Subgroups — #15777963

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718145	C₂	1	2	yes	maximal
2	C₄×#88052	C₂	1	2	yes	maximal, complemented
3	#13112920	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
8	C₁₃×#405	—	2	2	no	—
9	C₁₃×#405	—	2	2	no	—
10	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
11	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	4	yes	—
15	#11718145	C₄	1	8	yes	complemented
16	#11718053	—	2	2	no	—
17	C₄×#6090	—	2	2	no	—
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	—	2	1	no	—
24	C₂²×C₈×C₁₃	—	2	2	no	—
25	C₂²×C₈×C₁₃	C₈	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₁₃×#117	—	2	2	no	—
31	C₁₃×#117	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	C₈	1	2	yes	—
33	C₂×C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₁₃×#97	—	2	2	no	—
37	C₁₃×#97	—	2	2	no	—
38	C₄×C₈×C₁₃	—	2	1	no	—
39	C₄×C₈×C₁₃	—	2	1	no	—
40	C₄×C₈×C₁₃	D₄	1	2	yes	—
41	C₄×C₈×C₁₃	D₄	1	2	yes	—
42	#88052	—	2	4	no	—
43	#88052	C₂×C₄	1	8	yes	—
44	C₂×#6090	—	2	4	no	—
45	#12602	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	—	2	1	no	—
49	C₂²×C₄×C₁₃	—	2	1	no	—
50	C₂²×C₄×C₁₃	—	2	1	no	—
51	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₁₃×M₁₆	—	2	8	no	—
58	C₂×C₈×C₁₃	—	2	1	no	—
59	C₂×C₈×C₁₃	—	2	1	no	—
60	C₂×C₈×C₁₃	—	2	1	no	—
61	C₂×C₈×C₁₃	—	2	1	no	—
62	C₂×C₈×C₁₃	—	2	4	no	—
63	C₂×C₈×C₁₃	—	2	4	no	—
64	C₂×C₈×C₁₃	C₄²	1	2	yes	—
65	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
68	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
69	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₃	#41	1	2	yes	—
73	C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₄²×C₁₃	—	2	1	no	—
76	C₄²×C₁₃	—	2	1	no	—
77	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
78	C₄²×C₁₃	M₁₆	1	2	yes	—
79	#6090	—	2	8	no	—
80	C₂×#405	D₁₃	1	1	yes	characteristic
81	C₂×#349	—	13	2	no	—
82	C₄×M₃₂	—	13	2	no	—
83	#1377	—	13	2	no	—
84	C₂³×C₁₃	—	2	1	no	—
85	C₂³×C₁₃	—	2	1	no	—
86	C₂³×C₁₃	—	4	2	no	—
87	C₂³×C₁₃	C₄×C₈	1	2	yes	—
88	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	—	2	1	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
99	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
100	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
106	C₈×C₁₃	—	2	2	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
109	C₈×C₁₃	C₂²⋊C₈	1	2	yes	—
110	C₈×C₁₃	C₄×D₄	1	4	yes	—
111	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
112	C₂³×C₈	Dic₁₃	1	1	yes	characteristic
113	C₂×#117	Dic₁₃	1	1	yes	characteristic
114	C₂×M₃₂	—	13	4	no	—
115	#405	—	2	2	no	—
116	#405	—	2	2	no	—
117	C₂×#97	Dic₁₃	1	1	yes	characteristic
118	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
119	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
120	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
121	#349	—	13	8	no	—
122	#346	—	26	2	no	—
123	C₄×C₁₆	—	26	2	no	—
124	C₂²×C₁₃	—	2	2	no	—
125	C₂²×C₁₃	—	2	2	no	—
126	C₂²×C₁₃	—	4	2	no	—
127	C₂²×C₁₃	—	4	2	no	—
128	C₂²×C₁₃	—	4	2	no	—
129	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
131	C₂²×C₁₃	#431	1	1	yes	characteristic
132	C₄×C₁₃	—	2	4	no	—
133	C₄×C₁₃	—	2	2	no	—
134	C₄×C₁₃	—	4	2	no	—
135	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
136	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
137	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
138	C₄×C₁₃	#431	1	1	yes	characteristic
139	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
140	C₂×M₁₆	—	2	2	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	2	1	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	#1055	1	4	yes	—
