Subgroups — C₁₃×#60817 #15747156

Order 3328.

2258 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3220	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3207	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3205	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3041	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3008	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#550	—	2	2	no	—
18	C₁₃×#550	—	2	2	no	—
19	C₁₃×#546	—	2	4	no	—
20	D₄²×C₁₃	—	2	2	no	—
21	D₄²×C₁₃	—	2	4	no	—
22	C₁₃×#540	C₂²	1	4	yes	complemented
23	C₁₃×#535	C₂²	1	2	yes	—
24	C₁₃×#535	C₂²	1	2	yes	—
25	C₁₃×#535	C₂²	1	4	yes	complemented
26	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	2	yes	complemented
29	C₁₃×#532	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
33	C₁₃×#518	C₂²	1	2	yes	complemented
34	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
35	C₁₃×#496	C₂²	1	4	yes	complemented
36	C₁₃×#493	C₂²	1	4	yes	complemented
37	C₁₃×#493	C₂²	1	4	yes	complemented
38	C₁₃×#493	C₂²	1	2	yes	complemented
39	C₁₃×#492	C₂²	1	2	yes	complemented
40	C₁₃×#490	C₂²	1	4	yes	complemented
41	C₁₃×#488	C₂²	1	4	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#486	C₂²	1	2	yes	complemented
44	C₁₃×#486	C₂²	1	4	yes	complemented
45	C₁₃×#463	C₂²	1	16	yes	complemented
46	C₁₃×#459	C₂²	1	16	yes	complemented
47	C₁₃×#449	C₂²	1	16	yes	complemented
48	C₁₃×#447	C₂²	1	16	yes	complemented
49	C₁₃×#433	C₂²	1	4	yes	complemented
50	C₁₃×#431	C₂²	1	4	yes	complemented
51	C₁₃×#424	C₂²	1	2	yes	complemented
52	C₁₃×#418	C₂²	1	4	yes	complemented
53	C₁₃×#416	C₂²	1	4	yes	complemented
54	C₁₃×#408	C₂²	1	2	yes	—
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×H(5,𝔽₂)	—	4	8	no	—
58	C₂×C₁₃×#41	—	2	2	no	—
59	C₂×C₁₃×#41	—	2	4	no	—
60	C₂×C₁₃×#41	C₂³	1	2	yes	—
61	C₂×C₁₃×#41	C₂³	1	4	yes	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	4	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×D₈	—	4	8	no	—
74	C₂×C₁₃×D₈	C₂³	1	8	yes	—
75	C₂×C₁₃×D₈	C₂³	1	16	yes	—
76	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₃×#127	—	2	2	no	—
81	C₁₃×#127	—	2	2	no	—
82	C₁₃×#127	—	2	4	no	—
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	C₂³	1	4	yes	—
85	C₁₃×#127	C₂³	1	2	yes	—
86	C₁₃×#127	C₂³	1	1	yes	characteristic
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#127	C₂³	1	2	yes	—
90	C₁₃×#125	C₂³	1	2	yes	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	4	no	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	2	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#121	—	2	8	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₁₃×#120	—	2	4	no	—
105	C₁₃×#120	—	2	4	no	—
106	C₁₃×#120	—	2	8	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	D₄	1	2	yes	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	D₄	1	4	yes	—
114	C₄×D₄×C₁₃	D₄	1	2	yes	—
115	C₄×D₄×C₁₃	C₂³	1	8	yes	—
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₁₃×#117	C₂³	1	1	yes	characteristic
118	C₁₃×#117	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	16	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	2	yes	—
128	C₄×C₈×C₁₃	C₂³	1	2	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	#60817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₂⁴×C₁₃	—	2	4	no	—
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₁₃×#41	—	2	4	no	—
136	C₁₃×#41	—	2	8	no	—
137	C₁₃×#41	—	4	8	no	—
138	C₁₃×#41	—	4	8	no	—
139	C₁₃×#41	—	8	8	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	8	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	16	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	8	4	no	—
161	C₂×D₄×C₁₃	—	8	4	no	—
