Subgroups — C₂×#13125360 #16732535

Order 3328.

1902 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719175	C₂	1	2	yes	maximal
2	#13125360	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718363	C₂	1	8	yes	maximal, complemented
4	C₂×#11718767	C₂	1	4	yes	maximal
5	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88180	C₂²	1	4	yes	—
9	C₂×#88178	—	2	4	no	—
10	#11719175	—	2	8	no	—
11	#11719175	C₂²	1	16	yes	—
12	C₂×#88124	C₂²	1	4	yes	—
13	C₂×#88123	C₂²	1	4	yes	—
14	C₂×C₄×Dic₂₆	—	2	4	no	—
15	C₂×C₁₃×#97	C₂²	1	4	yes	—
16	C₂×C₁₃×#97	C₂²	1	8	yes	—
17	#11718767	C₂²	1	32	yes	—
18	C₂×#88058	C₂²	1	8	yes	—
19	C₂×#88057	C₂²	1	8	yes	—
20	#11718363	C₂²	1	64	yes	complemented
21	C₂³×C₄×C₁₃	D₄	1	2	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₂₆	—	2	4	no	—
24	C₂²×C₈×C₁₃	Q₈	1	16	yes	complemented
25	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
27	C₂×C₄²×C₁₃	D₄	1	2	yes	—
28	C₂×C₄²×C₁₃	D₄	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
31	C₂×C₂²⋊Dic₁₃	—	2	4	no	—
32	#88180	—	2	8	no	—
33	#88180	C₂³	1	16	yes	—
34	C₂×C₄⋊Dic₁₃	—	2	4	no	—
35	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
36	#88178	—	2	32	no	—
37	C₂×#6101	—	2	8	no	—
38	C₂×C₄×Dic₁₃	—	2	4	no	—
39	#88124	—	2	8	no	—
40	#88124	C₂³	1	16	yes	—
41	#88123	—	2	8	no	—
42	#88123	C₂³	1	16	yes	—
43	C₄×Dic₂₆	—	2	32	no	—
44	C₁₃×#97	C₂³	1	16	yes	—
45	#88058	C₂³	1	32	yes	—
46	#88057	C₂³	1	32	yes	—
47	C₂×#3162	—	13	1	no	maximal, Sylow
48	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	—	4	4	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
52	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
55	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
57	C₂²×Dic₁₃	—	2	8	no	—
58	C₂×Dic₂₆	—	2	16	no	—
59	C₂×Dic₂₆	—	4	16	no	—
60	C₂×C₈×C₁₃	C₂×Q₈	1	16	yes	—
61	C₂×C₈×C₁₃	C₂×Q₈	1	32	yes	complemented
62	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
63	C₄²×C₁₃	C₂×D₄	1	8	yes	—
64	C₄²×C₁₃	C₂×D₄	1	4	yes	—
65	C₄²×C₁₃	C₂⁴	1	4	yes	—
66	C₂²⋊Dic₁₃	—	2	16	no	—
67	C₄⋊Dic₁₃	—	2	16	no	—
68	C₄⋊Dic₁₃	—	2	8	no	—
69	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
70	#6101	—	2	32	no	—
71	C₄×Dic₁₃	—	2	16	no	—
72	C₂×#533	—	13	2	no	—
73	#3162	—	13	16	no	—
74	C₂×#501	—	13	8	no	—
75	C₂×#427	—	13	4	no	—
76	C₂²×#97	D₁₃	1	1	yes	characteristic
77	C₂³×C₁₃	—	2	4	no	—
78	C₂³×C₁₃	C₄⋊Q₈	1	4	yes	—
79	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
80	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	8	no	—
82	C₂×C₄×C₁₃	—	4	8	no	—
83	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
84	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
85	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
86	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
89	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
90	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
91	C₂×Dic₁₃	—	2	16	no	—
92	C₂×Dic₁₃	—	4	16	no	—
93	Dic₂₆	—	4	32	no	—
94	C₈×C₁₃	C₂²×Q₈	1	16	yes	—
95	C₂³×C₈	C₂×D₁₃	1	2	yes	—
96	#533	—	13	16	no	—
97	#533	—	26	8	no	—
98	C₂×C₄⋊Q₈	—	13	4	no	—
99	C₂×#125	—	13	4	no	—
100	C₂×C₂²⋊Q₈	—	26	4	no	—
101	C₂×C₄×Q₈	—	26	4	no	—
102	C₂×#117	—	13	4	no	—
103	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
104	#501	—	13	64	no	—
105	#427	—	13	32	no	—
106	C₂×#107	—	13	8	no	—
107	C₂×#106	—	13	8	no	—
108	C₂×#97	C₂×D₁₃	1	4	yes	—
109	C₂×#97	C₂×D₁₃	1	8	yes	—
110	C₂²×C₁₃	—	2	8	no	—
111	C₂²×C₁₃	—	2	4	no	—
112	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
113	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
114	C₂²×C₁₃	#575	1	4	yes	—
