Subgroups — #15778021

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718568	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718100	C₂	1	1	yes	maximal, characteristic
3	#13116433	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114675	C₂	1	1	yes	maximal, characteristic
6	#13112917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88155	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₃×#405	C₂²	1	1	yes	characteristic
12	C₂×#88065	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	1	yes	characteristic
15	C₂²×#6090	C₂²	1	1	yes	characteristic
16	#11718663	C₄	1	1	yes	characteristic
17	#11718568	—	2	2	no	—
18	#11718568	C₄	1	4	yes	complemented
19	C₂×#88038	—	2	1	no	—
20	C₂×C₁₆×D₁₃	—	2	1	no	—
21	#11718150	C₄	1	1	yes	characteristic
22	#11718124	C₄	1	1	yes	characteristic
23	#11718100	C₄	1	4	yes	complemented
24	C₁₆×Dic₁₃	—	2	2	no	—
25	#11718053	—	2	1	no	—
26	C₄×#6090	—	2	1	no	—
27	C₂×#6127	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×#6099	C₂×C₄	1	1	yes	characteristic
33	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
34	#88155	—	2	1	no	—
35	#88155	—	2	1	no	—
36	#88155	C₂×C₄	1	2	yes	—
37	#88155	C₂×C₄	1	2	yes	—
38	C₂×#6094	—	2	1	no	—
39	C₂×C₈×D₁₃	—	2	1	no	—
40	C₁₃×M₃₂	—	2	1	no	—
41	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₁₆	—	2	1	no	—
43	C₂×C₁₃×C₁₆	—	2	1	no	—
44	C₂×C₁₃×C₁₆	—	2	1	no	—
45	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
46	C₁₃×#97	—	2	1	no	—
47	C₄×C₈×C₁₃	—	2	1	no	—
48	#88065	C₈	1	4	yes	—
49	C₈×Dic₁₃	—	2	1	no	—
50	C₈×Dic₁₃	—	2	1	no	—
51	#88052	—	2	1	no	—
52	#88052	C₂×C₄	1	2	yes	—
53	C₂×#6090	—	2	1	no	—
54	C₂×#6090	C₂×C₄	1	2	yes	—
55	C₂×#6090	D₄	1	1	yes	characteristic
56	C₂×#6090	D₄	1	1	yes	characteristic
57	C₂×#6090	D₄	1	2	yes	—
58	#88050	C₈	1	2	yes	—
59	#88049	C₈	1	2	yes	—
60	#88038	—	2	4	no	—
61	C₁₆×D₁₃	—	2	4	no	—
62	#12614	—	13	1	no	maximal, Sylow
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₃	—	2	1	no	—
65	C₂²×Dic₁₃	—	2	1	no	—
66	#6127	—	2	1	no	—
67	#6127	—	2	1	no	—
68	#6127	C₄²	1	2	yes	—
69	#6127	C₂×C₈	1	2	yes	—
70	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
71	C₂×C₄×D₁₃	—	2	1	no	—
72	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
73	C₁₃×M₁₆	—	2	1	no	—
74	C₁₃×M₁₆	C₂×C₈	1	2	yes	—
75	C₂×C₈×C₁₃	—	2	1	no	—
76	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
81	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
82	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
83	C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₄²×C₁₃	—	2	1	no	—
85	C₄×Dic₁₃	—	2	1	no	—
86	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
87	#6099	—	2	1	no	—
88	#6099	C₄²	1	2	yes	—
89	C₂×#1055	—	2	1	no	—
90	C₂×#1055	—	2	1	no	—
91	C₂×#1055	—	2	1	no	—
92	C₂×#1055	C₂×C₈	1	2	yes	—
93	#6094	—	2	2	no	—
94	#6094	—	2	2	no	—
95	C₈×D₁₃	—	2	2	no	—
96	C₈×D₁₃	—	2	2	no	—
97	C₁₃×C₁₆	—	2	2	no	—
98	C₁₃×C₁₆	—	2	2	no	—
99	#6090	—	2	2	no	—
100	#6090	C₂²⋊C₄	1	2	yes	—
101	#6090	C₂²⋊C₄	1	2	yes	—
102	C₂×#504	—	13	1	no	—
103	C₂×#350	—	13	1	no	—
104	#2108	—	13	1	no	—
