Subgroups — C₂×C₁₃×#2020 #15709776

Order 3328.

1902 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal
2	C₂³×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#101	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2020	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
9	C₂×C₁₃×#137	—	2	4	no	—
10	C₂×C₁₃×#137	—	2	8	no	—
11	C₂×C₁₃×#137	—	2	8	no	—
12	C₂×C₁₃×#137	C₂²	1	8	yes	—
13	C₂²×C₁₃×Q₁₆	—	2	8	no	—
14	C₂²×C₁₃×Q₁₆	—	2	2	no	—
15	C₂²×C₁₃×Q₁₆	—	2	2	no	—
16	C₂²×C₁₃×Q₁₆	—	2	2	no	—
17	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×SD₁₆	—	2	2	no	—
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
21	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#101	—	2	8	no	—
23	C₂×C₁₃×#101	C₂²	1	8	yes	complemented
24	C₁₃×#408	—	2	2	no	—
25	C₁₃×#408	C₂²	1	4	yes	—
26	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
27	C₁₃×#341	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#41	—	2	1	no	—
29	C₂×C₁₃×#41	—	2	1	no	—
30	C₂×C₁₃×#41	—	2	4	no	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	D₄	1	2	yes	—
33	C₂×C₁₃×#41	C₂³	1	2	yes	—
34	C₂²×Q₈×C₁₃	—	2	4	no	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	—	2	4	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₃	—	2	4	no	—
42	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#137	—	2	32	no	—
51	C₁₃×#137	—	2	16	no	—
52	C₁₃×#137	—	2	16	no	—
53	C₂×C₁₃×Q₁₆	—	2	16	no	—
54	C₂×C₁₃×Q₁₆	—	2	16	no	—
55	C₂×C₁₃×Q₁₆	—	2	16	no	—
56	C₂×C₁₃×Q₁₆	—	2	16	no	—
57	C₂×C₁₃×Q₁₆	—	2	8	no	—
58	C₂×C₁₃×Q₁₆	—	2	8	no	—
59	C₂×C₁₃×SD₁₆	—	2	16	no	—
60	C₂×C₁₃×SD₁₆	—	2	8	no	—
61	C₂×C₁₃×M₁₆	—	2	4	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	4	no	—
65	C₂×C₁₃×M₁₆	D₄	1	8	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₃	—	2	4	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	1	no	—
71	C₂²×C₈×C₁₃	D₄	1	2	yes	—
72	C₂²×C₈×C₁₃	D₄	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×#101	—	2	16	no	—
75	C₁₃×C₂²⋊C₈	—	2	8	no	—
76	C₂×#2020	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	1	no	—
78	C₂⁴×C₁₃	#41	1	1	yes	characteristic
79	C₁₃×#41	—	2	8	no	—
80	C₁₃×#41	—	2	4	no	—
81	C₁₃×#41	—	2	4	no	—
82	C₁₃×#41	—	4	2	no	—
83	C₁₃×#41	—	4	4	no	—
84	C₁₃×#41	—	4	2	no	—
85	C₂×Q₈×C₁₃	—	2	8	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	8	no	—
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	2	8	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	8	no	—
93	C₂×Q₈×C₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	4	4	no	—
98	C₂×Q₈×C₁₃	—	4	4	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	—	4	4	no	—
102	C₂×Q₈×C₁₃	—	4	4	no	—
103	C₂×Q₈×C₁₃	—	4	4	no	—
104	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	4	4	no	—
111	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×Q₁₆	—	2	32	no	—
131	C₁₃×Q₁₆	—	2	32	no	—
132	C₁₃×SD₁₆	—	2	32	no	—
133	C₁₃×M₁₆	—	2	8	no	—
134	C₁₃×M₁₆	—	2	4	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	—	4	2	no	—
137	C₁₃×M₁₆	C₂×D₄	1	8	yes	—
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	4	2	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
146	C₂²×#137	C₂×C₁₃	1	2	yes	—
147	C₂³×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂²×#101	C₂×C₁₃	1	2	yes	complemented
