Subgroups — #15832529

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123792	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88186	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718673	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113717	C₂	1	2	yes	maximal, complemented
5	#13113703	C₂	1	2	yes	maximal, complemented
6	#13113682	C₂	1	2	yes	maximal, complemented
7	#13113668	C₂	1	2	yes	maximal, complemented
8	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113224	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88186	C₄	1	1	yes	characteristic
14	C₂²×#6099	—	2	1	no	—
15	C₄×#6127	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	C₁₃×#431	C₂²	1	1	yes	characteristic
18	#11718876	C₄	1	1	yes	characteristic
19	C₂×C₂²⋊#1055	—	2	1	no	—
20	#11718679	C₄	1	2	yes	—
21	C₄×#6105	C₂²	1	2	yes	—
22	#11718675	C₄	1	2	yes	—
23	C₄×#6104	C₂²	1	2	yes	—
24	#11718673	—	2	1	no	—
25	#11718673	—	2	1	no	—
26	#11718673	C₂²	1	2	yes	—
27	#11718673	C₂²	1	2	yes	—
28	#11718627	C₄	1	1	yes	characteristic
29	#11718625	C₄	1	1	yes	characteristic
30	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
31	C₄×#6099	C₂²	1	1	yes	characteristic
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	#11718495	C₂²	1	1	yes	characteristic, complemented
34	#11718495	C₂²	1	1	yes	characteristic, complemented
35	#11718491	C₂²	1	1	yes	characteristic, complemented
36	#11718491	C₂²	1	1	yes	characteristic, complemented
37	#11718386	—	2	1	no	—
38	#11718386	—	2	1	no	—
39	#11718346	—	2	1	no	—
40	C₄×C₈×D₁₃	—	2	1	no	—
41	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
42	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
43	#11718072	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718051	C₂²	1	2	yes	complemented
46	#11718048	C₂²	1	2	yes	complemented
47	#11718047	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×#6127	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
55	C₄×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6105	C₂×C₄	1	2	yes	—
60	#88186	—	2	4	no	—
61	C₂×#6104	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₁₃	—	2	1	no	—
63	C₄×C₂²⋊D₁₃	—	2	1	no	—
64	#88180	C₂×C₄	1	1	yes	characteristic
65	C₂×#6099	—	2	2	no	—
66	C₂×#6099	—	2	2	no	—
67	C₂×#6099	—	4	4	no	—
68	C₂×#6099	C₂×C₄	1	1	yes	characteristic
69	C₂×#6099	C₂×C₄	1	1	yes	characteristic
70	C₂²×#1055	—	2	1	no	—
71	C₂²×#1055	D₄	1	1	yes	characteristic
72	C₂²×#1055	D₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	—	2	1	no	—
74	C₂×C₈×D₁₃	—	2	1	no	—
75	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
76	C₄×D₅₂	C₂³	1	1	yes	characteristic
77	#88126	—	2	1	no	—
78	C₄²×D₁₃	—	2	1	no	—
79	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₁₃×C₂²⋊C₈	—	2	1	no	—
86	C₄×C₈×C₁₃	—	2	1	no	—
87	C₄×C₈×C₁₃	C₂³	1	2	yes	—
88	#88072	C₂×C₄	1	2	yes	—
89	#88072	C₂×C₄	1	2	yes	—
90	C₂²⋊#1055	—	2	2	no	—
91	C₂²⋊#1055	—	2	2	no	—
92	#88060	—	2	1	no	—
93	#88060	—	2	1	no	—
94	#88054	—	2	1	no	—
95	#88054	—	2	1	no	—
96	C₈×Dic₁₃	—	2	1	no	—
97	C₈×Dic₁₃	—	2	1	no	—
98	#88050	C₂×C₄	1	2	yes	—
99	#88049	C₂×C₄	1	2	yes	—
100	#88048	C₂×C₄	1	2	yes	—
101	#88047	C₂×C₄	1	2	yes	—
102	C₄⋊#1055	—	2	1	no	—
103	C₄⋊#1055	C₂³	1	2	yes	—
104	#88043	C₂×C₄	1	2	yes	—
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	D₄	1	1	yes	characteristic
