Subgroups — C₁₃×#60650 #15746989

Order 3328.

3274 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#576	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3155	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3154	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3153	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3151	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3150	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#496	C₂	1	3	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×H(5,𝔽₂)	C₂²	1	2	yes	—
15	C₁₃×#577	—	2	16	no	—
16	C₁₃×#576	—	2	16	no	—
17	C₂×C₁₃×#137	C₂²	1	6	yes	complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
24	C₂²×C₁₃×D₈	C₂²	1	6	yes	complemented
25	C₂×C₁₃×#131	C₂²	1	2	yes	—
26	C₁₃×#550	—	2	2	no	—
27	C₁₃×#548	—	2	2	no	—
28	C₁₃×#546	—	2	6	no	—
29	D₄²×C₁₃	—	2	6	no	—
30	C₁₃×#536	C₂²	1	3	yes	complemented
31	C₁₃×#535	C₂²	1	6	yes	complemented
32	C₁₃×#535	C₂²	1	3	yes	complemented
33	C₁₃×#532	C₂²	1	3	yes	complemented
34	C₁₃×#532	C₂²	1	3	yes	complemented
35	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#497	C₂²	1	3	yes	complemented
40	C₁₃×#497	C₂²	1	6	yes	complemented
41	C₁₃×#496	C₂²	1	3	yes	complemented
42	C₁₃×#496	C₂²	1	6	yes	complemented
43	C₁₃×#496	C₂²	1	12	yes	complemented
44	C₁₃×#496	C₂²	1	3	yes	complemented
45	C₁₃×#496	C₂²	1	6	yes	complemented
46	C₁₃×#495	C₂²	1	12	yes	complemented
47	C₁₃×#493	C₂²	1	6	yes	complemented
48	C₁₃×#492	C₂²	1	6	yes	complemented
49	C₁₃×#405	C₂²	1	6	yes	complemented
50	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
51	C₂×C₁₃×#97	C₂²	1	3	yes	complemented
52	C₁₃×2₋¹⁺⁴	—	2	8	no	—
53	C₁₃×H(5,𝔽₂)	—	2	8	no	—
54	C₁₃×H(5,𝔽₂)	—	2	8	no	—
55	C₁₃×H(5,𝔽₂)	—	2	8	no	—
56	C₂×C₁₃×#41	—	2	1	no	—
57	C₂×C₁₃×#41	—	2	2	no	—
58	C₂×C₁₃×#41	—	2	3	no	—
59	C₂×C₁₃×#41	C₂³	1	3	yes	—
60	C₂×C₁₃×#41	C₂³	1	6	yes	—
61	C₂×C₁₃×#41	C₂³	1	3	yes	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
65	C₂²×D₄×C₁₃	—	2	6	no	—
66	C₂²×D₄×C₁₃	—	2	3	no	—
67	C₂²×D₄×C₁₃	—	2	6	no	—
68	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
70	C₁₃×#137	—	2	24	no	—
71	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
73	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
74	C₁₃×#135	—	2	24	no	—
75	C₁₃×#135	—	2	24	no	—
76	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
77	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×SD₁₆	—	2	24	no	—
79	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
84	C₂×C₁₃×D₈	—	2	24	no	—
85	C₂×C₁₃×D₈	C₂³	1	6	yes	—
86	C₂×C₁₃×D₈	C₂³	1	12	yes	—
87	C₂×C₁₃×D₈	C₂³	1	6	yes	—
88	C₁₃×#131	D₄	1	16	yes	complemented
89	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
90	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₃×#127	—	2	6	no	—
94	C₁₃×#127	C₂³	1	6	yes	—
95	C₁₃×#127	C₂³	1	3	yes	—
96	C₁₃×#127	C₂³	1	3	yes	—
97	C₁₃×#124	—	2	6	no	—
98	C₁₃×#124	C₂³	1	6	yes	—
99	C₁₃×#124	C₂³	1	6	yes	—
100	C₁₃×#124	C₂³	1	3	yes	—
