Subgroups — #15869851

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124556	C₂	1	1	yes	maximal, characteristic
2	#13123735	C₂	1	2	yes	maximal, complemented
3	C₂×#11718556	C₂	1	1	yes	maximal, characteristic, complemented
4	#131×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115732	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115624	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115503	C₂	1	2	yes	maximal, complemented
8	#13115335	C₂	1	2	yes	maximal, complemented
9	#13114717	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114635	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	#41×Dic₁₃	C₂²	1	1	yes	characteristic
14	#11719527	C₂²	1	2	yes	—
15	C₂×#88202	C₂²	1	1	yes	characteristic
16	C₂×#88161	C₂²	1	2	yes	—
17	C₂×#88158	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₁₃×#427	C₂²	1	1	yes	characteristic
20	C₁₃×#421	C₂²	1	2	yes	—
21	#11718804	C₄	1	2	yes	complemented
22	#11718803	C₄	1	2	yes	complemented
23	#11718802	C₄	1	4	yes	complemented
24	C₂×#88065	C₂²	1	2	yes	—
25	#11718793	C₂²	1	2	yes	—
26	#11718785	C₂²	1	2	yes	—
27	#11718783	—	2	1	no	—
28	#11718783	C₂²	1	1	yes	characteristic
29	M₁₆×Dic₁₃	—	2	1	no	—
30	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂×#88059	C₂²	1	1	yes	characteristic
32	#11718762	—	2	1	no	—
33	#11718762	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₁₃	—	2	1	no	—
35	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
36	#11718667	C₂²	1	2	yes	—
37	#11718666	C₂²	1	2	yes	—
38	#11718658	C₂²	1	2	yes	—
39	#11718556	—	2	1	no	—
40	#11718556	—	2	1	no	—
41	#11718556	—	2	1	no	—
42	#11718556	—	2	1	no	—
43	#11718485	—	2	4	no	—
44	#11718484	—	2	4	no	—
45	C₁₃×#344	C₂²	1	2	yes	—
46	#11718148	C₂²	1	2	yes	—
47	#11718124	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂×#6127	C₂³	1	2	yes	—
50	C₁₃×#131	—	2	1	no	—
51	C₁₃×#131	—	2	1	no	—
52	C₁₃×#131	C₂×C₄	1	2	yes	—
53	C₁₃×#131	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	C₂³	1	2	yes	—
60	#88205	C₂×C₄	1	4	yes	—
61	#88204	—	2	4	no	—
62	#88203	C₂×C₄	1	4	yes	—
63	#88202	—	2	1	no	—
64	#88202	—	2	1	no	—
65	#88202	D₄	1	2	yes	—
66	#88202	D₄	1	2	yes	—
67	Q₈×Dic₁₃	—	2	1	no	—
68	#88196	—	2	2	no	—
69	D₄×Dic₁₃	—	2	1	no	—
70	D₄×Dic₁₃	—	2	2	no	—
71	#88186	—	2	2	no	—
72	#88180	—	2	1	no	—
73	#88180	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₁₃	—	2	1	no	—
75	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂×#6099	C₂³	1	1	yes	characteristic
79	C₂²×#1055	—	2	1	no	—
80	C₂²×#1055	C₂³	1	1	yes	characteristic
81	#88161	—	2	2	no	—
82	#88161	—	2	2	no	—
83	#88161	—	2	2	no	—
84	#88161	—	2	2	no	—
85	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
86	#88158	—	2	1	no	—
87	#88158	—	2	1	no	—
88	#88158	—	2	1	no	—
89	#88158	—	2	1	no	—
90	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂×#6095	C₂×C₄	1	2	yes	complemented
92	C₂×#6094	—	2	2	no	—
93	C₂×C₈×D₁₃	—	2	2	no	—
94	C₁₃×#108	—	2	1	no	—
