Subgroups — C₂×C₁₃×#2099 #15710080

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₃×#340	C₂	1	2	yes	maximal
5	C₂×C₁₃×#340	C₂	1	2	yes	maximal
6	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
9	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
10	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#389	—	2	2	no	—
16	C₁₃×#389	C₂²	1	4	yes	—
17	C₁₃×#384	—	2	2	no	—
18	C₁₃×#384	C₂²	1	4	yes	—
19	C₂×C₁₃×#95	—	2	1	no	—
20	C₁₃×#340	C₂²	1	8	yes	—
21	C₁₃×#340	C₂²	1	8	yes	—
22	C₁₃×#336	C₂²	1	4	yes	—
23	C₂³×C₄×C₁₃	—	2	1	no	—
24	C₂³×C₄×C₁₃	—	2	2	no	—
25	C₂³×C₄×C₁₃	—	2	1	no	—
26	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	—	2	4	no	—
30	C₂²×C₈×C₁₃	—	2	4	no	—
31	C₂²×C₈×C₁₃	—	2	4	no	—
32	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
33	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
42	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
43	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₃	—	2	4	no	—
50	C₂×C₄²×C₁₃	D₄	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
52	C₁₃×#95	—	2	4	no	—
53	C₂×#2099	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	—	4	2	no	—
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	—	4	4	no	—
67	C₂²×C₄×C₁₃	—	4	2	no	—
68	C₂²×C₄×C₁₃	—	4	4	no	—
69	C₂²×C₄×C₁₃	—	4	4	no	—
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	D₈	1	4	yes	—
72	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
73	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₃	#41	1	2	yes	—
78	C₂²×C₄×C₁₃	#41	1	4	yes	—
79	C₂²×C₄×C₁₃	#41	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₁₃	—	2	4	no	—
82	C₂×C₈×C₁₃	—	2	4	no	—
83	C₂×C₈×C₁₃	—	2	4	no	—
84	C₂×C₈×C₁₃	—	4	8	no	—
85	C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₁₃×C₄⋊C₄	—	2	4	no	—
88	C₁₃×C₄⋊C₄	—	2	8	no	—
89	C₁₃×C₄⋊C₄	—	4	2	no	—
90	C₁₃×C₄⋊C₄	—	4	4	no	—
91	C₁₃×C₄⋊C₄	—	4	8	no	—
92	C₁₃×C₄⋊C₄	—	4	8	no	—
93	C₁₃×C₄⋊C₄	—	4	8	no	—
94	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
95	C₄²×C₁₃	—	2	4	no	—
96	C₄²×C₁₃	—	2	4	no	—
97	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
98	C₂×#384	C₂×C₁₃	1	1	yes	characteristic
99	#2099	C₂×C₁₃	1	8	yes	direct product factor
100	C₂×#340	C₂×C₁₃	1	2	yes	—
101	C₂×#340	C₂×C₁₃	1	2	yes	—
102	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
103	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
104	C₂³×C₁₃	#123	1	2	yes	—
105	C₂³×C₁₃	#124	1	2	yes	—
106	C₂³×C₁₃	C₂×D₈	1	2	yes	—
107	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
108	C₂³×C₁₃	#137	1	2	yes	—
109	C₂³×C₁₃	#137	1	2	yes	—
110	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₃	—	2	2	no	—
112	C₂×C₄×C₁₃	—	2	2	no	—
113	C₂×C₄×C₁₃	—	2	2	no	—
114	C₂×C₄×C₁₃	—	2	2	no	—
115	C₂×C₄×C₁₃	—	2	8	no	—
116	C₂×C₄×C₁₃	—	2	8	no	—
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	—	4	2	no	—
119	C₂×C₄×C₁₃	—	4	2	no	—
120	C₂×C₄×C₁₃	—	4	8	no	—
121	C₂×C₄×C₁₃	—	4	2	no	—
122	C₂×C₄×C₁₃	—	4	4	no	—
123	C₂×C₄×C₁₃	—	4	2	no	—
124	C₂×C₄×C₁₃	—	4	4	no	—
125	C₂×C₄×C₁₃	—	4	4	no	—
126	C₂×C₄×C₁₃	—	4	2	no	—
127	C₂×C₄×C₁₃	—	8	4	no	—
128	C₂×C₄×C₁₃	—	8	8	no	—
129	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₁₃	#123	1	2	yes	—
131	C₂×C₄×C₁₃	#124	1	2	yes	—
132	C₂×C₄×C₁₃	#125	1	8	yes	—
133	C₂×C₄×C₁₃	#126	1	8	yes	—
134	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
135	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
136	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
139	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
140	C₈×C₁₃	—	4	4	no	—
141	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
142	C₂²×C₄⋊C₄	—	2	1	no	—
143	C₂²×C₄⋊C₄	—	2	1	no	—
144	C₂²×C₄⋊C₄	—	2	1	no	—
145	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
146	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
147	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
148	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
149	#389	—	2	2	no	—
150	#389	C₂²×C₁₃	1	4	yes	—
151	#384	—	2	2	no	—
152	#384	C₂²×C₁₃	1	4	yes	—
153	C₂×#95	—	2	1	no	—
154	#340	C₂²×C₁₃	1	8	yes	—
155	#340	C₂²×C₁₃	1	8	yes	—
156	#336	C₂²×C₁₃	1	4	yes	—
157	C₂²×C₁₃	#400	1	4	yes	—
158	C₂²×C₁₃	#474	1	4	yes	—
159	C₂²×C₁₃	#475	1	4	yes	—
160	C₂²×C₁₃	#480	1	4	yes	—
161	C₂²×C₁₃	#483	1	4	yes	—
162	C₂²×C₁₃	#486	1	4	yes	—
163	C₂²×C₁₃	#491	1	4	yes	—
164	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
166	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
167	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
168	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
169	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
170	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
171	C₄×C₁₃	—	2	4	no	—
172	C₄×C₁₃	—	2	4	no	—
173	C₄×C₁₃	—	4	4	no	—
174	C₄×C₁₃	—	8	2	no	—
175	C₄×C₁₃	—	8	4	no	—
176	C₄×C₁₃	#400	1	4	yes	—
177	C₄×C₁₃	C₂×#125	1	2	yes	—
178	C₄×C₁₃	C₂×#126	1	2	yes	—
179	C₂³×C₄	—	2	1	no	—
180	C₂³×C₄	—	2	2	no	—
181	C₂³×C₄	—	2	1	no	—
182	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
