Subgroups — C₅×#6554 #11765433

Order 1120.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×Q₈×D₇	C₂	1	2	yes	maximal, complemented
3	C₅×#1159	C₂	1	6	yes	maximal, complemented
4	C₅×#1157	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×Dic₁₄	C₂	1	3	yes	maximal, complemented
6	C₅×C₇×Q₈	C₂²	1	1	yes	characteristic
7	C₅×C₇×D₄	C₂²	1	3	yes	—
8	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
9	C₅×C₂²⋊D₇	C₂²	1	6	yes	—
10	C₂×C₅×Dic₇	C₂²	1	6	yes	—
11	C₅×D₂₈	C₂²	1	1	yes	characteristic
12	C₄×C₅×D₇	C₂²	1	6	yes	—
13	C₅×Dic₁₄	C₂²	1	3	yes	—
14	C₅×Dic₁₄	C₂²	1	6	yes	—
15	#6554	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×2₋¹⁺⁴	—	7	1	no	maximal, Hall
17	C₂²×C₅×C₇	C₂³	1	3	yes	—
18	C₂×C₅×D₇	C₂³	1	2	yes	—
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	C₄×C₅×C₇	C₂³	1	3	yes	—
21	C₅×Dic₇	C₂³	1	6	yes	—
22	C₇×#41	C₂×C₅	1	1	yes	characteristic, complemented
23	Q₈×D₇	C₂×C₅	1	2	yes	complemented
24	#1159	C₂×C₅	1	6	yes	complemented
25	#1157	C₂×C₅	1	3	yes	complemented
26	C₂×Dic₁₄	C₂×C₅	1	3	yes	complemented
27	C₅×#41	—	7	6	no	—
28	C₅×#41	—	7	3	no	—
29	C₅×#41	D₇	1	1	yes	characteristic, complemented
30	C₂×C₅×Q₈	—	7	2	no	—
31	C₂×C₅×Q₈	—	7	3	no	—
32	C₂×C₅×C₇	—	2	3	no	—
33	C₂×C₅×C₇	C₂⁴	1	1	yes	characteristic
34	C₅×D₇	—	2	2	no	—
35	C₇×Q₈	C₂²×C₅	1	1	yes	characteristic
36	C₇×D₄	C₂²×C₅	1	3	yes	—
37	C₂×C₄×C₇	C₂²×C₅	1	3	yes	—
38	C₂²⋊D₇	C₂²×C₅	1	6	yes	—
39	C₂×Dic₇	C₂²×C₅	1	6	yes	—
40	D₂₈	C₂²×C₅	1	1	yes	characteristic
41	C₄×D₇	C₂²×C₅	1	6	yes	—
42	Dic₁₄	C₂²×C₅	1	3	yes	—
43	Dic₁₄	C₂²×C₅	1	6	yes	—
44	C₅×Q₈	—	7	6	no	—
45	C₅×Q₈	—	7	3	no	—
46	C₅×Q₈	C₂×D₇	1	1	yes	characteristic
47	C₅×D₄	—	7	6	no	—
48	C₅×D₄	—	7	1	no	—
49	C₅×D₄	C₂×D₇	1	3	yes	—
50	C₂×C₄×C₅	—	7	6	no	—
51	C₂×C₄×C₅	—	7	6	no	—
52	C₂×C₄×C₅	C₂×D₇	1	3	yes	—
53	C₅×C₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
54	2₋¹⁺⁴	—	7	1	no	Sylow
55	C₂²×C₇	C₂³×C₅	1	3	yes	—
56	C₂×D₇	C₂³×C₅	1	2	yes	—
57	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
58	C₄×C₇	C₂³×C₅	1	3	yes	—
59	Dic₇	C₂³×C₅	1	6	yes	—
60	C₂²×C₅	—	7	2	no	—
61	C₂²×C₅	C₂²×D₇	1	3	yes	—
62	C₄×C₅	—	7	6	no	—
63	C₄×C₅	C₂²×D₇	1	3	yes	—
64	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
65	#41	—	7	6	no	—
66	#41	—	7	3	no	—
67	#41	C₅×D₇	1	1	yes	characteristic, complemented
68	C₂×Q₈	—	7	2	no	—
69	C₂×Q₈	—	7	3	no	—
70	C₂×C₇	—	2	3	no	—
71	C₂×C₇	C₂⁴×C₅	1	1	yes	characteristic
72	D₇	—	2	2	no	—
73	C₂×C₅	—	2	3	no	—
74	C₂×C₅	—	14	2	no	—
75	C₂×C₅	C₂³×D₇	1	1	yes	characteristic
76	Q₈	—	7	6	no	—
77	Q₈	—	7	3	no	—
78	Q₈	C₂×C₅×D₇	1	1	yes	characteristic
79	D₄	—	7	6	no	—
80	D₄	—	7	1	no	—
81	D₄	C₂×C₅×D₇	1	3	yes	—
82	C₂×C₄	—	7	6	no	—
83	C₂×C₄	—	7	6	no	—
84	C₂×C₄	C₂×C₅×D₇	1	3	yes	—
85	C₇	C₅×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
86	C₅	#6554	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	—	7	2	no	—
88	C₂²	C₂²×C₅×D₇	1	3	yes	—
89	C₄	—	7	6	no	—
90	C₄	C₂²×C₅×D₇	1	3	yes	—
91	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	—	14	2	no	—
94	C₂	C₂³×C₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂³×D₇
commutator, cosocle	C₂×C₇	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₇
Fitting	C₅×C₇×#41	C₂
socle	C₂×C₅×C₇	C₂⁴
hypercenter	C₅×#41	D₇
hypocenter	C₇	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×#41	C₂	semidirect
2. C₅×Q₈×D₇	C₂	semidirect
3. C₅×#1159	C₂	semidirect
4. C₅×#1157	C₂	semidirect
5. C₂×C₅×Dic₁₄	C₂	semidirect
15. #6554	C₅	direct (N × H)
22. C₇×#41	C₂×C₅	semidirect
23. Q₈×D₇	C₂×C₅	semidirect
24. #1159	C₂×C₅	semidirect
25. #1157	C₂×C₅	semidirect
26. C₂×Dic₁₄	C₂×C₅	semidirect
29. C₅×#41	D₇	semidirect
53. C₅×C₇	2₋¹⁺⁴	semidirect
67. #41	C₅×D₇	semidirect
85. C₇	C₅×2₋¹⁺⁴	semidirect
86. C₅	#6554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×#41	2
C₅×Q₈×D₇	2
C₅×#1159	2
C₅×#1157	2
C₂×C₅×Dic₁₄	2
#6554	5
C₅×2₋¹⁺⁴	7

Subgroups — C5×#6554 #11765433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6554 #11765433