Subgroups — #14581084

Order 2624.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050152	C₂	1	2	yes	maximal, complemented
2	#13050149	C₂	1	4	yes	maximal, complemented
3	#13050142	C₂	1	4	yes	maximal, complemented
4	#13050139	C₂	1	4	yes	maximal, complemented
5	#125×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₆₄	C₂²	1	4	yes	—
7	C₂×D₁₆₄	C₂²	1	2	yes	—
8	C₂×C₄×D₄₁	C₂²	1	4	yes	—
9	C₂×Dic₈₂	C₂²	1	2	yes	—
10	C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
11	C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
12	C₄²×C₄₁	C₂²	1	1	yes	characteristic
13	#10620281	C₂²	1	4	yes	—
14	#10620281	C₂²	1	4	yes	—
15	#10620281	C₂²	1	4	yes	—
16	#10620279	C₂²	1	4	yes	—
17	C₂²×D₄₁	C₂³	1	4	yes	—
18	C₂×C₄×C₄₁	C₂³	1	4	yes	—
19	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₁	C₂³	1	2	yes	—
21	C₂×Dic₄₁	C₂³	1	4	yes	—
22	D₁₆₄	—	4	2	no	—
23	D₁₆₄	—	4	4	no	—
24	C₄×D₄₁	—	4	4	no	—
25	Dic₈₂	—	4	2	no	—
26	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
27	C₂×D₄₁	—	2	4	no	—
28	C₂×D₄₁	—	2	4	no	—
29	C₂×D₄₁	—	2	4	no	—
30	C₄×C₄₁	—	2	2	no	—
31	C₄×C₄₁	—	2	4	no	—
32	C₄×C₄₁	—	2	1	no	—
33	Dic₄₁	—	2	4	no	—
34	C₂×C₄₁	H(5,𝔽₂)	1	2	yes	—
35	C₂×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
36	D₄₁	—	4	4	no	—
37	#562	—	41	1	no	maximal, Sylow
38	C₄₁	#562	1	1	yes	characteristic, complemented, Sylow
39	#125	D₄₁	1	1	yes	characteristic, complemented
40	#124	—	41	2	no	—
41	#123	—	41	4	no	—
42	C₂²⋊Q₈	—	41	4	no	—
43	#121	—	41	4	no	—
44	C₂×Q₈	—	41	2	no	—
45	C₂×D₄	—	41	4	no	—
46	C₂×D₄	—	41	2	no	—
47	C₂²×C₄	—	41	4	no	—
48	C₄⋊C₄	—	41	4	no	—
49	C₄⋊C₄	C₂×D₄₁	1	4	yes	—
50	C₄⋊C₄	C₂×D₄₁	1	2	yes	—
51	C₂²⋊C₄	—	41	4	no	—
52	C₂²⋊C₄	—	41	4	no	—
53	C₂²⋊C₄	—	41	4	no	—
54	C₄²	C₂×D₄₁	1	1	yes	characteristic
55	C₂³	—	41	4	no	—
56	Q₈	—	164	2	no	—
57	D₄	—	164	4	no	—
58	D₄	—	164	2	no	—
59	C₂×C₄	—	41	4	no	—
60	C₂×C₄	—	164	4	no	—
61	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₁	1	2	yes	—
63	C₂×C₄	C₂²×D₄₁	1	4	yes	—
64	C₂²	—	82	4	no	—
65	C₂²	—	82	4	no	—
66	C₂²	—	82	4	no	—
67	C₂²	C₂³×D₄₁	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	2	2	no	—
70	C₄	—	2	1	no	—
71	C₄	—	82	4	no	—
72	C₂	—	164	4	no	—
73	C₂	#13050210	1	2	yes	—
74	C₂	#13050212	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₁
commutator, socle, cosocle	C₂²×C₄₁	C₂⁴
Fitting	#125×C₄₁	C₂
hypercenter	#125	D₄₁
hypocenter	C₄₁	#562
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #13050152	C₂	semidirect
2. #13050149	C₂	semidirect
3. #13050142	C₂	semidirect
4. #13050139	C₂	semidirect
5. #125×C₄₁	C₂	semidirect
38. C₄₁	#562	semidirect
39. #125	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050152	2
#13050149	2
#13050142	2
#13050139	2
#125×C₄₁	2
#562	41