Subgroups — #15832448

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123797	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123792	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88158	C₂	1	1	yes	maximal, characteristic
4	#13113685	C₂	1	2	yes	maximal, complemented
5	#13113678	C₂	1	2	yes	maximal, complemented
6	#13113671	C₂	1	2	yes	maximal, complemented
7	#13113664	C₂	1	2	yes	maximal, complemented
8	#13113216	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718046	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88158	C₄	1	1	yes	characteristic
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718774	C₄	1	1	yes	characteristic
19	#11718774	C₄	1	1	yes	characteristic
20	#11718767	C₄	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	#11718499	C₂²	1	2	yes	—
24	#11718495	C₂²	1	2	yes	—
25	#11718492	C₂²	1	2	yes	—
26	#11718491	C₂²	1	2	yes	—
27	#11718391	—	2	2	no	—
28	#11718386	—	2	2	no	—
29	C₄×Dic₅₂	C₄	1	1	yes	characteristic
30	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
31	C₄×D₁₀₄	C₄	1	1	yes	characteristic
32	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
33	C₄×#6095	C₄	1	1	yes	characteristic
34	C₄×#6095	C₄	1	1	yes	characteristic
35	C₄×#6095	C₂²	1	1	yes	characteristic
36	C₄×#6095	C₂²	1	1	yes	characteristic
37	C₄×#6094	—	2	1	no	—
38	#11718346	—	2	1	no	—
39	#11718346	—	2	1	no	—
40	C₄×C₈×D₁₃	—	2	1	no	—
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718076	C₂²	1	2	yes	—
45	#11718075	C₂²	1	2	yes	—
46	#11718075	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×#6127	C₂×C₄	1	1	yes	characteristic
50	C₂×#6127	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	—	2	1	no	—
55	C₄×C₂²⋊D₁₃	—	2	1	no	—
56	C₄×C₂²⋊D₁₃	—	2	1	no	—
57	C₄×C₂²⋊D₁₃	—	2	1	no	—
58	#88180	C₂×C₄	1	1	yes	characteristic
59	#88180	C₂×C₄	1	1	yes	characteristic
60	C₂²×#1055	—	2	1	no	—
61	C₂²×#1055	D₄	1	2	yes	—
62	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
63	#88158	—	2	4	no	—
64	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
65	C₂×#6095	C₂×C₄	1	1	yes	characteristic
66	C₂×#6095	C₂×C₄	1	1	yes	characteristic
67	C₂×#6094	—	2	2	no	—
68	C₂×C₈×D₁₃	—	2	2	no	—
69	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
70	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
71	C₄×D₅₂	C₂³	1	1	yes	characteristic
72	C₄×D₅₂	C₂³	1	1	yes	characteristic
73	#88126	—	2	1	no	—
74	#88126	—	2	1	no	—
75	C₄²×D₁₃	—	2	1	no	—
76	C₄²×D₁₃	—	2	1	no	—
77	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
80	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₃×C₂²⋊C₈	—	2	1	no	—
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₄×C₈×C₁₃	—	2	1	no	—
86	C₄×C₈×C₁₃	—	2	1	no	—
