Subgroups — #15829460

Order 3328.

1268 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719182	C₂	1	1	yes	maximal, characteristic
2	#13123469	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113252	C₂	1	4	yes	maximal, complemented
4	#13113234	C₂	1	4	yes	maximal, complemented
5	#13113226	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6127	—	2	1	no	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88184	—	2	1	no	—
10	C₂×#88184	C₄	1	2	yes	—
11	#11719182	—	2	1	no	—
12	#11719182	—	2	1	no	—
13	#11719182	—	2	1	no	—
14	#11719182	—	2	1	no	—
15	#11719182	C₄	1	2	yes	—
16	#11719182	C₄	1	2	yes	—
17	#11719182	C₂²	1	2	yes	—
18	#11719182	C₂²	1	2	yes	—
19	C₂×#88129	—	2	1	no	—
20	C₂×#88128	C₄	1	1	yes	characteristic
21	C₂×C₄×D₅₂	—	2	1	no	—
22	C₂×C₄×D₅₂	C₂²	1	2	yes	—
23	C₂×#88123	C₄	1	1	yes	characteristic
24	C₁₃×#431	—	2	1	no	—
25	C₁₃×#431	—	2	1	no	—
26	C₁₃×#431	C₂²	1	2	yes	—
27	C₁₃×#431	C₂²	1	2	yes	complemented
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
30	C₂×C₄×C₈×C₁₃	—	2	1	no	—
31	#11718868	—	2	1	no	—
32	#11718587	—	2	1	no	—
33	#11718587	—	2	1	no	—
34	#11718586	C₂²	1	2	yes	—
35	#11718586	C₂²	1	2	yes	complemented
36	#11718585	—	2	1	no	—
37	C₄×#6099	C₂²	1	2	yes	complemented
38	#11718075	C₂²	1	16	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₂²⋊D₁₃	—	2	2	no	—
43	C₂×#6127	—	2	2	no	—
44	C₂×#6127	—	2	2	no	—
45	C₂×#6127	—	2	2	no	—
46	C₂×#6127	—	2	2	no	—
47	C₂×#6127	—	4	8	no	—
48	C₂²×D₅₂	—	2	1	no	—
49	C₂²×D₅₂	—	2	1	no	—
50	C₂²×D₅₂	C₂×C₄	1	2	yes	—
51	C₂²×C₄×D₁₃	—	2	2	no	—
52	C₂²×Dic₂₆	—	2	1	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	#88184	—	2	2	no	—
67	#88184	—	2	2	no	—
68	#88184	—	2	2	no	—
69	#88184	—	2	2	no	—
70	#88184	—	2	2	no	—
71	#88184	—	2	2	no	—
72	#88184	C₂×C₄	1	4	yes	—
73	#88184	C₂×C₄	1	4	yes	—
74	C₂×#6103	—	2	2	no	—
75	C₂×#6103	—	2	2	no	—
76	C₂×C₄⋊Dic₁₃	—	2	1	no	—
77	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
78	C₂×#6099	—	2	2	no	—
79	#88129	—	2	2	no	—
80	#88129	—	2	2	no	—
81	#88129	—	2	2	no	—
82	#88129	—	2	2	no	—
83	#88128	—	2	1	no	—
84	#88128	—	2	1	no	—
85	#88128	C₂×C₄	1	2	yes	—
86	#88128	C₂×C₄	1	2	yes	—
87	C₄×D₅₂	—	2	2	no	—
88	C₄×D₅₂	—	2	2	no	—
89	C₄×D₅₂	—	2	2	no	—
90	C₄×D₅₂	—	2	2	no	—
91	C₄×D₅₂	—	2	2	no	—
92	C₄×D₅₂	—	2	2	no	—
93	C₄×D₅₂	C₂×C₄	1	4	yes	—
94	C₄×D₅₂	C₂³	1	4	yes	—
95	#88123	—	2	1	no	—
96	#88123	—	2	1	no	—
97	#88123	C₂×C₄	1	2	yes	—
98	#88123	C₂×C₄	1	2	yes	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₃×C₂²⋊C₈	—	2	2	no	—
102	C₁₃×C₂²⋊C₈	—	2	2	no	—
103	C₄×C₈×C₁₃	—	2	2	no	—
104	C₄×C₈×C₁₃	—	2	2	no	—
105	C₂²⋊#1055	—	2	2	no	—
106	C₂²⋊#1055	—	2	2	no	—
107	C₄⋊#1055	—	2	2	no	—
108	C₄⋊#1055	—	2	2	no	—
109	#88043	—	2	2	no	—
110	C₄×#1055	C₂³	1	4	yes	—
111	#17463	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂³×D₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	—	2	4	no	—
136	C₂×C₂²⋊D₁₃	—	2	4	no	—
137	C₂×C₂²⋊D₁₃	—	4	8	no	—
138	C₂²×Dic₁₃	—	2	2	no	—
139	#6127	—	4	8	no	—
140	#6127	—	4	8	no	—
141	#6127	—	4	8	no	—
142	#6127	—	4	8	no	—
143	C₂×D₅₂	—	2	8	no	—
