Subgroups — #15869860

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	#13124557	C₂	1	1	yes	maximal, characteristic
2	#13123740	C₂	1	2	yes	maximal, complemented
3	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#88155	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115732	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115627	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115506	C₂	1	2	yes	maximal, complemented
8	#13115336	C₂	1	2	yes	maximal, complemented
9	#13114887	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114637	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719453	C₂²	1	2	yes	—
13	C₂×#88158	C₂²	1	1	yes	characteristic
14	C₂×#88155	C₂²	1	2	yes	—
15	C₂×#88155	C₂²	1	1	yes	characteristic
16	C₂×#88155	C₂²	1	1	yes	characteristic
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₁₃×#427	C₂²	1	1	yes	characteristic
20	C₁₃×#405	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	#11718793	C₂²	1	2	yes	—
23	#11718786	C₂²	1	2	yes	—
24	C₂×#88059	C₂²	1	1	yes	characteristic
25	#11718762	C₂²	1	1	yes	characteristic
26	#11718762	C₂²	1	1	yes	characteristic
27	#11718667	C₂²	1	2	yes	—
28	#11718666	C₂²	1	2	yes	—
29	#11718666	C₂²	1	2	yes	—
30	C₂×#88045	C₂²	1	2	yes	—
31	C₄×#6099	C₂²	1	1	yes	characteristic
32	#11718559	C₄	1	4	yes	complemented
33	#11718558	C₄	1	2	yes	complemented
34	#11718557	C₄	1	2	yes	complemented
35	#11718378	—	2	4	no	—
36	#11718361	—	2	4	no	—
37	#11718361	—	2	1	no	—
38	#11718361	—	2	1	no	—
39	#11718361	—	2	1	no	—
40	#11718361	—	2	1	no	—
41	#11718350	—	2	1	no	—
42	#11718350	—	2	1	no	—
43	C₄×#6094	—	2	1	no	—
44	C₄×C₈×D₁₃	—	2	1	no	—
45	C₁₃×#339	C₂²	1	2	yes	—
46	#11718151	C₂²	1	2	yes	—
47	#11718125	C₂²	1	2	yes	—
48	C₂×#6127	C₂³	1	2	yes	—
49	C₂×#6127	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#117	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	—	2	2	no	—
56	#88180	C₂³	1	1	yes	characteristic
57	C₂×#6099	C₂³	1	2	yes	—
58	C₂×#6099	C₂³	1	1	yes	characteristic
59	C₂×#6099	C₂³	1	1	yes	characteristic
60	#88163	—	2	2	no	—
61	#88163	C₂×C₄	1	4	yes	—
62	#88162	—	2	2	no	—
63	#88162	C₂×C₄	1	4	yes	—
64	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
65	#88158	—	2	4	no	—
66	#88158	—	2	1	no	—
67	#88158	—	2	1	no	—
68	#88158	—	2	1	no	—
69	#88158	—	2	1	no	—
70	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×#6095	C₂×C₄	1	2	yes	complemented
72	#88155	—	2	1	no	—
73	#88155	—	2	1	no	—
74	#88155	—	2	1	no	—
75	#88155	—	2	1	no	—
76	#88155	—	2	2	no	—
77	#88155	—	2	2	no	—
78	#88155	—	2	2	no	—
79	#88155	—	2	2	no	—
80	#88155	C₂×C₄	1	2	yes	—
81	#88155	C₂×C₄	1	2	yes	—
82	#88155	D₄	1	2	yes	—
83	#88155	D₄	1	2	yes	—
84	C₂×#6094	—	2	1	no	—
85	C₂×#6094	—	2	1	no	—
86	C₂×#6094	—	2	2	no	—
87	C₂×C₈×D₁₃	—	2	1	no	—
88	C₂×C₈×D₁₃	—	2	1	no	—
89	C₂×C₈×D₁₃	—	2	2	no	—
90	C₄×D₅₂	—	2	1	no	—
91	#88126	—	2	1	no	—
92	C₄²×D₁₃	—	2	1	no	—
93	C₄×Dic₂₆	—	2	1	no	—
94	C₁₃×#108	C₂×C₄	1	2	yes	complemented
95	C₁₃×#108	C₂×C₄	1	2	yes	complemented
96	C₁₃×#107	—	2	1	no	—
97	C₁₃×#106	—	2	1	no	—
98	C₁₃×#97	—	2	2	no	—
99	C₄×C₈×C₁₃	—	2	2	no	—
100	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	#88064	C₂×C₄	1	4	yes	complemented
105	#88063	C₂×C₄	1	4	yes	complemented
106	#88059	—	2	1	no	—
107	#88059	—	2	1	no	—
108	#88059	—	2	4	no	—
109	#88055	—	2	1	no	—
110	#88055	—	2	1	no	—
111	C₈×Dic₁₃	—	2	1	no	—
