Subgroups — #16797429

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#443	C₂	1	1	yes	maximal, characteristic
2	#13131590	C₂	1	1	yes	maximal, characteristic
3	#131×#261	C₂	1	2	yes	maximal, complemented
4	#13130657	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130642	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130641	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130614	C₂	1	2	yes	maximal, complemented
8	#13130612	C₂	1	2	yes	maximal, complemented
9	#13130601	C₂	1	2	yes	maximal, complemented
10	#13130494	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#444	C₂	1	1	yes	maximal, characteristic
12	#41×#261	C₂²	1	2	yes	—
13	D₁₃⋊#131	C₂²	1	2	yes	—
14	D₁₃×#135	C₂²	1	1	yes	characteristic
15	D₁₃×#131	C₂²	1	2	yes	—
16	#11719165	C₂²	1	2	yes	—
17	D₁₃⋊#104	C₂²	1	2	yes	—
18	#11719111	C₄	1	2	yes	complemented
19	#11719110	C₄	1	2	yes	complemented
20	#11719107	C₄	1	4	yes	complemented
21	#11719106	C₄	1	4	yes	complemented
22	#11719103	C₄	1	2	yes	complemented
23	#11719102	C₄	1	2	yes	complemented
24	#11719099	—	2	2	no	—
25	#11719099	C₂²	1	2	yes	—
26	M₁₆×#261	—	2	2	no	—
27	M₁₆×#261	C₂²	1	2	yes	—
28	D₁₃⋊#108	C₂²	1	1	yes	characteristic
29	#11719092	C₂²	1	1	yes	characteristic
30	#11719089	—	2	2	no	—
31	#11719089	C₂²	1	2	yes	—
32	C₂×#88100	C₂²	1	1	yes	characteristic
33	C₂×#88100	C₂²	1	1	yes	characteristic
34	C₂×C₈×#261	—	2	2	no	—
35	C₂×C₈×#261	C₂²	1	1	yes	characteristic
36	C₂×C₈×#261	C₂²	1	1	yes	characteristic
37	#11719057	C₂²	1	1	yes	characteristic
38	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#444	C₄	1	1	yes	characteristic, complemented
40	#11718858	C₄	1	1	yes	characteristic, complemented
41	#11718806	C₄	1	2	yes	complemented
42	#11718555	C₄	1	1	yes	characteristic, complemented
43	D₁₃×#108	C₂²	1	1	yes	characteristic
44	#11718484	C₄	1	2	yes	complemented
45	D₁₃×#104	C₂²	1	2	yes	—
46	#11718378	C₄	1	1	yes	characteristic, complemented
47	D₁₃×#97	C₂²	1	1	yes	characteristic
48	#11718273	C₂²	1	2	yes	—
49	#11718272	C₂²	1	2	yes	—
50	#11718234	C₂²	1	2	yes	—
51	#41×D₁₃	C₂³	1	2	yes	—
52	Q₈×#261	C₂×C₄	1	4	yes	—
53	#88240	C₂×C₄	1	4	yes	complemented
54	D₄×#261	—	2	4	no	—
55	D₄×#261	C₂×C₄	1	4	yes	—
56	#88238	—	2	4	no	—
57	#88238	C₂×C₄	1	4	yes	complemented
58	#88237	—	2	2	no	—
59	#88237	C₂³	1	2	yes	—
60	C₂×C₄×#261	—	2	2	no	—
61	C₂×C₄×#261	C₂³	1	1	yes	characteristic
62	C₂×C₄×#261	C₂³	1	1	yes	characteristic
63	D₁₃⋊M₁₆	—	2	2	no	—
64	D₁₃⋊M₁₆	C₂³	1	2	yes	—
65	C₂×D₁₃⋊C₈	—	2	2	no	—
66	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₁₃×#135	C₂×C₄	1	1	yes	characteristic
69	C₁₃×#131	C₂×C₄	1	2	yes	complemented
70	#88204	C₂×C₄	1	2	yes	—
71	#88202	C₂×C₄	1	2	yes	complemented
72	#88173	C₂×C₄	1	1	yes	characteristic
73	Q₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
