Subgroups — #16792765

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131645	C₂	1	1	yes	maximal, characteristic
2	#13131645	C₂	1	1	yes	maximal, characteristic
3	#13130059	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130057	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130057	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130055	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130053	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130053	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130051	C₂	1	1	yes	maximal, characteristic, complemented
10	#13130047	C₂	1	1	yes	maximal, characteristic, complemented
11	#13130045	C₂	1	1	yes	maximal, characteristic, complemented
12	#13130041	C₂	1	1	yes	maximal, characteristic, complemented
13	#13130037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#6122	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123476	C₂	1	1	yes	maximal, characteristic
16	#41×Dic₁₃	C₂²	1	1	yes	characteristic
17	#11719158	C₄	1	2	yes	—
18	#11719158	C₄	1	2	yes	—
19	#11719145	C₄	1	2	yes	—
20	#11719145	C₄	1	2	yes	—
21	#11719144	C₄	1	2	yes	—
22	#11719144	C₄	1	2	yes	—
23	#11719144	C₄	1	2	yes	—
24	#11719144	C₄	1	2	yes	—
25	#11719125	C₂²	1	1	yes	characteristic
26	#11719125	C₂²	1	1	yes	characteristic
27	#11719125	C₂²	1	1	yes	characteristic
28	#11719125	C₂²	1	1	yes	characteristic
29	C₄×#6122	C₂²	1	1	yes	characteristic
30	C₄×#6122	C₂²	1	1	yes	characteristic
31	C₄×#6122	C₂²	1	1	yes	characteristic
32	C₄×#6122	C₂²	1	1	yes	characteristic
33	#11719119	C₂²	1	1	yes	characteristic
34	#11719119	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
37	C₁₃×#408	C₄	1	1	yes	characteristic
38	#11718895	C₄	1	1	yes	characteristic
39	#11718780	C₄	1	1	yes	characteristic
40	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
41	#11718763	C₄	1	1	yes	characteristic
42	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
43	#11718381	C₄	1	1	yes	characteristic
44	#11718381	C₄	1	1	yes	characteristic
45	#11718381	C₄	1	1	yes	characteristic
46	#11718381	C₄	1	1	yes	characteristic
47	#11718379	C₂²	1	1	yes	characteristic
48	#11718379	C₂²	1	1	yes	characteristic
49	#11718379	C₂²	1	1	yes	characteristic
50	#11718379	C₂²	1	1	yes	characteristic
51	#1057⋊C₈	C₂²	1	1	yes	characteristic
52	#1057⋊C₈	C₂²	1	1	yes	characteristic
53	#1057⋊C₈	C₂²	1	1	yes	characteristic
54	#1057⋊C₈	C₂²	1	1	yes	characteristic
55	#1057⋊C₈	C₂²	1	1	yes	characteristic
56	#1057⋊C₈	C₂²	1	1	yes	characteristic
57	#1057⋊C₈	C₂²	1	1	yes	characteristic
58	#1057⋊C₈	C₂²	1	1	yes	characteristic
59	#11718251	C₂²	1	1	yes	characteristic
60	#11718251	C₂²	1	1	yes	characteristic
61	#11718251	C₂²	1	1	yes	characteristic
62	#11718251	C₂²	1	1	yes	characteristic
63	C₈×#1057	C₂²	1	1	yes	characteristic
64	C₈×#1057	C₂²	1	1	yes	characteristic
65	C₈×#1057	C₂²	1	1	yes	characteristic
66	C₈×#1057	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
68	C₂×#6122	C₂×C₄	1	2	yes	—
69	C₂×#6122	C₂×C₄	1	2	yes	—
70	C₂×#6122	C₂×C₄	1	2	yes	—
71	C₂×#6122	C₂×C₄	1	2	yes	—
72	C₂²×#1057	C₂×C₄	1	2	yes	—
