Subgroups — C₂×#13099498 #72253202

Order 3200.

672 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×#11716679	C₂	1	2	yes	maximal
3	#13099498	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₅²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₅²	C₄	1	1	yes	characteristic
7	C₅²×#97	C₄	1	2	yes	—
8	C₅²×#97	C₂²	1	2	yes	—
9	#11716679	C₄	1	4	yes	complemented
10	#11716679	C₂²	1	4	yes	—
11	C₂×#87756	C₄	1	4	yes	complemented
12	C₂×#64686	—	5	6	no	maximal
13	C₂²×C₄×C₅²	—	2	1	no	—
14	C₂²×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
15	C₂×C₅²×C₈	—	2	1	no	—
16	C₂×C₅²×C₈	—	2	1	no	—
17	C₂×C₅²×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₅²×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₅²×C₈	C₂×C₄	1	2	yes	—
20	C₂×C₅²×C₈	C₂×C₄	1	2	yes	—
21	C₂×C₅²×C₈	C₂³	1	1	yes	characteristic
22	C₄²×C₅²	—	2	1	no	—
23	C₄²×C₅²	C₂×C₄	1	2	yes	—
24	#87756	C₂×C₄	1	8	yes	complemented
25	C₂×C₅×#97	D₅	1	6	yes	—
26	C₂×#3944	—	5	12	no	—
27	#64686	—	5	24	no	—
28	C₂³×C₅²	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅²	—	2	2	no	—
30	C₂×C₄×C₅²	—	4	2	no	—
31	C₂×C₄×C₅²	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₅²	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₅²	M₁₆	1	1	yes	characteristic
34	C₂×C₄×C₅²	M₁₆	1	1	yes	characteristic
35	C₂×C₄×C₅²	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
37	C₅²×C₈	—	2	2	no	—
38	C₅²×C₈	C₄²	1	2	yes	—
39	C₅²×C₈	C₂²×C₄	1	2	yes	—
40	C₂²×C₅×C₈	Dic₅	1	6	yes	—
41	C₂²×C₅×C₈	C₂×D₅	1	6	yes	—
42	C₂×C₄²×C₅	Dic₅	1	6	yes	—
43	C₅×#97	Dic₅	1	12	yes	—
44	C₅×#97	C₂×D₅	1	12	yes	—
45	#3944	—	5	24	no	—
46	#3944	—	5	24	no	—
47	C₂×#672	—	5	24	no	—
48	C₂×#347	—	25	1	no	Sylow
49	C₂²×C₅²	—	2	2	no	—
50	C₂²×C₅²	#97	1	1	yes	characteristic
51	C₂²×C₅²	#97	1	1	yes	characteristic
52	C₂²×C₅²	C₂×M₁₆	1	1	yes	characteristic
53	C₄×C₅²	—	4	2	no	—
54	C₄×C₅²	#97	1	1	yes	characteristic
55	C₄×C₅²	#97	1	1	yes	characteristic
56	C₄×C₅²	C₂×C₄²	1	1	yes	characteristic
57	C₄×C₅²	C₂×M₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₅	—	2	6	no	—
59	C₂²×C₄×C₅	C₂×Dic₅	1	6	yes	—
60	C₂×C₅×C₈	—	2	6	no	—
61	C₂×C₅×C₈	—	2	6	no	—
62	C₂×C₅×C₈	C₄×D₅	1	12	yes	—
63	C₂×C₅×C₈	C₄×D₅	1	12	yes	—
64	C₂×C₅×C₈	C₂×Dic₅	1	12	yes	—
65	C₂×C₅×C₈	C₂×Dic₅	1	6	yes	—
66	C₂×C₅×C₈	C₂²×D₅	1	6	yes	—
67	C₄²×C₅	—	2	6	no	—
68	C₄²×C₅	C₂×Dic₅	1	12	yes	—
69	#672	—	5	48	no	—
70	C₂×M₃₂	—	25	2	no	—
71	C₂×#97	C₅⋊D₅	1	1	yes	characteristic
72	#347	—	25	4	no	—
73	C₂×C₅²	—	2	1	no	—
74	C₂×C₅²	—	2	1	no	—
75	C₂×C₅²	#347	1	2	yes	complemented
76	C₂×C₅²	C₂×#97	1	1	yes	characteristic
77	C₂³×C₅	#681	1	6	yes	—
78	C₂×C₄×C₅	—	2	12	no	—
79	C₂×C₄×C₅	—	4	12	no	—
80	C₂×C₄×C₅	#681	1	6	yes	—
81	C₂×C₄×C₅	#681	1	6	yes	—
82	C₂×C₄×C₅	#681	1	6	yes	—
83	C₂×C₄×C₅	C₄×Dic₅	1	6	yes	—
84	C₂×C₄×C₅	C₄×Dic₅	1	6	yes	—
