Subgroups — #15828573

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123464	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#13113133	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113131	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113131	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113124	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113124	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113122	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113122	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113115	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113115	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₁₃	C₄	1	2	yes	—
17	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	M₁₆×Dic₁₃	C₄	1	2	yes	—
22	#11718586	C₂²	1	1	yes	characteristic
23	#11718586	C₂²	1	1	yes	characteristic
24	C₄×#6099	C₂²	1	1	yes	characteristic
25	#11718498	C₄	1	2	yes	—
26	#11718496	C₄	1	2	yes	—
27	#11718494	C₄	1	2	yes	—
28	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
29	#11718387	C₄	1	2	yes	—
30	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
31	#11718380	C₄	1	2	yes	—
32	#11718379	C₄	1	2	yes	—
33	#11718368	C₄	1	2	yes	—
34	D₁₃×#97	C₄	1	2	yes	—
35	C₄×#6094	C₂²	1	1	yes	characteristic
36	C₄×#6094	C₂²	1	1	yes	characteristic
37	C₄×#6094	C₂²	1	1	yes	characteristic
38	C₄×#6094	C₂²	1	1	yes	characteristic
39	#11718346	C₂²	1	1	yes	characteristic
40	#11718346	C₂²	1	1	yes	characteristic
41	#11718346	C₂²	1	1	yes	characteristic
42	#11718346	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
50	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	#11718047	C₂²	1	1	yes	characteristic, complemented
52	#11718047	C₂²	1	1	yes	characteristic, complemented
53	#11718047	C₂²	1	1	yes	characteristic, complemented
54	#11718046	C₂²	1	1	yes	characteristic, complemented
55	#11718046	C₂²	1	1	yes	characteristic, complemented
56	#11718046	C₂²	1	1	yes	characteristic, complemented
57	#11718046	C₂²	1	1	yes	characteristic, complemented
58	#11718046	C₂²	1	1	yes	characteristic, complemented
59	#11718046	C₂²	1	1	yes	characteristic, complemented
60	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
61	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
62	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×#6099	C₂×C₄	1	2	yes	—
72	M₁₆×D₁₃	—	2	8	no	—
73	C₂×#6094	C₂×C₄	1	2	yes	—
74	C₂×#6094	C₂×C₄	1	2	yes	—
75	C₂×#6094	C₂×C₄	1	2	yes	—
76	C₂×#6094	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
81	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₃	C₂³	1	1	yes	characteristic
88	C₄²×D₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²⋊#1055	C₂×C₄	1	2	yes	—
101	C₂²⋊#1055	C₂×C₄	1	2	yes	—
102	#88060	C₂×C₄	1	2	yes	—
103	#88060	C₂×C₄	1	2	yes	—
104	#88060	C₂×C₄	1	2	yes	—
105	#88060	C₂×C₄	1	2	yes	—
106	#88055	C₂×C₄	1	2	yes	—
107	#88055	C₂×C₄	1	2	yes	—
108	#88055	C₂×C₄	1	2	yes	—
109	#88055	C₂×C₄	1	2	yes	—
110	#88054	C₂×C₄	1	2	yes	—
111	#88054	C₂×C₄	1	2	yes	—
112	#88054	C₂×C₄	1	2	yes	—