74	#88170	C₂×C₄	1	2	yes	—
75	SD₁₆×D₁₃	C₂×C₄	1	2	yes	—
76	#88166	C₂×C₄	1	1	yes	characteristic
77	D₈×D₁₃	C₂×C₄	1	1	yes	characteristic
78	#88161	—	2	2	no	—
79	#88161	C₂×C₄	1	2	yes	complemented
80	M₁₆×D₁₃	—	2	2	no	—
81	M₁₆×D₁₃	C₂³	1	2	yes	—
82	#88158	C₂×C₄	1	1	yes	characteristic
83	#88155	—	2	2	no	—
84	#88155	C₂×C₄	1	2	yes	complemented
85	C₂×C₈×D₁₃	—	2	2	no	—
86	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
88	C₄²×D₁₃	C₂³	1	1	yes	characteristic
89	#88118	C₂×C₄	1	4	yes	complemented
90	#88117	C₂×C₄	1	4	yes	—
91	#88116	C₂×C₄	1	4	yes	complemented
92	#88115	C₂×C₄	1	4	yes	—
93	(C₂×#261)⋊C₄	—	2	2	no	—
94	C₄×#1057	—	2	2	no	—
95	#88104	C₂×C₄	1	2	yes	complemented
96	#88103	C₂×C₄	1	2	yes	complemented
97	#88102	C₂×C₄	1	2	yes	—
98	#88101	C₂×C₄	1	2	yes	—
99	#88100	—	2	2	no	—
100	#88100	—	2	2	no	—
101	#88100	—	2	2	no	—
102	#88100	—	2	2	no	—
103	#88100	C₂×C₄	1	2	yes	—
104	#88100	C₂×C₄	1	2	yes	—
105	C₈×#261	—	2	2	no	—
106	C₈×#261	—	2	2	no	—
107	C₈×#261	—	2	2	no	—
108	C₈×#261	C₂×C₄	1	2	yes	complemented
109	C₈×#261	C₂×C₄	1	2	yes	complemented
110	C₈×#261	D₄	1	2	yes	—
111	C₈×#261	D₄	1	2	yes	—
112	C₁₃×#108	C₂×C₄	1	1	yes	characteristic, complemented
113	C₁₃×#104	C₂×C₄	1	2	yes	complemented
114	C₁₃×#97	C₂×C₄	1	1	yes	characteristic, complemented
115	#88077	C₂×C₄	1	2	yes	complemented
116	#88065	C₂×C₄	1	2	yes	complemented
117	#88062	C₂×C₄	1	2	yes	complemented
118	#88059	C₂×C₄	1	1	yes	characteristic, complemented
119	#88055	C₂×C₄	1	1	yes	characteristic, complemented
120	#88055	C₂×C₄	1	1	yes	characteristic, complemented
121	#88045	C₂×C₄	1	2	yes	complemented
122	#88043	C₂×C₄	1	1	yes	characteristic, complemented
123	#20510	—	13	1	no	maximal, Sylow
124	C₂²×#261	—	2	1	no	—
125	C₂²×#261	—	2	4	no	—
126	C₂²×#261	#41	1	2	yes	—
127	C₁₃×#41	C₂²×C₄	1	2	yes	—
128	#6131	C₂²×C₄	1	2	yes	—
129	Q₈×D₁₃	C₂²×C₄	1	2	yes	—
130	#6129	—	2	2	no	—
131	#6129	C₂²×C₄	1	2	yes	—
132	D₄×D₁₃	—	2	2	no	—
133	D₄×D₁₃	C₂²×C₄	1	2	yes	—
134	#6127	—	2	2	no	—
135	#6127	C₂²×C₄	1	2	yes	—
136	C₂×C₄×D₁₃	—	2	2	no	—
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊#261	—	2	2	no	—
140	C₂²⋊#261	—	2	4	no	—
141	#6122	—	2	2	no	—
142	#6122	—	2	4	no	—
143	C₂×#1057	—	2	1	no	—
144	C₂×#1057	—	2	4	no	—
145	C₂×#1057	#41	1	2	yes	—
146	C₄⋊#261	—	2	4	no	—
147	C₄⋊#261	C₂²×C₄	1	4	yes	—
148	C₄×#261	—	2	4	no	—
149	C₄×#261	—	2	2	no	—
150	C₄×#261	—	2	1	no	—
151	C₄×#261	C₂²×C₄	1	2	yes	—
152	C₄×#261	C₂²×C₄	1	2	yes	—
153	C₄×#261	C₂×D₄	1	2	yes	—
154	#6118	—	2	4	no	—
155	#6118	C₂²×C₄	1	4	yes	—
156	D₁₃⋊C₈	—	2	2	no	—
157	D₁₃⋊C₈	—	2	1	no	—
158	D₁₃⋊C₈	—	2	4	no	—
159	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
160	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
