Subgroups — #16797443

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 552 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	#135×#261	C₂	1	1	yes	maximal, characteristic
3	#13131406	C₂	1	2	yes	maximal, complemented
4	#108×#261	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130641	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130638	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130616	C₂	1	2	yes	maximal, complemented
8	#13130614	C₂	1	2	yes	maximal, complemented
9	#13130601	C₂	1	2	yes	maximal, complemented
10	#13130492	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#443	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	Q₁₆×#261	C₄	1	2	yes	complemented
20	#11719107	C₄	1	4	yes	complemented
21	SD₁₆×#261	C₄	1	4	yes	complemented
22	#11719103	C₄	1	2	yes	complemented
23	D₈×#261	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	—	2	2	no	—
33	C₂×#88100	C₂²	1	1	yes	characteristic
34	C₂×#88100	C₂²	1	1	yes	characteristic
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	#11719047	C₂²	1	1	yes	characteristic
39	C₁₃×#443	C₄	1	1	yes	characteristic, complemented
40	#11718857	C₄	1	1	yes	characteristic, complemented
41	#11718805	C₄	1	2	yes	complemented
42	#11718556	C₄	1	1	yes	characteristic, complemented
43	D₁₃×#108	C₂²	1	1	yes	characteristic
44	#11718485	C₄	1	2	yes	complemented
45	D₁₃×#104	C₂²	1	2	yes	—
46	#11718361	C₄	1	1	yes	characteristic, complemented
47	C₄×C₈×D₁₃	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	#88110	—	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	1	no	—
103	#88100	—	2	1	no	—
104	#88100	D₄	1	1	yes	characteristic
105	#88100	D₄	1	1	yes	characteristic
106	#88100	D₄	1	1	yes	characteristic
107	#88100	D₄	1	1	yes	characteristic
108	C₈×#261	—	2	2	no	—
109	C₈×#261	—	2	2	no	—
110	C₈×#261	—	2	2	no	—
111	C₈×#261	C₂×C₄	1	2	yes	—
112	C₈×#261	C₂×C₄	1	2	yes	—
113	C₈×#261	C₂×C₄	1	2	yes	complemented
114	C₈×#261	C₂×C₄	1	2	yes	complemented
115	C₁₃×#108	C₂×C₄	1	1	yes	characteristic, complemented
116	C₁₃×#104	C₂×C₄	1	2	yes	complemented
117	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
118	#88077	C₂×C₄	1	2	yes	complemented
119	#88065	C₂×C₄	1	2	yes	complemented
120	#88062	C₂×C₄	1	2	yes	complemented
121	#88059	C₂×C₄	1	1	yes	characteristic, complemented
122	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
123	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
124	#88045	C₂×C₄	1	2	yes	complemented
125	C₄×#1055	C₂×C₄	1	1	yes	characteristic, complemented
126	#20514	—	13	1	no	maximal, Sylow
127	C₂²×#261	—	2	1	no	—
128	C₂²×#261	—	2	4	no	—
129	C₂²×#261	#41	1	2	yes	—
130	C₁₃×#41	C₂²×C₄	1	2	yes	—
131	#6131	C₂²×C₄	1	2	yes	—
132	Q₈×D₁₃	C₂²×C₄	1	2	yes	—
133	#6129	—	2	2	no	—
134	#6129	C₂²×C₄	1	2	yes	—
135	D₄×D₁₃	—	2	2	no	—
136	D₄×D₁₃	C₂²×C₄	1	2	yes	—
137	#6127	—	2	2	no	—
138	#6127	C₂²×C₄	1	2	yes	—
139	C₂×C₄×D₁₃	—	2	2	no	—
140	C₂×C₄×D₁₃	—	2	1	no	—
141	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊#261	—	2	2	no	—
143	C₂²⋊#261	—	2	4	no	—
144	#6122	—	2	2	no	—
