Subgroups — C₁₃×#60390 #15746729

Order 3328.

4698 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3585	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3021	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3020	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3018	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#454	C₂	1	6	yes	maximal, complemented
8	C₁₃×#2901	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2889	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#585	—	2	8	no	—
11	C₁₃×#585	—	2	6	no	—
12	C₁₃×#585	C₂²	1	2	yes	—
13	C₁₃×#585	C₂²	1	6	yes	complemented
14	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
15	C₂×C₁₃×2₋¹⁺⁴	—	2	2	no	—
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	6	yes	complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#577	—	2	8	no	—
20	C₁₃×#576	—	2	8	no	—
21	C₁₃×#575	C₂²	1	12	yes	complemented
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
23	C₁₃×#568	C₂²	1	2	yes	complemented
24	C₁₃×#548	—	2	2	no	—
25	C₁₃×#546	—	2	6	no	—
26	C₁₃×#536	C₂²	1	3	yes	complemented
27	C₁₃×#535	C₂²	1	3	yes	complemented
28	C₁₃×#532	C₂²	1	3	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#456	C₂²	1	12	yes	complemented
32	C₁₃×#455	C₂²	1	4	yes	complemented
33	C₁₃×#454	C₂²	1	12	yes	complemented
34	C₁₃×#454	C₂²	1	24	yes	complemented
35	C₁₃×#453	C₂²	1	12	yes	complemented
36	C₁₃×#421	C₂²	1	12	yes	complemented
37	C₂×C₁₃×#104	C₂²	1	12	yes	complemented
38	C₁₃×#413	C₂²	1	6	yes	complemented
39	C₂×C₁₃×#101	C₂²	1	6	yes	complemented
40	C₁₃×2₋¹⁺⁴	—	2	24	no	—
41	C₁₃×2₋¹⁺⁴	—	2	16	no	—
42	C₁₃×2₋¹⁺⁴	—	2	8	no	—
43	C₁₃×2₋¹⁺⁴	—	2	24	no	—
44	C₁₃×2₋¹⁺⁴	—	2	2	no	—
45	C₁₃×2₋¹⁺⁴	—	2	12	no	—
46	C₁₃×2₋¹⁺⁴	—	2	12	no	—
47	C₁₃×2₋¹⁺⁴	D₄	1	8	yes	complemented
48	C₁₃×2₋¹⁺⁴	C₂³	1	12	yes	—
49	C₁₃×H(5,𝔽₂)	—	2	24	no	—
50	C₁₃×H(5,𝔽₂)	—	2	6	no	—
51	C₁₃×H(5,𝔽₂)	—	2	12	no	—
52	C₁₃×H(5,𝔽₂)	—	2	12	no	—
53	C₁₃×H(5,𝔽₂)	—	2	8	no	—
54	C₁₃×H(5,𝔽₂)	D₄	1	8	yes	complemented
55	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
56	C₂×C₁₃×#41	—	2	8	no	—
57	C₂×C₁₃×#41	—	2	48	no	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	—	2	24	no	—
60	C₂×C₁₃×#41	—	2	1	no	—
61	C₂×C₁₃×#41	—	2	12	no	—
62	C₂×C₁₃×#41	—	2	12	no	—
63	C₂×C₁₃×#41	—	2	12	no	—
64	C₂×C₁₃×#41	D₄	1	6	yes	—
65	C₂×C₁₃×#41	C₂³	1	12	yes	—
66	C₂×C₁₃×#41	C₂³	1	3	yes	—
67	C₂×C₁₃×#41	C₂³	1	3	yes	—
68	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	—	2	8	no	—
70	C₂²×Q₈×C₁₃	—	2	12	no	—
71	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
72	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
73	C₂²×D₄×C₁₃	—	2	3	no	—
74	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
75	C₁₃×#137	—	2	12	no	—
76	C₁₃×#137	C₂³	1	8	yes	—
77	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	12	no	—
