Subgroups — #16016110

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718562	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123543	C₂	1	1	yes	maximal, characteristic
4	#13116664	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116663	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116662	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116661	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116660	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116659	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116658	C₂	1	1	yes	maximal, characteristic, complemented
11	#13116590	C₂	1	1	yes	maximal, characteristic, complemented
12	#13116448	C₂	1	1	yes	maximal, characteristic, complemented
13	#13116448	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88155	C₂²	1	1	yes	characteristic
17	C₂×#88155	C₂²	1	1	yes	characteristic
18	#11719253	C₄	1	1	yes	characteristic
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88052	C₂²	1	1	yes	characteristic
25	C₂²×#6090	C₂²	1	1	yes	characteristic
26	#11718673	C₄	1	1	yes	characteristic
27	#11718568	—	2	4	no	—
28	#11718562	—	2	4	no	—
29	C₂×#88038	C₂²	1	1	yes	characteristic
30	C₂×#88038	C₂²	1	1	yes	characteristic
31	C₂×#88038	C₂²	1	1	yes	characteristic
32	C₂×#88038	C₂²	1	1	yes	characteristic
33	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
37	#11718499	C₄	1	1	yes	characteristic
38	#11718498	C₄	1	1	yes	characteristic
39	#11718390	C₄	1	1	yes	characteristic
40	#11718390	C₄	1	1	yes	characteristic
41	#11718388	C₄	1	1	yes	characteristic
42	#11718388	C₄	1	1	yes	characteristic
43	C₈×D₅₂	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
48	C₁₃×#346	C₂²	1	1	yes	characteristic
49	C₂²⋊#6090	C₂²	1	1	yes	characteristic
50	C₂²⋊#6090	C₂²	1	1	yes	characteristic
51	#11718099	C₂²	1	1	yes	characteristic
52	#11718099	C₂²	1	1	yes	characteristic
53	#11718099	C₂²	1	1	yes	characteristic
54	#11718099	C₂²	1	1	yes	characteristic
55	#11718094	C₂²	1	1	yes	characteristic
56	#11718094	C₂²	1	1	yes	characteristic
57	#11718093	C₂²	1	1	yes	characteristic
58	#11718093	C₂²	1	1	yes	characteristic
59	C₄⋊#6090	C₂²	1	1	yes	characteristic
60	#11718053	C₂²	1	1	yes	characteristic
61	C₂×#6127	C₂×C₄	1	1	yes	characteristic
62	C₂×#6127	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
66	#88194	C₈	1	1	yes	characteristic
67	#88192	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×#6099	C₂×C₄	1	1	yes	characteristic
71	C₂×#6099	C₂×C₄	1	1	yes	characteristic
72	#88155	—	2	2	no	—
73	#88155	—	2	2	no	—
74	#88155	—	2	2	no	—
75	#88155	—	2	2	no	—
76	C₂×#6094	C₂×C₄	1	1	yes	characteristic
77	C₂×#6094	C₂×C₄	1	1	yes	characteristic
78	C₂×#6094	C₂×C₄	1	1	yes	characteristic
79	C₂×#6094	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
84	#88149	C₈	1	1	yes	characteristic
85	#88142	C₈	1	1	yes	characteristic
86	#88139	C₈	1	1	yes	characteristic
87	#88139	C₈	1	1	yes	characteristic
88	#88138	C₈	1	1	yes	characteristic
89	#88138	C₈	1	1	yes	characteristic