73	C₂²×#1057	C₂×C₄	1	2	yes	—
74	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
77	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
80	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
81	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
82	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
83	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
84	#88180	C₂×C₄	1	1	yes	characteristic
85	#88180	C₂×C₄	1	1	yes	characteristic
86	#88180	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
90	C₂×#6099	C₂×C₄	1	1	yes	characteristic
91	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊#1057	C₂×C₄	1	2	yes	—
93	C₂²⋊#1057	C₂×C₄	1	2	yes	—
94	C₂²⋊#1057	C₂×C₄	1	2	yes	—
95	C₂²⋊#1057	C₂×C₄	1	2	yes	—
96	C₂²⋊#1057	C₂×C₄	1	2	yes	—
97	C₂²⋊#1057	C₂×C₄	1	2	yes	—
98	#88112	C₂×C₄	1	2	yes	—
99	#88112	C₂×C₄	1	2	yes	—
100	#88112	C₂×C₄	1	2	yes	—
101	#88112	C₂×C₄	1	2	yes	—
102	#88110	C₂×C₄	1	2	yes	—
103	#88110	C₂×C₄	1	2	yes	—
104	#88110	C₂×C₄	1	2	yes	—
105	#88110	C₂×C₄	1	2	yes	—
106	C₄⋊#1057	C₂×C₄	1	2	yes	—
107	C₄⋊#1057	C₂×C₄	1	2	yes	—
108	C₄×#1057	C₂×C₄	1	2	yes	—
109	C₄×#1057	C₂×C₄	1	2	yes	—
110	C₄×#1057	C₂³	1	1	yes	characteristic
111	C₄×#1057	C₂³	1	1	yes	characteristic
112	C₄×#1057	C₂³	1	1	yes	characteristic
113	C₄×#1057	C₂³	1	1	yes	characteristic
114	C₄×#1057	C₂³	1	1	yes	characteristic
115	C₄×#1057	C₂³	1	1	yes	characteristic
116	C₄×#1057	C₂³	1	1	yes	characteristic
117	C₄×#1057	C₂³	1	1	yes	characteristic
118	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
119	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
120	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
126	#88055	C₂×C₄	1	1	yes	characteristic
127	#88055	C₂×C₄	1	1	yes	characteristic
128	#88054	C₂×C₄	1	1	yes	characteristic
129	#88054	C₂×C₄	1	1	yes	characteristic
130	#88054	C₂×C₄	1	1	yes	characteristic
131	#88054	C₂×C₄	1	1	yes	characteristic
132	#88054	C₂×C₄	1	1	yes	characteristic
133	#88054	C₂×C₄	1	1	yes	characteristic
134	#88054	C₂×C₄	1	1	yes	characteristic
135	#88054	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
138	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
139	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
140	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
141	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
142	#17340	—	13	1	no	maximal, Sylow
143	C₁₃×#41	—	4	1	no	—
144	C₁₃×#41	—	4	1	no	—
145	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
146	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
147	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
148	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	#6122	—	2	4	no	—
159	#6122	—	2	4	no	—
160	#6122	—	4	2	no	—
161	#6122	—	4	2	no	—
162	C₂×#1057	—	2	4	no	—
163	C₂×#1057	—	4	2	no	—
164	C₂×#1057	C₂²×C₄	1	2	yes	—
165	C₂×#1057	C₂²×C₄	1	2	yes	—
166	C₂×#1057	C₂²×C₄	1	2	yes	—
167	C₂×#1057	C₂²×C₄	1	2	yes	—
168	C₂×#1057	C₂²×C₄	1	2	yes	—
169	C₂×#1057	C₂²×C₄	1	2	yes	—
170	C₂×#1057	C₂²×C₄	1	2	yes	—
171	C₂×#1057	C₂²×C₄	1	2	yes	—
172	C₁₃×M₁₆	—	4	1	no	—
173	C₂×C₈×C₁₃	—	4	1	no	—
