Subgroups — #15772125

Order 3328.

320 conjugacy classes of subgroups.

The subgroup lattice has 290 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	#13112776	C₂	1	2	yes	maximal, complemented
4	#13112760	C₂	1	2	yes	maximal
5	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
7	C₁₃×#433	—	2	1	no	—
8	C₁₃×#433	—	2	1	no	—
9	C₁₃×#433	—	2	1	no	—
10	C₁₃×#433	—	2	1	no	—
11	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²⋊#6090	C₂²	1	2	yes	—
18	C₂²⋊#6090	C₂²	1	2	yes	—
19	C₄⋊#6090	—	2	1	no	—
20	C₄⋊#6090	—	2	1	no	—
21	#11718053	—	2	1	no	—
22	C₄×#6090	—	2	1	no	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×#117	—	2	1	no	—
29	C₁₃×#117	—	2	1	no	—
30	C₁₃×#117	—	2	1	no	—
31	C₁₃×#117	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₁₃×C₄⋊C₈	—	2	1	no	—
39	C₁₃×C₄⋊C₈	—	2	1	no	—
40	C₁₃×C₄⋊C₈	—	2	1	no	—
41	C₁₃×C₄⋊C₈	—	2	1	no	—
42	C₁₃×C₂²⋊C₈	—	2	1	no	—
43	C₁₃×C₂²⋊C₈	—	2	1	no	—
44	C₁₃×C₂²⋊C₈	—	2	1	no	—
45	C₁₃×C₂²⋊C₈	—	2	1	no	—
46	C₁₃×#97	—	2	1	no	—
47	C₁₃×#97	—	2	1	no	—
48	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂×#6090	—	2	2	no	—
53	C₂×#6090	—	2	2	no	—
54	#11461	—	13	1	no	maximal, Sylow
55	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	—	2	1	no	—
57	C₂²×C₄×C₁₃	—	2	1	no	—
58	C₂²×C₄×C₁₃	—	4	1	no	—
59	C₂²×C₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	—	2	1	no	—
67	C₂×C₈×C₁₃	—	2	1	no	—
68	C₂×C₈×C₁₃	—	4	1	no	—
69	C₂×C₈×C₁₃	—	4	1	no	—
70	C₂×C₈×C₁₃	—	4	1	no	—
71	C₂×C₈×C₁₃	—	4	1	no	—
72	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₄²×C₁₃	—	2	1	no	—
85	C₄²×C₁₃	—	2	1	no	—
86	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
89	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
90	#6090	—	4	2	no	—
91	#6090	—	4	2	no	—
92	C₂×#433	D₁₃	1	1	yes	characteristic
93	#2163	—	13	1	no	—
94	#2162	—	13	1	no	—
95	#1322	—	13	2	no	—
96	#1314	—	13	2	no	—
97	C₂³×C₁₃	—	2	1	no	—
98	C₂³×C₁₃	—	2	2	no	—
99	C₂³×C₁₃	—	4	1	no	—
100	C₂³×C₁₃	—	4	1	no	—
101	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	1	no	—
104	C₂×C₄×C₁₃	—	2	1	no	—
105	C₂×C₄×C₁₃	—	2	1	no	—
106	C₂×C₄×C₁₃	—	2	1	no	—
107	C₂×C₄×C₁₃	—	2	1	no	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	4	1	no	—
110	C₂×C₄×C₁₃	—	4	2	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	4	1	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	1	no	—
115	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
116	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
121	C₈×C₁₃	—	2	1	no	—
122	C₈×C₁₃	—	2	1	no	—
123	C₈×C₁₃	—	2	1	no	—
124	C₈×C₁₃	—	2	1	no	—
125	C₈×C₁₃	—	4	1	no	—
126	C₈×C₁₃	—	4	1	no	—
127	C₂×#117	Dic₁₃	1	1	yes	characteristic
128	#433	—	2	1	no	—
129	#433	—	2	1	no	—
130	#433	—	2	1	no	—
131	#433	—	2	1	no	—
132	C₂×C₄⋊C₈	Dic₁₃	1	1	yes	characteristic
133	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
134	C₂×C₂²⋊C₈	Dic₁₃	1	1	yes	characteristic
135	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
136	C₂×#97	Dic₁₃	1	1	yes	characteristic
137	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
138	C₄⋊C₁₆	—	26	1	no	—
139	C₄⋊C₁₆	—	26	1	no	—
140	C₂²⋊C₁₆	—	13	2	no	—
141	C₂²⋊C₁₆	—	13	2	no	—
142	#346	—	26	1	no	—
143	C₄×C₁₆	—	26	1	no	—
144	C₂²×C₁₃	—	2	1	no	—
145	C₂²×C₁₃	—	2	1	no	—
146	C₂²×C₁₃	—	4	1	no	—
147	C₂²×C₁₃	—	4	1	no	—
148	C₂²×C₁₃	—	4	1	no	—
149	C₂²×C₁₃	—	8	2	no	—
150	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
151	C₂²×C₁₃	#504	1	2	yes	—
152	C₄×C₁₃	—	2	1	no	—
153	C₄×C₁₃	—	2	1	no	—
154	C₄×C₁₃	—	2	1	no	—
155	C₄×C₁₃	—	2	1	no	—
156	C₄×C₁₃	—	2	1	no	—
157	C₄×C₁₃	—	4	1	no	—
158	C₄×C₁₃	—	4	1	no	—
159	C₄×C₁₃	—	4	1	no	—
160	C₄×C₁₃	#410	1	1	yes	characteristic
161	C₄×C₁₃	#413	1	1	yes	characteristic
162	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
163	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
164	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
165	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
166	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