90	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
92	C₁₃×M₃₂	—	2	2	no	—
93	C₂×C₁₃×C₁₆	—	2	2	no	—
94	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
104	#88060	C₂×C₄	1	1	yes	characteristic
105	#88060	C₂×C₄	1	1	yes	characteristic
106	#88060	C₂×C₄	1	1	yes	characteristic
107	#88060	C₂×C₄	1	1	yes	characteristic
108	#88054	C₂×C₄	1	1	yes	characteristic
109	#88054	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
112	#88052	—	2	2	no	—
113	C₂×#6090	—	2	2	no	—
114	C₂×#6090	C₂³	1	1	yes	characteristic
115	C₂×#6090	C₂³	1	1	yes	characteristic
116	C₂×#6090	C₂³	1	1	yes	characteristic
117	C₂×#6090	C₂³	1	1	yes	characteristic
118	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
119	C₄×#1055	C₂×C₄	1	1	yes	characteristic
120	#88038	—	2	2	no	—
121	#88038	—	2	2	no	—
122	#88038	—	2	2	no	—
123	#88038	—	2	2	no	—
124	C₁₆×D₁₃	—	2	2	no	—
125	C₁₆×D₁₃	—	2	2	no	—
126	C₁₆×D₁₃	—	2	2	no	—
127	C₁₆×D₁₃	D₄	1	4	yes	complemented
128	#33435	—	13	1	no	maximal, Sylow
129	C₂×D₄×C₁₃	C₂×C₈	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	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
138	#6127	—	2	2	no	—
139	#6127	—	2	2	no	—
140	#6127	—	2	2	no	—
141	#6127	—	2	2	no	—
142	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
143	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
144	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂×C₈	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	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
151	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
161	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
165	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
166	#6103	C₂×C₈	1	1	yes	characteristic
167	#6103	C₂×C₈	1	1	yes	characteristic
168	#6103	C₂×C₈	1	1	yes	characteristic
169	#6103	C₂×C₈	1	1	yes	characteristic
170	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
171	#6101	C₂×C₈	1	1	yes	characteristic
172	#6101	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
176	#6099	—	2	2	no	—
177	#6099	—	2	2	no	—
178	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
181	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
182	#6094	—	2	2	no	—
183	#6094	—	2	2	no	—
184	#6094	—	2	2	no	—
185	#6094	—	2	2	no	—
186	C₈×D₁₃	—	2	2	no	—
187	C₈×D₁₃	—	2	1	no	—
188	C₈×D₁₃	—	2	1	no	—
189	C₈×D₁₃	—	2	1	no	—
190	C₈×D₁₃	—	2	1	no	—
191	C₈×D₁₃	C₂×D₄	1	2	yes	—
192	C₈×D₁₃	#41	1	2	yes	—
193	C₁₃×C₁₆	—	2	1	no	—
194	C₁₃×C₁₆	—	2	1	no	—
195	C₁₃×C₁₆	—	2	1	no	—
196	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
197	#6090	—	2	1	no	—
198	#6090	—	2	1	no	—
199	#6090	—	2	1	no	—
200	#6090	C₂×D₄	1	2	yes	—
201	C₂×#504	—	13	1	no	—
202	C₂×#504	—	13	1	no	—
203	#2931	—	13	1	no	—
204	#2168	—	13	1	no	—
205	#2168	—	13	1	no	—
206	#2168	—	13	1	no	—
207	#2168	—	13	1	no	—
208	#2168	—	13	1	no	—
209	#2168	—	13	1	no	—
210	#2168	—	13	1	no	—
211	#2168	D₁₃	1	1	yes	characteristic, complemented
212	#2150	—	13	1	no	—
213	#2113	—	13	1	no	—
214	#2113	—	13	1	no	—
215	C₂×#346	—	13	1	no	—
