Subgroups — #16789055

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	2	yes	maximal
2	#13129878	C₂	1	2	yes	maximal, complemented
3	#13129877	C₂	1	2	yes	maximal, complemented
4	C₂×D₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
8	C₂×#88106	C₂²	1	4	yes	—
9	D₁₃⋊M₃₂	—	2	4	no	—
10	D₁₃⋊M₃₂	—	2	4	no	—
11	C₂×#88098	C₄	1	4	yes	complemented
12	C₂×D₁₃⋊C₁₆	C₄	1	4	yes	complemented
13	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
14	C₂×#88055	C₄	1	1	yes	characteristic
15	C₂×#88055	C₂²	1	1	yes	characteristic
16	C₂×#88043	C₂²	1	1	yes	characteristic
17	D₁₃×#97	—	2	4	no	—
18	C₂²×C₄×D₁₃	—	2	1	no	—
19	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	—	2	1	no	—
24	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
26	C₂²×#1055	C₂³	1	1	yes	characteristic
27	C₂×C₈×D₁₃	—	2	2	no	—
28	C₂×C₈×D₁₃	—	2	1	no	—
29	C₂×C₈×D₁₃	—	2	1	no	—
30	C₂×C₈×D₁₃	C₈	1	4	yes	—
31	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
32	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₈×D₁₃	D₄	1	2	yes	—
34	C₂×C₈×D₁₃	D₄	1	4	yes	—
35	C₂×C₈×D₁₃	Q₈	1	2	yes	—
36	C₄²×D₁₃	—	2	2	no	—
37	C₄²×D₁₃	C₈	1	4	yes	—
38	#88106	—	2	4	no	—
39	#88106	—	2	4	no	—
40	C₂×#6092	C₂×C₄	1	8	yes	complemented
41	#88098	—	2	8	no	—
42	D₁₃⋊C₁₆	—	2	8	no	—
43	C₁₃×#97	—	2	2	no	—
44	#88055	—	2	2	no	—
45	#88055	—	2	2	no	—
46	#88043	—	2	2	no	—
47	C₂×#1375	—	13	1	no	maximal, Sylow
48	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	—	2	1	no	—
50	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×Dic₁₃	—	2	1	no	—
52	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
53	C₂×C₄×D₁₃	—	2	4	no	—
54	C₂×C₄×D₁₃	—	4	4	no	—
55	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
56	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
57	C₂×C₄×D₁₃	C₂²⋊C₄	1	2	yes	—
58	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
60	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
61	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
62	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
63	C₂×C₈×C₁₃	—	2	1	no	—
64	C₂×C₈×C₁₃	—	2	1	no	—
65	C₂×C₈×C₁₃	C₄²	1	2	yes	—
66	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
69	C₄²×C₁₃	—	2	1	no	—
70	C₄²×C₁₃	C₂×C₈	1	2	yes	—
71	C₄×Dic₁₃	—	2	1	no	—
72	C₄×Dic₁₃	—	2	4	no	—
73	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
74	C₂×#1055	—	2	1	no	—
75	C₂×#1055	—	2	1	no	—
76	C₂×#1055	C₂×C₈	1	2	yes	—
77	C₂×#1055	C₂²×C₄	1	2	yes	—
78	C₂×#1055	C₂×D₄	1	1	yes	characteristic
79	C₂×#1055	C₂×D₄	1	2	yes	—
80	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
81	C₈×D₁₃	—	2	4	no	—
82	C₈×D₁₃	—	2	4	no	—
83	C₈×D₁₃	C₂²⋊C₄	1	4	yes	—
84	C₈×D₁₃	C₂²⋊C₄	1	4	yes	—
85	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
86	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
87	#6092	—	2	8	no	—
88	C₂²×M₃₂	—	13	2	no	—
89	C₂²×#97	—	13	1	no	—
90	#1375	—	13	2	no	—
91	#1375	—	13	2	no	—
92	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂²×D₁₃	—	2	4	no	—
94	C₂²×D₁₃	#97	1	1	yes	characteristic