113	#88054	C₂×C₄	1	2	yes	—
114	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
117	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
118	C₄⋊#1055	C₂×C₄	1	2	yes	—
119	C₄⋊#1055	C₂×C₄	1	2	yes	—
120	#88043	C₂×C₄	1	2	yes	—
121	C₄×#1055	C₂³	1	1	yes	characteristic
122	C₄×#1055	C₂³	1	1	yes	characteristic
123	C₄×#1055	C₂³	1	1	yes	characteristic
124	C₄×#1055	C₂³	1	1	yes	characteristic
125	C₄×#1055	C₂³	1	1	yes	characteristic
126	C₄×#1055	C₂³	1	1	yes	characteristic
127	#17327	—	13	1	no	maximal, Sylow
128	C₂³×D₁₃	C₄²	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₂×C₄×D₁₃	—	2	4	no	—
136	C₂×C₄×D₁₃	—	2	4	no	—
137	C₂×C₄×D₁₃	—	4	2	no	—
138	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
140	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
141	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
142	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
143	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×M₁₆	—	2	4	no	—
151	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
157	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
162	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
163	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
164	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
165	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
166	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
167	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
173	#6099	—	2	4	no	—
174	C₂×#1055	C₂²×C₄	1	2	yes	—
175	C₂×#1055	C₂²×C₄	1	2	yes	—
176	C₂×#1055	C₂²×C₄	1	2	yes	—
177	C₂×#1055	C₂²×C₄	1	2	yes	—
178	C₂×#1055	C₂²×C₄	1	2	yes	—
179	C₂×#1055	C₂²×C₄	1	2	yes	—
180	#6094	—	2	4	no	—
181	#6094	—	2	4	no	—
182	#6094	—	2	4	no	—
183	#6094	M₁₆	1	8	yes	complemented
184	C₈×D₁₃	—	2	4	no	—
185	C₈×D₁₃	—	2	4	no	—
186	C₈×D₁₃	—	4	2	no	—
187	C₈×D₁₃	—	4	2	no	—
188	#2920	—	13	1	no	—
189	C₂×#431	—	13	1	no	—
190	C₂×C₄×M₁₆	—	13	1	no	—
191	#1453	—	13	1	no	—
192	#1453	—	13	1	no	—
193	#1453	—	13	1	no	—
194	#1453	D₁₃	1	1	yes	characteristic, complemented
195	#1451	—	13	1	no	—
196	#1451	—	13	1	no	—
197	#1451	—	13	1	no	—
198	#1451	—	13	1	no	—
199	C₈×M₁₆	—	13	1	no	—
200	C₈×M₁₆	—	13	1	no	—
201	C₈×M₁₆	—	13	1	no	—
202	C₈×M₁₆	—	13	1	no	—
203	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₁₃	—	2	2	no	—
205	C₂²×D₁₃	—	2	2	no	—
206	C₂²×D₁₃	—	4	1	no	—
207	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
208	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
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	C₂×C₄²	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
218	C₂×Dic₁₃	—	2	2	no	—
219	C₂×Dic₁₃	—	2	2	no	—
220	C₂×Dic₁₃	—	4	1	no	—
221	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
223	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
224	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
226	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
227	C₄×D₁₃	—	2	2	no	—
228	C₄×D₁₃	—	2	2	no	—
229	C₄×D₁₃	—	2	2	no	—
230	C₄×D₁₃	—	2	2	no	—
231	C₄×D₁₃	—	2	2	no	—
232	C₄×D₁₃	—	2	2	no	—
233	C₄×D₁₃	—	2	2	no	—