144	C₂×D₅₂	—	2	2	no	—
145	C₂×D₅₂	—	2	2	no	—
146	C₂×D₅₂	—	2	2	no	—
147	C₂×D₅₂	—	2	2	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	4	4	no	—
150	C₂×D₅₂	—	4	4	no	—
151	C₂×D₅₂	C₂²×C₄	1	4	yes	—
152	C₂×C₄×D₁₃	—	2	4	no	—
153	C₂×C₄×D₁₃	—	2	4	no	—
154	C₂×C₄×D₁₃	—	4	8	no	—
155	C₂×Dic₂₆	—	2	2	no	—
156	C₂×Dic₂₆	—	2	2	no	—
157	C₂×Dic₂₆	—	4	4	no	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₂×C₈×C₁₃	—	4	4	no	—
160	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
176	#6103	—	2	4	no	—
177	#6103	—	2	4	no	—
178	#6103	—	2	4	no	—
179	#6103	—	2	4	no	—
180	C₄⋊Dic₁₃	—	2	2	no	—
181	C₄⋊Dic₁₃	—	2	2	no	—
182	C₄⋊Dic₁₃	—	2	2	no	—
183	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
184	#6099	—	4	4	no	—
185	C₂×#1055	—	2	4	no	—
186	C₂×#532	—	13	1	no	—
187	#2920	—	13	1	no	—
188	C₂×#431	D₁₃	1	1	yes	characteristic, complemented
189	#1484	—	13	4	no	—
190	#1480	—	13	4	no	—
191	#1478	—	13	4	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×D₁₃	—	2	4	no	—
199	C₂²×D₁₃	—	4	4	no	—
200	C₂²×D₁₃	—	4	4	no	—
201	C₂²×D₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#131	1	4	yes	—
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂²⋊D₁₃	—	4	8	no	—
233	C₂²⋊D₁₃	—	4	8	no	—
234	C₂×Dic₁₃	—	2	4	no	—
235	C₂×Dic₁₃	—	4	4	no	—
236	D₅₂	—	2	8	no	—
237	D₅₂	—	4	4	no	—
238	D₅₂	—	4	4	no	—
239	D₅₂	—	4	4	no	—
240	D₅₂	—	4	4	no	—
241	D₅₂	—	4	4	no	—
242	C₄×D₁₃	—	4	8	no	—
243	C₄×D₁₃	—	4	8	no	—
244	Dic₂₆	—	4	4	no	—
245	Dic₂₆	—	4	4	no	—
246	C₈×C₁₃	—	4	4	no	—
247	#1055	—	4	4	no	—
248	C₂²×#41	—	26	1	no	—
249	#532	—	13	2	no	—
250	#532	—	13	2	no	—
251	#532	—	13	2	no	—
252	#532	—	13	2	no	—
253	#532	—	26	1	no	—
254	#532	—	26	1	no	—
255	#532	—	26	1	no	—
256	#532	—	26	1	no	—
257	C₂×C₄⋊Q₈	—	13	1	no	—
258	C₂×#127	—	13	1	no	—
259	C₂×#124	—	26	1	no	—
260	C₂×#121	—	13	2	no	—
261	C₂×#121	—	26	1	no	—
262	C₂×C₄×D₄	—	13	2	no	—
263	C₂×C₄×D₄	—	26	1	no	—
264	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
265	#432	—	26	1	no	—
266	#432	—	26	1	no	—
267	#431	—	2	1	no	—
268	#431	—	2	1	no	—
269	#431	—	13	2	no	—
270	#431	—	13	2	no	—
271	#431	C₂×D₁₃	1	2	yes	—
272	#431	C₂×D₁₃	1	2	yes	complemented
273	#423	—	26	1	no	—
274	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
275	#407	—	26	1	no	—
276	C₂×C₂²⋊C₈	—	2	1	no	—
277	C₄×M₁₆	—	13	2	no	—
278	C₂×C₄×C₈	—	2	1	no	—
279	D₄⋊C₈	—	13	16	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	#408	1	2	yes	—
289	C₂²×C₁₃	#418	1	2	yes	—
290	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×D₁₃	—	4	4	no	—
292	C₂×D₁₃	—	4	4	no	—
293	C₂×D₁₃	—	4	4	no	—
294	C₂×D₁₃	—	8	8	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	#408	1	2	yes	—
303	C₄×C₁₃	#418	1	2	yes	—
304	C₄×C₁₃	#421	1	2	yes	—
305	C₄×C₁₃	C₂×#131	1	2	yes	—
306	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
307	Dic₁₃	—	4	4	no	—
308	C₂×#41	—	26	2	no	—
309	C₂×#41	—	26	2	no	—
310	C₂×#41	—	26	2	no	—
311	C₂×#41	—	26	2	no	—
312	C₂×#41	—	52	8	no	—
313	C₂²×Q₈	—	26	1	no	—
314	C₂²×D₄	—	13	2	no	—
315	C₂²×D₄	—	26	2	no	—
316	C₂²×D₄	—	26	1	no	—
317	C₂²×D₄	—	26	1	no	—
318	C₂³×C₄	—	26	2	no	—
