Subgroups — #15871180

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13118134	C₂	1	1	yes	maximal, characteristic
2	#13115447	C₂	1	1	yes	maximal, characteristic
3	#13115440	C₂	1	1	yes	maximal, characteristic
4	#13115440	C₂	1	1	yes	maximal, characteristic
5	#13115398	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115391	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115391	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114709	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114707	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114702	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114611	C₂	1	1	yes	maximal, characteristic
12	#13114611	C₂	1	1	yes	maximal, characteristic
13	#13114606	C₂	1	1	yes	maximal, characteristic
14	#13114523	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#376	C₂²	1	1	yes	characteristic
18	C₂×#88060	C₂²	1	1	yes	characteristic
19	C₂×#88060	C₂²	1	1	yes	characteristic
20	C₂×#88060	C₂²	1	1	yes	characteristic
21	C₂×#88055	C₂²	1	1	yes	characteristic
22	C₂×#88055	C₂²	1	1	yes	characteristic
23	C₂×#88054	C₂²	1	1	yes	characteristic
24	C₂×#88054	C₂²	1	1	yes	characteristic
25	C₂×#88054	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₄×#6103	C₂²	1	1	yes	characteristic
28	C₄×#6103	C₂²	1	1	yes	characteristic
29	C₄×#6103	C₂²	1	1	yes	characteristic
30	C₄×#6101	C₂²	1	1	yes	characteristic
31	C₄×#6101	C₂²	1	1	yes	characteristic
32	C₄×#6101	C₂²	1	1	yes	characteristic
33	C₂×#88043	C₂²	1	1	yes	characteristic
34	C₂×#88043	C₂²	1	1	yes	characteristic
35	C₂×#88043	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
39	#11718337	C₄	1	1	yes	characteristic
40	#11718336	C₄	1	1	yes	characteristic
41	#11718336	C₄	1	1	yes	characteristic
42	#11718336	C₄	1	1	yes	characteristic
43	C₁₃⋊#401	C₄	1	1	yes	characteristic
44	#11718319	C₄	1	1	yes	characteristic
45	#11718319	C₄	1	1	yes	characteristic
46	#11718319	C₄	1	1	yes	characteristic
47	C₁₃×#336	C₂²	1	1	yes	characteristic
48	C₁₃×#336	C₂²	1	1	yes	characteristic
49	C₁₃×#336	C₂²	1	1	yes	characteristic
50	C₁₃×#336	C₂²	1	1	yes	characteristic
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	C₂²	1	1	yes	characteristic
53	#11718142	C₂²	1	1	yes	characteristic
54	#11718142	C₂²	1	1	yes	characteristic
55	#11718142	C₂²	1	1	yes	characteristic
56	#11718142	C₂²	1	1	yes	characteristic
57	#11718142	C₂²	1	1	yes	characteristic
58	#11718142	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×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	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×#6103	C₂×C₄	1	1	yes	characteristic
68	C₂×#6103	C₂×C₄	1	1	yes	characteristic
69	C₂×#6103	C₂×C₄	1	1	yes	characteristic
70	C₂×#6103	C₂×C₄	1	1	yes	characteristic
71	C₂×#6103	C₂×C₄	1	1	yes	characteristic
72	C₂×#6103	C₂×C₄	1	1	yes	characteristic
73	C₂×#6101	C₂×C₄	1	1	yes	characteristic
74	C₂×#6101	C₂×C₄	1	1	yes	characteristic
75	C₂×#6101	C₂×C₄	1	1	yes	characteristic