183	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
184	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
185	C₂²×C₈	—	2	4	no	—
186	C₂²×C₈	—	2	4	no	—
187	C₂²×C₈	—	2	4	no	—
188	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	4	no	—
192	C₂×C₄⋊C₄	—	2	8	no	—
193	C₂×C₄⋊C₄	—	2	4	no	—
194	C₂×C₄⋊C₄	—	2	4	no	—
195	C₂×C₄⋊C₄	—	2	4	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	1	no	—
198	C₂×C₄⋊C₄	—	4	4	no	—
199	C₂×C₄⋊C₄	—	4	4	no	—
200	C₂×C₄⋊C₄	—	4	4	no	—
201	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
202	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
203	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
204	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
205	C₂×C₄²	—	2	4	no	—
206	C₂×C₄²	D₄×C₁₃	1	2	yes	—
207	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
208	#95	—	2	4	no	—
209	C₂×C₁₃	#2099	1	8	yes	direct product factor
210	C₂×C₁₃	C₂×#400	1	1	yes	characteristic
211	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
212	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
213	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
214	C₂×C₁₃	C₂×#483	1	1	yes	characteristic
215	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
216	C₂×C₁₃	C₂×#491	1	1	yes	characteristic
217	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	—	4	4	no	—
230	C₂²×C₄	—	4	2	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	—	4	4	no	—
233	C₂²×C₄	—	4	2	no	—
234	C₂²×C₄	C₁₃×D₈	1	4	yes	—
235	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
236	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
237	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
238	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
239	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
240	C₂²×C₄	C₁₃×#41	1	2	yes	—
241	C₂²×C₄	C₁₃×#41	1	4	yes	—
242	C₂²×C₄	C₁₃×#41	1	4	yes	—
243	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	4	8	no	—
248	C₄⋊C₄	—	2	4	no	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	8	no	—
252	C₄⋊C₄	—	4	2	no	—
253	C₄⋊C₄	—	4	4	no	—
254	C₄⋊C₄	—	4	8	no	—
255	C₄⋊C₄	—	4	8	no	—
256	C₄⋊C₄	—	4	8	no	—
257	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	4	no	—
260	C₁₃	C₂×#2099	1	1	yes	characteristic, direct product factor, Sylow
261	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
262	C₂³	C₁₃×#123	1	2	yes	—
263	C₂³	C₁₃×#124	1	2	yes	—
264	C₂³	C₂×C₁₃×D₈	1	2	yes	—
265	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
266	C₂³	C₁₃×#137	1	2	yes	—
267	C₂³	C₁₃×#137	1	2	yes	—
268	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	2	8	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	4	8	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	8	4	no	—
286	C₂×C₄	—	8	8	no	—
287	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
288	C₂×C₄	C₁₃×#123	1	2	yes	—
289	C₂×C₄	C₁₃×#124	1	2	yes	—
290	C₂×C₄	C₁₃×#125	1	8	yes	—
291	C₂×C₄	C₁₃×#126	1	8	yes	—
292	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
293	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
294	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
295	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
296	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
297	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
298	C₈	—	4	4	no	—
299	C₂²	C₁₃×#400	1	4	yes	—
300	C₂²	C₁₃×#474	1	4	yes	—
301	C₂²	C₁₃×#475	1	4	yes	—
302	C₂²	C₁₃×#480	1	4	yes	—
303	C₂²	C₁₃×#483	1	4	yes	—
304	C₂²	C₁₃×#486	1	4	yes	—
305	C₂²	C₁₃×#491	1	4	yes	—
306	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
307	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
308	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
309	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
310	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
311	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
312	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
313	C₄	—	2	4	no	—
314	C₄	—	2	4	no	—
315	C₄	—	4	4	no	—
316	C₄	—	8	2	no	—
317	C₄	—	8	4	no	—
318	C₄	C₁₃×#400	1	4	yes	—
319	C₄	C₂×C₁₃×#125	1	2	yes	—
320	C₄	C₂×C₁₃×#126	1	2	yes	—
321	C₂	C₁₃×#2099	1	8	yes	direct product factor
322	C₂	C₂×C₁₃×#400	1	1	yes	characteristic
323	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
324	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
325	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
326	C₂	C₂×C₁₃×#483	1	1	yes	characteristic
327	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
328	C₂	C₂×C₁₃×#491	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2099	C₂	direct (N × H)
53. C₂×#2099	C₁₃	direct (N × H)
99. #2099	C₂×C₁₃	direct (N × H)
209. C₂×C₁₃	#2099	direct (N × H)
260. C₁₃	C₂×#2099	direct (N × H)
321. C₂	C₁₃×#2099	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×#389	2
C₂×C₁₃×#384	2
C₁₃×#2099	2
C₂×C₁₃×#340	2
C₂×C₁₃×#336	2
C₂×#2099	13

Subgroups — C2×C13×#2099 #15710080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2099 #15710080