174	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
184	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
185	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
186	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
188	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
189	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
190	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
200	#6099	—	4	1	no	—
201	C₂×#1055	—	4	1	no	—
202	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
203	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
204	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
205	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
206	#2965	—	13	1	no	—
207	#2965	—	13	1	no	—
208	#2922	—	13	1	no	—
209	#1455	—	13	1	no	—
210	#1454	—	13	1	no	—
211	#1454	—	13	1	no	—
212	#1453	—	13	1	no	—
213	#1453	—	13	1	no	—
214	#1453	—	13	1	no	—
215	#1452	—	13	1	no	—
216	#1451	—	13	1	no	—
217	#1451	—	13	1	no	—
218	#1450	—	13	1	no	—
219	C₈×M₁₆	—	13	1	no	—
220	C₈×M₁₆	—	13	1	no	—
221	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
223	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
224	Q₈×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	4	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	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×Dic₁₃	—	2	2	no	—
239	C₂×Dic₁₃	—	2	2	no	—
240	C₂×Dic₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	2	no	—
242	C₂×Dic₁₃	—	2	2	no	—
243	C₂×Dic₁₃	—	2	2	no	—
244	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
246	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
247	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
252	#1057	—	2	2	no	—
253	#1057	—	2	2	no	—
254	#1057	—	2	2	no	—
255	#1057	—	2	2	no	—
256	#1057	—	2	2	no	—
257	#1057	—	2	2	no	—
258	#1057	—	2	2	no	—
259	#1057	#131	1	4	yes	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	#1055	—	2	1	no	—
265	#1055	—	2	1	no	—
266	#1055	—	2	1	no	—
267	#1055	—	2	1	no	—
268	C₄×#41	—	13	1	no	—
269	#446	—	13	2	no	—
270	#446	—	13	2	no	—
271	#436	—	13	2	no	—
272	#436	—	13	2	no	—
273	#435	—	13	2	no	—
274	#435	—	13	2	no	—
275	#435	—	13	2	no	—
276	#435	—	13	2	no	—
277	#433	—	13	1	no	—
278	#433	—	13	1	no	—
279	#433	—	13	1	no	—
280	#433	—	13	1	no	—
281	#431	—	13	1	no	—
282	#431	—	13	1	no	—
283	#431	—	13	1	no	—
284	#431	—	13	1	no	—
285	#431	—	13	1	no	—
286	#431	—	13	1	no	—
287	#431	—	13	1	no	—
288	#431	—	13	1	no	—
289	#431	—	13	1	no	—
290	#431	—	13	1	no	—
291	#424	—	13	1	no	—
292	#424	—	13	1	no	—
293	#408	—	13	1	no	—
294	#408	#261	1	1	yes	characteristic
295	C₄×M₁₆	—	13	1	no	—
296	C₄×M₁₆	—	13	1	no	—
297	C₄×M₁₆	—	13	1	no	—
298	C₄×M₁₆	—	13	1	no	—
299	C₄×M₁₆	—	13	1	no	—
300	C₂×C₄×C₈	—	13	1	no	—
301	C₂×C₄×C₈	—	13	1	no	—
302	C₂×C₄×C₈	—	13	1	no	—
303	#322	—	13	1	no	—
304	#322	—	13	1	no	—
305	#322	—	13	1	no	—
306	#322	—	13	1	no	—
307	#322	—	13	1	no	—
308	#322	—	13	1	no	—
309	#322	—	13	1	no	—
310	#322	—	13	1	no	—
311	#322	—	13	1	no	—
312	#322	—	13	1	no	—
313	#322	—	13	1	no	—
314	#322	—	13	1	no	—
315	C₈²	—	13	1	no	—
316	C₈²	—	13	1	no	—