107	C₄×#1055	C₂³	1	2	yes	—
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	C₄×#1055	C₂³	1	1	yes	characteristic
110	#17871	—	13	1	no	maximal, Sylow
111	C₂⁴×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂×C₂²⋊D₁₃	—	2	1	no	—
125	#6127	—	2	2	no	—
126	#6127	M₁₆	1	4	yes	complemented
127	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	—	2	1	no	—
129	C₂×C₄×D₁₃	—	2	1	no	—
130	C₂×C₄×D₁₃	—	2	1	no	—
131	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	2	2	no	—
138	C₁₃×C₂²⋊C₄	—	2	2	no	—
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	#41	1	1	yes	characteristic
142	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₁₃	—	2	1	no	—
144	#6105	—	2	4	no	—
145	#6104	—	2	4	no	—
146	#6103	—	2	1	no	—
147	#6103	—	2	1	no	—
148	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	#6101	—	2	1	no	—
151	#6101	—	2	1	no	—
152	C₄×Dic₁₃	—	2	1	no	—
153	C₄×Dic₁₃	—	2	1	no	—
154	C₄×Dic₁₃	—	2	1	no	—
155	#6099	—	2	2	no	—
156	#6099	—	2	2	no	—
157	#6099	—	4	4	no	—
158	#6099	—	4	4	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	4	1	no	—
162	C₂×#1055	—	4	2	no	—
163	C₂×#1055	C₂²×C₄	1	2	yes	—
164	C₂×#1055	C₂²×C₄	1	2	yes	—
165	C₂×#1055	C₂×D₄	1	1	yes	characteristic
166	C₂×#1055	C₂×D₄	1	1	yes	characteristic
167	C₂×#1055	C₂×D₄	1	1	yes	characteristic
168	C₂×#1055	C₂×D₄	1	1	yes	characteristic
169	C₈×D₁₃	—	4	2	no	—
170	C₈×D₁₃	—	4	2	no	—
171	C₈×#41	—	13	1	no	—
172	C₄×AGL(1,ℤ/8)	—	13	1	no	—
173	C₂×#436	—	13	1	no	—
174	#1588	—	13	2	no	—
175	#1586	—	13	2	no	—
176	#1583	—	13	2	no	—
177	#1581	—	13	2	no	—
178	#1565	—	13	1	no	—
179	#1478	D₁₃	1	1	yes	characteristic, complemented
180	#1477	—	13	1	no	—
181	#1451	—	13	1	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂²×D₁₃	—	2	1	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
203	C₂×C₄×C₁₃	#131	1	2	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₁₃	—	2	4	no	—
208	C₂×Dic₁₃	—	2	1	no	—
209	C₂×Dic₁₃	—	2	1	no	—
210	C₂×Dic₁₃	—	2	1	no	—
211	D₅₂	—	2	1	no	—
212	D₅₂	C₂×M₁₆	1	2	yes	complemented
213	C₄×D₁₃	—	2	4	no	—
214	C₄×D₁₃	—	4	2	no	—
215	C₄×D₁₃	—	4	1	no	—
216	C₄×D₁₃	—	4	1	no	—
217	Dic₂₆	—	2	1	no	—
218	Dic₂₆	C₂×M₁₆	1	2	yes	complemented
219	C₈×C₁₃	—	4	2	no	—
220	C₈×C₁₃	—	4	1	no	—
221	C₈×C₁₃	—	4	1	no	—
222	#1055	—	2	2	no	—
223	#1055	—	2	2	no	—
224	#1055	—	2	1	no	—
225	#1055	—	2	1	no	—
226	#1055	—	2	1	no	—
227	#1055	—	4	2	no	—
228	#1055	AGL(1,ℤ/8)	1	2	yes	complemented
229	C₂×AGL(1,ℤ/8)	—	13	1	no	—
230	C₂²×M₁₆	—	26	1	no	—
231	C₄×#41	—	13	1	no	—
232	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
233	C₈×Q₈	—	13	1	no	—
234	C₈×Q₈	—	13	1	no	—
235	#442	—	13	2	no	—
236	#440	—	13	2	no	—
237	C₄×SD₁₆	—	13	2	no	—
238	C₄×D₈	—	13	2	no	—
239	#436	—	13	2	no	—
240	#436	—	13	2	no	—
241	#436	—	26	1	no	—
242	#436	—	26	1	no	—
243	C₈×D₄	—	13	1	no	—
244	C₈×D₄	—	13	1	no	—
245	C₈×D₄	—	26	1	no	—
246	C₈×D₄	—	26	1	no	—
247	#431	—	26	1	no	—
248	#431	C₂×D₁₃	1	1	yes	characteristic
249	#431	C₂×D₁₃	1	1	yes	characteristic
250	#428	—	13	1	no	—
251	C₂×C₄⋊C₈	—	13	1	no	—
252	#418	—	13	1	no	—
253	#417	—	13	1	no	—
254	C₂×C₂²⋊C₈	—	26	1	no	—
255	C₄×M₁₆	—	13	1	no	—
256	C₂×C₄×C₈	—	13	1	no	—
257	C₂×C₄×C₈	—	26	1	no	—
258	#335	—	13	2	no	—
259	#334	—	13	2	no	—
260	Q₈⋊C₈	—	13	2	no	—