162	C₂×D₄×C₁₃	—	8	8	no	—
163	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×SD₁₆	—	4	8	no	—
176	C₁₃×D₈	—	4	16	no	—
177	C₁₃×D₈	—	4	8	no	—
178	C₁₃×M₁₆	—	2	4	no	—
179	C₂×C₈×C₁₃	—	2	4	no	—
180	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
181	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	C₂×D₄	1	4	yes	—
197	C₄²×C₁₃	C₂×D₄	1	2	yes	—
198	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₄²×C₁₃	C₂⁴	1	2	yes	—
201	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#3220	C₂×C₁₃	1	8	yes	complemented
204	#3207	C₂×C₁₃	1	4	yes	complemented
205	#3205	C₂×C₁₃	1	4	yes	complemented
206	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#3041	C₂×C₁₃	1	4	yes	complemented
211	#3008	C₂×C₁₃	1	4	yes	complemented
212	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	4	8	no	—
217	C₂³×C₁₃	—	4	4	no	—
218	C₂³×C₁₃	—	4	4	no	—
219	C₂³×C₁₃	—	8	4	no	—
220	C₂³×C₁₃	—	8	4	no	—
221	C₂³×C₁₃	—	8	8	no	—
222	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	4	4	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	8	no	—
230	D₄×C₁₃	—	2	8	no	—
231	D₄×C₁₃	—	2	4	no	—
232	D₄×C₁₃	—	4	8	no	—
233	D₄×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	4	no	—
236	D₄×C₁₃	—	4	4	no	—
237	D₄×C₁₃	—	4	4	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	8	no	—
240	D₄×C₁₃	—	8	8	no	—
241	D₄×C₁₃	—	8	4	no	—
242	D₄×C₁₃	—	8	4	no	—
243	D₄×C₁₃	—	8	8	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	8	8	no	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
259	C₈×C₁₃	—	2	4	no	—
260	C₈×C₁₃	—	2	4	no	—
261	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
262	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
263	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
264	#559	—	2	2	no	—
265	#550	—	2	2	no	—
266	#550	—	2	2	no	—
267	#546	—	2	4	no	—
268	D₄²	—	2	2	no	—
269	D₄²	—	2	4	no	—
270	#540	C₂²×C₁₃	1	4	yes	complemented
271	#535	C₂²×C₁₃	1	2	yes	—
272	#535	C₂²×C₁₃	1	2	yes	—
273	#535	C₂²×C₁₃	1	4	yes	complemented
274	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	#532	C₂²×C₁₃	1	1	yes	characteristic
276	#532	C₂²×C₁₃	1	2	yes	complemented
277	#532	C₂²×C₁₃	1	4	yes	complemented
278	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
281	#518	C₂²×C₁₃	1	2	yes	complemented
282	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
283	#496	C₂²×C₁₃	1	4	yes	complemented
284	#493	C₂²×C₁₃	1	4	yes	complemented
285	#493	C₂²×C₁₃	1	4	yes	complemented
286	#493	C₂²×C₁₃	1	2	yes	complemented
287	#492	C₂²×C₁₃	1	2	yes	complemented
288	#490	C₂²×C₁₃	1	4	yes	complemented
289	#488	C₂²×C₁₃	1	4	yes	complemented
290	#487	C₂²×C₁₃	1	2	yes	complemented
291	#486	C₂²×C₁₃	1	2	yes	complemented
292	#486	C₂²×C₁₃	1	4	yes	complemented
293	#463	C₂²×C₁₃	1	16	yes	complemented
294	#459	C₂²×C₁₃	1	16	yes	complemented
295	#449	C₂²×C₁₃	1	16	yes	complemented
296	#447	C₂²×C₁₃	1	16	yes	complemented
297	#433	C₂²×C₁₃	1	4	yes	complemented
298	#431	C₂²×C₁₃	1	4	yes	complemented
299	#424	C₂²×C₁₃	1	2	yes	complemented
300	#418	C₂²×C₁₃	1	4	yes	complemented
301	#416	C₂²×C₁₃	1	4	yes	complemented
302	#408	C₂²×C₁₃	1	2	yes	—
303	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	8	no	—
312	C₂²×C₁₃	—	4	8	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	16	4	no	—
315	C₂²×C₁₃	—	16	4	no	—
316	C₂²×C₁₃	—	16	8	no	—
317	C₂²×C₁₃	#535	1	2	yes	—
318	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	#535	1	2	yes	—
325	C₄×C₁₃	#576	1	4	yes	—
326	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
327	H(5,𝔽₂)	—	4	8	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	C₂³×C₁₃	1	2	yes	—
331	C₂×#41	C₂³×C₁₃	1	4	yes	—
