Subgroups — C₂×#13114746 #15862023

Order 3328.

6110 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊#1055	C₂	1	6	yes	maximal, complemented
2	#13114746	C₂	1	8	yes	maximal, direct product factor
3	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁶×C₁₃	C₄	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₃	—	2	24	no	—
6	C₂⁴×C₄×C₁₃	C₄	1	3	yes	—
7	C₂⁴×C₄×C₁₃	C₄	1	4	yes	—
8	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
9	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
10	C₂³×#1055	C₂²	1	4	yes	complemented
11	C₂×C₂²⋊#1055	—	2	24	no	—
12	C₂×C₂²⋊#1055	C₂²	1	24	yes	complemented
13	C₂⁵×C₁₃	—	2	12	no	—
14	C₂⁵×C₁₃	—	2	12	no	—
15	C₂⁵×C₁₃	C₈	1	8	yes	complemented
16	C₂⁵×C₁₃	C₂×C₄	1	4	yes	—
17	C₂⁵×C₁₃	C₂×C₄	1	3	yes	—
18	C₂³×C₄×C₁₃	—	2	128	no	—
19	C₂³×C₄×C₁₃	—	2	12	no	—
20	C₂³×C₄×C₁₃	—	2	24	no	—
21	C₂³×C₄×C₁₃	—	2	48	no	—
22	C₂³×C₄×C₁₃	—	2	48	no	—
23	C₂³×C₄×C₁₃	—	2	24	no	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	12	yes	—
25	C₂³×C₄×C₁₃	C₂×C₄	1	3	yes	—
26	C₂³×C₄×C₁₃	C₂×C₄	1	6	yes	—
27	C₂³×C₄×C₁₃	D₄	1	24	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
29	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×#1055	—	2	24	no	—
31	C₂²×#1055	C₂³	1	8	yes	complemented
32	C₂²⋊#1055	—	2	48	no	—
33	C₂×#1779	—	13	1	no	maximal, Sylow
34	C₂⁴×C₁₃	—	2	32	no	—
35	C₂⁴×C₁₃	—	2	96	no	—
36	C₂⁴×C₁₃	—	2	96	no	—
37	C₂⁴×C₁₃	—	2	24	no	—
38	C₂⁴×C₁₃	—	2	12	no	—
39	C₂⁴×C₁₃	—	2	24	no	—
40	C₂⁴×C₁₃	—	2	12	no	—
41	C₂⁴×C₁₃	C₂²⋊C₄	1	12	yes	—
42	C₂⁴×C₁₃	C₂×C₈	1	12	yes	—
43	C₂⁴×C₁₃	C₂×C₈	1	16	yes	complemented
44	C₂⁴×C₁₃	M₁₆	1	12	yes	—
45	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
46	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	—	2	96	no	—
48	C₂²×C₄×C₁₃	—	2	128	no	—
49	C₂²×C₄×C₁₃	—	2	128	no	—
50	C₂²×C₄×C₁₃	—	2	24	no	—
51	C₂²×C₄×C₁₃	—	2	12	no	—
52	C₂²×C₄×C₁₃	—	2	48	no	—
53	C₂²×C₄×C₁₃	—	2	24	no	—
54	C₂²×C₄×C₁₃	—	2	96	no	—
55	C₂²×C₄×C₁₃	—	2	24	no	—
56	C₂²×C₄×C₁₃	C₂²⋊C₄	1	12	yes	—
57	C₂²×C₄×C₁₃	C₂²⋊C₄	1	24	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
61	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
62	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₂×#1055	—	2	24	no	—
64	C₂×#1055	—	4	16	no	—
65	C₂⁵×C₄	D₁₃	1	1	yes	characteristic
66	C₂²×C₂²⋊C₈	—	13	6	no	—
67	#1779	—	13	8	no	—
68	C₂³×C₁₃	—	2	32	no	—
69	C₂³×C₁₃	—	2	96	no	—
70	C₂³×C₁₃	—	2	256	no	—
71	C₂³×C₁₃	—	2	12	no	—
72	C₂³×C₁₃	—	2	12	no	—
73	C₂³×C₁₃	—	2	24	no	—
74	C₂³×C₁₃	—	2	48	no	—
75	C₂³×C₁₃	—	2	96	no	—
76	C₂³×C₁₃	—	2	24	no	—
77	C₂³×C₁₃	—	2	48	no	—
78	C₂³×C₁₃	C₂²⋊C₈	1	48	yes	complemented
79	C₂³×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
80	C₂³×C₁₃	C₂×C₂²⋊C₄	1	6	yes	—
81	C₂³×C₁₃	C₂²×C₈	1	12	yes	—
