Subgroups — C₂×C₂₉×#322 #16815162

Order 3712.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₂₉	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#322	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₂₉	C₄	1	4	yes	—
5	C₂²×C₈×C₂₉	C₄	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₉	C₄	1	4	yes	—
8	C₄×C₈×C₂₉	C₄	1	2	yes	—
9	C₄×C₈×C₂₉	C₂²	1	4	yes	—
10	C₄×C₈×C₂₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₉	—	2	8	no	—
14	C₂×C₈×C₂₉	C₈	1	8	yes	complemented
15	C₂×C₈×C₂₉	C₂×C₄	1	8	yes	—
16	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
17	C₄²×C₂₉	C₂×C₄	1	2	yes	—
18	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₂₉	C₂³	1	1	yes	characteristic
20	C₂³×C₂₉	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₄²	1	2	yes	—
23	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
24	C₂×C₄×C₂₉	M₁₆	1	8	yes	—
25	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
27	C₈×C₂₉	—	2	8	no	—
28	C₈×C₂₉	C₂×C₈	1	8	yes	complemented
29	C₂×#322	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₂₉	C₄×C₈	1	2	yes	—
31	C₂²×C₂₉	#97	1	4	yes	—
32	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
33	C₄×C₂₉	C₄×C₈	1	2	yes	—
34	C₄×C₂₉	#97	1	4	yes	—
35	C₄×C₂₉	C₂²×C₈	1	2	yes	—
36	C₄×C₂₉	C₂×M₁₆	1	4	yes	—
37	C₂×C₄×C₈	C₂×C₂₉	1	2	yes	—
38	C₂×C₄×C₈	C₂×C₂₉	1	1	yes	characteristic
39	#322	C₂×C₂₉	1	4	yes	direct product factor
40	C₂×C₂₉	#322	1	4	yes	direct product factor
41	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₂₉	C₂×#97	1	2	yes	—
43	C₂²×C₈	C₄×C₂₉	1	4	yes	—
44	C₂²×C₈	C₄×C₂₉	1	2	yes	—
45	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
46	C₄×C₈	C₄×C₂₉	1	4	yes	—
47	C₄×C₈	C₄×C₂₉	1	2	yes	—
48	C₄×C₈	C₂²×C₂₉	1	4	yes	—
49	C₄×C₈	C₂²×C₂₉	1	2	yes	—
50	C₂₉	C₂×#322	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
52	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
53	C₂×C₈	—	2	8	no	—
54	C₂×C₈	C₈×C₂₉	1	8	yes	complemented
55	C₂×C₈	C₂×C₄×C₂₉	1	8	yes	—
56	C₂×C₈	C₂×C₄×C₂₉	1	4	yes	—
57	C₄²	C₂×C₄×C₂₉	1	2	yes	—
58	C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
59	C₄²	C₂³×C₂₉	1	1	yes	characteristic
60	C₂³	C₄²×C₂₉	1	1	yes	characteristic
61	C₂×C₄	C₄²×C₂₉	1	1	yes	characteristic
62	C₂×C₄	C₄²×C₂₉	1	2	yes	—
63	C₂×C₄	C₂×C₈×C₂₉	1	4	yes	—
64	C₂×C₄	M₁₆×C₂₉	1	8	yes	—
65	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
66	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
67	C₈	—	2	8	no	—
68	C₈	C₂×C₈×C₂₉	1	8	yes	complemented
69	C₂²	C₄×C₈×C₂₉	1	2	yes	—
70	C₂²	C₂₉×#97	1	4	yes	—
71	C₂²	C₂×C₄²×C₂₉	1	1	yes	characteristic
72	C₄	C₄×C₈×C₂₉	1	2	yes	—
73	C₄	C₂₉×#97	1	4	yes	—
74	C₄	C₂²×C₈×C₂₉	1	2	yes	—
75	C₄	C₂×M₁₆×C₂₉	1	4	yes	—
76	C₂	C₂₉×#322	1	4	yes	direct product factor
77	C₂	C₂×C₄×C₈×C₂₉	1	1	yes	characteristic
78	C₂	C₂×C₂₉×#97	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₂₉	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₉
Frattini, cosocle	C₄²	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#322	C₂	direct (N × H)
14. C₂×C₈×C₂₉	C₈	semidirect
28. C₈×C₂₉	C₂×C₈	semidirect
29. C₂×#322	C₂₉	direct (N × H)
39. #322	C₂×C₂₉	direct (N × H)
40. C₂×C₂₉	#322	direct (N × H)
50. C₂₉	C₂×#322	direct (N × H)
54. C₂×C₈	C₈×C₂₉	semidirect
68. C₈	C₂×C₈×C₂₉	semidirect
76. C₂	C₂₉×#322	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₂₉	2
C₂₉×#322	2
C₂×#322	29

Subgroups — C2×C29×#322 #16815162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#322 #16815162