Subgroups — C₂×C₁₃×#2089 #15710011

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	2	yes	maximal
2	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2089	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#343	C₂	1	2	yes	maximal
6	C₂×C₁₃×#341	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₁₃×#428	—	2	4	no	—
13	C₁₃×#428	C₂²	1	8	yes	—
14	C₂×C₁₃×#107	—	2	2	no	—
15	C₂×C₁₃×#107	—	2	2	no	—
16	C₂×C₁₃×#107	—	2	2	no	—
17	C₂×C₁₃×#107	C₂²	1	4	yes	—
18	C₂×C₁₃×#106	—	2	2	no	—
19	C₁₃×#424	—	2	2	no	—
20	C₁₃×#424	C₂²	1	4	yes	—
21	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
22	C₁₃×#343	C₂²	1	8	yes	—
23	C₁₃×#341	C₂²	1	4	yes	—
24	C₂³×C₄×C₁₃	—	2	2	no	—
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	4	no	—
28	C₂×C₁₃×M₁₆	—	2	1	no	—
29	C₂×C₁₃×M₁₆	—	2	4	no	—
30	C₂×C₁₃×M₁₆	Q₈	1	8	yes	—
31	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
32	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
33	C₂²×C₈×C₁₃	—	2	2	no	—
34	C₂²×C₈×C₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	D₄	1	2	yes	—
37	C₂²×C₈×C₁₃	D₄	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₁₃×#117	—	2	1	no	—
40	C₁₃×#117	—	2	1	no	—
41	C₁₃×#117	D₄	1	2	yes	—
42	C₁₃×#117	C₂³	1	2	yes	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₂×C₄²×C₁₃	—	2	1	no	—
53	C₁₃×#107	—	2	8	no	—
54	C₁₃×#107	—	2	8	no	—
55	C₁₃×#106	—	2	8	no	—
56	C₁₃×C₄⋊C₈	—	2	8	no	—
57	C₂×#2089	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁴×C₁₃	#41	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	1	no	—
60	C₂²×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	4	2	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	—	8	4	no	—
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	#41	1	4	yes	—
72	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₁₃×M₁₆	—	2	8	no	—
74	C₁₃×M₁₆	—	2	4	no	—
75	C₁₃×M₁₆	—	2	4	no	—
76	C₁₃×M₁₆	—	4	2	no	—
77	C₁₃×M₁₆	C₂×Q₈	1	8	yes	—
78	C₂×C₈×C₁₃	—	2	8	no	—
79	C₂×C₈×C₁₃	—	2	4	no	—
80	C₂×C₈×C₁₃	—	2	4	no	—
81	C₂×C₈×C₁₃	—	2	4	no	—
82	C₂×C₈×C₁₃	—	2	4	no	—
83	C₂×C₈×C₁₃	—	2	2	no	—
84	C₂×C₈×C₁₃	—	4	2	no	—
85	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
86	C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₁₃×C₄⋊C₄	—	2	4	no	—
89	C₁₃×C₄⋊C₄	—	2	4	no	—
90	C₁₃×C₄⋊C₄	—	4	2	no	—
91	C₁₃×C₄⋊C₄	—	4	2	no	—
92	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
93	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
94	C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₄²×C₁₃	—	2	2	no	—
97	C₄²×C₁₃	—	2	2	no	—
98	C₂×#428	C₂×C₁₃	1	2	yes	—
99	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic
100	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
101	#2089	C₂×C₁₃	1	8	yes	direct product factor
102	C₂×#343	C₂×C₁₃	1	2	yes	—
103	C₂×#341	C₂×C₁₃	1	1	yes	characteristic
104	C₂³×C₁₃	—	2	2	no	—
105	C₂³×C₁₃	—	2	2	no	—
106	C₂³×C₁₃	#121	1	1	yes	characteristic
107	C₂³×C₁₃	#121	1	1	yes	characteristic
108	C₂³×C₁₃	#125	1	4	yes	—
109	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
110	C₂×C₄×C₁₃	—	2	2	no	—
111	C₂×C₄×C₁₃	—	2	2	no	—
112	C₂×C₄×C₁₃	—	4	2	no	—
113	C₂×C₄×C₁₃	—	4	2	no	—
114	C₂×C₄×C₁₃	—	4	4	no	—
115	C₂×C₄×C₁₃	—	8	4	no	—
116	C₂×C₄×C₁₃	—	8	4	no	—
117	C₂×C₄×C₁₃	—	8	4	no	—
118	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
119	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
121	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
122	C₂×C₄×C₁₃	#123	1	2	yes	—
123	C₂×C₄×C₁₃	#123	1	2	yes	—
124	C₂×C₄×C₁₃	#125	1	4	yes	—
125	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
126	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
127	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
130	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
131	C₈×C₁₃	—	2	8	no	—
132	C₈×C₁₃	—	2	4	no	—
133	C₈×C₁₃	—	4	2	no	—
134	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
135	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
136	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
138	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
139	#428	—	2	4	no	—
140	#428	C₂²×C₁₃	1	8	yes	—
141	C₂×#107	—	2	2	no	—
142	C₂×#107	—	2	2	no	—
143	C₂×#107	—	2	2	no	—
144	C₂×#107	C₂²×C₁₃	1	4	yes	—
145	C₂×#106	—	2	2	no	—
146	#424	—	2	2	no	—
147	#424	C₂²×C₁₃	1	4	yes	—
148	C₂×C₄⋊C₈	—	2	2	no	—
149	#343	C₂²×C₁₃	1	8	yes	—
150	#341	C₂²×C₁₃	1	4	yes	—
151	C₂²×C₁₃	—	2	8	no	—
152	C₂²×C₁₃	—	2	1	no	—
153	C₂²×C₁₃	—	2	1	no	—
154	C₂²×C₁₃	—	2	1	no	—
155	C₂²×C₁₃	—	2	1	no	—
156	C₂²×C₁₃	#398	1	2	yes	—
157	C₂²×C₁₃	#398	1	2	yes	—
158	C₂²×C₁₃	#472	1	2	yes	—
159	C₂²×C₁₃	#473	1	2	yes	—
160	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
161	C₂²×C₁₃	C₂×#125	1	2	yes	—
162	C₄×C₁₃	—	4	2	no	—