101	C₁₃×#124	C₂³	1	1	yes	characteristic
102	C₁₃×#123	—	2	6	no	—
103	C₁₃×C₂²⋊Q₈	—	2	6	no	—
104	C₁₃×#121	—	2	6	no	—
105	C₁₃×#121	—	2	6	no	—
106	C₁₃×#121	—	2	12	no	—
107	C₁₃×#121	—	2	6	no	—
108	C₁₃×#120	—	2	12	no	—
109	C₁₃×#120	—	2	6	no	—
110	C₄×Q₈×C₁₃	D₄	1	2	yes	—
111	C₄×D₄×C₁₃	—	2	6	no	—
112	C₄×D₄×C₁₃	—	2	6	no	—
113	C₄×D₄×C₁₃	D₄	1	6	yes	—
114	C₁₃×#117	C₂³	1	3	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
116	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
117	C₁₃×#97	C₂³	1	1	yes	characteristic
118	C₁₃×#97	C₂³	1	3	yes	—
119	C₁₃×#97	C₂³	1	6	yes	—
120	C₄×C₈×C₁₃	C₂³	1	6	yes	—
121	#60650	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	—	2	3	no	—
123	C₂⁴×C₁₃	—	2	6	no	—
124	C₁₃×#41	—	2	12	no	—
125	C₁₃×#41	—	2	12	no	—
126	C₁₃×#41	—	2	12	no	—
127	C₁₃×#41	—	2	12	no	—
128	C₁₃×#41	—	4	4	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₁₃×#41	—	4	12	no	—
131	C₁₃×#41	C₂×D₄	1	8	yes	—
132	C₂×Q₈×C₁₃	—	2	3	no	—
133	C₂×Q₈×C₁₃	—	2	12	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	3	no	—
141	C₂×D₄×C₁₃	—	2	3	no	—
142	C₂×D₄×C₁₃	—	2	12	no	—
143	C₂×D₄×C₁₃	—	2	12	no	—
144	C₂×D₄×C₁₃	—	2	12	no	—
145	C₂×D₄×C₁₃	—	2	6	no	—
146	C₂×D₄×C₁₃	—	2	3	no	—
147	C₂×D₄×C₁₃	—	2	6	no	—
148	C₂×D₄×C₁₃	—	2	6	no	—
149	C₂×D₄×C₁₃	—	2	12	no	—
150	C₂×D₄×C₁₃	—	4	24	no	—
151	C₂×D₄×C₁₃	—	4	12	no	—
152	C₂×D₄×C₁₃	—	8	12	no	—
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	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
157	C₂²×C₄×C₁₃	—	2	3	no	—
158	C₂²×C₄×C₁₃	—	2	6	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	C₂⁴	1	3	yes	—
163	C₁₃×Q₁₆	—	2	4	no	—
164	C₁₃×Q₁₆	—	2	12	no	—
165	C₁₃×SD₁₆	—	2	12	no	—
166	C₁₃×SD₁₆	—	2	24	no	—
167	C₁₃×SD₁₆	—	2	4	no	—
168	C₁₃×SD₁₆	—	2	12	no	—
169	C₁₃×SD₁₆	—	2	12	no	—
170	C₁₃×D₈	—	2	12	no	—
171	C₁₃×D₈	—	2	24	no	—
172	C₁₃×D₈	—	2	12	no	—
173	C₁₃×M₁₆	C₂×D₄	1	24	yes	complemented
174	C₂×C₈×C₁₃	C₂×D₄	1	24	yes	complemented
175	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	6	no	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
180	C₁₃×C₂²⋊C₄	—	2	6	no	—
181	C₁₃×C₂²⋊C₄	—	2	12	no	—
182	C₁₃×C₂²⋊C₄	—	2	2	no	—
183	C₁₃×C₂²⋊C₄	—	2	12	no	—
184	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
185	C₄²×C₁₃	C₂×D₄	1	6	yes	—
186	C₄²×C₁₃	C₂⁴	1	3	yes	—
187	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×#577	C₂×C₁₃	1	2	yes	complemented
189	C₂×#576	C₂×C₁₃	1	2	yes	complemented
190	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#3155	C₂×C₁₃	1	6	yes	complemented
193	#3154	C₂×C₁₃	1	6	yes	complemented
194	#3153	C₂×C₁₃	1	3	yes	complemented
195	#3151	C₂×C₁₃	1	3	yes	complemented
196	#3150	C₂×C₁₃	1	3	yes	complemented
197	C₂×#496	C₂×C₁₃	1	3	yes	complemented
198	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	3	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	6	no	—
202	C₂³×C₁₃	—	4	6	no	—
203	C₂³×C₁₃	—	4	12	no	—
204	C₂³×C₁₃	—	8	12	no	—
205	C₂³×C₁₃	—	8	6	no	—