332	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×D₄	—	2	4	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	—	2	4	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
339	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
341	AGL(1,ℤ/8)	—	4	8	no	—
342	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
343	C₂×D₈	—	4	8	no	—
344	C₂×D₈	C₂³×C₁₃	1	16	yes	—
345	C₂×D₈	C₂³×C₁₃	1	8	yes	—
346	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
348	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
350	#127	—	2	2	no	—
351	#127	—	2	2	no	—
352	#127	—	2	4	no	—
353	#127	—	2	2	no	—
354	#127	C₂³×C₁₃	1	2	yes	—
355	#127	C₂³×C₁₃	1	2	yes	—
356	#127	C₂³×C₁₃	1	1	yes	characteristic
357	#127	C₂³×C₁₃	1	2	yes	—
358	#127	C₂³×C₁₃	1	4	yes	—
359	#127	C₂³×C₁₃	1	2	yes	—
360	#125	C₂³×C₁₃	1	2	yes	—
361	#124	—	2	2	no	—
362	#124	—	2	4	no	—
363	#124	C₂³×C₁₃	1	2	yes	—
364	#124	C₂³×C₁₃	1	4	yes	—
365	#123	—	2	8	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	4	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	8	no	—
372	#121	—	2	8	no	—
373	#121	C₂³×C₁₃	1	8	yes	—
374	#120	—	2	4	no	—
375	#120	—	2	4	no	—
376	#120	—	2	8	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	D₄×C₁₃	1	2	yes	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	D₄×C₁₃	1	4	yes	—
384	C₄×D₄	D₄×C₁₃	1	2	yes	—
385	C₄×D₄	C₂³×C₁₃	1	8	yes	—
386	#117	C₂³×C₁₃	1	2	yes	—
387	#117	C₂³×C₁₃	1	1	yes	characteristic
388	#117	C₂³×C₁₃	1	2	yes	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
392	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
393	#103	C₂³×C₁₃	1	8	yes	—
394	#102	C₂³×C₁₃	1	8	yes	—
395	#102	C₂³×C₁₃	1	16	yes	—
396	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
397	#97	C₂³×C₁₃	1	2	yes	—
398	C₄×C₈	C₂³×C₁₃	1	2	yes	—
399	C₄×C₈	C₂³×C₁₃	1	2	yes	—
400	C₄×C₈	C₂³×C₁₃	1	2	yes	—
401	C₂×C₁₃	—	2	2	no	—
402	C₂×C₁₃	—	4	2	no	—
403	C₂×C₁₃	—	8	4	no	—
404	C₂×C₁₃	—	8	4	no	—
405	C₂×C₁₃	—	8	2	no	—
406	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
407	C₂×C₁₃	C₂×#576	1	2	yes	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	2	no	—
411	#41	—	2	4	no	—
412	#41	—	2	8	no	—
413	#41	—	4	8	no	—
414	#41	—	4	8	no	—
415	#41	—	8	8	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	—	4	16	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	8	4	no	—
437	C₂×D₄	—	8	4	no	—
438	C₂×D₄	—	8	8	no	—
439	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
451	SD₁₆	—	4	8	no	—
452	D₈	—	4	16	no	—
453	D₈	—	4	8	no	—
454	M₁₆	—	2	4	no	—
455	C₂×C₈	—	2	4	no	—
456	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
457	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
463	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
470	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
471	C₄²	—	2	2	no	—
472	C₄²	C₂×D₄×C₁₃	1	4	yes	—
473	C₄²	C₂×D₄×C₁₃	1	2	yes	—
474	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
476	C₄²	C₂⁴×C₁₃	1	2	yes	—
477	C₁₃	#60817	1	1	yes	characteristic, direct product factor, Sylow
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	8	no	—
487	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	2	2	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	4	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	8	no	—
495	D₄	—	2	8	no	—
496	D₄	—	2	4	no	—
497	D₄	—	4	8	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	4	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	8	no	—
505	D₄	—	8	8	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	8	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	8	8	no	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