95	C₁₃×#108	—	2	1	no	—
96	C₁₃×#107	—	2	1	no	—
97	C₁₃×#106	—	2	1	no	—
98	C₁₃×#104	—	2	4	no	—
99	#88065	—	2	2	no	—
100	#88065	—	2	2	no	—
101	#88064	C₂×C₄	1	4	yes	complemented
102	#88063	C₂×C₄	1	4	yes	complemented
103	#88062	—	2	4	no	—
104	#88059	C₂×C₄	1	2	yes	complemented
105	#88059	C₂×C₄	1	2	yes	complemented
106	#88055	—	2	1	no	—
107	#88055	—	2	1	no	—
108	#88055	—	2	1	no	—
109	C₈×Dic₁₃	—	2	1	no	—
110	C₈×Dic₁₃	—	2	1	no	—
111	C₈×Dic₁₃	—	2	1	no	—
112	C₈×Dic₁₃	D₄	1	1	yes	characteristic
113	C₈×Dic₁₃	D₄	1	1	yes	characteristic
114	C₈×Dic₁₃	D₄	1	1	yes	characteristic
115	C₈×Dic₁₃	D₄	1	1	yes	characteristic
116	#88046	—	2	4	no	—
117	#88045	—	2	4	no	—
118	#88043	—	2	2	no	—
119	C₄×#1055	—	2	2	no	—
120	#21558	—	13	1	no	maximal, Sylow
121	C₁₃×#41	—	2	1	no	—
122	C₁₃×#41	—	2	1	no	—
123	C₁₃×#41	C₂²×C₄	1	2	yes	—
124	C₁₃×#41	C₂×D₄	1	2	yes	—
125	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	—	2	2	no	—
131	C₂²×Dic₁₃	—	2	2	no	—
132	C₂²×Dic₁₃	—	2	1	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	#6127	—	2	2	no	—
136	#6127	—	2	2	no	—
137	C₂×D₅₂	C₂²×C₄	1	2	yes	—
138	C₂×C₄×D₁₃	—	2	2	no	—
139	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
140	C₁₃×M₁₆	—	2	1	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
155	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₂²⋊Dic₁₃	—	2	2	no	—
160	C₂²⋊Dic₁₃	#41	1	2	yes	—
161	#6107	—	2	4	no	—
162	#6106	—	2	4	no	—
163	#6105	—	2	4	no	—
164	#6104	—	2	4	no	—
165	C₄⋊Dic₁₃	—	2	2	no	—
166	C₄⋊Dic₁₃	—	2	1	no	—
167	C₄×Dic₁₃	—	2	2	no	—
168	C₄×Dic₁₃	—	2	1	no	—
169	C₄×Dic₁₃	—	2	1	no	—
170	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
172	#6099	—	2	2	no	—
173	#6099	—	2	1	no	—
174	#6099	—	2	2	no	—
175	#6099	—	2	2	no	—
176	#6099	C₂²×C₄	1	4	yes	—
177	#6099	C₂×D₄	1	2	yes	—
178	C₂×#1055	—	2	1	no	—
179	C₂×#1055	—	2	2	no	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	C₂×D₄	1	1	yes	characteristic
183	C₂×#1055	C₂×D₄	1	1	yes	characteristic
184	C₂×#1055	C₂×D₄	1	1	yes	characteristic
185	C₂×#1055	C₂×D₄	1	1	yes	characteristic
186	C₂×#1055	#41	1	1	yes	characteristic
187	C₂×#1055	#41	1	1	yes	characteristic
188	Dic₅₂	—	2	1	no	—
189	Dic₅₂	—	2	1	no	—
190	D₁₀₄	—	2	1	no	—
191	D₁₀₄	—	2	1	no	—
192	#6095	—	2	2	no	—
193	#6095	—	2	2	no	—
194	#6094	—	4	2	no	—
195	#6094	—	4	2	no	—
196	C₈×D₁₃	—	4	2	no	—
197	C₈×D₁₃	—	4	2	no	—
198	#3067	—	13	1	no	—
199	#2955	—	13	2	no	—
200	C₂×#443	—	13	1	no	—
201	C₄×#131	—	13	1	no	—
202	#1976	—	13	1	no	—
203	#1953	—	13	1	no	—
204	#1932	—	13	2	no	—
205	#1906	—	13	2	no	—
206	#1814	D₁₃	1	1	yes	characteristic, complemented
207	#1772	—	13	1	no	—
208	#1757	—	13	2	no	—
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂²×D₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	2	1	no	—
213	Q₈×C₁₃	C₄×D₄	1	2	yes	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	1	no	—
217	D₄×C₁₃	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