206	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
207	Q₈×C₁₃	—	2	6	no	—
208	Q₈×C₁₃	—	2	2	no	—
209	Q₈×C₁₃	—	2	2	no	—
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	4	6	no	—
212	Q₈×C₁₃	#127	1	4	yes	—
213	D₄×C₁₃	—	2	6	no	—
214	D₄×C₁₃	—	2	6	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	6	no	—
217	D₄×C₁₃	—	4	12	no	—
218	D₄×C₁₃	—	4	12	no	—
219	D₄×C₁₃	—	4	6	no	—
220	D₄×C₁₃	—	4	6	no	—
221	D₄×C₁₃	—	4	6	no	—
222	D₄×C₁₃	—	4	12	no	—
223	D₄×C₁₃	—	8	6	no	—
224	D₄×C₁₃	—	8	12	no	—
225	D₄×C₁₃	#127	1	12	yes	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	3	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	4	6	no	—
230	C₂×C₄×C₁₃	—	4	6	no	—
231	C₂×C₄×C₁₃	—	4	12	no	—
232	C₂×C₄×C₁₃	—	4	6	no	—
233	C₂×C₄×C₁₃	—	4	6	no	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
239	C₈×C₁₃	C₂²×D₄	1	4	yes	—
240	C₈×C₁₃	C₂²×D₄	1	12	yes	—
241	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
243	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
244	#577	—	2	16	no	—
245	#576	—	2	16	no	—
246	C₂×#137	C₂²×C₁₃	1	6	yes	complemented
247	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	complemented
248	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	complemented
249	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	complemented
250	C₂×#135	C₂²×C₁₃	1	6	yes	complemented
251	C₂×#135	C₂²×C₁₃	1	6	yes	complemented
252	C₂²×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
253	C₂²×D₈	C₂²×C₁₃	1	6	yes	complemented
254	C₂×#131	C₂²×C₁₃	1	2	yes	—
255	#550	—	2	2	no	—
256	#548	—	2	2	no	—
257	#546	—	2	6	no	—
258	D₄²	—	2	6	no	—
259	#536	C₂²×C₁₃	1	3	yes	complemented
260	#535	C₂²×C₁₃	1	6	yes	complemented
261	#535	C₂²×C₁₃	1	3	yes	complemented
262	#532	C₂²×C₁₃	1	3	yes	complemented
263	#532	C₂²×C₁₃	1	3	yes	complemented
264	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
265	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
266	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
267	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
268	#497	C₂²×C₁₃	1	3	yes	complemented
269	#497	C₂²×C₁₃	1	6	yes	complemented
270	#496	C₂²×C₁₃	1	3	yes	complemented
271	#496	C₂²×C₁₃	1	6	yes	complemented
272	#496	C₂²×C₁₃	1	12	yes	complemented
273	#496	C₂²×C₁₃	1	3	yes	complemented
274	#496	C₂²×C₁₃	1	6	yes	complemented
275	#495	C₂²×C₁₃	1	12	yes	complemented
276	#493	C₂²×C₁₃	1	6	yes	complemented
277	#492	C₂²×C₁₃	1	6	yes	complemented
278	#405	C₂²×C₁₃	1	6	yes	complemented
279	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
280	C₂×#97	C₂²×C₁₃	1	3	yes	complemented
281	C₂²×C₁₃	—	2	6	no	—
282	C₂²×C₁₃	—	4	12	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	6	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	3	no	—
287	C₂²×C₁₃	—	4	6	no	—
288	C₂²×C₁₃	—	16	12	no	—
289	C₂²×C₁₃	—	16	6	no	—
290	C₂²×C₁₃	C₂×#127	1	6	yes	—
291	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	6	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	1	no	—
