Subgroups — D₁₃×C₃⋊(C₃⋊(C₇⋊D₇)) #37525645

Order 22932.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×C₃⋊(C₇⋊D₇)	—	3	4	no	maximal
5	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₇⋊D₉₁)	—	3	4	no	—
7	C₁₃×C₃⋊(C₇⋊D₇)	—	3	4	no	—
8	C₃×C₇²×D₁₃	D₃	1	4	yes	complemented
9	D₁₃×C₃⋊D₂₁	—	7	8	no	maximal
10	D₁₃×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₃	C₂×D₃	1	4	yes	complemented
12	C₂×C₃⋊(C₃⋊(C₇⋊D₇))	—	13	1	no	maximal, Hall
13	C₃⋊D₂₇₃	—	7	8	no	—
14	C₁₃×C₃⋊D₂₁	—	7	8	no	—
15	C₃²×C₇×D₁₃	D₇	1	8	yes	complemented
16	C₇⋊D₉₁	—	9	1	no	—
17	C₁₃×C₇⋊D₇	—	9	1	no	—
18	C₇²×D₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
19	D₁₃×D₂₁	—	21	32	no	—
20	C₂×C₃²×C₇²	—	13	1	no	—
21	C₃⋊(C₃⋊(C₇⋊D₇))	—	13	1	no	—
22	C₃⋊(C₃⋊(C₇⋊D₇))	D₁₃	1	1	yes	characteristic, direct product factor
23	C₃²×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
24	C₇²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃⋊(C₇⋊D₇)	—	39	4	no	—
26	D₂₇₃	—	21	32	no	—
27	C₁₃×D₂₁	—	21	32	no	—
28	C₃×C₇×D₁₃	D₂₁	1	32	yes	complemented
29	C₃⋊D₃×D₁₃	—	49	1	no	Hall
30	C₃²×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₇×D₁₃	—	63	8	no	—
32	C₂×C₃×C₇²	—	13	4	no	—
33	C₃⋊(C₇⋊D₇)	—	3	4	no	—
34	C₃⋊(C₇⋊D₇)	—	39	4	no	—
35	C₃×C₇×C₁₃	C₂×D₂₁	1	32	yes	complemented
36	C₂×C₃⋊D₂₁	—	91	8	no	—
37	C₃⋊D₃₉	—	49	1	no	—
38	C₁₃×C₃⋊D₃	—	49	1	no	—
39	C₃²×D₁₃	C₇⋊D₇	1	1	yes	characteristic, complemented
40	C₂×C₇⋊D₇	—	117	1	no	Hall
41	D₉₁	—	63	8	no	—
42	C₇×D₁₃	C₃⋊D₂₁	1	8	yes	complemented
43	C₁₃×D₇	—	63	8	no	—
44	D₃×D₁₃	—	147	4	no	—
45	C₃×C₇²	D₃×D₁₃	1	4	yes	complemented
46	C₂×C₃²×C₇	—	13	8	no	—
47	C₃⋊D₂₁	—	7	8	no	—
48	C₃⋊D₂₁	—	91	8	no	—
49	C₃²×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇²	—	13	1	no	—
51	C₇⋊D₇	—	9	1	no	—
52	C₇⋊D₇	—	117	1	no	—
53	C₇×C₁₃	C₂×C₃⋊D₂₁	1	8	yes	complemented
54	C₂×D₂₁	—	273	32	no	—
55	D₃₉	—	147	4	no	—
56	C₃×D₁₃	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
57	D₃×C₁₃	—	147	4	no	—
58	C₃²×C₇	D₇×D₁₃	1	8	yes	complemented
59	C₂×D₁₃	—	441	1	no	Hall
60	C₇²	C₃⋊D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃×C₇	—	13	32	no	—
62	D₂₁	—	273	32	no	—
63	D₂₁	—	21	32	no	—
64	C₃×C₁₃	C₂×C₃⋊(C₇⋊D₇)	1	4	yes	complemented
65	C₂×C₃⋊D₃	—	637	1	no	Hall
66	C₂×D₇	—	819	8	no	—
67	C₂×C₁₃	—	441	1	no	—
68	D₁₃	—	441	1	no	—
69	D₁₃	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor
70	C₃×C₇	D₁₃×D₂₁	1	32	yes	complemented
71	C₂×C₃²	—	13	1	no	—
72	C₃⋊D₃	—	49	1	no	—
73	C₃⋊D₃	—	637	1	no	—
74	C₂×C₇	—	13	8	no	—
75	D₇	—	819	8	no	—
76	D₇	—	63	8	no	—
77	C₁₃	C₂×C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₃	—	1911	4	no	—
79	C₃²	D₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₁₃×C₃⋊D₂₁	1	8	yes	complemented
81	C₂×C₃	—	13	4	no	—
82	D₃	—	1911	4	no	—
83	D₃	—	147	4	no	—
84	C₂²	—	5733	1	no	Sylow
85	C₃	D₁₃×C₃⋊(C₇⋊D₇)	1	4	yes	complemented
86	C₂	—	13	1	no	—
87	C₂	—	5733	1	no	—
88	C₂	—	441	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×D₁₃	C₂	semidirect
2. C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	semidirect
3. C₃⋊(C₃⋊(C₇⋊D₉₁))	C₂	semidirect
5. C₃²×C₇²×C₁₃	C₂²	semidirect
8. C₃×C₇²×D₁₃	D₃	semidirect
11. C₃×C₇²×C₁₃	C₂×D₃	semidirect
15. C₃²×C₇×D₁₃	D₇	semidirect
18. C₇²×D₁₃	C₃⋊D₃	semidirect
22. C₃⋊(C₃⋊(C₇⋊D₇))	D₁₃	direct (N × H)
23. C₃²×C₇×C₁₃	C₂×D₇	semidirect
24. C₇²×C₁₃	C₂×C₃⋊D₃	semidirect
28. C₃×C₇×D₁₃	D₂₁	semidirect
30. C₃²×C₇²	C₂×D₁₃	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₁	semidirect
39. C₃²×D₁₃	C₇⋊D₇	semidirect
42. C₇×D₁₃	C₃⋊D₂₁	semidirect
45. C₃×C₇²	D₃×D₁₃	semidirect
49. C₃²×C₁₃	C₂×C₇⋊D₇	semidirect
53. C₇×C₁₃	C₂×C₃⋊D₂₁	semidirect
56. C₃×D₁₃	C₃⋊(C₇⋊D₇)	semidirect
58. C₃²×C₇	D₇×D₁₃	semidirect
60. C₇²	C₃⋊D₃×D₁₃	semidirect
64. C₃×C₁₃	C₂×C₃⋊(C₇⋊D₇)	semidirect
69. D₁₃	C₃⋊(C₃⋊(C₇⋊D₇))	direct (N × H)
70. C₃×C₇	D₁₃×D₂₁	semidirect
77. C₁₃	C₂×C₃⋊(C₃⋊(C₇⋊D₇))	semidirect
79. C₃²	D₁₃×C₇⋊D₇	semidirect
80. C₇	D₁₃×C₃⋊D₂₁	semidirect
85. C₃	D₁₃×C₃⋊(C₇⋊D₇)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×D₁₃	2
C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	2
C₃⋊(C₃⋊(C₇⋊D₉₁))	2
D₁₃×C₃⋊(C₇⋊D₇)	3
D₁₃×C₃⋊D₂₁	7
C₂×C₃⋊(C₃⋊(C₇⋊D₇))	13

Subgroups — D13×C3⋊(C3⋊(C7⋊D7)) #37525645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₃⋊(C₃⋊(C₇⋊D₇)) #37525645