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	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₁₃	—	4	2	no	—
229	C₂²⋊D₁₃	—	4	2	no	—
230	C₂×Dic₁₃	—	2	1	no	—
231	C₂×Dic₁₃	—	2	2	no	—
232	C₂×Dic₁₃	—	2	2	no	—
233	C₂×Dic₁₃	—	2	1	no	—
234	C₂×Dic₁₃	—	4	2	no	—
235	C₂×Dic₁₃	—	4	4	no	—
236	D₅₂	—	2	2	no	—
237	D₅₂	—	2	2	no	—
238	C₄×D₁₃	—	4	2	no	—
239	C₄×D₁₃	—	4	2	no	—
240	Dic₂₆	—	2	2	no	—
241	Dic₂₆	—	2	2	no	—
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
245	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
246	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
247	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
248	#1055	—	2	4	no	—
249	#1055	—	2	2	no	—
250	#1055	#121	1	1	yes	characteristic
251	#1055	#121	1	1	yes	characteristic
252	#1055	#121	1	1	yes	characteristic
253	#1055	#121	1	1	yes	characteristic
254	#575	—	13	2	no	—
255	C₂×#135	—	13	1	no	—
256	C₂×#131	—	13	1	no	—
257	C₂×#131	—	13	2	no	—
258	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
259	C₄×#41	—	13	1	no	—
260	#473	—	13	2	no	—
261	#472	—	13	2	no	—
262	#471	—	13	4	no	—
263	#444	—	26	4	no	—
264	#443	—	26	1	no	—
265	#443	—	26	1	no	—
266	#443	—	26	1	no	—
267	#443	—	26	1	no	—
268	#443	—	26	4	no	—
269	#430	—	13	2	no	—
270	C₂×#108	—	13	1	no	—
271	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
272	#427	C₂×D₁₃	1	1	yes	characteristic
273	#421	—	13	2	no	—
274	#421	C₂×D₁₃	1	2	yes	—
275	C₂×#104	—	13	2	no	—
276	#413	—	13	2	no	—
277	#410	—	13	2	no	—
278	#405	—	13	1	no	—
279	#405	—	13	1	no	—
280	#405	—	13	2	no	—
281	#405	—	26	1	no	—
282	#405	—	26	1	no	—
283	C₄×M₁₆	—	13	1	no	—
284	C₄×M₁₆	—	26	1	no	—
285	C₂×C₄×C₈	—	13	1	no	—
286	C₂×C₄×C₈	—	26	1	no	—
287	#344	—	13	2	no	—
288	#344	C₂×D₁₃	1	2	yes	—
289	#339	—	13	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
294	C₂²×C₁₃	#525	1	1	yes	characteristic
295	C₂²×C₁₃	#532	1	1	yes	characteristic
296	C₂×D₁₃	—	4	2	no	—
297	C₂×D₁₃	—	8	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	8	2	no	—
300	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
301	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
303	C₄×C₁₃	#529	1	1	yes	characteristic
304	Dic₁₃	—	2	2	no	—
305	Dic₁₃	—	4	2	no	—
306	Dic₁₃	—	4	1	no	—
307	Dic₁₃	—	4	2	no	—
308	C₂×#41	—	13	2	no	—
309	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
310	#137	—	13	4	no	—
311	#137	—	26	2	no	—
312	AGL(1,ℤ/8)	—	13	4	no	—
313	AGL(1,ℤ/8)	—	26	2	no	—
314	#135	—	26	4	no	—
315	#135	—	26	1	no	—
316	#135	—	26	1	no	—
317	#135	—	26	1	no	—
318	#135	—	26	1	no	—
319	C₂×Q₁₆	—	13	1	no	—
320	C₂×SD₁₆	—	13	2	no	—
321	C₂×D₈	—	13	1	no	—
322	#131	—	2	1	no	—
323	#131	—	2	1	no	—
324	#131	—	13	2	no	—
325	#131	—	13	2	no	—
326	#131	—	26	1	no	—
327	#131	—	26	1	no	—
328	#131	—	26	2	no	—
329	#131	—	26	2	no	—
330	#131	—	26	2	no	—
331	#131	—	26	2	no	—
332	#131	C₄×D₁₃	1	2	yes	—
333	#131	C₄×D₁₃	1	2	yes	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	13	1	no	—
336	C₂×M₁₆	—	13	2	no	—