234	C₄×D₁₃	—	2	2	no	—
235	C₄×D₁₃	—	4	1	no	—
236	C₄×D₁₃	—	4	1	no	—
237	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
238	C₄×D₁₃	#131	1	4	yes	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	2	no	—
241	C₈×C₁₃	—	2	2	no	—
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
245	#1055	—	2	2	no	—
246	#1055	—	2	2	no	—
247	#1055	—	2	2	no	—
248	#1055	—	2	2	no	—
249	#1055	—	2	2	no	—
250	#1055	C₂×M₁₆	1	4	yes	—
251	C₂²×M₁₆	—	13	2	no	—
252	C₂²×C₄²	—	13	1	no	—
253	#432	—	13	2	no	—
254	#432	—	13	2	no	—
255	#431	—	13	1	no	—
256	#431	—	13	1	no	—
257	#431	—	13	2	no	—
258	#431	—	13	2	no	—
259	#431	—	13	1	no	—
260	#431	—	13	1	no	—
261	#431	—	13	1	no	—
262	#431	—	13	1	no	—
263	#431	C₂×D₁₃	1	1	yes	characteristic
264	#431	C₂×D₁₃	1	1	yes	characteristic
265	#423	—	13	2	no	—
266	C₂×C₄⋊C₈	—	13	2	no	—
267	#407	—	13	2	no	—
268	C₂×C₂²⋊C₈	—	13	2	no	—
269	C₄×M₁₆	—	13	2	no	—
270	C₄×M₁₆	—	13	1	no	—
271	C₄×M₁₆	—	13	2	no	—
272	C₄×M₁₆	—	13	1	no	—
273	C₄×M₁₆	—	13	1	no	—
274	C₄×M₁₆	—	13	1	no	—
275	C₄×M₁₆	—	13	1	no	—
276	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
277	C₂×#97	—	13	2	no	—
278	C₂×C₄×C₈	—	13	1	no	—
279	C₂×C₄×C₈	—	13	1	no	—
280	C₂×C₄×C₈	—	13	1	no	—
281	C₂×C₄×C₈	—	13	1	no	—
282	#322	—	13	1	no	—
283	#322	—	13	1	no	—
284	#322	—	13	1	no	—
285	#322	—	13	1	no	—
286	#322	—	13	1	no	—
287	#322	—	13	1	no	—
288	#322	—	13	1	no	—
289	#322	—	13	1	no	—
290	#322	—	13	1	no	—
291	#322	C₂×D₁₃	1	1	yes	characteristic, complemented
292	#322	C₂×D₁₃	1	1	yes	characteristic, complemented
293	#322	C₂×D₁₃	1	1	yes	characteristic, complemented
294	C₈²	—	13	1	no	—
295	C₈²	—	13	1	no	—
296	C₈²	—	13	1	no	—
297	C₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
302	C₂×D₁₃	—	2	1	no	—
303	C₂×D₁₃	—	2	1	no	—
304	C₂×D₁₃	—	2	1	no	—
305	C₂×D₁₃	—	2	1	no	—
306	C₂×D₁₃	—	4	4	no	—
307	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
308	C₂×D₁₃	#405	1	2	yes	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
313	C₄×C₁₃	C₂×#131	1	2	yes	—
314	C₄×C₁₃	#568	1	2	yes	—
315	Dic₁₃	—	2	1	no	—
316	Dic₁₃	—	2	1	no	—
317	Dic₁₃	—	2	1	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	C₄×M₁₆	1	2	yes	—
320	Dic₁₃	#405	1	2	yes	—
321	C₂³×C₄	—	13	1	no	—
322	C₂³×C₄	—	13	1	no	—
323	C₂³×C₄	—	13	1	no	—
324	C₂×M₁₆	—	13	2	no	—
325	C₂×M₁₆	—	13	2	no	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂×M₁₆	—	13	2	no	—
328	C₂×M₁₆	—	13	2	no	—
329	C₂×M₁₆	—	26	8	no	—
330	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
331	C₂²×C₈	—	13	2	no	—
332	C₂²×C₈	—	13	2	no	—
333	C₂²×C₈	—	13	2	no	—
334	C₂²×C₈	—	13	2	no	—
335	C₂×C₄²	—	13	1	no	—
336	C₂×C₄²	—	13	1	no	—
337	C₂×C₄²	—	13	1	no	—
338	C₂×C₄²	—	13	1	no	—
339	C₂×C₄²	—	13	1	no	—
340	C₂×C₄²	—	13	1	no	—
341	C₂×C₄²	—	13	1	no	—
342	C₂×C₄²	—	13	1	no	—
343	C₂×C₄²	—	13	1	no	—
344	C₂×C₄²	—	13	1	no	—
345	C₂×C₄²	—	13	1	no	—
346	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
347	C₄⋊C₈	—	13	2	no	—
348	C₄⋊C₈	—	13	2	no	—
349	C₄⋊C₈	—	13	2	no	—
350	C₄⋊C₈	—	13	2	no	—
351	C₄⋊C₈	—	13	2	no	—
352	C₄⋊C₈	—	13	2	no	—
