Subgroups — C₂×#13112755 #15771906

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
3	#13112755	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	2	yes	—
8	C₂×C₄×#1055	C₄	1	1	yes	characteristic
9	C₂×C₄×#1055	C₄	1	1	yes	characteristic
10	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
11	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
12	C₄×#6090	C₄	1	2	yes	—
13	C₄×#6090	C₂²	1	2	yes	—
14	C₈×#1055	C₄	1	2	yes	—
15	C₈×#1055	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×#1055	C₈	1	2	yes	—
20	C₂²×#1055	C₈	1	2	yes	—
21	C₂×C₁₃×C₁₆	—	2	4	no	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×#6090	—	2	4	no	—
28	C₂×#6090	C₂×C₄	1	4	yes	—
29	C₄×#1055	C₈	1	2	yes	—
30	C₄×#1055	C₈	1	2	yes	—
31	C₄×#1055	C₂×C₄	1	2	yes	—
32	C₄×#1055	C₂×C₄	1	2	yes	—
33	C₂×#1312	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
40	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₁₃	C₄²	1	1	yes	characteristic
44	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×#1055	—	2	4	no	—
48	C₂×#1055	C₁₆	1	8	yes	complemented
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₂×#1055	C₂×C₈	1	4	yes	—
51	C₁₃×C₁₆	—	2	4	no	—
52	#6090	—	2	4	no	—
53	C₂×C₄×C₁₆	—	13	1	no	—
54	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
55	C₂×C₈²	—	13	1	no	—
56	#1312	—	13	4	no	—
57	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₃	#97	1	2	yes	—
62	C₂×C₄×C₁₃	#97	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
64	C₂×C₄×C₁₃	M₃₂	1	4	yes	—
65	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
68	C₈×C₁₃	#97	1	2	yes	—
69	C₈×C₁₃	#97	1	2	yes	—
70	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
71	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
72	#1055	—	2	4	no	—
73	#1055	C₂×C₁₆	1	8	yes	complemented
74	C₂²×C₁₆	—	13	2	no	—
75	C₂²×C₁₆	Dic₁₃	1	2	yes	—
76	C₂×C₄×C₈	—	13	1	no	—
77	C₂×C₄×C₈	—	13	1	no	—
78	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
79	C₄×C₁₆	—	13	2	no	—
80	C₄×C₁₆	—	13	2	no	—
81	C₄×C₁₆	Dic₁₃	1	2	yes	—
82	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
83	C₈²	—	13	2	no	—
84	C₈²	—	13	2	no	—
85	C₂²×C₁₃	#322	1	2	yes	—
86	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
87	C₂²×C₁₃	#346	1	2	yes	—
88	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
89	C₄×C₁₃	#322	1	2	yes	—
90	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
91	C₄×C₁₃	#346	1	2	yes	—
92	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
93	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
94	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
95	C₄×C₁₃	C₂×M₃₂	1	2	yes	—
96	C₂²×C₈	—	13	2	no	—
97	C₂²×C₈	—	13	2	no	—
98	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
99	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
100	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
101	C₂×C₁₆	—	2	4	no	—
102	C₂×C₁₆	—	13	4	no	—
103	C₂×C₁₆	—	26	4	no	—
104	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
105	C₄×C₈	—	13	2	no	—
106	C₄×C₈	—	13	2	no	—
107	C₄×C₈	—	13	2	no	—
108	C₄×C₈	—	13	2	no	—
109	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
110	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
111	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
112	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
113	C₂×C₁₃	#1312	1	4	yes	complemented
114	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
115	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
116	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
117	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
118	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
119	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
120	C₂×C₈	—	13	4	no	—
121	C₂×C₈	—	13	8	no	—
122	C₂×C₈	—	13	4	no	—
123	C₂×C₈	—	26	4	no	—
124	C₂×C₈	#6094	1	4	yes	—
125	C₂×C₈	#6099	1	4	yes	—
126	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
127	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
128	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
129	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
130	C₄²	C₈×D₁₃	1	1	yes	characteristic
131	C₄²	C₈×D₁₃	1	1	yes	characteristic
132	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
133	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
134	C₁₆	—	2	4	no	—
135	C₁₆	—	26	4	no	—
136	C₁₃	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
137	C₂³	C₈×Dic₁₃	1	1	yes	characteristic
138	C₂×C₄	C₁₆×D₁₃	1	4	yes	—
139	C₂×C₄	#88038	1	4	yes	—
140	C₂×C₄	#88043	1	2	yes	—
141	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
142	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
143	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
144	C₂×C₄	#88055	1	2	yes	—
145	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
146	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
147	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
148	C₈	—	13	8	no	—
149	C₈	—	26	4	no	—
150	C₈	#88043	1	2	yes	—
151	C₈	#88055	1	2	yes	—
152	C₈	C₂×#6094	1	2	yes	—
153	C₈	C₂×#6099	1	2	yes	—
154	C₂²	#11718046	1	2	yes	—
155	C₂²	C₁₆×Dic₁₃	1	2	yes	—
156	C₂²	#11718094	1	2	yes	—
157	C₂²	C₂×C₈×Dic₁₃	1	1	yes	characteristic
158	C₄	#11718046	1	2	yes	—
159	C₄	C₁₆×Dic₁₃	1	2	yes	—
160	C₄	#11718094	1	2	yes	—
161	C₄	C₂×C₁₆×D₁₃	1	2	yes	—
162	C₄	C₂×#88038	1	2	yes	—
163	C₄	C₂×#88043	1	1	yes	characteristic
164	C₄	C₂×#88055	1	1	yes	characteristic
165	C₂	#13112755	1	4	yes	direct product factor
166	C₂	C₂×#11718046	1	1	yes	characteristic
167	C₂	C₂×C₁₆×Dic₁₃	1	1	yes	characteristic
168	C₂	C₂×#11718094	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1312
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. #13112755	C₂	direct (N × H)
48. C₂×#1055	C₁₆	semidirect
73. #1055	C₂×C₁₆	semidirect
113. C₂×C₁₃	#1312	semidirect
136. C₁₃	C₂×#1312	semidirect
165. C₂	#13112755	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×C₄×#6090	2
C₂×C₈×#1055	2
#13112755	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#1312	13

Subgroups — C2×#13112755 #15771906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112755 #15771906