105	C₂×C₄×C₁₆	—	13	1	no	—
106	#1764	—	13	1	no	—
107	#1379	D₁₃	1	1	yes	characteristic, complemented
108	#1376	—	13	1	no	—
109	C₂³×C₁₃	#131	1	1	yes	characteristic
110	C₂²×D₁₃	—	2	1	no	—
111	C₂×C₄×C₁₃	—	2	2	no	—
112	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
116	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
118	C₂²⋊D₁₃	—	2	2	no	—
119	C₂²⋊D₁₃	—	2	2	no	—
120	C₂×Dic₁₃	—	2	4	no	—
121	C₂×Dic₁₃	—	2	2	no	—
122	C₂×Dic₁₃	—	2	1	no	—
123	D₅₂	—	2	1	no	—
124	D₅₂	C₄×C₈	1	2	yes	—
125	C₄×D₁₃	—	2	2	no	—
126	C₄×D₁₃	—	2	2	no	—
127	Dic₂₆	—	2	1	no	—
128	Dic₂₆	C₄×C₈	1	2	yes	—
129	C₈×C₁₃	—	2	2	no	—
130	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₈×C₁₃	#117	1	1	yes	characteristic
132	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
133	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
134	#1055	—	2	2	no	—
135	#1055	—	2	2	no	—
136	C₂×#131	—	13	1	no	—
137	#504	—	13	4	no	—
138	#504	—	26	2	no	—
139	C₂×M₃₂	—	13	1	no	—
140	C₂×M₃₂	—	26	1	no	—
141	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
142	C₂²×C₁₆	—	13	1	no	—
143	C₂²×C₁₆	—	26	1	no	—
144	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
145	C₂×#104	—	13	1	no	—
146	#416	—	13	1	no	—
147	#405	C₂×D₁₃	1	1	yes	characteristic
148	C₂×C₄×C₈	—	13	1	no	—
149	#350	—	13	4	no	—
150	#346	—	26	1	no	—
151	C₄×C₁₆	—	26	1	no	—
152	C₄×C₁₆	—	26	2	no	—
153	#341	—	13	1	no	—
154	#339	—	13	1	no	—
155	C₂²×C₁₃	—	2	2	no	—
156	C₂²×C₁₃	#405	1	1	yes	characteristic
157	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
158	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
159	C₂×D₁₃	—	2	2	no	—
160	C₂×D₁₃	—	4	2	no	—
161	C₄×C₁₃	—	4	2	no	—
162	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
164	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
165	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
166	Dic₁₃	—	2	4	no	—
167	Dic₁₃	—	2	2	no	—
168	C₂×#41	—	13	1	no	—
169	#131	—	13	2	no	—
170	#131	—	13	2	no	—
171	#131	—	26	1	no	—
172	#131	—	26	1	no	—
173	C₂×M₁₆	—	13	1	no	—
174	C₂×M₁₆	—	26	1	no	—
175	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
176	C₂²×C₈	—	13	1	no	—
177	C₂²×C₈	—	26	1	no	—
178	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
179	#117	C₄×D₁₃	1	1	yes	characteristic
180	C₂×C₄²	—	13	1	no	—
181	M₃₂	—	2	1	no	—
182	M₃₂	—	13	2	no	—
183	M₃₂	—	26	4	no	—
184	M₃₂	—	26	1	no	—
185	M₃₂	C₄×D₁₃	1	2	yes	—
186	C₂×C₁₆	—	2	1	no	—
187	C₂×C₁₆	—	2	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	13	2	no	—
190	C₂×C₁₆	—	13	2	no	—
191	C₂×C₁₆	—	13	1	no	—
192	C₂×C₁₆	—	13	1	no	—
193	C₂×C₁₆	—	26	4	no	—
194	C₂×C₁₆	—	26	1	no	—
195	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
196	#104	—	13	4	no	—
197	#103	—	13	2	no	—
198	#102	—	13	2	no	—
199	#97	—	2	1	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	26	1	no	—
202	C₄×C₈	—	26	1	no	—
203	C₂×C₁₃	—	2	1	no	—
204	C₂×C₁₃	—	2	1	no	—
205	C₂×C₁₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₁₃	#2170	1	2	yes	—
207	D₁₃	—	4	2	no	—
208	#41	—	13	2	no	—
209	#41	—	13	2	no	—
210	#41	—	26	1	no	—
211	#41	—	26	1	no	—
