Subgroups — C₂×#430 #2915

Order 128.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆	C₂	1	2	yes	maximal
2	C₂²×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#430	C₂	1	8	yes	maximal, direct product factor
4	C₂×#108	C₂	1	4	yes	maximal, complemented
5	C₂³×C₄	C₂²	1	1	yes	characteristic
6	C₂×M₁₆	—	2	4	no	—
7	C₂×M₁₆	—	2	2	no	—
8	C₂×M₁₆	C₄	1	4	yes	—
9	C₂×M₁₆	C₄	1	4	yes	—
10	C₂×M₁₆	C₂²	1	4	yes	—
11	C₂×M₁₆	C₂²	1	8	yes	—
12	C₂×M₁₆	C₂²	1	4	yes	—
13	C₂²×C₈	—	2	2	no	—
14	C₂²×C₈	C₂²	1	2	yes	—
15	#108	C₂²	1	16	yes	complemented
16	C₂⁴	Q₈	1	1	yes	characteristic
17	C₂²×C₄	C₂×C₄	1	2	yes	—
18	C₂²×C₄	C₂×C₄	1	2	yes	—
19	C₂²×C₄	D₄	1	2	yes	—
20	C₂²×C₄	D₄	1	2	yes	—
21	C₂²×C₄	Q₈	1	1	yes	characteristic
22	C₂²×C₄	Q₈	1	2	yes	—
23	C₂²×C₄	C₂³	1	2	yes	—
24	C₂²×C₄	C₂³	1	1	yes	characteristic
25	M₁₆	—	2	8	no	—
26	M₁₆	—	2	4	no	—
27	M₁₆	C₂×C₄	1	16	yes	—
28	M₁₆	C₂³	1	8	yes	—
29	C₂×C₈	—	2	8	no	—
30	C₂×C₈	—	2	4	no	—
31	C₂×C₈	C₂×C₄	1	4	yes	—
32	C₂×C₈	C₂×C₄	1	4	yes	—
33	C₂×C₈	C₂³	1	4	yes	—
34	C₂³	—	4	2	no	—
35	C₂³	C₄⋊C₄	1	2	yes	—
36	C₂³	C₄⋊C₄	1	2	yes	—
37	C₂³	C₂×Q₈	1	1	yes	characteristic
38	C₂³	C₂×Q₈	1	2	yes	—
39	C₂×C₄	C₄⋊C₄	1	4	yes	—
40	C₂×C₄	C₄⋊C₄	1	2	yes	—
41	C₂×C₄	C₄⋊C₄	1	2	yes	—
42	C₂×C₄	C₄⋊C₄	1	4	yes	—
43	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄	C₂²×C₄	1	4	yes	—
46	C₂×C₄	C₂×D₄	1	4	yes	—
47	C₂×C₄	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄	C₂×Q₈	1	2	yes	—
50	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄	C₂⁴	1	1	yes	characteristic
52	C₈	—	2	8	no	—
53	C₈	C₂²×C₄	1	8	yes	—
54	C₂²	—	2	4	no	—
55	C₂²	—	2	2	no	—
56	C₂²	—	4	2	no	—
57	C₂²	—	4	2	no	—
58	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂²	C₂×C₄⋊C₄	1	4	yes	—
60	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂²	C₂²×Q₈	1	1	yes	characteristic
62	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₄	C₂×C₄⋊C₄	1	4	yes	—
64	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₄	C₂³×C₄	1	1	yes	characteristic
66	C₄	C₂²×D₄	1	1	yes	characteristic
67	C₂	—	2	4	no	—
68	C₂	—	2	1	no	—
69	C₂	—	2	1	no	—
70	C₂	#430	1	2	yes	direct product factor
71	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂²	C₂×C₄⋊C₄
prime radical	C₂⁴	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #430	C₂	direct (N × H)
4. C₂×#108	C₂	semidirect
15. #108	C₂²	semidirect
70. C₂	#430	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×M₁₆	2
#430	2
C₂×#108	2

Subgroups — C2×#430 #2915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#430 #2915