Subgroups — C₁₃×#60625 #15746964

Order 3328.

2066 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3141	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3140	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3137	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3136	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3135	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#489	C₂	1	3	yes	maximal, complemented
9	C₁₃×#2898	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2897	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	Q₈²×C₁₃	—	2	1	no	—
16	C₁₃×#557	—	2	1	no	—
17	C₁₃×#554	—	2	3	no	—
18	D₄×Q₈×C₁₃	—	2	3	no	—
19	C₁₃×#548	—	2	1	no	—
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#546	—	2	3	no	—
22	C₁₃×#546	—	2	3	no	—
23	C₁₃×#544	C₂²	1	6	yes	complemented
24	C₁₃×#536	C₂²	1	3	yes	—
25	C₁₃×#535	C₂²	1	3	yes	—
26	C₁₃×#533	C₂²	1	3	yes	complemented
27	C₁₃×#532	C₂²	1	3	yes	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	3	yes	—
30	C₁₃×#520	C₂²	1	2	yes	—
31	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
32	C₁₃×#491	C₂²	1	6	yes	complemented
33	C₁₃×#490	C₂²	1	6	yes	complemented
34	C₁₃×#489	C₂²	1	3	yes	complemented
35	C₁₃×#489	C₂²	1	12	yes	complemented
36	C₁₃×#489	C₂²	1	6	yes	complemented
37	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#489	C₂²	1	3	yes	complemented
39	C₁₃×#489	C₂²	1	3	yes	complemented
40	C₁₃×#488	C₂²	1	12	yes	complemented
41	C₁₃×#487	C₂²	1	6	yes	complemented
42	C₁₃×#486	C₂²	1	6	yes	complemented
43	C₁₃×#419	C₂²	1	6	yes	complemented
44	C₁₃×#418	C₂²	1	6	yes	—
45	C₁₃×#417	C₂²	1	6	yes	—
46	C₁₃×#417	C₂²	1	6	yes	complemented
47	C₁₃×#416	C₂²	1	6	yes	—
48	C₁₃×#416	C₂²	1	6	yes	complemented
49	C₂×C₁₃×#103	C₂²	1	6	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	6	yes	—
51	C₁₃×#405	C₂²	1	6	yes	complemented
52	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
53	C₂×C₁₃×#97	C₂²	1	3	yes	complemented
54	C₁₃×2₋¹⁺⁴	—	2	8	no	—
55	C₁₃×H(5,𝔽₂)	—	2	8	no	—
56	C₂×C₁₃×#41	—	2	1	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	C₂³	1	3	yes	—
59	C₂×C₁₃×#41	C₂³	1	3	yes	—
60	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	—	2	3	no	—
63	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
64	C₂²×D₄×C₁₃	—	2	3	no	—
65	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
66	C₁₃×#131	—	2	8	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
69	C₁₃×C₄⋊Q₈	—	2	6	no	—
70	C₁₃×C₄⋊Q₈	—	2	3	no	—
71	C₁₃×C₄⋊Q₈	—	2	3	no	—
72	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₃×#127	C₂³	1	3	yes	—
77	C₁₃×#125	—	2	6	no	—
78	C₁₃×#125	C₂³	1	6	yes	—
79	C₁₃×#124	—	2	3	no	—
80	C₁₃×#124	—	2	3	no	—
81	C₁₃×#124	C₂³	1	6	yes	—
82	C₁₃×#124	C₂³	1	3	yes	—
83	C₁₃×#124	C₂³	1	1	yes	characteristic
84	C₁₃×#123	—	2	6	no	—
85	C₁₃×C₂²⋊Q₈	—	2	3	no	—
86	C₁₃×C₂²⋊Q₈	—	2	3	no	—
87	C₁₃×C₂²⋊Q₈	—	2	3	no	—
88	C₁₃×C₂²⋊Q₈	—	2	3	no	—
89	C₁₃×C₂²⋊Q₈	—	2	12	no	—
90	C₁₃×#121	—	2	3	no	—
91	C₁₃×#121	—	2	3	no	—
92	C₁₃×#121	—	2	3	no	—
93	C₁₃×#121	—	2	3	no	—
94	C₁₃×#120	—	2	6	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	3	no	—
97	C₄×Q₈×C₁₃	—	2	3	no	—
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	6	no	—
101	C₄×D₄×C₁₃	—	2	3	no	—
102	C₄×D₄×C₁₃	—	2	3	no	—
103	C₄×D₄×C₁₃	D₄	1	3	yes	—
104	C₄×D₄×C₁₃	D₄	1	3	yes	—
105	C₁₃×#117	C₂³	1	6	yes	—
106	C₁₃×#117	C₂³	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
111	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