79	C₁₃×AGL(1,ℤ/8)	C₂³	1	24	yes	—
80	C₁₃×#135	—	2	24	no	—
81	C₂×C₁₃×SD₁₆	—	2	12	no	—
82	C₂×C₁₃×D₈	—	2	12	no	—
83	C₁₃×#131	—	2	8	no	—
84	C₂×C₁₃×M₁₆	C₂³	1	12	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
86	C₁₃×#127	C₂³	1	3	yes	—
87	C₁₃×#124	—	2	6	no	—
88	C₁₃×#124	C₂³	1	3	yes	—
89	C₁₃×#124	C₂³	1	6	yes	—
90	C₁₃×#124	C₂³	1	1	yes	characteristic
91	C₁₃×#123	—	2	6	no	—
92	C₁₃×C₂²⋊Q₈	—	2	6	no	—
93	C₁₃×#121	—	2	6	no	—
94	C₁₃×#121	—	2	6	no	—
95	C₁₃×#120	—	2	6	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	6	no	—
99	C₁₃×#117	C₂³	1	3	yes	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
101	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#104	C₂³	1	8	yes	—
103	C₁₃×#104	C₂³	1	24	yes	—
104	C₁₃×#101	C₂³	1	12	yes	—
105	C₁₃×#100	C₂³	1	4	yes	—
106	#60390	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	3	no	—
108	C₁₃×#41	—	2	48	no	—
109	C₁₃×#41	—	2	48	no	—
110	C₁₃×#41	—	2	48	no	—
111	C₁₃×#41	—	2	24	no	—
112	C₁₃×#41	—	2	24	no	—
113	C₁₃×#41	—	2	8	no	—
114	C₁₃×#41	—	2	8	no	—
115	C₁₃×#41	—	2	24	no	—
116	C₁₃×#41	—	2	24	no	—
117	C₁₃×#41	—	2	24	no	—
118	C₁₃×#41	—	2	24	no	—
119	C₁₃×#41	—	2	12	no	—
120	C₁₃×#41	—	2	12	no	—
121	C₁₃×#41	—	2	12	no	—
122	C₁₃×#41	—	2	12	no	—
123	C₁₃×#41	—	4	4	no	—
124	C₁₃×#41	C₂×D₄	1	24	yes	—
125	C₁₃×#41	C₂×D₄	1	8	yes	—
126	C₁₃×#41	C₂⁴	1	8	yes	—
127	C₂×Q₈×C₁₃	—	2	48	no	—
128	C₂×Q₈×C₁₃	—	2	12	no	—
129	C₂×Q₈×C₁₃	—	2	12	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	2	8	no	—
132	C₂×Q₈×C₁₃	—	2	24	no	—
133	C₂×Q₈×C₁₃	—	2	12	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	12	yes	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	6	yes	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
139	C₂×D₄×C₁₃	—	2	48	no	—
140	C₂×D₄×C₁₃	—	2	12	no	—
141	C₂×D₄×C₁₃	—	2	12	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	12	no	—
144	C₂×D₄×C₁₃	—	2	24	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	3	no	—
147	C₂×D₄×C₁₃	—	2	6	no	—
148	C₂×D₄×C₁₃	—	2	12	no	—
149	C₂×D₄×C₁₃	—	2	3	no	—
150	C₂×D₄×C₁₃	—	4	12	no	—
151	C₂×D₄×C₁₃	C₂×D₄	1	6	yes	—
152	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	—	2	24	no	—
157	C₂²×C₄×C₁₃	—	2	24	no	—
158	C₂²×C₄×C₁₃	—	2	12	no	—
159	C₂²×C₄×C₁₃	—	2	3	no	—
160	C₂²×C₄×C₁₃	—	2	3	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
164	C₁₃×Q₁₆	—	2	8	no	—
165	C₁₃×SD₁₆	—	2	24	no	—
166	C₁₃×SD₁₆	—	2	8	no	—
167	C₁₃×D₈	—	2	24	no	—
168	C₁₃×M₁₆	—	2	12	no	—
169	C₁₃×M₁₆	C₂⁴	1	8	yes	—
170	C₂×C₈×C₁₃	—	2	12	no	—
171	C₁₃×C₄⋊C₄	—	2	3	no	—
172	C₁₃×C₄⋊C₄	—	2	6	no	—
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	6	no	—
176	C₁₃×C₂²⋊C₄	—	2	12	no	—
177	C₄²×C₁₃	—	2	3	no	—
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	3	yes	—
