Subgroups — #15777958

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718368	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718106	C₂	1	2	yes	maximal
3	M₃₂×Dic₁₃	C₂	1	2	yes	maximal, complemented
4	#13112920	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6094	C₄	1	1	yes	characteristic
7	C₂²×#6094	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88052	C₂²	1	2	yes	—
14	C₂×#88043	C₄	1	1	yes	characteristic
15	#11718368	—	2	2	no	—
16	#11718368	—	2	2	no	—
17	#11718106	C₄	1	8	yes	complemented
18	#11718094	—	2	2	no	—
19	C₁₆×Dic₁₃	—	2	2	no	—
20	C₂²×C₄×D₁₃	C₈	1	2	yes	—
21	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
26	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
28	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂×#6094	—	2	2	no	—
30	C₂×#6094	—	2	1	no	—
31	C₂×#6094	—	2	1	no	—
32	C₂×#6094	—	2	2	no	—
33	C₂×#6094	—	2	2	no	—
34	C₂×#6094	C₈	1	4	yes	—
35	C₂×#6094	C₂×C₄	1	4	yes	—
36	C₄²×D₁₃	—	2	1	no	—
37	C₄²×D₁₃	—	2	1	no	—
38	C₄²×D₁₃	—	2	2	no	—
39	C₁₃×M₃₂	—	2	2	no	—
40	C₁₃×M₃₂	C₂×C₄	1	4	yes	complemented
41	C₂×C₁₃×C₁₆	—	2	2	no	—
42	C₁₃×#97	—	2	2	no	—
43	C₈×Dic₁₃	—	2	1	no	—
44	C₈×Dic₁₃	—	2	1	no	—
45	C₈×Dic₁₃	D₄	1	2	yes	—
46	C₈×Dic₁₃	D₄	1	2	yes	—
47	#88052	—	2	2	no	—
48	#88052	C₂×C₄	1	4	yes	complemented
49	C₂×#6090	—	2	2	no	—
50	#88043	—	2	2	no	—
51	C₄×#349	—	13	1	no	maximal, Sylow
52	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
57	C₂×C₄×D₁₃	—	2	1	no	—
58	C₂×C₄×D₁₃	—	2	1	no	—
59	C₂×C₄×D₁₃	—	2	1	no	—
60	C₂×C₄×D₁₃	—	2	1	no	—
61	C₂×C₄×D₁₃	—	2	2	no	—
62	C₂×C₄×D₁₃	—	2	2	no	—
63	C₂×C₄×D₁₃	—	4	4	no	—
64	C₂×C₄×D₁₃	C₄²	1	2	yes	—
65	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
66	C₂×C₈×C₁₃	—	2	1	no	—
67	C₂×C₈×C₁₃	—	2	1	no	—
68	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
72	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
73	C₄²×C₁₃	—	2	1	no	—
74	C₄²×C₁₃	—	2	1	no	—
75	C₄×Dic₁₃	—	2	2	no	—
76	C₄×Dic₁₃	—	2	2	no	—
77	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₄×Dic₁₃	M₁₆	1	2	yes	—
80	C₂×#1055	—	2	1	no	—
81	C₂×#1055	—	2	1	no	—
82	C₂×#1055	C₄²	1	2	yes	—
83	C₂×#1055	C₂²⋊C₄	1	2	yes	—
84	C₂×#1055	C₂×C₈	1	2	yes	—
85	C₂×#1055	M₁₆	1	2	yes	—
86	#6094	—	2	4	no	—
87	#6094	—	2	4	no	—
88	#6094	—	2	8	no	—
89	C₁₃×C₁₆	—	2	4	no	—
90	#6090	—	2	4	no	—
91	C₂×C₄×M₁₆	—	13	1	no	—
92	C₂×#349	—	13	2	no	—
93	C₄×M₃₂	—	13	2	no	—
94	#1377	—	13	1	no	—
95	#1377	D₁₃	1	1	yes	characteristic, complemented
96	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
97	C₂²×D₁₃	—	2	1	no	—
98	C₂²×D₁₃	—	2	1	no	—
99	C₂²×D₁₃	—	4	2	no	—
100	C₂²×D₁₃	C₄×C₈	1	2	yes	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	4	2	no	—
103	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
109	C₂×Dic₁₃	—	2	1	no	—
110	C₂×Dic₁₃	—	2	1	no	—
111	C₂×Dic₁₃	—	2	4	no	—