317	C₈²	—	13	1	no	—
318	C₈²	—	13	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	#568	1	1	yes	characteristic
333	C₄×C₁₃	#568	1	1	yes	characteristic
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	—	2	1	no	—
336	Dic₁₃	—	2	1	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	C₂×#131	1	2	yes	—
341	Dic₁₃	#568	1	2	yes	—
342	C₂×#41	C₂×#261	1	1	yes	characteristic
343	C₂×M₁₆	—	13	2	no	—
344	C₂×M₁₆	—	13	2	no	—
345	C₂×M₁₆	—	13	2	no	—
346	C₂×M₁₆	—	13	2	no	—
347	C₂×M₁₆	—	13	1	no	—
348	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
349	C₂²×C₈	—	13	2	no	—
350	C₂²×C₈	—	13	2	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	C₂×#261	1	1	yes	characteristic
353	C₄×Q₈	—	13	1	no	—
354	C₄×Q₈	—	13	1	no	—
355	C₄×D₄	—	13	1	no	—
356	C₄×D₄	—	13	1	no	—
357	C₄×D₄	—	13	1	no	—
358	C₄×D₄	—	13	1	no	—
359	C₄×D₄	—	13	1	no	—
360	C₄×D₄	—	13	1	no	—
361	#117	—	13	1	no	—
362	#117	—	13	1	no	—
363	#117	—	13	1	no	—
364	C₂×C₄²	—	13	1	no	—
365	C₂×C₄²	—	13	1	no	—
366	C₂×C₄²	—	13	1	no	—
367	C₄⋊C₈	—	13	2	no	—
368	C₄⋊C₈	—	13	2	no	—
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	—	13	1	no	—
380	C₄⋊C₈	—	13	1	no	—
381	C₂²⋊C₈	—	13	2	no	—
382	C₂²⋊C₈	—	13	2	no	—
383	C₂²⋊C₈	—	13	2	no	—
384	C₂²⋊C₈	—	13	2	no	—
385	C₂²⋊C₈	—	13	2	no	—
386	C₂²⋊C₈	—	13	2	no	—
387	C₂²⋊C₈	—	13	1	no	—
388	C₂²⋊C₈	—	13	1	no	—
389	C₂²⋊C₈	—	13	1	no	—
390	C₂²⋊C₈	—	13	1	no	—
391	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
392	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
393	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
394	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
395	#97	—	13	2	no	—
396	#97	—	13	2	no	—
397	#97	—	13	2	no	—
398	#97	—	13	2	no	—
399	#97	—	13	1	no	—
400	#97	—	13	1	no	—
401	C₄×C₈	—	13	2	no	—
402	C₄×C₈	—	13	2	no	—
403	C₄×C₈	—	13	1	no	—
404	C₄×C₈	—	13	1	no	—
405	C₄×C₈	—	13	1	no	—
406	C₄×C₈	—	13	1	no	—
407	C₄×C₈	—	13	1	no	—
408	C₄×C₈	—	13	1	no	—
409	C₄×C₈	—	13	1	no	—
410	C₄×C₈	—	13	1	no	—
411	C₄×C₈	—	13	1	no	—
412	C₄×C₈	—	13	1	no	—
413	C₄×C₈	—	13	1	no	—
414	C₄×C₈	—	13	1	no	—
415	C₄×C₈	—	13	1	no	—
416	C₄×C₈	—	13	1	no	—
417	C₂×C₁₃	—	4	1	no	—
418	C₂×C₁₃	—	4	1	no	—
419	C₂×C₁₃	—	4	1	no	—
420	C₂×C₁₃	#2873	1	1	yes	characteristic
421	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
422	C₂×C₁₃	#2875	1	1	yes	characteristic
423	#41	—	4	1	no	—
424	#41	—	4	1	no	—
425	C₂×Q₈	C₄×#261	1	1	yes	characteristic
426	C₂×D₄	C₄×#261	1	1	yes	characteristic
427	C₂×D₄	C₄×#261	1	1	yes	characteristic
428	C₂×D₄	C₄×#261	1	1	yes	characteristic
429	C₂²×C₄	—	13	1	no	—
430	C₂²×C₄	—	13	1	no	—
431	C₂²×C₄	—	13	1	no	—
432	C₂²×C₄	—	13	1	no	—
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
436	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
437	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
438	M₁₆	—	4	1	no	—
439	M₁₆	—	26	4	no	—
440	M₁₆	—	26	4	no	—
441	M₁₆	—	52	1	no	—
442	M₁₆	—	52	2	no	—
443	M₁₆	—	52	2	no	—
444	C₂×C₈	—	4	1	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	13	2	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	—	13	1	no	—
454	C₂×C₈	—	13	1	no	—