337	C₂×M₁₆	—	26	2	no	—
338	C₂×M₁₆	—	26	1	no	—
339	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
340	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	13	1	no	—
343	C₂²×C₈	—	26	2	no	—
344	C₂²×C₈	—	26	1	no	—
345	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
346	C₄×Q₈	—	26	1	no	—
347	C₄×D₄	—	26	2	no	—
348	C₄×D₄	—	26	1	no	—
349	#117	—	13	1	no	—
350	#117	—	26	1	no	—
351	#117	C₂²×D₁₃	1	2	yes	—
352	C₂×C₄²	—	13	1	no	—
353	C₂×C₄²	—	26	1	no	—
354	#108	—	2	1	no	—
355	#108	—	2	1	no	—
356	#108	—	13	2	no	—
357	#108	—	13	2	no	—
358	#108	—	26	4	no	—
359	#107	—	2	1	no	—
360	#106	—	2	1	no	—
361	#104	—	2	4	no	—
362	#104	—	26	4	no	—
363	#104	—	26	2	no	—
364	#104	—	26	2	no	—
365	#101	—	13	4	no	—
366	#100	—	13	4	no	—
367	#99	—	26	4	no	—
368	#97	—	26	2	no	—
369	#97	—	26	1	no	—
370	#97	—	26	1	no	—
371	#97	—	26	1	no	—
372	C₄×C₈	—	13	1	no	—
373	C₄×C₈	—	13	1	no	—
374	C₄×C₈	—	13	1	no	—
375	C₄×C₈	—	13	1	no	—
376	C₄×C₈	—	26	2	no	—
377	C₄×C₈	—	26	1	no	—
378	C₄×C₈	—	26	1	no	—
379	C₄×C₈	—	26	1	no	—
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	2	1	no	—
382	C₂×C₁₃	—	2	1	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
385	D₁₃	—	8	2	no	—
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	26	2	no	—
389	#41	—	26	2	no	—
390	#41	—	26	2	no	—
391	#41	—	26	2	no	—
392	#41	C₂×C₄×D₁₃	1	2	yes	—
393	#41	D₄×D₁₃	1	2	yes	—
394	C₂×Q₈	—	13	2	no	—
395	C₂×Q₈	#6131	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	13	2	no	—
398	C₂×D₄	—	26	2	no	—
399	C₂×D₄	#6131	1	1	yes	characteristic
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	26	2	no	—
402	C₂²×C₄	—	26	1	no	—
403	C₂²×C₄	—	26	2	no	—
404	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
405	Q₁₆	—	26	4	no	—
406	Q₁₆	—	26	1	no	—
407	Q₁₆	—	26	1	no	—
408	SD₁₆	—	26	4	no	—
409	SD₁₆	—	26	4	no	—
410	SD₁₆	—	26	2	no	—
411	SD₁₆	—	26	2	no	—
412	D₈	—	26	4	no	—
413	D₈	—	26	1	no	—
414	D₈	—	26	1	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	13	4	no	—
421	M₁₆	—	13	2	no	—
422	M₁₆	—	26	2	no	—
423	M₁₆	—	26	2	no	—
424	M₁₆	—	26	2	no	—
425	M₁₆	—	26	1	no	—
426	M₁₆	—	52	2	no	—
427	M₁₆	—	52	2	no	—
428	M₁₆	C₂×C₄×D₁₃	1	2	yes	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	13	1	no	—
434	C₂×C₈	—	13	1	no	—
435	C₂×C₈	—	13	1	no	—
436	C₂×C₈	—	13	1	no	—
437	C₂×C₈	—	13	1	no	—
438	C₂×C₈	—	13	1	no	—
439	C₂×C₈	—	26	2	no	—
440	C₂×C₈	—	26	2	no	—
441	C₂×C₈	—	26	1	no	—
442	C₂×C₈	—	26	2	no	—
443	C₂×C₈	—	52	2	no	—
444	C₂×C₈	—	52	2	no	—
445	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
446	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
447	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
448	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
449	C₂×C₈	#6129	1	1	yes	characteristic
450	C₂×C₈	#6129	1	1	yes	characteristic
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	26	2	no	—
453	C₄⋊C₄	—	26	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	13	2	no	—