296	C₄×C₁₃	—	4	3	no	—
297	C₄×C₁₃	C₂×#127	1	6	yes	—
298	C₄×C₁₃	C₂³×D₄	1	2	yes	—
299	2₋¹⁺⁴	—	2	8	no	—
300	H(5,𝔽₂)	—	2	8	no	—
301	H(5,𝔽₂)	—	2	8	no	—
302	H(5,𝔽₂)	—	2	8	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	3	no	—
306	C₂×#41	C₂³×C₁₃	1	3	yes	—
307	C₂×#41	C₂³×C₁₃	1	6	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	C₂³×C₁₃	1	3	yes	—
312	C₂²×D₄	—	2	6	no	—
313	C₂²×D₄	—	2	3	no	—
314	C₂²×D₄	—	2	6	no	—
315	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
316	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
317	#137	—	2	24	no	—
318	AGL(1,ℤ/8)	—	2	24	no	—
319	AGL(1,ℤ/8)	—	2	24	no	—
320	AGL(1,ℤ/8)	—	2	24	no	—
321	#135	—	2	24	no	—
322	#135	—	2	24	no	—
323	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
324	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
325	C₂×SD₁₆	—	2	24	no	—
326	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
327	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
328	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
329	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
330	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
331	C₂×D₈	—	2	24	no	—
332	C₂×D₈	C₂³×C₁₃	1	6	yes	—
333	C₂×D₈	C₂³×C₁₃	1	12	yes	—
334	C₂×D₈	C₂³×C₁₃	1	6	yes	—
335	#131	D₄×C₁₃	1	16	yes	complemented
336	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
337	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
338	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
340	#127	—	2	6	no	—
341	#127	C₂³×C₁₃	1	3	yes	—
342	#127	C₂³×C₁₃	1	6	yes	—
343	#127	C₂³×C₁₃	1	3	yes	—
344	#124	—	2	6	no	—
345	#124	C₂³×C₁₃	1	3	yes	—
346	#124	C₂³×C₁₃	1	6	yes	—
347	#124	C₂³×C₁₃	1	1	yes	characteristic
348	#124	C₂³×C₁₃	1	6	yes	—
349	#123	—	2	6	no	—
350	C₂²⋊Q₈	—	2	6	no	—
351	#121	—	2	6	no	—
352	#121	—	2	6	no	—
353	#121	—	2	12	no	—
354	#121	—	2	6	no	—
355	#120	—	2	12	no	—
356	#120	—	2	6	no	—
357	C₄×Q₈	D₄×C₁₃	1	2	yes	—
358	C₄×D₄	—	2	6	no	—
359	C₄×D₄	—	2	6	no	—
360	C₄×D₄	D₄×C₁₃	1	6	yes	—
361	#117	C₂³×C₁₃	1	3	yes	—
362	C₂×C₂²⋊C₄	—	2	6	no	—
363	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
364	#97	C₂³×C₁₃	1	1	yes	characteristic
365	#97	C₂³×C₁₃	1	3	yes	—
366	#97	C₂³×C₁₃	1	6	yes	—
367	C₄×C₈	C₂³×C₁₃	1	6	yes	—
368	C₂×C₁₃	—	2	6	no	—
369	C₂×C₁₃	—	8	1	no	—
370	C₂×C₁₃	—	8	6	no	—
371	C₂×C₁₃	—	8	3	no	—
372	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
373	C₂×C₁₃	#3585	1	2	yes	—
374	C₂⁴	—	2	3	no	—
375	C₂⁴	—	2	6	no	—
376	#41	—	2	12	no	—
377	#41	—	2	12	no	—
378	#41	—	2	12	no	—
379	#41	—	2	12	no	—
380	#41	—	4	4	no	—
381	#41	—	4	8	no	—
382	#41	—	4	12	no	—
383	#41	C₂×D₄×C₁₃	1	8	yes	—
384	C₂×Q₈	—	2	3	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
389	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂×D₄	—	2	6	no	—
392	C₂×D₄	—	2	3	no	—
393	C₂×D₄	—	2	3	no	—
394	C₂×D₄	—	2	12	no	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	2	12	no	—