145	#6122	—	2	4	no	—
146	C₂×#1057	—	2	1	no	—
147	C₂×#1057	—	2	4	no	—
148	C₂×#1057	#41	1	2	yes	—
149	C₄⋊#261	—	2	4	no	—
150	C₄⋊#261	C₂²×C₄	1	4	yes	—
151	C₄×#261	—	2	4	no	—
152	C₄×#261	—	2	2	no	—
153	C₄×#261	—	2	1	no	—
154	C₄×#261	C₂²×C₄	1	2	yes	—
155	C₄×#261	C₂²×C₄	1	2	yes	—
156	C₄×#261	C₂×D₄	1	1	yes	characteristic
157	C₄×#261	C₂×D₄	1	1	yes	characteristic
158	#6118	—	2	4	no	—
159	#6118	C₂²×C₄	1	4	yes	—
160	D₁₃⋊C₈	—	2	2	no	—
161	D₁₃⋊C₈	—	2	1	no	—
162	D₁₃⋊C₈	—	2	4	no	—
163	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
164	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
165	D₁₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	D₁₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₁₃×Q₁₆	C₄²	1	1	yes	characteristic
168	C₁₃×SD₁₆	C₄²	1	2	yes	—
169	C₁₃×D₈	C₄²	1	1	yes	characteristic
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	#6107	C₄²	1	2	yes	—
177	#6106	C₄²	1	2	yes	—
178	#6105	C₄²	1	2	yes	—
179	#6104	C₄²	1	2	yes	—
180	C₄×Dic₁₃	—	2	1	no	—
181	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
182	#6099	—	2	2	no	—
183	#6099	C₂²×C₄	1	2	yes	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
186	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
187	Dic₅₂	C₄²	1	1	yes	characteristic
188	D₁₀₄	C₄²	1	1	yes	characteristic
189	#6095	C₄²	1	2	yes	—
190	#6094	—	2	2	no	—
191	#6094	—	2	2	no	—
192	#6094	—	2	2	no	—
193	C₈×D₁₃	—	2	2	no	—
194	C₈×D₁₃	—	2	2	no	—
195	C₈×D₁₃	—	2	2	no	—
196	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
197	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
199	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
201	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
202	C₈×D₁₃	#41	1	1	yes	characteristic
203	C₈×D₁₃	#41	1	1	yes	characteristic
204	C₂×#443	—	13	1	no	—
205	C₂×#443	—	13	1	no	—
206	C₄×#135	—	13	1	no	—
207	#2875	—	13	2	no	—
208	C₄×#108	—	13	1	no	—
209	#1772	—	13	1	no	—
210	#1772	—	13	1	no	—
211	#1765	—	13	2	no	—
212	#1765	—	13	2	no	—
213	#1759	—	13	2	no	—
214	#1726	—	13	1	no	—
215	C₂²×D₁₃	—	2	2	no	—
216	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×#261	—	2	4	no	—
218	C₂×#261	—	2	2	no	—
219	C₂×#261	—	4	2	no	—
220	C₂×#261	—	4	2	no	—
221	C₂×#261	—	8	4	no	—
222	C₂×#261	C₄×D₄	1	2	yes	—
223	C₂×#261	C₄×D₄	1	2	yes	—
224	Q₈×C₁₃	C₂×C₄²	1	2	yes	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	C₂×C₄²	1	2	yes	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
230	C₂²⋊D₁₃	—	2	2	no	—
231	C₂²⋊D₁₃	—	2	2	no	—
232	C₂²⋊D₁₃	—	2	2	no	—
233	C₂×Dic₁₃	—	2	2	no	—
234	C₂×Dic₁₃	—	2	1	no	—
235	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
236	D₅₂	—	2	2	no	—
237	D₅₂	C₂×C₄²	1	2	yes	—
238	C₄×D₁₃	—	2	2	no	—
239	C₄×D₁₃	—	2	2	no	—
240	C₄×D₁₃	—	2	2	no	—
241	C₄×D₁₃	—	4	2	no	—
242	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
243	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
244	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
246	Dic₂₆	—	2	2	no	—
247	Dic₂₆	C₂×C₄²	1	2	yes	—
248	#1057	—	2	4	no	—
249	#1057	—	2	2	no	—
250	#1057	C₄×D₄	1	2	yes	—