112	C₁₃×#103	C₂³	1	6	yes	—
113	C₁₃×#103	C₂³	1	12	yes	—
114	C₁₃×#103	C₂³	1	2	yes	—
115	C₁₃×#103	C₂³	1	6	yes	—
116	C₁₃×#103	C₂³	1	6	yes	—
117	C₁₃×#102	C₂³	1	6	yes	—
118	C₁₃×#102	C₂³	1	12	yes	—
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	2	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×#97	C₂³	1	1	yes	characteristic
123	C₁₃×#97	C₂³	1	3	yes	—
124	C₁₃×#97	C₂³	1	6	yes	—
125	C₄×C₈×C₁₃	C₂³	1	6	yes	—
126	#60625	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	3	no	—
128	C₁₃×#41	—	2	12	no	—
129	C₁₃×#41	—	2	12	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	12	no	—
132	C₁₃×#41	#41	1	8	yes	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	3	no	—
135	C₂×Q₈×C₁₃	—	2	3	no	—
136	C₂×Q₈×C₁₃	—	2	6	no	—
137	C₂×Q₈×C₁₃	—	2	12	no	—
138	C₂×Q₈×C₁₃	—	4	4	no	—
139	C₂×Q₈×C₁₃	—	8	6	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
142	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂×D₄×C₁₃	—	2	3	no	—
144	C₂×D₄×C₁₃	—	2	3	no	—
145	C₂×D₄×C₁₃	—	2	3	no	—
146	C₂×D₄×C₁₃	—	2	3	no	—
147	C₂×D₄×C₁₃	—	2	3	no	—
148	C₂×D₄×C₁₃	—	2	12	no	—
149	C₂×D₄×C₁₃	—	4	12	no	—
150	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	2	3	no	—
154	C₂²×C₄×C₁₃	—	2	6	no	—
155	C₂²×C₄×C₁₃	—	2	3	no	—
156	C₂²×C₄×C₁₃	—	2	3	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
160	C₁₃×M₁₆	—	2	12	no	—
161	C₂×C₈×C₁₃	—	2	12	no	—
162	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
163	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	6	no	—
166	C₁₃×C₄⋊C₄	—	2	6	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	—	2	3	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	6	no	—
171	C₁₃×C₄⋊C₄	—	2	6	no	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
174	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
175	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	3	no	—
178	C₁₃×C₂²⋊C₄	—	2	3	no	—
179	C₁₃×C₂²⋊C₄	—	2	6	no	—
180	C₁₃×C₂²⋊C₄	—	2	6	no	—
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
184	C₄²×C₁₃	—	2	6	no	—
185	C₄²×C₁₃	C₂×D₄	1	3	yes	—
186	C₄²×C₁₃	C₂×D₄	1	3	yes	—
187	C₄²×C₁₃	C₂⁴	1	3	yes	—
188	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
189	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#3500	C₂×C₁₃	1	1	yes	characteristic
191	#3141	C₂×C₁₃	1	3	yes	complemented
192	#3140	C₂×C₁₃	1	3	yes	complemented
193	#3137	C₂×C₁₃	1	6	yes	complemented
194	#3136	C₂×C₁₃	1	6	yes	complemented
195	#3135	C₂×C₁₃	1	3	yes	complemented
196	C₂×#489	C₂×C₁₃	1	3	yes	complemented
197	#2898	C₂×C₁₃	1	2	yes	complemented
198	#2897	C₂×C₁₃	1	2	yes	complemented
199	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂³×C₁₃	—	2	3	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	4	6	no	—
203	C₂³×C₁₃	—	8	3	no	—
204	C₂³×C₁₃	—	8	3	no	—
205	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
206	Q₈×C₁₃	—	2	6	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	—	4	2	no	—
209	Q₈×C₁₃	—	4	6	no	—
210	Q₈×C₁₃	—	4	6	no	—
211	Q₈×C₁₃	—	8	6	no	—
212	Q₈×C₁₃	#124	1	4	yes	—
213	D₄×C₁₃	—	2	6	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	4	6	no	—
216	D₄×C₁₃	—	4	6	no	—
217	D₄×C₁₃	—	4	6	no	—
218	D₄×C₁₃	—	8	3	no	—
219	D₄×C₁₃	—	8	3	no	—
220	D₄×C₁₃	#124	1	12	yes	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	6	no	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	4	3	no	—
226	C₂×C₄×C₁₃	—	4	3	no	—
227	C₂×C₄×C₁₃	—	4	6	no	—
228	C₂×C₄×C₁₃	—	4	6	no	—
229	C₂×C₄×C₁₃	—	4	6	no	—
230	C₂×C₄×C₁₃	—	8	6	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