112	C₈×Dic₁₃	—	2	1	no	—
113	#88046	—	2	4	no	—
114	#88045	—	2	4	no	—
115	#88045	—	2	2	no	—
116	#88045	—	2	2	no	—
117	#88045	—	2	4	no	—
118	#88043	—	2	1	no	—
119	C₄×#1055	—	2	1	no	—
120	#21558	—	13	1	no	maximal, Sylow
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₂²⋊D₁₃	—	2	1	no	—
124	C₂×C₂²⋊D₁₃	—	2	2	no	—
125	#6127	—	2	1	no	—
126	#6127	—	2	1	no	—
127	#6127	—	2	2	no	—
128	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	C₂²×C₄	1	2	yes	—
132	#6127	C₂×D₄	1	2	yes	—
133	C₂×D₅₂	C₂²×C₄	1	2	yes	—
134	C₂×D₅₂	#41	1	1	yes	characteristic
135	C₂×C₄×D₁₃	—	2	1	no	—
136	C₂×C₄×D₁₃	—	2	2	no	—
137	C₂×C₄×D₁₃	—	2	2	no	—
138	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
139	C₂×Dic₂₆	#41	1	1	yes	characteristic
140	C₁₃×M₁₆	—	2	2	no	—
141	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
152	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
153	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
154	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²⋊Dic₁₃	#41	1	2	yes	—
162	#6103	—	2	2	no	—
163	C₄⋊Dic₁₃	—	2	1	no	—
164	#6101	—	2	2	no	—
165	C₄×Dic₁₃	—	2	2	no	—
166	C₄×Dic₁₃	—	2	1	no	—
167	#6099	—	2	1	no	—
168	#6099	—	2	1	no	—
169	#6099	—	2	2	no	—
170	#6099	—	2	2	no	—
171	#6099	C₂²×C₄	1	2	yes	—
172	#6099	C₂×D₄	1	2	yes	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	2	no	—
176	Dic₅₂	—	2	4	no	—
177	Dic₅₂	—	2	1	no	—
178	Dic₅₂	—	2	1	no	—
179	D₁₀₄	—	2	4	no	—
180	D₁₀₄	—	2	1	no	—
181	D₁₀₄	—	2	1	no	—
182	#6095	—	2	4	no	—
183	#6095	—	2	4	no	—
184	#6095	—	2	2	no	—
185	#6095	—	2	2	no	—
186	#6094	—	2	2	no	—
187	#6094	—	2	2	no	—
188	#6094	—	2	2	no	—
189	#6094	—	2	2	no	—
190	#6094	—	4	2	no	—
191	#6094	—	4	2	no	—
192	C₈×D₁₃	—	2	2	no	—
193	C₈×D₁₃	—	2	2	no	—
194	C₈×D₁₃	—	2	2	no	—
195	C₈×D₁₃	—	2	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	—	13	1	no	—
207	#1772	D₁₃	1	1	yes	characteristic, complemented
208	#1757	—	13	2	no	—
209	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂²×D₁₃	—	2	1	no	—
211	C₂²×D₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂²⋊D₁₃	—	2	2	no	—
223	C₂²⋊D₁₃	—	2	2	no	—
224	C₂²⋊D₁₃	—	4	2	no	—
225	C₂²⋊D₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	2	1	no	—
227	C₂×Dic₁₃	—	2	2	no	—
228	C₂×Dic₁₃	—	2	2	no	—
229	D₅₂	—	2	2	no	—
230	D₅₂	—	2	2	no	—
231	D₅₂	—	2	1	no	—
232	D₅₂	C₄×D₄	1	2	yes	—
233	C₄×D₁₃	—	2	2	no	—
234	C₄×D₁₃	—	2	2	no	—
235	C₄×D₁₃	—	4	4	no	—
236	C₄×D₁₃	—	4	2	no	—
237	C₄×D₁₃	—	4	2	no	—
238	Dic₂₆	—	2	1	no	—
239	Dic₂₆	—	2	2	no	—
240	Dic₂₆	—	2	2	no	—
241	Dic₂₆	C₄×D₄	1	2	yes	—
242	C₈×C₁₃	—	2	4	no	—
243	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
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	#121	1	1	yes	characteristic
248	C₈×C₁₃	#121	1	1	yes	characteristic
249	C₈×C₁₃	#121	1	1	yes	characteristic
250	C₈×C₁₃	#121	1	1	yes	characteristic
251	#1055	—	2	2	no	—
252	#1055	—	2	2	no	—
253	#1055	—	4	2	no	—
254	#575	—	13	2	no	—
255	C₂×#135	—	13	1	no	—
256	C₂×#131	—	13	1	no	—
257	C₂×#131	—	13	1	no	—
258	C₂×#131	—	13	2	no	—
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	4	no	—
265	#443	—	26	1	no	—
266	#443	—	26	1	no	—
267	#443	—	26	1	no	—
268	#443	—	26	1	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	—	13	2	no	—
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	—	26	1	no	—
281	#405	—	26	1	no	—
282	#405	C₂×D₁₃	1	2	yes	—
283	C₄×M₁₆	—	13	1	no	—