112	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
113	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
114	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
115	C₄×D₁₃	—	2	2	no	—
116	C₄×D₁₃	—	2	2	no	—
117	C₄×D₁₃	—	2	2	no	—
118	C₄×D₁₃	—	2	2	no	—
119	C₄×D₁₃	—	4	4	no	—
120	C₄×D₁₃	—	4	4	no	—
121	C₈×C₁₃	—	2	2	no	—
122	C₈×C₁₃	C₄×D₄	1	2	yes	—
123	C₈×C₁₃	C₄×D₄	1	2	yes	—
124	#1055	—	2	2	no	—
125	#1055	C₂²⋊C₈	1	4	yes	—
126	C₂²×M₁₆	—	13	1	no	—
127	C₂²×M₁₆	—	13	1	no	—
128	C₂²×C₄²	—	13	1	no	—
129	C₂×M₃₂	—	13	2	no	—
130	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
131	C₄×M₁₆	—	26	2	no	—
132	C₄×M₁₆	—	26	2	no	—
133	C₂×#97	—	13	1	no	—
134	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
135	C₂×C₄×C₈	—	13	1	no	—
136	C₂×C₄×C₈	—	13	1	no	—
137	#349	—	13	8	no	—
138	#346	—	26	2	no	—
139	C₄×C₁₆	—	26	2	no	—
140	C₂²×C₁₃	—	2	2	no	—
141	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
142	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
143	C₂²×C₁₃	#431	1	1	yes	characteristic
144	C₂×D₁₃	—	2	2	no	—
145	C₂×D₁₃	—	4	2	no	—
146	C₂×D₁₃	—	4	2	no	—
147	C₂×D₁₃	—	4	2	no	—
148	C₄×C₁₃	—	4	2	no	—
149	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
150	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
151	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
152	C₄×C₁₃	#431	1	1	yes	characteristic
153	Dic₁₃	—	2	2	no	—
154	Dic₁₃	—	2	2	no	—
155	Dic₁₃	#349	1	4	yes	complemented
156	C₂³×C₄	—	13	1	no	—
157	C₂³×C₄	—	13	2	no	—
158	C₂×M₁₆	—	13	4	no	—
159	C₂×M₁₆	—	13	4	no	—
160	C₂×M₁₆	—	26	2	no	—
161	C₂×M₁₆	—	26	2	no	—
162	C₂×M₁₆	—	26	2	no	—
163	C₂×M₁₆	—	26	1	no	—
164	C₂×M₁₆	—	26	1	no	—
165	C₂²×C₈	—	13	1	no	—
166	C₂²×C₈	—	13	1	no	—
167	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
168	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
169	C₂×C₄²	—	13	1	no	—
170	C₂×C₄²	—	13	2	no	—
171	C₂×C₄²	—	26	1	no	—
172	C₂×C₄²	—	26	1	no	—
173	C₂×C₄²	—	26	2	no	—
174	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
175	M₃₂	—	2	2	no	—
176	M₃₂	—	13	4	no	—
177	M₃₂	—	26	2	no	—
178	M₃₂	C₄×D₁₃	1	4	yes	complemented
179	C₂×C₁₆	—	2	2	no	—
180	C₂×C₁₆	—	26	2	no	—
181	#97	—	2	2	no	—
182	#97	—	26	2	no	—
183	C₄×C₈	—	13	2	no	—
184	C₄×C₈	—	13	2	no	—
185	C₄×C₈	—	26	1	no	—
186	C₄×C₈	—	26	1	no	—
187	C₂×C₁₃	—	2	1	no	—
188	C₂×C₁₃	—	2	1	no	—
189	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
190	C₂×C₁₃	C₂×#349	1	2	yes	—
191	D₁₃	—	4	2	no	—
192	C₂⁴	—	13	1	no	—
193	C₂²×C₄	—	13	2	no	—
194	C₂²×C₄	—	13	1	no	—
195	C₂²×C₄	—	13	2	no	—
196	C₂²×C₄	—	13	2	no	—
197	C₂²×C₄	—	26	2	no	—
198	C₂²×C₄	—	26	2	no	—
199	C₂²×C₄	—	26	1	no	—
200	C₂²×C₄	—	26	1	no	—
201	C₂²×C₄	—	26	1	no	—
202	C₂²×C₄	—	26	1	no	—
203	C₂²×C₄	—	52	4	no	—
204	C₂²×C₄	C₈×D₁₃	1	2	yes	—
205	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
206	M₁₆	—	26	8	no	—
