Subgroups — C₁₃×#21782 #15708121

Order 3328.

1382 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2883	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1911	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1910	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1887	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1884	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1827	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1795	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
12	C₁₃×#568	C₂²	1	2	yes	complemented
13	C₁₃×#550	—	2	2	no	—
14	D₄²×C₁₃	—	2	4	no	—
15	D₄²×C₁₃	—	2	2	no	—
16	C₁₃×#535	C₄	1	2	yes	complemented
17	C₁₃×#535	C₄	1	2	yes	complemented
18	C₁₃×#535	C₂²	1	1	yes	characteristic
19	C₁₃×#535	C₂²	1	1	yes	characteristic
20	C₁₃×#532	C₄	1	2	yes	complemented
21	C₁₃×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#127	C₄	1	2	yes	complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₁₃×#518	C₂²	1	2	yes	complemented
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#421	C₂²	1	4	yes	complemented
27	C₁₃×#418	C₂²	1	4	yes	complemented
28	C₁₃×#413	—	2	2	no	—
29	C₁₃×#413	C₂²	1	2	yes	—
30	C₂×C₁₃×#100	—	2	2	no	—
31	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
32	C₁₃×#410	C₂²	1	2	yes	—
33	C₁₃×#410	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#99	—	2	4	no	—
35	C₁₃×#339	C₂²	1	4	yes	complemented
36	C₁₃×H(3,ℤ/4)	C₂²	1	4	yes	complemented
37	C₁₃×H(5,𝔽₂)	—	4	4	no	—
38	C₁₃×H(5,𝔽₂)	—	4	4	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
42	C₂×C₁₃×#41	D₄	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
52	C₂²×D₄×C₁₃	D₄	1	4	yes	—
53	C₂²×D₄×C₁₃	D₄	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#131	—	4	4	no	—
57	C₂×C₁₃×M₁₆	—	2	4	no	—
58	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₁₃×#127	—	2	4	no	—
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#127	C₂×C₄	1	2	yes	—
63	C₁₃×#127	C₂×C₄	1	2	yes	—
64	C₁₃×#127	C₂×C₄	1	2	yes	—
65	C₁₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
66	C₁₃×#127	C₂×C₄	1	2	yes	complemented
67	C₁₃×#124	C₂×C₄	1	2	yes	—
68	C₁₃×#124	C₂×C₄	1	2	yes	complemented
69	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
70	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	4	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#120	—	2	4	no	—
78	C₁₃×#120	—	2	2	no	—
79	C₁₃×#120	—	2	4	no	—
80	C₁₃×#120	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	1	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	4	4	no	—
87	C₁₃×#117	C₂×C₄	1	2	yes	complemented
88	C₁₃×#117	C₂³	1	4	yes	—
89	C₁₃×#117	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	complemented
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#104	—	4	4	no	—
94	C₁₃×#102	—	4	4	no	—
95	C₁₃×#101	—	2	2	no	—
96	C₁₃×#100	—	2	2	no	—
97	C₁₃×#100	—	2	4	no	—
98	C₁₃×#99	—	2	4	no	—
99	C₁₃×#99	—	2	4	no	—
100	#21782	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	C₂²⋊C₄	1	4	yes	—
104	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	2	4	no	—
107	C₁₃×#41	—	2	4	no	—
108	C₁₃×#41	—	4	4	no	—
109	C₁₃×#41	—	4	4	no	—
110	C₁₃×#41	—	4	4	no	—
111	C₁₃×#41	—	4	4	no	—
112	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	4	8	no	—
130	C₂×D₄×C₁₃	—	4	8	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	8	4	no	—
133	C₂×D₄×C₁₃	—	8	8	no	—
134	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
135	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
136	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₁₃×M₁₆	—	2	4	no	—
154	C₁₃×M₁₆	—	2	4	no	—
155	C₁₃×M₁₆	—	4	4	no	—
156	C₂×C₈×C₁₃	—	2	4	no	—
157	C₂×C₈×C₁₃	—	4	4	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₁₃×C₂²⋊C₄	—	2	4	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	4	no	—
173	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
175	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	#3498	C₂×C₁₃	1	1	yes	characteristic
177	#2888	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2883	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1911	C₂×C₁₃	1	2	yes	complemented
180	#1910	C₂×C₁₃	1	2	yes	complemented
181	#1887	C₂×C₁₃	1	2	yes	complemented
182	#1884	C₂×C₁₃	1	2	yes	complemented
183	#1827	C₂×C₁₃	1	2	yes	complemented
184	#1795	C₂×C₁₃	1	2	yes	complemented
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	4	4	no	—