284	C₄×M₁₆	—	26	1	no	—
285	C₂×C₄×C₈	—	26	1	no	—
286	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
287	#344	—	13	2	no	—
288	#344	—	13	2	no	—
289	#339	C₂×D₁₃	1	2	yes	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
292	C₂²×C₁₃	#525	1	1	yes	characteristic
293	C₂²×C₁₃	#532	1	1	yes	characteristic
294	C₂×D₁₃	—	2	2	no	—
295	C₂×D₁₃	—	4	2	no	—
296	C₂×D₁₃	—	4	2	no	—
297	C₂×D₁₃	—	8	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	—	8	2	no	—
301	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
304	C₄×C₁₃	#529	1	1	yes	characteristic
305	Dic₁₃	—	2	2	no	—
306	Dic₁₃	—	4	2	no	—
307	Dic₁₃	—	4	2	no	—
308	C₂×#41	—	13	1	no	—
309	C₂×#41	—	13	2	no	—
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	—	13	2	no	—
323	#131	—	13	2	no	—
324	#131	—	13	2	no	—
325	#131	—	13	2	no	—
326	#131	—	26	1	no	—
327	#131	—	26	1	no	—
328	#131	—	26	1	no	—
329	#131	—	26	1	no	—
330	#131	—	26	2	no	—
331	#131	—	26	2	no	—
332	#131	—	26	2	no	—
333	#131	—	26	2	no	—
334	C₂×M₁₆	—	13	1	no	—
335	C₂×M₁₆	—	13	1	no	—
336	C₂×M₁₆	—	13	2	no	—
337	C₂×M₁₆	—	26	1	no	—
338	C₂×M₁₆	—	26	1	no	—
339	C₂×M₁₆	—	26	2	no	—
340	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
341	C₂²×C₈	—	26	1	no	—
342	C₂²×C₈	—	26	1	no	—
343	C₂²×C₈	—	26	2	no	—
344	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
346	C₄×Q₈	—	26	1	no	—
347	C₄×D₄	—	26	1	no	—
348	C₄×D₄	—	26	2	no	—
349	#117	—	13	1	no	—
350	#117	—	26	1	no	—
351	#117	C₂²×D₁₃	1	2	yes	—
352	C₂×C₄²	—	26	1	no	—
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	#108	—	26	4	no	—
355	#108	—	26	1	no	—
356	#108	—	26	1	no	—
357	#108	C₄×D₁₃	1	2	yes	complemented
358	#108	C₄×D₁₃	1	2	yes	complemented
359	#107	—	2	1	no	—
360	#106	—	2	1	no	—
361	#104	—	26	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	—	2	2	no	—
369	#97	—	26	1	no	—
370	#97	—	26	1	no	—
371	#97	—	26	1	no	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	26	1	no	—
374	C₄×C₈	—	26	1	no	—
375	C₄×C₈	—	26	1	no	—
376	C₄×C₈	D₅₂	1	1	yes	characteristic
377	C₄×C₈	D₅₂	1	1	yes	characteristic
378	C₄×C₈	D₅₂	1	1	yes	characteristic
379	C₄×C₈	D₅₂	1	1	yes	characteristic
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	2	1	no	—
382	C₂×C₁₃	—	2	1	no	—
383	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
384	D₁₃	—	4	2	no	—
385	D₁₃	—	8	2	no	—
386	#41	—	13	2	no	—
387	#41	—	13	2	no	—
388	#41	—	26	1	no	—
389	#41	—	26	1	no	—
390	#41	—	26	2	no	—
391	#41	—	26	2	no	—
392	#41	—	26	2	no	—
393	#41	—	26	2	no	—
394	C₂×Q₈	—	13	2	no	—
395	C₂×Q₈	—	13	1	no	—
396	C₂×D₄	—	13	2	no	—
397	C₂×D₄	—	13	1	no	—
398	C₂×D₄	—	26	1	no	—
399	C₂×D₄	—	26	2	no	—
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	2	no	—
416	M₁₆	—	13	2	no	—
417	M₁₆	—	13	2	no	—
418	M₁₆	—	26	1	no	—
419	M₁₆	—	26	1	no	—
420	M₁₆	—	26	2	no	—
421	M₁₆	—	26	2	no	—
422	M₁₆	—	26	2	no	—
423	M₁₆	—	26	2	no	—
424	M₁₆	—	26	2	no	—
425	M₁₆	—	26	2	no	—
426	M₁₆	—	52	2	no	—
427	M₁₆	—	52	2	no	—
428	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	26	1	no	—
431	C₂×C₈	—	26	1	no	—
432	C₂×C₈	—	26	2	no	—
433	C₂×C₈	—	26	2	no	—
434	C₂×C₈	—	26	2	no	—
435	C₂×C₈	—	26	2	no	—
436	C₂×C₈	—	26	2	no	—
437	C₂×C₈	—	52	2	no	—
438	C₂×C₈	—	52	2	no	—
439	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
440	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
442	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
