Subgroups — C₂×#330 #1523

Order 128.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×#97	C₂	1	2	yes	maximal
3	#330	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	—	2	2	no	—
5	#125	—	2	2	no	—
6	#125	C₄	1	2	yes	—
7	#125	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄	—	2	2	no	—
9	C₂×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	#97	—	2	2	no	—
12	#97	C₂²	1	4	yes	—
13	C₂²×C₄	—	2	2	no	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄	D₄	1	2	yes	—
16	C₂×C₈	—	2	8	no	—
17	C₂×C₈	—	2	4	no	—
18	C₄⋊C₄	—	2	4	no	—
19	C₄⋊C₄	—	2	2	no	—
20	C₄⋊C₄	—	2	4	no	—
21	C₄⋊C₄	C₂×C₄	1	4	yes	—
22	C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄²	D₄	1	2	yes	—
24	C₄²	C₂³	1	1	yes	characteristic
25	C₂³	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	2	4	no	—
28	C₂×C₄	—	2	4	no	—
29	C₂×C₄	—	4	4	no	—
30	C₂×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄	C₂×D₄	1	2	yes	—
34	C₈	—	2	8	no	—
35	C₂²	#101	1	2	yes	—
36	C₂²	#104	1	4	yes	—
37	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	—	2	1	no	—
40	C₄	—	2	2	no	—
41	C₄	—	2	2	no	—
42	C₄	—	4	4	no	—
43	C₂	#330	1	4	yes	direct product factor
44	C₂	C₂×#101	1	1	yes	characteristic
45	C₂	C₂×#104	1	2	yes	—

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

N	H ≅ G/N	type
3. #330	C₂	direct (N × H)
43. C₂	#330	direct (N × H)

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