Subgroups — C₂×D₁₃×#498 #16732505

Order 3328.

2398 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₂×#11718341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718516	C₂	1	4	yes	maximal, complemented
4	C₂×#11718740	C₂	1	2	yes	maximal, complemented
5	D₁₃×#498	C₂	1	16	yes	maximal, direct product factor
6	C₂×D₁₃×#106	C₂	1	4	yes	maximal
7	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₁₃	—	2	2	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×#88198	—	2	2	no	—
12	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
13	D₁₃×C₄⋊Q₈	—	2	8	no	—
14	D₁₃×C₄⋊Q₈	C₂²	1	16	yes	—
15	C₂×C₄⋊C₄×D₁₃	—	2	2	no	—
16	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	—
17	C₂×#88142	—	2	2	no	—
18	C₂×#88142	C₂²	1	4	yes	—
19	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88123	C₂²	1	2	yes	—
21	C₁₃×#498	C₂²	1	8	yes	complemented
22	C₂×C₁₃×#106	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88057	C₂²	1	4	yes	—
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	#11718740	C₂²	1	16	yes	complemented
27	C₂×#88048	C₂²	1	8	yes	—
28	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
29	D₁₃×#106	C₂²	1	32	yes	—
30	#11718516	C₂²	1	32	yes	complemented
31	C₄×C₈×D₁₃	C₂²	1	8	yes	—
32	#11718341	C₂²	1	8	yes	complemented
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂×Q₈×D₁₃	—	2	16	no	—
35	C₂×Q₈×D₁₃	—	4	16	no	—
36	C₂²×C₄×D₁₃	—	2	4	no	—
37	C₂²×C₄×D₁₃	D₄	1	2	yes	—
38	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
39	C₂²×Dic₂₆	—	2	2	no	—
40	C₂²×Dic₂₆	—	2	4	no	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₁₃×C₄⋊Q₈	—	2	4	no	—
43	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
46	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
47	#88198	—	2	16	no	—
48	C₂×C₄⋊Dic₁₃	—	2	2	no	—
49	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
50	C₂×#6101	—	2	4	no	—
51	C₂×#6101	—	2	4	no	—
52	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
53	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
54	C₂²×#1055	C₂³	1	2	yes	—
55	C₂×C₈×D₁₃	Q₈	1	16	yes	complemented
56	C₂×C₈×D₁₃	C₂³	1	8	yes	—
57	C₄⋊C₄×D₁₃	—	2	8	no	—
58	C₄⋊C₄×D₁₃	—	2	16	no	—
59	C₄⋊C₄×D₁₃	C₂³	1	16	yes	—
60	#88142	—	2	8	no	—
61	#88142	—	2	16	no	—
62	#88142	C₂³	1	16	yes	—
63	C₄²×D₁₃	D₄	1	4	yes	—
64	C₄²×D₁₃	C₂³	1	4	yes	—
65	#88123	—	2	4	no	—
66	#88123	C₂³	1	8	yes	—
67	C₁₃×#106	C₂³	1	16	yes	—
68	C₄×C₈×C₁₃	C₂³	1	4	yes	—
69	#88057	C₂³	1	16	yes	—
70	C₈×Dic₁₃	C₂³	1	8	yes	—
71	#88048	C₂³	1	32	yes	—
72	C₄×#1055	C₂³	1	4	yes	—
73	C₂²×#498	—	13	1	no	maximal, Sylow
74	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₃	—	2	8	no	—
76	C₂×Q₈×C₁₃	—	4	8	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
80	C₂²×Dic₁₃	—	2	4	no	—
81	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