149	C₂×#408	C₂×C₁₃	1	1	yes	characteristic
150	#2020	C₂×C₁₃	1	8	yes	direct product factor
151	C₂×#341	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	#121	1	4	yes	—
157	C₂³×C₁₃	#121	1	1	yes	characteristic
158	C₂³×C₁₃	#121	1	1	yes	characteristic
159	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	8	no	—
161	Q₈×C₁₃	—	2	8	no	—
162	Q₈×C₁₃	—	2	4	no	—
163	Q₈×C₁₃	—	4	4	no	—
164	Q₈×C₁₃	—	4	4	no	—
165	Q₈×C₁₃	—	4	8	no	—
166	Q₈×C₁₃	—	4	8	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	4	4	no	—
170	D₄×C₁₃	—	4	4	no	—
171	D₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	8	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	8	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	#120	1	2	yes	—
183	C₂×C₄×C₁₃	#120	1	4	yes	—
184	C₂×C₄×C₁₃	#120	1	2	yes	—
185	C₂×C₄×C₁₃	#120	1	4	yes	—
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#121	1	4	yes	—
189	C₂×C₄×C₁₃	#127	1	2	yes	—
190	C₂×C₄×C₁₃	#127	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
195	C₈×C₁₃	—	2	4	no	—
196	C₈×C₁₃	—	2	8	no	—
197	C₈×C₁₃	—	4	2	no	—
198	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
199	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
200	C₂×#137	—	2	4	no	—
201	C₂×#137	—	2	8	no	—
202	C₂×#137	—	2	8	no	—
203	C₂×#137	C₂²×C₁₃	1	8	yes	—
204	C₂²×Q₁₆	—	2	8	no	—
205	C₂²×Q₁₆	—	2	2	no	—
206	C₂²×Q₁₆	—	2	2	no	—
207	C₂²×Q₁₆	—	2	2	no	—
208	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
209	C₂²×SD₁₆	—	2	2	no	—
210	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
212	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#101	—	2	8	no	—
214	C₂×#101	C₂²×C₁₃	1	8	yes	complemented
215	#408	—	2	2	no	—
216	#408	C₂²×C₁₃	1	4	yes	—
217	C₂×C₂²⋊C₈	—	2	2	no	—
218	#341	C₂²×C₁₃	1	4	yes	complemented
219	C₂²×C₁₃	—	2	8	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	8	4	no	—
225	C₂²×C₁₃	#392	1	2	yes	—
226	C₂²×C₁₃	#392	1	2	yes	—
227	C₂²×C₁₃	#473	1	4	yes	—
228	C₂²×C₁₃	C₂×#121	1	2	yes	—
229	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	8	no	—
232	C₄×C₁₃	#392	1	2	yes	—
233	C₄×C₁₃	#392	1	2	yes	—
234	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₃	C₂×#120	1	2	yes	—
236	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
237	C₂×#41	—	2	1	no	—
238	C₂×#41	—	2	1	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	D₄×C₁₃	1	2	yes	—
242	C₂×#41	C₂³×C₁₃	1	2	yes	—
243	C₂²×Q₈	—	2	4	no	—
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	4	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
252	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
253	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	#137	—	2	32	no	—
260	#137	—	2	16	no	—
261	#137	—	2	16	no	—
262	C₂×Q₁₆	—	2	16	no	—
263	C₂×Q₁₆	—	2	16	no	—
264	C₂×Q₁₆	—	2	16	no	—
265	C₂×Q₁₆	—	2	16	no	—
266	C₂×Q₁₆	—	2	8	no	—
267	C₂×Q₁₆	—	2	8	no	—
268	C₂×SD₁₆	—	2	16	no	—
269	C₂×SD₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂×M₁₆	D₄×C₁₃	1	8	yes	—
275	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
276	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	D₄×C₁₃	1	2	yes	—
281	C₂²×C₈	D₄×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
283	#101	—	2	16	no	—
284	C₂²⋊C₈	—	2	8	no	—
