Subgroups — #16732776

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128226	C₂	1	2	yes	maximal, complemented
2	#13125495	C₂	1	2	yes	maximal, complemented
3	#13125486	C₂	1	2	yes	maximal, complemented
4	#13125475	C₂	1	4	yes	maximal, complemented
5	#13125464	C₂	1	4	yes	maximal, complemented
6	#13125453	C₂	1	4	yes	maximal, complemented
7	#13125350	C₂	1	1	yes	maximal, characteristic, complemented
8	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
9	#13125182	C₂	1	2	yes	maximal, complemented
10	#13124445	C₂	1	2	yes	maximal, complemented
11	#13124417	C₂	1	2	yes	maximal, complemented
12	#13123638	C₂	1	2	yes	maximal, complemented
13	C₄×#88158	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	#11719496	C₂²	1	4	yes	—
19	C₂×#88158	C₂²	1	2	yes	—
20	C₂×#88158	C₂²	1	2	yes	—
21	#11719240	C₂²	1	4	yes	—
22	#11719239	C₂²	1	8	yes	—
23	#11719233	—	2	8	no	—
24	#11719223	C₂²	1	4	yes	—
25	#11719220	—	2	4	no	—
26	#11719199	—	2	4	no	—
27	#11719182	C₂²	1	2	yes	—
28	C₄×#6127	C₂²	1	4	yes	—
29	#11719175	C₂²	1	2	yes	—
30	C₁₃×#405	C₂²	1	2	yes	—
31	C₁₃×#405	C₂²	1	2	yes	—
32	C₁₃×#405	C₂²	1	2	yes	—
33	C₁₃×#405	C₂²	1	2	yes	—
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	#11718798	C₂²	1	4	yes	—
39	#11718796	C₂²	1	4	yes	—
40	#11718795	C₂²	1	8	yes	—
41	#11718777	C₂²	1	4	yes	—
42	#11718776	C₂²	1	4	yes	—
43	#11718775	C₂²	1	8	yes	—
44	#11718774	C₂²	1	4	yes	—
45	#11718774	C₂²	1	4	yes	—
46	#11718767	C₂²	1	2	yes	—
47	#11718767	C₂²	1	2	yes	—
48	#11718377	C₂²	1	4	yes	complemented
49	#11718375	C₂²	1	8	yes	complemented
50	#11718374	C₂²	1	4	yes	complemented
51	#11718372	C₂²	1	4	yes	complemented
52	#11718371	C₂²	1	8	yes	complemented
53	#11718364	C₂²	1	4	yes	complemented
54	#11718360	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₅₂	C₂²	1	4	yes	complemented
56	#11718357	C₂²	1	2	yes	complemented
57	#11718357	C₂²	1	2	yes	complemented
58	#11718356	C₂²	1	1	yes	characteristic, complemented
59	#11718354	C₂²	1	2	yes	complemented
60	C₄×D₁₀₄	C₂²	1	4	yes	complemented
61	C₄×#6095	C₂²	1	8	yes	complemented
62	#11718344	C₂²	1	2	yes	complemented
63	#11718344	C₂²	1	2	yes	complemented
64	#11718343	C₂²	1	2	yes	complemented
65	#11718341	C₂²	1	2	yes	complemented
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×#6127	C₂³	1	4	yes	—
68	C₂×C₁₃×M₁₆	—	2	4	no	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	4	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#117	D₄	1	4	yes	—
79	C₁₃×#117	C₂³	1	2	yes	—
80	C₁₃×#117	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	#88207	—	2	4	no	—
86	#88184	—	2	4	no	—
87	#88184	C₂³	1	8	yes	—
88	#88183	—	2	4	no	—
89	C₄×C₂²⋊D₁₃	—	2	8	no	—
90	C₄×C₂²⋊D₁₃	—	2	8	no	—
91	#88180	C₂³	1	4	yes	—
92	#88178	—	2	4	no	—
93	#88178	C₂³	1	8	yes	—
94	C₂×Dic₅₂	C₂³	1	2	yes	—
95	C₂×Dic₅₂	C₂³	1	2	yes	—
96	#88158	—	2	8	no	—