83	Q₈×D₁₃	—	4	64	no	—
84	C₂×C₄×D₁₃	—	2	16	no	—
85	C₂×C₄×D₁₃	—	4	16	no	—
86	C₂×C₄×D₁₃	SD₁₆	1	16	yes	—
87	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
88	C₂×C₄×D₁₃	C₂×D₄	1	8	yes	—
89	C₂×C₄×D₁₃	C₂×Q₈	1	8	yes	—
90	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
91	C₂×Dic₂₆	—	2	8	no	—
92	C₂×Dic₂₆	—	2	16	no	—
93	C₂×Dic₂₆	—	4	8	no	—
94	C₂×Dic₂₆	—	4	16	no	—
95	C₂×C₈×C₁₃	C₂×Q₈	1	8	yes	complemented
96	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
97	C₁₃×C₄⋊C₄	—	2	8	no	—
98	C₁₃×C₄⋊C₄	—	2	4	no	—
99	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
100	C₄²×C₁₃	C₂×D₄	1	2	yes	—
101	C₄²×C₁₃	C₂⁴	1	2	yes	—
102	C₄⋊Dic₁₃	—	2	4	no	—
103	C₄⋊Dic₁₃	—	2	8	no	—
104	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
105	#6101	—	2	16	no	—
106	#6101	—	2	16	no	—
107	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
108	C₄×Dic₁₃	C₂×D₄	1	8	yes	—
109	C₄×Dic₁₃	C₂⁴	1	2	yes	—
110	C₂×#1055	C₂×Q₈	1	8	yes	complemented
111	C₂×#1055	C₂⁴	1	4	yes	—
112	C₈×D₁₃	C₂×Q₈	1	32	yes	complemented
113	C₂²×C₄⋊Q₈	—	13	2	no	—
114	C₂×#498	—	13	16	no	—
115	C₂×#498	—	13	4	no	—
116	C₂×#498	—	13	1	no	—
117	C₂×#498	—	13	2	no	—
118	C₂×#498	D₁₃	1	1	yes	characteristic, direct product factor
119	C₂²×#106	—	13	4	no	—
120	C₂²×C₄×C₈	—	13	1	no	—
121	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
122	C₂²×D₁₃	C₄⋊Q₈	1	4	yes	—
123	C₂²×D₁₃	C₂×SD₁₆	1	8	yes	—
124	C₂²×D₁₃	C₂²×D₄	1	2	yes	—
125	Q₈×C₁₃	—	4	16	no	—
126	C₂×C₄×C₁₃	—	2	8	no	—
127	C₂×C₄×C₁₃	—	4	8	no	—
128	C₂×C₄×C₁₃	C₂×SD₁₆	1	8	yes	—
129	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
132	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
133	C₂×Dic₁₃	—	2	8	no	—
134	C₂×Dic₁₃	—	4	8	no	—
135	C₂×Dic₁₃	C₄⋊Q₈	1	4	yes	—
136	C₂×Dic₁₃	C₂×SD₁₆	1	8	yes	—
137	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
138	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
139	C₄×D₁₃	—	4	32	no	—
140	C₄×D₁₃	C₄⋊Q₈	1	8	yes	—
141	C₄×D₁₃	C₂×SD₁₆	1	32	yes	—
142	C₄×D₁₃	C₂²×Q₈	1	8	yes	—
143	Dic₂₆	—	4	16	no	—
144	Dic₂₆	—	4	32	no	—
145	C₈×C₁₃	C₂²×Q₈	1	8	yes	complemented
146	#1055	C₂²×Q₈	1	8	yes	complemented
147	C₂³×Q₈	—	26	2	no	—
148	C₂³×C₈	—	13	2	no	—
149	C₂×C₄⋊Q₈	—	13	16	no	—
150	C₂×C₄⋊Q₈	—	13	4	no	—
151	C₂×C₄⋊Q₈	—	13	2	no	—
152	C₂×C₄⋊Q₈	—	26	2	no	—
153	C₂×C₄⋊Q₈	—	26	8	no	—
154	C₂×C₄⋊Q₈	—	26	2	no	—
155	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
156	C₂²×C₄⋊C₄	—	13	4	no	—
157	C₂²×C₄⋊C₄	—	26	2	no	—
158	C₂²×C₄²	—	13	1	no	—
159	#498	—	13	16	no	—
160	#498	—	13	32	no	—
161	#498	—	13	8	no	—
162	#498	C₂×D₁₃	1	8	yes	direct product factor
163	C₂×#106	—	13	4	no	—
164	C₂×#106	—	13	8	no	—
165	C₂×#106	—	13	32	no	—
166	C₂×#106	C₂×D₁₃	1	4	yes	—
167	C₂×C₄×C₈	—	13	2	no	—
168	C₂×C₄×C₈	—	13	1	no	—
