Subgroups — C₂×#13112905 #15774486

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 186 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	#13112905	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	—	2	1	no	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	—	2	1	no	—
8	C₂×C₄×#1055	C₄	1	1	yes	characteristic
9	C₂×C₄×#1055	C₄	1	1	yes	characteristic
10	C₁₃×C₄⋊C₁₆	—	2	1	no	—
11	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
12	C₄⋊#6090	—	2	1	no	—
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	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×#1055	—	2	1	no	—
20	C₂²×#1055	C₈	1	1	yes	characteristic
21	C₂²×#1055	C₈	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	—	2	2	no	—
23	C₂×C₁₃×C₁₆	—	4	2	no	—
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×#6090	—	2	2	no	—
29	C₂×#6090	—	4	2	no	—
30	C₄×#1055	—	2	1	no	—
31	C₄×#1055	C₈	1	2	yes	—
32	C₄×#1055	C₂×C₄	1	2	yes	—
33	C₄×#1055	C₂×C₄	1	2	yes	—
34	C₂×#1370	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
38	C₂×C₈×C₁₃	—	2	2	no	—
39	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	D₈	1	2	yes	—
42	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
48	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×#1055	—	2	4	no	—
50	C₂×#1055	—	2	2	no	—
51	C₂×#1055	—	2	2	no	—
52	C₂×#1055	C₁₆	1	4	yes	complemented
53	C₂×#1055	C₂×C₈	1	2	yes	—
54	C₂×#1055	C₂×C₈	1	2	yes	—
55	C₁₃×C₁₆	—	4	2	no	—
56	#6090	—	4	2	no	—
57	C₂×C₄⋊C₁₆	—	13	1	no	—
58	C₂×C₄⋊C₁₆	D₁₃	1	1	yes	characteristic
59	C₂×C₈²	—	13	1	no	—
60	#1370	—	13	4	no	—
61	C₂³×C₁₃	C₄⋊C₈	1	1	yes	characteristic
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	#107	1	2	yes	—
67	C₂×C₄×C₁₃	#108	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
69	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
73	C₈×C₁₃	—	2	1	no	—
74	C₈×C₁₃	—	2	1	no	—
75	C₈×C₁₃	#107	1	2	yes	—
76	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
77	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
78	#1055	—	2	4	no	—
79	#1055	—	2	2	no	—
80	#1055	C₂×C₁₆	1	4	yes	complemented
81	C₂²×C₁₆	—	2	1	no	—
82	C₂²×C₁₆	—	26	1	no	—
83	C₂×C₄×C₈	—	13	1	no	—
84	C₂×C₄×C₈	—	13	1	no	—
85	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
86	C₄⋊C₁₆	—	2	1	no	—
87	C₄⋊C₁₆	—	13	2	no	—
88	C₄⋊C₁₆	—	26	1	no	—
89	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
90	C₈²	—	13	2	no	—
91	C₈²	—	13	2	no	—
92	C₂²×C₁₃	#335	1	2	yes	—
93	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
94	C₂²×C₁₃	#364	1	2	yes	—
95	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
96	C₄×C₁₃	—	2	1	no	—
97	C₄×C₁₃	—	2	1	no	—
98	C₄×C₁₃	#335	1	2	yes	—
99	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
100	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
101	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
102	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
103	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
104	C₂²×C₈	—	13	1	no	—
105	C₂²×C₈	—	13	1	no	—
106	C₂²×C₈	—	26	1	no	—
107	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
108	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
110	C₂×C₁₆	—	2	2	no	—
111	C₂×C₁₆	—	4	2	no	—
112	C₂×C₁₆	—	26	2	no	—
113	C₂×C₁₆	—	52	2	no	—
114	C₄×C₈	—	13	2	no	—
115	C₄×C₈	—	13	2	no	—
116	C₄×C₈	—	13	2	no	—
117	C₄×C₈	—	26	1	no	—
118	C₄×C₈	Dic₂₆	1	1	yes	characteristic
119	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
120	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
121	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
122	C₂×C₁₃	#1370	1	4	yes	complemented
123	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
124	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
125	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
126	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
127	C₂²×C₄	#6094	1	1	yes	characteristic
128	C₂²×C₄	#6101	1	1	yes	characteristic
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	13	4	no	—
132	C₂×C₈	—	13	2	no	—
133	C₂×C₈	—	26	4	no	—
134	C₂×C₈	—	26	2	no	—
135	C₂×C₈	—	26	2	no	—
136	C₂×C₈	#6101	1	1	yes	characteristic
137	C₂×C₈	#6101	1	1	yes	characteristic
138	C₂×C₈	#6104	1	2	yes	—
139	C₂×C₈	#6107	1	2	yes	—
140	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
141	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
142	C₄²	C₈×D₁₃	1	1	yes	characteristic
143	C₄²	#6094	1	1	yes	characteristic
144	C₄²	#6101	1	1	yes	characteristic
145	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
146	C₁₆	—	4	2	no	—
147	C₁₆	—	52	2	no	—
148	C₁₃	C₂×#1370	1	1	yes	characteristic, complemented, Sylow
149	C₂³	#88054	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	C₁₆×D₁₃	1	2	yes	—
152	C₂×C₄	#88038	1	2	yes	—
153	C₂×C₄	#88047	1	2	yes	—
154	C₂×C₄	#88054	1	1	yes	characteristic
155	C₂×C₄	#88054	1	1	yes	characteristic
156	C₂×C₄	#88054	1	1	yes	characteristic
157	C₂×C₄	#88062	1	2	yes	—
158	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
159	C₂×C₄	C₂×#6094	1	1	yes	characteristic
160	C₂×C₄	C₂×#6101	1	1	yes	characteristic
161	C₈	—	2	1	no	—
162	C₈	—	2	1	no	—
163	C₈	—	13	4	no	—
164	C₈	—	26	4	no	—
165	C₈	—	26	2	no	—
166	C₈	#88047	1	2	yes	—
167	C₈	C₂×#6104	1	1	yes	characteristic
168	C₈	C₂×#6107	1	1	yes	characteristic
169	C₂²	#11718071	1	2	yes	—
170	C₂²	#11718093	1	2	yes	—
171	C₂²	#11718103	1	2	yes	—
172	C₂²	C₂×#88054	1	1	yes	characteristic
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	#11718071	1	2	yes	—
176	C₄	#11718093	1	2	yes	—
177	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
178	C₄	C₂×#88038	1	1	yes	characteristic
179	C₄	C₂×#88047	1	1	yes	characteristic
180	C₄	C₂×#88062	1	1	yes	characteristic
181	C₂	#13112905	1	4	yes	direct product factor
182	C₂	C₂×#11718071	1	1	yes	characteristic
183	C₂	C₂×#11718093	1	1	yes	characteristic
184	C₂	C₂×#11718103	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1370
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
3. #13112905	C₂	direct (N × H)
52. C₂×#1055	C₁₆	semidirect
80. #1055	C₂×C₁₆	semidirect
122. C₂×C₁₃	#1370	semidirect
148. C₁₃	C₂×#1370	semidirect
181. C₂	#13112905	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
#13112905	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×#1370	13

Subgroups — C2×#13112905 #15774486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112905 #15774486