95	C₂²×D₁₃	#97	1	1	yes	characteristic
96	C₂²×D₁₃	C₂²⋊C₈	1	2	yes	—
97	C₂²×D₁₃	C₄⋊C₈	1	2	yes	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	—	4	2	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂×Dic₁₃	—	2	2	no	—
107	C₂×Dic₁₃	—	4	2	no	—
108	C₂×Dic₁₃	#97	1	1	yes	characteristic
109	C₂×Dic₁₃	#97	1	1	yes	characteristic
110	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
111	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
112	C₄×D₁₃	—	4	8	no	—
113	C₄×D₁₃	#95	1	2	yes	—
114	C₄×D₁₃	#95	1	2	yes	—
115	C₄×D₁₃	C₄×C₈	1	2	yes	—
116	C₄×D₁₃	C₄×C₈	1	2	yes	—
117	C₄×D₁₃	C₂²⋊C₈	1	2	yes	—
118	C₄×D₁₃	C₂²⋊C₈	1	2	yes	—
119	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
120	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
121	C₈×C₁₃	—	2	2	no	—
122	C₈×C₁₃	#95	1	4	yes	—
123	#1055	—	2	2	no	—
124	#1055	C₂×C₂²⋊C₄	1	2	yes	—
125	#1055	C₂×C₄⋊C₄	1	2	yes	—
126	C₂³×C₈	—	13	1	no	—
127	C₂³×C₈	—	13	1	no	—
128	C₂²×C₄²	—	13	1	no	—
129	C₂×M₃₂	—	13	4	no	—
130	C₂×M₃₂	—	13	4	no	—
131	C₂×M₃₂	—	26	4	no	—
132	C₂×M₃₂	—	26	4	no	—
133	C₂²×C₁₆	—	13	4	no	—
134	C₂×#97	—	13	1	no	—
135	C₂×#97	—	13	1	no	—
136	C₂×#97	—	13	1	no	—
137	C₂×#97	—	26	4	no	—
138	C₂×#97	#261	1	1	yes	characteristic
139	C₂²×C₁₃	—	2	2	no	—
140	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
141	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
142	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
143	C₂×D₁₃	—	2	2	no	—
144	C₂×D₁₃	—	2	4	no	—
145	C₂×D₁₃	—	2	4	no	—
146	C₂×D₁₃	#336	1	2	yes	—
147	C₂×D₁₃	#336	1	2	yes	—
148	C₂×D₁₃	#347	1	4	yes	—
149	C₄×C₁₃	—	4	2	no	—
150	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
151	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
152	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
153	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
154	Dic₁₃	—	4	2	no	—
155	Dic₁₃	#336	1	2	yes	—
156	Dic₁₃	#336	1	2	yes	—
157	C₂³×C₄	—	13	1	no	—
158	C₂³×C₄	—	26	1	no	—
159	C₂²×C₈	—	13	1	no	—
160	C₂²×C₈	—	13	2	no	—
161	C₂²×C₈	—	13	2	no	—
162	C₂²×C₈	—	13	2	no	—
163	C₂²×C₈	—	13	2	no	—
164	C₂²×C₈	—	13	4	no	—
165	C₂²×C₈	—	13	1	no	—
166	C₂²×C₈	—	13	4	no	—
167	C₂²×C₈	—	26	1	no	—
168	C₂²×C₈	—	26	1	no	—
169	C₂²×C₈	—	26	2	no	—
170	C₂²×C₈	C₂×#261	1	1	yes	characteristic
171	C₂²×C₈	C₂×#261	1	1	yes	characteristic
172	C₂×C₄²	—	13	1	no	—
173	C₂×C₄²	—	13	4	no	—
174	C₂×C₄²	—	26	2	no	—
175	C₂×C₄²	—	26	1	no	—
176	C₂×C₄²	C₂×#261	1	1	yes	characteristic
177	M₃₂	—	26	8	no	—
178	M₃₂	—	26	4	no	—
179	M₃₂	—	26	4	no	—
180	C₂×C₁₆	—	13	8	no	—
181	C₂×C₁₆	—	26	8	no	—
182	#97	—	2	2	no	—
183	#97	—	26	2	no	—
184	#97	—	26	2	no	—
185	#97	—	26	2	no	—
186	C₂×C₁₃	—	2	1	no	—
187	C₂×C₁₃	—	2	1	no	—
188	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
189	C₂×C₁₃	C₂×#347	1	2	yes	—
190	D₁₃	—	2	2	no	—
191	D₁₃	#1375	1	4	yes	complemented
192	C₂⁴	—	13	1	no	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	13	1	no	—
195	C₂²×C₄	—	13	2	no	—
196	C₂²×C₄	—	13	2	no	—
197	C₂²×C₄	—	13	1	no	—