163	C₄×C₁₃	—	4	2	no	—
164	C₄×C₁₃	—	8	4	no	—
165	C₄×C₁₃	#398	1	2	yes	—
166	C₄×C₁₃	#398	1	2	yes	—
167	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
168	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
169	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
170	C₂³×C₄	—	2	2	no	—
171	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	—	2	4	no	—
174	C₂×M₁₆	—	2	1	no	—
175	C₂×M₁₆	—	2	4	no	—
176	C₂×M₁₆	Q₈×C₁₃	1	8	yes	—
177	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
178	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	—	2	4	no	—
181	C₂²×C₈	—	2	1	no	—
182	C₂²×C₈	D₄×C₁₃	1	2	yes	—
183	C₂²×C₈	D₄×C₁₃	1	2	yes	—
184	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
185	#117	—	2	1	no	—
186	#117	—	2	1	no	—
187	#117	D₄×C₁₃	1	2	yes	—
188	#117	C₂³×C₁₃	1	2	yes	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
197	C₂×C₂²⋊C₄	—	2	1	no	—
198	C₂×C₄²	—	2	1	no	—
199	#107	—	2	8	no	—
200	#107	—	2	8	no	—
201	#106	—	2	8	no	—
202	C₄⋊C₈	—	2	8	no	—
203	C₂×C₁₃	—	2	2	no	—
204	C₂×C₁₃	—	2	2	no	—
205	C₂×C₁₃	#2089	1	4	yes	direct product factor
206	C₂×C₁₃	C₂×#398	1	1	yes	characteristic
207	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
208	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
209	C₂⁴	C₁₃×#41	1	1	yes	characteristic
210	C₂²×C₄	—	2	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	4	2	no	—
214	C₂²×C₄	—	4	2	no	—
215	C₂²×C₄	—	8	4	no	—
216	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
217	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
218	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
219	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
220	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
221	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
222	C₂²×C₄	C₁₃×#41	1	4	yes	—
223	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
224	M₁₆	—	2	8	no	—
225	M₁₆	—	2	4	no	—
226	M₁₆	—	2	4	no	—
227	M₁₆	—	4	2	no	—
228	M₁₆	C₂×Q₈×C₁₃	1	8	yes	—
229	C₂×C₈	—	2	8	no	—
230	C₂×C₈	—	2	4	no	—
231	C₂×C₈	—	2	4	no	—
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
237	C₄⋊C₄	—	2	1	no	—
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	2	4	no	—
241	C₄⋊C₄	—	4	2	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
244	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
245	C₂²⋊C₄	—	2	2	no	—
246	C₂²⋊C₄	—	2	2	no	—
247	C₄²	—	2	2	no	—
248	C₄²	—	2	2	no	—
249	C₁₃	C₂×#2089	1	1	yes	characteristic, direct product factor, Sylow
250	C₂³	—	2	2	no	—
251	C₂³	—	2	2	no	—
252	C₂³	C₁₃×#121	1	1	yes	characteristic
253	C₂³	C₁₃×#121	1	1	yes	characteristic
254	C₂³	C₁₃×#125	1	4	yes	—
255	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	—	8	4	no	—
262	C₂×C₄	—	8	4	no	—
263	C₂×C₄	—	8	4	no	—
264	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
265	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
266	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
267	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
268	C₂×C₄	C₁₃×#123	1	2	yes	—
269	C₂×C₄	C₁₃×#123	1	2	yes	—
270	C₂×C₄	C₁₃×#125	1	4	yes	—
271	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
272	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
273	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
274	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
276	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
277	C₈	—	2	8	no	—
278	C₈	—	2	4	no	—
279	C₈	—	4	2	no	—
280	C₂²	—	2	1	no	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	—	2	8	no	—
285	C₂²	C₁₃×#398	1	2	yes	—
286	C₂²	C₁₃×#398	1	2	yes	—
287	C₂²	C₁₃×#472	1	2	yes	—
288	C₂²	C₁₃×#473	1	2	yes	—
289	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
290	C₂²	C₂×C₁₃×#125	1	2	yes	—
291	C₄	—	4	2	no	—
292	C₄	—	4	2	no	—
293	C₄	—	8	4	no	—
294	C₄	C₁₃×#398	1	2	yes	—
295	C₄	C₁₃×#398	1	2	yes	—
296	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
297	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
298	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
299	C₂	—	2	2	no	—
300	C₂	—	2	2	no	—
301	C₂	C₁₃×#2089	1	4	yes	direct product factor
302	C₂	C₂×C₁₃×#398	1	1	yes	characteristic
303	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
304	C₂	C₂×C₁₃×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#2089	C₂	direct (N × H)
57. C₂×#2089	C₁₃	direct (N × H)
101. #2089	C₂×C₁₃	direct (N × H)
205. C₂×C₁₃	#2089	direct (N × H)
249. C₁₃	C₂×#2089	direct (N × H)
301. C₂	C₁₃×#2089	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×C₁₃×#428	2
C₂²×C₁₃×#107	2
C₂×C₁₃×#424	2
C₁₃×#2089	2
C₂×C₁₃×#343	2
C₂×C₁₃×#341	2
C₂×#2089	13

Subgroups — C2×C13×#2089 #15710011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2089 #15710011