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	#88061	C₂×C₄	1	1	yes	characteristic
92	#88061	C₂×C₄	1	1	yes	characteristic
93	#88061	C₂×C₄	1	1	yes	characteristic
94	#88061	C₂×C₄	1	1	yes	characteristic
95	#88060	—	2	2	no	—
96	#88060	—	2	2	no	—
97	#88058	C₂×C₄	1	1	yes	characteristic
98	#88058	C₂×C₄	1	1	yes	characteristic
99	#88057	C₂×C₄	1	1	yes	characteristic
100	#88057	C₂×C₄	1	1	yes	characteristic
101	#88056	C₂×C₄	1	1	yes	characteristic
102	#88056	C₂×C₄	1	1	yes	characteristic
103	#88056	C₂×C₄	1	1	yes	characteristic
104	#88056	C₂×C₄	1	1	yes	characteristic
105	#88055	—	2	2	no	—
106	#88054	—	2	2	no	—
107	#88054	—	2	2	no	—
108	C₈×Dic₁₃	—	2	2	no	—
109	C₄×#1055	—	2	1	no	—
110	C₄×#1055	D₄	1	1	yes	characteristic
111	C₄×#1055	D₄	1	1	yes	characteristic
112	C₄×#1055	C₂³	1	2	yes	—
113	C₄×#1055	C₂³	1	2	yes	—
114	#17863	—	13	1	no	maximal, Sylow
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₃	—	2	1	no	—
119	C₂×C₂²⋊D₁₃	—	2	1	no	—
120	#6127	—	2	2	no	—
121	#6127	—	2	2	no	—
122	#6127	—	2	2	no	—
123	#6127	M₁₆	1	4	yes	complemented
124	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	—	2	1	no	—
127	C₂×C₄×D₁₃	—	2	1	no	—
128	C₂×C₄×D₁₃	—	2	1	no	—
129	C₂×C₄×D₁₃	—	2	1	no	—
130	C₂×C₄×D₁₃	—	2	1	no	—
131	C₂×C₄×D₁₃	—	2	1	no	—
132	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
133	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₃	#41	1	1	yes	characteristic
145	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²⋊Dic₁₃	—	2	1	no	—
147	C₂²⋊Dic₁₃	—	2	1	no	—
148	#6103	—	2	1	no	—
149	#6103	—	2	1	no	—
150	#6103	—	2	1	no	—
151	#6103	—	2	1	no	—
152	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	#6101	—	2	1	no	—
157	#6101	—	2	1	no	—
158	#6101	—	2	1	no	—
159	#6101	—	2	1	no	—
160	C₄×Dic₁₃	—	2	1	no	—
161	C₄×Dic₁₃	—	2	1	no	—
162	C₄×Dic₁₃	—	2	1	no	—
163	C₄×Dic₁₃	—	2	1	no	—
164	C₄×Dic₁₃	—	2	1	no	—
165	C₄×Dic₁₃	—	2	1	no	—
166	C₂×#1055	—	2	4	no	—
167	C₂×#1055	—	2	2	no	—
168	C₂×#1055	—	4	2	no	—
169	C₂×#1055	C₂×D₄	1	2	yes	—
170	C₂×#1055	C₂×D₄	1	2	yes	—
171	Dic₅₂	—	2	2	no	—
172	D₁₀₄	—	2	2	no	—
173	#6095	—	2	2	no	—
174	#6095	—	2	2	no	—
175	#6094	—	4	4	no	—
176	C₈×D₁₃	—	4	4	no	—
177	#2965	—	13	1	no	—
178	C₈×#41	—	13	1	no	—
179	C₄×#135	—	13	1	no	—
180	#1584	—	13	2	no	—
181	#1583	—	13	2	no	—
182	#1582	—	13	2	no	—
183	#1581	—	13	2	no	—
184	#1564	D₁₃	1	1	yes	characteristic, complemented
185	#1476	—	13	1	no	—
186	#1476	—	13	1	no	—
187	C₂×#322	—	13	1	no	—
188	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂²×D₁₃	—	2	1	no	—
190	C₂²×D₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
197	C₂×C₄×C₁₃	#131	1	2	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂²⋊D₁₃	—	2	4	no	—
202	C₂²⋊D₁₃	—	4	2	no	—
203	C₂×Dic₁₃	—	2	1	no	—