198	C₂²×C₄	—	13	1	no	—
199	C₂²×C₄	—	13	1	no	—
200	C₂²×C₄	—	13	1	no	—
201	C₂²×C₄	—	13	2	no	—
202	C₂²×C₄	—	13	2	no	—
203	C₂²×C₄	—	26	4	no	—
204	C₂²×C₄	—	26	1	no	—
205	C₂²×C₄	—	52	4	no	—
206	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	13	2	no	—
210	C₂×C₈	—	13	1	no	—
211	C₂×C₈	—	13	1	no	—
212	C₂×C₈	—	13	2	no	—
213	C₂×C₈	—	13	4	no	—
214	C₂×C₈	—	13	4	no	—
215	C₂×C₈	—	13	4	no	—
216	C₂×C₈	—	13	4	no	—
217	C₂×C₈	—	13	2	no	—
218	C₂×C₈	—	26	4	no	—
219	C₂×C₈	—	26	4	no	—
220	C₂×C₈	—	26	1	no	—
221	C₂×C₈	—	26	1	no	—
222	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
223	C₂×C₈	C₄×#261	1	2	yes	—
224	C₂×C₈	C₄⋊#261	1	2	yes	—
225	C₂×C₈	C₂²⋊#261	1	2	yes	—
226	C₄²	—	2	1	no	—
227	C₄²	—	13	2	no	—
228	C₄²	—	26	4	no	—
229	C₄²	—	26	1	no	—
230	C₄²	D₁₃⋊C₈	1	2	yes	—
231	C₁₆	—	26	8	no	—
232	C₁₃	C₂×#1375	1	1	yes	characteristic, complemented, Sylow
233	C₂³	—	13	1	no	—
234	C₂³	—	13	1	no	—
235	C₂³	—	13	2	no	—
236	C₂³	—	13	2	no	—
237	C₂³	—	26	4	no	—
238	C₂³	D₁₃⋊M₁₆	1	1	yes	characteristic
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	13	1	no	—
242	C₂×C₄	—	13	1	no	—
243	C₂×C₄	—	13	2	no	—
244	C₂×C₄	—	13	2	no	—
245	C₂×C₄	—	13	2	no	—
246	C₂×C₄	—	13	2	no	—
247	C₂×C₄	—	13	2	no	—
248	C₂×C₄	—	13	2	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	2	no	—
251	C₂×C₄	—	13	2	no	—
252	C₂×C₄	—	13	2	no	—
253	C₂×C₄	—	26	2	no	—
254	C₂×C₄	—	52	8	no	—
255	C₂×C₄	—	52	2	no	—
256	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
257	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
258	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
259	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
260	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
261	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
262	C₈	—	2	2	no	—
263	C₈	—	13	2	no	—
264	C₈	—	13	2	no	—
265	C₈	—	26	2	no	—
266	C₈	(C₂×#261)⋊C₄	1	4	yes	—
267	C₂²	—	2	2	no	—
268	C₂²	—	13	2	no	—
269	C₂²	—	13	4	no	—
270	C₂²	—	13	2	no	—
271	C₂²	—	26	4	no	—
272	C₂²	—	26	4	no	—
273	C₂²	—	26	2	no	—
274	C₂²	#11719047	1	1	yes	characteristic
275	C₂²	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
276	C₂²	D₁₃⋊(C₂²⋊C₈)	1	1	yes	characteristic
277	C₄	—	4	2	no	—
278	C₄	—	13	2	no	—
279	C₄	—	13	2	no	—
280	C₄	—	52	2	no	—
281	C₄	C₄×D₁₃⋊C₈	1	1	yes	characteristic
282	C₄	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
283	C₄	D₁₃⋊(C₂²⋊C₈)	1	1	yes	characteristic
284	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
285	C₂	—	2	1	no	—
286	C₂	—	2	1	no	—
287	C₂	—	13	4	no	—
288	C₂	—	26	2	no	—
289	C₂	#13130497	1	1	yes	characteristic
290	C₂	#13131053	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	C₂×#1375
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #13129878	C₂	semidirect
3. #13129877	C₂	semidirect
11. C₂×#88098	C₄	semidirect
12. C₂×D₁₃⋊C₁₆	C₄	semidirect
40. C₂×#6092	C₂×C₄	semidirect
191. D₁₃	#1375	semidirect
232. C₁₃	C₂×#1375	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
#13129878	2
#13129877	2
C₂×D₁₃×#97	2
C₂×#1375	13