167	#117	—	2	1	no	—
168	#117	—	2	1	no	—
169	#117	—	2	1	no	—
170	#117	—	2	1	no	—
171	C₂×C₄⋊C₄	#1055	1	1	yes	characteristic
172	C₂×C₄⋊C₄	#1055	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	#1055	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	#1055	1	1	yes	characteristic
175	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
176	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
177	C₂×C₁₆	—	26	2	no	—
178	C₂×C₁₆	—	26	2	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	2	1	no	—
183	C₂²⋊C₈	—	2	1	no	—
184	C₂²⋊C₈	—	2	1	no	—
185	C₂²⋊C₈	—	2	1	no	—
186	C₂²⋊C₈	—	2	1	no	—
187	#97	—	2	1	no	—
188	#97	—	2	1	no	—
189	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
190	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
191	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
192	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
193	C₂×C₁₃	—	2	2	no	—
194	C₂×C₁₃	—	8	1	no	—
195	C₂×C₁₃	#1458	1	1	yes	characteristic
196	C₂×C₁₃	#2113	1	1	yes	characteristic
197	C₂×C₁₃	#2115	1	1	yes	characteristic
198	C₂⁴	C₂×#1055	1	1	yes	characteristic
199	C₂²×C₄	—	2	1	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	4	1	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
204	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
205	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
206	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
207	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
208	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	—	4	1	no	—
213	C₂×C₈	—	4	1	no	—
214	C₂×C₈	—	4	1	no	—
215	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
216	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
217	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
218	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
219	C₄⋊C₄	—	2	1	no	—
220	C₄⋊C₄	—	2	1	no	—
221	C₄⋊C₄	—	2	1	no	—
222	C₄⋊C₄	—	2	1	no	—
223	C₂²⋊C₄	—	2	1	no	—
224	C₂²⋊C₄	—	2	1	no	—
225	C₂²⋊C₄	—	2	1	no	—
226	C₂²⋊C₄	—	2	1	no	—
227	C₄²	—	2	1	no	—
228	C₄²	—	2	1	no	—
229	C₄²	#6099	1	1	yes	characteristic
230	C₄²	#6099	1	1	yes	characteristic
231	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
232	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
233	C₁₆	—	52	2	no	—
234	C₁₆	—	52	2	no	—
235	C₁₃	#11461	1	1	yes	characteristic, complemented, Sylow
236	C₂³	—	2	1	no	—
237	C₂³	—	2	2	no	—
238	C₂³	—	4	1	no	—
239	C₂³	—	4	1	no	—
240	C₂³	C₂²×#1055	1	1	yes	characteristic
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	2	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
255	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
256	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
257	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
258	C₂×C₄	C₂×#6099	1	1	yes	characteristic
259	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
260	C₈	—	2	1	no	—
261	C₈	—	2	1	no	—
262	C₈	—	2	1	no	—
263	C₈	—	2	1	no	—
264	C₈	—	4	1	no	—
265	C₈	—	4	1	no	—
266	C₂²	—	2	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	—	4	1	no	—
269	C₂²	—	4	1	no	—
270	C₂²	—	4	1	no	—
271	C₂²	—	8	2	no	—
272	C₂²	#11718801	1	2	yes	—
273	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	2	1	no	—
278	C₄	—	2	1	no	—
279	C₄	—	4	1	no	—
280	C₄	—	4	1	no	—
281	C₄	—	4	1	no	—
282	C₄	#11718898	1	1	yes	characteristic
283	C₄	#11718901	1	1	yes	characteristic
284	C₂	—	2	2	no	—
285	C₂	—	8	1	no	—
286	C₂	#13113150	1	1	yes	characteristic
287	C₂	#13116450	1	1	yes	characteristic
288	C₂	#13116457	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×#433	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#433	D₁₃
hypocenter	C₁₃	#11461
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#433

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. #13112776	C₂	semidirect
235. C₁₃	#11461	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
#13112776	2
#13112760	2
C₂×C₁₃×#433	2
#11461	13