161	D₁₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	D₁₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₁₃×Q₁₆	C₄²	1	1	yes	characteristic
164	C₁₃×SD₁₆	C₄²	1	2	yes	—
165	C₁₃×D₈	C₄²	1	1	yes	characteristic
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	#6107	C₄²	1	2	yes	—
173	#6106	C₄²	1	2	yes	—
174	#6105	C₄²	1	2	yes	—
175	#6104	C₄²	1	2	yes	—
176	C₄×Dic₁₃	—	2	1	no	—
177	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
178	#6099	—	2	2	no	—
179	#6099	C₂²×C₄	1	2	yes	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
182	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
183	Dic₅₂	C₄²	1	1	yes	characteristic
184	D₁₀₄	C₄²	1	1	yes	characteristic
185	#6095	C₄²	1	2	yes	—
186	#6094	—	2	2	no	—
187	#6094	—	2	2	no	—
188	#6094	—	2	2	no	—
189	C₈×D₁₃	—	2	2	no	—
190	C₈×D₁₃	—	2	2	no	—
191	C₈×D₁₃	—	2	2	no	—
192	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
193	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
194	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
195	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
196	C₈×D₁₃	C₂×D₄	1	2	yes	—
197	C₈×D₁₃	#41	1	2	yes	—
198	C₂×#444	—	13	1	no	—
199	C₂×#443	—	13	1	no	—
200	#2943	—	13	1	no	—
201	C₄×#131	—	13	2	no	—
202	#1778	—	13	1	no	—
203	#1773	—	13	1	no	—
204	#1772	—	13	1	no	—
205	#1765	—	13	2	no	—
206	#1764	—	13	2	no	—
207	#1759	—	13	2	no	—
208	#1726	—	13	1	no	—
209	C₂²×D₁₃	—	2	2	no	—
210	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×#261	—	2	4	no	—
212	C₂×#261	—	2	2	no	—
213	C₂×#261	—	4	2	no	—
214	C₂×#261	—	4	8	no	—
215	C₂×#261	—	4	2	no	—
216	C₂×#261	C₄×D₄	1	4	yes	—
217	Q₈×C₁₃	C₂×C₄²	1	2	yes	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	C₂×C₄²	1	2	yes	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
223	C₂²⋊D₁₃	—	2	2	no	—
224	C₂²⋊D₁₃	—	2	2	no	—
225	C₂²⋊D₁₃	—	2	2	no	—
226	C₂×Dic₁₃	—	2	2	no	—
227	C₂×Dic₁₃	—	2	1	no	—
228	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
229	D₅₂	—	2	2	no	—
230	D₅₂	C₂×C₄²	1	2	yes	—
231	C₄×D₁₃	—	2	2	no	—
232	C₄×D₁₃	—	2	2	no	—
233	C₄×D₁₃	—	2	2	no	—
234	C₄×D₁₃	—	4	2	no	—
235	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
236	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
237	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
239	Dic₂₆	—	2	2	no	—
240	Dic₂₆	C₂×C₄²	1	2	yes	—
241	#1057	—	2	4	no	—
242	#1057	—	2	2	no	—
243	#1057	C₄×D₄	1	2	yes	—
244	#1057	C₄×D₄	1	2	yes	—
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
247	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
248	C₈×C₁₃	C₄×D₄	1	2	yes	—
249	#1055	—	2	2	no	—
250	#1055	C₂×C₄²	1	1	yes	characteristic
251	#1055	C₂×C₄²	1	1	yes	characteristic
252	#1055	C₄×D₄	1	2	yes	—
253	C₂×#135	—	13	1	no	—
254	C₂×#131	—	13	2	no	—
255	C₂×#131	—	13	2	no	—
256	C₄×#41	—	13	2	no	—
257	#444	—	13	1	no	—
258	#444	—	13	2	no	—
259	#444	—	13	1	no	—
