Subgroups — C₁₃×#24747 #15711086

Order 3328.

968 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	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×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#464	—	2	8	no	—
20	C₁₃×#460	—	2	4	no	—
21	C₁₃×#441	—	2	4	no	—
22	C₂×C₁₃×#106	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×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
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	—	2	2	no	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#382	—	2	1	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×SD₁₆	—	2	4	no	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×#124	—	2	4	no	—
61	C₁₃×#124	—	4	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	4	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	4	2	no	—
67	C₄×Q₈×C₁₃	D₄	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	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×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	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×#106	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	4	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	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	2	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	D₄	1	1	yes	characteristic
99	C₁₃×#95	D₄	1	1	yes	characteristic
100	#24747	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	1	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	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₁₃	#41	1	2	yes	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂×D₄×C₁₃	—	8	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	2	8	no	—
135	C₁₃×SD₁₆	—	4	8	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₁₃×C₂²⋊C₄	—	8	2	no	—
159	C₁₃×C₂²⋊C₄	—	8	2	no	—
160	C₄²×C₁₃	—	2	4	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	4	4	no	—
164	C₄²×C₁₃	—	4	2	no	—
165	C₄²×C₁₃	C₂×D₄	1	2	yes	—
166	C₄²×C₁₃	#41	1	2	yes	—
167	C₂×#464	C₂×C₁₃	1	2	yes	complemented
168	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
169	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2548	C₂×C₁₃	1	1	yes	characteristic
171	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2065	C₂×C₁₃	1	2	yes	complemented
173	#2042	C₂×C₁₃	1	2	yes	complemented
174	#1961	C₂×C₁₃	1	1	yes	characteristic
175	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1880	C₂×C₁₃	1	2	yes	complemented
177	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	2	2	no	—
191	Q₈×C₁₃	—	4	1	no	—
192	Q₈×C₁₃	—	4	1	no	—
193	Q₈×C₁₃	#121	1	4	yes	—
194	D₄×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	4	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	8	4	no	—
199	D₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
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	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	#121	1	2	yes	—
222	C₂×C₄×C₁₃	#121	1	2	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₈×C₁₃	—	4	1	no	—
232	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
234	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#124	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	#464	—	2	8	no	—
240	#460	—	2	4	no	—
241	#441	—	2	4	no	—
242	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×#103	C₂²×C₁₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
252	#394	—	2	1	no	—
253	#394	—	2	1	no	—
254	#390	—	2	2	no	—
255	#390	C₂²×C₁₃	1	2	yes	—
256	#389	—	2	2	no	—
257	#389	C₂²×C₁₃	1	2	yes	—
258	#382	—	2	1	no	—
259	#382	C₂²×C₁₃	1	1	yes	characteristic
260	C₄×C₄⋊C₄	—	2	1	no	—
261	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	#340	C₂²×C₁₃	1	2	yes	—
263	#336	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	8	2	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	—	8	2	no	—
270	C₂²×C₁₃	—	8	2	no	—
271	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
272	C₂²×C₁₃	D₄²	1	1	yes	characteristic
273	C₂²×C₁₃	#548	1	1	yes	characteristic
274	C₂²×C₁₃	#575	1	2	yes	—
275	C₂²×C₁₃	#577	1	2	yes	—
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	—	8	1	no	—
285	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
286	C₄×C₁₃	#537	1	1	yes	characteristic
287	C₄×C₁₃	#547	1	1	yes	characteristic
288	C₄×C₁₃	#553	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	#127	—	2	2	no	—
304	#127	—	2	2	no	—
305	#124	—	2	4	no	—
306	#124	—	4	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	4	2	no	—
312	C₄×Q₈	D₄×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	#106	—	2	2	no	—
331	C₄⋊C₈	—	2	4	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#103	—	2	2	no	—
334	#103	—	2	4	no	—
335	#103	—	2	2	no	—
336	#102	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	4	2	no	—
339	#97	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	1	no	—
343	#95	D₄×C₁₃	1	1	yes	characteristic
344	#95	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₁₃	—	16	2	no	—
346	C₂×C₁₃	#2416	1	1	yes	characteristic
347	C₂×C₁₃	#3040	1	1	yes	characteristic
348	C₂×C₁₃	#3043	1	1	yes	characteristic
349	C₂×C₁₃	#3271	1	2	yes	—
350	C₂×C₁₃	#3371	1	2	yes	—
351	C₂⁴	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
363	C₂×Q₈	C₁₃×#41	1	2	yes	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	SD₁₆	—	4	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	4	4	no	—
414	C₄²	—	4	2	no	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₁₃×#41	1	2	yes	—
417	C₁₃	#24747	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	2	2	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	C₁₃×#121	1	4	yes	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	8	4	no	—
439	D₄	—	8	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	C₁₃×#121	1	2	yes	—
462	C₂×C₄	C₁₃×#121	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
467	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	2	no	—
471	C₈	—	4	1	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
480	C₂²	D₄²×C₁₃	1	1	yes	characteristic
481	C₂²	C₁₃×#548	1	1	yes	characteristic
482	C₂²	C₁₃×#575	1	2	yes	—
483	C₂²	C₁₃×#577	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	1	no	—
493	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
494	C₄	C₁₃×#537	1	1	yes	characteristic
495	C₄	C₁₃×#547	1	1	yes	characteristic
496	C₄	C₁₃×#553	1	1	yes	characteristic
497	C₂	—	16	2	no	—
498	C₂	C₁₃×#2416	1	1	yes	characteristic
499	C₂	C₁₃×#3040	1	1	yes	characteristic
500	C₂	C₁₃×#3043	1	1	yes	characteristic
501	C₂	C₁₃×#3271	1	2	yes	—
502	C₂	C₁₃×#3371	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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×#464	C₂	semidirect
3. C₂×C₁₃×#441	C₂	semidirect
5. C₁₃×#2351	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#2042	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1880	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
51. C₂×C₁₃×Q₁₆	D₄	semidirect
100. #24747	C₁₃	direct (N × H)
167. C₂×#464	C₂×C₁₃	semidirect
169. C₂×#441	C₂×C₁₃	semidirect
171. #2351	C₂×C₁₃	semidirect
172. #2065	C₂×C₁₃	semidirect
173. #2042	C₂×C₁₃	semidirect
175. #1940	C₂×C₁₃	semidirect
176. #1880	C₂×C₁₃	semidirect
177. #1805	C₂×C₁₃	semidirect
296. C₂×Q₁₆	D₄×C₁₃	semidirect
417. C₁₃	#24747	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×#464	2
C₂×C₁₃×#460	2
C₂×C₁₃×#441	2
C₁₃×#2548	2
C₁₃×#2351	2
C₁₃×#2065	2
C₁₃×#2042	2
C₁₃×#1961	2
C₁₃×#1940	2
C₁₃×#1880	2
C₁₃×#1805	2
#24747	13

Subgroups — C13×#24747 #15711086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24747 #15711086