236	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	2	6	no	—
240	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#131	C₂²×C₁₃	1	2	yes	—
243	Q₈²	—	2	1	no	—
244	#557	—	2	1	no	—
245	#554	—	2	3	no	—
246	D₄×Q₈	—	2	3	no	—
247	#548	—	2	1	no	—
248	#548	—	2	1	no	—
249	#546	—	2	3	no	—
250	#546	—	2	3	no	—
251	#544	C₂²×C₁₃	1	6	yes	complemented
252	#536	C₂²×C₁₃	1	3	yes	—
253	#535	C₂²×C₁₃	1	3	yes	—
254	#533	C₂²×C₁₃	1	3	yes	complemented
255	#532	C₂²×C₁₃	1	3	yes	—
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
257	C₂×#124	C₂²×C₁₃	1	3	yes	—
258	#520	C₂²×C₁₃	1	2	yes	—
259	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
260	#491	C₂²×C₁₃	1	6	yes	complemented
261	#490	C₂²×C₁₃	1	6	yes	complemented
262	#489	C₂²×C₁₃	1	3	yes	complemented
263	#489	C₂²×C₁₃	1	12	yes	complemented
264	#489	C₂²×C₁₃	1	6	yes	complemented
265	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#489	C₂²×C₁₃	1	3	yes	complemented
267	#489	C₂²×C₁₃	1	3	yes	complemented
268	#488	C₂²×C₁₃	1	12	yes	complemented
269	#487	C₂²×C₁₃	1	6	yes	complemented
270	#486	C₂²×C₁₃	1	6	yes	complemented
271	#419	C₂²×C₁₃	1	6	yes	complemented
272	#418	C₂²×C₁₃	1	6	yes	—
273	#417	C₂²×C₁₃	1	6	yes	—
274	#417	C₂²×C₁₃	1	6	yes	complemented
275	#416	C₂²×C₁₃	1	6	yes	—
276	#416	C₂²×C₁₃	1	6	yes	complemented
277	C₂×#103	C₂²×C₁₃	1	6	yes	complemented
278	C₂×#102	C₂²×C₁₃	1	6	yes	—
279	#405	C₂²×C₁₃	1	6	yes	complemented
280	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
281	C₂×#97	C₂²×C₁₃	1	3	yes	complemented
282	C₂²×C₁₃	—	2	3	no	—
283	C₂²×C₁₃	—	2	3	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	3	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	—	4	3	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	3	no	—
290	C₂²×C₁₃	—	16	6	no	—
291	C₂²×C₁₃	C₂×#124	1	6	yes	—
292	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	3	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	3	no	—
297	C₄×C₁₃	—	4	6	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	—	4	3	no	—
301	C₄×C₁₃	C₂×#124	1	6	yes	—
302	C₄×C₁₃	C₂²×#41	1	2	yes	—
303	2₋¹⁺⁴	—	2	8	no	—
304	H(5,𝔽₂)	—	2	8	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	3	no	—
307	C₂×#41	C₂³×C₁₃	1	3	yes	—
308	C₂×#41	C₂³×C₁₃	1	3	yes	—
309	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	2	3	no	—
312	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
313	C₂²×D₄	—	2	3	no	—
314	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
315	#131	—	2	8	no	—
316	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
317	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
318	C₄⋊Q₈	—	2	6	no	—
319	C₄⋊Q₈	—	2	3	no	—
320	C₄⋊Q₈	—	2	3	no	—
321	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
322	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
323	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
324	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
325	#127	C₂³×C₁₃	1	3	yes	—
326	#125	—	2	6	no	—
327	#125	C₂³×C₁₃	1	6	yes	—
328	#124	—	2	3	no	—
329	#124	—	2	3	no	—
330	#124	C₂³×C₁₃	1	3	yes	—
331	#124	C₂³×C₁₃	1	6	yes	—
332	#124	C₂³×C₁₃	1	1	yes	characteristic
333	#123	—	2	6	no	—
334	C₂²⋊Q₈	—	2	3	no	—
335	C₂²⋊Q₈	—	2	3	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	—	2	3	no	—
338	C₂²⋊Q₈	—	2	12	no	—
339	#121	—	2	3	no	—
340	#121	—	2	3	no	—
341	#121	—	2	3	no	—
342	#121	—	2	3	no	—
343	#120	—	2	6	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	3	no	—
