Subgroups — C₁₃×#24749 #15711088

Order 3328.

1044 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#463	—	2	8	no	—
20	C₁₃×#459	—	2	4	no	—
21	C₁₃×#440	—	2	4	no	—
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₁₃×#394	—	2	1	no	—
33	C₁₃×#394	—	2	1	no	—
34	C₁₃×#390	—	2	2	no	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	2	yes	—
37	C₁₃×#385	—	2	2	no	—
38	C₁₃×#382	C₂²	1	1	yes	characteristic
39	C₁₃×#380	—	2	1	no	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#95	—	2	1	no	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
54	C₂×C₁₃×D₈	—	2	4	no	—
55	C₂×C₁₃×D₈	—	2	4	no	—
56	C₂×C₁₃×D₈	—	2	4	no	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#127	—	2	2	no	—
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#124	—	2	4	no	—
63	C₁₃×#124	—	4	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	4	2	no	—
69	C₄×D₄×C₁₃	D₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#107	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	4	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#102	—	4	2	no	—
94	C₁₃×#97	—	2	2	no	—
95	C₁₃×#95	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	D₄	1	1	yes	characteristic
99	C₁₃×#95	D₄	1	1	yes	characteristic
100	#24749	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	1	no	—
102	C₂⁴×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	4	4	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	—	8	2	no	—
122	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₃	#41	1	2	yes	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	4	4	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	8	2	no	—
133	C₂²×C₄×C₁₃	—	8	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×SD₁₆	—	2	8	no	—
140	C₁₃×D₈	—	4	8	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	4	2	no	—
157	C₁₃×C₄⋊C₄	—	8	2	no	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₁₃×C₂²⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	8	2	no	—
164	C₁₃×C₂²⋊C₄	—	8	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	4	2	no	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₃	#41	1	2	yes	—
170	C₂×#463	C₂×C₁₃	1	2	yes	complemented
171	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
172	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2548	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2067	C₂×C₁₃	1	2	yes	complemented
176	#2042	C₂×C₁₃	1	2	yes	complemented
177	#1961	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1879	C₂×C₁₃	1	2	yes	complemented
180	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	2	no	—
196	Q₈×C₁₃	—	4	1	no	—
197	Q₈×C₁₃	—	4	1	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	—	2	2	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	4	2	no	—
202	D₄×C₁₃	—	4	2	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	8	4	no	—
206	D₄×C₁₃	—	8	4	no	—
207	D₄×C₁₃	#121	1	4	yes	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	8	4	no	—
227	C₂×C₄×C₁₃	—	8	8	no	—
228	C₂×C₄×C₁₃	#121	1	2	yes	—
229	C₂×C₄×C₁₃	#121	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₈×C₁₃	—	4	1	no	—
239	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
241	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#124	C₂²×C₁₃	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	#463	—	2	8	no	—
247	#459	—	2	4	no	—
248	#440	—	2	4	no	—
249	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
252	C₂×#103	C₂²×C₁₃	1	2	yes	—
253	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#102	C₂²×C₁₃	1	2	yes	—
255	C₂×#102	C₂²×C₁₃	1	2	yes	—
256	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃	1	2	yes	—
258	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
259	#394	—	2	1	no	—
260	#394	—	2	1	no	—
261	#390	—	2	2	no	—
262	#390	C₂²×C₁₃	1	2	yes	—
263	#389	C₂²×C₁₃	1	2	yes	—
264	#385	—	2	2	no	—
265	#382	C₂²×C₁₃	1	1	yes	characteristic
266	#380	—	2	1	no	—
267	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#95	—	2	1	no	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	#336	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₁₃	—	2	4	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	8	2	no	—