353	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
354	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
355	C₂²⋊C₈	—	13	2	no	—
356	C₂²⋊C₈	—	13	2	no	—
357	C₂²⋊C₈	—	13	2	no	—
358	C₂²⋊C₈	—	13	2	no	—
359	C₂²⋊C₈	—	13	2	no	—
360	C₂²⋊C₈	—	13	2	no	—
361	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
362	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
363	#97	—	13	2	no	—
364	#97	—	13	2	no	—
365	#97	—	13	2	no	—
366	#97	—	13	2	no	—
367	#97	—	13	2	no	—
368	#97	C₄×D₁₃	1	2	yes	—
369	C₄×C₈	—	13	2	no	—
370	C₄×C₈	—	13	2	no	—
371	C₄×C₈	—	13	2	no	—
372	C₄×C₈	—	13	2	no	—
373	C₄×C₈	—	13	1	no	—
374	C₄×C₈	—	13	1	no	—
375	C₄×C₈	—	13	1	no	—
376	C₄×C₈	—	13	1	no	—
377	C₄×C₈	—	13	1	no	—
378	C₄×C₈	—	13	1	no	—
379	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
381	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
382	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
383	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
384	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
385	C₂×C₁₃	—	4	1	no	—
386	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
387	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
388	C₂×C₁₃	#2873	1	1	yes	characteristic
389	D₁₃	—	2	2	no	—
390	D₁₃	—	2	2	no	—
391	C₂⁴	—	13	1	no	—
392	C₂²×C₄	—	13	1	no	—
393	C₂²×C₄	—	13	1	no	—
394	C₂²×C₄	—	13	1	no	—
395	C₂²×C₄	—	13	1	no	—
396	C₂²×C₄	—	13	1	no	—
397	C₂²×C₄	—	13	1	no	—
398	C₂²×C₄	—	13	1	no	—
399	C₂²×C₄	—	13	1	no	—
400	C₂²×C₄	—	13	1	no	—
401	C₂²×C₄	—	13	1	no	—
402	C₂²×C₄	—	13	1	no	—
403	C₂²×C₄	—	13	1	no	—
404	C₂²×C₄	—	13	1	no	—
405	C₂²×C₄	—	13	1	no	—
406	C₂²×C₄	—	13	1	no	—
407	C₂²×C₄	—	26	4	no	—
408	C₂²×C₄	—	26	4	no	—
409	C₂²×C₄	—	52	2	no	—
410	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
413	M₁₆	—	2	4	no	—
414	M₁₆	—	13	8	no	—
415	M₁₆	—	26	4	no	—
416	M₁₆	—	26	4	no	—
417	M₁₆	—	26	4	no	—
418	M₁₆	—	26	4	no	—
419	C₂×C₈	—	13	2	no	—
420	C₂×C₈	—	13	2	no	—
421	C₂×C₈	—	13	2	no	—
422	C₂×C₈	—	13	2	no	—
423	C₂×C₈	—	13	2	no	—
424	C₂×C₈	—	13	2	no	—
425	C₂×C₈	—	26	4	no	—
426	C₂×C₈	—	26	4	no	—
427	C₂×C₈	—	52	2	no	—
428	C₂×C₈	—	52	2	no	—
429	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
430	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
431	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
432	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
433	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
434	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
435	C₄²	—	13	1	no	—
436	C₄²	—	13	1	no	—
437	C₄²	—	13	1	no	—
438	C₄²	—	13	1	no	—
439	C₄²	—	13	1	no	—
440	C₄²	—	13	1	no	—
441	C₄²	—	13	1	no	—
442	C₄²	—	13	1	no	—
443	C₄²	—	13	1	no	—
444	C₄²	—	13	1	no	—
445	C₄²	—	13	1	no	—
446	C₄²	—	13	1	no	—
447	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
448	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
449	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
450	C₄²	C₂³×D₁₃	1	1	yes	characteristic
451	C₁₃	#17327	1	1	yes	characteristic, complemented, Sylow
452	C₂³	—	13	1	no	—
453	C₂³	—	13	1	no	—
454	C₂³	—	26	2	no	—