97	#88158	—	2	8	no	—
98	C₂×D₁₀₄	C₂³	1	2	yes	—
99	C₂×D₁₀₄	C₂³	1	2	yes	—
100	C₂×#6095	C₂³	1	4	yes	—
101	C₂×#6095	C₂³	1	4	yes	—
102	#88152	—	2	8	no	—
103	#88150	—	2	8	no	—
104	#88148	—	2	8	no	—
105	#88143	—	2	8	no	—
106	#88139	—	2	8	no	—
107	#88138	—	2	8	no	—
108	#88137	—	2	8	no	—
109	#88133	—	2	8	no	—
110	#88129	C₂³	1	4	yes	—
111	#88128	C₂³	1	2	yes	—
112	C₄×D₅₂	—	2	4	no	—
113	C₄×D₅₂	C₂³	1	8	yes	—
114	#88126	—	2	4	no	—
115	C₄²×D₁₃	—	2	4	no	—
116	#88124	C₂³	1	4	yes	—
117	#88123	C₂³	1	2	yes	—
118	#88123	C₂³	1	4	yes	—
119	C₄×Dic₂₆	—	2	4	no	—
120	C₄×Dic₂₆	C₂³	1	8	yes	—
121	C₁₃×#97	C₂³	1	2	yes	—
122	C₁₃×#97	C₂³	1	2	yes	—
123	C₁₃×#97	C₂³	1	2	yes	—
124	C₁₃×#97	C₂³	1	2	yes	—
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	#88061	C₂³	1	8	yes	—
132	#88061	C₂³	1	8	yes	—
133	#88058	C₂³	1	4	yes	—
134	#88058	C₂³	1	4	yes	—
135	#88057	C₂³	1	4	yes	—
136	#88057	C₂³	1	4	yes	—
137	#88056	C₂³	1	8	yes	—
138	#88056	C₂³	1	8	yes	—
139	#60682	—	13	1	no	maximal, Sylow
140	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₃	—	2	4	no	—
150	C₂×C₂²⋊D₁₃	—	2	8	no	—
151	#6127	—	2	8	no	—
152	#6127	—	2	8	no	—
153	C₂×D₅₂	—	2	4	no	—
154	C₂×D₅₂	C₂⁴	1	4	yes	—
155	C₂×C₄×D₁₃	—	2	4	no	—
156	C₂×C₄×D₁₃	—	2	8	no	—
157	C₂×Dic₂₆	—	2	4	no	—
158	C₂×Dic₂₆	C₂⁴	1	4	yes	—
159	C₁₃×M₁₆	—	2	4	no	—
160	C₁₃×M₁₆	—	2	4	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₂×C₈×C₁₃	#41	1	4	yes	—
166	C₂×C₈×C₁₃	#41	1	4	yes	—
167	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
175	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
177	C₄²×C₁₃	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	C₂⁴	1	2	yes	—
180	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	—	2	8	no	—
183	C₂²⋊Dic₁₃	—	2	4	no	—
184	#6103	—	2	8	no	—
185	#6103	—	2	8	no	—
186	#6103	—	2	8	no	—
187	C₄⋊Dic₁₃	—	2	4	no	—
188	C₄⋊Dic₁₃	—	2	4	no	—
189	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
190	#6101	—	2	8	no	—
191	#6101	—	2	8	no	—
192	#6101	—	2	8	no	—
193	C₄×Dic₁₃	—	2	4	no	—
194	C₄×Dic₁₃	—	2	8	no	—
195	Dic₅₂	—	2	4	no	—
196	Dic₅₂	—	2	4	no	—
197	D₁₀₄	—	2	4	no	—
198	D₁₀₄	—	2	4	no	—
199	#6095	—	2	8	no	—
200	#6095	—	2	8	no	—
201	#3455	—	13	2	no	—
202	#3177	—	13	2	no	—
203	#3176	—	13	2	no	—
204	#3175	—	13	4	no	—
205	#3174	—	13	4	no	—
206	#3173	—	13	4	no	—
207	#3160	—	13	1	no	—
208	#3147	—	13	1	no	—
209	#3135	—	13	2	no	—
210	#3054	—	13	2	no	—
211	#3050	—	13	2	no	—
212	#2943	—	13	2	no	—
213	C₄×#135	—	13	2	no	—
214	C₂×#405	D₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂²×D₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₂²⋊D₁₃	—	4	8	no	—
235	C₂²⋊D₁₃	—	8	8	no	—
236	C₂×Dic₁₃	—	2	4	no	—
237	C₂×Dic₁₃	—	2	8	no	—
238	D₅₂	—	2	4	no	—
239	D₅₂	—	2	4	no	—
240	D₅₂	—	8	4	no	—
241	C₄×D₁₃	—	4	8	no	—
242	C₄×D₁₃	—	8	8	no	—
243	Dic₂₆	—	2	4	no	—
244	Dic₂₆	—	2	4	no	—
245	Dic₂₆	—	8	4	no	—