189	C₂³×C₁₃	—	4	4	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	8	2	no	—
192	C₂³×C₁₃	—	8	2	no	—
193	C₂³×C₁₃	—	8	4	no	—
194	C₂³×C₁₃	—	8	4	no	—
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	2	2	no	—
202	D₄×C₁₃	—	2	4	no	—
203	D₄×C₁₃	—	2	4	no	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	4	4	no	—
211	D₄×C₁₃	—	4	4	no	—
212	D₄×C₁₃	—	4	4	no	—
213	D₄×C₁₃	—	4	8	no	—
214	D₄×C₁₃	—	4	4	no	—
215	D₄×C₁₃	—	4	4	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	8	4	no	—
220	D₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	16	4	no	—
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
239	C₈×C₁₃	—	4	4	no	—
240	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
242	#568	C₂²×C₁₃	1	2	yes	complemented
243	#550	—	2	2	no	—
244	D₄²	—	2	4	no	—
245	D₄²	—	2	2	no	—
246	#535	C₄×C₁₃	1	2	yes	complemented
247	#535	C₄×C₁₃	1	2	yes	complemented
248	#535	C₂²×C₁₃	1	1	yes	characteristic
249	#535	C₂²×C₁₃	1	1	yes	characteristic
250	#532	C₄×C₁₃	1	2	yes	complemented
251	#532	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#127	C₄×C₁₃	1	2	yes	complemented
253	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
254	#518	C₂²×C₁₃	1	2	yes	complemented
255	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
256	#421	C₂²×C₁₃	1	4	yes	complemented
257	#418	C₂²×C₁₃	1	4	yes	complemented
258	#413	—	2	2	no	—
259	#413	C₂²×C₁₃	1	2	yes	—
260	C₂×#100	—	2	2	no	—
261	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
262	#410	C₂²×C₁₃	1	2	yes	—
263	#410	C₂²×C₁₃	1	2	yes	complemented
264	C₂×#99	—	2	4	no	—
265	#339	C₂²×C₁₃	1	4	yes	complemented
266	H(3,ℤ/4)	C₂²×C₁₃	1	4	yes	complemented
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	4	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	8	4	no	—
279	C₂²×C₁₃	—	16	2	no	—
280	C₂²×C₁₃	—	16	4	no	—
281	C₂²×C₁₃	—	16	4	no	—
282	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₁₃	#534	1	2	yes	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	8	4	no	—
291	C₄×C₁₃	#518	1	2	yes	—
292	C₄×C₁₃	#534	1	2	yes	—
293	H(5,𝔽₂)	—	4	4	no	—
294	H(5,𝔽₂)	—	4	4	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
297	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
298	C₂×#41	D₄×C₁₃	1	2	yes	—
299	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
307	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
308	C₂²×D₄	D₄×C₁₃	1	4	yes	—
309	C₂²×D₄	D₄×C₁₃	1	2	yes	—
310	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
312	#131	—	4	4	no	—
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
315	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
316	#127	—	2	4	no	—
317	#127	—	2	2	no	—
318	#127	C₂×C₄×C₁₃	1	2	yes	—
319	#127	C₂×C₄×C₁₃	1	2	yes	—
320	#127	C₂×C₄×C₁₃	1	2	yes	—
321	#127	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
322	#127	C₂×C₄×C₁₃	1	2	yes	complemented
323	#124	C₂×C₄×C₁₃	1	2	yes	—
324	#124	C₂×C₄×C₁₃	1	2	yes	complemented
325	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
326	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	2	2	no	—
330	#121	—	2	2	no	—
331	#121	—	2	4	no	—
332	#121	—	2	2	no	—
333	#120	—	2	4	no	—
334	#120	—	2	2	no	—
335	#120	—	2	4	no	—
336	#120	—	2	2	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	4	4	no	—
343	#117	C₂×C₄×C₁₃	1	2	yes	complemented
344	#117	C₂³×C₁₃	1	4	yes	—
345	#117	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	complemented
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	#104	—	4	4	no	—
350	#102	—	4	4	no	—
351	#101	—	2	2	no	—
352	#100	—	2	2	no	—
353	#100	—	2	4	no	—
354	#99	—	2	4	no	—
355	#99	—	2	4	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	—	2	2	no	—
358	C₂×C₁₃	—	4	4	no	—
359	C₂×C₁₃	—	4	2	no	—
360	C₂×C₁₃	—	4	2	no	—
361	C₂×C₁₃	—	8	2	no	—
362	C₂×C₁₃	—	8	1	no	—
363	C₂×C₁₃	#2308	1	1	yes	characteristic
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	1	no	—
366	C₂⁴	C₁₃×C₂²⋊C₄	1	4	yes	—
367	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
368	#41	—	2	4	no	—
369	#41	—	2	4	no	—
370	#41	—	2	4	no	—
371	#41	—	4	4	no	—
372	#41	—	4	4	no	—
373	#41	—	4	4	no	—
374	#41	—	4	4	no	—
375	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
376	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
377	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	8	4	no	—