216	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
217	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
218	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
219	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
220	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
221	D₄×C₁₃	—	4	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	C₂²×C₈	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
231	C₂²⋊D₁₃	—	2	2	no	—
232	C₂²⋊D₁₃	—	2	2	no	—
233	C₂²⋊D₁₃	—	2	2	no	—
234	C₂²⋊D₁₃	—	2	2	no	—
235	C₂²⋊D₁₃	—	4	1	no	—
236	C₂²⋊D₁₃	—	4	1	no	—
237	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
241	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
242	D₅₂	—	2	2	no	—
243	D₅₂	—	2	2	no	—
244	D₅₂	—	4	1	no	—
245	C₄×D₁₃	—	2	1	no	—
246	C₄×D₁₃	—	2	1	no	—
247	C₄×D₁₃	—	2	1	no	—
248	C₄×D₁₃	—	2	1	no	—
249	C₄×D₁₃	—	4	1	no	—
250	C₄×D₁₃	—	4	1	no	—
251	C₄×D₁₃	C₄×D₄	1	2	yes	—
252	C₄×D₁₃	#131	1	2	yes	—
253	Dic₂₆	—	2	2	no	—
254	Dic₂₆	—	2	2	no	—
255	C₈×C₁₃	—	2	1	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
260	#1055	—	2	1	no	—
261	#1055	—	2	1	no	—
262	#1055	—	2	1	no	—
263	#1055	C₄×D₄	1	2	yes	—
264	C₂×#131	—	13	1	no	—
265	C₂×#131	—	13	1	no	—
266	#532	—	13	1	no	—
267	#504	—	26	4	no	—
268	#504	—	26	4	no	—
269	C₂×M₃₂	—	13	1	no	—
270	C₂×M₃₂	—	13	1	no	—
271	C₂×M₃₂	—	13	1	no	—
272	C₂×M₃₂	—	13	1	no	—
273	C₂×M₃₂	—	13	1	no	—
274	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
275	C₂²×C₁₆	—	13	1	no	—
276	C₂²×C₁₆	—	13	1	no	—
277	C₂²×C₁₆	—	13	1	no	—
278	C₂²×C₁₆	—	13	1	no	—
279	C₂²×C₁₆	—	13	1	no	—
280	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
281	#436	—	13	1	no	—
282	#436	—	13	1	no	—
283	#436	—	13	1	no	—
284	#436	—	13	1	no	—
285	C₈×D₄	—	13	1	no	—
286	C₈×D₄	—	13	1	no	—
287	C₈×D₄	—	13	1	no	—
288	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
289	#423	—	13	1	no	—
290	#408	—	13	1	no	—
291	#408	—	13	1	no	—
292	C₂×C₄×C₈	—	13	1	no	—
293	C₄⋊C₁₆	—	13	1	no	—
294	C₄⋊C₁₆	—	13	1	no	—
295	C₄⋊C₁₆	—	13	1	no	—
296	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
297	C₂²⋊C₁₆	—	13	1	no	—
298	C₂²⋊C₁₆	—	13	1	no	—
299	C₂²⋊C₁₆	—	13	1	no	—
300	C₂²⋊C₁₆	—	13	1	no	—
301	C₂²⋊C₁₆	—	13	1	no	—
302	C₂²⋊C₁₆	—	13	1	no	—
303	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
304	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
305	#346	—	13	1	no	—
306	#346	—	13	1	no	—
307	#346	—	13	1	no	—
308	#346	C₂×D₁₃	1	1	yes	characteristic
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	C₈×D₄	1	2	yes	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	1	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	C₈×D₄	1	2	yes	—
336	C₂×#41	—	13	1	no	—
337	C₂×#41	—	13	1	no	—
338	#131	—	26	2	no	—
339	#131	—	26	2	no	—
340	#131	—	26	2	no	—
341	#131	—	26	2	no	—
342	C₂×M₁₆	—	13	1	no	—
343	C₂×M₁₆	—	13	1	no	—
344	C₂×M₁₆	—	13	1	no	—
345	C₂×M₁₆	—	13	1	no	—
346	C₂×M₁₆	—	13	1	no	—
347	C₂×M₁₆	—	13	1	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
354	C₄⋊Q₈	—	13	1	no	—
355	#127	—	13	1	no	—
356	#124	—	13	1	no	—