76	C₂×#6101	C₂×C₄	1	1	yes	characteristic
77	C₂×#6101	C₂×C₄	1	1	yes	characteristic
78	C₂×#6101	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂²×#1055	C₂³	1	1	yes	characteristic
83	C₂²×#1055	C₂³	1	1	yes	characteristic
84	C₂²×#1055	C₂³	1	1	yes	characteristic
85	C₂²×#1055	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₁₃	—	2	2	no	—
87	C₂×C₈×D₁₃	—	2	2	no	—
88	C₂×C₈×D₁₃	—	2	2	no	—
89	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
93	#88071	C₂×C₄	1	1	yes	characteristic
94	#88071	C₂×C₄	1	1	yes	characteristic
95	#88071	C₂×C₄	1	1	yes	characteristic
96	#88071	C₂×C₄	1	1	yes	characteristic
97	#88071	C₂×C₄	1	1	yes	characteristic
98	#88071	C₂×C₄	1	1	yes	characteristic
99	#88071	C₂×C₄	1	1	yes	characteristic
100	#88071	C₂×C₄	1	1	yes	characteristic
101	#88071	C₂×C₄	1	1	yes	characteristic
102	#88071	C₂×C₄	1	1	yes	characteristic
103	#88071	C₂×C₄	1	1	yes	characteristic
104	#88071	C₂×C₄	1	1	yes	characteristic
105	#88060	—	2	2	no	—
106	#88060	—	2	2	no	—
107	#88060	—	2	2	no	—
108	#88055	—	2	2	no	—
109	#88055	—	2	2	no	—
110	#88054	—	2	2	no	—
111	#88054	—	2	2	no	—
112	#88054	—	2	2	no	—
113	C₈×Dic₁₃	—	2	2	no	—
114	#88043	—	2	2	no	—
115	#88043	—	2	2	no	—
116	#88043	—	2	2	no	—
117	C₄×#1055	—	2	2	no	—
118	C₄×#1055	—	2	2	no	—
119	C₄×#1055	—	2	2	no	—
120	#21669	—	13	1	no	maximal, Sylow
121	C₂³×D₁₃	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	C₂⁴	1	1	yes	characteristic
129	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	—	2	1	no	—
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	—	2	1	no	—
139	C₂×C₄×D₁₃	—	2	1	no	—
140	C₂×C₄×D₁₃	—	2	1	no	—
141	C₂×C₄×D₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	#6103	—	2	2	no	—
161	#6103	—	2	2	no	—
162	#6103	—	2	2	no	—
163	#6103	—	2	2	no	—
164	#6103	—	4	1	no	—
165	#6103	—	4	1	no	—
166	#6101	—	2	2	no	—
167	#6101	—	2	2	no	—
168	#6101	—	4	1	no	—
169	#6101	—	4	1	no	—
170	#6101	—	4	1	no	—
171	#6101	—	4	1	no	—
172	C₄×Dic₁₃	—	2	1	no	—
173	C₄×Dic₁₃	—	2	1	no	—
174	C₄×Dic₁₃	—	2	1	no	—
175	C₄×Dic₁₃	—	2	1	no	—
176	C₄×Dic₁₃	—	2	1	no	—
177	C₄×Dic₁₃	—	2	1	no	—
178	C₂×#1055	—	2	1	no	—
179	C₂×#1055	—	2	1	no	—
180	C₂×#1055	—	2	1	no	—
181	C₂×#1055	—	2	1	no	—
182	C₂×#1055	—	2	1	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	#41	1	2	yes	—
185	C₂×#1055	#41	1	2	yes	—
186	C₂×#1055	#41	1	2	yes	—
187	C₂×#1055	#41	1	2	yes	—
188	C₂×#1055	#41	1	2	yes	—
189	C₂×#1055	#41	1	2	yes	—
190	C₈×D₁₃	—	4	4	no	—
191	#2401	—	13	1	no	—
192	#1924	—	13	1	no	—
193	#1923	—	13	1	no	—
194	#1923	—	13	1	no	—
195	#1917	—	13	1	no	—
196	#1916	—	13	1	no	—
197	#1916	—	13	1	no	—
198	#1840	D₁₃	1	1	yes	characteristic, complemented
199	#1771	—	13	1	no	—
200	#1771	—	13	1	no	—
201	#1770	—	13	1	no	—
202	#1752	—	13	1	no	—
203	#1752	—	13	1	no	—
204	C₈×C₂²⋊C₄	—	13	1	no	—
205	#1726	—	13	1	no	—
206	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	C₂²×D₁₃	—	2	1	no	—
208	C₂²×D₁₃	—	2	1	no	—
209	C₂²×D₁₃	—	2	1	no	—