260	#444	—	13	2	no	—
261	#444	—	13	1	no	—
262	#444	#261	1	1	yes	characteristic, complemented
263	#443	—	13	2	no	—
264	#443	—	13	4	no	—
265	#443	—	13	2	no	—
266	#442	—	13	2	no	—
267	#441	—	13	2	no	—
268	#440	—	13	4	no	—
269	C₂×#108	—	13	1	no	—
270	C₂×#108	—	13	1	no	—
271	#427	—	13	1	no	—
272	C₂×#104	—	13	2	no	—
273	C₂×#104	—	13	2	no	—
274	#416	—	13	2	no	—
275	#405	—	13	2	no	—
276	#405	—	13	2	no	—
277	#405	—	26	2	no	—
278	#405	—	26	2	no	—
279	C₄×M₁₆	—	13	2	no	—
280	C₄×M₁₆	—	26	2	no	—
281	C₂×#97	—	13	1	no	—
282	C₂×#97	—	13	1	no	—
283	C₂×#97	—	13	1	no	—
284	C₂×C₄×C₈	—	13	1	no	—
285	C₂×C₄×C₈	—	13	1	no	—
286	C₂×C₄×C₈	—	13	1	no	—
287	C₂×C₄×C₈	—	26	2	no	—
288	#376	—	13	1	no	—
289	#341	—	13	2	no	—
290	#339	—	13	2	no	—
291	#339	—	13	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
294	C₂×D₁₃	—	2	2	no	—
295	C₂×D₁₃	—	2	2	no	—
296	C₂×D₁₃	—	4	4	no	—
297	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
299	#261	—	2	4	no	—
300	#261	—	4	2	no	—
301	#261	—	4	4	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	4	1	no	—
304	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
305	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
306	Dic₁₃	—	2	2	no	—
307	Dic₁₃	—	4	1	no	—
308	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
309	Dic₁₃	C₄×#41	1	1	yes	characteristic
310	C₂×#41	—	13	2	no	—
311	#135	—	13	2	no	—
312	#135	—	13	1	no	—
313	#135	—	13	2	no	—
314	#135	—	13	1	no	—
315	#135	—	13	1	no	—
316	#135	C₂×#261	1	1	yes	characteristic
317	C₂×Q₁₆	—	13	1	no	—
318	C₂×SD₁₆	—	13	2	no	—
319	C₂×D₈	—	13	1	no	—
320	#131	—	13	4	no	—
321	#131	—	13	4	no	—
322	#131	—	13	2	no	—
323	#131	—	13	2	no	—
324	#131	—	13	2	no	—
325	#131	—	26	2	no	—
326	#131	—	26	2	no	—
327	#131	—	26	4	no	—
328	#131	C₂×#261	1	2	yes	complemented
329	C₂×M₁₆	—	13	2	no	—
330	C₂×M₁₆	—	13	2	no	—
331	C₂×M₁₆	—	26	2	no	—
332	C₂×M₁₆	—	26	2	no	—
333	C₂²×C₈	—	13	1	no	—
334	C₂²×C₈	—	13	1	no	—
335	C₂²×C₈	—	13	1	no	—
336	C₂²×C₈	—	13	1	no	—
337	C₂²×C₈	—	26	2	no	—
338	C₂²×C₈	—	26	2	no	—
339	C₄×Q₈	—	13	4	no	—
340	C₄×D₄	—	13	4	no	—
341	C₄×D₄	—	26	4	no	—
342	#117	—	13	2	no	—
343	#117	—	26	2	no	—
344	C₂×C₄²	—	13	1	no	—
345	C₂×C₄²	—	13	1	no	—
346	C₂×C₄²	—	13	1	no	—
347	C₂×C₄²	—	26	2	no	—
348	#108	—	13	2	no	—
349	#108	—	13	2	no	—
350	#108	—	13	2	no	—
351	#108	—	13	1	no	—
352	#108	C₂×#261	1	1	yes	characteristic, complemented
353	#107	—	13	2	no	—
354	#106	—	13	2	no	—
355	#104	—	13	4	no	—
356	#104	—	13	4	no	—
357	#104	—	13	2	no	—
358	#104	—	13	2	no	—
359	#104	—	13	2	no	—
360	#104	C₂×#261	1	2	yes	complemented
361	#103	—	13	4	no	—
362	#102	—	13	4	no	—
363	#97	—	13	2	no	—
364	#97	—	13	2	no	—
365	#97	—	13	1	no	—
366	#97	—	13	1	no	—
367	#97	—	13	1	no	—
368	#97	—	26	2	no	—
369	#97	—	26	2	no	—
370	#97	—	26	2	no	—
371	#97	—	26	2	no	—