204	C₂×Dic₁₃	—	2	1	no	—
205	C₂×Dic₁₃	—	2	1	no	—
206	C₂×Dic₁₃	—	2	1	no	—
207	C₂×Dic₁₃	—	2	1	no	—
208	C₂×Dic₁₃	—	2	1	no	—
209	D₅₂	—	2	1	no	—
210	D₅₂	—	2	1	no	—
211	D₅₂	—	2	1	no	—
212	D₅₂	C₂×M₁₆	1	2	yes	—
213	C₄×D₁₃	—	2	4	no	—
214	C₄×D₁₃	—	4	2	no	—
215	C₄×D₁₃	—	4	2	no	—
216	C₄×D₁₃	—	4	2	no	—
217	C₄×D₁₃	—	4	2	no	—
218	C₄×D₁₃	—	4	2	no	—
219	Dic₂₆	—	2	1	no	—
220	Dic₂₆	—	2	1	no	—
221	Dic₂₆	—	2	1	no	—
222	Dic₂₆	C₂×M₁₆	1	2	yes	—
223	C₈×C₁₃	—	2	1	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	—	2	1	no	—
227	C₈×C₁₃	—	4	2	no	—
228	C₈×C₁₃	—	4	2	no	—
229	#1055	—	2	2	no	—
230	#1055	—	4	2	no	—
231	#1055	#135	1	4	yes	complemented
232	C₂×#135	—	13	1	no	—
233	C₄×#41	—	13	1	no	—
234	C₄×#41	—	13	1	no	—
235	#446	—	13	2	no	—
236	C₈×Q₈	—	13	2	no	—
237	C₄×Q₁₆	—	13	1	no	—
238	C₄×Q₁₆	—	13	1	no	—
239	C₄×SD₁₆	—	13	1	no	—
240	C₄×SD₁₆	—	13	1	no	—
241	C₄×SD₁₆	—	13	1	no	—
242	C₄×SD₁₆	—	13	1	no	—
243	C₄×D₈	—	13	1	no	—
244	C₄×D₈	—	13	1	no	—
245	#436	—	13	2	no	—
246	#435	—	26	2	no	—
247	C₈×D₄	—	13	2	no	—
248	C₈×D₄	—	26	2	no	—
249	#431	—	26	1	no	—
250	#431	—	26	1	no	—
251	#431	C₂×D₁₃	1	1	yes	characteristic
252	#431	C₂×D₁₃	1	1	yes	characteristic
253	#427	—	13	1	no	—
254	#416	—	13	1	no	—
255	#416	—	13	1	no	—
256	C₄×M₁₆	—	26	1	no	—
257	C₂×C₄×C₈	—	13	1	no	—
258	C₂×C₄×C₈	—	13	1	no	—
259	C₂×C₄×C₈	—	26	1	no	—
260	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
261	#335	C₂×D₁₃	1	2	yes	—
262	#334	C₂×D₁₃	1	2	yes	—
263	Q₈⋊C₈	—	13	2	no	—
264	Q₈⋊C₈	—	13	2	no	—
265	D₄⋊C₈	—	13	2	no	—
266	D₄⋊C₈	—	13	2	no	—
267	#322	—	13	2	no	—
268	#322	—	13	2	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	#435	1	2	yes	—
272	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×D₁₃	—	2	2	no	—
274	C₂×D₁₃	—	4	1	no	—
275	C₂×D₁₃	—	4	1	no	—
276	C₂×D₁₃	—	4	1	no	—
277	C₂×D₁₃	—	4	1	no	—
278	C₂×D₁₃	—	4	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	#435	1	2	yes	—
282	C₄×C₁₃	#444	1	2	yes	—
283	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
284	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₃	C₂×#135	1	2	yes	—
286	Dic₁₃	—	2	2	no	—
287	Dic₁₃	—	4	1	no	—
288	Dic₁₃	—	4	1	no	—
289	Dic₁₃	—	4	1	no	—
290	Dic₁₃	—	4	1	no	—
291	Dic₁₃	—	4	1	no	—
292	C₂×#41	—	13	1	no	—
293	C₂×#41	—	13	1	no	—
294	#135	—	26	4	no	—
295	C₂×Q₁₆	—	13	1	no	—
296	C₂×SD₁₆	—	13	1	no	—
297	C₂×SD₁₆	—	13	1	no	—
298	C₂×D₈	—	13	1	no	—
299	C₂×M₁₆	—	26	2	no	—
300	C₂²×C₈	—	13	2	no	—
301	C₂²×C₈	—	26	2	no	—
302	C₂²×C₈	—	26	1	no	—
303	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
305	C₄×Q₈	—	13	1	no	—
306	C₄×Q₈	—	13	1	no	—
307	C₄×Q₈	—	13	1	no	—
308	C₄×Q₈	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	—	13	1	no	—
312	C₄×D₄	—	13	1	no	—
313	C₄×D₄	—	26	1	no	—