251	#1057	C₄×D₄	1	2	yes	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
254	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
255	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
256	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
257	#1055	—	2	2	no	—
258	#1055	C₂×C₄²	1	1	yes	characteristic
259	#1055	C₂×C₄²	1	1	yes	characteristic
260	#1055	C₄×D₄	1	1	yes	characteristic
261	#1055	C₄×D₄	1	1	yes	characteristic
262	C₂×#135	—	13	1	no	—
263	C₂×#131	—	13	2	no	—
264	C₂×#131	—	13	2	no	—
265	C₄×#41	—	13	2	no	—
266	#443	—	13	2	no	—
267	#443	—	13	4	no	—
268	#443	—	13	2	no	—
269	#443	—	13	1	no	—
270	#443	—	13	2	no	—
271	#443	—	13	1	no	—
272	#443	—	13	2	no	—
273	#443	—	13	1	no	—
274	#443	#261	1	1	yes	characteristic, complemented
275	C₄×Q₁₆	—	13	2	no	—
276	C₄×SD₁₆	—	13	4	no	—
277	C₄×D₈	—	13	2	no	—
278	C₂×#108	—	13	1	no	—
279	C₂×#108	—	13	1	no	—
280	#427	—	13	1	no	—
281	C₂×#104	—	13	2	no	—
282	C₂×#104	—	13	2	no	—
283	#416	—	13	2	no	—
284	#405	—	13	2	no	—
285	#405	—	13	2	no	—
286	#405	—	26	2	no	—
287	#405	—	26	2	no	—
288	C₄×M₁₆	—	13	2	no	—
289	C₄×M₁₆	—	26	2	no	—
290	C₂×#97	—	13	1	no	—
291	C₂×#97	—	13	1	no	—
292	C₂×#97	—	13	1	no	—
293	C₂×#97	—	26	2	no	—
294	C₂×C₄×C₈	—	13	1	no	—
295	C₂×C₄×C₈	—	13	1	no	—
296	C₂×C₄×C₈	—	13	1	no	—
297	#376	—	13	1	no	—
298	#341	—	13	2	no	—
299	#339	—	13	2	no	—
300	#339	—	13	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
303	C₂×D₁₃	—	2	2	no	—
304	C₂×D₁₃	—	2	2	no	—
305	C₂×D₁₃	—	4	4	no	—
306	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
307	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
308	#261	—	2	2	no	—
309	#261	—	2	2	no	—
310	#261	—	4	2	no	—
311	#261	—	4	4	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
315	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
316	Dic₁₃	—	2	2	no	—
317	Dic₁₃	—	4	1	no	—
318	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
319	Dic₁₃	C₄×#41	1	1	yes	characteristic
320	C₂×#41	—	13	2	no	—
321	#135	—	13	2	no	—
322	#135	—	13	1	no	—
323	#135	—	13	2	no	—
324	#135	—	13	1	no	—
325	#135	—	13	1	no	—
326	#135	C₂×#261	1	1	yes	characteristic
327	C₂×Q₁₆	—	13	1	no	—
328	C₂×SD₁₆	—	13	2	no	—
329	C₂×D₈	—	13	1	no	—
330	#131	—	13	4	no	—
331	#131	—	13	4	no	—
332	#131	—	13	2	no	—
333	#131	—	13	2	no	—
334	#131	—	13	2	no	—
335	#131	—	26	2	no	—
336	#131	—	26	2	no	—
337	#131	—	26	4	no	—
338	#131	C₂×#261	1	2	yes	complemented
339	C₂×M₁₆	—	13	2	no	—
340	C₂×M₁₆	—	13	2	no	—
341	C₂×M₁₆	—	26	2	no	—
342	C₂×M₁₆	—	26	2	no	—
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	13	1	no	—
345	C₂²×C₈	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	26	2	no	—
348	C₂²×C₈	—	26	2	no	—
349	C₄×Q₈	—	13	4	no	—
350	C₄×D₄	—	13	4	no	—
351	C₄×D₄	—	26	4	no	—
352	#117	—	13	2	no	—
353	#117	—	26	2	no	—
354	C₂×C₄²	—	13	1	no	—
355	C₂×C₄²	—	13	1	no	—
356	C₂×C₄²	—	13	1	no	—
357	C₂×C₄²	—	26	2	no	—
358	#108	—	13	2	no	—
359	#108	—	13	2	no	—
360	#108	—	13	2	no	—
361	#108	—	13	1	no	—
362	#108	C₂×#261	1	1	yes	characteristic, complemented
363	#107	—	13	2	no	—
364	#106	—	13	2	no	—