180	2₋¹⁺⁶	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#3585	C₂×C₁₃	1	2	yes	complemented
182	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3021	C₂×C₁₃	1	6	yes	complemented
184	#3020	C₂×C₁₃	1	6	yes	complemented
185	#3018	C₂×C₁₃	1	6	yes	complemented
186	C₂×#454	C₂×C₁₃	1	6	yes	complemented
187	#2901	C₂×C₁₃	1	2	yes	complemented
188	#2889	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	12	no	—
191	C₂³×C₁₃	—	2	3	no	—
192	C₂³×C₁₃	—	4	6	no	—
193	C₂³×C₁₃	—	8	6	no	—
194	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
196	Q₈×C₁₃	—	2	24	no	—
197	Q₈×C₁₃	—	2	12	no	—
198	Q₈×C₁₃	—	2	12	no	—
199	Q₈×C₁₃	—	2	6	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	#120	1	4	yes	—
202	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
203	D₄×C₁₃	—	2	16	no	—
204	D₄×C₁₃	—	2	24	no	—
205	D₄×C₁₃	—	2	24	no	—
206	D₄×C₁₃	—	2	12	no	—
207	D₄×C₁₃	—	2	8	no	—
208	D₄×C₁₃	—	2	12	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	6	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	—	4	6	no	—
213	D₄×C₁₃	—	8	6	no	—
214	D₄×C₁₃	#120	1	12	yes	—
215	D₄×C₁₃	C₂²×D₄	1	8	yes	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	48	no	—
218	C₂×C₄×C₁₃	—	2	12	no	—
219	C₂×C₄×C₁₃	—	2	12	no	—
220	C₂×C₄×C₁₃	—	2	24	no	—
221	C₂×C₄×C₁₃	—	2	12	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	3	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	4	6	no	—
227	C₂×C₄×C₁₃	—	8	3	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
232	C₈×C₁₃	—	2	8	no	—
233	#585	—	2	8	no	—
234	#585	—	2	6	no	—
235	#585	C₂²×C₁₃	1	2	yes	—
236	#585	C₂²×C₁₃	1	6	yes	complemented
237	C₂×2₋¹⁺⁴	—	2	8	no	—
238	C₂×2₋¹⁺⁴	—	2	2	no	—
239	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	6	yes	complemented
241	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	#577	—	2	8	no	—
243	#576	—	2	8	no	—
244	#575	C₂²×C₁₃	1	12	yes	complemented
245	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	12	yes	complemented
246	#568	C₂²×C₁₃	1	2	yes	complemented
247	#548	—	2	2	no	—
248	#546	—	2	6	no	—
249	#536	C₂²×C₁₃	1	3	yes	complemented
250	#535	C₂²×C₁₃	1	3	yes	complemented
251	#532	C₂²×C₁₃	1	3	yes	complemented
252	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
253	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
254	#456	C₂²×C₁₃	1	12	yes	complemented
255	#455	C₂²×C₁₃	1	4	yes	complemented
256	#454	C₂²×C₁₃	1	12	yes	complemented
257	#454	C₂²×C₁₃	1	24	yes	complemented
258	#453	C₂²×C₁₃	1	12	yes	complemented
259	#421	C₂²×C₁₃	1	12	yes	complemented
260	C₂×#104	C₂²×C₁₃	1	12	yes	complemented
261	#413	C₂²×C₁₃	1	6	yes	complemented
262	C₂×#101	C₂²×C₁₃	1	6	yes	complemented
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	8	no	—
265	C₂²×C₁₃	—	4	3	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	6	no	—
268	C₂²×C₁₃	—	4	3	no	—