357	#124	—	13	1	no	—
358	#121	—	13	1	no	—
359	#121	—	13	1	no	—
360	#121	—	13	1	no	—
361	#121	—	13	1	no	—
362	C₄×D₄	—	13	1	no	—
363	C₄×D₄	—	13	1	no	—
364	C₄×D₄	—	13	1	no	—
365	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
366	C₂×C₄²	—	13	1	no	—
367	M₃₂	—	2	2	no	—
368	M₃₂	—	26	2	no	—
369	M₃₂	—	26	2	no	—
370	M₃₂	—	26	2	no	—
371	M₃₂	—	26	2	no	—
372	M₃₂	—	26	2	no	—
373	C₂×C₁₆	—	2	2	no	—
374	C₂×C₁₆	—	13	1	no	—
375	C₂×C₁₆	—	13	4	no	—
376	C₂×C₁₆	—	13	1	no	—
377	C₂×C₁₆	—	13	1	no	—
378	C₂×C₁₆	—	13	1	no	—
379	C₂×C₁₆	—	26	2	no	—
380	C₂×C₁₆	—	26	2	no	—
381	C₂×C₁₆	—	26	2	no	—
382	C₂×C₁₆	—	26	2	no	—
383	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
384	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
385	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
386	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
387	C₄⋊C₈	—	13	1	no	—
388	C₄⋊C₈	—	13	1	no	—
389	C₄⋊C₈	—	13	1	no	—
390	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
391	C₂²⋊C₈	—	13	1	no	—
392	C₂²⋊C₈	—	13	1	no	—
393	C₂²⋊C₈	—	13	1	no	—
394	C₂²⋊C₈	—	13	1	no	—
395	C₂²⋊C₈	—	13	1	no	—
396	C₂²⋊C₈	—	13	1	no	—
397	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
398	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
399	C₄×C₈	—	13	1	no	—
400	C₄×C₈	—	13	1	no	—
401	C₄×C₈	—	13	1	no	—
402	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
403	C₂×C₁₃	—	4	1	no	—
404	C₂×C₁₃	—	4	1	no	—
405	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
406	C₂×C₁₃	#3407	1	1	yes	characteristic
407	C₂×C₁₃	#3407	1	1	yes	characteristic
408	D₁₃	—	2	2	no	—
409	D₁₃	—	4	1	no	—
410	D₁₃	—	4	1	no	—
411	#41	—	26	2	no	—
412	#41	—	26	2	no	—
413	#41	—	26	2	no	—
414	#41	—	26	2	no	—
415	C₂×Q₈	—	13	1	no	—
416	C₂×Q₈	—	13	1	no	—
417	C₂×D₄	—	13	1	no	—
418	C₂×D₄	—	13	1	no	—
419	C₂×D₄	—	13	1	no	—
420	C₂×D₄	—	13	1	no	—
421	C₂×D₄	—	13	1	no	—
422	C₂×D₄	—	13	1	no	—
423	C₂×D₄	—	13	1	no	—
424	C₂×D₄	—	13	1	no	—
425	C₂×D₄	—	13	1	no	—
426	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
427	C₂²×C₄	—	13	1	no	—
428	C₂²×C₄	—	13	1	no	—
429	C₂²×C₄	—	13	1	no	—
430	C₂²×C₄	—	13	1	no	—
431	C₂²×C₄	—	13	1	no	—
432	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
434	M₁₆	—	26	2	no	—
435	M₁₆	—	26	2	no	—
436	M₁₆	—	26	2	no	—
437	M₁₆	—	26	2	no	—
438	M₁₆	—	26	2	no	—
439	M₁₆	—	26	2	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	—	13	1	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	13	2	no	—
447	C₂×C₈	—	13	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	13	1	no	—
450	C₂×C₈	—	26	2	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	—	26	1	no	—
455	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
458	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
459	C₄⋊C₄	—	13	1	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	13	1	no	—
462	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
463	C₂²⋊C₄	—	13	1	no	—
464	C₂²⋊C₄	—	13	1	no	—
465	C₂²⋊C₄	—	13	1	no	—
466	C₂²⋊C₄	—	13	1	no	—
467	C₂²⋊C₄	—	13	1	no	—
468	C₂²⋊C₄	—	13	1	no	—