277	C₂²×C₁₃	—	8	2	no	—
278	C₂²×C₁₃	—	8	2	no	—
279	C₂²×C₁₃	—	8	2	no	—
280	C₂²×C₁₃	—	8	2	no	—
281	C₂²×C₁₃	—	8	2	no	—
282	C₂²×C₁₃	—	8	2	no	—
283	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
284	C₂²×C₁₃	D₄²	1	1	yes	characteristic
285	C₂²×C₁₃	#548	1	1	yes	characteristic
286	C₂²×C₁₃	#575	1	2	yes	—
287	C₂²×C₁₃	#576	1	2	yes	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	8	2	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
297	C₄×C₁₃	#537	1	1	yes	characteristic
298	C₄×C₁₃	#547	1	1	yes	characteristic
299	C₄×C₁₃	#553	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
310	C₂×D₈	—	2	4	no	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
316	#127	—	2	2	no	—
317	#127	—	2	2	no	—
318	#124	—	2	4	no	—
319	#124	—	4	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	4	2	no	—
325	C₄×D₄	D₄×C₁₃	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	C₄⋊C₈	—	2	4	no	—
343	C₄⋊C₈	—	2	2	no	—
344	#103	—	2	4	no	—
345	#103	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	#102	—	4	2	no	—
350	#97	—	2	2	no	—
351	#95	—	2	1	no	—
352	#95	—	2	2	no	—
353	#95	—	2	1	no	—
354	#95	D₄×C₁₃	1	1	yes	characteristic
355	#95	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₁₃	—	4	4	no	—
357	C₂×C₁₃	—	16	2	no	—
358	C₂×C₁₃	#2416	1	1	yes	characteristic
359	C₂×C₁₃	#3040	1	1	yes	characteristic
360	C₂×C₁₃	#3041	1	1	yes	characteristic
361	C₂×C₁₃	#3268	1	2	yes	—
362	C₂×C₁₃	#3370	1	2	yes	—
363	C₂⁴	—	2	1	no	—
364	C₂⁴	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂×D₄	C₁₃×#41	1	2	yes	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	8	2	no	—
395	C₂²×C₄	—	8	2	no	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	SD₁₆	—	2	8	no	—
402	D₈	—	4	8	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	8	2	no	—
420	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	8	2	no	—
426	C₂²⋊C₄	—	8	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	4	2	no	—
430	C₄²	C₂×D₄×C₁₃	1	2	yes	—
431	C₄²	C₁₃×#41	1	2	yes	—
432	C₁₃	#24749	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	4	no	—
459	D₄	C₁₃×#121	1	4	yes	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	—	8	8	no	—
480	C₂×C₄	C₁₃×#121	1	2	yes	—
481	C₂×C₄	C₁₃×#121	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
486	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
504	C₂²	D₄²×C₁₃	1	1	yes	characteristic
505	C₂²	C₁₃×#548	1	1	yes	characteristic
506	C₂²	C₁₃×#575	1	2	yes	—
507	C₂²	C₁₃×#576	1	2	yes	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	2	no	—
515	C₄	—	8	1	no	—
516	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
517	C₄	C₁₃×#537	1	1	yes	characteristic
518	C₄	C₁₃×#547	1	1	yes	characteristic
519	C₄	C₁₃×#553	1	1	yes	characteristic
520	C₂	—	4	4	no	—
521	C₂	—	16	2	no	—
522	C₂	C₁₃×#2416	1	1	yes	characteristic
523	C₂	C₁₃×#3040	1	1	yes	characteristic
524	C₂	C₁₃×#3041	1	1	yes	characteristic
525	C₂	C₁₃×#3268	1	2	yes	—
526	C₂	C₁₃×#3370	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#463	C₂	semidirect
3. C₂×C₁₃×#440	C₂	semidirect
4. C₁₃×#2548	C₂	semidirect
5. C₁₃×#2349	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2042	C₂	semidirect
8. C₁₃×#1961	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
53. C₂×C₁₃×SD₁₆	D₄	semidirect
100. #24749	C₁₃	direct (N × H)
170. C₂×#463	C₂×C₁₃	semidirect
172. C₂×#440	C₂×C₁₃	semidirect
173. #2548	C₂×C₁₃	semidirect
174. #2349	C₂×C₁₃	semidirect
175. #2067	C₂×C₁₃	semidirect
176. #2042	C₂×C₁₃	semidirect
177. #1961	C₂×C₁₃	semidirect
178. #1940	C₂×C₁₃	semidirect
179. #1879	C₂×C₁₃	semidirect
180. #1805	C₂×C₁₃	semidirect
309. C₂×SD₁₆	D₄×C₁₃	semidirect
432. C₁₃	#24749	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×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#440	2
C₁₃×#2548	2
C₁₃×#2349	2
C₁₃×#2067	2
C₁₃×#2042	2
C₁₃×#1961	2
C₁₃×#1940	2
C₁₃×#1879	2
C₁₃×#1805	2
#24749	13

Subgroups — C13×#24749 #15711088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24749 #15711088