269	C₂²×C₁₃	—	8	12	no	—
270	C₂²×C₁₃	—	8	8	no	—
271	C₂²×C₁₃	—	16	6	no	—
272	C₂²×C₁₃	C₂×#120	1	6	yes	—
273	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₁₃	—	2	8	no	—
275	C₄×C₁₃	—	2	6	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	3	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	C₂×#120	1	6	yes	—
280	C₄×C₁₃	C₂³×D₄	1	2	yes	—
281	2₋¹⁺⁴	—	2	24	no	—
282	2₋¹⁺⁴	—	2	16	no	—
283	2₋¹⁺⁴	—	2	8	no	—
284	2₋¹⁺⁴	—	2	24	no	—
285	2₋¹⁺⁴	—	2	2	no	—
286	2₋¹⁺⁴	—	2	12	no	—
287	2₋¹⁺⁴	—	2	12	no	—
288	2₋¹⁺⁴	D₄×C₁₃	1	8	yes	complemented
289	2₋¹⁺⁴	C₂³×C₁₃	1	12	yes	—
290	H(5,𝔽₂)	—	2	24	no	—
291	H(5,𝔽₂)	—	2	6	no	—
292	H(5,𝔽₂)	—	2	12	no	—
293	H(5,𝔽₂)	—	2	12	no	—
294	H(5,𝔽₂)	—	2	8	no	—
295	H(5,𝔽₂)	D₄×C₁₃	1	8	yes	complemented
296	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	—	2	48	no	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	2	24	no	—
301	C₂×#41	—	2	1	no	—
302	C₂×#41	—	2	12	no	—
303	C₂×#41	—	2	12	no	—
304	C₂×#41	—	2	12	no	—
305	C₂×#41	D₄×C₁₃	1	6	yes	—
306	C₂×#41	C₂³×C₁₃	1	12	yes	—
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	8	no	—
311	C₂²×Q₈	—	2	12	no	—
312	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
313	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
314	C₂²×D₄	—	2	3	no	—
315	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
316	#137	—	2	12	no	—
317	#137	C₂³×C₁₃	1	8	yes	—
318	AGL(1,ℤ/8)	—	2	24	no	—
319	AGL(1,ℤ/8)	—	2	12	no	—
320	AGL(1,ℤ/8)	C₂³×C₁₃	1	24	yes	—
321	#135	—	2	24	no	—
322	C₂×SD₁₆	—	2	12	no	—
323	C₂×D₈	—	2	12	no	—
324	#131	—	2	8	no	—
325	C₂×M₁₆	C₂³×C₁₃	1	12	yes	—
326	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
327	#127	C₂³×C₁₃	1	3	yes	—
328	#124	—	2	6	no	—
329	#124	C₂³×C₁₃	1	3	yes	—
330	#124	C₂³×C₁₃	1	6	yes	—
331	#124	C₂³×C₁₃	1	1	yes	characteristic
332	#123	—	2	6	no	—
333	C₂²⋊Q₈	—	2	6	no	—
334	#121	—	2	6	no	—
335	#121	—	2	6	no	—
336	#120	—	2	6	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	6	no	—
340	#117	C₂³×C₁₃	1	3	yes	—
341	C₂×C₂²⋊C₄	—	2	6	no	—
342	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
343	#104	C₂³×C₁₃	1	8	yes	—
344	#104	C₂³×C₁₃	1	24	yes	—
345	#101	C₂³×C₁₃	1	12	yes	—
346	#100	C₂³×C₁₃	1	4	yes	—
347	C₂×C₁₃	—	2	1	no	—
348	C₂×C₁₃	—	2	6	no	—
349	C₂×C₁₃	—	4	2	no	—
350	C₂×C₁₃	—	4	8	no	—
351	C₂×C₁₃	—	8	3	no	—
352	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
353	C₂⁴	—	2	3	no	—
354	#41	—	2	48	no	—
355	#41	—	2	48	no	—
356	#41	—	2	48	no	—
357	#41	—	2	24	no	—
358	#41	—	2	24	no	—
359	#41	—	2	8	no	—
360	#41	—	2	8	no	—
361	#41	—	2	24	no	—
362	#41	—	2	24	no	—
363	#41	—	2	24	no	—
364	#41	—	2	24	no	—
365	#41	—	2	12	no	—
366	#41	—	2	12	no	—
367	#41	—	2	12	no	—
368	#41	—	2	12	no	—
369	#41	—	4	4	no	—
370	#41	C₂×D₄×C₁₃	1	24	yes	—
371	#41	C₂×D₄×C₁₃	1	8	yes	—