397	C₂×D₄	—	2	6	no	—
398	C₂×D₄	—	2	3	no	—
399	C₂×D₄	—	2	6	no	—
400	C₂×D₄	—	2	6	no	—
401	C₂×D₄	—	2	12	no	—
402	C₂×D₄	—	4	24	no	—
403	C₂×D₄	—	4	12	no	—
404	C₂×D₄	—	8	12	no	—
405	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
406	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
407	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
408	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
409	C₂²×C₄	—	2	3	no	—
410	C₂²×C₄	—	2	6	no	—
411	C₂²×C₄	—	2	3	no	—
412	C₂²×C₄	—	2	3	no	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
415	Q₁₆	—	2	4	no	—
416	Q₁₆	—	2	12	no	—
417	SD₁₆	—	2	12	no	—
418	SD₁₆	—	2	24	no	—
419	SD₁₆	—	2	4	no	—
420	SD₁₆	—	2	12	no	—
421	SD₁₆	—	2	12	no	—
422	D₈	—	2	12	no	—
423	D₈	—	2	24	no	—
424	D₈	—	2	12	no	—
425	M₁₆	C₂×D₄×C₁₃	1	24	yes	complemented
426	C₂×C₈	C₂×D₄×C₁₃	1	24	yes	complemented
427	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
428	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	6	no	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
432	C₂²⋊C₄	—	2	6	no	—
433	C₂²⋊C₄	—	2	12	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	12	no	—
436	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
437	C₄²	C₂×D₄×C₁₃	1	6	yes	—
438	C₄²	C₂⁴×C₁₃	1	3	yes	—
439	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₁₃	#60650	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³	—	2	3	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	6	no	—
444	C₂³	—	4	6	no	—
445	C₂³	—	4	12	no	—
446	C₂³	—	8	12	no	—
447	C₂³	—	8	6	no	—
448	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
449	Q₈	—	2	6	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	6	no	—
454	Q₈	C₁₃×#127	1	4	yes	—
455	D₄	—	2	6	no	—
456	D₄	—	2	6	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	6	no	—
459	D₄	—	4	12	no	—
460	D₄	—	4	12	no	—
461	D₄	—	4	6	no	—
462	D₄	—	4	6	no	—
463	D₄	—	4	6	no	—
464	D₄	—	4	12	no	—
465	D₄	—	8	12	no	—
466	D₄	—	8	6	no	—
467	D₄	C₁₃×#127	1	12	yes	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	3	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	6	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	4	12	no	—
474	C₂×C₄	—	4	6	no	—
475	C₂×C₄	—	4	6	no	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
480	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
481	C₈	C₂²×D₄×C₁₃	1	4	yes	—
482	C₈	C₂²×D₄×C₁₃	1	12	yes	—
483	C₂²	—	2	6	no	—
484	C₂²	—	4	12	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	6	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	3	no	—
489	C₂²	—	4	6	no	—
490	C₂²	—	16	12	no	—
491	C₂²	—	16	6	no	—
492	C₂²	C₂×C₁₃×#127	1	6	yes	—
493	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	6	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	3	no	—
499	C₄	C₂×C₁₃×#127	1	6	yes	—
500	C₄	C₂³×D₄×C₁₃	1	2	yes	—
501	C₂	—	2	6	no	—
502	C₂	—	8	6	no	—
503	C₂	—	8	3	no	—
504	C₂	—	8	1	no	—
505	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