372	#97	C₂×#261	1	1	yes	characteristic, complemented
373	C₄×C₈	—	13	2	no	—
374	C₄×C₈	—	13	2	no	—
375	C₄×C₈	—	13	2	no	—
376	C₄×C₈	—	13	2	no	—
377	C₄×C₈	—	26	2	no	—
378	C₄×C₈	—	26	2	no	—
379	C₄×C₈	—	26	2	no	—
380	C₄×C₈	—	26	2	no	—
381	#95	—	26	2	no	—
382	C₂×C₁₃	—	2	1	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
385	D₁₃	—	2	1	no	—
386	D₁₃	—	4	2	no	—
387	D₁₃	#2955	1	2	yes	—
388	#41	—	13	2	no	—
389	#41	—	13	2	no	—
390	#41	—	13	2	no	—
391	#41	—	26	2	no	—
392	#41	—	26	2	no	—
393	#41	C₂²×#261	1	2	yes	—
394	C₂×Q₈	—	13	2	no	—
395	C₂×D₄	—	13	2	no	—
396	C₂×D₄	—	26	2	no	—
397	C₂²×C₄	—	13	1	no	—
398	C₂²×C₄	—	13	2	no	—
399	C₂²×C₄	—	26	2	no	—
400	C₂²×C₄	—	26	1	no	—
401	C₂²×C₄	—	26	4	no	—
402	C₂²×C₄	—	26	1	no	—
403	Q₁₆	—	13	2	no	—
404	Q₁₆	—	13	1	no	—
405	Q₁₆	C₄×#261	1	1	yes	characteristic
406	SD₁₆	—	13	2	no	—
407	SD₁₆	—	13	2	no	—
408	SD₁₆	—	13	2	no	—
409	SD₁₆	C₄×#261	1	2	yes	—
410	D₈	—	13	2	no	—
411	D₈	—	13	1	no	—
412	D₈	C₄×#261	1	1	yes	characteristic
413	M₁₆	—	2	2	no	—
414	M₁₆	—	13	4	no	—
415	M₁₆	—	13	2	no	—
416	M₁₆	—	26	2	no	—
417	M₁₆	—	26	2	no	—
418	M₁₆	—	26	2	no	—
419	M₁₆	—	26	4	no	—
420	M₁₆	—	26	4	no	—
421	M₁₆	—	26	2	no	—
422	M₁₆	—	26	2	no	—
423	M₁₆	C₂²×#261	1	2	yes	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	13	1	no	—
426	C₂×C₈	—	13	1	no	—
427	C₂×C₈	—	13	2	no	—
428	C₂×C₈	—	13	2	no	—
429	C₂×C₈	—	13	1	no	—
430	C₂×C₈	—	13	1	no	—
431	C₂×C₈	—	13	1	no	—
432	C₂×C₈	—	13	1	no	—
433	C₂×C₈	—	13	1	no	—
434	C₂×C₈	—	13	1	no	—
435	C₂×C₈	—	13	2	no	—
436	C₂×C₈	—	13	2	no	—
437	C₂×C₈	—	13	2	no	—
438	C₂×C₈	—	26	2	no	—
439	C₂×C₈	—	26	2	no	—
440	C₂×C₈	—	26	2	no	—
441	C₂×C₈	—	26	4	no	—
442	C₂×C₈	—	26	4	no	—
443	C₂×C₈	—	26	2	no	—
444	C₂×C₈	—	26	1	no	—
445	C₂×C₈	—	26	1	no	—
446	C₂×C₈	—	26	2	no	—
447	C₂×C₈	C₂²×#261	1	1	yes	characteristic
448	C₂×C₈	C₂²×#261	1	1	yes	characteristic
449	C₄⋊C₄	—	13	4	no	—
450	C₄⋊C₄	—	26	4	no	—
451	C₂²⋊C₄	—	26	4	no	—
452	C₂²⋊C₄	—	26	2	no	—
453	C₄²	—	13	2	no	—
454	C₄²	—	13	2	no	—
455	C₄²	—	13	2	no	—
456	C₄²	—	13	1	no	—
457	C₄²	—	26	1	no	—
458	C₄²	—	26	2	no	—
459	C₄²	—	26	1	no	—
460	C₄²	—	26	4	no	—
461	C₄²	C₂²×#261	1	1	yes	characteristic
462	C₁₃	#20510	1	1	yes	characteristic, complemented, Sylow
463	C₂³	—	13	1	no	—
464	C₂³	—	26	2	no	—
465	Q₈	—	13	2	no	—
466	Q₈	—	26	2	no	—
467	Q₈	C₂×C₄×#261	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	13	2	no	—
470	D₄	—	26	2	no	—
471	D₄	—	26	2	no	—
472	D₄	—	26	2	no	—
473	D₄	—	26	2	no	—
474	D₄	C₂×C₄×#261	1	2	yes	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	13	1	no	—
478	C₂×C₄	—	13	1	no	—
479	C₂×C₄	—	13	1	no	—
480	C₂×C₄	—	13	1	no	—
481	C₂×C₄	—	13	1	no	—
482	C₂×C₄	—	13	4	no	—
483	C₂×C₄	—	26	2	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	—	26	4	no	—
489	C₂×C₄	—	26	1	no	—