319	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
320	C₂³×C₄	D₅₂	1	1	yes	characteristic
321	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
322	C₂×M₁₆	—	26	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₄⋊Q₈	—	13	2	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	26	1	no	—
327	C₄⋊Q₈	—	26	1	no	—
328	#127	—	13	2	no	—
329	#127	—	13	2	no	—
330	#127	—	26	1	no	—
331	#127	—	26	1	no	—
332	#124	—	26	2	no	—
333	#124	—	26	2	no	—
334	#124	—	26	2	no	—
335	#124	—	26	2	no	—
336	#121	—	13	4	no	—
337	#121	—	13	4	no	—
338	#121	—	26	2	no	—
339	#121	—	26	2	no	—
340	#121	—	26	2	no	—
341	#121	—	26	2	no	—
342	#121	—	26	2	no	—
343	#121	—	26	2	no	—
344	C₄×D₄	—	13	4	no	—
345	C₄×D₄	—	13	4	no	—
346	C₄×D₄	—	26	2	no	—
347	C₄×D₄	—	26	2	no	—
348	C₄×D₄	—	26	2	no	—
349	C₄×D₄	—	26	2	no	—
350	C₄×D₄	—	26	2	no	—
351	C₄×D₄	—	26	2	no	—
352	C₂×C₄⋊C₄	—	13	2	no	—
353	C₂×C₄⋊C₄	—	26	1	no	—
354	C₂×C₂²⋊C₄	—	26	2	no	—
355	C₂×C₂²⋊C₄	—	26	2	no	—
356	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
359	C₂×C₄²	D₅₂	1	1	yes	characteristic
360	C₂×C₄²	D₅₂	1	1	yes	characteristic
361	C₂×C₄²	D₅₂	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	26	2	no	—
370	C₄⋊C₈	—	26	2	no	—
371	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₂²⋊C₈	—	26	2	no	—
375	C₂²⋊C₈	—	26	2	no	—
376	#97	—	26	2	no	—
377	C₄×C₈	—	2	2	no	—
378	C₄×C₈	—	2	2	no	—
379	C₄×C₈	—	13	4	no	—
380	C₂×C₁₃	—	2	2	no	—
381	C₂×C₁₃	—	2	2	no	—
382	C₂×C₁₃	—	4	1	no	—
383	C₂×C₁₃	C₂×#408	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
385	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
386	D₁₃	—	8	4	no	—
387	C₂⁴	—	26	2	no	—
388	C₂⁴	#6103	1	1	yes	characteristic
389	#41	—	52	8	no	—
390	#41	—	52	8	no	—
391	#41	—	52	8	no	—
392	#41	—	52	8	no	—
393	C₂×Q₈	—	26	2	no	—
394	C₂×Q₈	—	26	2	no	—
395	C₂×Q₈	—	52	4	no	—
396	C₂×D₄	—	13	4	no	—
397	C₂×D₄	—	26	4	no	—
398	C₂×D₄	—	26	4	no	—
399	C₂×D₄	—	26	8	no	—
400	C₂×D₄	—	26	2	no	—
401	C₂×D₄	—	26	2	no	—
402	C₂×D₄	—	26	2	no	—
403	C₂×D₄	—	26	2	no	—
404	C₂×D₄	—	26	2	no	—
405	C₂×D₄	—	52	4	no	—
406	C₂×D₄	—	52	4	no	—
407	C₂×D₄	—	52	8	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	26	2	no	—
412	C₂²×C₄	—	26	4	no	—
413	C₂²×C₄	—	26	4	no	—
414	C₂²×C₄	—	52	8	no	—
415	C₂²×C₄	#6103	1	1	yes	characteristic
416	C₂²×C₄	#6103	1	1	yes	characteristic
417	C₂²×C₄	#6103	1	1	yes	characteristic
418	C₂²×C₄	#6103	1	1	yes	characteristic
419	C₂²×C₄	#6103	1	1	yes	characteristic
420	C₂²×C₄	#6103	1	1	yes	characteristic
421	C₂²×C₄	#6103	1	1	yes	characteristic
422	C₂²×C₄	#6103	1	1	yes	characteristic
423	C₂²×C₄	#6103	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
433	M₁₆	—	52	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	4	4	no	—
436	C₂×C₈	—	26	4	no	—
437	C₄⋊C₄	—	13	4	no	—
438	C₄⋊C₄	—	26	2	no	—
439	C₄⋊C₄	—	26	2	no	—
440	C₄⋊C₄	—	26	2	no	—
441	C₂²⋊C₄	—	26	4	no	—
442	C₂²⋊C₄	—	26	4	no	—
443	C₂²⋊C₄	—	26	4	no	—
444	C₂²⋊C₄	—	26	4	no	—
445	C₄²	#6103	1	1	yes	characteristic
446	C₄²	#6103	1	1	yes	characteristic
447	C₄²	#6103	1	1	yes	characteristic