365	#104	—	13	4	no	—
366	#104	—	13	4	no	—
367	#104	—	13	2	no	—
368	#104	—	13	2	no	—
369	#104	—	13	2	no	—
370	#104	C₂×#261	1	2	yes	complemented
371	#103	—	13	4	no	—
372	#102	—	13	4	no	—
373	#97	—	13	1	no	—
374	#97	—	13	1	no	—
375	#97	—	13	1	no	—
376	#97	—	13	1	no	—
377	#97	—	26	2	no	—
378	#97	—	26	1	no	—
379	#97	—	26	1	no	—
380	#97	—	26	2	no	—
381	#97	—	26	2	no	—
382	#97	—	26	2	no	—
383	C₄×C₈	—	13	2	no	—
384	C₄×C₈	—	13	2	no	—
385	C₄×C₈	—	13	2	no	—
386	C₄×C₈	—	13	2	no	—
387	C₄×C₈	—	13	1	no	—
388	C₄×C₈	—	13	1	no	—
389	C₄×C₈	—	13	1	no	—
390	C₄×C₈	—	26	2	no	—
391	C₄×C₈	—	26	2	no	—
392	C₄×C₈	—	26	2	no	—
393	C₄×C₈	C₂×#261	1	1	yes	characteristic, complemented
394	#95	—	26	2	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	4	2	no	—
397	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
398	D₁₃	—	2	1	no	—
399	D₁₃	—	4	2	no	—
400	D₁₃	#2957	1	2	yes	—
401	#41	—	13	2	no	—
402	#41	—	13	2	no	—
403	#41	—	13	2	no	—
404	#41	—	26	2	no	—
405	#41	—	26	2	no	—
406	#41	C₂²×#261	1	2	yes	—
407	C₂×Q₈	—	13	2	no	—
408	C₂×D₄	—	13	2	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂²×C₄	—	13	1	no	—
411	C₂²×C₄	—	13	2	no	—
412	C₂²×C₄	—	26	2	no	—
413	C₂²×C₄	—	26	1	no	—
414	C₂²×C₄	—	26	4	no	—
415	C₂²×C₄	—	26	1	no	—
416	Q₁₆	—	13	2	no	—
417	Q₁₆	—	13	1	no	—
418	Q₁₆	C₄×#261	1	1	yes	characteristic
419	SD₁₆	—	13	2	no	—
420	SD₁₆	—	13	2	no	—
421	SD₁₆	—	13	2	no	—
422	SD₁₆	C₄×#261	1	2	yes	—
423	D₈	—	13	2	no	—
424	D₈	—	13	1	no	—
425	D₈	C₄×#261	1	1	yes	characteristic
426	M₁₆	—	2	2	no	—
427	M₁₆	—	13	4	no	—
428	M₁₆	—	13	2	no	—
429	M₁₆	—	26	2	no	—
430	M₁₆	—	26	2	no	—
431	M₁₆	—	26	2	no	—
432	M₁₆	—	26	4	no	—
433	M₁₆	—	26	4	no	—
434	M₁₆	—	26	2	no	—
435	M₁₆	—	26	2	no	—
436	M₁₆	C₂²×#261	1	2	yes	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	13	2	no	—
439	C₂×C₈	—	13	1	no	—
440	C₂×C₈	—	13	1	no	—
441	C₂×C₈	—	13	2	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	13	1	no	—
445	C₂×C₈	—	13	1	no	—
446	C₂×C₈	—	13	1	no	—
447	C₂×C₈	—	13	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	13	1	no	—
450	C₂×C₈	—	13	1	no	—
451	C₂×C₈	—	13	1	no	—
452	C₂×C₈	—	13	2	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	26	2	no	—
455	C₂×C₈	—	26	2	no	—
456	C₂×C₈	—	26	4	no	—
457	C₂×C₈	—	26	4	no	—
458	C₂×C₈	—	26	2	no	—
459	C₂×C₈	—	26	1	no	—
460	C₂×C₈	—	26	1	no	—
461	C₂×C₈	—	26	2	no	—
462	C₂×C₈	C₂²×#261	1	1	yes	characteristic
463	C₂×C₈	C₂²×#261	1	1	yes	characteristic
464	C₄⋊C₄	—	13	4	no	—
465	C₄⋊C₄	—	26	4	no	—
466	C₂²⋊C₄	—	26	4	no	—
467	C₂²⋊C₄	—	26	2	no	—
468	C₄²	—	13	2	no	—
469	C₄²	—	13	1	no	—
470	C₄²	—	13	1	no	—
471	C₄²	—	13	2	no	—
472	C₄²	—	13	1	no	—
473	C₄²	—	26	1	no	—
474	C₄²	—	26	2	no	—
475	C₄²	—	26	1	no	—
476	C₄²	—	26	4	no	—
477	C₄²	C₂²×#261	1	1	yes	characteristic
478	C₁₃	#20514	1	1	yes	characteristic, complemented, Sylow
479	C₂³	—	13	1	no	—
480	C₂³	—	26	2	no	—
481	Q₈	—	13	2	no	—
482	Q₈	—	26	2	no	—
483	Q₈	C₂×C₄×#261	1	2	yes	—
484	D₄	—	2	2	no	—
485	D₄	—	13	2	no	—
486	D₄	—	26	2	no	—
487	D₄	—	26	2	no	—
488	D₄	—	26	2	no	—
489	D₄	—	26	2	no	—
