Subgroups — D₁₅₅⋊(C₇⋊D₇) #44477194

Order 30380.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇⋊D₂₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₁×C₇⋊D₇	—	5	1	no	maximal, Hall
6	D₃₅⋊D₃₁	—	7	8	no	maximal
7	C₇⋊D₂₁₇	D₅	1	1	yes	characteristic, complemented
8	C₃₁×C₇⋊D₇	—	5	1	no	—
9	C₇²×D₃₁	—	5	1	no	—
10	C₃₁×D₃₅	—	7	8	no	—
11	C₇×D₁₅₅	D₇	1	8	yes	complemented
12	C₅×D₂₁₇	—	7	8	no	—
13	C₇²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇×C₃₁	C₂×D₇	1	8	yes	complemented
15	D₅×C₇⋊D₇	—	31	1	no	maximal, Hall
16	D₇×D₃₁	—	35	8	no	—
17	D₅×D₃₁	—	49	1	no	Hall
18	C₅⋊(C₇⋊D₇)	D₃₁	1	1	yes	characteristic, complemented
19	C₇²×D₅	—	31	1	no	—
20	C₅×C₇⋊D₇	—	31	1	no	—
21	D₂₁₇	—	7	8	no	—
22	C₇×D₃₁	—	5	8	no	—
23	D₇×C₃₁	—	35	8	no	—
24	D₁₅₅	C₇⋊D₇	1	1	yes	characteristic, complemented
25	C₅×D₃₁	—	49	1	no	—
26	D₅×C₃₁	—	49	1	no	—
27	C₅×C₇²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₇×C₃₁	D₅×D₇	1	8	yes	complemented
29	C₂×C₇⋊D₇	—	155	1	no	Hall
30	C₅×C₃₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
31	D₅×D₇	—	217	8	no	—
32	C₂×D₃₁	—	245	1	no	Hall
33	C₂×C₇²	—	155	1	no	—
34	C₇⋊D₇	—	5	1	no	—
35	C₇⋊D₇	—	31	1	no	—
36	D₃₅	—	7	8	no	—
37	C₅×D₇	—	217	8	no	—
38	C₇×D₅	—	31	8	no	—
39	C₂×C₃₁	—	245	1	no	—
40	D₃₁	—	5	1	no	—
41	D₃₁	—	49	1	no	—
42	C₇²	D₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
43	C₅×C₇	D₇×D₃₁	1	8	yes	complemented
44	C₃₁	D₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₇	—	1085	8	no	—
46	C₂×D₅	—	1519	1	no	Hall
47	C₂×C₇	—	155	8	no	—
48	D₇	—	35	8	no	—
49	D₇	—	217	8	no	—
50	C₂×C₅	—	1519	1	no	—
51	D₅	—	31	1	no	—
52	D₅	—	49	1	no	—
53	C₇	D₃₅⋊D₃₁	1	8	yes	complemented
54	C₅	D₃₁×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	7595	1	no	Sylow
56	C₂	—	155	1	no	—
57	C₂	—	1519	1	no	—
58	C₂	—	245	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₃₁	C₂²
LCS	G ▷ C₅×C₇²×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇⋊D₂₁₇	C₂	semidirect
2. C₇²×D₁₅₅	C₂	semidirect
3. C₃₁×C₅⋊(C₇⋊D₇)	C₂	semidirect
4. C₅×C₇²×C₃₁	C₂²	semidirect
7. C₇⋊D₂₁₇	D₅	semidirect
11. C₇×D₁₅₅	D₇	semidirect
13. C₇²×C₃₁	C₂×D₅	semidirect
14. C₅×C₇×C₃₁	C₂×D₇	semidirect
18. C₅⋊(C₇⋊D₇)	D₃₁	semidirect
24. D₁₅₅	C₇⋊D₇	semidirect
27. C₅×C₇²	C₂×D₃₁	semidirect
28. C₇×C₃₁	D₅×D₇	semidirect
30. C₅×C₃₁	C₂×C₇⋊D₇	semidirect
42. C₇²	D₅×D₃₁	semidirect
43. C₅×C₇	D₇×D₃₁	semidirect
44. C₃₁	D₅×C₇⋊D₇	semidirect
53. C₇	D₃₅⋊D₃₁	semidirect
54. C₅	D₃₁×C₇⋊D₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₇⋊D₂₁₇	2
C₇²×D₁₅₅	2
C₃₁×C₅⋊(C₇⋊D₇)	2
D₃₁×C₇⋊D₇	5
D₃₅⋊D₃₁	7
D₅×C₇⋊D₇	31

Subgroups — D155⋊(C7⋊D7) #44477194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅₅⋊(C₇⋊D₇) #44477194