Subgroups — #15772242

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116639	C₂	1	1	yes	maximal, characteristic, complemented
2	#13116635	C₂	1	1	yes	maximal, characteristic, complemented
3	#13112760	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	2	yes	—
6	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
7	C₁₃×#436	—	2	1	no	—
8	C₁₃×#436	—	2	1	no	—
9	C₁₃×#436	—	2	1	no	—
10	C₁₃×#436	—	2	1	no	—
11	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²⋊#6090	C₂²	1	2	yes	—
15	C₂²⋊#6090	C₂²	1	2	yes	—
16	C₄⋊#6090	—	2	1	no	—
17	C₄⋊#6090	—	2	1	no	—
18	#11718053	—	2	1	no	—
19	C₄×#6090	—	2	1	no	—
20	C₂²×D₄×C₁₃	C₈	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₁₃×M₁₆	—	2	2	no	—
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂×C₁₃×M₁₆	—	4	4	no	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₄×D₄×C₁₃	—	2	1	no	—
29	C₄×D₄×C₁₃	—	2	1	no	—
30	C₄×D₄×C₁₃	—	2	1	no	—
31	C₄×D₄×C₁₃	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₁₃×C₄⋊C₈	—	2	1	no	—
36	C₁₃×C₄⋊C₈	—	2	1	no	—
37	C₁₃×C₂²⋊C₈	—	2	2	no	—
38	C₁₃×C₂²⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
43	C₂×#6090	—	2	2	no	—
44	C₂×#6090	—	2	2	no	—
45	#11489	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂×C₈	1	2	yes	—
47	C₂×D₄×C₁₃	—	2	1	no	—
48	C₂×D₄×C₁₃	—	2	1	no	—
49	C₂×D₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₁₃×M₁₆	—	4	4	no	—
59	C₁₃×M₁₆	—	4	4	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	2	no	—
64	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
75	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
76	#6090	—	4	2	no	—
77	#6090	—	4	2	no	—
78	C₂×#436	D₁₃	1	1	yes	characteristic
79	#2163	—	13	1	no	—
80	#2162	—	13	1	no	—
81	#1314	—	13	4	no	—
82	C₂³×C₁₃	—	2	2	no	—
83	C₂³×C₁₃	—	2	4	no	—
84	C₂³×C₁₃	—	4	2	no	—
85	C₂³×C₁₃	—	4	2	no	—
86	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
87	D₄×C₁₃	—	4	2	no	—
88	D₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
104	C₈×C₁₃	—	2	1	no	—
105	C₈×C₁₃	—	2	1	no	—
106	C₈×C₁₃	—	2	1	no	—
107	C₈×C₁₃	—	4	2	no	—
108	C₈×C₁₃	#100	1	2	yes	—
109	C₂²×M₁₆	Dic₁₃	1	2	yes	—
110	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
111	#436	—	2	1	no	—
112	#436	—	2	1	no	—
113	#436	—	2	1	no	—
114	#436	—	2	1	no	—
115	C₂×C₄⋊C₈	Dic₁₃	1	1	yes	characteristic
116	C₂×C₂²⋊C₈	C₂×D₁₃	1	2	yes	—
117	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
118	C₄⋊C₁₆	—	26	1	no	—
119	C₄⋊C₁₆	—	26	1	no	—
120	C₂²⋊C₁₆	—	13	2	no	—
121	C₂²⋊C₁₆	—	13	2	no	—
122	#346	—	26	1	no	—
123	C₄×C₁₆	—	26	1	no	—
124	C₂²×C₁₃	—	2	1	no	—
125	C₂²×C₁₃	—	2	1	no	—
126	C₂²×C₁₃	—	4	2	no	—
127	C₂²×C₁₃	—	4	2	no	—
128	C₂²×C₁₃	—	4	2	no	—
129	C₂²×C₁₃	—	8	4	no	—
130	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
131	C₂²×C₁₃	#504	1	2	yes	—
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	4	2	no	—
137	C₄×C₁₃	#349	1	2	yes	—
138	C₄×C₁₃	#410	1	1	yes	characteristic
139	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
140	C₂²×D₄	#1055	1	1	yes	characteristic
141	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
142	C₂×M₁₆	—	2	2	no	—
143	C₂×M₁₆	—	2	2	no	—
144	C₂×M₁₆	—	4	4	no	—
145	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
146	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
147	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
148	C₄×D₄	—	2	1	no	—
149	C₄×D₄	—	2	1	no	—
150	C₄×D₄	—	2	1	no	—
151	C₄×D₄	—	2	1	no	—
152	C₂×C₄⋊C₄	#1055	1	1	yes	characteristic
153	C₂×C₂²⋊C₄	#1055	1	2	yes	—
154	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
155	C₂×C₁₆	—	26	2	no	—
156	C₂×C₁₆	—	26	2	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₂²⋊C₈	—	2	2	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
162	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
165	C₂×C₁₃	—	2	2	no	—
166	C₂×C₁₃	—	8	2	no	—
167	C₂×C₁₃	#1460	1	1	yes	characteristic
168	C₂×C₁₃	#2113	1	1	yes	characteristic
169	C₂×C₁₃	C₂×#349	1	1	yes	characteristic
170	C₂⁴	C₂×#1055	1	2	yes	—
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	—	2	1	no	—
173	C₂×D₄	—	4	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
179	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
180	C₂²×C₄	C₂×#1055	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
182	M₁₆	—	4	4	no	—
183	M₁₆	—	4	4	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
189	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
190	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
191	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
192	C₄⋊C₄	—	2	1	no	—
193	C₄⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	2	2	no	—
195	C₂²⋊C₄	—	2	2	no	—
196	C₄²	#6099	1	1	yes	characteristic
197	C₄²	#6099	1	1	yes	characteristic
198	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
199	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
200	C₁₆	—	52	2	no	—
201	C₁₆	—	52	2	no	—
202	C₁₃	#11489	1	1	yes	characteristic, complemented, Sylow
203	C₂³	—	2	2	no	—
204	C₂³	—	2	4	no	—
205	C₂³	—	4	2	no	—
206	C₂³	—	4	2	no	—
207	C₂³	C₂²×#1055	1	1	yes	characteristic
208	D₄	—	4	2	no	—
209	D₄	—	4	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	4	4	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
220	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
221	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
222	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
223	C₂×C₄	C₂×#6099	1	1	yes	characteristic
224	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	2	1	no	—
228	C₈	—	4	2	no	—
229	C₈	#88073	1	2	yes	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	4	2	no	—
233	C₂²	—	4	2	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	8	4	no	—
236	C₂²	#11718801	1	2	yes	—
237	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	4	2	no	—
243	C₄	#11718145	1	2	yes	—
244	C₄	C₂×#88073	1	1	yes	characteristic
245	C₄	#11718901	1	1	yes	characteristic
246	C₂	—	2	2	no	—
247	C₂	—	8	2	no	—
248	C₂	#13113157	1	1	yes	characteristic
249	C₂	#13116450	1	1	yes	characteristic
250	C₂	C₂×#11718145	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₃
commutator	C₂³×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#436	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₁₃	C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#436	D₁₃
hypocenter	C₁₃	#11489
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. #13116639	C₂	semidirect
2. #13116635	C₂	semidirect
3. #13112760	C₂	semidirect
202. C₁₃	#11489	semidirect

Maximal subgroups

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

subgroup	index
#13116639	2
#13116635	2
#13112760	2
C₂×C₁₃×#436	2
#11489	13