210	C₂²×D₁₃	—	2	1	no	—
211	C₂²×D₁₃	—	2	1	no	—
212	C₂²×D₁₃	—	2	1	no	—
213	C₂²×D₁₃	#131	1	2	yes	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
238	C₂×Dic₁₃	—	2	1	no	—
239	C₂×Dic₁₃	—	2	1	no	—
240	C₂×Dic₁₃	—	2	1	no	—
241	C₂×Dic₁₃	—	2	1	no	—
242	C₂×Dic₁₃	—	2	1	no	—
243	C₂×Dic₁₃	—	2	1	no	—
244	C₂×Dic₁₃	—	2	1	no	—
245	C₂×Dic₁₃	—	2	1	no	—
246	C₂×Dic₁₃	—	2	1	no	—
247	C₂×Dic₁₃	—	2	1	no	—
248	C₂×Dic₁₃	—	2	1	no	—
249	C₂×Dic₁₃	—	2	1	no	—
250	C₂×Dic₁₃	—	2	1	no	—
251	C₂×Dic₁₃	—	2	1	no	—
252	C₂×Dic₁₃	—	2	1	no	—
253	C₂×Dic₁₃	—	2	1	no	—
254	C₂×Dic₁₃	—	2	1	no	—
255	C₂×Dic₁₃	—	2	1	no	—
256	C₂×Dic₁₃	—	2	1	no	—
257	C₂×Dic₁₃	—	2	1	no	—
258	C₂×Dic₁₃	#131	1	2	yes	—
259	C₄×D₁₃	—	4	1	no	—
260	C₄×D₁₃	—	4	1	no	—
261	C₄×D₁₃	—	4	1	no	—
262	C₄×D₁₃	—	4	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	#1055	—	2	2	no	—
268	#1055	—	2	2	no	—
269	#1055	—	2	2	no	—
270	#1055	#126	1	4	yes	—
271	C₂³×C₈	—	13	1	no	—
272	C₂×C₄⋊C₈	—	13	1	no	—
273	C₂×C₄⋊C₈	—	13	1	no	—
274	C₂×C₄⋊C₈	—	13	1	no	—
275	C₂×C₂²⋊C₈	—	13	1	no	—
276	C₂×C₂²⋊C₈	—	13	1	no	—
277	C₂×C₂²⋊C₈	—	13	1	no	—
278	C₂×#97	—	13	1	no	—
279	C₂×#97	—	13	1	no	—
280	C₂×#97	—	13	1	no	—
281	C₂×#97	—	13	1	no	—
282	C₂×#97	—	13	1	no	—
283	C₂×C₄×C₈	—	13	1	no	—
284	C₂×C₄×C₈	—	13	1	no	—
285	C₂×C₄×C₈	—	13	1	no	—
286	C₂×C₄×C₈	—	13	1	no	—
287	#401	—	13	1	no	—
288	#400	—	13	1	no	—
289	#400	—	13	1	no	—
290	#400	—	13	1	no	—
291	#397	—	13	1	no	—
292	#397	—	13	1	no	—
293	#397	—	13	1	no	—
294	#396	—	13	1	no	—
295	C₄×C₄⋊C₄	—	13	1	no	—
296	C₄×C₄⋊C₄	—	13	1	no	—
297	C₄×C₄⋊C₄	—	13	1	no	—
298	C₄×C₂²⋊C₄	—	13	1	no	—
299	C₄×C₂²⋊C₄	—	13	1	no	—
300	C₄×C₂²⋊C₄	—	13	1	no	—
301	#376	C₂×D₁₃	1	1	yes	characteristic
302	#336	—	13	1	no	—
303	#336	—	13	1	no	—
304	#336	—	13	1	no	—
305	#336	—	13	1	no	—
306	#336	—	13	1	no	—
307	#336	—	13	1	no	—
308	#336	C₂×D₁₃	1	1	yes	characteristic
309	#336	C₂×D₁₃	1	1	yes	characteristic
310	#336	C₂×D₁₃	1	1	yes	characteristic
311	#336	C₂×D₁₃	1	1	yes	characteristic
312	#336	C₂×D₁₃	1	1	yes	characteristic
313	#336	C₂×D₁₃	1	1	yes	characteristic
314	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
315	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
316	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
318	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
319	C₂²×C₁₃	#568	1	1	yes	characteristic
320	C₂²×C₁₃	#568	1	1	yes	characteristic
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	2	no	—
323	C₂×D₁₃	—	2	2	no	—
324	C₂×D₁₃	—	4	1	no	—
325	C₂×D₁₃	—	4	1	no	—
326	C₂×D₁₃	—	4	1	no	—
327	C₂×D₁₃	—	4	1	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
335	C₄×C₁₃	#529	1	1	yes	characteristic
336	C₄×C₁₃	#529	1	1	yes	characteristic
337	C₄×C₁₃	#529	1	1	yes	characteristic
338	Dic₁₃	—	2	2	no	—
339	Dic₁₃	—	4	1	no	—
340	Dic₁₃	—	4	1	no	—
341	Dic₁₃	—	4	1	no	—
342	Dic₁₃	—	4	1	no	—
343	Dic₁₃	—	4	1	no	—
344	Dic₁₃	—	4	1	no	—
345	C₂³×C₄	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	13	1	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	26	2	no	—