207	M₁₆	—	26	4	no	—
208	M₁₆	—	26	4	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	13	2	no	—
212	C₂×C₈	—	13	2	no	—
213	C₂×C₈	—	13	2	no	—
214	C₂×C₈	—	13	2	no	—
215	C₂×C₈	—	26	1	no	—
216	C₂×C₈	—	26	1	no	—
217	C₂×C₈	C₈×D₁₃	1	2	yes	—
218	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
219	C₂×C₈	D₄×D₁₃	1	2	yes	—
220	C₂×C₈	#6129	1	1	yes	characteristic
221	C₂×C₈	#6131	1	1	yes	characteristic
222	C₄²	—	2	1	no	—
223	C₄²	—	2	1	no	—
224	C₄²	—	13	1	no	—
225	C₄²	—	13	1	no	—
226	C₄²	—	13	2	no	—
227	C₄²	—	26	2	no	—
228	C₄²	—	26	2	no	—
229	C₁₆	—	2	4	no	—
230	C₁₆	—	26	4	no	—
231	C₁₃	C₄×#349	1	1	yes	characteristic, complemented, Sylow
232	C₂³	—	13	2	no	—
233	C₂³	—	26	1	no	—
234	C₂³	—	26	1	no	—
235	C₂³	—	52	2	no	—
236	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	13	2	no	—
240	C₂×C₄	—	13	2	no	—
241	C₂×C₄	—	13	2	no	—
242	C₂×C₄	—	26	4	no	—
243	C₂×C₄	—	26	1	no	—
244	C₂×C₄	—	26	1	no	—
245	C₂×C₄	—	26	2	no	—
246	C₂×C₄	—	26	2	no	—
247	C₂×C₄	—	26	2	no	—
248	C₂×C₄	—	26	2	no	—
249	C₂×C₄	—	52	4	no	—
250	C₂×C₄	—	52	4	no	—
251	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
252	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
253	C₂×C₄	#88146	1	1	yes	characteristic
254	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
255	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
256	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	13	4	no	—
259	C₈	—	26	2	no	—
260	C₈	#88135	1	2	yes	—
261	C₈	#88147	1	2	yes	—
262	C₂²	—	2	2	no	—
263	C₂²	—	26	2	no	—
264	C₂²	—	52	2	no	—
265	C₂²	—	52	2	no	—
266	C₂²	—	52	2	no	—
267	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
268	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
269	C₂²	#11718494	1	1	yes	characteristic
270	C₄	—	4	2	no	—
271	C₄	—	13	4	no	—
272	C₄	—	26	2	no	—
273	C₄	—	26	2	no	—
274	C₄	#11718327	1	1	yes	characteristic
275	C₄	#11718368	1	1	yes	characteristic
276	C₄	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
277	C₄	#11718494	1	1	yes	characteristic
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	—	52	2	no	—
281	C₂	#13114593	1	1	yes	characteristic
282	C₂	D₁₃×#349	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1377	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1377	D₁₃
hypocenter	C₁₃	C₄×#349
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

Complements

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

N	H ≅ G/N	type
3. M₃₂×Dic₁₃	C₂	semidirect
4. #13112920	C₂	semidirect
5. C₁₃×#1377	C₂	semidirect
17. #11718106	C₄	semidirect
40. C₁₃×M₃₂	C₂×C₄	semidirect
48. #88052	C₂×C₄	semidirect
95. #1377	D₁₃	semidirect
155. Dic₁₃	#349	semidirect
178. M₃₂	C₄×D₁₃	semidirect
231. C₁₃	C₄×#349	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718368	2
C₂×#11718106	2
M₃₂×Dic₁₃	2
#13112920	2
C₁₃×#1377	2
C₄×#349	13