443	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
444	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
445	C₂×C₈	#6127	1	1	yes	characteristic
446	C₂×C₈	#6127	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	#6131	1	1	yes	characteristic
450	C₂×C₈	#6131	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	1	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	26	2	no	—
460	C₄²	—	26	1	no	—
461	C₄²	C₂×D₅₂	1	1	yes	characteristic
462	C₄²	C₂×D₅₂	1	1	yes	characteristic
463	C₁₃	#21558	1	1	yes	characteristic, complemented, Sylow
464	C₂³	—	26	1	no	—
465	C₂³	—	26	2	no	—
466	C₂³	#41×D₁₃	1	1	yes	characteristic
467	Q₈	—	13	2	no	—
468	Q₈	—	26	1	no	—
469	Q₈	—	26	2	no	—
470	Q₈	—	26	2	no	—
471	D₄	—	13	2	no	—
472	D₄	—	26	2	no	—
473	D₄	—	26	2	no	—
474	D₄	—	26	2	no	—
475	D₄	—	26	2	no	—
476	D₄	—	26	1	no	—
477	D₄	—	52	2	no	—
478	D₄	—	52	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	26	1	no	—
484	C₂×C₄	—	26	2	no	—
485	C₂×C₄	—	26	2	no	—
486	C₂×C₄	—	26	2	no	—
487	C₂×C₄	—	26	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	C₂²×D₅₂	1	1	yes	characteristic
493	C₂×C₄	C₂×#6127	1	1	yes	characteristic
494	C₂×C₄	C₂×D₄×D₁₃	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	4	no	—
498	C₈	—	26	2	no	—
499	C₈	—	26	2	no	—
500	C₈	—	52	2	no	—
501	C₈	C₄×D₅₂	1	1	yes	characteristic
502	C₈	C₄×D₅₂	1	1	yes	characteristic
503	C₈	C₄×D₅₂	1	1	yes	characteristic
504	C₈	C₄×D₅₂	1	1	yes	characteristic
505	C₈	#88149	1	1	yes	characteristic
506	C₈	#88149	1	1	yes	characteristic
507	C₈	#88149	1	1	yes	characteristic
508	C₈	#88149	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	26	2	no	—
511	C₂²	—	52	2	no	—
512	C₂²	—	52	2	no	—
513	C₂²	—	104	2	no	—
514	C₂²	#11719229	1	1	yes	characteristic
515	C₂²	#11719253	1	1	yes	characteristic
516	C₂²	C₄×#6131	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	8	2	no	—
520	C₄	—	26	2	no	—
521	C₄	—	52	2	no	—
522	C₄	—	52	2	no	—
523	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
524	C₄	C₂×#88149	1	1	yes	characteristic
525	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
526	C₄	#11719285	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	52	2	no	—
531	C₂	—	104	2	no	—
532	C₂	C₄×#88149	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#88149
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1772	C₂
socle	C₂×C₁₃	C₄×#121
prime radical	#13124557	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1772	D₁₃
hypocenter	C₁₃	#21558
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #13123740	C₂	semidirect
3. C₂×#11718361	C₂	semidirect
4. C₄×#88155	C₂	semidirect
5. #13115732	C₂	semidirect
6. #13115627	C₂	semidirect
7. #13115506	C₂	semidirect
8. #13115336	C₂	semidirect
9. #13114887	C₂	semidirect
10. #13114637	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
32. #11718559	C₄	semidirect
33. #11718558	C₄	semidirect
34. #11718557	C₄	semidirect
64. C₂×Dic₅₂	C₂×C₄	semidirect
70. C₂×D₁₀₄	C₂×C₄	semidirect
71. C₂×#6095	C₂×C₄	semidirect
94. C₁₃×#108	C₂×C₄	semidirect
95. C₁₃×#108	C₂×C₄	semidirect
104. #88064	C₂×C₄	semidirect
105. #88063	C₂×C₄	semidirect
207. #1772	D₁₃	semidirect
357. #108	C₄×D₁₃	semidirect
358. #108	C₄×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
#13124557	2
#13123740	2
C₂×#11718361	2
C₄×#88155	2
#13115732	2
#13115627	2
#13115506	2
#13115336	2
#13114887	2
#13114637	2
C₁₃×#1772	2
#21558	13