169	C₂×C₄×C₈	—	13	8	no	—
170	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
171	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
172	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
173	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
174	C₂×D₁₃	#498	1	16	yes	direct product factor
175	C₂×D₁₃	C₂×C₄⋊Q₈	1	4	yes	—
176	C₂×D₁₃	C₂²×SD₁₆	1	8	yes	—
177	C₄×C₁₃	—	4	8	no	—
178	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
179	C₄×C₁₃	C₂²×SD₁₆	1	8	yes	—
180	C₄×C₁₃	C₂³×Q₈	1	2	yes	—
181	Dic₁₃	—	4	8	no	—
182	Dic₁₃	C₂×C₄⋊Q₈	1	4	yes	—
183	Dic₁₃	C₂²×SD₁₆	1	8	yes	—
184	C₂²×Q₈	—	2	2	no	—
185	C₂²×Q₈	—	26	4	no	—
186	C₂²×Q₈	—	26	16	no	—
187	C₂²×Q₈	—	26	2	no	—
188	C₂²×Q₈	—	52	16	no	—
189	C₂³×C₄	—	13	2	no	—
190	C₂³×C₄	—	13	1	no	—
191	C₂³×C₄	—	26	4	no	—
192	C₂²×C₈	—	13	2	no	—
193	C₂²×C₈	—	13	16	no	—
194	C₂²×C₈	—	13	8	no	—
195	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
196	C₄⋊Q₈	—	2	4	no	—
197	C₄⋊Q₈	—	13	16	no	—
198	C₄⋊Q₈	—	13	8	no	—
199	C₄⋊Q₈	—	26	16	no	—
200	C₄⋊Q₈	—	26	8	no	—
201	C₄⋊Q₈	—	26	16	no	—
202	C₄⋊Q₈	—	26	4	no	—
203	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	13	4	no	—
206	C₂×C₄⋊C₄	—	13	16	no	—
207	C₂×C₄⋊C₄	—	26	8	no	—
208	C₂×C₄⋊C₄	—	26	16	no	—
209	C₂×C₄⋊C₄	—	26	4	no	—
210	C₂×C₄⋊C₄	—	26	4	no	—
211	C₂×C₄⋊C₄	—	26	2	no	—
212	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
213	C₂×C₄²	—	13	2	no	—
214	C₂×C₄²	—	13	1	no	—
215	C₂×C₄²	—	13	4	no	—
216	C₂×C₄²	—	13	4	no	—
217	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
218	#106	—	13	16	no	—
219	#106	—	13	32	no	—
220	#106	C₂²×D₁₃	1	16	yes	—
221	C₄×C₈	—	13	8	no	—
222	C₄×C₈	—	13	4	no	—
223	C₄×C₈	C₂²×D₁₃	1	4	yes	—
224	C₂×C₁₃	C₂×#498	1	4	yes	complemented
225	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
226	C₂×C₁₃	C₂³×SD₁₆	1	2	yes	—
227	D₁₃	C₂×#498	1	8	yes	direct product factor
228	C₂⁴	—	13	1	no	—
229	C₂×Q₈	—	2	8	no	—
230	C₂×Q₈	—	4	8	no	—
231	C₂×Q₈	—	26	16	no	—
232	C₂×Q₈	—	26	8	no	—
233	C₂×Q₈	—	52	16	no	—
234	C₂×Q₈	—	52	64	no	—
235	C₂×Q₈	—	52	8	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	13	1	no	—
238	C₂²×C₄	—	13	2	no	—
239	C₂²×C₄	—	13	16	no	—
240	C₂²×C₄	—	13	2	no	—
241	C₂²×C₄	—	13	8	no	—
242	C₂²×C₄	—	13	8	no	—
243	C₂²×C₄	—	13	2	no	—
244	C₂²×C₄	—	26	16	no	—
245	C₂²×C₄	—	26	4	no	—
246	C₂²×C₄	—	52	16	no	—
247	C₂²×C₄	D₄×D₁₃	1	2	yes	—
248	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
249	C₂×C₈	—	13	8	no	—
250	C₂×C₈	—	13	4	no	—
251	C₂×C₈	—	13	32	no	—
252	C₂×C₈	Q₈×D₁₃	1	8	yes	complemented
253	C₂×C₈	C₂³×D₁₃	1	4	yes	—
254	C₄⋊C₄	—	2	8	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	—	13	8	no	—
257	C₄⋊C₄	—	26	16	no	—
258	C₄⋊C₄	—	26	16	no	—
259	C₄⋊C₄	—	26	4	no	—
260	C₄⋊C₄	—	26	8	no	—