396	C₂×D₄	—	8	8	no	—
397	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
398	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
399	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
400	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
401	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
402	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
403	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
413	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
416	M₁₆	—	2	4	no	—
417	M₁₆	—	2	4	no	—
418	M₁₆	—	4	4	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	4	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	4	no	—
436	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
438	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
439	C₁₃	#21782	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	8	2	no	—
447	C₂³	—	8	4	no	—
448	C₂³	—	8	2	no	—
449	C₂³	—	8	4	no	—
450	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
451	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
452	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
453	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	4	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	4	no	—
474	D₄	—	8	4	no	—
475	D₄	—	8	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	16	4	no	—
489	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
490	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
491	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
494	C₈	—	4	4	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	16	2	no	—
508	C₂²	—	16	4	no	—
509	C₂²	—	16	4	no	—
510	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
511	C₂²	C₁₃×#534	1	2	yes	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	8	4	no	—
519	C₄	C₁₃×#518	1	2	yes	—
520	C₄	C₁₃×#534	1	2	yes	—
521	C₂	—	2	1	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	4	no	—
524	C₂	—	4	2	no	—
525	C₂	—	4	2	no	—
526	C₂	—	8	2	no	—
527	C₂	—	8	1	no	—
528	C₂	C₁₃×#2308	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2308
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2888	C₂	semidirect
3. C₁₃×#2883	C₂	semidirect
4. C₁₃×#1911	C₂	semidirect
5. C₁₃×#1910	C₂	semidirect
6. C₁₃×#1887	C₂	semidirect
7. C₁₃×#1884	C₂	semidirect
8. C₁₃×#1827	C₂	semidirect
9. C₁₃×#1795	C₂	semidirect
12. C₁₃×#568	C₂²	semidirect
16. C₁₃×#535	C₄	semidirect
17. C₁₃×#535	C₄	semidirect
20. C₁₃×#532	C₄	semidirect
22. C₂×C₁₃×#127	C₄	semidirect
24. C₁₃×#518	C₂²	semidirect
26. C₁₃×#421	C₂²	semidirect
27. C₁₃×#418	C₂²	semidirect
31. C₂×C₁₃×#100	C₂²	semidirect
33. C₁₃×#410	C₂²	semidirect
35. C₁₃×#339	C₂²	semidirect
36. C₁₃×H(3,ℤ/4)	C₂²	semidirect
41. C₂×C₁₃×#41	C₂×C₄	semidirect
51. C₂²×D₄×C₁₃	C₂×C₄	semidirect
59. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
65. C₁₃×#127	C₂×C₄	semidirect
66. C₁₃×#127	C₂×C₄	semidirect
68. C₁₃×#124	C₂×C₄	semidirect
69. C₁₃×#124	C₂×C₄	semidirect
70. C₁₃×#124	C₂×C₄	semidirect
87. C₁₃×#117	C₂×C₄	semidirect
91. C₂×C₄²×C₁₃	C₂×C₄	semidirect
100. #21782	C₁₃	direct (N × H)
177. #2888	C₂×C₁₃	semidirect
178. #2883	C₂×C₁₃	semidirect
179. #1911	C₂×C₁₃	semidirect
180. #1910	C₂×C₁₃	semidirect
181. #1887	C₂×C₁₃	semidirect
182. #1884	C₂×C₁₃	semidirect
183. #1827	C₂×C₁₃	semidirect
184. #1795	C₂×C₁₃	semidirect
242. #568	C₂²×C₁₃	semidirect
246. #535	C₄×C₁₃	semidirect
247. #535	C₄×C₁₃	semidirect
250. #532	C₄×C₁₃	semidirect
252. C₂×#127	C₄×C₁₃	semidirect
254. #518	C₂²×C₁₃	semidirect
256. #421	C₂²×C₁₃	semidirect
257. #418	C₂²×C₁₃	semidirect
261. C₂×#100	C₂²×C₁₃	semidirect
263. #410	C₂²×C₁₃	semidirect
265. #339	C₂²×C₁₃	semidirect
266. H(3,ℤ/4)	C₂²×C₁₃	semidirect
297. C₂×#41	C₂×C₄×C₁₃	semidirect
307. C₂²×D₄	C₂×C₄×C₁₃	semidirect
315. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
321. #127	C₂×C₄×C₁₃	semidirect
322. #127	C₂×C₄×C₁₃	semidirect
324. #124	C₂×C₄×C₁₃	semidirect
325. #124	C₂×C₄×C₁₃	semidirect
326. #124	C₂×C₄×C₁₃	semidirect
343. #117	C₂×C₄×C₁₃	semidirect
347. C₂×C₄²	C₂×C₄×C₁₃	semidirect
439. C₁₃	#21782	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3498	2
C₁₃×#2888	2
C₁₃×#2883	2
C₁₃×#1911	2
C₁₃×#1910	2
C₁₃×#1887	2
C₁₃×#1884	2
C₁₃×#1827	2
C₁₃×#1795	2
#21782	13

Subgroups — C13×#21782 #15708121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21782 #15708121