212	C₂×Q₈	—	13	1	no	—
213	C₂×D₄	—	13	1	no	—
214	C₂×D₄	—	26	1	no	—
215	C₂²×C₄	—	26	1	no	—
216	C₂²×C₄	—	26	1	no	—
217	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
218	M₁₆	—	2	1	no	—
219	M₁₆	—	13	2	no	—
220	M₁₆	—	26	1	no	—
221	M₁₆	—	26	2	no	—
222	M₁₆	—	26	2	no	—
223	M₁₆	C₈×D₁₃	1	2	yes	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	13	2	no	—
226	C₂×C₈	—	26	1	no	—
227	C₂×C₈	—	26	1	no	—
228	C₂×C₈	—	26	1	no	—
229	C₂×C₈	—	26	2	no	—
230	C₂×C₈	—	26	2	no	—
231	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
232	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
233	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
234	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
235	C₂×C₈	#6129	1	1	yes	characteristic
236	C₂×C₈	#6131	1	1	yes	characteristic
237	C₄⋊C₄	C₈×D₁₃	1	2	yes	—
238	C₂²⋊C₄	—	2	1	no	—
239	C₄²	—	2	1	no	—
240	C₄²	—	13	2	no	—
241	C₄²	—	26	1	no	—
242	C₁₆	—	2	2	no	—
243	C₁₆	—	2	2	no	—
244	C₁₆	—	13	2	no	—
245	C₁₆	—	13	2	no	—
246	C₁₆	—	26	2	no	—
247	C₁₃	#12614	1	1	yes	characteristic, complemented, Sylow
248	C₂³	—	26	1	no	—
249	C₂³	#88161	1	1	yes	characteristic
250	Q₈	—	13	2	no	—
251	Q₈	—	26	1	no	—
252	D₄	—	13	2	no	—
253	D₄	—	26	2	no	—
254	D₄	—	26	2	no	—
255	D₄	—	26	1	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	26	4	no	—
258	C₂×C₄	—	26	2	no	—
259	C₂×C₄	—	26	1	no	—
260	C₂×C₄	—	26	2	no	—
261	C₂×C₄	—	26	2	no	—
262	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
263	C₂×C₄	#88135	1	1	yes	characteristic
264	C₂×C₄	#88147	1	1	yes	characteristic
265	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
266	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
267	C₂×C₄	#88161	1	1	yes	characteristic
268	C₈	—	2	2	no	—
269	C₈	—	26	2	no	—
270	C₈	—	26	2	no	—
271	C₈	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
272	C₈	#88135	1	1	yes	characteristic
273	C₈	#88146	1	1	yes	characteristic
274	C₈	#88147	1	1	yes	characteristic
275	C₂²	—	2	2	no	—
276	C₂²	—	26	2	no	—
277	C₂²	—	52	2	no	—
278	C₂²	#11718369	1	1	yes	characteristic
279	C₂²	#11718386	1	1	yes	characteristic
280	C₂²	#11718495	1	1	yes	characteristic
281	C₄	—	4	2	no	—
282	C₄	—	26	4	no	—
283	C₄	—	26	2	no	—
284	C₄	#11718327	1	1	yes	characteristic
285	C₄	C₄×C₈×D₁₃	1	1	yes	characteristic
286	C₄	#11718386	1	1	yes	characteristic
287	C₄	#11718495	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	—	52	2	no	—
291	C₂	#13114606	1	1	yes	characteristic
292	C₂	#13116670	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1379	C₂
socle	C₂²×C₁₃	C₈×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1379	D₁₃
hypocenter	C₁₃	#12614
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
3. #13116433	C₂	semidirect
4. C₂×C₁₆×Dic₁₃	C₂	semidirect
6. #13112917	C₂	semidirect
7. C₁₃×#1379	C₂	semidirect
18. #11718568	C₄	semidirect
23. #11718100	C₄	semidirect
107. #1379	D₁₃	semidirect
247. C₁₃	#12614	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718568	2
C₂×#11718100	2
#13116433	2
C₂×C₁₆×Dic₁₃	2
#13114675	2
#13112917	2
C₁₃×#1379	2
#12614	13