Subgroups — C₂×#11719222 #13128123

Order 1664.

1168 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×#88180	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#11719222	C₂	1	16	yes	maximal, direct product factor
5	C₂×#88144	C₂	1	2	yes	maximal, complemented
6	C₂×#88142	C₂	1	2	yes	maximal, complemented
7	C₂×#88132	C₂	1	4	yes	maximal
8	C₂×C₄×Dic₂₆	C₂	1	4	yes	maximal, complemented
9	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×Dic₁₃	C₂²	1	2	yes	—
11	C₂²×Dic₂₆	C₂²	1	4	yes	—
12	C₁₃×#117	C₂²	1	8	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
17	#88180	C₂²	1	8	yes	—
18	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
19	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
20	C₂×#6101	C₂²	1	4	yes	—
21	C₂×#6101	C₂²	1	4	yes	—
22	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
24	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	C₂²	1	8	yes	—
27	#88144	C₂²	1	16	yes	complemented
28	#88142	C₂²	1	16	yes	complemented
29	#88132	C₂²	1	32	yes	—
30	C₄×Dic₂₆	C₂²	1	32	yes	complemented
31	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	Q₈	1	8	yes	complemented
33	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₃	—	2	8	no	—
38	C₂²×Dic₁₃	C₂³	1	8	yes	—
39	C₂²×Dic₁₃	C₂³	1	2	yes	—
40	C₂²×Dic₁₃	C₂³	1	4	yes	—
41	C₂²×Dic₁₃	C₂³	1	2	yes	—
42	C₂×Dic₂₆	—	2	16	no	—
43	C₂×Dic₂₆	C₂³	1	16	yes	—
44	C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
45	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
46	C₄²×C₁₃	C₂³	1	8	yes	—
47	C₂²⋊Dic₁₃	C₂³	1	8	yes	—
48	C₄⋊Dic₁₃	C₂³	1	16	yes	—
49	C₄⋊Dic₁₃	C₂³	1	8	yes	—
50	#6101	C₂³	1	16	yes	—
51	#6101	C₂³	1	16	yes	—
52	C₄×Dic₁₃	C₂³	1	8	yes	—
53	C₄×Dic₁₃	C₂³	1	8	yes	—
54	C₄×Dic₁₃	C₂³	1	4	yes	—
55	C₄×Dic₁₃	C₂³	1	4	yes	—
56	C₂×#533	—	13	1	no	maximal, Sylow
57	C₂³×C₁₃	—	2	4	no	—
58	C₂³×C₁₃	C₂×Q₈	1	4	yes	—
59	C₂³×C₁₃	C₂⁴	1	2	yes	—
60	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	8	no	—
62	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
63	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
64	C₂×C₄×C₁₃	C₂×Q₈	1	16	yes	complemented
65	C₂×C₄×C₁₃	C₂⁴	1	8	yes	—
66	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
67	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
68	C₂×Dic₁₃	—	2	8	no	—
69	C₂×Dic₁₃	—	2	4	no	—
70	C₂×Dic₁₃	—	2	16	no	—
71	C₂×Dic₁₃	#41	1	8	yes	—
72	C₂×Dic₁₃	C₂⁴	1	4	yes	—
73	C₂×Dic₁₃	C₂⁴	1	8	yes	—
74	C₂×Dic₁₃	C₂⁴	1	4	yes	—
75	Dic₂₆	—	2	32	no	—
76	#533	—	13	16	no	—
77	C₂×C₄⋊Q₈	—	13	2	no	—
78	C₂×#125	—	13	2	no	—
79	C₂×C₂²⋊Q₈	—	13	4	no	—
80	C₂×C₄×Q₈	—	13	4	no	—
81	C₂×#117	—	13	1	no	—
82	C₂×#117	D₁₃	1	1	yes	characteristic
83	C₂²×C₄²	—	13	1	no	—
84	C₂²×C₁₃	—	2	8	no	—
85	C₂²×C₁₃	—	2	4	no	—
86	C₂²×C₁₃	C₂²×Q₈	1	4	yes	—
87	C₂²×C₁₃	C₂²×Q₈	1	2	yes	—
88	C₂²×C₁₃	C₂×#41	1	4	yes	—
89	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
90	C₄×C₁₃	—	2	8	no	—
91	C₄×C₁₃	C₂²×Q₈	1	4	yes	—
92	C₄×C₁₃	C₂²×Q₈	1	4	yes	—
93	Dic₁₃	—	2	8	no	—
94	Dic₁₃	—	2	4	no	—
95	Dic₁₃	C₂×#41	1	8	yes	—
96	C₂²×Q₈	—	13	4	no	—
97	C₂³×C₄	—	13	2	no	—
98	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
99	C₄⋊Q₈	—	13	16	no	—
100	#125	—	13	16	no	—
101	C₂²⋊Q₈	—	13	32	no	—
102	C₄×Q₈	—	13	32	no	—
103	#117	—	13	8	no	—
104	#117	C₂×D₁₃	1	8	yes	—
105	C₂×C₄⋊C₄	—	13	2	no	—
106	C₂×C₄⋊C₄	—	13	4	no	—