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	C₂×#41	1	2	yes	—
249	C₈×C₁₃	C₂×#41	1	2	yes	—
250	C₈×C₁₃	C₂×#41	1	2	yes	—
251	C₈×C₁₃	C₂×#41	1	2	yes	—
252	C₂×#135	—	13	2	no	—
253	C₂×#135	—	13	2	no	—
254	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
255	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
256	#542	—	13	8	no	—
257	#541	—	13	4	no	—
258	#540	—	13	4	no	—
259	#539	—	26	4	no	—
260	#538	—	26	4	no	—
261	#533	—	13	2	no	—
262	#532	—	13	2	no	—
263	#529	—	26	8	no	—
264	#525	—	13	4	no	—
265	C₄×#41	—	13	4	no	—
266	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
267	#500	—	13	2	no	—
268	#499	—	13	2	no	—
269	#499	—	13	2	no	—
270	#498	—	13	2	no	—
271	#495	—	13	2	no	—
272	#495	—	13	2	no	—
273	#494	—	13	1	no	—
274	#493	—	13	1	no	—
275	#492	—	13	2	no	—
276	#491	—	13	4	no	—
277	#490	—	13	4	no	—
278	#489	—	13	8	no	—
279	#470	—	13	4	no	—
280	#469	—	13	4	no	—
281	#468	—	13	8	no	—
282	#467	—	13	4	no	—
283	#466	—	13	4	no	—
284	#465	—	13	8	no	—
285	#442	—	13	4	no	—
286	#441	—	13	4	no	—
287	#440	—	13	8	no	—
288	C₄×Q₁₆	—	13	4	no	—
289	C₄×SD₁₆	—	13	8	no	—
290	C₄×D₈	—	13	4	no	—
291	#427	—	13	2	no	—
292	#427	—	13	2	no	—
293	#416	—	13	4	no	—
294	#416	—	13	4	no	—
295	#405	C₂×D₁₃	1	2	yes	—
296	#405	C₂×D₁₃	1	2	yes	—
297	#405	C₂×D₁₃	1	2	yes	—
298	#405	C₂×D₁₃	1	2	yes	—
299	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
300	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	#532	1	2	yes	—
308	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
309	C₂×D₁₃	—	4	8	no	—
310	C₂×D₁₃	—	4	4	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	4	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	#532	1	2	yes	—
316	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
318	Dic₁₃	—	4	8	no	—
319	Dic₁₃	—	4	4	no	—
320	C₂×#41	—	13	4	no	—
321	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
322	#135	—	26	8	no	—
323	#135	—	26	8	no	—
324	C₂×Q₁₆	—	13	2	no	—
325	C₂×Q₁₆	—	13	2	no	—
326	C₂×SD₁₆	—	13	4	no	—
327	C₂×SD₁₆	—	13	4	no	—
328	C₂×D₈	—	13	2	no	—
329	C₂×D₈	—	13	2	no	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
332	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
333	C₂²×C₈	—	2	4	no	—
334	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
336	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
337	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
340	C₄⋊Q₈	—	13	4	no	—
341	C₄⋊Q₈	—	13	2	no	—
342	#127	—	13	2	no	—
343	#126	—	26	8	no	—
344	#126	—	26	8	no	—
345	#125	—	13	4	no	—
346	#125	—	26	8	no	—
347	#124	—	13	4	no	—
348	#124	—	26	8	no	—
349	#123	—	26	4	no	—
350	#123	—	26	8	no	—
351	#123	—	26	8	no	—
352	C₂²⋊Q₈	—	13	8	no	—
353	C₂²⋊Q₈	—	26	4	no	—
354	C₂²⋊Q₈	—	26	8	no	—
355	#121	—	13	8	no	—
356	#121	—	26	4	no	—
357	#121	—	26	8	no	—
358	#120	—	26	4	no	—
359	C₄×Q₈	—	13	8	no	—
360	C₄×Q₈	—	26	4	no	—