85	C₂×C₄×C₅	C₂²×Dic₅	1	6	yes	—
86	C₅×C₈	—	2	12	no	—
87	C₅×C₈	C₄×Dic₅	1	12	yes	—
88	C₅×C₈	C₂×C₄×D₅	1	12	yes	—
89	C₂²×C₈	#1039	1	1	yes	characteristic
90	C₂²×C₈	C₂×C₅⋊D₅	1	1	yes	characteristic
91	C₂×C₄²	#1039	1	1	yes	characteristic
92	M₃₂	—	25	4	no	—
93	M₃₂	—	25	4	no	—
94	C₂×C₁₆	—	25	4	no	—
95	#97	#1039	1	2	yes	—
96	#97	C₂×C₅⋊D₅	1	2	yes	—
97	C₅²	C₂×#347	1	1	yes	characteristic, complemented, Sylow
98	C₂²×C₅	—	2	12	no	—
99	C₂²×C₅	#3935	1	6	yes	—
100	C₂²×C₅	#3935	1	6	yes	—
101	C₂²×C₅	C₂×#681	1	6	yes	—
102	C₄×C₅	—	4	12	no	—
103	C₄×C₅	#3935	1	6	yes	—
104	C₄×C₅	#3935	1	6	yes	—
105	C₄×C₅	C₂×#681	1	6	yes	—
106	C₄×C₅	C₂×C₄×Dic₅	1	6	yes	—
107	C₂²×C₄	—	2	1	no	—
108	C₂²×C₄	C₂×#1039	1	1	yes	characteristic
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	C₄×C₅⋊D₅	1	2	yes	—
112	C₂×C₈	C₄×C₅⋊D₅	1	2	yes	—
113	C₂×C₈	C₂×#1039	1	2	yes	—
114	C₂×C₈	C₂×#1039	1	1	yes	characteristic
115	C₂×C₈	C₂²×C₅⋊D₅	1	1	yes	characteristic
116	C₄²	—	2	1	no	—
117	C₄²	C₂×#1039	1	2	yes	—
118	C₁₆	—	25	8	no	—
119	C₂×C₅	—	2	6	no	—
120	C₂×C₅	—	2	6	no	—
121	C₂×C₅	#64686	1	12	yes	complemented
122	C₂×C₅	C₂×#3935	1	6	yes	—
123	C₂³	#87804	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	#87804	1	1	yes	characteristic
127	C₂×C₄	#87804	1	1	yes	characteristic
128	C₂×C₄	#87804	1	1	yes	characteristic
129	C₂×C₄	C₄×#1039	1	1	yes	characteristic
130	C₂×C₄	C₄×#1039	1	1	yes	characteristic
131	C₂×C₄	C₂²×#1039	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	C₄×#1039	1	2	yes	—
134	C₈	C₂×C₄×C₅⋊D₅	1	2	yes	—
135	C₅	C₂×#64686	1	6	yes	complemented
136	C₂²	—	2	2	no	—
137	C₂²	#11716670	1	1	yes	characteristic
138	C₂²	#11716670	1	1	yes	characteristic
139	C₂²	C₂×#87804	1	1	yes	characteristic
140	C₄	—	4	2	no	—
141	C₄	#11716670	1	1	yes	characteristic
142	C₄	#11716670	1	1	yes	characteristic
143	C₄	C₂×#87804	1	1	yes	characteristic
144	C₄	C₂×C₄×#1039	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	2	1	no	—
147	C₂	#13099498	1	2	yes	direct product factor
148	C₂	C₂×#11716670	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#1039
commutator	C₄×C₅²	C₂×C₄²
Frattini	C₂×C₈	C₂²×C₅⋊D₅
Fitting	C₂×C₅²×#97	C₂
socle	C₂²×C₅²	#97
prime radical	C₂³×C₅²	M₁₆
cosocle	C₂×C₅²×C₈	C₂³
hypercenter	C₂×#97	C₅⋊D₅
hypocenter	C₅²	C₂×#347
LCS	G ▷ C₄×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
3. #13099498	C₂	direct (N × H)
9. #11716679	C₄	semidirect
11. C₂×#87756	C₄	semidirect
24. #87756	C₂×C₄	semidirect
75. C₂×C₅²	#347	semidirect
97. C₅²	C₂×#347	semidirect
121. C₂×C₅	#64686	semidirect
135. C₅	C₂×#64686	semidirect
147. C₂	#13099498	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×C₅²×#97	2
C₂×#11716679	2
#13099498	2
C₂×#64686	5

Subgroups — C2×#13099498 #72253202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13099498 #72253202