448	C₄²	#6103	1	1	yes	characteristic
449	C₄²	#6103	1	1	yes	characteristic
450	C₄²	#6103	1	1	yes	characteristic
451	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
453	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
454	C₄²	C₂×D₅₂	1	1	yes	characteristic
455	C₄²	C₂×D₅₂	1	1	yes	characteristic
456	C₄²	C₂×D₅₂	1	1	yes	characteristic
457	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
458	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
459	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
460	C₄²	C₂³×D₁₃	1	1	yes	characteristic
461	C₁₃	#17463	1	1	yes	characteristic, complemented, Sylow
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	26	4	no	—
466	C₂³	—	52	4	no	—
467	C₂³	—	52	4	no	—
468	C₂³	—	52	4	no	—
469	C₂³	C₂×#6103	1	1	yes	characteristic
470	C₂³	C₂×#6103	1	1	yes	characteristic
471	C₂³	C₂×#6103	1	1	yes	characteristic
472	Q₈	—	52	4	no	—
473	Q₈	—	52	4	no	—
474	D₄	—	26	8	no	—
475	D₄	—	52	4	no	—
476	D₄	—	52	4	no	—
477	D₄	—	52	8	no	—
478	D₄	—	52	8	no	—
479	D₄	—	52	4	no	—
480	D₄	—	52	4	no	—
481	D₄	—	52	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	26	4	no	—
499	C₂×C₄	—	52	8	no	—
500	C₂×C₄	—	52	4	no	—
501	C₂×C₄	—	52	8	no	—
502	C₂×C₄	#88155	1	4	yes	—
503	C₂×C₄	C₂×#6103	1	1	yes	characteristic
504	C₂×C₄	C₂×#6103	1	1	yes	characteristic
505	C₂×C₄	C₂×#6103	1	1	yes	characteristic
506	C₂×C₄	C₂×#6103	1	1	yes	characteristic
507	C₂×C₄	C₂×#6103	1	1	yes	characteristic
508	C₂×C₄	C₂×#6103	1	1	yes	characteristic
509	C₂×C₄	C₂×#6103	1	1	yes	characteristic
510	C₂×C₄	C₂×#6103	1	1	yes	characteristic
511	C₂×C₄	C₂×#6103	1	1	yes	characteristic
512	C₂×C₄	#88203	1	4	yes	—
513	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
516	C₈	—	4	4	no	—
517	C₈	—	52	4	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	52	4	no	—
527	C₂²	—	52	4	no	—
528	C₂²	—	52	4	no	—
529	C₂²	—	104	8	no	—
530	C₂²	#11718662	1	2	yes	—
531	C₂²	#11718771	1	2	yes	—
532	C₂²	C₂²×#6103	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	52	4	no	—
541	C₄	#11718662	1	2	yes	—
542	C₄	#11718771	1	2	yes	—
543	C₄	#11718800	1	2	yes	—
544	C₄	C₂×#88155	1	2	yes	—
545	C₄	C₂×#88203	1	2	yes	—
546	C₂	—	2	2	no	—
547	C₂	—	2	2	no	—
548	C₂	—	4	1	no	—
549	C₂	—	104	4	no	—
550	C₂	C₂×#11718771	1	1	yes	characteristic
551	C₂	C₂×#11718662	1	1	yes	characteristic
552	C₂	C₂×#11718800	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×#11719182	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17463
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #13123469	C₂	semidirect
3. #13113252	C₂	semidirect
4. #13113234	C₂	semidirect
5. #13113226	C₂	semidirect
6. C₂×C₁₃×#431	C₂	semidirect
27. C₁₃×#431	C₂²	semidirect
28. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. #11718586	C₂²	semidirect
37. C₄×#6099	C₂²	semidirect
38. #11718075	C₂²	semidirect
188. C₂×#431	D₁₃	semidirect
272. #431	C₂×D₁₃	semidirect
274. C₂×C₄⋊C₈	C₂×D₁₃	semidirect
461. C₁₃	#17463	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719182	2
#13123469	2
#13113252	2
#13113234	2
#13113226	2
C₂×C₁₃×#431	2
#17463	13