455	C₂³	—	26	2	no	—
456	C₂³	—	52	1	no	—
457	C₂³	C₄²×D₁₃	1	1	yes	characteristic
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	13	1	no	—
462	C₂×C₄	—	13	1	no	—
463	C₂×C₄	—	13	4	no	—
464	C₂×C₄	—	13	4	no	—
465	C₂×C₄	—	13	1	no	—
466	C₂×C₄	—	13	1	no	—
467	C₂×C₄	—	13	1	no	—
468	C₂×C₄	—	13	1	no	—
469	C₂×C₄	—	26	2	no	—
470	C₂×C₄	—	26	2	no	—
471	C₂×C₄	—	26	2	no	—
472	C₂×C₄	—	26	2	no	—
473	C₂×C₄	—	26	2	no	—
474	C₂×C₄	—	26	2	no	—
475	C₂×C₄	—	26	2	no	—
476	C₂×C₄	—	26	2	no	—
477	C₂×C₄	—	26	2	no	—
478	C₂×C₄	—	26	2	no	—
479	C₂×C₄	—	52	1	no	—
480	C₂×C₄	—	52	1	no	—
481	C₂×C₄	—	52	1	no	—
482	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
483	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
484	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	13	4	no	—
494	C₈	—	26	2	no	—
495	C₈	—	26	2	no	—
496	C₈	—	26	2	no	—
497	C₈	—	26	2	no	—
498	C₈	—	26	2	no	—
499	C₈	M₁₆×D₁₃	1	4	yes	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	13	2	no	—
504	C₂²	—	13	2	no	—
505	C₂²	—	26	1	no	—
506	C₂²	—	26	1	no	—
507	C₂²	—	26	1	no	—
508	C₂²	—	26	1	no	—
509	C₂²	—	52	4	no	—
510	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	13	2	no	—
515	C₄	—	13	2	no	—
516	C₄	—	26	1	no	—
517	C₄	—	26	1	no	—
518	C₄	—	26	1	no	—
519	C₄	—	26	1	no	—
520	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
521	C₄	D₁₃×#131	1	2	yes	—
522	C₄	#11719455	1	2	yes	—
523	C₂	—	4	1	no	—
524	C₂	—	26	2	no	—
525	C₂	—	26	2	no	—
526	C₂	C₄×M₁₆×D₁₃	1	1	yes	characteristic
527	C₂	D₁₃×#405	1	1	yes	characteristic
528	C₂	#13123252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1453	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1453	D₁₃
hypocenter	C₁₃	#17327
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1453

Complements

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

N	H ≅ G/N	type
4. #13113133	C₂	semidirect
5. #13113131	C₂	semidirect
6. #13113131	C₂	semidirect
7. #13113124	C₂	semidirect
8. #13113124	C₂	semidirect
9. #13113122	C₂	semidirect
10. #13113122	C₂	semidirect
11. #13113115	C₂	semidirect
12. #13113115	C₂	semidirect
13. C₈×#6094	C₂	semidirect
14. C₈×#6094	C₂	semidirect
15. C₁₃×#1453	C₂	semidirect
47. C₁₃×#322	C₂²	semidirect
48. C₁₃×#322	C₂²	semidirect
49. C₁₃×#322	C₂²	semidirect
50. C₈²×C₁₃	C₂²	semidirect
51. #11718047	C₂²	semidirect
52. #11718047	C₂²	semidirect
53. #11718047	C₂²	semidirect
54. #11718046	C₂²	semidirect
55. #11718046	C₂²	semidirect
56. #11718046	C₂²	semidirect
57. #11718046	C₂²	semidirect
58. #11718046	C₂²	semidirect
59. #11718046	C₂²	semidirect
60. C₈×#1055	C₂²	semidirect
61. C₈×#1055	C₂²	semidirect
62. C₈×#1055	C₂²	semidirect
183. #6094	M₁₆	semidirect
194. #1453	D₁₃	semidirect
291. #322	C₂×D₁₃	semidirect
292. #322	C₂×D₁₃	semidirect
293. #322	C₂×D₁₃	semidirect
297. C₈²	C₂×D₁₃	semidirect
451. C₁₃	#17327	semidirect

Maximal subgroups

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

subgroup	index
#13123464	2
D₁₃×#431	2
C₄×M₁₆×D₁₃	2
#13113133	2
#13113131	2
#13113124	2
#13113122	2
#13113115	2
C₈×#6094	2
C₁₃×#1453	2
#17327	13