361	C₄×D₄	—	13	8	no	—
362	C₄×D₄	—	26	8	no	—
363	C₄×D₄	—	26	8	no	—
364	C₄×D₄	—	26	4	no	—
365	#117	—	13	4	no	—
366	#117	—	26	4	no	—
367	#117	D₅₂	1	4	yes	—
368	#117	C₂²×D₁₃	1	2	yes	—
369	#117	C₂²×D₁₃	1	2	yes	—
370	C₂×C₄⋊C₄	D₅₂	1	2	yes	—
371	C₂×C₂²⋊C₄	D₅₂	1	2	yes	—
372	C₂×C₄²	—	26	4	no	—
373	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
375	#107	—	13	4	no	—
376	#107	—	13	4	no	—
377	#106	—	13	4	no	—
378	#106	—	13	4	no	—
379	#103	—	13	8	no	—
380	#103	—	13	8	no	—
381	#102	—	13	8	no	—
382	#102	—	13	8	no	—
383	#97	C₂²×D₁₃	1	2	yes	—
384	#97	C₂²×D₁₃	1	2	yes	—
385	#97	C₂²×D₁₃	1	2	yes	—
386	#97	C₂²×D₁₃	1	2	yes	—
387	C₄×C₈	C₂²×D₁₃	1	2	yes	—
388	C₄×C₈	C₂²×D₁₃	1	2	yes	—
389	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
390	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
391	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
392	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
393	C₂×C₁₃	—	2	2	no	—
394	C₂×C₁₃	—	4	2	no	—
395	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
396	C₂×C₁₃	#3584	1	2	yes	—
397	D₁₃	—	8	4	no	—
398	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
399	#41	—	26	8	no	—
400	#41	—	26	8	no	—
401	C₂×Q₈	—	13	4	no	—
402	C₂×Q₈	—	26	4	no	—
403	C₂×D₄	—	13	4	no	—
404	C₂×D₄	—	26	4	no	—
405	C₂×D₄	—	26	8	no	—
406	C₂×D₄	—	26	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	26	4	no	—
410	C₂²×C₄	—	26	8	no	—
411	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₅₂	1	2	yes	—
413	C₂²×C₄	C₂×D₅₂	1	2	yes	—
414	C₂²×C₄	C₂×D₅₂	1	2	yes	—
415	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
416	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
417	Q₁₆	—	26	4	no	—
418	Q₁₆	—	26	4	no	—
419	SD₁₆	—	26	8	no	—
420	SD₁₆	—	26	8	no	—
421	D₈	—	26	4	no	—
422	D₈	—	26	4	no	—
423	M₁₆	—	2	4	no	—
424	M₁₆	—	2	4	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	#6127	1	4	yes	—
430	C₂×C₈	#6127	1	4	yes	—
431	C₂×C₈	C₂³×D₁₃	1	2	yes	—
432	C₂×C₈	C₂³×D₁₃	1	2	yes	—
433	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
434	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
435	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
436	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
437	C₄⋊C₄	—	13	8	no	—
438	C₄⋊C₄	—	26	8	no	—
439	C₄⋊C₄	—	26	4	no	—
440	C₄⋊C₄	—	26	8	no	—
441	C₄⋊C₄	—	26	8	no	—
442	C₄⋊C₄	—	26	4	no	—
443	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
444	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
445	C₂²⋊C₄	—	26	4	no	—
446	C₂²⋊C₄	—	26	8	no	—
447	C₂²⋊C₄	—	26	8	no	—
448	C₂²⋊C₄	—	26	8	no	—
449	C₂²⋊C₄	—	26	8	no	—
450	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
451	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
452	C₄²	—	26	8	no	—
453	C₄²	—	26	4	no	—
454	C₄²	C₂×D₅₂	1	2	yes	—
455	C₄²	C₂×D₅₂	1	2	yes	—
456	C₄²	C₂³×D₁₃	1	2	yes	—