346	C₄×Q₈	—	2	3	no	—
347	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
348	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
349	C₄×D₄	—	2	6	no	—
350	C₄×D₄	—	2	3	no	—
351	C₄×D₄	—	2	3	no	—
352	C₄×D₄	D₄×C₁₃	1	3	yes	—
353	C₄×D₄	D₄×C₁₃	1	3	yes	—
354	#117	C₂³×C₁₃	1	6	yes	—
355	#117	C₂³×C₁₃	1	3	yes	—
356	C₂×C₄⋊C₄	—	2	3	no	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
358	C₂×C₂²⋊C₄	—	2	3	no	—
359	C₂×C₂²⋊C₄	—	2	3	no	—
360	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
361	#103	C₂³×C₁₃	1	6	yes	—
362	#103	C₂³×C₁₃	1	12	yes	—
363	#103	C₂³×C₁₃	1	2	yes	—
364	#103	C₂³×C₁₃	1	6	yes	—
365	#103	C₂³×C₁₃	1	6	yes	—
366	#102	C₂³×C₁₃	1	6	yes	—
367	#102	C₂³×C₁₃	1	12	yes	—
368	#102	C₂³×C₁₃	1	6	yes	—
369	#102	C₂³×C₁₃	1	2	yes	—
370	#102	C₂³×C₁₃	1	6	yes	—
371	#97	C₂³×C₁₃	1	1	yes	characteristic
372	#97	C₂³×C₁₃	1	3	yes	—
373	#97	C₂³×C₁₃	1	6	yes	—
374	C₄×C₈	C₂³×C₁₃	1	6	yes	—
375	C₂×C₁₃	—	2	6	no	—
376	C₂×C₁₃	—	8	1	no	—
377	C₂×C₁₃	—	8	3	no	—
378	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
379	C₂×C₁₃	#3585	1	1	yes	characteristic
380	C₂×C₁₃	#3586	1	1	yes	characteristic
381	C₂⁴	—	2	3	no	—
382	#41	—	2	12	no	—
383	#41	—	2	12	no	—
384	#41	—	4	4	no	—
385	#41	—	4	12	no	—
386	#41	C₁₃×#41	1	8	yes	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	3	no	—
389	C₂×Q₈	—	2	3	no	—
390	C₂×Q₈	—	2	6	no	—
391	C₂×Q₈	—	2	12	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	8	6	no	—
394	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
396	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂×D₄	—	2	3	no	—
398	C₂×D₄	—	2	3	no	—
399	C₂×D₄	—	2	3	no	—
400	C₂×D₄	—	2	3	no	—
401	C₂×D₄	—	2	3	no	—
402	C₂×D₄	—	2	12	no	—
403	C₂×D₄	—	4	12	no	—
404	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
405	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
406	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	2	6	no	—
409	C₂²×C₄	—	2	3	no	—
410	C₂²×C₄	—	2	3	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
414	M₁₆	—	2	12	no	—
415	C₂×C₈	—	2	12	no	—
416	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
417	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
418	C₄⋊C₄	—	2	3	no	—
419	C₄⋊C₄	—	2	6	no	—
420	C₄⋊C₄	—	2	6	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	—	2	3	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	6	no	—
425	C₄⋊C₄	—	2	6	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
427	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
428	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
429	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
430	C₂²⋊C₄	—	2	6	no	—
431	C₂²⋊C₄	—	2	3	no	—
432	C₂²⋊C₄	—	2	3	no	—
433	C₂²⋊C₄	—	2	6	no	—
434	C₂²⋊C₄	—	2	6	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
438	C₄²	—	2	6	no	—
439	C₄²	C₂×D₄×C₁₃	1	3	yes	—
440	C₄²	C₂×D₄×C₁₃	1	3	yes	—
441	C₄²	C₂⁴×C₁₃	1	3	yes	—
442	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₁₃	#60625	1	1	yes	characteristic, direct product factor, Sylow
444	C₂³	—	2	3	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	4	6	no	—
447	C₂³	—	8	3	no	—
448	C₂³	—	8	3	no	—
449	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
450	Q₈	—	2	6	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	4	6	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	6	no	—
455	Q₈	—	8	6	no	—
456	Q₈	C₁₃×#124	1	4	yes	—
457	D₄	—	2	6	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	6	no	—
460	D₄	—	4	6	no	—
461	D₄	—	4	6	no	—