314	C₄×D₄	—	26	1	no	—
315	C₄×D₄	—	26	1	no	—
316	C₄×D₄	—	26	1	no	—
317	#117	—	13	1	no	—
318	#117	—	13	1	no	—
319	#117	—	26	1	no	—
320	#117	—	26	1	no	—
321	C₂×C₄²	—	26	1	no	—
322	C₂×C₄²	—	26	1	no	—
323	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
324	#107	—	13	1	no	—
325	#107	—	13	1	no	—
326	#106	—	13	1	no	—
327	#106	—	13	1	no	—
328	C₄⋊C₈	—	26	2	no	—
329	C₄⋊C₈	—	26	2	no	—
330	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
331	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
332	#103	—	13	1	no	—
333	#103	—	13	1	no	—
334	#103	—	13	1	no	—
335	#103	—	13	1	no	—
336	#102	—	13	1	no	—
337	#102	—	13	1	no	—
338	#102	—	13	1	no	—
339	#102	—	13	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	26	2	no	—
343	C₂²⋊C₈	—	26	2	no	—
344	#97	—	26	2	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	13	1	no	—
348	C₄×C₈	—	13	1	no	—
349	C₄×C₈	—	13	2	no	—
350	C₄×C₈	—	13	2	no	—
351	C₄×C₈	—	26	2	no	—
352	C₄×C₈	—	26	1	no	—
353	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
354	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
357	C₂×C₁₃	—	2	2	no	—
358	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
359	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
361	D₁₃	—	4	2	no	—
362	D₁₃	—	8	1	no	—
363	#41	—	13	4	no	—
364	#41	—	26	2	no	—
365	#41	—	26	2	no	—
366	#41	—	26	2	no	—
367	C₂×Q₈	—	13	1	no	—
368	C₂×Q₈	—	13	1	no	—
369	C₂×D₄	—	13	1	no	—
370	C₂×D₄	—	13	1	no	—
371	C₂×D₄	—	26	1	no	—
372	C₂×D₄	—	26	1	no	—
373	C₂²×C₄	—	26	1	no	—
374	C₂²×C₄	—	26	1	no	—
375	C₂²×C₄	—	26	1	no	—
376	C₂²×C₄	—	26	1	no	—
377	C₂²×C₄	—	26	1	no	—
378	C₂²×C₄	—	26	1	no	—
379	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
381	C₂²×C₄	#6131	1	1	yes	characteristic
382	Q₁₆	—	26	2	no	—
383	SD₁₆	—	26	2	no	—
384	SD₁₆	—	26	2	no	—
385	D₈	—	26	2	no	—
386	M₁₆	—	52	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	13	2	no	—
392	C₂×C₈	—	13	2	no	—
393	C₂×C₈	—	26	4	no	—
394	C₂×C₈	—	26	2	no	—
395	C₂×C₈	—	52	4	no	—
396	C₂×C₈	—	52	2	no	—
397	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
398	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
399	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
400	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
401	C₄⋊C₄	—	13	1	no	—
402	C₄⋊C₄	—	13	1	no	—
403	C₄⋊C₄	—	13	1	no	—
404	C₄⋊C₄	—	13	1	no	—
405	C₄⋊C₄	—	26	1	no	—
406	C₄⋊C₄	—	26	1	no	—
407	C₄⋊C₄	—	26	1	no	—
408	C₄⋊C₄	—	26	1	no	—
409	C₂²⋊C₄	—	26	1	no	—
410	C₂²⋊C₄	—	26	1	no	—
411	C₂²⋊C₄	—	26	1	no	—
412	C₂²⋊C₄	—	26	1	no	—
413	C₂²⋊C₄	—	26	1	no	—
414	C₂²⋊C₄	—	26	1	no	—
415	C₄²	—	26	1	no	—
416	C₄²	—	26	1	no	—
417	C₄²	—	26	1	no	—
418	C₄²	—	26	1	no	—
419	C₄²	—	26	1	no	—
420	C₄²	—	26	1	no	—
421	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