456	C₂²⋊C₄	—	26	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	13	1	no	—
459	C₄²	—	13	1	no	—
460	C₄²	—	26	2	no	—
461	C₄²	—	26	1	no	—
462	C₄²	—	26	1	no	—
463	C₁₃	#21558	1	1	yes	characteristic, complemented, Sylow
464	C₂³	—	2	1	no	—
465	C₂³	—	26	2	no	—
466	C₂³	#41×D₁₃	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	26	2	no	—
469	Q₈	—	26	2	no	—
470	Q₈	#88147	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	26	2	no	—
475	D₄	—	26	2	no	—
476	D₄	—	52	2	no	—
477	D₄	—	52	2	no	—
478	D₄	#88147	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	26	1	no	—
484	C₂×C₄	—	26	2	no	—
485	C₂×C₄	—	26	1	no	—
486	C₂×C₄	—	26	2	no	—
487	C₂×C₄	—	52	2	no	—
488	C₂×C₄	—	52	4	no	—
489	C₂×C₄	—	52	2	no	—
490	C₂×C₄	—	52	2	no	—
491	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#6129	1	1	yes	characteristic
495	C₂×C₄	C₂×#6131	1	1	yes	characteristic
496	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	2	no	—
499	C₈	—	13	1	no	—
500	C₈	—	13	1	no	—
501	C₈	—	13	1	no	—
502	C₈	—	13	1	no	—
503	C₈	—	26	4	no	—
504	C₈	—	26	2	no	—
505	C₈	#88135	1	1	yes	characteristic
506	C₈	#88135	1	1	yes	characteristic
507	C₈	#88135	1	1	yes	characteristic
508	C₈	#88135	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	52	2	no	—
513	C₂²	—	104	2	no	—
514	C₂²	#11719227	1	1	yes	characteristic
515	C₂²	#11719301	1	1	yes	characteristic
516	C₂²	#11719332	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	8	2	no	—
519	C₄	—	26	2	no	—
520	C₄	—	52	1	no	—
521	C₄	—	52	2	no	—
522	C₄	—	52	2	no	—
523	C₄	C₂×#88135	1	1	yes	characteristic
524	C₄	C₂×#88147	1	1	yes	characteristic
525	C₄	D₁₃×#121	1	1	yes	characteristic
526	C₄	#11719329	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	104	2	no	—
532	C₂	#13117342	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#121
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1814	C₂
socle	C₂×C₁₃	C₄×#121
prime radical	#13124556	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1814	D₁₃
hypocenter	C₁₃	#21558
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
2. #13123735	C₂	semidirect
3. C₂×#11718556	C₂	semidirect
4. #131×Dic₁₃	C₂	semidirect
5. #13115732	C₂	semidirect
6. #13115624	C₂	semidirect
7. #13115503	C₂	semidirect
8. #13115335	C₂	semidirect
9. #13114717	C₂	semidirect
10. #13114635	C₂	semidirect
11. C₁₃×#1814	C₂	semidirect
21. #11718804	C₄	semidirect
22. #11718803	C₄	semidirect
23. #11718802	C₄	semidirect
85. C₂×Dic₅₂	C₂×C₄	semidirect
90. C₂×D₁₀₄	C₂×C₄	semidirect
91. C₂×#6095	C₂×C₄	semidirect
101. #88064	C₂×C₄	semidirect
102. #88063	C₂×C₄	semidirect
104. #88059	C₂×C₄	semidirect
105. #88059	C₂×C₄	semidirect
206. #1814	D₁₃	semidirect
463. C₁₃	#21558	semidirect

Maximal subgroups

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

subgroup	index
#13124556	2
#13123735	2
C₂×#11718556	2
#131×Dic₁₃	2
#13115732	2
#13115624	2
#13115503	2
#13115335	2
#13114717	2
#13114635	2
C₁₃×#1814	2
#21558	13