82	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
83	C₂³×C₁₃	C₂×M₁₆	1	12	yes	—
84	C₂³×C₁₃	C₂×M₁₆	1	6	yes	—
85	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	—	2	96	no	—
87	C₂×C₄×C₁₃	—	2	12	no	—
88	C₂×C₄×C₁₃	—	2	24	no	—
89	C₂×C₄×C₁₃	—	2	48	no	—
90	C₂×C₄×C₁₃	—	2	48	no	—
91	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
92	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	6	yes	—
93	C₂×C₄×C₁₃	#120	1	16	yes	—
94	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
95	#1055	—	4	8	no	—
96	C₂⁶	Dic₁₃	1	1	yes	characteristic
97	C₂⁴×C₄	—	2	24	no	—
98	C₂⁴×C₄	Dic₁₃	1	3	yes	—
99	C₂⁴×C₄	Dic₁₃	1	4	yes	—
100	C₂⁴×C₄	C₂×D₁₃	1	4	yes	—
101	C₂⁴×C₄	C₂×D₁₃	1	3	yes	—
102	C₂³×C₈	—	13	4	no	—
103	C₂×C₂²⋊C₈	—	13	24	no	—
104	C₂×C₂²⋊C₈	—	26	24	no	—
105	C₂²×C₁₃	—	2	128	no	—
106	C₂²×C₁₃	—	2	24	no	—
107	C₂²×C₁₃	—	2	12	no	—
108	C₂²×C₁₃	—	2	24	no	—
109	C₂²×C₁₃	—	2	12	no	—
110	C₂²×C₁₃	—	2	96	no	—
111	C₂²×C₁₃	#379	1	4	yes	—
112	C₂²×C₁₃	C₂×C₂²⋊C₈	1	12	yes	—
113	C₂²×C₁₃	C₂×C₂²⋊C₈	1	24	yes	complemented
114	C₂²×C₁₃	#407	1	12	yes	—
115	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	3	yes	—
116	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
117	C₂²×C₁₃	C₂²×M₁₆	1	3	yes	—
118	C₄×C₁₃	—	2	12	no	—
119	C₄×C₁₃	#379	1	4	yes	—
120	C₄×C₁₃	C₂×#120	1	4	yes	—
121	C₂⁵	—	2	12	no	—
122	C₂⁵	—	2	12	no	—
123	C₂⁵	#1055	1	8	yes	complemented
124	C₂⁵	C₂×Dic₁₃	1	4	yes	—
125	C₂⁵	C₂×Dic₁₃	1	3	yes	—
126	C₂³×C₄	—	2	128	no	—
127	C₂³×C₄	—	2	12	no	—
128	C₂³×C₄	—	2	24	no	—
129	C₂³×C₄	—	2	48	no	—
130	C₂³×C₄	—	2	48	no	—
131	C₂³×C₄	—	2	24	no	—
132	C₂³×C₄	C₂×Dic₁₃	1	12	yes	—
133	C₂³×C₄	C₂×Dic₁₃	1	3	yes	—
134	C₂³×C₄	C₂×Dic₁₃	1	6	yes	—
135	C₂³×C₄	C₂²⋊D₁₃	1	24	yes	—
136	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
137	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
138	C₂²×C₈	—	13	8	no	—
139	C₂²×C₈	—	26	24	no	—
140	C₂²⋊C₈	—	26	48	no	—
141	C₂×C₁₃	—	2	24	no	—
142	C₂×C₁₃	#1779	1	8	yes	complemented
143	C₂×C₁₃	C₂×#379	1	1	yes	characteristic
144	C₂×C₁₃	C₂²×C₂²⋊C₈	1	3	yes	—
145	C₂×C₁₃	C₂×#407	1	3	yes	—
146	C₂⁴	—	2	32	no	—
147	C₂⁴	—	2	96	no	—
148	C₂⁴	—	2	96	no	—
149	C₂⁴	—	2	24	no	—
150	C₂⁴	—	2	12	no	—
151	C₂⁴	—	2	24	no	—
152	C₂⁴	—	2	12	no	—
153	C₂⁴	C₂×#1055	1	12	yes	—
154	C₂⁴	C₂×#1055	1	16	yes	complemented
155	C₂⁴	#6099	1	12	yes	—
156	C₂⁴	C₂²⋊Dic₁₃	1	12	yes	—
157	C₂⁴	C₂²×Dic₁₃	1	6	yes	—
158	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
159	C₂²×C₄	—	2	96	no	—
160	C₂²×C₄	—	2	128	no	—
161	C₂²×C₄	—	2	128	no	—
162	C₂²×C₄	—	2	24	no	—
163	C₂²×C₄	—	2	12	no	—
164	C₂²×C₄	—	2	48	no	—
165	C₂²×C₄	—	2	24	no	—
166	C₂²×C₄	—	2	96	no	—
167	C₂²×C₄	—	2	24	no	—
168	C₂²×C₄	C₂²⋊Dic₁₃	1	12	yes	—
169	C₂²×C₄	C₂²⋊Dic₁₃	1	24	yes	—