351	C₂²×C₈	—	26	2	no	—
352	C₂²×C₈	—	26	2	no	—
353	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	13	1	no	—
358	C₂×C₄⋊C₄	—	13	1	no	—
359	C₂×C₄⋊C₄	—	13	1	no	—
360	C₂×C₄⋊C₄	—	13	1	no	—
361	C₂×C₄⋊C₄	—	13	1	no	—
362	C₂×C₄⋊C₄	—	13	1	no	—
363	C₂×C₂²⋊C₄	—	13	1	no	—
364	C₂×C₂²⋊C₄	—	13	1	no	—
365	C₂×C₂²⋊C₄	—	13	1	no	—
366	C₂×C₂²⋊C₄	—	13	1	no	—
367	C₂×C₂²⋊C₄	—	13	1	no	—
368	C₂×C₂²⋊C₄	—	13	1	no	—
369	C₂×C₄²	—	13	1	no	—
370	C₂×C₄²	—	13	1	no	—
371	C₂×C₄²	—	13	1	no	—
372	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
375	C₄⋊C₈	—	26	2	no	—
376	C₄⋊C₈	—	26	2	no	—
377	C₄⋊C₈	—	26	2	no	—
378	C₂²⋊C₈	—	26	2	no	—
379	C₂²⋊C₈	—	26	2	no	—
380	C₂²⋊C₈	—	26	2	no	—
381	#97	—	26	2	no	—
382	#97	—	26	2	no	—
383	#97	—	26	2	no	—
384	#97	—	26	2	no	—
385	#97	—	26	2	no	—
386	C₄×C₈	—	26	2	no	—
387	C₄×C₈	—	26	2	no	—
388	C₄×C₈	—	26	2	no	—
389	C₄×C₈	—	26	2	no	—
390	#95	—	13	1	no	—
391	#95	—	13	1	no	—
392	#95	—	13	1	no	—
393	#95	—	13	1	no	—
394	#95	—	13	1	no	—
395	#95	—	13	1	no	—
396	#95	—	13	1	no	—
397	#95	—	13	1	no	—
398	#95	—	13	1	no	—
399	#95	—	13	1	no	—
400	#95	—	13	1	no	—
401	#95	—	13	1	no	—
402	#95	C₄×D₁₃	1	1	yes	characteristic
403	#95	C₄×D₁₃	1	1	yes	characteristic
404	#95	C₄×D₁₃	1	1	yes	characteristic
405	#95	C₄×D₁₃	1	1	yes	characteristic
406	C₂×C₁₃	C₄×#126	1	1	yes	characteristic
407	C₂×C₁₃	#2966	1	1	yes	characteristic
408	C₂×C₁₃	#2967	1	1	yes	characteristic
409	C₂×C₁₃	#2968	1	1	yes	characteristic
410	C₂×C₁₃	#2968	1	1	yes	characteristic
411	C₂×C₁₃	#2968	1	1	yes	characteristic
412	C₂×C₁₃	#2969	1	1	yes	characteristic
413	D₁₃	—	4	2	no	—
414	C₂⁴	—	13	1	no	—
415	C₂²×C₄	—	13	1	no	—
416	C₂²×C₄	—	13	1	no	—
417	C₂²×C₄	—	13	1	no	—
418	C₂²×C₄	—	13	1	no	—
419	C₂²×C₄	—	13	1	no	—
420	C₂²×C₄	—	13	1	no	—
421	C₂²×C₄	—	13	1	no	—
422	C₂²×C₄	—	26	1	no	—
423	C₂²×C₄	—	26	1	no	—
424	C₂²×C₄	—	26	1	no	—
425	C₂²×C₄	—	26	1	no	—
426	C₂²×C₄	—	26	1	no	—
427	C₂²×C₄	—	26	1	no	—
428	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	13	2	no	—
448	C₂×C₈	—	13	2	no	—
449	C₂×C₈	—	13	2	no	—
450	C₂×C₈	—	13	2	no	—
451	C₂×C₈	—	13	2	no	—
452	C₂×C₈	—	13	2	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	—	26	1	no	—
455	C₂×C₈	—	26	1	no	—
456	C₂×C₈	—	26	1	no	—
457	C₂×C₈	—	26	1	no	—
458	C₂×C₈	—	26	1	no	—
459	C₂×C₈	—	52	4	no	—
460	C₄⋊C₄	—	26	2	no	—
461	C₄⋊C₄	—	26	2	no	—
462	C₄⋊C₄	—	52	1	no	—
463	C₄⋊C₄	—	52	1	no	—
464	C₄⋊C₄	—	52	1	no	—
465	C₄⋊C₄	—	52	1	no	—
466	C₂²⋊C₄	—	26	2	no	—
467	C₂²⋊C₄	—	26	2	no	—
468	C₂²⋊C₄	—	26	2	no	—
469	C₂²⋊C₄	—	26	2	no	—
470	C₂²⋊C₄	—	52	1	no	—
471	C₂²⋊C₄	—	52	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	26	1	no	—
479	C₄²	—	26	1	no	—
480	C₄²	—	26	1	no	—
481	C₄²	—	26	1	no	—
482	C₄²	—	26	1	no	—
483	C₄²	—	26	1	no	—
484	C₁₃	#21669	1	1	yes	characteristic, complemented, Sylow
485	C₂³	—	13	2	no	—
486	C₂³	—	26	1	no	—
487	C₂³	—	26	1	no	—
488	C₂³	—	26	1	no	—
489	C₂³	—	26	1	no	—
490	C₂³	—	26	1	no	—