462	D₄	—	8	3	no	—
463	D₄	—	8	3	no	—
464	D₄	C₁₃×#124	1	12	yes	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	6	no	—
467	C₂×C₄	—	2	3	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	3	no	—
470	C₂×C₄	—	4	3	no	—
471	C₂×C₄	—	4	6	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	4	6	no	—
474	C₂×C₄	—	8	6	no	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
480	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
481	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	6	no	—
484	C₂²	—	2	3	no	—
485	C₂²	—	2	3	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	3	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	3	no	—
492	C₂²	—	16	6	no	—
493	C₂²	C₂×C₁₃×#124	1	6	yes	—
494	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	3	no	—
499	C₄	—	4	6	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	3	no	—
503	C₄	C₂×C₁₃×#124	1	6	yes	—
504	C₄	C₂²×C₁₃×#41	1	2	yes	—
505	C₂	—	2	6	no	—
506	C₂	—	8	3	no	—
507	C₂	—	8	1	no	—
508	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
509	C₂	C₁₃×#3585	1	1	yes	characteristic
510	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3500	C₂
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×#3503	C₂	semidirect
3. C₁₃×#3141	C₂	semidirect
4. C₁₃×#3140	C₂	semidirect
5. C₁₃×#3137	C₂	semidirect
6. C₁₃×#3136	C₂	semidirect
7. C₁₃×#3135	C₂	semidirect
8. C₂×C₁₃×#489	C₂	semidirect
9. C₁₃×#2898	C₂	semidirect
10. C₁₃×#2897	C₂	semidirect
11. C₁₃×#2875	C₂	semidirect
23. C₁₃×#544	C₂²	semidirect
26. C₁₃×#533	C₂²	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₁₃×#491	C₂²	semidirect
33. C₁₃×#490	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#489	C₂²	semidirect
36. C₁₃×#489	C₂²	semidirect
37. C₁₃×#489	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
39. C₁₃×#489	C₂²	semidirect
40. C₁₃×#488	C₂²	semidirect
41. C₁₃×#487	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
43. C₁₃×#419	C₂²	semidirect
46. C₁₃×#417	C₂²	semidirect
48. C₁₃×#416	C₂²	semidirect
49. C₂×C₁₃×#103	C₂²	semidirect
51. C₁₃×#405	C₂²	semidirect
52. C₄×C₁₃×M₁₆	C₂²	semidirect
53. C₂×C₁₃×#97	C₂²	semidirect
126. #60625	C₁₃	direct (N × H)
189. #3503	C₂×C₁₃	semidirect
191. #3141	C₂×C₁₃	semidirect
192. #3140	C₂×C₁₃	semidirect
193. #3137	C₂×C₁₃	semidirect
194. #3136	C₂×C₁₃	semidirect
195. #3135	C₂×C₁₃	semidirect
196. C₂×#489	C₂×C₁₃	semidirect
197. #2898	C₂×C₁₃	semidirect
198. #2897	C₂×C₁₃	semidirect
199. #2875	C₂×C₁₃	semidirect
251. #544	C₂²×C₁₃	semidirect
254. #533	C₂²×C₁₃	semidirect
256. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
260. #491	C₂²×C₁₃	semidirect
261. #490	C₂²×C₁₃	semidirect
262. #489	C₂²×C₁₃	semidirect
263. #489	C₂²×C₁₃	semidirect
264. #489	C₂²×C₁₃	semidirect
265. #489	C₂²×C₁₃	semidirect
266. #489	C₂²×C₁₃	semidirect
267. #489	C₂²×C₁₃	semidirect
268. #488	C₂²×C₁₃	semidirect
269. #487	C₂²×C₁₃	semidirect
270. #486	C₂²×C₁₃	semidirect
271. #419	C₂²×C₁₃	semidirect
274. #417	C₂²×C₁₃	semidirect
276. #416	C₂²×C₁₃	semidirect
277. C₂×#103	C₂²×C₁₃	semidirect
279. #405	C₂²×C₁₃	semidirect
280. C₄×M₁₆	C₂²×C₁₃	semidirect
281. C₂×#97	C₂²×C₁₃	semidirect
443. C₁₃	#60625	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×#3503	2
C₁₃×#3500	2
C₁₃×#3141	2
C₁₃×#3140	2
C₁₃×#3137	2
C₁₃×#3136	2
C₁₃×#3135	2
C₂×C₁₃×#489	2
C₁₃×#2898	2
C₁₃×#2897	2
C₁₃×#2875	2
#60625	13

Subgroups — C13×#60625 #15746964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60625 #15746964