170	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
171	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₁₃	1	24	yes	—
173	C₂²×C₄	C₂×C₂²⋊D₁₃	1	12	yes	—
174	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
175	C₂×C₈	—	26	24	no	—
176	C₂×C₈	—	52	16	no	—
177	C₁₃	C₂×#1779	1	1	yes	characteristic, complemented, Sylow
178	C₂³	—	2	32	no	—
179	C₂³	—	2	256	no	—
180	C₂³	—	2	96	no	—
181	C₂³	—	2	12	no	—
182	C₂³	—	2	12	no	—
183	C₂³	—	2	48	no	—
184	C₂³	—	2	96	no	—
185	C₂³	—	2	48	no	—
186	C₂³	—	2	24	no	—
187	C₂³	—	2	24	no	—
188	C₂³	C₂²⋊#1055	1	48	yes	complemented
189	C₂³	C₂²×#1055	1	12	yes	—
190	C₂³	C₂²×#1055	1	2	yes	—
191	C₂³	C₂×#6099	1	12	yes	—
192	C₂³	C₂×#6099	1	6	yes	—
193	C₂³	C₂×C₂²⋊Dic₁₃	1	12	yes	—
194	C₂³	C₂×C₂²⋊Dic₁₃	1	6	yes	—
195	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
196	C₂×C₄	—	2	96	no	—
197	C₂×C₄	—	2	12	no	—
198	C₂×C₄	—	2	24	no	—
199	C₂×C₄	—	2	48	no	—
200	C₂×C₄	—	2	48	no	—
201	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	12	yes	—
202	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	6	yes	—
203	C₂×C₄	#88207	1	16	yes	—
204	C₂×C₄	C₂²×C₂²⋊D₁₃	1	6	yes	—
205	C₈	—	52	8	no	—
206	C₂²	—	2	128	no	—
207	C₂²	—	2	12	no	—
208	C₂²	—	2	96	no	—
209	C₂²	—	2	24	no	—
210	C₂²	—	2	24	no	—
211	C₂²	—	2	12	no	—
212	C₂²	C₂×C₂²⋊#1055	1	12	yes	—
213	C₂²	C₂×C₂²⋊#1055	1	24	yes	complemented
214	C₂²	#11718868	1	12	yes	—
215	C₂²	#11718908	1	4	yes	—
216	C₂²	C₂³×#1055	1	1	yes	characteristic
217	C₂²	C₂²×#6099	1	3	yes	—
218	C₂²	C₂²×C₂²⋊Dic₁₃	1	3	yes	—
219	C₄	—	2	12	no	—
220	C₄	#11718908	1	4	yes	—
221	C₄	C₂×#88207	1	4	yes	—
222	C₂	—	2	24	no	—
223	C₂	#13114746	1	8	yes	direct product factor
224	C₂	C₂×#11718908	1	1	yes	characteristic
225	C₂	C₂²×C₂²⋊#1055	1	3	yes	—
226	C₂	C₂×#11718868	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂⁵×C₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂²×C₄
prime radical	C₂⁶×C₁₃	C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂⁵×C₄	D₁₃
hypocenter	C₁₃	C₂×#1779
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊#1055	C₂	semidirect
2. #13114746	C₂	direct (N × H)
10. C₂³×#1055	C₂²	semidirect
12. C₂×C₂²⋊#1055	C₂²	semidirect
15. C₂⁵×C₁₃	C₈	semidirect
31. C₂²×#1055	C₂³	semidirect
43. C₂⁴×C₁₃	C₂×C₈	semidirect
78. C₂³×C₁₃	C₂²⋊C₈	semidirect
113. C₂²×C₁₃	C₂×C₂²⋊C₈	semidirect
123. C₂⁵	#1055	semidirect
142. C₂×C₁₃	#1779	semidirect
154. C₂⁴	C₂×#1055	semidirect
177. C₁₃	C₂×#1779	semidirect
188. C₂³	C₂²⋊#1055	semidirect
213. C₂²	C₂×C₂²⋊#1055	semidirect
223. C₂	#13114746	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂²⋊#1055	2
#13114746	2
C₂⁵×C₄×C₁₃	2
C₂×#1779	13

Subgroups — C2×#13114746 #15862023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114746 #15862023