522	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
523	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
524	C₈	—	2	4	no	—
525	C₈	—	2	4	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	8	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	16	4	no	—
536	C₂²	—	16	4	no	—
537	C₂²	—	16	8	no	—
538	C₂²	C₁₃×#535	1	2	yes	—
539	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
540	C₄	—	2	4	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	C₁₃×#535	1	2	yes	—
546	C₄	C₁₃×#576	1	4	yes	—
547	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
548	C₂	—	2	2	no	—
549	C₂	—	4	2	no	—
550	C₂	—	8	4	no	—
551	C₂	—	8	2	no	—
552	C₂	—	8	4	no	—
553	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
554	C₂	C₂×C₁₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3220	C₂	semidirect
4. C₁₃×#3207	C₂	semidirect
5. C₁₃×#3205	C₂	semidirect
6. C₁₃×#3151	C₂	semidirect
7. C₂×C₁₃×#493	C₂	semidirect
8. C₁₃×#3138	C₂	semidirect
9. C₁₃×#3131	C₂	semidirect
10. C₁₃×#3041	C₂	semidirect
11. C₁₃×#3008	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
22. C₁₃×#540	C₂²	semidirect
25. C₁₃×#535	C₂²	semidirect
26. C₁₃×#533	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
31. C₂×C₁₃×#127	C₂²	semidirect
32. C₂×C₁₃×#127	C₂²	semidirect
33. C₁₃×#518	C₂²	semidirect
35. C₁₃×#496	C₂²	semidirect
36. C₁₃×#493	C₂²	semidirect
37. C₁₃×#493	C₂²	semidirect
38. C₁₃×#493	C₂²	semidirect
39. C₁₃×#492	C₂²	semidirect
40. C₁₃×#490	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#486	C₂²	semidirect
44. C₁₃×#486	C₂²	semidirect
45. C₁₃×#463	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
47. C₁₃×#449	C₂²	semidirect
48. C₁₃×#447	C₂²	semidirect
49. C₁₃×#433	C₂²	semidirect
50. C₁₃×#431	C₂²	semidirect
51. C₁₃×#424	C₂²	semidirect
52. C₁₃×#418	C₂²	semidirect
53. C₁₃×#416	C₂²	semidirect
55. C₄×C₁₃×M₁₆	C₂²	semidirect
56. C₂×C₄×C₈×C₁₃	C₂²	semidirect
131. #60817	C₁₃	direct (N × H)
201. #3508	C₂×C₁₃	semidirect
202. #3498	C₂×C₁₃	semidirect
203. #3220	C₂×C₁₃	semidirect
204. #3207	C₂×C₁₃	semidirect
205. #3205	C₂×C₁₃	semidirect
206. #3151	C₂×C₁₃	semidirect
207. C₂×#493	C₂×C₁₃	semidirect
208. #3138	C₂×C₁₃	semidirect
209. #3131	C₂×C₁₃	semidirect
210. #3041	C₂×C₁₃	semidirect
211. #3008	C₂×C₁₃	semidirect
212. #2922	C₂×C₁₃	semidirect
262. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
263. C₂²×D₈	C₂²×C₁₃	semidirect
270. #540	C₂²×C₁₃	semidirect
273. #535	C₂²×C₁₃	semidirect
274. #533	C₂²×C₁₃	semidirect
276. #532	C₂²×C₁₃	semidirect
277. #532	C₂²×C₁₃	semidirect
279. C₂×#127	C₂²×C₁₃	semidirect
280. C₂×#127	C₂²×C₁₃	semidirect
281. #518	C₂²×C₁₃	semidirect
283. #496	C₂²×C₁₃	semidirect
284. #493	C₂²×C₁₃	semidirect
285. #493	C₂²×C₁₃	semidirect
286. #493	C₂²×C₁₃	semidirect
287. #492	C₂²×C₁₃	semidirect
288. #490	C₂²×C₁₃	semidirect
289. #488	C₂²×C₁₃	semidirect
290. #487	C₂²×C₁₃	semidirect
291. #486	C₂²×C₁₃	semidirect
292. #486	C₂²×C₁₃	semidirect
293. #463	C₂²×C₁₃	semidirect
294. #459	C₂²×C₁₃	semidirect
295. #449	C₂²×C₁₃	semidirect
296. #447	C₂²×C₁₃	semidirect
297. #433	C₂²×C₁₃	semidirect
298. #431	C₂²×C₁₃	semidirect
299. #424	C₂²×C₁₃	semidirect
300. #418	C₂²×C₁₃	semidirect
301. #416	C₂²×C₁₃	semidirect
303. C₄×M₁₆	C₂²×C₁₃	semidirect
304. C₂×C₄×C₈	C₂²×C₁₃	semidirect
477. C₁₃	#60817	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×#3508	2
C₁₃×#3498	2
C₁₃×#3220	2
C₁₃×#3207	2
C₁₃×#3205	2
C₁₃×#3151	2
C₂×C₁₃×#493	2
C₁₃×#3138	2
C₁₃×#3131	2
C₁₃×#3041	2
C₁₃×#3008	2
C₁₃×#2922	2
#60817	13

Subgroups — C13×#60817 #15747156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60817 #15747156