261	D₄⋊C₈	—	13	2	no	—
262	D₄⋊C₈	C₂×D₁₃	1	2	yes	—
263	D₄⋊C₈	C₂×D₁₃	1	2	yes	—
264	#322	—	13	2	no	—
265	#322	—	13	2	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	8	4	no	—
272	C₂²×C₁₃	#435	1	2	yes	—
273	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂×D₁₃	—	2	2	no	—
275	C₂×D₁₃	—	4	1	no	—
276	C₂×D₁₃	—	4	1	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	#435	1	2	yes	—
282	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
283	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
284	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₁₃	#575	1	1	yes	characteristic
286	Dic₁₃	—	2	2	no	—
287	Dic₁₃	—	4	1	no	—
288	Dic₁₃	—	4	1	no	—
289	C₂×#41	—	13	1	no	—
290	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	AGL(1,ℤ/8)	—	26	4	no	—
293	C₂×SD₁₆	—	13	2	no	—
294	C₂×D₈	—	13	2	no	—
295	C₂×M₁₆	—	13	1	no	—
296	C₂×M₁₆	—	13	1	no	—
297	C₂×M₁₆	—	26	2	no	—
298	C₂×M₁₆	—	26	2	no	—
299	C₂×M₁₆	—	52	4	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	26	1	no	—
303	C₂²×C₈	—	26	1	no	—
304	C₂²×C₈	—	26	1	no	—
305	C₄×Q₈	—	13	1	no	—
306	C₄×Q₈	—	13	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	—	26	1	no	—
312	C₄×D₄	—	26	1	no	—
313	C₄×D₄	C₄×D₁₃	1	2	yes	—
314	C₄×D₄	C₂²×D₁₃	1	2	yes	—
315	#117	—	13	1	no	—
316	#117	—	26	1	no	—
317	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	26	1	no	—
320	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
321	#107	—	13	2	no	—
322	#106	—	13	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	13	2	no	—
325	C₄⋊C₈	—	26	1	no	—
326	C₄⋊C₈	—	26	1	no	—
327	C₄⋊C₈	—	26	1	no	—
328	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
330	#103	—	13	2	no	—
331	#102	—	13	2	no	—
332	#102	—	13	2	no	—
333	#102	—	13	2	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	26	1	no	—
337	C₂²⋊C₈	—	26	1	no	—
338	C₂²⋊C₈	—	26	2	no	—
339	C₂²⋊C₈	—	26	2	no	—
340	#97	—	13	2	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	13	1	no	—
343	C₄×C₈	—	13	1	no	—
344	C₄×C₈	—	13	2	no	—
345	C₄×C₈	—	13	1	no	—
346	C₄×C₈	—	13	1	no	—
347	C₄×C₈	—	26	1	no	—
348	C₄×C₈	—	26	1	no	—
349	C₄×C₈	C₂²×D₁₃	1	2	yes	—
350	C₂×C₁₃	—	2	2	no	—
351	C₂×C₁₃	—	8	2	no	—
352	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
353	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂×C₁₃	#2955	1	1	yes	characteristic
355	D₁₃	—	4	2	no	—
356	C₂⁴	—	2	1	no	—
357	#41	—	13	4	no	—
358	#41	—	26	2	no	—
359	C₂×Q₈	—	13	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	13	1	no	—
364	C₂×D₄	—	26	1	no	—
365	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	26	1	no	—
372	C₂²×C₄	—	26	1	no	—
373	C₂²×C₄	—	26	1	no	—
374	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
376	C₂²×C₄	#6129	1	1	yes	characteristic
377	SD₁₆	—	26	4	no	—
378	D₈	—	26	4	no	—
379	M₁₆	—	26	2	no	—
380	M₁₆	—	26	2	no	—
381	M₁₆	—	52	4	no	—
382	M₁₆	—	52	4	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	13	1	no	—
387	C₂×C₈	—	13	2	no	—
388	C₂×C₈	—	13	2	no	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	13	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	26	2	no	—
393	C₂×C₈	—	26	2	no	—
394	C₂×C₈	—	52	2	no	—
395	C₂×C₈	—	52	2	no	—
396	C₂×C₈	—	52	1	no	—
397	C₂×C₈	—	52	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	13	1	no	—
400	C₄⋊C₄	—	13	1	no	—
401	C₄⋊C₄	—	26	1	no	—