422	C₄²	D₄×D₁₃	1	1	yes	characteristic
423	C₄²	#6131	1	1	yes	characteristic
424	C₄²	C₂³×D₁₃	1	1	yes	characteristic
425	C₁₃	#17863	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	26	1	no	—
427	C₂³	—	26	1	no	—
428	C₂³	#88147	1	1	yes	characteristic
429	Q₈	—	13	2	no	—
430	Q₈	—	26	1	no	—
431	Q₈	—	26	1	no	—
432	Q₈	—	26	1	no	—
433	D₄	—	13	2	no	—
434	D₄	—	26	4	no	—
435	D₄	—	26	1	no	—
436	D₄	—	26	1	no	—
437	D₄	—	26	1	no	—
438	D₄	—	52	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	4	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	1	no	—
445	C₂×C₄	—	26	1	no	—
446	C₂×C₄	—	26	1	no	—
447	C₂×C₄	—	26	1	no	—
448	C₂×C₄	—	52	2	no	—
449	C₂×C₄	—	52	2	no	—
450	C₂×C₄	—	52	2	no	—
451	C₂×C₄	—	52	2	no	—
452	C₂×C₄	—	52	2	no	—
453	C₂×C₄	#88147	1	1	yes	characteristic
454	C₂×C₄	#88147	1	1	yes	characteristic
455	C₂×C₄	#88147	1	1	yes	characteristic
456	C₂×C₄	#88155	1	2	yes	—
457	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#6131	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	—	13	4	no	—
468	C₈	—	26	2	no	—
469	C₈	—	52	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	26	2	no	—
473	C₂²	—	52	1	no	—
474	C₂²	—	52	1	no	—
475	C₂²	—	52	1	no	—
476	C₂²	—	52	1	no	—
477	C₂²	—	52	1	no	—
478	C₂²	#11718497	1	2	yes	—
479	C₂²	C₂×#88147	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	26	2	no	—
483	C₄	—	52	1	no	—
484	C₄	—	52	1	no	—
485	C₄	—	52	1	no	—
486	C₄	—	52	1	no	—
487	C₄	—	52	1	no	—
488	C₄	#11718497	1	2	yes	—
489	C₄	#11718555	1	2	yes	—
490	C₄	C₂×#88155	1	1	yes	characteristic
491	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
492	C₄	D₁₃×#135	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	52	2	no	—
495	C₂	—	104	1	no	—
496	C₂	C₂×#11718497	1	1	yes	characteristic
497	C₂	#13123607	1	1	yes	characteristic
498	C₂	C₂×#11718555	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1564	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88158	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1564	D₁₃
hypocenter	C₁₃	#17863
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #13123797	C₂	semidirect
2. #13123792	C₂	semidirect
4. #13113685	C₂	semidirect
5. #13113678	C₂	semidirect
6. #13113671	C₂	semidirect
7. #13113664	C₂	semidirect
8. #13113216	C₂	semidirect
9. #13113216	C₂	semidirect
10. C₂×#11718046	C₂	semidirect
11. C₁₃×#1564	C₂	semidirect
123. #6127	M₁₆	semidirect
184. #1564	D₁₃	semidirect
231. #1055	#135	semidirect
425. C₁₃	#17863	semidirect

Maximal subgroups

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

subgroup	index
#13123797	2
#13123792	2
C₄×#88158	2
#13113685	2
#13113678	2
#13113671	2
#13113664	2
#13113216	2
C₂×#11718046	2
C₁₃×#1564	2
#17863	13