372	#41	C₂⁴×C₁₃	1	8	yes	—
373	C₂×Q₈	—	2	48	no	—
374	C₂×Q₈	—	2	12	no	—
375	C₂×Q₈	—	2	12	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	24	no	—
379	C₂×Q₈	—	2	12	no	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	12	yes	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	6	yes	—
382	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
384	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
385	C₂×D₄	—	2	48	no	—
386	C₂×D₄	—	2	12	no	—
387	C₂×D₄	—	2	12	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	12	no	—
390	C₂×D₄	—	2	24	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	3	no	—
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	12	no	—
395	C₂×D₄	—	2	3	no	—
396	C₂×D₄	—	4	12	no	—
397	C₂×D₄	C₂×D₄×C₁₃	1	6	yes	—
398	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
399	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
400	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
401	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	—	2	24	no	—
403	C₂²×C₄	—	2	24	no	—
404	C₂²×C₄	—	2	12	no	—
405	C₂²×C₄	—	2	3	no	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
410	Q₁₆	—	2	8	no	—
411	SD₁₆	—	2	24	no	—
412	SD₁₆	—	2	8	no	—
413	D₈	—	2	24	no	—
414	M₁₆	—	2	12	no	—
415	M₁₆	C₂⁴×C₁₃	1	8	yes	—
416	C₂×C₈	—	2	12	no	—
417	C₄⋊C₄	—	2	3	no	—
418	C₄⋊C₄	—	2	6	no	—
419	C₂²⋊C₄	—	2	3	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	6	no	—
422	C₂²⋊C₄	—	2	12	no	—
423	C₄²	—	2	3	no	—
424	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₄²	C₂⁴×C₁₃	1	3	yes	—
426	C₁₃	#60390	1	1	yes	characteristic, direct product factor, Sylow
427	C₂³	—	2	8	no	—
428	C₂³	—	2	12	no	—
429	C₂³	—	2	3	no	—
430	C₂³	—	4	6	no	—
431	C₂³	—	8	6	no	—
432	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
433	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
434	Q₈	—	2	24	no	—
435	Q₈	—	2	12	no	—
436	Q₈	—	2	12	no	—
437	Q₈	—	2	6	no	—
438	Q₈	—	2	2	no	—
439	Q₈	C₁₃×#120	1	4	yes	—
440	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
441	D₄	—	2	16	no	—
442	D₄	—	2	24	no	—
443	D₄	—	2	24	no	—
444	D₄	—	2	12	no	—
445	D₄	—	2	8	no	—
446	D₄	—	2	12	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	6	no	—
449	D₄	—	4	6	no	—
450	D₄	—	4	6	no	—
451	D₄	—	8	6	no	—
452	D₄	C₁₃×#120	1	12	yes	—
453	D₄	C₂²×D₄×C₁₃	1	8	yes	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	48	no	—
456	C₂×C₄	—	2	12	no	—
457	C₂×C₄	—	2	12	no	—
458	C₂×C₄	—	2	24	no	—
459	C₂×C₄	—	2	12	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	3	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	6	no	—
465	C₂×C₄	—	8	3	no	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
469	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
470	C₈	—	2	8	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	6	no	—