107	C₂×C₄⋊C₄	—	13	4	no	—
108	C₂×C₄⋊C₄	—	13	4	no	—
109	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
110	C₂×C₂²⋊C₄	—	13	2	no	—
111	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
112	C₂×C₄²	—	13	1	no	—
113	C₂×C₄²	—	13	1	no	—
114	C₂×C₄²	—	13	8	no	—
115	C₂×C₄²	—	13	2	no	—
116	C₂×C₄²	—	13	2	no	—
117	C₂×C₄²	C₂×D₁₃	1	2	yes	—
118	C₂×C₁₃	—	2	4	no	—
119	C₂×C₁₃	#533	1	4	yes	complemented
120	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
121	C₂×C₁₃	C₂²×#41	1	2	yes	—
122	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
123	C₂×Q₈	—	13	16	no	—
124	C₂×Q₈	—	26	16	no	—
125	C₂²×C₄	—	13	2	no	—
126	C₂²×C₄	—	13	2	no	—
127	C₂²×C₄	—	13	8	no	—
128	C₂²×C₄	—	13	4	no	—
129	C₂²×C₄	—	26	8	no	—
130	C₂²×C₄	Dic₂₆	1	8	yes	complemented
131	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
132	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
133	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
134	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
135	C₄⋊C₄	—	13	8	no	—
136	C₄⋊C₄	—	13	16	no	—
137	C₄⋊C₄	—	13	16	no	—
138	C₄⋊C₄	—	13	16	no	—
139	C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
140	C₂²⋊C₄	—	13	8	no	—
141	C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
142	C₄²	—	13	8	no	—
143	C₄²	—	13	4	no	—
144	C₄²	—	13	4	no	—
145	C₄²	—	13	8	no	—
146	C₄²	C₂²×D₁₃	1	8	yes	—
147	C₁₃	C₂×#533	1	1	yes	characteristic, complemented, Sylow
148	C₂³	—	2	4	no	—
149	C₂³	C₂×Dic₂₆	1	4	yes	—
150	C₂³	C₂³×D₁₃	1	2	yes	—
151	C₂³	C₂³×D₁₃	1	1	yes	characteristic
152	Q₈	—	26	32	no	—
153	C₂×C₄	—	2	8	no	—
154	C₂×C₄	—	13	8	no	—
155	C₂×C₄	—	13	4	no	—
156	C₂×C₄	—	13	4	no	—
157	C₂×C₄	—	13	8	no	—
158	C₂×C₄	—	26	16	no	—
159	C₂×C₄	—	26	4	no	—
160	C₂×C₄	—	26	8	no	—
161	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
162	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
163	C₂×C₄	C₂×Dic₂₆	1	16	yes	complemented
164	C₂×C₄	C₂³×D₁₃	1	8	yes	—
165	C₂×C₄	C₂³×D₁₃	1	2	yes	—
166	C₂×C₄	C₂³×D₁₃	1	2	yes	—
167	C₂²	—	2	8	no	—
168	C₂²	—	2	4	no	—
169	C₂²	C₂²×Dic₂₆	1	4	yes	—
170	C₂²	C₂²×Dic₂₆	1	2	yes	—
171	C₂²	#41×D₁₃	1	4	yes	—
172	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
173	C₄	—	2	8	no	—
174	C₄	—	13	8	no	—
175	C₄	—	26	4	no	—
176	C₄	—	26	8	no	—
177	C₄	C₂²×Dic₂₆	1	4	yes	—
178	C₄	C₂²×Dic₂₆	1	4	yes	—
179	C₂	—	2	4	no	—
180	C₂	#11719222	1	4	yes	direct product factor
181	C₂	C₂³×Dic₂₆	1	1	yes	characteristic
182	C₂	C₂×#41×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂⁴
prime radical	C₂⁴×C₁₃	C₂³
hypercenter	C₂×#117	D₁₃
hypocenter	C₁₃	C₂×#533
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
4. #11719222	C₂	direct (N × H)
5. C₂×#88144	C₂	semidirect
6. C₂×#88142	C₂	semidirect
8. C₂×C₄×Dic₂₆	C₂	semidirect
27. #88144	C₂²	semidirect
28. #88142	C₂²	semidirect
30. C₄×Dic₂₆	C₂²	semidirect
32. C₂²×C₄×C₁₃	Q₈	semidirect
64. C₂×C₄×C₁₃	C₂×Q₈	semidirect
119. C₂×C₁₃	#533	semidirect
130. C₂²×C₄	Dic₂₆	semidirect
147. C₁₃	C₂×#533	semidirect
163. C₂×C₄	C₂×Dic₂₆	semidirect
180. C₂	#11719222	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×C₁₃×#117	2
C₂×#88180	2
C₂²×C₄×Dic₁₃	2
#11719222	2
C₂×#88144	2
C₂×#88142	2
C₂×#88132	2
C₂×C₄×Dic₂₆	2
C₂×#533	13

Subgroups — C2×#11719222 #13128123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719222 #13128123