491	C₂³	—	26	1	no	—
492	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	13	2	no	—
512	C₂×C₄	—	26	1	no	—
513	C₂×C₄	—	26	1	no	—
514	C₂×C₄	—	26	1	no	—
515	C₂×C₄	—	26	1	no	—
516	C₂×C₄	—	26	1	no	—
517	C₂×C₄	—	26	1	no	—
518	C₂×C₄	—	26	1	no	—
519	C₂×C₄	—	26	1	no	—
520	C₂×C₄	—	26	1	no	—
521	C₂×C₄	—	26	1	no	—
522	C₂×C₄	—	26	1	no	—
523	C₂×C₄	—	26	1	no	—
524	C₂×C₄	—	26	1	no	—
525	C₂×C₄	—	26	1	no	—
526	C₂×C₄	—	26	1	no	—
527	C₂×C₄	—	26	1	no	—
528	C₂×C₄	—	26	1	no	—
529	C₂×C₄	—	26	1	no	—
530	C₂×C₄	—	26	1	no	—
531	C₂×C₄	—	26	1	no	—
532	C₂×C₄	—	52	1	no	—
533	C₂×C₄	—	52	1	no	—
534	C₂×C₄	—	52	1	no	—
535	C₂×C₄	—	52	1	no	—
536	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
537	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
538	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
539	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
540	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
541	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	13	4	no	—
547	C₈	—	26	2	no	—
548	C₈	—	26	2	no	—
549	C₈	—	26	2	no	—
550	C₂²	—	26	2	no	—
551	C₂²	—	26	2	no	—
552	C₂²	—	26	2	no	—
553	C₂²	—	52	1	no	—
554	C₂²	—	52	1	no	—
555	C₂²	—	52	1	no	—
556	C₂²	—	52	1	no	—
557	C₂²	#11719227	1	1	yes	characteristic
558	C₂²	#11719227	1	1	yes	characteristic
559	C₂²	#11719227	1	1	yes	characteristic
560	C₂²	D₁₃×#131	1	1	yes	characteristic
561	C₂²	D₁₃×#131	1	1	yes	characteristic
562	C₂²	#11719455	1	1	yes	characteristic
563	C₂²	#11719455	1	1	yes	characteristic
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	26	2	no	—
571	C₄	—	52	1	no	—
572	C₄	—	52	1	no	—
573	C₄	—	52	1	no	—
574	C₄	—	52	1	no	—
575	C₄	—	52	1	no	—
576	C₄	—	52	1	no	—
577	C₄	D₁₃×#126	1	1	yes	characteristic
578	C₄	#11719411	1	1	yes	characteristic
579	C₄	#11719411	1	1	yes	characteristic
580	C₄	#11719411	1	1	yes	characteristic
581	C₂	—	52	2	no	—
582	C₂	#13117384	1	1	yes	characteristic
583	C₂	#13123809	1	1	yes	characteristic
584	C₂	#13123819	1	1	yes	characteristic
585	C₂	#13123828	1	1	yes	characteristic
586	C₂	#13123828	1	1	yes	characteristic
587	C₂	#13123828	1	1	yes	characteristic
588	C₂	#13123838	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1840	C₂
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1840	D₁₃
hypocenter	C₁₃	#21669
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

Complements

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

N	H ≅ G/N	type
5. #13115398	C₂	semidirect
6. #13115391	C₂	semidirect
7. #13115391	C₂	semidirect
8. #13114709	C₂	semidirect
9. #13114707	C₂	semidirect
10. #13114702	C₂	semidirect
14. #13114523	C₂	semidirect
15. C₁₃×#1840	C₂	semidirect
198. #1840	D₁₃	semidirect
484. C₁₃	#21669	semidirect

Maximal subgroups

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

subgroup	index
#13118134	2
#13115447	2
#13115440	2
#13115398	2
#13115391	2
#13114709	2
#13114707	2
#13114702	2
#13114611	2
#13114606	2
#13114523	2
C₁₃×#1840	2
#21669	13