Subgroups — D₉₃⋊D₉₅ #47977752

Order 35340.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₂₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₉₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₁×D₉₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅₇⋊D₃₁	—	5	1	no	maximal, Hall
7	D₂₉₄₅	D₃	1	1	yes	characteristic, complemented
8	C₃₁×D₉₅	—	3	1	no	—
9	C₅×C₁₉×D₃₁	—	3	1	no	—
10	C₃₁×D₅₇	—	5	1	no	—
11	C₁₉×D₉₃	D₅	1	1	yes	characteristic, complemented
12	C₃×D₅₈₉	—	5	1	no	—
13	C₅×C₁₉×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₉×D₃₁	—	15	1	no	Hall
15	D₁₅⋊D₃₁	—	19	1	no	maximal, Hall
16	C₃×C₁₉×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₅₈₉	—	5	1	no	—
18	C₁₉×D₃₁	—	3	1	no	—
19	C₃₁×D₁₉	—	15	1	no	—
20	D₃×D₉₅	—	31	1	no	maximal, Hall
21	D₁₅×C₃₁	—	19	1	no	—
22	C₅×D₉₃	D₁₉	1	1	yes	characteristic, complemented
23	C₃×D₁₅₅	—	19	1	no	—
24	D₅×D₃₁	—	57	1	no	Hall
25	C₁₉×C₃₁	D₃×D₅	1	1	yes	characteristic, complemented, Hall
26	D₂₈₅	D₃₁	1	1	yes	characteristic, complemented
27	C₅×D₃×C₁₉	—	31	1	no	—
28	C₃×D₉₅	—	31	1	no	—
29	C₃×C₅×C₃₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×D₉₅	—	93	1	no	Hall
31	D₃×D₃₁	—	95	1	no	Hall
32	D₁₅₅	—	19	1	no	—
33	C₅×D₃₁	—	3	1	no	—
34	D₅×C₃₁	—	57	1	no	—
35	C₃×C₅×C₁₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₉	—	155	1	no	Hall
37	C₂×C₅×C₁₉	—	93	1	no	—
38	D₉₅	—	3	1	no	—
39	D₉₅	—	31	1	no	—
40	D₉₃	D₉₅	1	1	yes	characteristic, complemented
41	C₃×D₃₁	—	95	1	no	—
42	D₃×C₃₁	—	95	1	no	—
43	C₅×C₃₁	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	285	1	no	Hall
45	D₅₇	—	5	1	no	—
46	C₃×D₁₉	—	155	1	no	—
47	D₃×C₁₉	—	31	1	no	—
48	C₅×C₁₉	D₃×D₃₁	1	1	yes	characteristic, complemented, Hall
49	C₃×C₃₁	C₂×D₉₅	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₉	—	465	1	no	Hall
51	C₂×C₃₁	—	285	1	no	—
52	D₃₁	—	3	1	no	—
53	D₃₁	—	95	1	no	—
54	D₃×D₅	—	589	1	no	Hall
55	C₃×C₁₉	D₅×D₃₁	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	93	1	no	—
57	D₁₉	—	15	1	no	—
58	D₁₉	—	155	1	no	—
59	C₃₁	D₃×D₉₅	1	1	yes	characteristic, complemented, Sylow
60	D₁₅	—	19	1	no	—
61	C₃×D₅	—	589	1	no	—
62	C₅×D₃	—	31	1	no	—
63	C₂×D₅	—	1767	1	no	Hall
64	C₁₉	D₁₅⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	D₁₉×D₃₁	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	2945	1	no	Hall
67	C₂×C₅	—	93	1	no	—
68	D₅	—	57	1	no	—
69	D₅	—	589	1	no	—
70	C₂×C₃	—	2945	1	no	—
71	D₃	—	31	1	no	—
72	D₃	—	95	1	no	—
73	C₅	D₅₇⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	8835	1	no	Sylow
75	C₃	D₃₁×D₉₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	285	1	no	—
77	C₂	—	93	1	no	—
78	C₂	—	2945	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₉×C₃₁	C₂²
LCS	G ▷ C₃×C₅×C₁₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₈₅	C₂	semidirect
2. C₅×C₁₉×D₉₃	C₂	semidirect
3. C₃×D₂₉₄₅	C₂	semidirect
5. C₃×C₅×C₁₉×C₃₁	C₂²	semidirect
7. D₂₉₄₅	D₃	semidirect
11. C₁₉×D₉₃	D₅	semidirect
13. C₅×C₁₉×C₃₁	C₂×D₃	semidirect
16. C₃×C₁₉×C₃₁	C₂×D₅	semidirect
22. C₅×D₉₃	D₁₉	semidirect
25. C₁₉×C₃₁	D₃×D₅	semidirect
26. D₂₈₅	D₃₁	semidirect
29. C₃×C₅×C₃₁	C₂×D₁₉	semidirect
35. C₃×C₅×C₁₉	C₂×D₃₁	semidirect
40. D₉₃	D₉₅	semidirect
43. C₅×C₃₁	D₃×D₁₉	semidirect
48. C₅×C₁₉	D₃×D₃₁	semidirect
49. C₃×C₃₁	C₂×D₉₅	semidirect
55. C₃×C₁₉	D₅×D₃₁	semidirect
59. C₃₁	D₃×D₉₅	semidirect
64. C₁₉	D₁₅⋊D₃₁	semidirect
65. C₃×C₅	D₁₉×D₃₁	semidirect
73. C₅	D₅₇⋊D₃₁	semidirect
75. C₃	D₃₁×D₉₅	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×D₂₈₅	2
C₅×C₁₉×D₉₃	2
C₃×D₂₉₄₅	2
D₃₁×D₉₅	3
D₅₇⋊D₃₁	5
D₁₅⋊D₃₁	19
D₃×D₉₅	31

Subgroups — D93⋊D95 #47977752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉₃⋊D₉₅ #47977752