1	4	yes	direct product factor
21	C₂²	C₈×C₁₇₉	1	4	yes	direct product factor
22	C₂²	C₂×C₄×C₁₇₉	1	3	yes	—
23	C₄	C₂×C₄×C₁₇₉	1	3	yes	—
24	C₄	C₂³×C₁₇₉	1	1	yes	characteristic
25	C₂	C₂×C₈×C₁₇₉	1	6	yes	direct product factor
26	C₂	C₂²×C₄×C₁₇₉	1	1	yes	characteristic

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