115	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
116	C₄×C₁₃	—	2	8	no	—
117	C₄×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
118	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
119	C₄×C₁₃	C₂³×Q₈	1	2	yes	—
120	Dic₁₃	—	4	16	no	—
121	C₂²×Q₈	—	26	4	no	—
122	C₂³×C₄	D₅₂	1	2	yes	—
123	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
124	C₂²×C₈	Dic₂₆	1	16	yes	complemented
125	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
126	C₂²×C₈	C₂²×D₁₃	1	8	yes	—
127	C₄⋊Q₈	—	13	16	no	—
128	C₄⋊Q₈	—	26	8	no	—
129	#125	—	13	16	no	—
130	#125	—	26	8	no	—
131	C₂²⋊Q₈	—	26	32	no	—
132	C₄×Q₈	—	26	32	no	—
133	#117	—	13	16	no	—
134	#117	—	26	8	no	—
135	C₂×C₄⋊C₄	—	13	8	no	—
136	C₂×C₄⋊C₄	—	26	8	no	—
137	C₂×C₄⋊C₄	—	26	4	no	—
138	C₂×C₂²⋊C₄	—	26	4	no	—
139	C₂×C₄²	—	26	4	no	—
140	C₂×C₄²	D₅₂	1	4	yes	—
141	C₂×C₄²	D₅₂	1	2	yes	—
142	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
143	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
144	#107	—	13	32	no	—
145	#106	—	13	32	no	—
146	#97	C₂²×D₁₃	1	16	yes	—
147	C₂×C₁₃	—	2	4	no	—
148	C₂×C₁₃	#3162	1	4	yes	complemented
149	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
150	C₂×C₁₃	C₂×#575	1	2	yes	—
151	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
152	C₂×Q₈	—	26	16	no	—
153	C₂×Q₈	—	52	16	no	—
154	C₂²×C₄	—	4	4	no	—
155	C₂²×C₄	—	26	8	no	—
156	C₂²×C₄	C₂×Dic₂₆	1	8	yes	—
157	C₂²×C₄	C₂×D₅₂	1	4	yes	—
158	C₂²×C₄	C₂×D₅₂	1	8	yes	—
159	C₂²×C₄	C₂×D₅₂	1	2	yes	—
160	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
161	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
163	C₂×C₈	C₂×Dic₂₆	1	16	yes	—
164	C₂×C₈	C₂×Dic₂₆	1	32	yes	complemented
165	C₂×C₈	C₂³×D₁₃	1	8	yes	—
166	C₄⋊C₄	—	13	16	no	—
167	C₄⋊C₄	—	26	8	no	—
168	C₄⋊C₄	—	26	32	no	—
169	C₄⋊C₄	—	26	16	no	—
170	C₂²⋊C₄	—	26	16	no	—
171	C₄²	—	26	16	no	—
172	C₄²	C₂×D₅₂	1	8	yes	—
173	C₄²	C₂×D₅₂	1	4	yes	—
174	C₄²	C₂³×D₁₃	1	4	yes	—
175	C₁₃	C₂×#3162	1	1	yes	characteristic, complemented, Sylow
176	C₂³	—	2	4	no	—
177	C₂³	#88123	1	4	yes	—
178	C₂³	C₂²×D₅₂	1	2	yes	—
179	C₂³	C₂²×D₅₂	1	1	yes	characteristic
180	Q₈	—	52	32	no	—
181	C₂×C₄	—	2	8	no	—
182	C₂×C₄	—	4	8	no	—
183	C₂×C₄	—	26	16	no	—
184	C₂×C₄	—	52	16	no	—
185	C₂×C₄	#88123	1	8	yes	—
186	C₂×C₄	#88123	1	4	yes	—
187	C₂×C₄	C₂²×Dic₂₆	1	4	yes	—
188	C₂×C₄	C₂²×Dic₂₆	1	8	yes	—
189	C₂×C₄	C₂²×D₅₂	1	8	yes	—
190	C₂×C₄	C₂²×D₅₂	1	2	yes	—
191	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
192	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
193	C₈	C₂²×Dic₂₆	1	16	yes	—
194	C₂²	—	2	4	no	—
195	C₂²	—	2	8	no	—
196	C₂²	C₂×#88123	1	4	yes	—
197	C₂²	C₂×#88123	1	2	yes	—
198	C₂²	#11719453	1	4	yes	—
199	C₂²	C₂³×D₅₂	1	1	yes	characteristic
200	C₄	—	2	8	no	—
201	C₄	—	52	16	no	—
202	C₄	C₂×#88123	1	2	yes	—
203	C₄	C₂×#88123	1	4	yes	—
204	C₄	C₂³×Dic₂₆	1	2	yes	—
205	C₂	—	2	4	no	—
206	C₂	#13125360	1	4	yes	direct product factor
207	C₂	C₂²×#88123	1	1	yes	characteristic
208	C₂	C₂×#11719453	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	C₂×#3162
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
2. #13125360	C₂	direct (N × H)
3. C₂×#11718363	C₂	semidirect
20. #11718363	C₂²	semidirect
24. C₂²×C₈×C₁₃	Q₈	semidirect
61. C₂×C₈×C₁₃	C₂×Q₈	semidirect
124. C₂²×C₈	Dic₂₆	semidirect
148. C₂×C₁₃	#3162	semidirect
164. C₂×C₈	C₂×Dic₂₆	semidirect
175. C₁₃	C₂×#3162	semidirect
206. C₂	#13125360	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×#11719175	2
#13125360	2
C₂×#11718363	2
C₂×#11718767	2
C₂²×C₁₃×#97	2
C₂×#3162	13

Subgroups — C2×#13125360 #16732535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13125360 #16732535