402	C₄⋊C₄	—	26	1	no	—
403	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	26	1	no	—
407	C₂²⋊C₄	—	26	1	no	—
408	C₂²⋊C₄	—	26	1	no	—
409	C₄²	—	26	1	no	—
410	C₄²	—	26	1	no	—
411	C₄²	—	26	1	no	—
412	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
413	C₄²	D₄×D₁₃	1	1	yes	characteristic
414	C₄²	#6129	1	1	yes	characteristic
415	C₄²	C₂³×D₁₃	1	1	yes	characteristic
416	C₁₃	#17871	1	1	yes	characteristic, complemented, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	26	1	no	—
422	C₂³	#88135	1	1	yes	characteristic
423	Q₈	—	13	2	no	—
424	Q₈	—	26	1	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	13	2	no	—
429	D₄	—	26	4	no	—
430	D₄	—	26	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	26	1	no	—
440	C₂×C₄	—	26	4	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	—	52	2	no	—
444	C₂×C₄	—	52	1	no	—
445	C₂×C₄	—	52	1	no	—
446	C₂×C₄	#88135	1	1	yes	characteristic
447	C₂×C₄	#88135	1	1	yes	characteristic
448	C₂×C₄	#88135	1	1	yes	characteristic
449	C₂×C₄	#88155	1	2	yes	—
450	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#6129	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	13	2	no	—
458	C₈	—	26	2	no	—
459	C₈	—	26	2	no	—
460	C₈	—	26	1	no	—
461	C₈	—	26	1	no	—
462	C₈	—	26	1	no	—
463	C₈	—	52	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	26	2	no	—
471	C₂²	—	52	1	no	—
472	C₂²	—	52	1	no	—
473	C₂²	#11718389	1	2	yes	—
474	C₂²	C₂×#88135	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	26	2	no	—
480	C₄	—	52	1	no	—
481	C₄	—	52	1	no	—
482	C₄	#11718389	1	2	yes	—
483	C₄	C₂×#88155	1	1	yes	characteristic
484	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
485	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	#11719478	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	2	no	—
489	C₂	—	52	2	no	—
490	C₂	C₂×#11718389	1	1	yes	characteristic
491	C₂	#13123640	1	1	yes	characteristic
492	C₂	#13123735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1478	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88186	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1478	D₁₃
hypocenter	C₁₃	#17871
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1478

Complements

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

N	H ≅ G/N	type
1. #13123792	C₂	semidirect
3. C₂×#11718673	C₂	semidirect
4. #13113717	C₂	semidirect
5. #13113703	C₂	semidirect
6. #13113682	C₂	semidirect
7. #13113668	C₂	semidirect
8. #13113589	C₂	semidirect
9. #13113224	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#1478	C₂	semidirect
33. #11718495	C₂²	semidirect
34. #11718495	C₂²	semidirect
35. #11718491	C₂²	semidirect
36. #11718491	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718071	C₂²	semidirect
45. #11718051	C₂²	semidirect
46. #11718048	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. #11718046	C₂²	semidirect
126. #6127	M₁₆	semidirect
179. #1478	D₁₃	semidirect
212. D₅₂	C₂×M₁₆	semidirect
218. Dic₂₆	C₂×M₁₆	semidirect
228. #1055	AGL(1,ℤ/8)	semidirect
416. C₁₃	#17871	semidirect

Maximal subgroups

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

subgroup	index
#13123792	2
C₄×#88186	2
C₂×#11718673	2
#13113717	2
#13113703	2
#13113682	2
#13113668	2
#13113589	2
#13113224	2
#13113126	2
C₁₃×#1478	2
#17871	13