261	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
262	C₄²	—	13	8	no	—
263	C₄²	—	13	2	no	—
264	C₄²	—	13	2	no	—
265	C₄²	D₄×D₁₃	1	2	yes	—
266	C₄²	C₂³×D₁₃	1	2	yes	—
267	C₁₃	C₂²×#498	1	1	yes	characteristic, complemented, Sylow
268	C₂³	—	13	4	no	—
269	C₂³	—	13	8	no	—
270	C₂³	—	13	2	no	—
271	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
272	Q₈	—	4	16	no	—
273	Q₈	—	52	32	no	—
274	Q₈	—	52	16	no	—
275	C₂×C₄	—	2	8	no	—
276	C₂×C₄	—	4	8	no	—
277	C₂×C₄	—	13	4	no	—
278	C₂×C₄	—	13	8	no	—
279	C₂×C₄	—	13	2	no	—
280	C₂×C₄	—	13	4	no	—
281	C₂×C₄	—	13	8	no	—
282	C₂×C₄	—	13	32	no	—
283	C₂×C₄	—	13	8	no	—
284	C₂×C₄	—	26	8	no	—
285	C₂×C₄	—	52	32	no	—
286	C₂×C₄	—	52	8	no	—
287	C₂×C₄	SD₁₆×D₁₃	1	8	yes	—
288	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
289	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
290	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	—
291	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
292	C₈	—	13	8	no	—
293	C₈	C₂×Q₈×D₁₃	1	8	yes	complemented
294	C₂²	—	13	8	no	—
295	C₂²	—	13	4	no	—
296	C₂²	—	13	16	no	—
297	C₂²	D₁₃×C₄⋊Q₈	1	2	yes	—
298	C₂²	C₂×SD₁₆×D₁₃	1	4	yes	—
299	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
300	C₄	—	4	8	no	—
301	C₄	—	13	8	no	—
302	C₄	—	13	4	no	—
303	C₄	—	52	8	no	—
304	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
305	C₄	C₂×SD₁₆×D₁₃	1	8	yes	—
306	C₄	C₂²×Q₈×D₁₃	1	2	yes	—
307	C₂	—	13	8	no	—
308	C₂	D₁₃×#498	1	4	yes	direct product factor
309	C₂	C₂×D₁₃×C₄⋊Q₈	1	1	yes	characteristic
310	C₂	C₂²×SD₁₆×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#498	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂³×D₁₃	C₂×D₄
hypercenter	C₂×#498	D₁₃
hypocenter	C₁₃	C₂²×#498
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
2. C₂×#11718341	C₂	semidirect
3. C₂×#11718516	C₂	semidirect
4. C₂×#11718740	C₂	semidirect
5. D₁₃×#498	C₂	direct (N × H)
8. C₂×C₁₃×#498	C₂	semidirect
21. C₁₃×#498	C₂²	semidirect
26. #11718740	C₂²	semidirect
30. #11718516	C₂²	semidirect
32. #11718341	C₂²	semidirect
55. C₂×C₈×D₁₃	Q₈	semidirect
95. C₂×C₈×C₁₃	C₂×Q₈	semidirect
110. C₂×#1055	C₂×Q₈	semidirect
112. C₈×D₁₃	C₂×Q₈	semidirect
118. C₂×#498	D₁₃	direct (N × H)
145. C₈×C₁₃	C₂²×Q₈	semidirect
146. #1055	C₂²×Q₈	semidirect
162. #498	C₂×D₁₃	direct (N × H)
174. C₂×D₁₃	#498	direct (N × H)
224. C₂×C₁₃	C₂×#498	semidirect
227. D₁₃	C₂×#498	direct (N × H)
252. C₂×C₈	Q₈×D₁₃	semidirect
267. C₁₃	C₂²×#498	semidirect
293. C₈	C₂×Q₈×D₁₃	semidirect
308. C₂	D₁₃×#498	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₃×C₄⋊Q₈	2
C₂×#11718341	2
C₂×#11718516	2
C₂×#11718740	2
D₁₃×#498	2
C₂×D₁₃×#106	2
C₂×C₄×C₈×D₁₃	2
C₂×C₁₃×#498	2
C₂²×#498	13

Subgroups — C2×D13×#498 #16732505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#498 #16732505