147	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
148	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
149	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
150	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
151	#117	—	2	2	no	—
152	#117	—	2	2	no	—
153	C₂×C₄⋊C₄	#1055	1	2	yes	—
154	C₂×C₂²⋊C₄	#1055	1	2	yes	—
155	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
156	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
157	M₃₂	—	13	8	no	—
158	M₃₂	—	26	4	no	—
159	C₂×C₁₆	—	26	4	no	—
160	#97	—	2	2	no	—
161	#97	—	2	2	no	—
162	C₄×C₈	—	2	1	no	—
163	C₄×C₈	—	2	1	no	—
164	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
165	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
166	C₂×C₁₃	—	2	1	no	—
167	C₂×C₁₃	—	2	1	no	—
168	C₂×C₁₃	—	4	2	no	—
169	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
170	C₂×C₁₃	#2115	1	2	yes	—
171	C₂⁴	C₂×#1055	1	1	yes	characteristic
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	C₂×#1055	1	2	yes	—
177	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
178	C₂²×C₄	C₂×#1055	1	2	yes	—
179	C₂²×C₄	C₂×#1055	1	2	yes	—
180	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
182	M₁₆	—	2	8	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	2	1	no	—
185	C₂×C₈	—	2	1	no	—
186	C₂×C₈	—	2	1	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	C₂×#1055	1	2	yes	—
190	C₂×C₈	C₂×#1055	1	2	yes	—
191	C₂×C₈	#6099	1	2	yes	—
192	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
193	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
194	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
195	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
196	C₂×C₈	#6127	1	2	yes	—
197	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
198	C₄⋊C₄	—	2	4	no	—
199	C₂²⋊C₄	—	2	4	no	—
200	C₄²	—	2	1	no	—
201	C₄²	—	2	1	no	—
202	C₄²	#6099	1	2	yes	—
203	C₄²	C₂²⋊Dic₁₃	1	2	yes	—
204	C₁₆	—	26	8	no	—
205	C₁₃	#12602	1	1	yes	characteristic, complemented, Sylow
206	C₂³	—	2	1	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	4	2	no	—
209	C₂³	C₄×#1055	1	2	yes	—
210	C₂³	C₂²×#1055	1	1	yes	characteristic
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	C₄×#1055	1	2	yes	—
221	C₂×C₄	C₂²⋊#1055	1	4	yes	—
222	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
223	C₂×C₄	C₂×#6099	1	1	yes	characteristic
224	C₂×C₄	C₂×#6099	1	1	yes	characteristic
225	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
226	C₂×C₄	#88180	1	1	yes	characteristic
227	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	C₂²⋊#1055	1	2	yes	—
231	C₈	C₂²⋊#1055	1	2	yes	—
232	C₈	C₄×C₂²⋊D₁₃	1	4	yes	—
233	C₂²	—	2	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	4	2	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	4	2	no	—
238	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
239	C₂²	#11718586	1	1	yes	characteristic
240	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
241	C₄	—	2	4	no	—
242	C₄	—	2	2	no	—
243	C₄	—	4	2	no	—
244	C₄	C₄×#6099	1	1	yes	characteristic
245	C₄	#11718586	1	1	yes	characteristic
246	C₄	C₂×C₂²⋊#1055	1	1	yes	characteristic
247	C₄	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	—	4	2	no	—
251	C₂	C₄×C₂²⋊#1055	1	1	yes	characteristic
252	C₂	#13116457	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²⋊Dic₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#12602
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₄×#88052	C₂	semidirect
3. #13112920	C₂	semidirect
15. #11718145	C₄	semidirect
205. C₁₃	#12602	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718145	2
C₄×#88052	2
#13112920	2
C₂×C₁₃×#405	2
#12602	13