490	D₄	C₂×C₄×#261	1	2	yes	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	13	1	no	—
494	C₂×C₄	—	13	1	no	—
495	C₂×C₄	—	13	1	no	—
496	C₂×C₄	—	13	1	no	—
497	C₂×C₄	—	13	1	no	—
498	C₂×C₄	—	13	2	no	—
499	C₂×C₄	—	13	2	no	—
500	C₂×C₄	—	26	2	no	—
501	C₂×C₄	—	26	2	no	—
502	C₂×C₄	—	26	2	no	—
503	C₂×C₄	—	26	2	no	—
504	C₂×C₄	—	26	2	no	—
505	C₂×C₄	—	26	4	no	—
506	C₂×C₄	—	26	1	no	—
507	C₂×C₄	—	52	2	no	—
508	C₂×C₄	—	52	2	no	—
509	C₂×C₄	—	52	2	no	—
510	C₂×C₄	—	104	4	no	—
511	C₂×C₄	C₂³×#261	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	13	2	no	—
514	C₈	—	13	2	no	—
515	C₈	—	13	1	no	—
516	C₈	—	13	1	no	—
517	C₈	—	13	1	no	—
518	C₈	—	13	1	no	—
519	C₈	—	26	2	no	—
520	C₈	—	26	4	no	—
521	C₈	—	26	2	no	—
522	C₈	C₂×C₄×#261	1	1	yes	characteristic
523	C₈	C₂×C₄×#261	1	1	yes	characteristic
524	C₈	D₄×#261	1	1	yes	characteristic
525	C₈	D₄×#261	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	13	1	no	—
528	C₂²	—	13	1	no	—
529	C₂²	—	26	2	no	—
530	C₂²	—	26	2	no	—
531	C₂²	—	52	4	no	—
532	C₂²	#41×#261	1	1	yes	characteristic
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	13	1	no	—
536	C₄	—	13	1	no	—
537	C₄	—	26	2	no	—
538	C₄	—	26	2	no	—
539	C₄	—	26	2	no	—
540	C₄	—	52	1	no	—
541	C₄	—	52	4	no	—
542	C₄	—	52	2	no	—
543	C₄	C₂²×C₄×#261	1	1	yes	characteristic
544	C₄	C₂×D₄×#261	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	4	2	no	—
547	C₂	—	13	2	no	—
548	C₂	—	26	1	no	—
549	C₂	—	52	2	no	—
550	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×#443	C₄
socle	C₂×C₁₃	C₄²×D₄
prime radical	D₁₃×#135	C₂²
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#443	#261
hypocenter	C₁₃	#20514
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #13131406	C₂	semidirect
4. #108×#261	C₂	semidirect
5. #13130641	C₂	semidirect
6. #13130638	C₂	semidirect
7. #13130616	C₂	semidirect
8. #13130614	C₂	semidirect
9. #13130601	C₂	semidirect
10. #13130492	C₂	semidirect
18. #11719111	C₄	semidirect
19. Q₁₆×#261	C₄	semidirect
20. #11719107	C₄	semidirect
21. SD₁₆×#261	C₄	semidirect
22. #11719103	C₄	semidirect
23. D₈×#261	C₄	semidirect
39. C₁₃×#443	C₄	semidirect
40. #11718857	C₄	semidirect
41. #11718805	C₄	semidirect
42. #11718556	C₄	semidirect
44. #11718485	C₄	semidirect
46. #11718361	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
113. C₈×#261	C₂×C₄	semidirect
114. C₈×#261	C₂×C₄	semidirect
115. C₁₃×#108	C₂×C₄	semidirect
116. C₁₃×#104	C₂×C₄	semidirect
117. C₄×C₈×C₁₃	C₂×C₄	semidirect
118. #88077	C₂×C₄	semidirect
119. #88065	C₂×C₄	semidirect
120. #88062	C₂×C₄	semidirect
121. #88059	C₂×C₄	semidirect
122. C₈×Dic₁₃	C₂×C₄	semidirect
123. C₈×Dic₁₃	C₂×C₄	semidirect
124. #88045	C₂×C₄	semidirect
125. C₄×#1055	C₂×C₄	semidirect
274. #443	#261	semidirect
338. #131	C₂×#261	semidirect
362. #108	C₂×#261	semidirect
370. #104	C₂×#261	semidirect
393. C₄×C₈	C₂×#261	semidirect
478. C₁₃	#20514	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
#135×#261	2
#13131406	2
#108×#261	2
#13130641	2
#13130638	2
#13130616	2
#13130614	2
#13130601	2
#13130492	2
D₁₃×#443	2
#20514	13