476	C₂²	—	4	3	no	—
477	C₂²	—	8	12	no	—
478	C₂²	—	8	8	no	—
479	C₂²	—	16	6	no	—
480	C₂²	C₂×C₁₃×#120	1	6	yes	—
481	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
482	C₄	—	2	8	no	—
483	C₄	—	2	6	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	3	no	—
486	C₄	—	4	1	no	—
487	C₄	C₂×C₁₃×#120	1	6	yes	—
488	C₄	C₂³×D₄×C₁₃	1	2	yes	—
489	C₂	—	2	1	no	—
490	C₂	—	2	6	no	—
491	C₂	—	4	2	no	—
492	C₂	—	4	8	no	—
493	C₂	—	8	3	no	—
494	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×2₋¹⁺⁶	C₂	semidirect
2. C₁₃×#3585	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3021	C₂	semidirect
5. C₁₃×#3020	C₂	semidirect
6. C₁₃×#3018	C₂	semidirect
7. C₂×C₁₃×#454	C₂	semidirect
8. C₁₃×#2901	C₂	semidirect
9. C₁₃×#2889	C₂	semidirect
13. C₁₃×#585	C₂²	semidirect
17. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
21. C₁₃×#575	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₁₃×#568	C₂²	semidirect
26. C₁₃×#536	C₂²	semidirect
27. C₁₃×#535	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
30. C₄×C₁₃×#41	C₂²	semidirect
31. C₁₃×#456	C₂²	semidirect
32. C₁₃×#455	C₂²	semidirect
33. C₁₃×#454	C₂²	semidirect
34. C₁₃×#454	C₂²	semidirect
35. C₁₃×#453	C₂²	semidirect
36. C₁₃×#421	C₂²	semidirect
37. C₂×C₁₃×#104	C₂²	semidirect
38. C₁₃×#413	C₂²	semidirect
39. C₂×C₁₃×#101	C₂²	semidirect
47. C₁₃×2₋¹⁺⁴	D₄	semidirect
54. C₁₃×H(5,𝔽₂)	D₄	semidirect
106. #60390	C₁₃	direct (N × H)
180. 2₋¹⁺⁶	C₂×C₁₃	semidirect
181. #3585	C₂×C₁₃	semidirect
182. #3500	C₂×C₁₃	semidirect
183. #3021	C₂×C₁₃	semidirect
184. #3020	C₂×C₁₃	semidirect
185. #3018	C₂×C₁₃	semidirect
186. C₂×#454	C₂×C₁₃	semidirect
187. #2901	C₂×C₁₃	semidirect
188. #2889	C₂×C₁₃	semidirect
236. #585	C₂²×C₁₃	semidirect
240. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
241. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
244. #575	C₂²×C₁₃	semidirect
245. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
246. #568	C₂²×C₁₃	semidirect
249. #536	C₂²×C₁₃	semidirect
250. #535	C₂²×C₁₃	semidirect
251. #532	C₂²×C₁₃	semidirect
252. C₂×#124	C₂²×C₁₃	semidirect
253. C₄×#41	C₂²×C₁₃	semidirect
254. #456	C₂²×C₁₃	semidirect
255. #455	C₂²×C₁₃	semidirect
256. #454	C₂²×C₁₃	semidirect
257. #454	C₂²×C₁₃	semidirect
258. #453	C₂²×C₁₃	semidirect
259. #421	C₂²×C₁₃	semidirect
260. C₂×#104	C₂²×C₁₃	semidirect
261. #413	C₂²×C₁₃	semidirect
262. C₂×#101	C₂²×C₁₃	semidirect
288. 2₋¹⁺⁴	D₄×C₁₃	semidirect
295. H(5,𝔽₂)	D₄×C₁₃	semidirect
426. C₁₃	#60390	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×2₋¹⁺⁶	2
C₁₃×#3585	2
C₁₃×#3500	2
C₁₃×#3021	2
C₁₃×#3020	2
C₁₃×#3018	2
C₂×C₁₃×#454	2
C₁₃×#2901	2
C₁₃×#2889	2
#60390	13

Subgroups — C13×#60390 #15746729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60390 #15746729