285	C₂×C₁₃	—	2	2	no	—
286	C₂×C₁₃	—	2	2	no	—
287	C₂×C₁₃	—	8	2	no	—
288	C₂×C₁₃	#2020	1	4	yes	direct product factor
289	C₂×C₁₃	C₂×#392	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#473	1	2	yes	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	C₁₃×#41	1	1	yes	characteristic
293	#41	—	2	8	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	4	2	no	—
297	#41	—	4	4	no	—
298	#41	—	4	2	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	—	4	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
319	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
344	Q₁₆	—	2	32	no	—
345	Q₁₆	—	2	32	no	—
346	SD₁₆	—	2	32	no	—
347	M₁₆	—	2	8	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	C₂×D₄×C₁₃	1	8	yes	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
360	C₁₃	C₂×#2020	1	1	yes	characteristic, direct product factor, Sylow
361	C₂³	—	2	4	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	C₁₃×#121	1	4	yes	—
366	C₂³	C₁₃×#121	1	1	yes	characteristic
367	C₂³	C₁₃×#121	1	1	yes	characteristic
368	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
369	Q₈	—	2	8	no	—
370	Q₈	—	2	8	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	8	no	—
373	Q₈	—	4	8	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	4	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	C₁₃×#120	1	2	yes	—
392	C₂×C₄	C₁₃×#120	1	4	yes	—
393	C₂×C₄	C₁₃×#120	1	2	yes	—
394	C₂×C₄	C₁₃×#120	1	4	yes	—
395	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
396	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
397	C₂×C₄	C₁₃×#121	1	4	yes	—
398	C₂×C₄	C₁₃×#127	1	2	yes	—
399	C₂×C₄	C₁₃×#127	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	2	8	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	C₁₃×#392	1	2	yes	—
414	C₂²	C₁₃×#392	1	2	yes	—
415	C₂²	C₁₃×#473	1	4	yes	—
416	C₂²	C₂×C₁₃×#121	1	2	yes	—
417	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
418	C₄	—	4	2	no	—
419	C₄	—	4	8	no	—
420	C₄	C₁₃×#392	1	2	yes	—
421	C₄	C₁₃×#392	1	2	yes	—
422	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
423	C₄	C₂×C₁₃×#120	1	2	yes	—
424	C₄	C₂×C₁₃×#127	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	2	2	no	—
427	C₂	—	8	2	no	—
428	C₂	C₁₃×#2020	1	4	yes	direct product factor
429	C₂	C₂×C₁₃×#392	1	1	yes	characteristic
430	C₂	C₂×C₁₃×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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
2. C₂³×C₁₃×Q₁₆	C₂	semidirect
3. C₂²×C₁₃×#101	C₂	semidirect
5. C₁₃×#2020	C₂	direct (N × H)
6. C₂×C₁₃×#341	C₂	semidirect
17. C₂²×C₁₃×Q₁₆	C₂²	semidirect
23. C₂×C₁₃×#101	C₂²	semidirect
27. C₁₃×#341	C₂²	semidirect
76. C₂×#2020	C₁₃	direct (N × H)
147. C₂³×Q₁₆	C₂×C₁₃	semidirect
148. C₂²×#101	C₂×C₁₃	semidirect
150. #2020	C₂×C₁₃	direct (N × H)
151. C₂×#341	C₂×C₁₃	semidirect
208. C₂²×Q₁₆	C₂²×C₁₃	semidirect
214. C₂×#101	C₂²×C₁₃	semidirect
218. #341	C₂²×C₁₃	semidirect
288. C₂×C₁₃	#2020	direct (N × H)
360. C₁₃	C₂×#2020	direct (N × H)
428. C₂	C₁₃×#2020	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂³×C₁₃×Q₁₆	2
C₂²×C₁₃×#101	2
C₂×C₁₃×#408	2
C₁₃×#2020	2
C₂×C₁₃×#341	2
C₂×#2020	13

Subgroups — C2×C13×#2020 #15709776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2020 #15709776