457	C₄²	C₂³×D₁₃	1	1	yes	characteristic
458	C₄²	C₂³×D₁₃	1	1	yes	characteristic
459	C₁₃	#60682	1	1	yes	characteristic, complemented, Sylow
460	C₂³	—	2	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	26	4	no	—
463	C₂³	C₂²×D₅₂	1	2	yes	—
464	C₂³	C₂²×D₅₂	1	1	yes	characteristic
465	Q₈	—	26	4	no	—
466	Q₈	—	26	4	no	—
467	Q₈	—	104	4	no	—
468	D₄	—	26	4	no	—
469	D₄	—	26	4	no	—
470	D₄	—	52	8	no	—
471	D₄	—	104	4	no	—
472	D₄	—	104	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	26	8	no	—
480	C₂×C₄	—	26	4	no	—
481	C₂×C₄	—	52	8	no	—
482	C₂×C₄	—	104	8	no	—
483	C₂×C₄	C₂²×D₅₂	1	4	yes	—
484	C₂×C₄	C₂²×D₅₂	1	2	yes	—
485	C₂×C₄	C₂²×D₅₂	1	2	yes	—
486	C₂×C₄	C₂²×D₅₂	1	2	yes	—
487	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
488	C₂×C₄	C₂×#6127	1	2	yes	—
489	C₂×C₄	C₂×#6127	1	2	yes	—
490	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂×#6127	1	2	yes	—
494	C₈	C₂×#6127	1	2	yes	—
495	C₈	C₂×#6127	1	2	yes	—
496	C₈	C₂×#6127	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	52	8	no	—
502	C₂²	—	52	4	no	—
503	C₂²	#11719182	1	2	yes	—
504	C₂²	C₂³×D₅₂	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	52	8	no	—
510	C₄	—	52	4	no	—
511	C₄	#11719182	1	2	yes	—
512	C₄	C₂²×#6127	1	1	yes	characteristic
513	C₄	C₂²×#6127	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	2	no	—
516	C₂	—	104	4	no	—
517	C₂	C₂×#11719182	1	1	yes	characteristic
518	C₂	#13129610	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂³×D₄
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#60682
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #13128226	C₂	semidirect
2. #13125495	C₂	semidirect
3. #13125486	C₂	semidirect
4. #13125475	C₂	semidirect
5. #13125464	C₂	semidirect
6. #13125453	C₂	semidirect
7. #13125350	C₂	semidirect
8. #13125264	C₂	semidirect
9. #13125182	C₂	semidirect
10. #13124445	C₂	semidirect
11. #13124417	C₂	semidirect
12. #13123638	C₂	semidirect
13. C₄×#88158	C₂	semidirect
14. C₂×C₁₃×#405	C₂	semidirect
48. #11718377	C₂²	semidirect
49. #11718375	C₂²	semidirect
50. #11718374	C₂²	semidirect
51. #11718372	C₂²	semidirect
52. #11718371	C₂²	semidirect
53. #11718364	C₂²	semidirect
54. #11718360	C₂²	semidirect
55. C₄×Dic₅₂	C₂²	semidirect
56. #11718357	C₂²	semidirect
57. #11718357	C₂²	semidirect
58. #11718356	C₂²	semidirect
59. #11718354	C₂²	semidirect
60. C₄×D₁₀₄	C₂²	semidirect
61. C₄×#6095	C₂²	semidirect
62. #11718344	C₂²	semidirect
63. #11718344	C₂²	semidirect
64. #11718343	C₂²	semidirect
65. #11718341	C₂²	semidirect
214. C₂×#405	D₁₃	semidirect
459. C₁₃	#60682	semidirect

Maximal subgroups

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

subgroup	index
#13128226	2
#13125495	2
#13125486	2
#13125475	2
#13125464	2
#13125453	2
#13125350	2
#13125264	2
#13125182	2
#13124445	2
#13124417	2
#13123638	2
C₄×#88158	2
C₂×C₁₃×#405	2
#60682	13