490	C₂×C₄	—	52	2	no	—
491	C₂×C₄	—	52	2	no	—
492	C₂×C₄	—	52	8	no	—
493	C₂×C₄	—	52	2	no	—
494	C₂×C₄	C₂³×#261	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	13	2	no	—
497	C₈	—	13	2	no	—
498	C₈	—	13	1	no	—
499	C₈	—	13	1	no	—
500	C₈	—	13	2	no	—
501	C₈	—	26	2	no	—
502	C₈	—	26	4	no	—
503	C₈	—	26	2	no	—
504	C₈	C₂×C₄×#261	1	1	yes	characteristic
505	C₈	C₂×C₄×#261	1	1	yes	characteristic
506	C₈	D₄×#261	1	2	yes	—
507	C₂²	—	2	2	no	—
508	C₂²	—	13	1	no	—
509	C₂²	—	13	1	no	—
510	C₂²	—	26	2	no	—
511	C₂²	—	26	2	no	—
512	C₂²	—	52	4	no	—
513	C₂²	#41×#261	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	13	1	no	—
517	C₄	—	13	1	no	—
518	C₄	—	26	4	no	—
519	C₄	—	26	2	no	—
520	C₄	—	52	1	no	—
521	C₄	—	52	4	no	—
522	C₄	—	52	2	no	—
523	C₄	C₂²×C₄×#261	1	1	yes	characteristic
524	C₄	C₂×D₄×#261	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	13	2	no	—
528	C₂	—	26	1	no	—
529	C₂	—	52	2	no	—
530	C₂	C₄×D₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#444	C₄
socle	C₂×C₁₃	C₄²×D₄
prime radical	D₁₃×#135	C₂²
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#444	#261
hypocenter	C₁₃	#20510
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
3. #131×#261	C₂	semidirect
4. #13130657	C₂	semidirect
5. #13130642	C₂	semidirect
6. #13130641	C₂	semidirect
7. #13130614	C₂	semidirect
8. #13130612	C₂	semidirect
9. #13130601	C₂	semidirect
10. #13130494	C₂	semidirect
18. #11719111	C₄	semidirect
19. #11719110	C₄	semidirect
20. #11719107	C₄	semidirect
21. #11719106	C₄	semidirect
22. #11719103	C₄	semidirect
23. #11719102	C₄	semidirect
39. C₁₃×#444	C₄	semidirect
40. #11718858	C₄	semidirect
41. #11718806	C₄	semidirect
42. #11718555	C₄	semidirect
44. #11718484	C₄	semidirect
46. #11718378	C₄	semidirect
53. #88240	C₂×C₄	semidirect
57. #88238	C₂×C₄	semidirect
69. C₁₃×#131	C₂×C₄	semidirect
71. #88202	C₂×C₄	semidirect
79. #88161	C₂×C₄	semidirect
84. #88155	C₂×C₄	semidirect
89. #88118	C₂×C₄	semidirect
91. #88116	C₂×C₄	semidirect
95. #88104	C₂×C₄	semidirect
96. #88103	C₂×C₄	semidirect
108. C₈×#261	C₂×C₄	semidirect
109. C₈×#261	C₂×C₄	semidirect
112. C₁₃×#108	C₂×C₄	semidirect
113. C₁₃×#104	C₂×C₄	semidirect
114. C₁₃×#97	C₂×C₄	semidirect
115. #88077	C₂×C₄	semidirect
116. #88065	C₂×C₄	semidirect
117. #88062	C₂×C₄	semidirect
118. #88059	C₂×C₄	semidirect
119. #88055	C₂×C₄	semidirect
120. #88055	C₂×C₄	semidirect
121. #88045	C₂×C₄	semidirect
122. #88043	C₂×C₄	semidirect
262. #444	#261	semidirect
328. #131	C₂×#261	semidirect
352. #108	C₂×#261	semidirect
360. #104	C₂×#261	semidirect
372. #97	C₂×#261	semidirect
462. C₁₃	#20510	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#443	2
#13131590	2
#131×#261	2
#13130657	2
#13130642	2
#13130641	2
#13130614	2
#13130612	2
#13130601	2
#13130494	2
D₁₃×#444	2
#20510	13