455	C₂×C₈	—	13	1	no	—
456	C₂×C₈	—	13	1	no	—
457	C₂×C₈	—	26	4	no	—
458	C₂×C₈	—	52	1	no	—
459	C₂×C₈	—	52	2	no	—
460	C₂×C₈	C₂²×#261	1	1	yes	characteristic
461	C₂×C₈	C₂²×#261	1	1	yes	characteristic
462	C₂×C₈	C₂²×#261	1	1	yes	characteristic
463	C₂×C₈	C₂²×#261	1	1	yes	characteristic
464	C₄⋊C₄	—	13	1	no	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	1	no	—
467	C₄⋊C₄	—	13	1	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₂²⋊C₄	—	13	1	no	—
471	C₂²⋊C₄	—	13	1	no	—
472	C₂²⋊C₄	—	13	1	no	—
473	C₂²⋊C₄	—	13	1	no	—
474	C₂²⋊C₄	—	13	1	no	—
475	C₂²⋊C₄	—	13	1	no	—
476	C₄²	—	13	1	no	—
477	C₄²	—	13	1	no	—
478	C₄²	—	13	1	no	—
479	C₄²	—	13	1	no	—
480	C₄²	—	13	1	no	—
481	C₄²	—	13	1	no	—
482	C₄²	—	13	1	no	—
483	C₄²	—	13	1	no	—
484	C₄²	—	13	1	no	—
485	C₄²	—	13	1	no	—
486	C₁₃	#17340	1	1	yes	characteristic, complemented, Sylow
487	C₂³	C₂×C₄×#261	1	1	yes	characteristic
488	C₂³	C₂×C₄×#261	1	1	yes	characteristic
489	C₂³	C₂×C₄×#261	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	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	—	13	1	no	—
501	C₂×C₄	—	13	1	no	—
502	C₂×C₄	—	13	1	no	—
503	C₂×C₄	—	13	1	no	—
504	C₂×C₄	—	13	1	no	—
505	C₂×C₄	—	13	1	no	—
506	C₂×C₄	—	13	1	no	—
507	C₂×C₄	—	13	1	no	—
508	C₂×C₄	—	26	2	no	—
509	C₂×C₄	—	26	2	no	—
510	C₂×C₄	—	26	2	no	—
511	C₂×C₄	—	26	2	no	—
512	C₂×C₄	—	26	2	no	—
513	C₂×C₄	—	26	2	no	—
514	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
515	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
516	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
517	C₂×C₄	C₂³×#261	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	13	4	no	—
523	C₈	—	26	2	no	—
524	C₈	—	26	2	no	—
525	C₈	—	26	2	no	—
526	C₈	—	26	2	no	—
527	C₈	—	26	2	no	—
528	C₈	—	26	2	no	—
529	C₈	—	26	2	no	—
530	C₈	—	26	1	no	—
531	C₈	—	26	1	no	—
532	C₈	—	26	1	no	—
533	C₈	—	26	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	13	2	no	—
548	C₄	—	13	2	no	—
549	C₄	—	26	1	no	—
550	C₄	—	26	1	no	—
551	C₄	—	26	1	no	—
552	C₄	—	26	1	no	—
553	C₄	—	26	1	no	—
554	C₄	—	26	1	no	—
555	C₄	#11719621	1	1	yes	characteristic
556	C₄	#11719621	1	1	yes	characteristic
557	C₂	—	4	1	no	—
558	C₂	—	4	1	no	—
559	C₂	—	4	1	no	—
560	C₂	#13131400	1	1	yes	characteristic
561	C₂	#131×#261	1	1	yes	characteristic
562	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#408	C₄
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#408	#261
hypocenter	C₁₃	#17340
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
3. #13130059	C₂	semidirect
4. #13130057	C₂	semidirect
5. #13130057	C₂	semidirect
6. #13130055	C₂	semidirect
7. #13130053	C₂	semidirect
8. #13130053	C₂	semidirect
9. #13130051	C₂	semidirect
10. #13130047	C₂	semidirect
11. #13130045	C₂	semidirect
12. #13130041	C₂	semidirect
13. #13130037	C₂	semidirect
14. C₈×#6122	C₂	semidirect
486. C₁₃	#17340	semidirect

Maximal subgroups

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

subgroup	index
#13131645	2
#13130059	2
#13130057	2
#13130055	2
#13130053	2
#13130051	2
#13130047	2
#13130045	2
#13130041	2
#13130037	2
C₈×#6122	2
#13123476	2
#17340	13