506	C₂	C₁₃×#3585	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. C₂×C₁₃×#577	C₂	semidirect
2. C₂×C₁₃×#576	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3498	C₂	semidirect
5. C₁₃×#3155	C₂	semidirect
6. C₁₃×#3154	C₂	semidirect
7. C₁₃×#3153	C₂	semidirect
8. C₁₃×#3151	C₂	semidirect
9. C₁₃×#3150	C₂	semidirect
10. C₂×C₁₃×#496	C₂	semidirect
11. C₁₃×#2875	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
24. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₁₃×#536	C₂²	semidirect
31. C₁₃×#535	C₂²	semidirect
32. C₁₃×#535	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×#127	C₂²	semidirect
36. C₂×C₁₃×#124	C₂²	semidirect
38. C₁₃×#497	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#497	C₂²	semidirect
41. C₁₃×#496	C₂²	semidirect
42. C₁₃×#496	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#496	C₂²	semidirect
45. C₁₃×#496	C₂²	semidirect
46. C₁₃×#495	C₂²	semidirect
47. C₁₃×#493	C₂²	semidirect
48. C₁₃×#492	C₂²	semidirect
49. C₁₃×#405	C₂²	semidirect
50. C₄×C₁₃×M₁₆	C₂²	semidirect
51. C₂×C₁₃×#97	C₂²	semidirect
88. C₁₃×#131	D₄	semidirect
121. #60650	C₁₃	direct (N × H)
173. C₁₃×M₁₆	C₂×D₄	semidirect
174. C₂×C₈×C₁₃	C₂×D₄	semidirect
188. C₂×#577	C₂×C₁₃	semidirect
189. C₂×#576	C₂×C₁₃	semidirect
190. #3500	C₂×C₁₃	semidirect
191. #3498	C₂×C₁₃	semidirect
192. #3155	C₂×C₁₃	semidirect
193. #3154	C₂×C₁₃	semidirect
194. #3153	C₂×C₁₃	semidirect
195. #3151	C₂×C₁₃	semidirect
196. #3150	C₂×C₁₃	semidirect
197. C₂×#496	C₂×C₁₃	semidirect
198. #2875	C₂×C₁₃	semidirect
246. C₂×#137	C₂²×C₁₃	semidirect
247. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
248. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
249. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
250. C₂×#135	C₂²×C₁₃	semidirect
251. C₂×#135	C₂²×C₁₃	semidirect
252. C₂²×SD₁₆	C₂²×C₁₃	semidirect
253. C₂²×D₈	C₂²×C₁₃	semidirect
259. #536	C₂²×C₁₃	semidirect
260. #535	C₂²×C₁₃	semidirect
261. #535	C₂²×C₁₃	semidirect
262. #532	C₂²×C₁₃	semidirect
263. #532	C₂²×C₁₃	semidirect
264. C₂×#127	C₂²×C₁₃	semidirect
265. C₂×#124	C₂²×C₁₃	semidirect
267. #497	C₂²×C₁₃	semidirect
268. #497	C₂²×C₁₃	semidirect
269. #497	C₂²×C₁₃	semidirect
270. #496	C₂²×C₁₃	semidirect
271. #496	C₂²×C₁₃	semidirect
272. #496	C₂²×C₁₃	semidirect
273. #496	C₂²×C₁₃	semidirect
274. #496	C₂²×C₁₃	semidirect
275. #495	C₂²×C₁₃	semidirect
276. #493	C₂²×C₁₃	semidirect
277. #492	C₂²×C₁₃	semidirect
278. #405	C₂²×C₁₃	semidirect
279. C₄×M₁₆	C₂²×C₁₃	semidirect
280. C₂×#97	C₂²×C₁₃	semidirect
335. #131	D₄×C₁₃	semidirect
425. M₁₆	C₂×D₄×C₁₃	semidirect
426. C₂×C₈	C₂×D₄×C₁₃	semidirect
440. C₁₃	#60650	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#577	2
C₂×C₁₃×#576	2
C₁₃×#3500	2
C₁₃×#3498	2
C₁₃×#3155	2
C₁₃×#3154	2
C₁₃×#3153	2
C₁₃×#3151	2
C₁₃×#3150	2
C₂×C₁₃×#496	2
C₁₃×#2875	2
#60650	13

Subgroups — C13×#60650 #15746989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60650 #15746989