469	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
470	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
471	C₄²	—	13	1	no	—
472	C₄²	—	13	1	no	—
473	C₄²	—	13	1	no	—
474	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₁₆	—	2	1	no	—
476	C₁₆	—	2	1	no	—
477	C₁₆	—	2	1	no	—
478	C₁₆	—	13	2	no	—
479	C₁₆	—	26	1	no	—
480	C₁₆	—	26	1	no	—
481	C₁₆	—	26	1	no	—
482	C₁₆	D₄×D₁₃	1	2	yes	—
483	C₁₃	#33435	1	1	yes	characteristic, complemented, Sylow
484	C₂³	—	13	1	no	—
485	C₂³	—	13	1	no	—
486	C₂³	—	13	1	no	—
487	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
488	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
489	Q₈	—	26	2	no	—
490	Q₈	—	26	2	no	—
491	D₄	—	4	1	no	—
492	D₄	—	26	2	no	—
493	D₄	—	26	2	no	—
494	D₄	—	26	2	no	—
495	D₄	—	26	2	no	—
496	D₄	—	26	2	no	—
497	D₄	—	26	2	no	—
498	D₄	—	52	1	no	—
499	D₄	—	52	1	no	—
500	D₄	—	52	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	—	13	1	no	—
506	C₂×C₄	—	13	2	no	—
507	C₂×C₄	—	13	2	no	—
508	C₂×C₄	—	13	1	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	1	no	—
511	C₂×C₄	—	13	1	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	—	52	1	no	—
517	C₂×C₄	—	52	1	no	—
518	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	13	2	no	—
527	C₈	—	26	1	no	—
528	C₈	—	26	1	no	—
529	C₈	—	26	1	no	—
530	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
531	C₈	#41×D₁₃	1	1	yes	characteristic
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	13	2	no	—
539	C₂²	—	26	1	no	—
540	C₂²	—	26	1	no	—
541	C₂²	—	26	1	no	—
542	C₂²	—	26	1	no	—
543	C₂²	—	26	1	no	—
544	C₂²	—	26	1	no	—
545	C₂²	—	26	1	no	—
546	C₂²	—	26	1	no	—
547	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	13	2	no	—
553	C₄	—	26	1	no	—
554	C₄	—	26	1	no	—
555	C₄	—	26	1	no	—
556	C₄	—	26	1	no	—
557	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
558	C₄	D₁₃×#131	1	1	yes	characteristic
559	C₂	—	4	1	no	—
560	C₂	—	4	1	no	—
561	C₂	—	26	2	no	—
562	C₂	—	52	1	no	—
563	C₂	—	52	1	no	—
564	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
565	C₂	#13127937	1	1	yes	characteristic
566	C₂	#13127938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2168	C₂
prime radical	#11719253	C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2168	D₁₃
hypocenter	C₁₃	#33435
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×#11718568	C₂	semidirect
2. C₂×#11718562	C₂	semidirect
4. #13116664	C₂	semidirect
5. #13116663	C₂	semidirect
6. #13116662	C₂	semidirect
7. #13116661	C₂	semidirect
8. #13116660	C₂	semidirect
9. #13116659	C₂	semidirect
10. #13116658	C₂	semidirect
11. #13116590	C₂	semidirect
12. #13116448	C₂	semidirect
13. #13116448	C₂	semidirect
14. D₁₃×#346	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
127. C₁₆×D₁₃	D₄	semidirect
211. #2168	D₁₃	semidirect
483. C₁₃	#33435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718568	2
C₂×#11718562	2
#13123543	2
#13116664	2
#13116663	2
#13116662	2
#13116661	2
#13116660	2
#13116659	2
#13116658	2
#13116590	2
#13116448	2
D₁₃×#346	2
C₁₃×#2168	2
#33435	13